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How to Detect and Remove Temporal Autocorrelation in Vehicular Crash Data
Temporal autocorrelation (also called serial correlation) refers to the relationship between successive values (i.e. lags) of the same variable. Although it has long been a major concern in time series models, however, in-depth treatments of temporal autocorrelation in modeling vehicle crash data are lacking. This paper presents several test statistics to detect the amount of temporal autocorrelation and its level of significance in crash data. The tests employed are: 1) the Durbin-Watson (DW); 2) the Breusch-Godfrey (LM); and 3) the Ljung-Box Q (LBQ). When temporal autocorrelation is statistically significant in crash data, it could adversely bias the parameter estimates. As such, if present, temporal autocorrelation should be removed prior to use the data in crash modeling. Two procedures are presented in this paper to remove the temporal autocorrelation: 1) Differencing; and 2) the Cochrane-Orcutt method.
Introduction
Temporal autocorrelation (i.e.serial correlation) is a special case of correlation, and refers not to the relationship between two or more variables, but to the relationship between successive values of the same variable.Temporal autocorrelation is closely related to the correlation coefficient between two or more variables, except that in this case we do not deal with variables X and Y, but with lagged values of the same variable.Most regression methods that are used in crash modeling assume that the error terms are independent from one another, and they are uncorrelated.This assumption is formally expressed [1] as: where, E: the expected value of all pair-wise products of error terms, i j ε ε : error terms of the i and j observations respectively, which means that the expected value of all pair-wise products of error terms is zero, and when the error terms are uncorrelated, the positive products will cancel those that are negative leaving an expected value of 0.0 [1].If this assumption is violated, the standard errors of the estimates of the regression parameters are significantly underestimated which leads to erroneously inflated coefficients values, and incorrect confidence intervals.The presence of correlated error terms means that these types of inferences cannot be made reliably [2].The violation of this assumption occurs because of some temporal (time) component (i.e.heterogeneity due to time) that can affect the observations drawn across the time, such as time series data, panel data in the form of serial correlation, and any other dataset that might be collected over a period of time.
In this context, the error in a first time period influences the error in a subsequent time period (either the previous period, or the next period or beyond) [3].
For example, we might expect the disturbance (i.e.error term) in year t to be correlated with the disturbance in year t − 1 and with the disturbance in year t + 1, t + 2, and so on.If there are factors responsible for inflating the observation at some point in time to an extent larger than expected (i.e. a positive error), then it is reasonable to expect that the effects of those same factors linger creating an upward (positive) bias in the error term of a subsequent period.This phenomenon is called positive first-order autocorrelation, which is the most common manner in which the assumption of independence of errors is violated.For instance, if a dataset influenced by quarterly seasonal factors, then a resulting model that ignores the seasonal factors will have correlated error terms with a lag of four periods.There are different structure types of temporal autocorrelation: 1 st order, 2 nd order, and so on.The form of temporal autocorrelation that is encountered most often is called the first order temporal autocorrelation in the first autoregressive term, which is denoted by AR (1).The AR (1) autocorrelation assumes that the disturbance in time period t (current period) depends upon the disturbance in time period t − 1 (previous period) plus some additional amount, which is an error, and can be modeled as [3]: where, ε t :the disturbance in time period t, ε t − 1 : the disturbance in time period t − 1, ρ: the autocorrelation coefficient, i ∈ : the model error term.
The parameter ρ can take any value between negative one and positive one.If ρ > 0, then the disturbances in period t are positively correlated with the disturbances in period t − 1.In this case, positive autocorrelation exists which means that when disturbances in period t − 1 are positive disturbances, then disturbances in period t tend to be positive.When disturbances in period t − 1 are negative disturbances, then disturbances in period t tend to be negative.Temporal datasets are usually characterized by positive autocorrelation.If ρ < 0, then the disturbances in period t are negatively correlated with the disturbances in period t − 1.In this case there is negative autocorrelation.This means that when disturbances in period t − 1 are positive disturbances, then disturbances in period t tend to be negative.When disturbances in period t − 1 are negative disturbances, then disturbances in period t tend to be positive.
The second order temporal auto correlation is called the second-order autoregressive process or AR (2).The AR (2) autocorrelation assumes that the disturbance in period t is related to both the disturbance in period t − 1 and the disturbance in period t -2, and can be modeled as [3]: where, ρ 1 : the autocorrelation coefficient in time period t − 1. ρ 1: the autocorrelation coefficient in time period t -2.
The disturbance in period t depends upon the disturbance in period t − 1, the disturbance in period t -2, and some additional amount, which is an error (∈ t ).In a similar manner, the temporal autocorrelation can be extended to the ρth order autocorrelation AR (ρ).However, the most often used temporal autocorrelation is the first-order autoregressive process [3].If the temporal autocorrelation is found to be significant in crash data, then it must be removed before using the data in the modeling process [4] [5] [6].
Sources of Temporal Autocorrelation
Temporal autocorrelation can arise from the following sources: • Omitted Explanatory Variables: Omitting some important explanatory variables from the modeling process can create temporal autocorrelation that can produce biased parameter estimates and incorrect inferences, especially if the omitted variable is correlated with variables included in the model [1] [7] [8] [9].
• Misspecification of the Mathematical Form of the model can create temporal autocorrelation.For example, if a linear form of the model is specified when the true form of the model is non-linear, the resulting errors may reflect some temporal autocorrelation [10] [11] [12] [13].
• Misspecification of The Error Terms of the model due to some purely random factors, such as changes in weather conditions, economic factors, and other unaccounted for variables, which could have changing effects over successive periods.In such instances, the value of the error terms in the model could be miss pecified [3].
Detection of Temporal Autocorrelation
Several methods are available to detect the existence of the temporal autocorrela-tion in the crash dataset, including the residuals scatter plots, the Durbin-Watson test, the Durbin h test, the Breusch-Godfrey test, the Ljung-Box Q test, and correlograms.These will be described in detail below: • Scatter Plot of Residuals The error for the i th observation in the dataset is usually unknown and unobservable.However, the residual for this observation can be used as an estimate of the error, then the residuals can be plotted against the variables that may be related to time.The residual would be measured on the vertical axis.The temporal variables such as, years, months, or days would be measured on the horizontal axis.Next, the residual plot can be examined to determine if the residuals appear to exhibit a pattern of temporal autocorrelation.If the data are independent, then the residuals should be randomly scattered about 0.0.However, if a noticeable pattern emerges (particularly one that is cyclical or seasonal) then temporal autocorrelation is likely an issue.It must be emphasized that this is not a formal test of serial correlation.It would only suggest whether temporal autocorrelation may exist.We should not substitute a residual plot for a formal test [1] [13].
• The Durbin-Watson (DW) Test The most often used test for first order temporal autocorrelation is the Durbin-Watson DW test [13].The DW test is a measure of the first order autocorrelation and it cannot be used to test for higher order temporal autocorrelation.
The DW test is constructed to test the null and alternative hypotheses regarding the temporal autocorrelation coefficient (ρ): The null hypothesis of ρ = 0.0 means that the error term in one period is not correlated with the error term in the previous period, while the alternative hypothesis of ρ ≠ 0.0 means the error term in one period is either positively or negatively correlated with the error term in the previous period.To test the hypothesis, the DW test statistic on a dataset of size n is formulated as [1]: where, DW: the Durbin-Watson statistic, e t : the residual error term in time period t, e t -1 : the residual error term in the previous time period t − 1.
The DW statistics ranges from 0.0 to 4.0, and it can be shown that: ( ) A rule of thumb that is sometimes used is to conclude that there is no first order temporal autocorrelation if the DW statistic is between 1.5 and 2.5.A DW statistic below 1.5 indicates positive first order autocorrelation.A DW statistic of greater than 2.5 indicates negative first order autocorrelation [3].Alternatively, a significant p-value for the DW statistic would suggest rejecting the null hypothesis and concluding that there is first order autocorrelation in the residuals, and a non-significant p-value would suggest accepting the null hypothesis and concluding that there is no evidence of first order autocorrelation in the residuals.
• The Durbin h Test When one or more lagged dependent variables are present in the data, the DW statistic will be biased towards 2.0, this means that even if temporal autocorrelation is present it may be close to 2.0, and hence it cannot detect it.Durbin suggests a test for temporal autocorrelation when there is a lagged dependent variable in the dataset, and it is based on the h statistics.The Durbin h statistics is defined as: ( ) where, T: the number of observations in the dataset, ρ^: the temporal autocorrelation coefficient of the residuals, VAR (β^): the variance of the coefficient on the lagged dependent variable.Durbin has shown that the h statistics is approximately normally distributed with a unit variance, hence the test for first order autocorrelation can be done using the standard normal distribution.If Durbin h statistic is equal to or greater than 1.96, it is likely that temporal autocorrelation exists [1].
• The Breusch-Godfrey Lagrange Multiplier (LM) Test The Breusch-Godfrey test is a general test of serial correlation and can be used to test for first order temporal autocorrelation or higher order autocorrelation.
This test is a specific type of Lagrange Multiplier test.The LM test is particularly useful because it is not only suitable for testing for temporal autocorrelation of any order, but also suitable for models with or without lagged dependent variables [14].The null and alternative hypotheses used with this test for a second order autocorrelation are: The LM test statistic is given by: where, LM: the Lagrange multiplier test statistic, n: the number of observations in the dataset, i: the order of the autocorrelation, R 2 : the unadjusted R 2 statistic (coefficient of determination) of the model.The LM statistic has a chi-square distribution with two degrees of freedom, χ 2 (2) [15].
The Ljung-Box Q test (sometimes called the Portmanteau test) is used to test whether or not observations taken over time are random and independent for any order of temporal autocorrelation.It is based on asymptotic Chi-Square distribution χ 2 .In particular, for a given i lag, it tests the following hypotheses [16]: H 0 : the autocorrelations up to i lags are all zero (10) H a : the autocorrelations of one or more lags differ from zero (11) The test statistic is determined as follows [16]: where, LBQ i : the Ljung-Box Q statistic, n: the number of observations in the data, j: the lag being considered, i: the autocorrelation order, r: the residual error term in lag j.
• Correlograms
Correlograms are autocorrelation plots that can show the presence of temporal autocorrelation.The autocorrelation would appear in lag 1.0 and progress for n lags then disappear.In these plots the residual autocorrelation coefficient (ρ^) is plotted against n lags to develop a correlogram.This will give a visual look at a range of autocorrelation coefficients at relevant time lags so that significant values may be seen [17].In most software packages, two types of autocorrelation functions are presented: the autocorrelation function (ACF), and the partial autocorrelation function (PACF).The ACF is the amount of autocorrelation between a variable and a lag that is not explained by correlations at all lower-orderlags, and the PACF is the difference between the actual correlation at specific lag PACF: cuts off abruptly after lag 1.0.
If the ACF of a specific variable shows a declining geometric progression from the highest value at lag 1.0, and the PACF shows an abrupt cut off after lag 1.0., this would indicate that this variable has not encountered temporal autocorrelation.More advanced methods can also be used for big datasets such as: Fourier series analysis; and the spectral analysis [17] [18].
Data
Missouri The data included a wide range of independent variables (i.e.risk factors) in the analysis: • Road geometry (grade or level; number of lanes) • Road classification (rural or urban; existing of construction zones) • Environment (light conditions) • Traffic operation (annual average daily traffic, AADT)
Methodology
In this paper, three of the most widely used tests to detect the existence of tem-poral autocorrelation in the crash data are investigated, namely: The Durbin-Watson (DW), the Breusch-Godfrey (LM), and the Ljung-Box Q (LBQ) tests.
The three temporal independent variables in the dataset month, weekday, hour) are used in the application of each test.
The tests can be applied at different levels of temporal aggregation (i.e. over one year, over two years, three years, etc.) to help identify any hidden effects of the temporal autocorrelation that might exist within a timeframe.In this paper, the JMP12 software package is used to compute the DW statistics, the associated residual temporal autocorrelation coefficients, and their significance at the 95% confidence level (i.e.p-values).JMP requires that the input format of the crash data be in either excel spreadsheet (i.e.*.xlsx) or in text (i.e.delimited or *.csv) and then the output is produced as excel spreadsheet or delimited text.The Eviews 9 software is used to compute the LM statistics, and their significance at the 95% confidence level (i.e.p-values).The software requires that the input format of the crash data be in either excel spreadsheet (i.e.*.xlsx) or in text (i.e.delimited or *.csv) and then the output is produced as excel spreadsheet or delimited text.The Stata 14 software is used to compute the Box-Ljung Q statistic (LBQ) at each lag separately with the autocorrelation function (ACF) and the partial autocorrelation function (PACF) at each lag as well, and their significance at the 95% confidence level (i.e.p-values).The software requires that the input format of the crash data be in either excel spreadsheet (i.e.*.xlsx) or in text (i.e.delimited or *.csv) and then the output is produced as excel spreadsheet or delimited text.
The Durbin Watson (DW) test is applied to the I-70 data at two temporal levels; aggregation by year, and aggregation over all three years.Data for each year in aggregate is separately tested using (month, weekday, and hour) as the independent temporal variables, and then the aggregate three-year period is tested using the same independent variables.The Breusch-Godfrey (LM) test is applied to the I-70 data for the first 36 lags at two temporal levels; aggregation by year, and aggregation over all three years.Data for each year in aggregate is separately tested using (month, weekday, and hour) as the independent temporal variables, and then the aggregate three-year period is tested.The LM test is applied with degrees of freedom equal to the number of lags (i.e.36 degrees of freedom).The minimum recommended number of lags that should be considered for the LM and LBQ tests is roughly taken as the natural logarithm of the number of observations within the dataset [19],
The Durbin-Watson Test Results
Table 1 shows the results of the Durbin-Watson (DW) test for the I-70 at the one-year aggregate level.It can be seen that the temporal autocorrelation of the I-70 dataset for the year 2013 is found to be 3.64% with p value of 0.0512 (which is non-significant at alpha of 0.05); for the year 2014 year is found to be 7.19% with p-value of 0.0002 (which is significant at alpha of 0.01); and for the year 2015 is found to be 2.38% with p-value of 0.1371 (non-significant at alpha of 0.05).So, the only significant temporal autocorrelation is existed within the I-70 (2014) data, which should be removed before using this dataset in any modeling process.
The Breusch-Godfrey Test Results
Table 2 shows the results of the LM test for the I-70 crash data at the one-year aggregate level.The LM value (using 36 lags or 36 degrees of freedom) of the I-70 dataset for the year 2013 is found to be 31.022with p-value of 0.7042 (nonsignificant at alpha of 0.05); for the year 2014 is found to be 60.129 with p-value of 0.0071 (significant at alpha of 0.01); and for the year 2015 is found to be 50.876with p-value of 0.0512 (non-significant at alpha of 0.05).The results of the LM test confirm the results of the DW test that the I-70 dataset for the year 2014 contains a significant temporal autocorrelation as shown in Table 2.
Removal of the Temporal Autocorrelation from Crash Data
Since both the DW and the LM tests have shown the existence of temporal autocorrelation in the I-70 (2014) crash data, the next step is to remove it before using the data in any modeling process.Two approaches are investigated in this paper for the removal of temporal autocorrelation, the differencing procedure, and the Cochrane-Orcutt procedure.
The Differencing Procedure
Since a significant temporal autocorrelation is found to be existed within the I-70 (2014) data, then this should be removed before using the dataset in any potential modeling process [4] [5] [6].In order to remove any significant temporal autocorrelation that may be existed in a dataset, one of the first remedial measures should be to investigate the omission of one or more of the explanatory vaespecially variables that are related to time.Assuming that, the three time variables in the datasets (month, weekday, hour) have potential influence on the dependent variable, then they are unlikely to be removed from the analysis.Hence, the next step is to apply a differencing procedure to all time independent variables in the dataset to convert them into their differences values.
The differencing procedure can be applied by subtracting the previous observation from the current observation, as shown in Equation ( 13) [20]: ( ) where, D (Y): the difference of variable Y at lag t, Y t : the value of Y at lag t, Y t − 1 : the value of Y at lag t − 1.
The rho (i.e. the residual autocorrelation coefficient) is assumed to be (1.0) in the differencing procedure, which could overestimate the true rho value [21].
The first order differencing is applied to the I-70 (2014) dataset, and the ordinary least square residuals were obtained, then the Durbin-Watson (DW) test is calculated to check for the temporal autocorrelation.The result of the DW statistic showed that the temporal autocorrelation was still existed even after applying the first order differencing.Although the first order differencing is enough to show whether the differencing procedure can be used to remove the serial (temporal) correlation or not [21], however, more differencing orders (up to 7 orders) are applied to the I-70 (2014) dataset, and the Durbin-Watson test (DW statistic) is calculated each time to check for the temporal autocorrelation.The results showed that the temporal autocorrelation was not removed by this method.Table 3 shows seven differencing orders that were applied to the data and their DW statistics.
The Cochrane-Orcutt Procedure
When the differencing procedure cannot eliminate the temporal autocorrelation in a dataset, then the Cochrane-Orcutt procedure should be applied for the Autoregressive AR (1) term of this dataset [20].The procedure uses the ordinary least square residuals to obtain the value of rho which minimizes the sum of squared residuals.Rho is then used to transform the observations of the variables.The process continues until convergence is reached [20] [22].Considering the general ordinary least squared regression model: where, Y t : the dependent variable at time (lag) t, α: the intercept, β: the vector of regression coefficients, X t : the vector of explanatory variables at time (lag) t, ε t : the error term of the model at time (lag) t.
When applying the DW test, if the (DW) statistic revealed that the temporal autocorrelation exists among the model error terms, then the residuals must be modeled for the first order autoregressive term AR (1) such that: where, ρ: the temporal autocorrelation coefficient (rho) between pairs of observations, 0 < ρ < 1, e t : the error term of the residuals at time (lag) t.
The Cochrane-Orcutt procedure is obtained by taking a quasi-differencing or generalized differencing, such that the sum of squared residuals is minimized [20] [22]: The Cochrane-Orcutt iterative procedure starts by obtaining parameter estimates by the ordinary least square regression (OLS).Applying Equation ( 15 which is non-significant, as shown in Table 5.
The LM value for the aggregated three years' period using 36 lags is 41.203 for the I-70 dataset, which is non-significant, as shown in
The LBQ Test Results
The Box-Ljung Q statistic (LBQ) is applied to the aggregated three-year period (2013-2015).Table 7 shows the Box-Ljung Q statistic, the auto correlation function (ACF) and the partial autocorrelation function (PACF) with their p-values for the I-70 dataset for the first 36 lags.It can be seen that the LBQ statistic, the ACF, and the PACF for all 36 lags are non-significant for the I-70 crash data.
The LBQ statistic increases with the lag progress, indicating no temporal autocorrelation within the dataset and confirming the results of the DW test and the LM test.
Conclusion
Temporal autocorrelation (also called serial correlation) refers to the relationship between successive values (i.e.lags) of the same variable.Although it is a major concern in time series models, however, it is very important to be checked in crash data modeling as well.The results of crash data modeling can be improved when several years of crash data are utilized in the analysis, such as a period of three years instead of one year.However, this means that the same roadway will generate multiple observations over time, which could be correlated due to some
1 ) 3 )
residual temporal autocorrelation coefficient.When ρ^ = 0.0, (i.e.no autocorrelation), then DW = 2.0.When ρ^ tends to 1.0, then DW = 0.0.When ρ^ tends to −1.0, then DW = 4.0.The critical values of DW for a given level of significance, sample size and number of independent variables can be obtained from published tables that are tabulated as pairs of values: DL (lower limit of DW) and DU (upper limit of DW).To evaluate DW[3]: Locate values of DL and DU in Durbin-Watson statistic table.2)For positive temporal autocorrelation: a) If DW < DL then there is positive autocorrelation.b) If DW > DU then there is no positive autocorrelation.c) If DL < DW < DU then the test is inconclusive.For negative temporal autocorrelation: a) If DW < (4.0 -DU) then there is no negative autocorrelation.b) If DW > (4.0 -DL) then there is negative autocorrelation.c) If (4.0 -DU) < DW < (4.0 -DL) then the test is inconclusive.
and the expected correlation due to propagation of correlation at the previous lag.If the PACF displays a sharp cutoff while the ACF decays more slowly we conclude that the data displays an autoregressive model (AR), and the lag at which the PACF cuts off is the indicated number of AR terms.If the ACF of the data displays a sharp cutoff and/or the lag-1 autocorrelation is negative then we have to consider adding a moving average term (MA) to the model, and the lag at which the ACF cuts off is the indicated number of MA terms.In general, the diagnostic patterns of ACF and PACF for an AR (1) term[18] are: ACF: declines in geometric progression from its highest value at lag 1.0.
temporal autocorrelation is determined to be present in the dataset, then one of the first remedial measures should be to investigate the omission of one or more of the key explanatory variables, especially variables that are related to time.If such a variable does not aid in reducing or eliminating temporal autocorrelation of the error terms, then a differencing procedure should be applied to all temporal independent variables in the dataset to convert them into their differences values, and rerun the regression model by deleting the intercept from the model[17].If this remedy does not help in eliminating temporal autocorrelation, then certain transformations on all variables can be performed for the AR (1) term.These transformations aim at performing repeated iterative steps to minimize the squared sum of errors in the regression model.Examples of such transformations are: Cochrane-Orcutt procedure; and Hildreth-Lu procedure.
crash data for three years (2013-2015) for the Interstate I-70, MO, USA are used in this paper as reported by the Missouri State Highway Patrol (MSHP) and recorded in the Missouri Statewide Traffic Accident Records System (STARS).
Driver factors (driver's age; speeding; aggressive driving; driver intoxicated conditions; the use of cell phone or texting) • Vehicle type (passenger car; motorcycles; truck) • Number of vehicles involved in the crash • Time factors (hour of crash occurrence; weekday; month) • Accident type (animal; fixed object; overturn; pedestrian; vehicle in transport).
and larger values are recommended to detect the existence of temporal autocorrelation.For the I-70 dataset, the number of observations of the aggregated three years (2013-2015) is 5869, and the minimum recommended number of lags = ln (5869) = 8.7.This paper uses 36 lags in both the LM and LBQ tests instead of the minimum recommended number.The Box-LjungQ statistic (LBQ) is applied to the I-70 data for the aggregated three-year period (2013-2015) using the time independent variables (month, weekday, and hour) and for the first 36 lags.In addition, correlograms of the autocorrelation function (ACF) and partial autocorrelation function (PACF) for the I-70 data for the aggregated three-year period (2013-2015) are presented.
), the OLS residuals are then used to obtain an estimate of rho from the OLS regression.This estimate of rho is then used to produce transformed observations, and parameter estimates are obtained again by applying OLS to the transformed model.A new estimate of rho is computed and another round of parameter estimates is obtained.The iterations stop when successive parameter estimates differ by less than 0.001[20].The iterative Cochrane-Orcutt procedure was applied to the I-70 (2014) dataset, and an optimized rho (i.e. the residual autocorrelation coefficient) value of 0.07333 was obtained using the Stata 14 software that minimizes the estimated sum of squared residuals (ESS), then the DW statistic was calculated for the transformed residuals.The results showed that the temporal autocorrelation was removed from the I-70 (2014) dataset, as shown in Table 4.The DW statistic for the I-70 (2014) dataset is changed after applying the Cochrane-Orcutt procedure from 1.843 (with a significant p-value of 0.0002) to 1.992 (with a non-significant p-value of 0.7167).After removing the temporal autocorrelation from the I-70 (2014) dataset, the DW test and the LM test were applied for the aggregated three years' period (2013-2015) for the I-70 dataset.The DW statistic for the three years' period (2013-2015) is 1.971 with temporal autocorrelation of 1.47% for the I-70 dataset, temporal (time) component and could adversely affect the precision of parame-ter estimates.There are several methods that can be used to detect the existence of the temporal autocorrelation in the crash dataset, such as: 1) the residuals scatter plots; 2) the Durbin-Watson (DW) test; 3) the Durbin h test; 4) the Breusch-Godfrey (LM) test; 5) the Ljung-Box Q (LBQ) test; and 6) correlograms.The residuals scatter plots and correlograms are not formal tests, and they would only suggest whether temporal autocorrelation may exist within crash data.The Durbin h can only be used when there is a lagged dependent variable in the data.This paper used the Durbin-Watson (DW), Breusch-Godfrey (LM), and the LBQ tests to detect the temporal autocorrelation among the temporal independent variables in the crash data (i.e.hour, weekday, month) for the interstate I-70 in Missouri for the years(2013)(2014)(2015).Although the applications of these tests can be found in time series models, they have not been addressed in modeling crash data.As such, this paper thoroughly investigated the applicability of these tests to crash data.
Table 1 .
DW statistic for I-70 crash data.
Table 2 .
LM statistic for I-70 crash data.
Table 6 .
The results from the DW test and the LM test indicate that there is no significant temporal autocorrelation among each of the temporal independent variables (i.e.month, weekday, and hour) in the (2013-2015) dataset.
Table 5 .
Overall DW statistic for I-70 crash data.
Table 6 .
Overall LM statistic for I-70 crash data.
Table 7 .
LBQ test results for I-70 crash data. | 6,844.6 | 2017-03-13T00:00:00.000 | [
"Engineering",
"Environmental Science"
] |
Event-by-event $v_n$ correlations of soft hadrons and heavy mesons in heavy ion collisions
Combining event-by-event hydrodynamics with heavy quark energy loss we compute correlations between the heavy and soft sectors for elliptic and triangular flow harmonics $v_2$ and $v_3$ of D$^0$ mesons in PbPb collisions at $2.76$ TeV and $5.02$ TeV. Our results indicate that $v_3$ is strongly influenced by the fragmentation temperature and that it builds up later than $v_2$ during the evolution of the system.
Introduction
It is known that final state flow anisotropies are converted from medium density gradients present in early stages of heavy ion collisions due to the nearly perfect fluidity property of the Quark-Gluon Plasma (qgp). Event-by-event viscous hydrodynamics has been shown to accurately describe the anisotropic flow coefficients, v n , in the soft limit (p T < 2 GeV) [1]. However, at high p T the underlying physical mechanism behind anisotropic flow changes and v n is driven by differences in the path length of jets flowing through the plasma [1,2], a picture that has been confirmed by event-by-event jet energy loss combined with viscous hydrodynamics calculations [3]. In this picture, there is an approximate linear response relation between the high p T v 2 and the initial state eccentricity 2 .
Recent calculations using event shape engineering techniques [4,5] has shown that heavy flavor meson azimuthal anisotropy at high p T are linearly correlated with the anisotropy in the soft sector [6]. Following these calculations, in this proceeding, we further investigate the correlations between D 0 mesons with p T 10 GeV to all charged particles in the soft sector for PbPb at √ s = 2.76 TeV and √ s = 5.02 TeV collisions. This is done by combining a heavy quark energy loss model with event-by-event viscous hydrodynamic backgrounds, which allows for computing the nuclear modification factor, R AA , and the corresponding flow coefficients v 2 and v 3 .
Development of the simulation
In order to study the evolution of the heavy quarks inside the qgp we developed the so-called dab-mod [6], a modular Monte Carlo simulation program written in C++, using root [7] and pythia8 [8] libraries. The arXiv:1704.04654v2 [nucl-th] 27 Jul 2017 modular characteristic of the program allows for one to select different energy loss models, medium backgrounds or hadronization processes while studying the evolution of the system. In the simulation, bottom and charm quarks are sampled within the transverse plane at midrapidity of the qgp medium with their initial momentum given by pqcd calculation using fonll [9,10]. Each sampled heavy quark travels along the transverse plane with a velocity v and a constant direction ϕ quark . We implement a simple parametrization of the energy loss per unit length given as: where T is the local temperature, is the flow factor with ϕ flow the local azimuthal angle of the underlying flow.
In this work we consider f (T, v) = α, inspired by the study performed in Ref. [11], which showed that a non decreasing drag coefficient near the phase transition is favored for a simultaneous description of heavy flavor R AA (p T ) and v 2 (p T ). The free parameter α in the energy loss expression is fixed by matching the D 0 R AA computed by dab-mod to data for p T ∼ 10 GeV in the central collisions.
We use the v-usphydro event-by-event relativistic viscous hydrodynamical model [12,13,14] for the temperature and flow profiles of the medium. For initial conditions, mckln [15] is used with η/s = 0.11 and an initial time τ 0 = 0.6 fm, which leads to a good description of experimental data for the flow harmonics at low p T . Currently, no coalescence is implemented in the code and hadronization of the heavy quarks is assumed to occur when the local temperature reaches a chosen temperature T d , at which fragmentation [16] is performed. Also, no effect on the medium from the traversing heavy quarks is considered during this calculation and the heavy quarks are treated as probes.
The event-by-event analysis uses a couple of thousand hydro events in each centrality bin. Heavy quarks are oversampled for each event. That allows us to compute the nuclear modification factor R q AA (p T , ϕ), for a given heavy quark flavor q or heavy meson from q, and its corresponding flow coefficients v q n . The reason for the oversampling is to give a sufficient probability to find v q n (p T ) in a hydro event with a certain v n in the soft sector. From the flow coefficients in the hydro events we compute the multi-particle cumulants [17,18] following the procedure performed in Refs. [19] using multiplicity weighting and centrality rebinning.
Results
We show in Fig. 1 a comparison of D 0 R AA computed by dab-mod with experimental data [20,21,22] for both √ s = 2.76 TeV and √ s = 5.02 TeV PbPb central collisions. In the considered region of p T 10 GeV our results lead to a good agreement with the data and are similar for both fragmentation temperatures of T d = 120 MeV and T d = 160 MeV. In Fig. 2 we compute the multi-particle cumulants v 2 {m} of D 0 mesons for the same collision energies at a different centrality range of 30-40% and compare with currently available experimental data [23,24]. One can see that our results are consistent with data at high p T for the two collision energies. At low p T 10 GeV one must consider that coalescence is not negligible and our results fall bellow experimental data. Furthermore, different energy loss mechanisms come into play in the low p T regime [25], which may contribute to the overall magnitude of the computed flow harmonics. Using event-by-event correlations [6] one can examine different parameters of the simulation and study their effects. In Fig. 3 That might be related to the build up time of each harmonic, since, the higher the T d , the less time the quark has to interact with the medium before hadronization occurs. The plots indicate that for this energy loss parametrization, v 3 takes longer to build up than v 2 , which should get most of its effect from the initial interaction with the medium.
Conclusions
This work combines event-by-event hydrodynamic flow and temperature profiles with a parametrization for heavy quark energy loss, which allows for the computation of R AA and v 2 of D 0 mesons at high p T . By implementing these calculations into a Monte Carlo simulation, called dab-mod, we were able to obtain the correlations between the heavy flavor and soft sectors for the elliptic and triangular flow harmonics v 2 and v 3 using an event engineering technique first described in [6]. Our results show that the v 3 magnitude is highly affected by the fragmentation temperature which indicates that it might be built up at later stages during the evolution of heavy quarks within the medium when compared to v 2 . | 1,653.4 | 2016-11-09T00:00:00.000 | [
"Physics"
] |
Into the Origin of Electrical Conductivity for the Metal-Semiconductor Junction at the Atomic Level
The metal-semiconductor (M-S) junction based devices are commonly used in all sorts of electronic devices. Their electrical properties are defined by the metallic phase properties with a respect to the semiconductor used. Here we make an in-depth survey on the origin of the M-S junction at the atomic scale by studying the properties of the AuIn2 nanoelectrodes formed on the InP(001) surface by the in situ electrical measurements in combination with a detailed investigation of atomically resolved structure supported by the first-principle calculations of its local electrical properties. We have found that a different crystallographic orientation of the same metallic phase with a respect to the semiconductor structure influences strongly the M-S junction rectifying properties by subtle change of the metal Fermi level and influencing the band edge moving at the interface. This ultimately changes conductivity regime between Ohmic and Schottky type. The effect of crystallographic orientation has to be taken into account in the engineering of the M-S junction-based electronic devices.
Introduction
Electronic devices based on metal-semiconductor (M-S) junction were one of the earliest electronic devices. Controlling of the electrical properties of the M-S junctions is critical because in all currently available electronic devices the electrodes are made of metal [1][2][3][4]. The metal-semiconductor junction is formed when a metal is brought into contact with a semiconductor material. In the very simple scenario, the M-S junction could possess rectifying or non-rectifying properties depending on the electronic properties of the materials it consists of, i.e. the work function of the metal and the electron affinity (n-type) or the ionization energy (p-type) of the semiconductor [5][6][7]. The nonrectifying M-S junction is called the Ohmic contact while the rectifying onethe Schottky diode or the Schottky contact. The behaviour of the rectifying properties of the M-S junction, discovered by Braun [8], was explained by Schottky [9] by introducing the so-called effective Schottky barrier (potential energy barrier) formed at the M-S interface [29][30][31]. The atomic arrangement at the M-S interface plays an essential role in defining its electrical properties. The simplest way to distinguish between the Ohmic contact or the Schottky diode is to analyze the Current-Voltage (I-V) characteristics of the device. The I-V relationship of the Ohmic contact is linear and follows the Ohm's law: V = I⋅R, where V is the applied voltage, Ithe flowing current, and Rthe device resistance. Usually, also the specific contact resistance can be calculated as r c = RA, where A is the active area. The I-V characteristic of the Schottky contact is non-linear and follows the thermionic emission equation [ This is true for the common semiconductors (Si, GaAs, GaN, InP, etc.) with high mobility where the barriers are not so thick, so the drift diffusion could be neglected. The M-S junction is usually characterized by the effective parameters obtained by fitting the I-V dependence to either the Ohm's Law or to the thermionic emission equation. These approaches characterize the electrical properties of the junction quite effectively without going into detail at the atomic scale.
Here, we present a comprehensive study, at the atomic scale, of the M-S junction formed between the Au-rich nanoelectrodes grown on the InP(0 0 1) single crystals, by the combination of the Conductive AFM (C-AFM) technique together with the atomically resolved High Angle Annular Dark Field Scanning Transmission Electron Microscopy (HAADF STEM) measurements corroborated by the Density Functional Theory (DFT) calculations. The structurally characterised junction together with the Local Density of States (LDOS) and the C-AFM electrical measurements allowed us not only to effectively describe and understand the formed M-S junction by deriving its parameters, but also to depict it quantitatively at its origin, i.e at the atomic interface. Additionally, we see that the crystallographic orientation of the metal with respect to the semiconductor plays an essential role and defines the M-S junction rectifying or non-rectifying character by changing the nanoelectrode Fermi level and band edge moving at the interface.
Results and discussion
The AIII-BV semiconductors, in particular InP used in optoelectronic applications [12] or as a field-effect transistor (FET) based biosensor [13], are considered promising materials to overcome the limitations of the silicon-based technology. In all these device applications usually the Au-rich nanoelectrodes are used to provide the electric contact between the ambient and the fabricated device. It is hence important to study and to understand the electrical performance of the nanoelectrodes since they can influence also the performance of the final device. In the present study, the Au-rich nanoelectrodes made of AuIn 2 alloy were formed in the process of thermally induced self-assembly [11] of Au deposited by MBE on InP(0 0 1) n-doped single crystals. After samples preparation, the nanoelectrodes were electrically characterized in situ (in UHV) with C-AFM measurements. The I-V data were collected in a hyperspectral mode and the resultant map which shows the regions with the same I-V characteristics, was obtained together with average I-V characteristics in that region. The HAADF STEM measurements were performed on Focused Ion Beam (FIB) prepared sample's cross-sections. The Density Functional Theory (DFT) calculations of electronic properties, i.e. the Local Density of States (LDOS), were performed with the use of the VASP [17] code (for details please look into Methods Section). In Fig. 1a), the SEM morphology of AuIn 2 nanoelectrodes, formed on InP(0 0 1) surface, of 20-30 nm in diameter, is shown. A high-resolution AFM imaging, as depicted in Fig. 1(b-d), has shown that the AuIn 2 nanostructures are of two types of morphology. Some of the nanostructures exhibit fewer side facets with "Flat Top" (Fig. 1c) and the other facet-ones with "Sharp Top" (Fig. 1d). The C-AFM I-V hyperspectral data with simultaneously collected sample topography are presented in Fig. 1(e and f) (see also Supporting Information visualisation of the I-V data cube as a movie). The average current map in Fig. 1(e) clearly shows that there are nanoelectrodes which exhibit higher conductivity (higher average current) and lower conductivity (lower average current). The grouping (clustering) of the collected I-V hyperspectral data shows in detail the corresponding topography (f). Low conductivity "Flat Top" and High conductivity "Sharp Top" nanoelectrodes are visible. Results of grouping (clustering) by k-means of current-voltage (I-V) hyperspectral data: map showing different I-V regions g) together with corresponding average I-V characteristics in these regions h). Three different regions are visible: low conductivity nanoelectrodes region (blue) which exhibit nonlinear I-V behavior, high conductivity nanoelectrodes region (red) with linear I-V characteristic, InP surface region (green). It is seen that ~70% of all nanoelectrodes are of lower conductivity. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) three different regions in terms of electrical properties as presented in the map (Fig. 1g) and corresponding average I-V of these regions presented in Fig. 1(h). The first region (blue colouring) of a lower conductivity corresponds to the nanoelectrodes which are of "Flat Top". This sample region exhibits the non-linear I-V characteristics. The second region (marked with red) of a higher conductivity corresponds to the area of nanoelectrodes with "Sharp Top" and exhibits the linear I-V characteristics. The third region (green) corresponds to the InP surface which shows typical for a semiconductor material, non-linear I-V behaviour. From our C-AFM measurements it has been found that ~70% of all AuIn 2 nanoelectrodes are of lower conductivity.
To investigate the details of the AuIn 2 nanostructure/substrate interface, the atomic scale HAADF STEM measurements were performed. Fig. 2(a) and (b) show the HAADF STEM image of "Flat Top", low conductivity nanoelectrodes together with details of the I-V measurement results. The I-V data were fitted by thermionic Schottky equation, and the effective parameters of this M-S junction were extracted (see Fig. 2b). The Schottky barrier height of Φ B = (0.2555 ± 0.0080(stat) ± 0.014(syst) )eV and the ideality factor η = (2.22 ± 0.31(stat) ± 0.12(syst) ) were obtained. It can be noted that the fitted Schottky barrier height is very similar to the pure indium to InP contacts which is in the order of 0.32 eV [19]. It can be seen from the HAADF STEM image that the (1 -1 1) crystallographic plane of the formed AuIn 2 nanoelectrode is exposed towards the substrate. Resulting in the It is seen that the Conduction Band Edge (Ec) moves as one approaches the interface region. The LDOS state ~4 eV melts completely at the interface (see green arrow). Comparing Ec at interface with the Fermi energy of AuIn 2 , the Schottky barrier of ~0.8 eV was approximated from DFT.
following crystallographic orientation (1 -1 1)AuIn 2 //(0 0 1)InP and [1 1 0]AuIn 2 //[1 1 0]InP. Detail information on the crystal structures of the metal (AuIn 2 ) and InP is presented in Fig. S3 in Supporting Information. In Fig. 2c the atomically resolved AuIn 2 /InP interface, with indium and phosphorus atomic columns clearly resolved, is depicted and overlaid with the DFT calculated atomic structural model. The model uncovers in detail the structure of the AuIn 2 /InP interface. In the interface, the last layer of the substrate consists of In-P dimers with structurally disturbed positions of In atoms along the column (see Fig. 2c). On the other side, at the bottom of the nanoelectrode there is only one layer of Au-In dimers (see Fig. 2c) which are organized differently that the rest of AuIn 2 nanoelectrode arranged as linear trimers with Au atoms in their centre. The interface structure is not a perfect crystalline structure but rather a disturbed one, what is also reflected in the HAADF image. However, we do not observed any misfit dislocations or strain fields on the both, i.e. the nanoelectrode and substrate side. Furthermore, the local electronic properties of the M-S junction were characterised with the DFT calculations providing the computed LDOS along the direction normal to the AuIn 2 /InP interface (see Fig. 2(d) and (e)). The LDOS colour map ( Fig. 2d) composed of the slices reflecting the average electronic structures of subsequent atomic monolayers, shows the changes of electronic structure across the studied interface. To see the details of the electronic structure at the vicinity of the M-S junction interface we looked at the LDOS slices as from the DFT calculations (Fig. 2e). The InP LDOS is presented for three different regions, i.e., the bulk InP, the vicinity of the interface, and at the interface. For the comparison, also the LDOS for the AuIn 2 metal alloy is presented. The LDOS is calculated relative to vacuum at 0 eV. The valence band and the conduction band states of the InP can be clearly seen. The DFT calculated Fermi energy of AuIn 2 metal alloy in (1 1 1) configuration of E F = 4.247 eV is presented as a red dashed line in Fig. 2(d)-(e). It can be noticed that the local band structure of InP is changing as one approaches the interface with the AuIn 2 nanoelectrode, i.e., the Conduction Band Edge (E c ) of InP is moving towards the vacuum level (energy of 0 eV). This is related to the disturbed atomic structure of the Interface at InP side, as can be inferred from the DFT model (Fig. 2c). This disturbed structure induces the localized states at the band gap region, so the band gap and Conduction Band Minimum (CBM) cannot be unambiguously defined, in contrast to the Conduction Band Edge (E c ), similarly as for the amorphous material case [21]. The effective E c movement is realized by a total melting of the InP LDOS state at ~4 eV (see DFT LDOS in Fig. 2(d) and (e)). This LDOS melting effect extends over around three InP atomic layers. Since now there are almost no InP LDOS states at metal Fermi energy level, the flowing electron current from the nanoelectrode toward InP will effectively feel the barrier at the interface region. From the difference between the E c of InP at the interface and the Fermi Energy of AuIn 2 the value of the Schottky barrier height can be approximated as ~0.8 eV. This simple approximation, stemming from the DFT calculations, is different from the experimental value due to the calculation of the exchange-correlation energy which is a well known effect [20]. This, however, agrees qualitatively with the experimental results which show the appearance of the Schottky behaviour.
We now analyse the high conductivity AuIn 2 nanoelectrodes. Fig. 3 (a) and (b) show the HAADF STEM image of the high conductivity "Sharp Top" nanoelectrodes together with the details of the I-V measurements. The linear I-V data were fitted to the Ohm's law and the specific contact resistance was extracted: r c = (1.43 ± 0.19(stat) ± 0.20(syst) )*10 − 4 Ωcm 2 . This value is consistent with a bulk gold Ohmic contacts to InP [19]. It can be seen from the HAADF STEM image that these AuIn 2 nanoelectrodes expose a (2 1 1) crystallographic plane towards the InP(0 0 1) substrate surface, which is different compared to the case of the low conductivity nanoelectrodes. This results in the crystallographic orientation of (2 1 1)AuIn 2 //(0 0 1) InP and [1][2][3][4][5][6][7][8][9][10][11]AuIn 2 //[1 1 0]InP. The atomically resolved HAADF STEM image of the AuIn 2 /InP interface is shown in Fig. 3(c) together with the DFT calculated atomic structural model of this M-S junction. The interface region at the InP side consists of the In-P dimers with disturbed atomic structure in columns. While interface at the AuIn 2 side consists of the In-Au-In trimers, also with the disturbed structure in atomic columns. The HAADF contrast blur indicates a reduced atomic order of the interface. However, we do not observed any misfit dislocations or strain fields on the both, i.e. the nanoelectrode and substrate side. The calculated LDOS along the direction normal to the AuIn 2 /InP interface in presented Fig. 3(d)-(e). The LDOS colour map Fig. 3(d) shows similarly how the local electronic structure changes when the atomic structure changes from InP to AuIn 2 . The detailed LDOS slices are presented in Fig. 3(e). The DFT calculated Fermi Energy of AuIn 2 metal alloy in the (2 1 1) configuration of E F = 4.051 eV is presented as a red dashed line in Fig. 3(d)-(e). It can be noticed that the local band structure is not changing as one approaches the interface, i.e. the Conduction Band Edge (Ec) of InP is not moving. This time the LDOS state at ~4 eV does not melt as shown in Fig. 3(d) and (e). We have, therefore, no Schottky barrier and the contact is fully Ohmic. This agrees with the experimental results which show the Ohmic behaviour.
It is now important to note that the difference between these two nanoelectrodes is the crystallographic orientation of the metal AuIn 2 phase with respect to the InP substrate resulting in one case, in formation of a Schottky-type junction and, in another one, the Ohmic contact. The nanoelectrodes were formed during self-assembling process, where during ad-atoms diffusion and aggregation the AuIn 2 nanoelectrode grows on InP surface by the formation of the most energetic favourable planes, having low surface energies i.e. (1 1 1) and (2 1 1) planes, which are very common for metals with cubic crystal structure [28]. This finally results in a two types of nanoelectrodes. The effect of the formation of Schottky nanodiode or Ohmic nanocontact is related to the crystallographic orientation implying changes in the Fermi level of the AuIn 2 metal alloy phase at the interface. The particular atomic structure at the interface provide the differences in LDOS electronic states and, consequently, is responsible for the appearance of the band edge movement, or the lack thereof, at the interface. We also see that in the case of the Ohmic-type junction the atomic structure, as seen from a top surface view, of InP and AuIn 2 is better matched together than in the case of Schottky-type junction, see Fig. S4 in Supporting Information. This is also directly seen in the calculated lattice misfit, see Table S1 in Supporting Information. It is seen that on average the lattice misfit is lower for high conductivity nanoelectrodes.
What we also see is that in case of the studied here AuIn 2 /InP(n-type) the change in M-S junction behaviour between the Ohmic and Schottky regimes is significant since the work function (E f ) of metal nanoelectrode (AuIn 2 ) is close to the Conduction Band Minimum (CBM), for p-type semiconductor this will be when E f will be close to the Valence Band Maximum (VBM). The work function (E f ) changes induced by crystallography are significant to allow here for the switching between the Ohmic and Schottky conduction regimes. As we think, this effect could be also applicable to other semiconductor systems. The corresponding energy relations between the metal E f and substrate semiconductors' CBM and VBM are presented in Fig. 4. By comparing CMB (n-type) or VBM (p-type) with a work functions for the selected metals [24][25][26], we proposed the M-S systems where the effect of crystallographic orientation of metal with a respect to the semiconductor will cause a changes in conductivity behaviour between Ohmic and Schottky regime. The conductivity behaviour changes of the M-S junction related to the crystallographic orientation of the metal are a consequence of the metal work function changes at the interface. This effect could be used to tune the parameters of M-S junction to desired behaviour within a single metal or alloy phase by controlling the growth of a metal with a desired orientation on semiconductors substrates using various advanced heteroepitaxy methods.
Conclusions
Based on the studied AuIn 2 nanoelectrodes which form two types of M-S junctions, i.e. the Schottky or the Ohmic contacts, on InP(0 0 1) substrate surface, we have shown directly at atomic scale that the different crystallographic orientation of the same metal with respect to the semiconductor, thus different structure of the interface, determines the electrical properties of the M-S junction. Hence, the rectifying junction in one case, and the non-rectifying one in the other case, is formed by changing the Fermi level of the AuIn 2 metal alloy phase and influencing local changes in electronic structure, i.e. band edge moving at the disturbed interface. We directly see that the origin of this different conductivity behaviour has its roots in the mutual crystallographic orientation of the metal nanoelectrode and the semiconductor. The effect of the crystallographic orientation of the metal electrode with respect to the substrate, implying the Fermi level changes at the interface, can be used to control the electrical properties of the M-S junction based devices by utilizing only single metal/alloy phase to change between Ohmic-Schottky conductivity regimes. Our findings could be also applicable to other metal-semiconductors systems. This gives a possibility for the engineering of the new desired future electronic devices using metal electrodes with defined optimally suited crystallographic orientation in particular in the area of AIII-BV based devices.
Sample preparation
Indium phosphide InP(0 0 1) n-doped crystal was mounted on molybdenum plate and introduced into the UHV Molecular Beam Epitaxy (MBE) system, with a base pressure of 10 -10 mbar. The sample was initially out-gassed for 1 h at 150 C and exposed to low energy, 700 eV Ar + ion bombardment at a 60 deg incident angle at room temperature (RT). The sample surface was cleaned in cycles of ion-beam irradiation at T = 450 C (InP) until the (4 × 2) InP(0 0 1) reflection high energy diffraction (RHEED) pattern was observed (see Supporting Information Fig. S1). The applied cleaning procedure results in atomically flat surfaces. Next, 2 ML (mono-layers) of Au was deposited on the sample surface at temperature of 330 C and a rate of 0.1 ML/min as checked with a quartz micro-balance. After the deposition, the sample was cooled down to RT at a rate of 10 C/min. The sample temperature during all experiments was measured with a pyrometer (LumaSense, model IGA 140) with emissivity ε = 0.5. The applied sample preparation results in the formation of the metallic nanoelectrodes on the sample surface made of AuIn 2 alloy [11].
Sample characterization
The electrical characterization of the nanoelectrodes in the form of current voltage (I-V) measurements was carried out in situ (in UHV) just after sample preparation by Conductive Atomic Force Microscopy (C-AFM) using Omicron RT AFM/STM microscope. The I-V data were collected in a hyperspectral mode in the form of the three dimensional Spectrum Image stack, where for each sample grid point (x, y) a full I-V curve was collected as z-axis. The C-AFM data were grouped together (clustered) using K-Means method as implemented in Scikit-Learn [14].
The resultant map, which shows the regions with the same I-V characteristics, was obtained together with average I-V characteristics in that region. To extract the Schottky barrier height and ideality factor, the collected I-V data by C-AFM were fitted by the thermionic emission equation [3,10] Beam SEM/FIB FEI Quanta 3D FEG microscope from FEI. Later, the atomically resolved HAADF STEM measurements, where the contrast is proportional to the atomic number Z and to the sample thickness, were performed using a FEI (S)TEM Titan3 G2 60-300 microscope operated at 300 kV. The HAADF-STEM images were acquired with a convergence angle of 20 mrad and a probe current of 80 pA. To get rid of the scanning artefacts the HAADF STEM data were collected as an image stack of ten 4 k HAADF STEM images, which next were registered by Non-rigid registration using free software ImageJ/FIJI [27] and median stacked. Before median stacking the registered images were scaled by a factor of four. The obtained HAADF-STEM images were deconvoluted to remove the overall blur caused by different effects (source size, aberration, other instabilities, etc.) and to increase the image resolution. We used the assumption of ideal microscope and ideal crystal structure in the bulk i. e. the ideal crystal structure in the ideal microscope will be visible as points. By this assumption the transfer function is derived, by the fit in the Fourier space, as an asymmetric Gaussian function, which includes all the blurring effects. The derived transfer function is later used for the deconvolution of the whole image. As we checked in details, such a deconvolution approach does not introduce any artefacts, the image resolution is increased making the interpretation of the structure easier. All the deconvolution approach steps were done by the free software Gwyddion [16]. For details please see Supporting Information Fig. S2. The STEM measurements were performance on the Focused Ion Beam (FIB) prepared thin foils from nanoelectrodes sample which was covered by thermally evaporated carbon layer in the UHV Chamber to prevent surface contamination and damage [15]. The quantum-chemical calculations of electronic properties i.e. the Local Density of States (LDOS), were performed by the Density Functional Theory (DFT) calculations with the use of the VASP [17] code. To reliably extract the information of the AuIn 2 /InP atomic interface (which is not trivial), the atomic model was derived purely from DFT calculations, which used as an input only orientations of both structures, i.e. the nanoelectrode and the substrate, which are indisputably visible. Only then the optimized by DFT model is validated on the HAADF data. This kind of approach, which we used does not depend on the HAADF STEM interface data directly, which contains non trivial disturbed atomic structure. The DFT optimized model of the atomic interface delivered the same atomic structure as in the HAADF STEM data, which finally validated our approach. The derived full atomic model together with disturbed atomic structure was used for the electronic properties calculations. The Γ point sampling of the irreducible Brillouin zone was used for the AuIn 2 /InP interface supercell LDOS calculations together with the Methfessel-Paxton smearing of 0.01 eV and the PBE [22,23] functional. The plane wave energy cut-off was chosen as 400 eV. In the Fig. 4. Energy relative to the vacuum as a function of electron affinity (CBM) and ionization potential (VBM) for AIII-BV semiconductors. Work functions of selected metals are presented as a horizontal lines. Work function for the studied here AuIn 2 on InP is also presented as a black line. Based on our work on AuIn 2 /InP system, by comparing CBM for n type semiconductors and VMB for p type semiconductors with a metals work function (E f ), the table which presents potential systems, where M-S junction conductivity regime changes (Ohmic-Schottky) caused by different metal crystallographic orientation is derived.
DFT LDOS calculations, the electron affinity of pristine InP was cali-
Nanoelectrodes sythesis and in situ formation dynamics
Nanoelectrodes formation dynamics was studies during synthesis in UHV conditions by in situ RHEED diffraction analysis Figure S1. The RHEED shows that the InP(001) surface is before Au deposition is atomically clean and Figure S1a). The obtained results show that the nanoelectrodes start to from from 0.5ML of Au, where the first 3D RHEED pattern appears.
S2 Figure S1: Figure S2 (top row). Next the assumption of ideal microscope and ideal crystal lattice in the bulk was used i.e. the ideal crystal structure in the ideal microscope will be visible as points. The asymmetric Gaussian transfer function was extracted by the fit in Fourier space, which includes all the blurring effects (using "Statistics→Transfer Function Fit").
Later the extracted transfer function Figure S2 (top row) was used to deconvolve the collected HAADF STEM data (using "Multidata → Deconvolve"). High frequency noise was removed from deconvoluted image by performing standard 2D FFT filtering (using "Correct Data → 2D FFT Filtering"). The results of the deconvolution were compared with the original image by comparing exactly the same line profiles of the atomic columns Figure S2 (down row). It is seen that in the deconvoluted data the atomic columns are much more clearly visible, the resolution is increased. The Phosphorus atomic columns are much more clearly resolved. As we see in details, such a deconvolution approach does not introduce any artefact's, the image resolution is increased making the interpretation of the structure easier.
Phases Crystallography
In Figure InP is Zincblende, Sphalerite structured and crystallizes in the cubic F-43m space group. The structure is three-dimensional. In3+ is bonded to four equivalent P3-atoms to form corner-sharing InP4 tetrahedra. All In-P bond lengths are 2.58 Å. P3-is bonded to four equivalent In3+ atoms to form corner-sharing PIn4 tetrahedra [1].
AuIn 2 is Fluorite structured and crystallizes in the cubic Fm-3m space group. The structure is threedimensional. Au is bonded in a body-centered cubic geometry to eight equivalent In atoms. All Au-In bond lengths are 2.90 Å. In is bonded to four equivalent Au atoms to form a mixture of edge and corner-sharing InAu4 tetrahedra [1]. Nanoelectrodes atomic models Figure S4 shows atomic structural models of a top surface view of AuIn 2 nanoelectrodes in respect to InP(001) surface. Models for InP and AuIn 2 phase are shown for two different crystallographic S6 Figure S4: Atomic structural models of a top surface view of AuIn 2 nanoelectrodes in respect to the InP(001) surface. Upper row shows atomic models of InP and AuIn 2 phase together with models overlay for low conductivity nanoelectrodes, lower row shows models for high conductivity nanoelectrodes respectively, crystallographic directions indicated. From the lattice overlay it is seen that the InP and AuIn 2 structures are better matched for high conductivity nanostructures.
orientations corresponding to low conductivity nanoelectrodes ( Figure S4 upper row) and to high conductivity nanoelectrodes ( Figure S4 lower row). From the atomic models overlay ( Figure S4 right column) it is seen that InP and AuIn 2 structures are better matched together for high conductivity nanoelectrodes. This is directly seen also in the calculated lattice misfit Table S1. It is seen that on average the lattice misfit is lower for high conductivity nanoelectreodes. | 6,498.8 | 2021-01-19T00:00:00.000 | [
"Physics",
"Materials Science"
] |
ENDO CROWN: AN APPROACH FOR RESTORING ENDODONTICALLY TREATED RIGHT MANDIBULAR FIRST MOLARS WITH LARGE CORONAL DESTRUCTION- A CASE REPORT
Rehabilitation of endodontically treated molar stilla challenge. After endodontic management of extensively carious molars, theyhave decreased mechanical characteristics. They became fragile and that is in relation with the removal of pulp and adjacent dentin tissues. Endocrown which is a single partial restoration could be measured as a good alternative for restoring molars having large coronal destruction and presenting endodontic treatment complications. We discuss the indication and use of endocrown to substitute single crowns with intraradicular retention and to present a clinical case report of an endocrown-type restoration, made-up from lithium disilicate ceramic (IPS e.Max CAD) in a mandibular first molar with widespread coronal destruction.
79
Endo Crown is a one-piece ceramic structure fixed to the internal walls of the pulp chamber and on the cavity margins to advance macro mechanical retention and the use of adhesive cementation would also improve micro retention [4].
The aim of the present paper is topresent a clinical case, in which an aesthetic and conservative posterior endocrown was used to restore a right mandibular first molar that presented endodontic treatment and extensive coronal destruction. We will deliberate through this work the indication and the use of endocrown [5].
Case Report
A 23-year-old male patient reported to the Department of Conservative Dentistry and Endodontics, NPDCH, Visnagar, Gujarat, India, for treatment of tooth #46. He suffered from major coronal destruction and needed to have his first molar restored. Medical history was non-contributory. Radiographic and clinical examinations were performed initially anda nonvital tooth (46) was identified with caries (Figures 1). Tooth was treated endodontically. The patient had a satisfactory oral hygiene and a favourable occlusion. The prosthetic decision was to restore tooth (46) with an endo crown made-up from lithium disilicate ceramic (IPS e.Max CAD). The preparation for the endocrown is different from the conservativewhole crown. Monolithic, ceramic adhesive restoration requires specific preparation techniques to be appropriate for biomechanical needs. This is achieved by an overall reduction in the height of the occlusal surface of tooth by at least 2 mm in the axial direction and to get a cervical margin or "cervical sidewalk" in the form of a butt joint. The cervical 80 margin has to be supragingival and enamel walls less than 2 mm have to be removed. Differences in levels between the various parts of the cervical margin should be linked by a slope of no more than 60° to seepage a staircase effect. We used a cylindrical-conical diamond bur apprehended parallel to the occlusal plane, to decrease the occlusal surface. Then we used a diamond wheel bur to control the orientation of the reduction and to assurance a flat surface thanks to its shape. We used a cylindrical-conical diamond bur with a total occlusal convergence of 8° to create continuity between the coronal pulp chamber and endodontic access cavity. The bur was positioned along the long axis of the tooth; the preparation was done without too much pressure and without moving the pulpal floor. The molar after preparation ( Figure 3). We ended the preparation with lining the root canal entrances with glass ionomer cement to protect the orifice of the canal ( Figure 4). Then we completed a try-in of the endo crown and tested occlusion, internal, and proximal adjustments. The internal surface of the endo crown was etched with 9 percent hydrofluoric acid, washed with water, and dried with an air syringe. A coat of a silane coupling agent was applied for 2 minute and dried. Rubber dam was used to attain proper isolationand then phosphoric acid was applied onto the tooth surface for 15 sec on dentin and 30 sec on enamel, then profusely washed and dried, applied with adhesive, and polymerized for 20 sec with light curing. A thin layer of a dual polymerizing resin was applied to the prosthetic endocrown and then was introduced into the tooth and polymerized at intervals of 5 seconds, making it easy to eliminate cement excesses. It was polymerized for 50 seconds on all surfaces. The crown was examined for any occlusal interfering using ceramic finishing instruments.
Discussion:-
Therestorative treatment of molars with a large coronal destruction is a clinical challenge, requires careful planning [6].
That is why the dentist has to choose for the best treatment option to ensure an efficient treatment providing clinical longevity of molars. The endo crown is suitable for all molars, chiefly those with clinically little crowns, calcified root canals, or narrow canals. But it is not suggested if adhesion cannot be assured, if the pulpal chamber is less than 2 mm deep, or if the cervical margin is less than 2 mm wide for most of its circumference [7].
82
This has been shown to be a beneficial technique as the procedure is easy.It facilitates the steps of impression taking and protects the periodontium. The use of ceramic has the advantages of biocompatibility and biomimicry and its wear coefficient is close to that of the natural tooth [8].
The single interface of a one-piece restoration makes cohesion better. The objective of the preparation is to get anextensive and stable surface resisting the compressive stresses that are frequent in molars [9].
The prepared surface is parallel to the occlusal plane thusdeliver stress resistance along the major axis of the tooth. The stress levels in teeth with endocrowns were lower than in teeth withcrowns. Because of the development of adhesive cementation systems, the need for macroretentive preparation for crowns has decreased [10].
The pulpal chamber cavity also deliversretention and stability. Its trapezoidal shape in mandibular molars and triangular shape in maxillary molars increase the restoration's stabilityand additional preparation is not desirable. The saddle form of the pulpal floor increases solidity. The adhesive qualities of the bonding material, makes it nonessential to attempt further use of post-involving root canals. The root canals do not need any exactshape.They are not fragilized by the drilling and they will not obtain the stresses associated with the use of post [11].
The compressive stresses are concentrated, being spread over the cervical butt joint and the walls of the pulp chamber. Dartora et al. haveevaluated the biomechanical behaviour of endodontically treated teeth restored using different extensions of endocrowns inside the pulp chamber and concluded that the greater extension of endocrowns provided improved mechanical performance. A 6 mm extension presented lower intensity and a better stress distribution pattern than a 2 mm extension which offered a low fracture resistance and a high possibility of rotating the piece when in function [12].
An in vitro study performed by Taha et al. was done to evaluate the effect of varying the margin designs on the fracture resistance of endodontically treated teeth restored with polymer-infiltrated ceramic endocrown restorationsThe results presented that endocrowns with axial reduction and a shoulder finish line had higher mean fracture resistance values than endocrowns with butt margin design. [13]. It has been also shown that butt joint designs providing a stable surface that resists the compressive stresses because it is prepared parallel to the occlusal plane [14].
Biacchi and Basting compared the fracture strength of two types of full ceramic crowns: indirect conservative crowns retained by glass fibre posts and endocrowns. They came to the conclusion that endocrowns were more resistant to compressive forces than the first ones. Finite element study highlighted the role of endocrowns in stress distribution [15].
According to Schultheis et al., endocrown seems to be a more reliable other for posterior loadbearing teeth, a bilayer configuration is more susceptible to reduce load fracture failure [16].
As stated by Biacchi et al., endocrowns procure acceptable function and aesthetics and reserve the biomechanical integrity of nonvital posterior teeth. The restoration is described to be less exposed to the adverse effects of degradation of the hybrid layer [17].
Researchlinking equivalent stresses in molars restored with endocrowns as well as posts and cores during masticatory simulation using finite element analysis revealed that teeth restored by endocrowns are potentially more resilient to failure than those with FRC posts. This study also showed that under physiological loads, ceramic endocrowns ideally cemented in molars should not be deboned [18].
A systematic review done by Sedrez-Porto et al. has compared clinical (survival) and in vitro (fracture-strength) studies of endocrown restorations associated to conventional treatments using intraradicular posts, direct composite resin, or inlay/onlay restorations; it has been shown that endocrowns may perform similarly or better than the conservative treatments [19].
Altier et al. evaluated the fracture resistance of three different endocrowns made of lithium disilicate ceramic and two different indirect resin composites and concluded that lithium disilicate ceramic endocrowns exhibited higher fracture strength than the indirect composite groups. It has been shown that endocrowns made of lithium disilicate-83 based ceramics are measured among the best restorative materials because of their adhesive properties;they promoted micromechanical interlocking with resin cement [20].
In vitro study accomplished by Gresnigt et al. evaluated the consequence of axial and lateral forces on the strength of endocrowns made of Metastable Lithium Disilicate and multiphase resin composite. It has been concluded that under axial loading, both Metastable Lithium Disilicate and multiphase resin composite used as endocrown material existing similar fracture strength but under lateral forces, the latter exhibited suggestively lower results. Tribst et al. evaluated the effect of a restorative material type on the biomechanical behaviour of endocrown restorations and concluded that Leucite presents a well stress distribution and it can be anauspicious alternative to lithium disilicate for the manufacture of endo crown restorations. Study conducted by Skalskyi et al. compared the fracture resistance of different restorative materials used in dental endocrown restorations. It has demonstrated that the mechanical behaviour of Zirconium dioxide in the tooth restorations altered [21].
The zirconium dioxide endocrowns cracked subsequent to crack propagation in the tooth. It has been also shown that the use of metal ceramic as endocrown material may deliver the lowest risk of failure during clinical use and had the highest fracture strength [22].
A study done by Darwish et al. showed that endodontically treated maxillary premolars restored with resin nanoceramic endocrowns obtainable better internal adaptation associated to those restored with lithium disilicate endocrowns and that endocrown preparation with smaller axial wall divergence ("6"degree) if better internal fit [23].
In a recent study, Zoidis et al. proposed polyetheretherketone (PEEK) as a substitute framework material for endocrown restorations. They demonstrated that the elastic modulus of the polyetheretherketone framework (5 GPa) veneered with indirect composite resin could dampen the occlusal forces defensive tooth structures better than ceramic materials. But further long-term clinical indication is required. CAD-CAM system, with aprojected success of 90.5% for molars and 75% for premolars in 58 patients [24].
According to Belleflamme et al., even in the presence of widespread coronal tissue loss or occlusal risk factors, for example bruxism or unfavourable occlusal relationships, endo crowns could be a dependable approach to restore severely damaged molars and premolars [25].
Conclusion:-
The preparation for endocrowns is modest and can be achieved quickly. Root canals are not engaged in the processand the procedure is not as much of traumatic as other preparations. The supragingival position of the cervical margin protects the marginal periodontium, enables impression taking, and conserves the solid substance of the remaining tooth. Forces are discrete over the cervical butt jointand axial walls, thus governing the load on the pulpal floor. The endocrown signifies a very hopeful treatment alternative for endodontically treated molars, it allows preserving of tooth structure, it is compatible with goal slightly invasive dentistry, and it is satisfactory for the concept of biointegration. It is a conservative method for mechanical and aesthetic restoration of nonvital posterior teeth. This type of reconstruction, which is still unusual, should be more extensively known and practised.
Conflicts Of Interest
The authorshave no conflicts of interest. | 2,748.2 | 2022-01-31T00:00:00.000 | [
"Medicine",
"Materials Science"
] |
Sentiment Analysis Algorithms through Azure Machine Learning : Analysis and Comparison
The Sentimental Analysis (SA) is a widely known and used technique in the natural language processing realm. It is often used in determining the sentiment of a text. It can be used to perform social media analytics. This study sought to compare two algorithms; Logistic Regression, and Support Vector Machine (SVM) using Microsoft Azure Machine Learning. This was demonstrated by performing a series of experiments on three Twitter datasets (TD). Accordingly, data was sourced from Twitter a microblogging platform. Data were obtained in the form of individuals’ opinions, image, views, and twits from Twitter. Azure cloud-based sentiment analytics models were created based on the two algorithms. This work was extended with more in-depth analysis from another Master research conducted lately. Results confirmed that Microsoft Azure ML platform can be used to build effective SA models that can be used to perform data analytics.
Introduction
The Sentimental Analysis is a widely known and used technique in the natural language processing realm.It is often used in determining the sentiment of a text.It encompasses studying peoples' attitudes, feelings and opinions towards a product, an event or organization computationally (Kasture & Bhilare, 2017;Li & Wu, 2010;Thomas, et al., 2011).It can be used to assess reviews posted by people online about their decisions regarding the food they consume, items the use and other issues affecting them.As such, sentiment analysis involves assessing a piece of writing intending to determine whether is neutral, negative or positive.It is often applied in several areas namely plagiarism checking; intellectual property, social media analytics, product reviews, and document/case classification.In social media analytics, which is the focus on the present study, studies have demonstrated the possibility of using sentiment analysis (SA) through platforms like Microsoft Azure Machine learning; Amazon SageMaker and Amazon Machine Learning; and Google Cloud Machine Learning to analyse social media analytics.
For example, Liu, et al. (2015) used Microsoft Azure Machine learning to perform Twitter sentiment analysis and to develop a model for classifying machine learning that allows for the identification of tweet sentiments and content that illustrate positive-value user contribution.Liu, et al. (2015) used Al-powered cognitive and data mining tools to analyse factors of social influence.The predictive sentiment analysis model developed from this study encompassed a combination of custom-developed natural language model and a traditional supervised machine language algorithm for identifying promotional tweets.In a similar study, Qaisi & Aljarah (2016) used sentiment analysis performed through Microsoft Azure and Amazon machine learning to analyze the opinions and reviews of Amazon and Microsoft.Results confirmed the possibility of using sentiment analysis via Azure and Microsoft to perform social media analytics.It was revealed based on the sentiment analysis that Azure had more positive tweets (65%) than Amazon (45%) and that Amazon had more negative polarity (50%) than the Microsoft Azure (25%).Similarly, Barbosa & Feng (2010) used sentiment analysis to classify data obtained from Twitter and proposed that syntax features such as links, exclamation marks, punctuation, retweets, and hashtags should be used alongside POS of words and polarity in performing sentiment analysis.
Results of these studies demonstrate that the sentiment analysis built on various machine language platform namely Microsoft Azure or any other platform can be used to perform data analytics.However, there is hardly studies that have used demonstrated the side by side use of sentiment analysis built on Azure ML for social media analytics.This study demonstrated that Microsoft Azure Machine Learning (ML) based on two Machine Learning (ML) algorithms: Logistic Regression, and Support Vector Machine (SVM) can be used to build sentiment analysis (SA) models used to perform data analytics.Moreover, a comparison between the two algorithms is carried out.
Microsoft Azure Machine Learning
Microsoft Azure Machine Learning encompasses cloud services that enable the creation, deployment, and management of applications by developers via a global network of datacentres for Microsoft.This cloud computing model emphasizes the cloud platform's differentiating features namely flexibility, agility and scalability.Currently, Azure calculates the contribution score of the user based on social media metrics.This allows for the easy quantification of the value of users of Microsoft add to its cloud business on social media to enable it to provide differentiated services.
Azure ML also supports multiple ML algorithms related to regression, classification, and clustering.It allows for the customization of models using python and R (Qasem et al., 2015).Azure ML studio allows for the dragging and dropping of Modules and datasets (i.e., Ml algorithms, feature selection, and pre-processing) and links them together.This experiment can be trained and transformed into a predictive experiment.This predictive experiment allows users to build their models (Ericson et al., 2016;Rajpurohit, 2014).
In general, Microsoft Azure is designed to set a playground for experienced and newcomers data scientists.It provides a variety of algorithms with only a single clustering algorithm.Azure ML is often characterized by the Cortana Intelligence Gallery, which is a collection of ML solutions created by the community to be reused and explored by data scientists.Azure services can be categorized into two: Azure Bot Service and Azure Machine Learning Studio.
Azure ML studio requires users to complete all the operations manually.This includes, data preprocessing, exploration, validating modeling results, and choosing methods.It supports about 100 techniques that address regression, anomaly detection, classification (binary and multiclass), text analysis, and recommendation.
Machine Learning Algorithms
There are different machine language algorithms such as Support Vector Machine (SVM), Logistic Regression, Network Regression (NNR), and Decision Forest.Logistic regression is a statistical linear algorithm used in task classification.It is usually used to solve simple problems.It can be used as a prediction model.It predicts values by applying statistical analysis (Chen, 2011).The Support Vector Machine algorithm is supervised learning approach used to solve classification problems.It accepts labelled training data and produces hyperplane which is used to maximize the margin between high-dimensional space classes (Wu et al., 2014).The Decision Forest algorithm is a learning method consisting of multiple classification methods.It can construct decision trees each with a different classification.It can perform aggregation and sum histograms to obtain each label's probabilities.The decision forest selects the decision tree with the most votes (Topouzelis & Psyllos, 2012).Neutral Network Regression Algorithm builds a classification model by combining two algorithms: Neural Network and Logistic Regression.It utilizes a logistic function.As such, its output is similar to that of Logistic Regression.It requires the use of a dataset to test an algorithm.
Sentiment Classification Techniques
There are two approaches to performing SA: lexicon-based approach and ML approach (Devika et al., 2016).ML approach, which is the focus of the present study, is dependent on the training dataset as it involves training the algorithm using a training dataset followed by applying the algorithm to the actual dataset.The classification of SA using the ML approach involves two datasets: testing and training datasets.The classification algorithm utilizes these datasets to verify algorithm performance and to learn dataset.In particular, the training dataset is used in learning dataset while the testing dataset is used in verifying the performance of the algorithm (Sharef et al., 2016).
There are two ways through which ML approaches sentiment classification: supervised learning method; and unsupervised learning method.The supervised learning method utilizes training dataset which includes the score and input label.It enables the classification model to learn using classification algorithms.It is also used in predicting the value for new inputs.On the other hand, the unsupervised learning model does not utilize labelled dataset.It is trained using datasets involving a group of inputs (Sharef et al., 2016;Tramer et al., 2016).
Test Methodology
This study sought to demonstrate that Microsoft Azure ML-based on two Machine Learning algorithms can be used to build sentiment analysis (SA) models used to perform data analytics.This study was extended from a Master thesis with more depth analysis for the data and a new series of experiments to compare the two specific algorithms based on one single machine Learning platform (Hasan, 2017).Moreover, a comparison between the two algorithms' outputs is carried out.This was undertaken using experimental research design.Accordingly, data was sourced from Twitter a microblogging platform.Data were obtained in the form of individuals' opinions, image, views, and twits from Twitter.
Procedurally, SA models were built on the Azure ML platform based on Logistic Regression and Support Vector Machine.Next, the accuracy and performance of these SA models were evaluated.The outcome informed the decision made regarding the machine language that offered the best SA in terms of performance and accuracy.Several experiments were performed and SA model was tested using datasets A, B, and C, and the model executed using each data set.
Azure Sentiment Analysis Model
Azure SA Model was created on Microsoft Azure.It was used to determine the tweets' sentiment.This was done by building the Azure ML model, training it on how to detect the sentiment, and finally setting it as a predictive model to facilitate it to detect and identify sentiments as neutral, negative or positive.
The sentiment analytics model was created based on the Logistic Regression and Support Vector Machine algorithms.The model was trained using dataset (TD).This was done after subjecting the dataset to normalization, which involved getting rid of punctuations, numbers and stop words as well as removing URLs and emails from the tweets.A Hashing of bit size 10 and with n-grams was also applied to the tweets before training the model using TD.Lastly, modifications were made to the model to make it detect sentiment.
This study utilized Coachella 2015 Twitter sentiment dataset.This dataset was created by "CrowdFlower" data mining company.It has tweets on Coachella arts and music festival which was held in 2015.The classification results are generated be processed connected elements (Vallejos & Mckinnon, 2013).
The original Coachella dataset consisted of 10 columns and 3800 tweets (Figure 1).The columns consisted of 10 associated fields: tweet created; Coachella yn; Coachella sentiment; name; text; retweet count; tweet Id; user time zone; and tweet location.Two columns were used to test Sentiment Analysis algorithm.Coachella sentiment is the first column and encompasses the sentiment of a tweet.The second column is a text of a tweet.
Azure Sentiment Analysis Training Model Process for Coachella
Azure-based Sentiment Analysis training model had several steps used to build Twitter SA for Coachella model (Figure 2).First of all, Coachella DB was created and served as the tagged dataset.It included a label column and tweet text column.It consisted of a total of 350 tweets with 128 tweets representing neutral sentiment, 106 tweets representing negative sentiment, and 116 tweets representing positive sentiment.Dataset file Coachella served as a comma-separated value file.Other options included Azure ML used to import data.This Machine Learning employed several techniques: Azure table; Azure SQL database; Azure blob; and HTML.Data used in this study was obtained from the Coachella comma-separated value file.
With regard to the pre-process text, Coachella DB was the input step.It involved applying pre-processed procedures to each Coachella DB tweet with stop words and numbers being extracted and URLs and e-mail address removed.Verb contractions were also expanded, and duplicate characters eliminated.
Second
Step is executing R-script; The modified dataset version of the previous step was the input for this execute R-script step.This stage involves the execution of the R-script.Punctuation is replaced, and special characters and digits are replaced with space and tweet converted into lowercase.
The execution of R-script step was modified and used an input to edit metadata step.This step handled the modified metadata, and was designed for use to alter the definition of text column of the tweet to convert it into a noncategorical format.
The previous step's dataset served as the input to the feature hashing step.The Feature Hashing module in Azure ML is designed in accordance with the Vowpal Wabbit framework (Qasem et al., 2015).This framework is used to hash features into in-memory indexes.The next step is to rank featured based on Chi-Squared feature selection.A database that encompassed finer features defined by high predictive power was the input of the chi-squared module.High score features were included whereas low-score features were removed.
The multiclass classification model was built from the Logistic Regression algorithm.To train the classification model, the tagged dataset and ML algorithm were provided as inputs to the model (Figure 2).This enabled the trained model to predict the sentiment for new tweets.The score model was used to predict the trained model.It has two appearances (Figure 2).These appearances had trained dataset and trained models as input, and a set-aside dataset for model testing.This score model generated predicted values and the probability of the values that were predicted.The scored dataset was its output and was in performance evaluation.
Azure SA Predictive Model for Coachella
The training experiment was converted into the predictive experiment used for sentiment prediction.This predictive experiment was deployed as Azure web service to enable it to receive users' inputs as shown in Figure 3.
Test Results
The evaluation metrics are used in this experiment in order to assess the quality of SA model that have been created in Azure ML.Usually, Accuracy and Precisions metrics that are used for evaluation of text classification tasks in this test.Accuracy measures how much the algorithm an accurate prediction of the results.Precision measures how values are close to each other.For evaluating the performance of SA model that classifies the tweet as positive, neutral or negative, the confusion matrix is used.Figure 4 As aforementioned, the evaluation model used in building SA model on Azure ML presents accurate evaluation of the trained model, however, when the model was working on the new datasets, the accuracy was different.In brief, SA model was built on Azure ML using two different algorithms; Logistics Regression and Support Vector Machine.Model was tested using three different datasets (A, B, C).The following subsections summarized the results of the test.
Testing Azure SA Model with Logistics Regression Algorithm
As shown in Table 1, The sentiment score results of the SA model based on Logistic Regression algorithm for the dataset (A) were 31, 48, 21 for positive, neutral and negative respectively.While for dataset (B), they were 102, 119, 79.Dataset (C) values were 164, 204, 132 respectively.Table 2 shows the confusion matrix for the three datasets (A, B, C) based on the Logistics Regression algorithm with the evaluation metrices.
Sentiment Analysis Models Comparison
In previous sections, the results and the evaluation metrics for each SA model with the three datasets were presented.This section will compare between the two SA models built on Azure ML taking into consideration the Accuracy and Precision attributes.
Discussion and Conclusion
As demonstrated in this study, sentiment analysis can be built on Microsoft Azure machine language based on two ML algorithms: Logistic Regression and Support Vector Machine (SVM).This is done by performing a series of experiments on three Twitter datasets.Microsoft Azure ML can be used reliably, accurately and securely be used to build SA models.This shows that companies can leverage Microsoft ML to detect customer sentiment and perform topic modelling from several documents.The ability of this service to detect sentiment is achieved using state-of-art learning algorithms that employ scoring attributes and mechanisms when evaluating the text.
Results of this study confirm that prediction models can be implemented on the cloud-based ML platforms.They confirm that SA classification models can be built on cloud-based ML platforms notably Azure ML.This is in line with previous studies that implemented SA systems based on various cloud-based ML platforms (Mulholland et al., 2015;Roychowdhury, 2015;Bornstein et al., 2016).
Similarly, Bihis & Roychowdhury (2015) tested the Generalized Flow performance model built of Azure ML.This model was found to have the ability to perform multi-class and two-class classification.This model was tested using local fundus images dataset, and three Azure datasets: German Credit Card, Wisconsin Breast Cancer, and Telescope.It was revealed that classification accuracy is increased by performing classification based on the Azure ML platform.
In order to identify the quality of SA model that was built using Azure ML, a series of experiments were carried out using different datasets.For assessing the quality of SA models that were built over Azure ML, two evaluation metrics have been used; Accuracy and Precision.Based on these evaluation metrics, this paper stated that building SA models using Support Vector Machine algorithm achieved higher results than Logistics Regression algorithm, though the results were very close for dataset B and C; this research determined that using Support Vector Machine algorithm in building the models attained higher accuracy and Precision values.
As a conclusion, this paper approves that using cloud-based Machine Learning to build Sentiment Analysis models is beneficial, and that is because cloud environment characteristics.Moreover, cloud-based ML platforms are producing reliable models since these platforms are offering users with a set of tools to simplify the process of building the models and to enhance their accuracy.
Figure 1 .
Figure 1.Tweet example The train model was designed to provide the classification model with a trained dataset aimed at discovering patterns.The two inputs to this module were Logistic Regression algorithm model or configured ML model and the trained dataset.The trained model was the outcome.It was used to create the predictive model used in detecting sentiments of tweets regarding the Coachella event.
Figure 2 .
Figure 2. Twitter SA for the Coachella Training Model Process in the Azure ML studio
Figure 4
Figure 4 shows the Accuracy values for the three datasets (A, B, C) based on the Logistic Regression and Support Vector Machine algorithms.Results show that for dataset A, dataset B and dataset, Support Vector Machine algorithm achieved higher Accuracy values at 0.73, 0.59 and 0.60 respectively compared to 0.53, 0.53 and 0.57 for the Logistics Regression algorithm.
Figure 4 .Figure 5 .
Figure 4. Comparison between two Algorithms based on Accuracy values
Table 1 .
SA Model results -Logistics Regression Algorithm
Table 2 .
Confusion Matrix based on Logistics Regression Algorithm (Dataset A, B, C)As shown in Table3, The sentiment score results of the SA model based on Vector Machine Algorithm for the dataset (A) were 37, 40, 23 for positive, neutral and negative respectively.While for dataset (B), they were 87, 127, 86.Dataset (C) values were 196, 175, 129 respectively.Table4shows the confusion matrix for the three datasets (A, B, C) based on the Vector Machine Algorithms with the evaluation metrices.
Table 4 .
Confusion Matrix based on Vector Machine Algorithm | 4,194.4 | 2018-06-21T00:00:00.000 | [
"Computer Science"
] |
Challenges in the development of the cocoa and chocolate industry in Indonesia: A case study in Madiun, East Java
: The development of the cocoa agroindustry in Indonesia is of considerable importance to respond the global demand for high quality cocoa beans and cocoa-derived products. This study analyzes the issues concerning the cocoa production in Indonesia, including cocoa productivity, post-harvest treatments, and smallholder farmer profitability, in order to confirm the theories regarding cocoa farming previously published in many works as well as to offer insights into challenges for future cocoa farming and cocoa downstream industry development in Indonesia. A simple random sampling method was used to select a total of 25 cocoa farmers from the five regions in Madiun, East Java. The selected farmers were interviewed using a semi-structured questionnaire consisting of 39 questions regarding demographic and farm characteristics, farm management and postharvest practices, and farm training and social capital. The results indicated that approximately 40% of farmers are 60 years old and over. Besides, most of the cocoa farmers (76%) have not received any proper education or have attended to primary school only. Furthermore, according to the data, the cocoa productivity is inversely correlated with the farm size. Finally, almost half of the farmers in Madiun sell their cocoa beans as non-fermented. From this study, it was clear that in order to improve the quality of cocoa beans, farmers should be encouraged to improve agricultural practices and postharvest processes. This research gives empirical evidence of some constraints for high-quality cocoa production in Indonesia.
Introduction
Chocolate has been acknowledged as the most popular confectionery products in the world [1]. In this instance, Switzerland was the country with the highest chocolate consumption per capita followed by Austria, Germany and Ireland, with an average consumption of 7.9 to 8.8 kg per capita, in 2017 [2]. The popularity of chocolate might be due to the awareness of people to the fact that cocoa (Theobroma cacao L.), the main ingredient of chocolate, contains bioactive compounds potentially providing beneficial health effects [3]. In more detail, chocolate is rich in antioxidants such as flavonoids and flavanols, responsible for destroying free radicals in the body. Free radicals are unstable molecules that can cause damage to DNA and other cell components within the body, accelerating aging and possibly contributing to heart disease, cancer or other diseases [4][5][6][7]. Currently, many food scientists and industries even consistently develop a new type of cocoa-derived food and beverage products [8][9][10][11][12][13][14][15]. This condition results in a high demand of cocoa beans from major worldwide cocoa producing countries such as Ivory Coast, Ghana, Nigeria, Cameroon, and Indonesia [16].
Cocoa is in fact originated from Ancient Central America and was brought to Indonesia by the Dutch before 1900. Nowadays, Indonesia has approximately 1.5 million hectares of cocoa plantations mainly located in Sulawesi, North Sumatra, Papua, and Java [17]. Approximately 95% of cocoa plantations in this country belong to smallholder farmers, and thus cocoa production is the main income source for over 1,400,000 farmers and their families. East Java Province is one the most promising regions to be developed as cocoa agroindustry center, in addition to Sulawesi, Sumatera, and Papua as the main central production of cocoa in Indonesia. This is because East Java has the largest cocoa farming area with small-holder farmers, and also the highest cocoa producing region in Java [18]. The production of cocoa in Indonesia demonstrates several advantages such as low cost, high production capacity, efficient infrastructure for shipping and transporting the beans in open trading ways [19]. Most of the Indonesian cocoa production is exported to Malaysia, the USA, and Singapore as raw beans [20].
Regarding the current situation of cocoa production, the Indonesian government has committed to develop cocoa agroindustry. In this context, the Ministry of Industry has spent more than IDR 109.000.000.000 (equal to US $ 7.340.000) to build cocoa downstream industries in Sulawesi and Java during 2014-2019 [21]. Not with standing, according to the National Bureau of Statistics of Indonesia [17], the Indonesian cocoa production has gradually decreased about 29% from around 410.000 tons in 2012/2013 to 290.000 tons in 2018/2019 making this country downgraded from the 3 rd to the 5 th highest cocoa producing country in the world. The decrease of cocoa productivity might be attributed to poor farm management practices, aging cocoa trees and inadequate use of fertilizers [22]. Some other factors, such as incidence of pests and diseases as well as climate change, could also affect cocoa productivity [23][24]. In any case, it is crucial to overcome these problems and also to identify the most effective and sustainable ways to strengthen cocoa productivity and supply high-quality cocoa beans to the world. It has been widely acknowledged that sustainable production of agricultural products, including cocoa, plays a pivotal role in the society as it provides sufficient raw material that meets the market requirements without compromising the environment and/or the natural resources, and strengthening the agriculture economy by both, increasing the profitable farm income and enhancing the life quality of farmers and communities [25][26].
The district of Kare located in Madiun Regency, East Java Province, is an important agricultural center producing cocoa beans. Kare has a population of 32,014 people and covers an area of 19,085 hectares. In Kare, most of people are smallholder farmers and use their home yards as cocoa plantations [27]. According to Hatani and his co-worker [28], the development of cocoa agroindustry with competitive advantages can be approached by market orientation, supply chain flexibility, and strategic location. They reported that market orientation, selecting strategic location and variable control of institutional support had significant effect towards the increasing of competitive advantage, but could not prove that supply chain flexibility gave significant contribution towards the increasing of competitive advantage in cocoa agroindustry. The uncertainty of supplier (cacao farmers) was found to be the main cause of it. Therefore, the involvement of smallholder farmers is needed to get a more serious concern, instead of other factors affecting cocoa productivity. Moreover, farmers should be encouraged to sustainably intensify farm management by adopting good agricultural practices that may enhance productivity, improve livelihoods by raising profitability as well as protecting environment for ensuring sustainability [29]. Kare, therefore, is an interesting and a suitable sample for investigating challenges in the development of cocoa and chocolate industry in Indonesia. Thus, the main objective of this research was to analyze the cocoa farming issues at farm-level through the perception of farming and postharvest practices in Madiun, East Java. This is important to validate the theories regarding cocoa farming that have been previously published in many works as well as identify the most effective and sustainable ways to strengthen cocoa productivity in Indonesia. Moreover, this work is significant to provide insights into challenges for the development of the downstream cocoa industry, particularly in Madiun. The dataset of demographic characteristics, farm characteristics, farm management practices, post-harvest practices as well as the farmers training and social capital are highly required to get a better insight of the cocoa farming conditions.
Sampling and data collection
The study was conducted in April 2019. A simple random sampling technique was used to select a representative sample of cocoa farmers in Madiun, East Java. Five cocoa farmers were randomly selected from each one of the sub-districts (Karangagung, Randualas, Dawung, Slaji and Kajen). Faceto-face interviews with the selected farmers were conducted using a semi structured questionnaire following the study of Kongor et al. [29]. The questionnaire covered five issues including demographic characteristics, farm characteristics, farm management practices, post-harvest practices and farmers training and social capital. Demographic characteristics of the farmers included age, gender, educational level, marital status, number of children they have, willingness of children to become farmers, support of parents with the farmers children's desire to become or not farmers, and years of experience in cocoa cultivation. Farm characteristics included size of cocoa farms (in hectares), age of the farms, quantity (kg) of dried cocoa beans obtained, and opinion about the fertility of the soil. Farm management practices included the type of farming system, type of plants used as shade trees, major diseases and pests that attack cocoa trees, way of weed control, spraying of diseases and pests, fertilizer application, way of pruning, and mistletoe removal. Post-harvest practices included times number of cocoa pods harvesting, conditions of pods storage, and cacao beans fermentation and drying. Farmers training and social capital included kind of training received in the last 12 months, kind of training desired to receive from buyers, way of selling the cocoa beans, typical buyer of cocoa beans, amount of money gotten for 1 kg of fermented or non-fermented cocoa beans, agreement of selling fermented and dried cocoa beans to buyers, and desired price for 1 kg of fermented and dried cocoa beans.
Data analysis
Simple calculation by dividing total quantity of dried fermented beans by total farm size was conducted to estimate the productivity. To analyze the socio-economic characteristics of the farmers, the descriptive statistics was used. The data obtained from the descriptive research was then used for further analysis to draw a better description as well as a conclusion [30].
Demographic characteristics
The results of the investigation on the demographic characteristics of cocoa farmers are presented in Table 1. The majority of cocoa farmers were male (96%). There was only one female farmer in the district of Dawung (4%). It was identified that 52% of the cocoa farmers are between 41-60 years old, 40% of farmers are older than 60 years old, and only 8 % of farmers are younger than 40 years old. With respect to the educational level, most of the farmers (96%) have education at different level and only 4% of them have not received any education. The majority of the farmers (72%) have received primary education, 20% of the farmers have attended to secondary school and 4% of the farmers have a tertiary education level.
About marital status of farmers, 100% of them are married. Most of the farmers (84%) have 2 or 3 children. Only 12% of the farmers have 4 children and 4% of them have 1 child. According the farmers, most of their children (60%) are not interested about becoming farmers in the future as the children want to execute another profession, mainly in the big cities. With respect to the farming experience, the majority of the farmers (32%) have between 11-20 years of cocoa farming experience; only 12% have between 1-10 years of experience; 28% of farmers have 21-30 years of experience; equally, 28% of farmers have more than 30 years of farming experience. The relatively long farming experience should enhance knowledge of cocoa production and postharvest processes. Finally, 68% of people interviewed execute the role of farming as main activity, and hence farming is the main income source. Nevertheless, it was identified that the income is the result of several products such as cacao, coffee, clove, banana, mango, teak, avocado and orange. The farmers do not focus in one product only because the production together with the price varies during the year. Consequently, they need to have various products available to generate profit.
Farm characteristics
The overview of farm characteristics of cocoa farmers interviewed in Madiun are presented in Table 2. The majority of cocoa farmers (56%) own one farm. However, 40% of them own 2 and 4% owns 3. The farmers grow two varieties of cocoa: Forastero and Criollo. All of the farmers from Dawung assessed that their farms are 1-10 years old, representing 44% of the total farmers. Another 44% of the farmers indicated that their farms are 11-20 years old. Few farmers have farms between 21-30 years old and, only 4% of the farmers indicated that their farms are older than 30 years. The average farms age and size are presented in Figure 1. Figure 1 also shows the productivity of the cocoa farms. With respect to the quantity of dried cocoa beans, most of the farmers (60%) indicated that they obtain 50-200 kg/year; 32% of them get 210-300 kg/year; 4% of the farmers obtain 310-400 kg/year and, also 4% of them achieve more than 400 kg/year. The level of dried cocoa beans productivity was in the order of Dawung > Slaji > Kaje > Randualas > Karangagung. All of the farms from Dawung are 1-10 years old. Karangagung on the other hand, has farms which trees vary from one to more than 30 years old.
Farm management practices
The summary of farm management practices of cocoa farmers interviewed in Madiun are presented in Table 3. All of the farmers ensured that the type of farming system was mixed cropping. Most of the farmers (84%) have more than two types of crops mainly cloves, mango, banana, durian, coffee, orange and lemon. The rest of the farmers (16%) mix their cacao crops with cloves only. Besides, 72% of cocoa farmers practiced intercropped farming system. The rest of them (28%) dispose of specific areas for each of the crops planted. The crop that 68% of the farmers use as shade trees for cocoa is clove; 12% of the farmers use mango, and the remaining 20% of people use banana, teak or avocado. Regarding the weed control, 12% of farmers do not apply any measure, 56% of the farmers perform weeding and 32% of them use herbicides. Moreover, 32% of the farmers apply weed control measurements 12 times/year, 24% of the farmers 24 times/year and 32% of them 36 or more times/year. A summary of the weed control application of the different region is presented in Figure 2. It can be appreciated that Karangagung, the region with the biggest farms, apply weed control more times per year than the rest of the regions. However, the productivity is the lowest. With respect to the major diseases, 64% of the farmers stated that black pods are the one that attack the most to their cocoa crops, 12% of the farmers indicated moniliasis as the most severe disease and 24% of the farmers stated that both black pods and moniliasis are the major diseases in their cocoa crops.
Most of the farmers (72%) use spray machine to counteract the diseases of their crops. However, 28% of the farmers prefer not to spend money and cut the diseased part of the plant. Regarding the major pests, 52% of the cocoa farmers stated that capsids are the ones that attack the most to their cocoa crops, 28% of the farmers indicated fruit flies and 20% of the farmers agreed that the major pests are ants, white flies and squirrels. The majority of the farmers (88%) use spraying machines with insecticides to control pests. Nonetheless, 12% of them use pest traps (Petrogenol) to counteract them. With respect to the pruning, most of the farmers (64%) rather using cutlass and 36% of them prefer the use sickle. Finally, 48% of the farmers remove mistletoes from the cocoa plants but 52% of them do not remove mistletoes.
A great number of farmers (84%) specified that they apply fertilizers to the crops. Only 16% of them do not apply any type of fertilizer. The majority of the farmers (36%) that apply fertilizer to their crops do it three times/year, 20% of the farmers do it twice a year and 28% of them do it just once a year. The fertilizers mostly used by the farmers are compost, EM4 and TSP posca. Dawung is the most productive region despite the fact that this region applies fertilizers fewest times/year. All the farmers from Dawung fertilize their cocoa crops two or less times/year. In the region of Karangagung, on the other hand, 40% of the farmers fertilize their crops three or more times/year. A summary of the fertilizer application of the different region is presented in Figure 2.
Postharvest practices
The results of postharvest practices assessment to the cocoa farmers in Madiun are presented in Table 4. The majority of the farmers (80%) harvest the cocoa pods once a week, 12% of them harvest once every two weeks and 8% of the farmers harvest twice every week. It is important to mention that farmers do not keep count of the quantity of cocoa pods harvested. They only have an idea of the amount of dried beans produced at the end of the week; which is the same quantity used to calculate the productivity presented in Table 2.
Regarding postharvest practices, there are at least three important aspects that should be taken into account for evaluations. Firstly, none of the cocoa farmers store the pods prior opening. The farmers harvest all of the pods and proceed to open them immediately to obtain the beans. Secondly, only 56% of the farmers ferment the cocoa beans. The remaining 44% of the farmers proceed to the drying of the beans after the pods opening. Half of the farmers that ferment the beans use plastic containers for the process, 21.4% of them use baskets, 14.3% of them prefer heap and another 14.3% use sacks. Besides, 71.4% of the farmers that ferment the beans do it for two or three days, while the rest (28.6%) do the fermentation for four or five days. Finally, only 42.8% of cocoa farmers turn or mix the beans for aeration during fermentation and the remaining 57.2% do not move the beans during the process. Thirdly, all of the farmers interviewed dried the cocoa beans by sun drying. Most of the farmers (80%) using bamboo mats, whereas the rest of the farmers (20%) dry the beans in sacks. Moreover, the majority of the farmers (72%) dry the beans during two or three days and the remaining 28% of farmers dry the beans for four or five days. Table 5 shows postharvest practices conducted by the cocoa farmers interviewed in Madiun. Most of the farmers (80%) have not received any kind of training within the last 12 months. Only 20% of the farmers have received training, 80% of them received training from the government and the remaining 20% from the buying company. All of the farmers that received training, learnt about farming practices and health and safety. With respect to the kind of training that the farmers would like to receive from other parties, the results are presented in Figure 3. Most of the farmers (72%) are interested about farming practices and postharvest treatment. Meanwhile, the rest of them are interested about cocoa beans processing and entrepreneurship. It was identified that 52% of the farmers sell fermented cocoa beans while 48% of them sell the beans in non-fermented way. The average price of fermented beans is IDR 22.400 (equal to USD 1.61) and the average price of non-fermented beans is IDR 22.000 (equal to USD 1.58). The majority of farmers (80%) sell the dried beans to the collector; 12% of them sell the dried cacao beans to the market seller and 8% of the farmers sell the beans to the government. Besides, when the farmers knew about the interest of another company about buying fermented and dried cocoa beans, 100% of them agreed in selling the product for a higher price which in average is IDR 30.840 (equal to USD 2.22).
Discussion
Sustainable production of cocoa plays a significant role in the sustainability of chocolate industry. Particularly in Indonesia, information of cocoa production is very crucial as the basis of the development of cocoa-based industry that is being directed by the government. To give insight in the cocoa production in Indonesia, the dataset of demographic characteristics, farm characteristics, farm management practices, post-harvest practices and the farmers training and social capital is important. Thus, a study about cocoa farming and production in Madiun was then conducted. This study is also important to confirm the theories regarding constraints in global cocoa farming previously published in many works by different research groups.
In this research, it was found that the majority of cocoa farmers were male despite the fact that women may be significant players. This tendency might be because agricultural work performed by women is seen as secondary to their domestic responsibilities [31]. Agreeing to the finding of Kongor et al. [29], cocoa farming requires physical strength giving a reason why cocoa farming is dominated by male. Among the farmers, as shown in the results, less than 10% of interviewed farmers are below 40 years old. It might affect the cacao productivity as the age of farmers is highly correlated to physical strength.
In addition to the age, education can contribute to the productivity of cocoa farm. The region with least education level is Karangagung, which at the same time, is the least productive region. Education helps farmers to better understand the Good Agricultural Practices on cocoa farming as well as to implement innovative processes and technologies in the farms. Moreover, education is the key component to make agriculture more appealing to children. In order to make people realize that mostly smallholder farmers are the ones who feed the world, important actions have to be taken. For instance, it is necessary to emphasize the importance of agriculture in schools, constantly train farmers, improve public policies, create role models that show how success agriculture looks like and better support farmers regarding access to inputs and markets to sell their products at a fair price. Furthermore, it is necessary to highlight the importance of agriculture through training and educational programs so the farmer's income is fair and allows them to apply good agricultural practices.
Aside from the current situation of ages and education level of the farmers, the future cocoa farming in Madiun must get more attention from the government. As such, most of the farmer's children are not interested about becoming farmers in the future as they want to have another profession in the big cities. In fact, the parents respect and support the decisions of their children. The parents are aware that the farming work is hard and, at the same time not well recognized nor well paid. The cocoa productivity as well as the amount of money that farmers earn from selling dried cocoa beans is not enough for covering their expenses. Consequently, instead of exclusively selling cocoa beans, farmers prefer to plant different types of crops and sell as much products as they can in order to have better income. Thus, despite the fact that they own lands, the parents support their children with the decision of performing another better paid occupation. If measurements are not taken, in the future years, fewer smallholder farmers will be working on their lands and the cocoa production will be less and less. Probably most of them will sell their lands to environmental destructive agribusiness companies which only care about revenues. Young people aspire to study in order to be part of formal employment sector and have modern urban lifestyles. However, it is a fact that education does not necessarily lead to employment.
The present situation of cocoa productivity in Madiun appears to be highly correlated with the ages of the trees and the size of the farm. According to Binam et al. [32], the production of cocoa trees increases after four years of planting and its yield increases annually until about 18 years of age, afterwards it starts to decrease. It was shown in this study that all of the farms in Dawung are 1 to 10 years old. Besides, in this region, the average size of the farms is the smallest (0.2 ha) which makes maintenance and care of trees and soil easier than in bigger farms from the other regions. Therefore, the cocoa trees of Dawung are the most productive. Karangagung, on the other hand, has farms which trees vary from one to more than 30 years old. Hence, the production of the old trees has begun its decline. Besides, the big average area of the farms (0.6 ha) makes difficult the maintenance and care of soil and trees which also affects the cocoa productivity. These results are consistent with the ones from Kongor et al. [29] who found that cocoa productivity is inversely correlated with the size of the farm.
The cocoa productivity in Madiun is influenced by the presence of diseases, such as black pod and moniliasis. Black pod, caused by Phytophthora palmivora or Phytophthora megakarya is a fungal disease of cocoa characterized by browning, blackening and rotting pods and beans [33]. Moniliasis is also a fungal disease caused by Moniliophthora roreri which is responsible for dark spots on the surface of pods followed by the appearance of "white powder" or fungus conidia that rot the pods [34]. Both diseases can cause serious losses and are economically important. The high incidence of black pod and moniliasis diseases in Madiun might be because the average rainfall is 1912 mm annually and the average temperature is 27 ℃. The high humidity and temperature favor fungal growth. Another factor affecting cocoa productivity is the incidence of pests. The major pests reported in this study are capsids, ants, white flies and squirrels. All of these pests are responsible for damaging the surface of cocoa stems, branches, or pods, sucking the sap of the tree or feeding the pods and causing necrotic lesions. As the high incidence of diseases and pests affects the productivity of cocoa trees, it is necessary to manage adequately these problems by increasing the control times per year. As found in this study, to counteract the diseases of their crops, most of the farmers use spray machine. The spraying machine is also used with insecticides to control pests.
To help improving the productivity, the cocoa farmers (more than 80%) use fertilizers. Fertilizers are essential to provide adequate nutrients for crop growth and assure a successful harvest. However, according to Dubos et al. [35], prolonged fertilizer application has an impact on the structure and composition of the soil. For instance, ammonia-based fertilizers (nitrate, phosphate, sulphate, or chloride) drop the pH of the soil in a short time span of 10 years by almost two pH units. Excessive acidity or alkalinity can affect the cocoa tree growth and production. International Cocoa Organization [36] recommended an optimum pH for cocoa growth which is in the range of 5.0 to 7.5. Another long-term risk of using fertilizers is the accumulation of contaminant trace elements into the soil. Elements such as As, Cd, and Pb may threat the inherent soil quality and harm human health [37]. Fertilizer requirements of cocoa depends on different factors such as nutrition quality of the soil, age of the trees, peak cropping period, competition from weeds and rainfall pattern. It is often recommended that fertilizer application should be done twice a year: April and September [38].
Nevertheless, it was found in this study that the fertilizer has less effect on cocoa productivity than the age of the cocoa tree. As such, the fertilizer application by farmers in Slaji and Kajen is more frequently than those in Dawung. As Dawung has the smallest farms (0.2 ha) and the youngest trees (1 to 10 years old), this region has the highest cocoa productivity (651.5 kg dried cocoa beans/ha/year). In the region of Karangagung, 40% of the farmers fertilize their crops three or more times/year. Because of the old age of some of the trees (> 30 years) and the multiple fertilizer application, the original composition and pH of the soil have been altered and, the cocoa productivity is lower than in the other regions (188 kg dried cocoa beans/ha/year). Furthermore, the old trees had lost their natural defense mechanisms against pathogens and had started their senescence period, which affect seriously their productivity [39]. It would be proper to clear away old cocoa trees and re-plant [40].
It would be interesting to perform statistical analyses to investigate deeper the correlation between productivity and farm age, farm size, weed control as well as fertilizer application. However, as in this region the cocoa farming is done in the farmers' home yard, the number of the cocoa tree per hectare of yard is not similar, and thus the statistical analysis is not possible to perform. Nevertheless, the descriptive analysis can already provide insight to draw a conclusion about the condition of cocoa farming in Madiun.
The quality of cocoa beans is not only affected by farming practices, but also strongly influenced by the post-harvest treatment. Maintaining the quality of cocoa beans is highly important as at the end, it determines the quality of chocolate. According to Afoakwa [41], the ideal postharvest processes of cocoa beans include: (a) storage of the pods; (b) opening of the pods with a thick piece of wood; (c) fermentation of the cocoa beans for at least five days; and (d) drying of the cocoa beans to remove the moisture content.
Unfortunately, the postharvest treatments in Madiun have not met those ideal conditions. For instance, none of the cocoa farmers store the pods prior opening as they proceed to open them immediately to obtain the beans. According to Hinneh et al. [42], the storage of the cocoa pods leads to the reduction of nib acidification during subsequent fermentation, reduction of the acid note and an increase in cocoa flavor in the resulting raw cocoa. Consequently, the lack of pods storage will affect the quality of the cocoa beans.
Aside from the pod storage issue, it was also found that almost half of cocoa farmers interviewed in Madiun do not perform the fermentation processes. Fermentation is very pivotal for developing appropriate flavour precursors [42]. During the fermentation, microorganisms such as yeast and bacteria grow on the pulp surrounding the beans. Shortly, yeast converts the sugars in the pulp to ethanol. Afterwards, bacteria oxidize ethanol to acetic acid and then to carbon dioxide and water raising the temperature. Eventually, the acetic acid and high temperature kill the cocoa bean resulting in the breakage of cells. Hence, all of the released components mix, allowing complex chemical changes such as enzyme activity, oxidation and breakdown of proteins. The interaction of these metabolites together with the enzyme activity, oxidation, and brake down of proteins into amino acids, are the precursors for cocoa bean flavor [43]. Even though cocoa bean fermentation is a very important process, almost half of the farmers directly dry the beans after harvesting without doing fermentation. Consequently, the flavor of the resulting beans will have poor quality.
The main reasons why farmers prefer not doing fermentation are economic constraints such as immediately cash necessity and no price difference between fermented and non-fermented cocoa beans. The average price of fermented beans is IDR 22.400 and the average price of non-fermented beans is IDR 22.000 (USD 1 is about equal to IDR 13.900). There is no significant difference between the price of fermented and non-fermented beans. Moreover, the farmers also consider the fermentation duration that required at least 5 days. Those reasons make a great number of farmers prefer to avoid fermentation process. Hence, they directly dry the beans and sell them as fast as possible so they dispose immediately of cash.
Another issue related to post-harvest treatment is faced during the drying process. It was identified that all of the farmers dried the cocoa beans by sun drying, mostly layered using bamboo mats for two or three days. The aim of drying is to decrease the moisture content from about 60% to about 7.5%. With adequate sunshine the drying of the beans may take around one week. If the beans are dried too quickly, some of the chemical reactions started during fermentation are not allowed to complete resulting in acid beans with bitter flavor. Conversely, if the beans are dried too slowly, mold can grow and develop off-flavors [36]. Apparently, the drying time that most of the farmers apply is not enough to decrease the moisture content to 7.5%. Consequently, the beans might be contaminated with mold and thus the cocoa beans can contain ochratoxin making the beans have low quality.
To increase the cocoa productivity and to improve the cocoa bean quality, educating the farmers through training programs is highly required. The soil characteristics together with the weather conditions in Madiun may be optimal for cocoa growth. Nevertheless, the limited farmers education and training restricts their good agricultural practices and cocoa productivity. There have been some cocoa farming training programs in Indonesia organized by different organizations such as Cocoa Life of Mondelez International, Rikolto Mars and Sustainable Cocoa Production Program (SCPP) [44][45][46]. However, as reported by the farmers, the programs have been developed in Sumatra and Sulawesi; none of them in Madiun. Briefly, it can be stated that there is a lack of cocoa training in Madiun. Based on the interview, most of farmers wanted to get trainings in cocoa farming practices and post-harvest treatments. Nevertheless, some of them seems interesting to improve their skills and knowledges in cocoa bean processing and entrepreneurship.
There are still a lot of constraints in the cocoa farming in Madiun, and therefore, the development of cocoa downstream industry in Indonesia becomes much more challenging. The quality of cocoa beans highly influences the quality of chocolate. To make chocolate from cocoa beans, there are several consecutive steps, including fermentation of the beans in order to develop the flavor precursor, roasting of the beans aiming to darken the color and develop the flavor characteristics of chocolate, and the process of breaking and winnowing aiming at removing the cocoa shell and obtaining the cocoa nib. To obtain the cocoa liquor, the process of grinding of the nib is required. The cocoa liquor is then mixed with the proper amounts of cocoa butter, sugar, milk and lecithin depending on the type of chocolate to prepare. After mixing, a refining process is needed to reduce the particle size and to get smooth texture, followed by conching process aiming to develop the chocolate flavors, to eliminate undesirable volatile compounds and to reduce the moisture content. Next, tempering is required to get desired crystal form and to obtain solid state chocolate, and then finally, molding is necessity to shape the chocolate [47].
The most important quality attribute of chocolate resides on the flavor. The flavor consists of the intensity of the cocoa flavor together with any ancillary notes and the absence of flavor defects. Fermentation is a vital stage of postharvest processes that can influence the quality of cocoa beans, in particular taste and aroma and color, and thus it has a vital role on the flavor profile of the chocolate [43]. As previously showed, a great number of farmers in Madiun do not perform fermentation of cocoa beans. To overcome this problem, it would be appropriate to educate and train farmers about good agricultural practices and post-harvest treatments. It is also important to improve government policies in order for the farmers to be paid fair and distinctive prices for good quality cocoa beans. In our view, this can be a significant starting point to develop downstream cocoa industry producing high quality chocolate in Indonesia.
The findings in this study confirm the conclusion drawn by Kongor et al. [29] that good farm management practices would significantly increase cocoa productivity, and thus ensure sustainable production of cocoa production. Furthermore, this research provides empirical evidence of some other constraints for high-quality cocoa production in Indonesia, including socio-economic aspects as abovediscussed.
Conclusions
Cocoa production in Madiun are dominated by the smallholder farmers with an average farm size about 0.5 ha. Most of the farmers are older than 40 years with lack of formal education (most of the farmers have attended to primary school). An interesting finding in this research is that even though the fertilizer application times is lower than in other regions, Dawung was found to be the most productive cocoa region with 651.5 kg/ha/year. At the same time, this region has the youngest farmers and smallest farm size. Although most of the farmers have more than 10 years of farming experience, they still need to learn or improve their cocoa farming and postharvest skills. In fact, the cocoa productivity is still lower than the average cocoa productivity in the world and almost half of the farmers sell their cocoa beans as non-fermented. With an appropriate and regular training about cocoa farming, the use of integrated pest management, organic fertilizers, intercropping system and postharvest practices, the farmers can develop skills in good agricultural practices, counteract the pests and diseases issues, optimize their production capacity and increase productivity and profitability of the farms. Education and training are pivotal to produce high quality cocoa beans that is crucial as raw materials for the food industry. It is necessary to educate people, not only farmers but also collectors, market sellers and intermediates buyers, about the importance of high quality fermented dried cocoa beans so they can appreciate their value and pay a fair price. In this regard, government policies are required. | 8,555.4 | 2020-11-02T00:00:00.000 | [
"Economics",
"Agricultural And Food Sciences"
] |
A Unified Framework for Generalizing the Gromov-Hausdorff Metric
In this paper, an approach for generalizing the Gromov-Hausdorff metric is presented, which applies to metric spaces equipped with some additional structure. A special case is the Gromov-Hausdorff-Prokhorov metric between measured metric spaces. This abstract framework unifies several existing Gromov-Hausdorff-type metrics for metric spaces equipped with a measure, a point, a closed subset, a curve, a tuple of such structures, etc. Along with reviewing these special cases in the literature, several new examples are also presented. Two frameworks are provided, one for compact metric spaces and the other for boundedly-compact pointed metric spaces. In both cases, a Gromov-Hausdorff-type metric is defined and its topological properties are studied. In particular, completeness and separability is proved under some conditions. This enables one to study random metric spaces equipped with additional structures, which is the main motivation of this work.
The Gromov-Hausdorff Metric
How can one measure the similarity of two metric spaces? Heuristically, the scaled lattice δZ d = {δx : x ∈ Z d } converges to R d as δ → 0. Gromov defined various notions of convergence of metric spaces in his novel book [29], which was published in French in 1981. He used these notions to study limits of manifolds and Cayley graphs. In particular, he proved the celebrated result that a finitelygenerated group has polynomial growth if and only if it is virtually nilpotent [28]. Here, we are interested in Gromov's notion of Hausdorff convergence, which is now know as Gromov-Hausdorff convergence. This is induced by the Gromov-Hausdorff (GH) distance of two metric spaces X and Y defined by where the infimum is over all metric spaces Z and all pairs of isometric embeddings f : X → Z and g : Y → Z. Here, d H denotes the Hausdorff distance of subsets of Z. In words, X and Y are close to each other if one can embed them isometrically in a common larger metric space such that their images are close to each other. This notion is practically useful if X and Y are compact. Indeed, d c GH is a metric on the space of compact metric spaces (if isometric metric spaces are considered identical). For non-compact metric spaces, Gromov defined another notion of convergence which will be discussed in Subsection 1. 4.
In fact, the Gromov-Hausdorff metric (1.1) was defined before Gromov by Edwards [19]. He has also proved some basic properties of this metric like completeness and separability, which is essential for probabilistic applications. However, the work of Edward was not (and still is not) well known and the works mentioned here do not refer to it. See also [43].
Independently of Gromov's works, Aldous studied scaling limits of random trees in 1991 in his seminal paper [3]. Among all of the trees with n given vertices, let T n be a tree chosen randomly and uniformly. Aldous showed that by scaling the graph-distance metric on T n by factor 1/ √ n, the result converges to some random fractal called the (Brownian) continuum random tree. To formalize this convergence, he embedded the trees isometrically in the infinite-dimensional space l 1 and used the notion of weak convergence of random compact subsets of a given space [3]. Later, this convergence was expressed equivalently 1 using the Gromov-Hausdorff metric as follows ( [20], see also [18] and [34]), which is more natural and can be applied to more models: Let M be the space of compact metric spaces. The Gromov-Hausdorff metric d c GH makes M a complete and separable metric space. So, the convergence of the sequence 1 √ n T n can be formalized by the theory of weak convergence of random elements of M. Defining random real trees and their convergence is the first place where the Gromov-Hausdorff metric has been used in probability theory ( [20], see also [21]). Since then, the Gromov-Hausdorff metric and its generalizations have been extensively used in the literature to study the scaling limits of various random discrete objects.
Aldous also strengthened the above convergence by proving that the uniform measure on the vertices of 1 √ n T n converges to a probability measure on l 1 . This was also expressed later ( [20]) in terms of weak convergence under the Gromov-Hausdorff-Prokhorov (GHP) metric: If X = (X, µ) and Y = (Y, ν) are two measured metric spaces; i.e., metric spaces X and Y equipped with finite measures µ and ν, define d c GHP (X , Y) := inf{d H (f (X), g(Y )) ∨ d P (f * µ, g * ν)}, (1.2) where the infimum is over all Z, f, g as in (1.1). Here, ∨ means 'maximum', f * µ and g * ν denote the pushforwards of the measures µ and ν and d P denotes the Prokhorov distance of two probability measures on Z, recalled in (2.2) below. In [6], Aldous studied the convergence of trees via the convergence of finitedimensional distributions: The distribution of the random tree spanned by k randomly chosen vertices (and the paths connecting them) is convergent as k is fixed and n → ∞. Later, this was extended to (probability-) measured metric spaces and was called Gromov-weak convergence in [27]. Also, it was shown to be equivalent to convergence under the Gromov-Prokhorov (GP) metric: This is weaker than GHP-convergence; e.g., it ignores the parts of X and Y that are not in the supports of µ and ν. The GP metric will not be studied in this paper since GP-convergence does not imply the GH-convergence of the underlying metric spaces. See [7] for more discussion on various types of convergence of measured metric spaces. In fact, the study of convergence of measured metric spaces goes back to Fukaya [24] with the aim of using it to study the eigenvalues of the Laplace operator on Riemannian manifolds equipped with the volume measure (it has also been used to study optimal transport and Ricci curvature on measured metric spaces [36]). Gromov also defined the box metric in the new chapter 3 1 2 added to the English version [30] of his book published in 1999. This metric was shown later to be bi-Lipschitz-equivalent to the GP metric [35]. Some of the ideas in this chapter overlap with Aldous's work (e.g., the reconstruction theorem and Section 3 1 2 .14 are related to finite-dimensional distributions and their convergence), but it seems that this has been done independently.
Generalizations in the Literature
The idea of Gromov-Hausdorff convergence (or metric) has been generalized in various papers to study the convergence (or perturbations) of objects of the type (X, a), where X is a compact metric space and a is some additional structure on X (the non-compact case will be discussed in Subsection 1.4). We have already mentioned the case where the additional structure is a finite measure on X. The following are some other instances which will be discussed further in the paper.
Gromov defined a metric between pointed metric spaces, where the additional structure a on X is a selected point of X. This was used for the definition of convergence in the non-compact case. In [2], the additional structure is a tuple of k points of X, l measures on X or a combination of them. This is used in the study of the scaling limit of another class of random trees. The paper [38] defines a metric on the set of compact metric spaces equipped with k compact subsets. It is used in the study of the scaling limit of random quadrangulations. In [31], the additional structure is a continuous curve. It is used for the scaling limit of random half-plane quadrangulations to keep track of the boundary curve. [8] uses the case where a is a càdlàg curve or a càdlàg process in X to study limits of random walks on graphs and some analogous stochastic processes defined on measured metric spaces. The latter only defines a notion of convergence, and not a metric. Various other generalizations will be discussed throughout the paper, mostly in Section 4.
The generalizations in the literature either define a GH-type metric or just a notion of convergence. Defining a metric is usually required in probabilistic applications where the underlying metric spaces are random, as explained in the next paragraph. The methods of defining such metrics will be discussed in Subsection 1.3. Convergence is defined, for instance, in [24] for measured metric spaces and in [8] for càdlàg processes. In such works, the convergence is defined based on one of the characterizations of the Gromov-Hausdorff convergence; e.g., by the notion of ǫ-isometries (skipped in this paper; see e.g., [24] or Chapter 7 of [13]) or by embedding a sequence of metric spaces in a common larger space (see e.g., Lemma 2.5 and also [8]). Indeed, such convergence can also be expressed by GH-type metrics discussed in the next subsection. We can also mention that Gromov has defined a notion of convergence (and not a metric) in the non-compact case as explained in Subsection 1. 4. In the generalizations of the GH metric, further properties are needed for the desired application. In the works where only convergence is defined, it is sometimes proved that the convergence gives rise to a notion of topology on the set C of (equivalence classes of) compact metric spaces equipped with an additional structure, and the resulting topological space is Hausdorff or separable (e.g., in [24]). For probabilistic applications, it is usually shown that C is a separable metric space. This is convenient for using weak convergence (e.g., scaling limits) of random objects of the type (X, a). For instance, separability allows one to use Prokhorov's theorem on tightness of probability measures on C. In addition, proving completeness of C is useful if one desires to have a standard probability space. This enables one; e.g., to use regular conditional distribution. However, completeness is not always necessary. This is similar to the case in the theory of (simple) point processes, where the state space is not complete. Instead, it is a Borel subset of some complete metric space (e.g., the space of locally finite measures on R d ). Instances where completeness does not hold for GH-type metrics will be discussed throughout the paper. In addition, some convergence, pre-compactness or tightness criteria are also needed. Of course, an important task in applications is to actually prove the convergence in specific models, which is out of the scope of this paper. Other tasks that are of interest in the literature are studying the properties of the limiting space and using those properties to derive conclusions regarding the sequence of spaces converging to it (see e.g., [5]).
A Unified Framework for Generalizations
Many of the generalizations of the Gromov-Hausdorff metric in the literature have similar properties with similar proofs, but none of them are implied by the properties of the Gromov-Hausdorff metric. So the corresponding papers fall in one of these two classes: Some of them dedicate a lot of space to stating and proving the properties, which is technical and is usually a deviation from the main purpose of the papers. Some others only claim the statements without proof. The latter have some errors occasionally since there are many things to check and the proofs are technical. In particular, the claim of completeness is wrong in some papers, which are discussed in Section 4. Some other errors are mentioned in Subsection 3.1.
This paper provides an abstract framework for generalizing the Gromov-Hausdorff metric that covers all of the current generalizations to the best of the author's knowledge (excluding the GP-type metrics as already mentioned). A framework will also be provided in the non-compact case, which will be introduced in the next subsection. The framework is based on a small number of assumptions that are usually straightforward to verify (or disprove) in special cases.
Several new examples will also be presented. This generalization is thus useful for studying random metric spaces equipped with new types of additional structures, without needing to replicate the proofs each time. We hope that this makes the use of Gromov-Hausdorff-type metrics easier, quicker and more accessible to the researchers and helps to avoid the technicalities and traps.
The framework applies to the objects of the form (X, a), where X is a compact metric space and a belongs to a given metric space τ (X), which represents a set of possible additional structures on X (e.g., the set of finite measures on X). The distance of two such objects is defined by an equation similarly to that of the GHP metric (1.2). Under some assumptions on τ , which are intended to be as minimalistic as possible (in short, being a functor and having some kind of continuity), it is shown that the formula is indeed a metric. Separability (resp. completeness) of the metric is also proved by assuming separability (resp. completeness) of τ (X) for every X and an additional continuity property of τ . This provides the measure-theoretic requirements for defining random compact metric spaces equipped with additional structures and to have a standard probability space. A general pre-compactness result is also provided.
We will also discuss in detail, mainly in Section 4, how this framework extends the existing generalizations of the GH metric. The metrics in the literature are defined in mainly two ways: Some are based on embedding in a larger metric space as in (1.1) and (1.2). These are directly special cases of the framework, possibly after a minor modification that changes the metric up to a constant factor (e.g., the GHP metric is sometimes defined by using + instead of ∨ in (1.2)). Some other papers extend the idea of the equivalent formulation of the GH metric by the notion of correspondences, discussed in Subsection 2.7. For instance, an analogous formulation of the GHP metric is available in terms of correspondences and approximate couplings based on Strassen's theorem. Here, we call such definitions Strassen-type metrics. Although the general framework in this paper is based on the first approach, Subsection 2.7 provides a Strassen-type reformulation of the metric as well for some types of additional structures. This extends the existing Strassen-type metrics in the literature with minor modifications that change the metrics up to a constant factor; e.g., using + instead of ∨ or having different coefficients in the formulas. We preferred to use ∨ in the formula since it is the right choice for having exact Strassen-type formulations.
The main novelty of the paper is the unification of the GH-type metrics and the generality and simplicity of the framework. The use of functors is new in this context. Also, while sometimes more arguments are needed due to few assumptions, the proofs simplify the existing proofs in the literature and show the ideas more clearly (in fact, we extend the proofs of the previous work [32] which in turn simplify those in [1]). For instance, there is no need to use ǫ-nets in the proofs. Additionally, a new result is using the framework to show that in the examples where completeness does not hold, the space is still Polish by showing that it is a G δ subspace of another Polish space (Subsections 2.6.7, 4.3, 4.4, 4.5 and 4.9). We also correct some errors in the literature (where completeness does not hold ; e.g., Subsections 4.3 and 4.4, or where the metric needs a correction; see Remark 3.1). In addition, GH-type metrics for some new examples of additional structures are also presented; e.g., marked measures, marked closed subsets, continuous functions, ends, processes of closed subsets, and operations on examples (e.g., composition and product). We hope that the framework can be used in the future for studying convergence of metric spaces with new types of additional structures.
The Non-Compact Case
Gromov defined a notion of convergence for pointed metric spaces (X i , o i ) (i = 1, 2, . . .) under the assumption that X i is boundedly-compact ; i.e., every bounded closed subset of X i is compact (Section 3.B of [30]). There are some generalizations in the literature in which an additional structure a i is assumed on X i . For instance, one can mention Gromov-Hausdorff-Prokhorov convergence for measured metric spaces (also called measured Gromov-Hausdorff convergence or Gromov-Hausdorff-vague convergence). See e.g., Section 27 of [44]. It is known that these two topologies are metrizable and Polish. This was shown for length spaces and discrete metric spaces in [1] and [9] respectively and the general case is done in [32]. 2 This enables one to study random (measured) non-compact metric spaces; see e.g., [1], [9] or the references of (and citations to) [1].
In such generalizations, various formulas have been proposed to defined a notion of metric or convergence, all of which have the following philosophy (which is sometimes called localization): Two tuples (X 1 , o 1 ; a 1 ) and (X 2 , o 2 ; a 2 ) are close to each other when two large compact portions of them are close. (1.4) Here, a large portion of X i means a (closed) ball with large radius centered at o i , or a subset close to (or containing) such a large ball. Also, the distance of two compact portions is measured with a GH-type metric in the compact case. This shows why it is important to consider pointed spaces; otherwise, a large part of the space might look like a line and another large part might look like a plane.
To formalize (1.4), one should be careful that the distance of the balls of radius r centered at o 1 and o 2 is not necessarily monotone in r. Some papers have fallen into this trap and their definitions should be corrected. Further introduction to the non-compact case is given in Subsection 3.1 in order to avoid technicalities at this point.
Among other examples, one can mention the cases where the additional structure on X i is a continuous curve in X i [31], a càdlàg curve in X i [8], an isometry from X i to itself (Section 6 of [30]) or a function on X i [18]. These examples will be studied in detail in Section 4. The same philosophy (1.4) can also be used when the underlying spaces X 1 = X 2 are identical. This has been used in stochastic geometry to defined random closed subsets, random measures, point processes, random marked measures and particle processes in a fixed metric space (see e.g., [41]).
In this paper, a unified framework is presented as well for the generalizations in the noncompact case. This is based on the framework of compact spaces, mentioned in the previous subsection, under additional assumptions on the map τ . In order to have a more coherent presentation, the introduction to this framework is moved to Subsection 3.1 (the reader may jump there right now if he or she wishes). As in the compact case, the framework unifies several existing generalizations and various new examples will also be provided in Sections 3 and 4.
As a final remark, Benjamini and Schramm's notion of convergence of rooted graphs (also known as local weak convergence), defined in [11] in 2001, is also closely related to Gromov-Hausdorff convergence, but seems to be done independently. It is in fact stronger than GH-convergence since the edges of a graph are not uniquely determined by the graph-distance metric. It will be shown in Subsection 4.2 that Benjamini-Schramm convergence is equivalent to the convergence in one of the examples of this paper, namely, marked metric spaces.
The Structure of the Paper
In this introduction, we reviewed convergence of metric spaces and the Gromov-Hausdorff-type metrics in the literature. Further discussion on the literature will be given through the examples. The general framework is presented in Section 2 for compact metric spaces and in Section 3 for non-compact metric spaces. For the sake of mathematical rigor, all proofs are included in these two sections. Some examples are also given in Subsections 2.6 and 3.7 for illustrating the framework. More involved examples are provided in Section 4 together with discussing how the framework generalizes the existing examples in the literature.
The Framework for Compact Metric Spaces
This section provides the abstract framework for generalizing the Gromov-Hausdorff metric in the compact case. The proofs of all of the results are postponed to Subsection 2.8.
Notation and Basic Definitions
The minimum and maximum binary operators are denoted by ∧ and ∨ respectively. For all metric spaces X in this paper, the metric on X is usually denoted by d if there is no ambiguity. An extended metric is similar to a metric, but might take the value ∞. The complement of a subset A ⊆ X is denoted by A c or X \ A. Also, all measures µ on X are assume to be Borel measures. The total mass of µ is denoted by ||µ||. If in addition, ρ : X → Y is measurable, ρ * µ denotes the push-forward of µ under ρ; i.e., ρ * µ(·) = µ(ρ −1 (·)). For x ∈ X and r ≥ 0, the closed ball of radius r centered at x is defined by B r (x) := B r (X, x) := {y ∈ X : d(x, y) ≤ r}. The metric space X is boundedly-compact (also called proper or Heine-Borel in the literature) if every closed ball in X is compact. Given metric spaces X and Z, a function f : X → Z is an isometric embedding if it preserves the metric; i.e., It is an isometry if it is a surjective isometric embedding. The image of f : X → Z is denoted by either f (X) or Im(f ). A measured metric space is a pair (X, µ), where X is a metric space and µ is a Borel measure on X. By convention, (X, µ) is called compact in this paper if X is compact and µ is a finite measure. Two measured metric spaces (X, µ) and (Y, ν) are called equivalent if there exists an isometry f : X → Y such that f * µ = ν.
The Hausdorff distance of two subsets A and B of a metric space Z is It is well known that d H is a metric when restricted to the set of nonempty compact subsets of Z. In addition, if Z is complete (resp. separable, resp. compact), then the latter is also complete (resp. separable, resp. compact). See e.g., Proposition 7.3.7 and Theorem 7.3.8 of [13]. The Prokhorov distance of finite measures µ and ν on Z is defined by where A runs over all closed subsets of Z. This is a metric on the set of finite Borel measures on Z. In addition, if Z is complete and separable, then the latter is also complete and separable. In this case, convergence w.r.t. the Prokhorov metric is equivalent to weak convergence. See Section 6 of [12].
To recall, M is the set of equivalence classes of compact metric spaces up to isometry. Equipped with the Gromov-Hausdorff metric (1.1), M is complete and separable. A similar claim holds for the Gromov-Hausdorff-Prokhorov (GHP) metric (1.2). See e.g., Chapter 7 of [13] and [1].
Recall that a topological space is Polish when there exists a metrization that turns it into a complete separable metric space. By Alexandrov's theorem, a subset of a Polish space is Polish if and only if it is a G δ subset; i.e., a countable intersection of open subsets.
Motivation
We would like to define the distance of the objects of the form (X, a), where X is a compact metric space and a is an additional structure on X. Let τ (X) be a set which represents the set of additional structures on X under study (e.g., the set of finite measures on X). Motivated by the GHP metric (1.2), the distance of two such objects (X, a) and (Y, b) will be defined by an equation of the form where the infimum is over all compact metric spaces Z and all isometric embeddings f : X → Z and g : Y → Z. Here, a ′ and b ′ are the images of a and b under f and g respectively and are considered as structures on Z. So a function from τ (X) to τ (Z) corresponding to f should be predefined, which is denoted by τ f here (e.g., if a is a measure on X, define τ f (a) := f * a). Also, in order to make sense of d(a ′ , b ′ ), it is required that τ (Z) is a metric space for all compact metric spaces Z. The philosophy of the formula is to embed (X, a) and (Y, b) in a common space such that their images are close to each other. This philosophy is based on the assumption that such an embedding does not distort the geometry of X and the geometry of the set of additional structures on X. So we assume that τ f : τ (X) → τ (Z) is always an isometric embedding. In addition, the philosophy is hardly justifiable without the following assumptions: (1) If X = Z and f is the identity function on X, then τ f is also the identity function on τ (X) and (2) If f : X → Z and h : Z → Z ′ are isometric embeddings, then τ h•f = τ h •τ f . By using the language of category theory, all of these assumptions can be summarized by one simple sentence: τ should be a functor from the category of compact metric spaces to the category of metric spaces. This will be explained in more details in the next subsection. The notions of categories and functors are useful to simplify the presentation, but no results or background in category theory are needed here.
The following basic examples will be updated step by step for illustrating the definitions and results (see the conclusion in Example 2.18). Further examples will be discussed in Subsection 2.6 and also in Section 4.
Example 2.1. In the following examples, X and Z represent general compact metric spaces and τ f is an isometric embedding from τ (X) to τ (Z), which is defined for an arbitrary isometric embedding f : X → Z.
(i) Points. To consider compact metric spaces equipped with a distinguished point, let τ (X) := X and τ f := f .
(ii) Compact subsets. To consider compact metric spaces equipped with a nonempty compact subset, one can let τ (X) be the set of nonempty compact subsets of X. If one equips τ (X) with the Hausdorff metric and lets τ f (K) := f (K) for all K ∈ τ (X), then τ f is an isometric embedding.
(iii) Measures. To consider compact measured metric spaces, let τ (X) be the set of all finite measures (or probability measures) on X. One can consider the Prokhorov metric on τ (X) and let τ f (µ) := f * µ. It is straightforward that τ f is an isometric embedding.
(iv) Finite subsets. Let τ (X) be the set of finite subsets of X and τ f (S) := f (S). One can equip τ (X) either with the Hausdorff metric or with the Prokhorov metric. For the latter, which is more convenient in point process theory, one may regard every finite subset S as the counting measure x∈S δ x . Then, objects of the form (X, S) are special cases of one of the previous examples depending on the choice of the metric. Note that the two metrics induce different topologies on τ (X) and have different completions.
Remark 2.2. In the above example, one can also let τ (X) be the set of compact subsets of X including the empty set. For this, it is convenient to extend the Hausdorff metric by letting d H (∅, K) := ∞ for all K = ∅, which leads to an extended metric on τ (X).
Many other examples can be constructed by combining these simple examples. For instance, for considering compact metric spaces equipped with multiple additional structures (e.g., k points and l measures), it is enough to consider a product space τ (X) := τ 1 (X) × τ 2 (X) × . . .. This will be discussed more in Subsection 2.6.
The Space C τ
We now formalize the motivation given in Subsection 2.2. Let Comp denote the class of compact metric spaces. For two compact metric spaces X and Y , let Hom(X, Y ) be the set of isometric embeddings of X into Y . In the language of category theory, Comp is a category and the elements of Hom(X, Y ) are called morphisms. An isomorphism is a morphism which has an inverse. Also, every compact metric space is called an object of Comp. The general definition of categories is omitted for brevity.
Let also Met be the category of metric spaces in which the morphisms are isometric embeddings 3 . Definition 2.3. A functor τ : Comp → Met is a map that assigns to every compact metric space X a metric space τ (X), and assigns to every isometric embedding f : X → Y an isometric embedding τ f : τ (X) → τ (Y ), such that (i) For all isometric embeddings f : X → Y and g : Y → Z, one has τ g•f = τ g • τ f .
(ii) For every X, if f is the identity function on X, then τ f is the identity function on τ (X).
Note that f, g are morphisms in Comp and τ f , τ g are morphisms in Met. Definition 2.4. Given a functor τ as in Definition 2.3, let C τ be the category whose objects are of the form (X, a), where X is an object in Comp and a ∈ τ (X). Let the set of morphisms between (X, a) and (Y, b) be {f ∈ Hom(X, Y ) : τ f (a) = b}. Let C τ be the set of isomorphism-classes of the objects of C τ (it can be seen that C τ is indeed a set).
The Generalized Gromov-Hausdorff Metric
Given a functor τ : Comp → Met as in the previous subsection, one can formalize (2.3) as follows: For two elements (X, a) and where the infimum is over all compact metric spaces Z and all isometric embeddings f : X → Z and g : Y → Z. It is clear that this definition depends only on the equivalence class of (X, a) and (Y, b), and hence, is indeed well defined on C τ . Also, by part (iii) of Example 2.1, the function d c τ generalizes the GHP metric (1.2). More examples will be discussed later.
The following lemma rephrases convergence of a sequence under d c τ by embedding them into a common metric space. As mentioned in the introduction, this is used in some works to define a GH-type notion of convergence without defining a metric (see also Lemma 3.28 for the non-compact case).
Lemma 2.5. d c τ (X n , a n ), (X, a) → 0 if and only if then there exists a compact metric space Z and isometric embeddings f : X → Z and f n : X n → Z such that f n (X n ) → f (X) in the Hausdorff metric and τ fn (a n ) → τ f (a).
The following is the main result of this subsection. The proofs of all of the results are postponed to Subsection 2.8. (ii) If τ is pointwise-continuous (Definition 2.7 below), then d c τ is a metric and also the infimum in (2.4) is attained. Definition 2.7. A functor τ : Comp → Met is called pointwise-continuous when for all compact metric spaces X and Y and all sequences of isometric where d sup is the sup metric.
In many examples, the functor under study has the pointwise-1-Lipschitz property, which is stronger than pointwise-continuity, and even equality holds in (2.5). The following lemma provides basic examples. Sketch of the proof. Let f, g : X → Y be isometric embeddings. It is an easy exercise to show that for all a ∈ τ (X), one has d(τ f (a), τ g (a)) ≤ d sup (f, g) and equality holds for some a. This proves the claim.
The following lemma is required for proving the next theorems. Lemma 2.9. It τ is pointwise-continuous, then for every compact metric space X, the map from τ (X) to C τ defined by a → (X, a) is continuous and proper.
Remark 2.10 (Extended Metrics). If τ (X) is allowed to be an extended metric space, then it can be seen that C τ is an extended metric space. The key example is the functor of compact subsets (Remark 2.2), which will be needed in Section 3. In addition, the other results of this section remain valid (note that the definitions of compactness, completeness and separability can be applied to extended metric spaces as well).
As before, many examples have the Hausdorff-1-Lipschitz property, which is stronger than Hausdorff-continuity, and even equality holds in (2.6). The following lemma provides basic examples. However, some natural examples fail to be Hausdorff-continuous; e.g., continuous curves (Subsection 2.6.4). Remark 2.14 below provides weaker assumptions sufficient for Theorem 2.12. Proof. Let f : X → Z and g : Y → Z be isometric embeddings and ǫ := d H (f (X), g(Y )). For every a ∈ τ (X), one can construct b ∈ τ (Y ) such that d(τ f (a), τ g (b)) ≤ ǫ. For instance, if a is a closed subset, let b := g −1 (N ǫ (f (a))). Also, if a is a measure, let b := (g −1 πf ) * a, where π : f (X) → f (Y ) assigns to every point of f (X) its closest point in f (Y ). This proves the Hausdorff-1-Lipschitz property. One can show equality in (2.6) by letting a be a single point chosen suitably.
Remark 2.14. The proof of the above theorem shows that the assumption of Hausdorff-continuity can be replaced by the following assumptions: For every sequence of compact metric spaces Z, X, X 1 , X 2 , . . . and isometric embeddings f : X → Z and f n : X n → Z (for n = 1, 2, . . .) such that d H (Im(f n ), Im(f )) → 0, (i) If b ∈ τ (Z) and a n ∈ τ (X n ) (for infinitely many values of n) are such that τ fn (a n ) → b, then b ∈ Im(τ f ).
(ii) For every a ∈ τ (X), there exists a sequence a n ∈ τ (X n ) such that τ fn (a n ) → τ f (a).
Remark 2.15. Condition (ii) in Remark 2.14 is always implied by Hausdorff continuity. So does (i), if we assume that τ (X) is complete for every X (which implies that Im(τ f ) is closed in τ (Z)). Conditions (i) and (ii) together mean that Im(τ fn ) → Im(τ f ) in the sense of Painleve-Koratowski convergence (Definition B.4 of [39]). Assuming completeness and separability in addition, the latter is equivalent to convergence in the Fell topology (Theorem B.6 of [39]). (ii) One can select a compact subset τ ′ (X) ⊆ τ (X) for every X ∈ Comp such that τ ′ is a functor (by letting τ ′ f be the restriction of τ f , for every morphism f of Comp) and C τ ′ ⊇ A.
Condition (i) in the above theorem can be characterized by the diameter and the size of ǫ-nets; see e.g., Section 7.4.2 of [13]. For measured metric spaces, Condition (ii) is equivalent to the existence of a uniform upper bound on total masses of the measures (see Theorem 2.6 of [1]). This fact is generalized in the following proposition (e.g., let h X (µ) be the total mass of µ). This result will also be used for marked measures and marked closed subsets, which will be defined in Subsection 2.6.7.
Proposition 2.17. Let τ and A be as in Theorem 2.16 such that Condition (i) of the theorem holds. Assume that there exists a fixed metric space E and a continuous function h X : τ (X) → E for every object X of Comp such that h X is a proper map and is compatible with the morphisms (i.e., h Y •τ f = h X for every morphism f : X → Y ). Then, Condition (ii) in Theorem 2.16 is equivalent to the existence of a compact set E ′ ⊆ E such that all elements (X, a) ∈ A satisfy h X (a) ∈ E ′ .
Examples
The following are some examples for illustrating the framework of this section. Further examples are provided in Section 4 and their connections to the literature are discussed therein.
Basic Examples
Example 2.18 (Points, Compact Subsets and Measures). Let C be the space of compact metric spaces X equipped with a point p ∈ X, a compact subset K ⊆ X or a finite measure µ on X. In each case, the results of this section imply that C is a complete separable metric space. See Lemmas 2.8 and 2.13. . Hence, C τ = M × Ξ with the max product metric (the case where Ξ is a singleton can be interpreted as no additional structure). This trivial example is useful for Subsection 2.6.7.
Example 2.20 (Basic Operations). Given two functors τ 1 and τ 2 , the intersection τ 1 (X) ∩ τ 2 (X) and the union τ 1 (X) ∪ τ 2 (X) (with the maximal consistent metric) are also functors (if the metrics are compatible on the intersection). Also, the completion of τ 1 (X) is a functor. The reader can verify that pointwisecontinuity is inherited, and hence, (2.4) defines a metric.
Functorial Subsets
In some examples were completeness does not hold, one would like that the space C τ is a Borel subset of some Polish space. In such examples, we will prove this property by considering a larger functor. Let τ ′ be another pointwise-continuous functor such that τ (X) is a metric subspace of τ ′ (X) for every X and τ f agrees with (the restriction of) τ ′ f for every morphism f : X → Y . It is clear that C τ is also a subspace of C τ ′ , but the topological properties need further assumptions.
Call τ a functorial subset of τ ′ if for every isometric embedding f : , where a ′ n ∈ τ (X n ) and a ∈ τ ′ (X). By Lemma 2.5, there exists a common metric space Z and isometric embeddings f n : X n → Z and f : . So, being a functorial subset implies that τ ′ f (a) ∈ Im(τ f ), and the claim is proved. Now assume that τ (X) is a Borel subset of τ ′ (X) for every X. Does it imply that C τ is also a Borel subset of C τ ′ ? The answer is not known to the author. It seems that one needs to specify the Borel class in a functorial way as follows.
This claim is immediately implied by the previous lemma. A similar statement can be given for any other Borel class like F σ , G δσ , . . ..
In some examples, different metrics can be considered on τ (X); e.g., the sup metric between curves and the Hausdorff metric between the graphs of the curves (see Subsection 2.6.4 below). The following lemma is useful for comparing the topologies.
Lemma 2.23. Let τ and τ ′ be pointwise-continuous functors such that τ (X) ⊆ τ ′ (X) for all X, τ f is the restriction of τ ′ f for every f and the topology of τ (X) is coarser (resp. finer) than that of τ ′ (X) (restricted to τ (X)). Then, C τ is a subset of C τ ′ and has a coarser (resp. finer) topology. In particular, in the coarser case, if C τ ′ is separable, then so is C τ .
The proof is similarly to that of Lemma 2.21 and is skipped.
Multiple Additional Structures
Let τ 1 , τ 2 , . . . , τ n be functors and τ (X) := i τ i (X). Then, C τ is the set of compact metric spaces X equipped with a tuple (a 1 , . . . , a n ) of n additional structures such that a i ∈ τ i (X). Here, we prefer to equip τ (X) with the max product metric This metric is more convenient for the Lipschitz properties (Lemma 2.24) and for Strassen-type formulations (Subsection 2.7). Similarly, for the product of countably many functors τ 1 , τ 2 , . . ., the following metric is more convenient: Also, every isometric embedding f : X → Z induces a function from τ (X) to τ (Z) naturally, which is an isometric embedding. Hence, τ is a functor.
(i) If τ i is pointwise-continuous for every i, then so is τ . A similar result holds for Hausdorff-continuity, the pointwise-M -Lipschitz property and the Hausdorff-M-Lipschitz property.
(ii) If τ i satisfies the assumptions of Theorem 2.12 for every i, then C τ is complete and separable.
The proof is straightforward and is left to the reader. For instance, [38] defines a GH-type metric for compact metric spaces equipped with k distinguished closed subsets. According to Lemma 2.24, this is a special case of the framework of this section. Also, [2] considers the set of compact metric spaces equipped with k distinguished points and l finite Borel measures. It is claimed that this space is complete and separable. This is also implied by Lemma 2.24. In fact, the metric in [2] differs from the metric of Lemma 2.24 up to a constant factor. This will be explained in Subsection 2.7.
Continuous Curves and Mappings
Let C be the space of compact metric spaces X equipped with a continuous function η : I → X, where I is a given compact metric space. If I is an interval, then η is a curve and the results of [31] show that C is a Polish space. Here, we represent it as an example of our framework and also generalize it to an arbitrary I. See also Subsection 3.7.4 (for non-compact I) and Subsection 4.3.
Let τ (X) be the set of continuous functions η : I → X equipped with the sup metric. Also, by letting τ f (η) := f • η, τ f is an isometric embedding. Here, τ is a functor and C τ = C.
Proposition 2.25. The functor τ , defined above, is pointwise-1-Lipschitz, satisfies Condition (i) of Remark 2.14, but is not Hausdorff-continuous in general. Nevertheless, the space C τ of compact metric spaces X equipped with a continuous function η : I → X is complete and separable.
Here, τ is not generally Hausdorff-continuous. For instance, if one approximates X by finite metric spaces X 1 , X 2 , . . ., then a continuous curve in X cannot necessarily be approximated by continuous curves in X n . By the same reason, condition (ii) of Remark 2.14 does not necessarily hold. So separability is not implied by Theorem 2.12. In the case when I is an interval, one can prove separability directly as in [31], but the method of [31] does not work in the general case. Here we will prove it by using Theorem 2.12 for a larger functor as in Lemma 2.23.
Proof. Assume f, g : X → Y are isometric embeddings. For any η : . This means that τ is pointwise-1-Lipschitz. Now, assume f n : X n → Z is an isometric embedding as in Remark 2.14 and d H (Im(f n ), Im(f )) → 0. Assume η n : I → X n is continuous and This proves condition (i) of Remark 2.14. Since τ (X) is complete for every X, Remark 2.14 implies that C τ is complete. For proving separability of C τ , identify every continuous function η : I → X with its graph, which is a closed subset of I × X. So τ (X) can be regarded as a subset of the set τ ′ (X) of closed subsets of I × X equipped with the Hausdorff metric. In Subsection 2.6.7, it will be shown that τ ′ is Hausdorff-continuous and C τ ′ is separable. So, separability of C τ is implied by Lemma 2.23 and the fact that the topology on τ (X) is identical to that induced from τ ′ (X), which is left to the reader (use modulus of continuity).
Càdlàg Curves
For all compact metric spaces X, let τ 0 (X) be the set of càdlàg curves η : I → X, where I is a compact or non-compact interval (a càdlàg curve is a function that is right-continuous and has left-limits at all points). τ 0 (X) is complete and separable under the Skorokhod metric (Sections 12 and 16 of [12]). One can regard τ 0 as a functor similarly to Subsection 2.6.4. In contrast with continuous functions, this example is Hausdorff continuous. More generally: To prove this claim, assume X, Y ⊆ Z and η is a càdlàg curve in X. The reader can verify that there exists a càdlàg curve η ′ in Y such that d sup (η, η ′ ) ≤ (1 + ǫ)d H (X, Y ) (take a sufficiently fine net in Y and let η ′ be piece-wise constant). The details are skipped for brevity. This example will be discussed further in Subsections 3.7.5 and 4.9.
Composition of Functors
Assume ρ and τ are functors from Comp to Met as in Subsection 2.4. If ρ(X) is compact for every X, then one can define the functor τ • ρ : The following lemma is straightforward to prove.
Lemma 2.27. If both ρ and τ are pointwise-continuous (resp., Hausdorffcontinuous), then so is τ • ρ. A similar statement holds for the Lipschitz properties and the conditions in Remark 2.14.
Therefore, if both ρ and τ satisfy the assumptions of the results of this section, then so does τ • ρ. In addition, it can be seen that if ρ is Hausdorff-M -Lipschitz, then the map from C τ •ρ to C τ defined by (X, a) → (ρ(X), a) is an M -Lipschitz function.
For example, composition is useful if one wants to study compact metric spaces X equipped with a family of elements in ρ(X); e.g., k elements of ρ(X), finitely many points in ρ(X), a closed subset of ρ(X) or a probability measure on ρ(X) (i.e., a random element of ρ(X)). These are special cases of composition of functors by choosing τ suitably. Various specific examples will be studied in Subsection 4.6 and 4.7 together with their extension to boundedly-compact metric spaces (based on Example 3. 38).
Some examples of ρ in which ρ(X) is always compact are the functors of closed subsets, probability measures and finite measures with total mass at most M , where M is a constant. The same holds for marked measures and marked closed subsets (defined in the next subsection) if the mark space is compact. For boundedly-compact mark space, one can also let ρ be the functor of marked closed subsets. See the next subsection for more details.
Remark 2.28.
In some examples of composition, ρ(X) is not compact. This is useful for the study of marks in the next subsection (Proposition 2.31) and for more general two-level measures (Subsection 4.7.4). For this, one needs that τ is a functor τ : Met → Met. Such a functor can be defined similarly to Definition 2.3. Here, although (2.4) is not well behaved (since the GH metric between noncompact metric spaces is too strict, is an extended metric and the corresponding space is not separable), but the definitions of pointwise-continuity, Hausdorff-continuity, the Lipschitz properties and the conditions of Remark 2.14 are still valid and are useful for composition of functors. These properties are inherited to the composition τ • ρ similarly to Lemma 2.27.
Marks
Fix a complete separable metric space Ξ as the mark space. Heuristically, we consider metric spaces X equipped with marks on points or marks on tuples of points. Due to measurability issues regarding Ξ X , the following definitions are introduced.
Definition 2.29. Let X be a compact metric space and k ∈ N. A k-fold marked measure on X is a Borel measure on X k × Ξ. Also, a k-fold marked closed (resp. compact) subset of X is a closed (resp. compact) subset of X k ×Ξ. The number k is called the order of the marked measure/closed subset.
In the case k = 1, this definition is inspired by the notion of marked random measures in stochastic geometry (see Subsection 4.1). Also, 1-fold marked measures are studied in [17] and [33], but with a version of the Gromov-Prokhorov topology, which is weaker than the topology we are considering.
Definition 2. 30. Let τ f (X) be the set of finite k-fold marked measures with the Prokhorov metric. Also, let τ c (X) be the set of nonempty k-fold marked compact subsets of X with the Hausdorff metric.
Note that these functors contain the basic examples of Example 2.1 (points, measures and closed subsets) as functorial subsets. When Ξ is not compact, one can also study marked closed subsets (not necessarily compact) and boundedlyfinite marked measures, but the Hausdorff and Prokhorov metrics are no longer suitable. This will be studied in Example 3.29 with another metric.
Proof. First, assume the mark space Ξ is compact. In this case, the functor τ (f ) is the composition of the functor X → X k × Ξ (which is itself a product of the identity functor X → X and the constant functor X → Ξ of Subsection 2.6.2) with the functor of finite measures (Example 2.1). So the claim is implied by Lemmas 2.27, 2.8 and 2.13. The proof for the functor τ (c) is similar. In the case Ξ is not compact, the above argument is still valid by Remark 2.28 (one can also prove the claim directly similarly to Lemmas 2.8 and 2.13).
The following example motivates the names 'marked measure' and 'marked closed subset'.
x ∈ C} is a marked compact subset of X. This can be extended to k-fold marks similarly.
A compact space with a simple 1-fold marked measure is called a functionally marked metric measure space in [33]. It is proved in [33] that the set of such spaces is Polish (with the GP-type topology). By the tools presented here, we modify and shorten the proof of [33] to show the same with a stronger topology.
Proposition 2.33. Let τ (X) be the set of simple k-fold marked closed subsets of X (resp. simple k-fold marked measures on X). Then, τ is pointwise-continuous and C τ is a G δ subspace of some Polish space, and hence, C τ is Polish itself.
Proof. We only prove the case k = 1 for simplicity. Pointwise-continuity is straightforward. For marked closed subsets, we use modulus of continuity. Given m, n ∈ N, let τ (m,n) (X) be the set of marked closed subsets K ⊆ X × Ξ such for every (x, a), (y, b) ∈ K, if d(x, y) ≤ 1/m, then d(a, b) < 1/n. It can be seen that τ (m,n) (X) is open in τ (c) (X) and is a functorial subset. Also, the set of simple marked closed subsets is exactly For marked measures, we use the characterization of simple marked measures in [33] as follows. In [33], an explicit function β : 2) and (2.5) of [33]. So, Lemma 2.21 can be used as above to deduce that C τ is a G δ subset of the Polish space C τ f , and hence, is Polish by itself. This completes the proof. Proposition 2.17 gives an explicit pre-compactness result for marks as follows.
Then, the claim is implied by Proposition 2.17. For the second part, let h X (µ) := (||µ||, π * µ) and the claim is implied by Proposition 2.17 and Prokhorov's theorem on tightness of measures.
Strassen-Type Formulations
A correspondence between metric spaces X and Y is a closed subset of X × Y such that, regarded as a relation between X and Y , every point of X corresponds to at least one point of Y and vice versa. The distortion of R is defined by Some generalization of the Gromov-Hausdorff metric in the literature are defined in terms of correspondences (instead of isometric embeddings) with a formula of the following type: where p is some criterion in terms of X, Y, a, b, ǫ, R. For instance, the GH metric is obtained by p ≡ 1. Also, if a and b are probability measures, the GHP metric is obtained by the criterion of the existence of a coupling α of a and b such that α(R) ≥ 1 − ǫ. This is based on Strassen's theorem [42] and is generalized to finite measures in [32] using approximate couplings. Formulas like (2.9) are sometimes easier to use than (2.4) and are called Strassen-type formulations here. Although there is no isometric embedding in (2.9), it seems that the existence of a Strassen-type formulation is a property of a functor which is hidden beyond: Let p(X, Y, a, b, ǫ, R) be a formula which represents this criterion.
Proposition 2.36. If τ is a Strassen-type functor, then the GHP-type metric d c τ is equal to (2.9) and the minimum in (2.9) is attained. This result is immediate from the definition. It justifies the use of ∨ in the definition of the metric (2.4) (one could also use + and it would give an equivalent metric).
Some trivial examples are points and closed subsets (Example 2.1), continuous curves (Subsection 2.6.4), càdlàg curves (Subsection 2.6.5) and a constant functor (Subsection 2.6.2). For finite measures, two formulas p can be given, one in terms of Strassen's theorem, mentioned above, and one by the original definition (2.2) of the Prokhorov metric. In contrast, Wasserstein metrics for finite measures (see e.g., Section 6 of [44]) give functors which are not Strassen-type (but are still pointwise-1-Lipschitz and Hausdorff-1-Lipschitz).
As another example, marked compact subsets and marked finite measures (Definition 2.30) are also Strassen-type. This is implied by the following lemma and the fact that these functors are obtained by product and composition of simpler functors (see the proof of Proposition 2.31). See also Example 3.29.
The proof is straightforward and is skipped. This lemma justifies the use of the max product metric for products.
Example 2.38. Proposition 9 of [38] provides a Strassen-type formulation for compact metric spaces equipped with k closed subsets. This is a special case of products in Lemma 2.37. Also, when the additional structure is a tuple of k distinguished points and l finite measures, [2] defines a metric using a Strassentype formula directly. After a minor modification that changes the metric up to a constant factor (changing a ∨ to +; see [32]), this is also a special case of products in Lemma 2.37. Another example is given in Subsection 4.4.
Proofs and Auxiliary Lemmas
In order to prove the main results of this section, we start by some lemmas. The first two lemmas are classical and their proofs are skipped.
Lemma 2.39. For compact metric spaces X and Z, the set of isometric embeddings f : X → Z, equipped with the sup metric, is compact. In addition, the topology of this set is identical to the topology of pointwise convergence. Proof. Let Z, f, g be as in (2.4). Let Z ′ := f (X) ∪ g(Y ) and ι : Z ′ ֒→ Z be the inclusion map. Let f ′ ∈ Hom(X, Z ′ ) and g ′ ∈ Hom(Y, Z ′ ) be obtained by restrictions of f and g respectively. One has ι • f ′ = f and ι • g ′ = g as morphisms in Comp. By the definition of functors ( ). This proves the claim.
Lemma 2.42. Let X n = (X n , a n ) be an object in C τ and ǫ n > 0 for n = 1, 2, . . . such that d c τ (X n , X n+1 ) < ǫ n for each n. If ǫ n < ∞, then there exists a compact set Z and isometric embeddings f n : X n → Z such that for all n, Proof. By (2.4), there exists a compact metric space Z n for every n and isometric embeddings g n : X n → Z n and h n : X n+1 → Z n such that (2.13) By Lemma 2.41, one can assume Z n = g n (X n ) ∪ h n (X n+1 ) without loss of generality.
Let Z ∞ be the gluing of the spaces Z n ; i.e., the quotient of the disjoint union ⊔ n Z n by identifying h n (x) ∈ Z n with g n+1 (x) ∈ Z n+1 for every n and every x ∈ X n+1 . By considering the quotient metric on Z ∞ , the natural map from Z n to Z ∞ is an isometric embedding for each n. Let Z be the metric completion of Z ∞ andZ n be the quotient of Z 1 ⊔ · · · ⊔ Z n defined similarly. We may regard Z n as a subset of Z, which gives Z ∞ = ∪ nZn . Inequality (2.12) implies that d H (Z n ,Z n+1 ) ≤ ǫ n . So the assumption ǫ n < ∞ implies that d H (Z n , Z) is finite and tends to zero as n → ∞. Since Z is complete and eachZ n is compact, Lemma 2.40 implies that Z is compact.
Remark 2.43. Lemma 2.42 is similar to Lemma 5.7 in [27]. The latter is for metric measure spaces and does not assume ǫ n < ∞. So the metric space Z is not necessarily compact therein.
Proof of Lemma 2.5. The proof is similar to that of Lemma 2.42 and is only sketched here. Let ǫ n > d c τ (X n , a n ), (X, a) such that ǫ n → 0. Embed X n and X in a common space Z n as in (2.4). Then, let Z be the gluing all of Z 1 , Z 2 , . . . along the copies of X in all of the sets Z n . It can be proved similarly to Lemma 2.42 that Z is compact and can be used as the desired space.
We are now ready to prove the theorems.
Proof of Theorem 2.6. It is clear that d c τ is symmetric. For the triangle in- Here, we use the fact that the infimum in (2.4) is attained (this will be proved below and there is no circular argument). So, there exists a compact metric space Z and isometric embeddings f : . By (2.4), for every n > 0, there exists a compact metric space Z n and isometric embeddings f n : X → Z n and g n : Y → Z n such that Also, by Lemma 2.41, one can assume f n (X) ∪ g n (Y ) = Z n . This implies that diam(Z n ) ≤ diam(X) + 2ǫ + 2/n, which is uniformly bounded. So, by Theorem 7.4.15 of [13], one can show that the sequence (Z n ) n is pre-compact under the metric d c GH . Therefore, by taking a subsequence if necessary, we can assume d c GH (Z n , K) ≤ 2 −n for some K without loss of generality. By Lemma 2.42, there exists a compact metric space Z and isometric embeddings h n : Z n → Z (this is all we need from Lemma 2.42). By Lemma 2.39 and passing to a subsequence, one can assume h n •f n → f and h n •g n → g uniformly for some isometric embeddings f : X → Z and g : Y → Z without loss of generality. Since satisfy the claim and the claim is proved. a 2 ). This implies that the map is continuous (and also 1-Lipschitz). To prove properness of the map, let K ⊆ C τ be a compact set and a 1 , a 2 , . . . ∈ τ (X) be such that (X, a n ) ∈ K. To show the compactness of the inverse image of K, it is enough to show that the sequence (a n ) n has a convergent subsequence (note that by continuity, the inverse image of K is closed). Since K is compact, by taking a subsequence, we may assume (X, a n ) → (Y, b), where (Y, b) ∈ K. It follows that Y is isometric to X. So there exists c ∈ X such that (X, c) is equivalent to (Y, b) as elements of C τ . So (X, a n ) → (X, c) ∈ K. By Lemma 2.5, there exists a compact metric space Z and isometric embeddings f n : X → Z and f : X → Z such that f n (X) → f (X) and τ fn (a n ) → τ f (c). By Lemma 2.39 and passing to a subsequence, we may assume there exists g : X → Z such that d sup (f n , g) → 0. This implies that f n (X) → g(X), and hence, f (X) = g(X). So there exists an isometry h : X → X such that f = g • h. Let a := τ h (c). Pointwisecontinuity and f n → g implies that τ fn (a) → τ g (a) = τ f (c) = lim n τ fn (a n ). So d(τ fn (a n ), τ fn (a)) → 0. Since τ fn is an isometry, one gets that d(a n , a) → 0; i.e., a n → a. This completes the proof.
Proof of Theorem 2.12. The 'only if' parts can be deduced from Lemma 2.9. Here, we prove the 'if' parts. Let (X n , a n ) be a sequence of elements of C τ such that the corresponding elements in C τ form a Cauchy sequence. By taking a subsequence (if necessary) and using Lemma 2.42, one can assume there exists a compact metric space Z and isometric embeddings f n : X n → Z such that (2.14) d(τ fn (a n ), τ fn+1 (a n+1 )) ≤ 2 −n . (2.15) So the sequences (f n (X n )) n and (τ fn (a n )) n are Cauchy. Lemma 2.40 and the assumption of completeness of τ (Z) imply that there exists a compact subset X ⊆ Z and b ∈ τ (Z) such that f n (X n ) → X and τ fn (a n ) → b. Let ι : X ֒→ Z be the inclusion map. The definition of Hausdorff-continuity implies that d H (Im(τ fn ), Im(τ ι )) → 0. This implies that b is in the closure of Im(τ ι ). On the other hand, since τ (X) is complete (by assumption) and τ ι is an isometric embedding, one gets that Im(τ ι ) is also complete, and hence, closed in τ (Z). So b ∈ Im(τ ι ); i.e., there exists a ∈ τ (X) such that τ ι (a) = b. Now, one can obtain that d c τ ((X n , a n ), (X, a)) → 0. This proves that C τ is complete. Now assume that τ (X) is separable for every X. Let A be a sequence of compact metric spaces which is dense in M. By assumption, for every X ∈ A, there exists a countable dense subset C(X) of τ (X). It is enough to prove that the set E := {(X, a) : X ∈ A, a ∈ C(X)} is dense in C τ .
Let (X, a) ∈ C τ be arbitrary. For every n > 0, there exists X n ∈ A such that d c GH (X n , X) ≤ 2 −n . By Lemma 2.5, there exists a compact metric space Z and isometric embeddings f : X → Z and f n : The assumption of Hausdorff-continuity of τ implies that d H Im(τ fn ), Im(τ f ) → 0. So one can select an element a n ∈ τ (X n ) for each n such that d(τ fn (a n ), τ f (a)) → 0. Since C(X n ) is dense in τ (X n ), one can choose a n such that a n ∈ C(X n ). This implies that d c τ ((X n , a n ), (X, a)) → 0 and the claim is proved.
Proof of Theorem 2.16. (⇐). Assume (i) and (ii) hold. Let (X n , a n ) be a sequence in A. We should prove that it has a convergent subsequence in C τ . By (i), one can assume X n → X for some compact metric space X without loss of generality. So Lemma 2.5 implies that there exists a compact metric space Z and isometric embeddings f n : X n → Z and f : X → Z such that f n (X n ) → f (X). By assumption, a n ∈ τ ′ (X n ). Since τ ′ is a functor, one gets τ fn (a n ) ∈ τ ′ (Z). Since the latter is compact, by passing to a subsequence, one can assume that there exists b ∈ τ ′ (Z) such that τ fn (a n ) → b. Similarly to the proof of completeness in Theorem 2.12, one can show that there exists a ∈ τ ′ (X) such that τ f (a) = b. Now, it can be seen that (X n , a n ) → (X, b) and the claim is proved.
(⇒). Assume A is pre-compact. The claim of (i) is straightforward. To prove (ii), for every compact metric space X, define Let τ ′ (X) be the closure of τ 0 (X) in τ (X). It is straightforward that τ 0 and τ ′ are functors and C τ ′ ⊇ A. So it is enough to show that τ ′ (X) is compact for every X; i.e., τ 0 (X) is pre-compact in τ (X). Let a 1 , a 2 , . . . ∈ τ 0 (X). We should prove that it has a convergent subsequence. By the definition of τ 0 , for every n there exists (Y n , b n ) ∈ A and f n : Y n → X such that τ fn (b n ) = a n . Since A is pre-compact, we can assume that (Y, b) := lim n (Y n , b n ) exists. By Lemma 2.5, there exists a compact metric space Z, g n : Y n → Z and g : Y → Z such that For each n, let K n be the gluing of X and Z along the two copies of Y n . Note that diam(K n ) ≤ diam(X) + diam(Z). So the diameters of K n are uniformly bounded. By using Theorem 7.4.15 of [13], one can show that the sequence (K n ) n is pre-compact under the metric d c GH . So, by taking a subsequence, we may assume that (K n ) n is convergent under d c GH . So, by Lemma 2.5, all of K 1 , K 2 , . . . are isometrically embeddable into a common compact metric space H such that their images in H are convergent.
By composing the isometric embeddings (see the above diagram), one finds isometric embeddings h n : X → H and ι n : Z → H (for each n) such that h n • f n = ι n • g n for each n (in fact, one may do this such that the maps ι n are equal). See the diagram below. By Lemma 2.39 and passing to a subsequence, we may assume there exist isometric embeddings h : X → H and ι : Z → H such that d sup (h n , h) → 0 and d sup (ι n , ι) → 0. Equation (2.16) implies that ι n (g n (Y n )) → ι(g(Y )). On the other hand, ι n (g n (Y n )) = h n (f n (Y n )) ⊆ h n (X). These facts imply that ι(g(Y )) ⊆ h(X). It follows that there exists an isometric Therefore, by letting c n := τ gn (b n ) and c := τ g (b), one has So, (2.17) and pointwise-continuity imply that τ hn (a n ) → τ h (a). Since we had h n (X) → h(X), one gets that (X, a n ) → (X, a) under the metric d c τ . In particular, the sequence (X, a n ) is pre-compact in C τ . So Lemma 2.9 implies that the sequence a 1 , a 2 , . . . has a convergent subsequence in τ (X). This completes the proof.
Proof of Proposition 2.17. First, assume that such E ′ exists. For every X, let τ ′ (X) := h −1 X (E ′ ). Since h X is a proper function, τ ′ (X) is a compact subset of τ (X). It is straightforward that τ ′ is a functor from Comp to Met. So Condition (ii) of Theorem 2.16 holds.
Conversely, assume that Condition (ii) of Theorem 2.16 holds but E ′ does not exist with the desired conditions. The latter implies that there exists a sequence (X n , a n ) ∈ A such that (h Xn (a n )) n does not have any convergent subsequence. By Theorem 2.16, we may assume that (X n , a n ) → (X, a) for some (X, a) ∈ C τ . By Lemma 2.5, there exists a compact metric space Z and isometric embeddings f : X → Z and f n : X n → Z such that τ fn (a n ) → τ f (a) in τ (Z). Continuity of h Z implies that h Xn (a n ) = h Z (τ fn (a n )) → h Z (τ f (a)) = h X (a), which is a contradiction. So the claim is proved.
Motivation
In this section, the term bcm abbreviates boundedly-compact metric space. Let X i (i = 1, 2) be metric spaces and o i ∈ X. Such a pair (X i , o i ) is called a pointed metric space and we call o i the root here. According to Subsection 1.4 of the introduction, we will use the idea (1.4) to extend the framework of Section 2 to pointed bcms. Let a i ∈ ϕ(X i ), where for every bcm X, ϕ(X) is a set of possible additional structures (under some conditions specified later). For example, one can let a i be a closed subset, a measure or a discrete subset.
For defining a metric with the intuition (1.4), a formula that has always been successful in the literature is the following integral formula (e.g., in [1] for measured length spaces): Define the distance of where X is measured with a rooted GHtype metric. In the latter, the root is taken into account as an additional structure on X (r) i . For instance, the rooted GHP metric (when X i = (X i , o i ; µ i ) is compact) is a special case of (2.4) and Example 2.1: 2 ) is neither monotone nor continuous in r in general. In addition, in order to have X n → X , the balls X does not converge to X (1) = X . Also, formulas like inf{ǫ : d(X ) ≤ ǫ} do not satisfy the triangle inequality (a counter example is constructed in Example 3.2 below) and also do not treat the exceptional radii shown in the above example (equation (3.2) below is a correction of this formula). Some earlier works in the literature have made these mistakes and their definitions or proofs need to be corrected; e.g., Appendix A.2.6 of [16] has the monotonicity issue and Subsection 4.8 below mentions references having the other issues.
Returning to (3.1) in the general case, the integral is well defined if d(X is a measurable function of r. In fact, it is usually a càdàg function. If so, it is immediate that (3.1) is a pseudo-metric. Extra effort has been done to show that it is indeed a metric in various examples. Here, we extend the simple proof of [32] which is based on a generalization of König's infinity lemma (under the conditions specified later). However, separability and completeness (or being a Borel subset of a complete space) seem to require further assumptions which are discussed below.
As mentioned earlier, the idea of (1.4) is formulated in various ways in the literature. Some papers use (3.1), approximate isometries or embedding into a common metric space (for the latter, see Lemma 3.28 below). Here, we prefer to use the formulation in the previous work [32], which we think is easier to axiomatize and more convenient to use: For ǫ < 1, and Y (1/ǫ+ǫ) such that d(X (1/ǫ) , Y ′ ) < ǫ/2 and vice versa.
See (3.5) for a more formal definition. This metric generates the same topology as (3.1) for (measured) metric spaces and has a Strassen-type property (similarly to Subsection 2.7). The main task in the present section is to extend this definition to metric spaces equipped with additional structures, together with extending the results and proofs of [32] (being a metric, completeness, separability, etc). This framework will be applied to various types of additional structures in Subsection 3.7 and Section 4. To formalize the above definitions, we require more than a functor τ : Comp → Met. The philosophy of (1.4) is based on the assumption that an additional structure a on X can be truncated to a compact subset K ⊆ X. For instance, if a is a measure on X (resp. a closed subset of X), one can let the truncation be a| K (resp. a ∩ K). In general, for any isometric embedding f : Y → X, we assume a truncation map τ t f : τ (X) → τ (Y ) is given. We require τ t be a functor, as explained later. In addition, the term 'between' used in (3.2) assumes that one can compare two additional structures on the same space. So we will assume that τ (X) is a metric space equipped with a partial order. It should be noted that, while a partial order is not explicitly assumed in (3.1), it is still used for proving the properties of (3.1) in the specif examples in the literature.
An obvious limitation of the philosophy of (1.4) is that one can only consider the additional structures that are uniquely determined by their truncation to compact subsets (if not, one might try to enlarge the set of additional structures under study to ensure that this property is satisfied; e.g., the example of ends in Subsection 4.10). Therefore, we start by only having a functor on Comp. Then, when X is non-compact, we define an additional structure on X as an abstract object that its truncations to compact subsets of X are known (Definition 3.5). This is an instance of the notion of inverse limits.
The Space D
Now, the precise definitions regarding the framework are presented. Let Pos be the category of partially ordered sets (abbreviated by posets). The symbol ≤ is used to denote the order on any poset. A morphism between objects A and A ′ of Pos is an order-preserving function f : A → A ′ ; i.e., if a 1 ≤ a 2 , then f (a 1 ) ≤ f (a 2 ). Let Pos m be the category of metric posets defined as follows. Every object of Pos m is an extended metric space A equipped with a partial order such that for all a ∈ A, the lower cone {a ′ ∈ A : a ′ ≤ a} and the upper cone {a ′ ∈ A : a ≤ a ′ } are closed subsets of A (in most of the examples, the lower cones are compact, but this will be assumed only in some results in Subsection 3.4). A morphism between objects A and A ′ of Pos m is a function f : A → A ′ which is both an isometric embedding and is order-preserving.
From now on, we assume a functor τ : Comp → Pos m is given. The examples of compact subsets and finite measures will be updated step by step to illustrate the definitions (see the conclusion in Example 3.30). Example 3.3. Let τ (X) be the set of compact subsets of X, including the empty set (equipped with the Hausdorff metric and the inclusion order), or the set of finite measures on X (equipped with the Prokhorov metric and the natural partial order µ 1 ≤ µ 2 ). It is easy to check that all of the above assumptions are satisfied. Note that in the first example, τ (X) is an extended metric space. It is necessary to include the empty set for the assumptions given later.
Assume that for every isometric embedding f : X → Y , a truncation map τ t f : τ (Y ) → τ (X) is given. By letting τ t (X) be the underlying poset of τ (X), we assume τ t : Comp → Pos is a contra-variant functor (defined similarly to Definition 2.3, but with the morphisms in the reverse direction). It is called the truncation functor here. Also, assume that for every morphism f : X → Y of Comp, a ∈ τ (X) and b ∈ τ (Y ), A)) respectively. Note that f −1 (K) might be the empty set, which justifies why the empty set was included in Example 3.3. Now, τ is extended to bcms as follows. Here, ϕ(X) represents the set of additional structures on X when X is not compact.
Definition 3.5 (The functor ϕ). For a bcm X, let I X be the set of compact subsets of X. In the language of category theory, let ϕ(X) be the inverse limit in Pos of the diagram consisting of the objects τ (K) for K ∈ I X , where the arrows are the truncation maps. More explicitly, ϕ(X) is a poset equipped with order-preserving functions ϕ(X) → τ (K) for every K ∈ I X (which are called truncation maps again) such that (i) For every K 1 ⊆ K 2 ∈ I X and the inclusion map ι : K 1 → K 2 , the following diagram is commutative (i.e. the composition of two of the maps is identical to the third map): (ii) For every other poset ϕ ′ (X) equipped with truncation maps ϕ ′ (X) → τ (K) as above, there is a unique order-preserving map ϕ ′ (X) → ϕ(X) such that the following diagram is commutative for every K ∈ I X : The second condition is called the universal property. Such a ϕ(X) (together with the truncation maps) is defined uniquely up to isomorphism (in Pos).
Example 3.6. In explicit examples, it is usually clear what ϕ(X) is.
For examples, for the example of compact subsets (resp. finite measures) discussed above, ϕ(X) can be the set of closed subsets of X (resp. boundedly-finite measures). As another example, if X is compact, one can let ϕ(X) be simply the underlying poset of τ (X). In the general case, ϕ(X) can be constructed explicitly as follows: An element of ϕ(X) is a collection of elements a := {a K : K ∈ I X } that are compatible with truncation maps; i.e., for every inclusion map ι : K 1 → K 2 , one has τ t ι (a K2 ) = a K1 . The partial order can be defined by a ≤ a ′ when a K ≤ a ′ K for all K ∈ I X . Note that τ (K) is naturally embedded in ϕ(X) for every compact K ⊆ X (see Definition 3.7 below).
Note that no metric is assumed on ϕ(X). In fact, one cannot define such a metric in a functorial way for non-rooted bcms (see Definition 3.26).
It can be seen that ϕ is a functor and ϕ t is a contravariant functor from the category of bcms to Pos. In addition, (3.3) holds for ϕ and ϕ t . , o; a), where X is a bcm, o ∈ X and a ∈ ϕ(X) (it can be seen that D is indeed a set). Also, let C be the subset of D comprising the tuples in which X is compact. Equivalently, C = C τ ′ in Definition 2.4, where τ ′ : Comp → Met is the functor defined by τ ′ (X) := X × τ (X) equipped with the max product metric (taking the product of X and τ (X) is due to considering rooted metric spaces). Note that (2.4) defines a metric d c τ ′ on C.
The Metric on D
with the convention that inf ∅ := 1. Note that because of the bound ǫ/2 in the above definition, one could assume Y ′ Y (1/ǫ+ǫ) and (3.5) would not change. This is due to the fact that an ǫ/2-perturbation in the rooted GH metric results in an at most ǫ-perturbation of the radius.
To ensure that this equation defines a metric on D, we assume that the following further assumptions hold. Definition 3.9. Let X = (X, o X ; a X ) and Y = (Y, o Y ; a Y ) be compact. For isometric embeddings f : X → Z and g : Y → Z, define Note that by taking infimum over all Z, f, g, one obtains d c τ ′ (X , Y). Assumption 3.10. In the setting of Definition 3.9, assume that for all
In this assumption, if
. For the other way, we add the following assumption.
Assumption 3.11. In the previous assumption, assume that if X (r) It should be noted that for Assumptions 3.10 and 3.11 to hold, the metric on τ (X) should be carefully chosen. Subsection 3.7 discusses some new examples where this assumption does not hold and provides other suitable metrics. It is not known by the author whether or not the next theorems hold for other metrics on D (e.g., (3.1)) under weaker assumptions.
Assumptions (3.10) and (3.11) straightforwardly lead to the following result, the proof of which is left to the reader (see Lemmas 3.11 and 3.12 of [32] for the case of measures).
Theorem 3.14 (Metric on D). Let τ, τ t and D be as above. Assume that τ is pointwise-continuous. Then, (3.5) defines a metric on D.
Note that the metric (3.5) is always bounded by 1 even if τ (X) is an extended metric space.
Finally, assume d(X , Y) = 0. Lemma 3.13 implies that for every ǫ > 0, X (1/ǫ) is ǫ 2 -close to some subspace of Y. By letting ǫ = 1 n → 0 and keeping r fixed, Assumption 3.10 implies that X (r) is 1 2n -close to some subspace . By passing to a subsequence, as- . A challenge is to show that b ′ can be chosen such that a subsequence of (b n ) n converges to b ′ after embedding them in τ (B r+1 (o Y )) (this is immediate if the lower cones are compact, see Assumption 3.17, but we have not assumed it yet). This will be proved in the next paragraph. Assuming this, one can use closedness of cones to deduce that Y ′ Y . In addition, if Y n is chosen according to Assumption 3.11, then closedness of upper cones implies that Y (r−ǫ) Y ′ for every ǫ. This implies that X (r/2) is isometric to Y (r/2) for every r. Note that the set of isomorphisms between X (r/2) and Y (r/2) is compact under the sup metric (which is implied by pointwise-continuity). Now, by a version of König's infinity lemma for compact sets (Lemma 3.13 in [32]), one can choose an isometry between X (r/2) and Y (r/2) for every integer r and glue them to obtain an isometry between X and Y. So, X is isometric to Y. It remains to show that b ′ can be chosen such that a subsequence of (b n ) n converges to b ′ (after embedding them in τ (B r+1 (o Y ))). This is proved below similarly to the proof of Lemma 2.9. First, one can safely replace Y n (resp. b n ) by Y ′ n := Y n ∪ Y ′ (resp. the image of b n in τ (Y ′ n )). So we might assume Y ′ ⊆ Y n from the beginning. Let ι n : Y ′ → Y n be the inclusion map. Since Y n → Y ′ , Lemma 2.5 gives a compact metric space Z and isometric embeddings f : Y ′ → Z and f n : . By Lemma 2.39 and taking a subsequence, one might assume that f n • ι n : Y ′ → Z is convergent pointwise, namely converging to g : where the limits are under the Hausdorff metric. So there exists an isometry
The Topology of D
From now on, we assume that τ is pointwise-continuous, and hence, (3.5) is a metric by Theorem 3.14.
Lemma 3.15. Let X , X 1 , X 2 , . . . ∈ D. Then X n → X if and only if for every r > 0 and ǫ > 0, there exists a sequence X n , X ′ n ) → 0. As a corollary, (3.5) is a metrization of Gromov's notion of convergence (Section 3.B of [30]) when there is no additional structure (see Example 2.19).
The proof of the lemma is straightforward and is left to the reader. Note that X (r) n does not necessarily converge to X (r) . Further characterizations of convergence will be provided in Theorems 3.19 and 3.21 and Lemma 3.28.
Theorem 3.16 (Completeness and Separability). In the setting of Theorem 3.14, assume that τ is Hausdorff-continuous. If τ (X) is complete (resp. separable) for every compact metric space X, then D is also complete (resp. separable).
One can also replace the assumption of Hausdorff-continuity by the assumptions in Remark 2.14.
Proof. The definition of the metric (3.5) directly implies that d(X , X (r) ) ≤ 1/r for every X ∈ D. So C τ ′ is dense as a subset of D. By Assumptions 3.10 and 3.11, one can show that the induced topology on C τ ′ is coarser than that of the metric d c τ ′ . So, separability of D is implied by Theorem 2.12. For completeness, assume (X n ) n is a Cauchy sequence in D. By taking a subsequence, it is enough to assume d(X n , X m ) ≤ 2 −n for every m ≥ n. Let r n := 2 n and ǫ n,m := 2 −n−1 + · · · + 2 −m−1 . Let n be fixed. Inductively, construct subspaces X n,m X m for all m ≥ n such that X n,n = X . This is possible because of Assumptions 3.10 and 3.11. Therefore, (X n,m ) m is a Cauchy sequence under d c τ ′ , and hence is convergent by Theorem 2.12. Let Y n := lim m X n,m .
Note that X n,m is a subspace of X n+1,m and contains the large ball X (rn−ǫn,m) n+1,m . So, Assumptions 3.10 and 3.11 imply that X n,m is close to some subspace of Y n+1 . This way, one finds a sequence of subspaces of Y n+1 that converge to Y n under d c τ ′ . So, an argument similar to the proof of Theorem 3.14 shows that Y n is isomorphic to a subspace of Y n+1 which contains the large ball Y (rn−1) n+1 . In particular, by letting Z n := Y (rn−1) n , then Z n is isomorphic to a large ball in Z n+1 . So, the spaces Z n can be paste together to construct an element Z ∈ D (see the explicit construction after Definition 3.5). It is straightforward to show that X n converge to Z. This proves the claim.
For further studying convergence in D, we assume the following. Most of the examples satisfy this assumption (an exception is càdlàg curves in Subsection 3.7.5). In the next subsection, we study what happens without this assumption.
Assumption 3.17. For every compact X and a ∈ τ (X), the lower cone {a ′ ∈ τ (X) : a ′ ≤ a} is compact. Proof. Let r < s. For every r < t < s, one has h(r) ≤ h(t) ≤ h(s). By compactness of the cone below h(s), one can find t n ↓ r such that a := lim n h(t n ) exists and a ≤ h(s). By the same argument, a ≤ h(t) for every t > r. Also, since upper cones are closed, one has a ≥ h(r). Assume t ′ n ↓ r and a ′ := lim n h(t ′ n ) exists. Since a ≤ h(t ′ n ) for every n and upper cones are closed, one gets a ≤ a ′ . Similarly, a ′ ≤ a, and hence, a ′ = a. This implies that a is the right limit at r. The claim for left limits is proved similarly.
For instance, for the functor of compact subsets discussed earlier, the curve h is càdlàg. In particular, this implies that the curve r → B r (o) is càdlàg. In the general case, a radius r 0 ≥ 0 is called a continuity radius of X if both curves r → B r (o) and r → a| Br (o) are continuous at r 0 . Therefore, X has at most countably many discontinuity radii.
Note that for every continuity radius r 0 of X , the curve r → X (r) is also continuous at r 0 . This implies that the integral (3.1) is well defined.
The following are equivalent.
(i) X n → X .
(ii) For every continuity radius r of X , X (r) n → X (r) for every r ∈ I.
(iv) X n converges to X under (3.1) (which is a metric by the next theorem). Proof. Let a ′ be in the intersection. Since the upper (resp. lower) cone at a ′ is closed, one gets a ′ ≤ lim ǫ a Br+ǫ(o) = a Br (o) (resp. a ′ ≥ a Br(o) ). This proves the claim. Proof. It is immediate that (3.1) is a pseudo-metric. If X and Y have zero distance under (3.1), then X (r) is isomorphic to Y (r) for almost every r. As in the proof of Theorem 3.14, one can deduce that X is isomorphic to Y by the extension of König's infinity lemma to compact sets. Hence, (3.1) is a metric. Theorem 3.19 proves that the two metrics generate the same topology. Let ǫ > 0 be given and assume that X and Y have distance less than 1 2 ǫe −1/ǫ under (3.1). This implies that d c τ ′ (X (r) , Y (r) ) < ǫ 2 for some r ≥ 1 ǫ . So, Assumptions 3.10 and 3.11 imply that a ǫ (X , Y) < ǫ 2 ; i.e., d(X , Y) ≤ ǫ. This implies that every Cauchy sequence under (3.1) is also a Cauchy sequence under (3.5). This implies the claim.
For studying pre-compactness, we add the following assumption.
Assumption 3.22. Assume also that condition (i) of Remark 2.14 holds.
Lemma 3.23. For every compact X = (X, o; a), the set of X ′ such that X ′ X is compact under the metric d c τ ′ . Hence, the infimum in (3.4) is attained. Proof. Let X n := (X n , o; a n ) X . By the assumption of compactness of cones and taking a subsequence, one may assume lim X n =: X ′ (under the Hausdorff metric) and lim τ ιn (a n ) =: b ′ ≤ a exist, where ι n : X n → X is the inclusion map. Assumption 3.22 implies that b ′ = τ ι ′ (a ′ ) for some a ′ ∈ τ (X ′ ). This proves the claim. Let (X n ) n be an arbitrary sequence in A. By passing to a subsequence and a diagonal argument, one can assume that for every m ∈ N, the sequence (X for all m to obtain a Y ∈ D. In addition, Lemma 3.15 implies that X n → Y and the claim is proved.
Weaker Assumptions
There exist examples in which the cones are not compact; i.e., Assumption 3.17 does not hold (e.g., càdlàg curves in Subsection 3.7.5). Nevertheless, D is still a metric space and completeness and separability hold under the assumptions of Theorems 3.14 and 3.16. However, the forward implication in the precompactness theorem (Theorem 3.24) may fail without Assumption 3.17.
Also, Lemma 3.18 may fail. To ensure that the integral (3.1) is well defined, one may add the assumption that the curve r → a Br(o) (defined in Lemma 3.18) is continuous at almost every point (this property holds for the example of càdlàg curves). However, it is still not clear whether this metric generates the same topology as the metric (3.5) (the proof of Theorem 3.19 shows that the topology of the integral metric (3.1) is finer than that of (3.5)). The reason is that the nested closed sets in Lemma 3.20 are not necessarily compact, and hence, are not known to converge under the Hausdorff metric. If the latter is added as an assumption, then the proof of Theorem 3.19 is valid and the two metrics generate the same topology.
Fixed Underlying Space
Given a bcm S, Definition 3.5 defines a set ϕ(S) of additional structures on S. In various cases, one might be interested in considering a random element in ϕ(S) while S is fixed. Some examples are the notions of random closed sets, random measures and point processes in stochastic geometry (see also Subsection 4.1). The following topology on ϕ(S) can be used for this purpose.
Definition 3.25. Let S be a bcm and a, a 1 , a 2 , . . . ∈ ϕ(S). Define a n → a if for every o ∈ S and 0 < ǫ ≤ r, there exists a sequence (b n ) n in ϕ(S) such that b n → a B r (o) and a n B r−ǫ (o) ≤ b n ≤ a n B r+ǫ (o) (the last convergence is regarded in τ (B r+ǫ (o)) by an abuse of notation). Note that a n B r (o) does not need to converge to a Br(o) .
By fixing an arbitrary root for S, the following defines a metrization of this topology (one could also define a metric by the integral formula (3.1)). Similarly to the previous subsections, it can be seen that this is indeed a metric and ϕ(S) is complete and separable under the assumptions of Theorem 3.16. This allows one to define a random element in ϕ(S). One could also regard the latter as a random element of D by considering the map a → (S, o; a) from ϕ(S) to D, where o ∈ S is arbitrary (it can be seen that this map is continuous). This is at the cost of considering the elements of ϕ(S) up to equivalence under automorphisms of (S, o). (3.5). By Assumptions 3.10 and 3.11, it can be seen that the topology of this metric coincides with Definition 3.25.
Example 3.27. For the functor of closed subsets (resp. boundedly-finite measures), Definition 3.25 coincides with the Fell topology (resp. vague convergence) and Definition 3.26 gives a metrization of this topology.
The topology on ϕ(S) allows one to characterize convergence in D in terms of embedding into a common space as follows. This lemma does not require Assumption 3.17 of compactness of the cones.
Lemma 3.28. A sequence X n = (X n , o n ; a n ) in D converges to X = (X, o; a) if and only if there exists a bcm S and isometric embeddings f n : X n → S and f : X → S such that f n (o n ) → f (o), f n (X n ) → f (X) in the Fell topology and ϕ fn (a n ) → ϕ f (a) in ϕ(S).
Proof. Assume d(X n , X ) → 0. For each n, one can embed X n and X in a common bcm S n such that the images of o n , X n and a n are close to those of o, X and a respectively (for this, it is enough to embed two large compact portions of them and then attach the remaining parts). Then, glue S 1 , S 2 , . . . by identifying the copies of X in them. It can be seen that the resulting metric space is boundedly-compact and satisfies the claim.
Example 3.29 (Non-Compact/Infinite Marks). Fix k ∈ N. For compact X, let τ (s) (X) be the set of k-fold marked closed subsets of X (not necessarily compact) and τ (m) (X) be the set of boundedly-finite k-fold marked measures on X defined in Definition 2.29. Assuming that the mark space Ξ is boundedlycompact, then one can equip τ (s) (X) and τ (m) (X) with the Fell topology and the vague topology respectively. Note that one needs a metrization of these topologies in a functorial way (Definition 2.3). In particular, the metrics in Definition 3.26 or the integral metric (3.1) do not work since they need a root. To correct this, consider truncating marked measures/subsets to sets of the form X k × B r (ξ 0 ), where ξ 0 ∈ Ξ is fixed arbitrarily (instead of truncating to balls in X k × Ξ). Using this truncation, modify Definition 3.26 accordingly. It can be seen that these are Strassen-type metrics and make τ (s) (X) and τ (m) (X) complete and separable. In addition, τ (s) and τ (m) are functors which are pointwise-continuous and Hausdorff-continuous. Therefore, the corresponding spaces C τ (s) and C τ (m) are also complete separable metric spaces. This example will be extended to bcms in Example 3.33 (one can also modify the integral metric (3.1) similarly, but it is no longer Strassen-type and Assumption 3.10 does not hold).
Examples
Here, some examples are provided for illustrating the framework of this section. Further examples will be presented in Section 4.
Marked Measures and Marked Closed Subsets
The following example is the conclusion of the running examples 3.3, 3.4, 3.6 and 3.12. It is generalized to marked subsets/measures in the next examples. For µ ∈ τ (X) and f : Y → X, let the truncation τ t f (µ) be the inverse image (under τ f ) of µ f (Y ) k ×Ξ . Then, D is the set of pointed bcms (X, o) equipped with a k-fold marked measure ν on X such that the ground measure of ν (i.e., the projection of ν on X k ) is boundedly-finite. The results of this section imply that (3.5) is a metric and D is complete and separable.
Example 3.32 (Marked Compact Subsets). Let τ (X) be the set of k-fold marked compact subsets K of X, including the empty set. Equip τ (X) with the Hausdorff extended metric and the inclusion partial order. Define the truncation by τ t f (K) : Then, D is the set of pointed bcms (X, o) equipped with a closed subset C of X k × Ξ such that for every compact subset K ⊆ X k , C ∩ (K k × Ξ) is compact. Again, the results of this section imply that D is complete and separable.
Example 3.33. Let D be the space of pointed bcms equipped with a k-fold marked closed subset (resp. a boundedly-finite k-fold marked measure) with no restrictions. Similarly to the previous examples, if the mark space is boundedlycompact, then D can be obtained by considering the functor τ (s) (resp. τ (m) ) of non-compact marked closed subsets (resp. non-finite marked measures) defined in Example 3.29. So the results of this section imply that D is complete and separable.
Example 3.34 (Vague vs Weak convergence). Let D ′ be the space of pointed bcms equipped with a finite measure (resp. a compact subset). This is a subset of the set in Example 3.30, but here we consider the following finer topology which prevents escaping to infinity: (X n , o n ; a n ) → (X, o; a) if they can be embedded in a common bcm such that, after the embedding, a n converges to a weakly (resp. under the Hausdorff metric), X n converges to X in the Fell topology and o n converges to o (the topology of Example 3.30 uses vague convergence instead of weak convergence, see [7]). To use the framework of this section, let τ (X) be the set of pairs (µ, s), where µ is a finite measure on X and µ(X) ≤ s ∈ R (resp. (K, s) where K is a compact subset and diam(K) ≤ s). Define the truncation by truncating only the measure/subset while keeping s unchanged. The reader can verify that all of the assumptions of this section are satisfied and the corresponding space D is a Polish space which contains D ′ as a closed subspace.
Additional Point and Discrete Subset
Let D ′ be the set of doubly-pointed bcms; i.e., equipped with one additional point other than the origin. One can regard the additional point as a closed subset (or as a Dirac measure) and show that D ′ is a G δ subset of the set D of Example 3.30 (in fact, the difference of two closed subsets), and hence is Polish. The following example gives a more direct method as a basic illustration of the method of this section. It can be seen that it produces the same metric on D. One can also regard D ′ as a subset of the space in the following example. This generates the same topology on D ′ . Example 3.36 (Discrete Subsets). Let D ′′ the space of pointed bcms equipped with a discrete subset. This is a subspace of Example 3.30, but can also be obtained directly by the functor of finite subsets (Example 2.1) and all of the assumptions are satisfied except completeness. If one uses the Prokhorov metric (resp. the Hausdorff metric) between finite subsets, the completion of D ′′ is the space of pointed bcms equipped with a discrete multi-set (resp. a closed subset).
Product and Composition of Functors
Example 3.37 (Product). Let D be the space of pointed bcms (X, o) equipped with a tuple (a 1 , . . . , a n ), where each a i belongs to a set ϕ i (X). Assume each ϕ i (X) is obtained by a functor τ (i) and a truncation functor τ (i),t that satisfy the assumptions of this section. Define τ (X) := i τ (i) (X) with the max product metric (if n = ∞, use the metric (2.8)). Define the truncation functor τ t and the partial order on τ (X) element by element. It can be seen that τ and τ t satisfy all of the assumptions as well, and hence, D is complete and separable with the resulting metric.
Continuous Curves
Let I be a closed interval in R containing zero. Here, the set D ′ of pointed bcms X equipped with a continuous curve η : I → X is studied. By splitting η into two curves η I∩[0,∞) and η I∩(−∞,0] and using Example 3.37, it is enough to study the cases I = [0, T ] and I = [0, ∞).
To define a metric on D ′ , we define the truncation of curves as follows. This is in fact a modification of the method of [31] (see Subsection 4.3). A simpler method will also be discussed after the example, which can be generalized to the case where I is an arbitrary compact (or boundedly-compact) metric space. For compact X, let τ (X) be the set of continuous curves η : I → X ∪{∆} equipped with the sup (extended) metric, where ∆ is a grave as in Example 3.35. Define η ′ ≤ η when either η ′ (·) = ∆ or η ′ is obtained by stopping η at some time t 0 ∈ I; i.e., η ′ (t) = η(t ∧ t 0 ). For all f : . It can be seen that these definitions satisfy the assumptions of Subsections 3.2 and 3.3 except Hausdorff-continuity (see Subsection 2.6.4). So the corresponding set D is a complete metric space. Since compact spaces with an additional structure are dense in D, separability of D is implied by separability in the compact case (Subsection 2.6.4). By Definition 3.8, it can be seen that D is the set of pointed bcms (X, o) with a continuous curve η in X ∪ {∆} such that either (1) η is defined on the entire of [0, T ] or (2) η is defined on some interval [0, T ′ ) ⊆ [0, T ] and exits any compact subset of X before time T ′ . One can see that D ′ is an open subset of the Polish space D, and hence, is D ′ is Polish.
Example 3.40. Let I := [0, ∞) and define D ′ , the set τ (X), the partial order and the truncations similarly to the previous example. The metric on τ (X) should be carefully chosen to ensure that Assumption 3.11 holds. A suitable metric on τ (X) is the following, which is a Strassen-type metric: It is left to the reader that τ satisfies the assumptions of this section except Hausdorff-continuity. Similarly to the previous example, it can be seen that the corresponding set D is a complete separable metric space and D ′ is a G δ subset of D (the cases where the curve does not explode until time N is open in D), and hence D ′ is Polish.
Another method to define a metric on D ′ is by regarding curves as marked closed subsets similarly to Subsection 2.6.4. Similarly to the proofs of Propositions 2.25 and 2.33, one can prove the following. Proposition 3.41. Let I = [0, T ] (resp. I = [0, ∞)). By regarding curves as marked closed subsets, D ′ is an open (resp. G δ ) subset of the Polish space in Example 3.32 (resp. Example 3.33), and hence, D ′ is Polish. In addition, the topology on D ′ coincides with the induced topology.
Càdlàg Curves
Let D ′ be the set of tuples X = (X, η), where X is a bcm and η : I → X is a càdlàg curve, where I := [0, T ] is a compact interval. We show that D ′ is not complete but it is still a Polish space. This is an example where cones are not compact, but the weaker assumptions in Subsection 3.5 are satisfied.
Example 3.42. For compact X, let τ (X) be the set of càdlàg curves η : I → X ∪ {∆} (where ∆ is a grave as in Example 3.35), such that η −1 (∆) is either the empty set or an interval of the form [T η , T ]. For η, η ′ ∈ τ (X), define η ≤ η ′ if ∀t < T η : η(t) = η ′ (t); i.e., η is obtained by killing η ′ at time T η . For all isometric embeddings f : X → Y and η ∈ τ (X), let τ f (η) := f • η ∈ τ (Y ). Also, for η ′ ∈ τ (Y ), let the truncation τ t f (η ′ ) be f −1 • η ′ killed at the first exit time of η ′ from f (X) (note that if η ′ (0) ∈ f (X), then τ t f (η ′ )(·) = ∆). The set τ (X) is a closed subset of the set of càdlàg curves in X ∪ {∆} endowed with the Skorokhod metric (which is an extended metric here). So τ (X) is a complete separable extended metric space. It is left to the reader to show that τ and τ t satisfy all of the assumptions of this section except Assumption 3.17; e.g., if η is not continuous on [0, T η ), then the lower cone of η is not compact. However, since τ is both pointwise-continuous and Hausdorff-continuous (see Subsection 2.6.5), the results of this section imply that the corresponding set D is a complete separable metric space. The set D is larger than D ′ as described below. When X is not compact, an additional structure on X (Definition 3.5) is a function η : I → X ∪ {∆} such that either (1) η is càdlàg and is killed at the first hitting to ∆ or (2) . then h has no right limit at r = 1. However, in the general case, it can be seen that h is continuous except at countably many points (r is a continuity point if ∂B r (o) does not contain any jump points or local maximum of distance from o). It can be seen that the weaker assumptions in Subsection 3.5 hold, and hence, the convergence result (Theorem 3.19) is valid. In addition, the pre-compactness result (Theorem 3.24) fails in this example. For instance, for n ≥ 1, let η n (t) := t when 0 ≤ t < 1 and η n (t) := t + 1 − 1/n when 1 ≤ t ≤ T . Then, X n := (R, 0, η n ) is convergent, but X (2) n is not precompact.
Example 3.44. For the case I := [0, ∞), similar arguments can be applied, but the metric on τ (X) should be carefully chosen to ensure that Assumption 3.11 holds. A suitable metric on τ (X) is the following, which has the same idea as (3.5) and generates the same topology as the Skorokhod metric (Section 16 of [12]): If kill t0 (η) denotes η killed at time t 0 , let where d S denotes the Skorokhod metric defined by the same equation (12.16) of [12]. Then, define the distance of η and η ′ by a formula similar to (3.5). It can be seen that this is a metric on τ (X) and satisfies the assumptions of this section and the weaker assumptions of Subsection 3.5, except compactness of cones. So the claims of Example 3.42 hold also in the case I = [0, ∞). Similar results can also be obtained for the case I = R.
Further Examples and Connections to Other Notions
In this section, some Gromov-Hausdorff-type metrics in the literature are discussed and it is shown how they can be considered as special cases of the general framework of this paper. In addition, some new examples of the framework are provided; e.g., in Subsections 4.7 and 4.10.
Random Objects in Stochastic Geometry
According to Subsection 3.6, the notions of random measures and random closed sets on a fixed space are special cases of the framework of Section 3, when the underlying space S is boundedly-compact (in stochastic geometry, one can also assume that S is a locally-compact second-countable Hausdorff topological space). By Example 3.36, the same holds for point processes, which are random discrete (multi-) subsets of S. The framework covers some other notions in stochastic geometry as follows. For instance, a marked random measure on S is defined in the literature as a random measure on S × Ξ. Sometimes, it is assumed that the ground measure; i.e., the projection of the measure onto S, is a boundedly-finite. So, this notion is the case k = 1 of k-fold marked measures in Subsection 3.7.1. Also, the notion of marked point processes is a special case of marked random measures defined similarly (one can use the framework directly as well, similarly to Example 3.36). The notion of particle processes will be discussed in Subsection 4.6. Additionally, Examples 3.32 and 3.33 allow one to define marked random closed subsets of S. As mentioned in Subsection 3.6, all of these notions in stochastic geometry can be extended to the case where the base space S is a random pointed bcm, at the cost of considering them up to automorphisms of the base space.
Graphs, Networks and Discrete Spaces
The edges of a graph can be represented as a marking of the pairs of vertices. Therefore, with the graph-distance metric, graphs can be regarded as a metric space equipped with a 2-fold marked closed subset. It can be seen that the corresponding topology (Example 3.32) extends the Benjamini-Schramm convergence of rooted graphs [11]. The same holds for local weak convergence of networks [4], where a network is a graph with an additional marking of vertices and edges. For local weak convergence of doubly-rooted graphs and networks, one can use product of functors (see Examples 3.32, 3.35 and 3.38) and the same claim holds.
In [9], a complete metric is defined on the space of marked discrete metric spaces. When there is no marks, by equipping every discrete space with the corresponding counting measure, this is a special case of the metrization of the GHP metric ( [1], [32] and Example 3.6 above). The marked case is also a special case of the case where the additional structure is a measure and a marked closed subset, which can be obtained by a product of functors.
The Gromov-Hausdorff-Prokhorov-Uniform Metric
The GHPu metric is defined in [31] on the space M u of compact metric spaces X equipped with a finite measure µ on X and a continuous curve η : R → X that is convergent as t → ∞ and t → −∞. It is also proved that M u is complete and separable. This can be expressed in the framework of this paper. Indeed, this is just the product of the functors of measures (Example 2.18) and curves (a slight generalization of Subsection 2.6.4).
In addition, using a specific formula to truncate curves, [31] studies the space M u ∞ of complete locally-compact length spaces X together with a locally finite measure µ on X and a continuous curve η : R → X pointed at the distinguished point η(0). However, despite the claim of [31], M u ∞ is not complete. This issue will be resolved below.
To express M u ∞ in the framework of this paper, one can use the product of the functors of measures (Example 3.30) and curves (Subsection 3.7.4). The truncation in Subsection 3.7.4 is slightly different from that of [31] (the latter depends on the radius of the ball), but the resulting topology on M u ∞ coincides with that of [31]. Note that Subsection 3.7.4 adds the curves in X that are defined on an open interval or half-line containing 0 and blow up at the end points (this is necessary for completeness). Similarly to Proposition 3.41, M u ∞ is a G δ subset of the corresponding space D, which is a Polish space. Hence, M u ∞ is Polish (it is complete with another metric). The above discussion generalizes the approach of [31] in several aspects. First, the spaces are not limited to length spaces and the curves do not necessarily start at the root. Also, curves can be generalized to continuous functions from a given space to X. In addition, a simpler method to define a metric is discussed in Subsections 2.6.4 and 3.7.4 by regarding (the graphs of) curves as marked closed subsets.
Spatial Trees
Let Ξ be a complete separable metric space and T be the set of pairs (X, ϕ), where X is a compact metric spaces and ϕ ∈ C(X, Ξ) is a continuous function from X to Ξ. Consider the following distance function on T : where the infimum is over all correspondences R of X and Y and dis(R) is the distortion of R (see Subsection 2.7). This distance function is defined in [18] for the case of spatial trees; i.e., when X and Y are real trees (except that the ∨ in the formula is a + in [18] and the coefficients are slightly different, which are unimportant changes). It is claimed in [18] that 'it is easy to verify that T is a Polish space'. However, as observed in [15] and [10], T is not complete. The results of [10] imply that T is separable. Here, we prove the following.
Proposition 4.1. The space T is a G δ subspace of some complete separable metric space, and hence, T is a Polish space (i.e., it is complete under another metric that generates the same topology).
Proof. Note that C(X, Ξ) is not a functor since continuous functions cannot be pushed forward under isometric embeddings naturally. However, one can identify an element ϕ ∈ C(X, Ξ) with its graph gr ϕ ⊆ X × Ξ and regard it as a simple marked closed subset defined in Example 2.32. Also, the metrics are identical; indeed, the Strassen-type results mentioned in Subsection 2.7 imply that (4.1) can be rewritten as where the infimum is over all metric spaces Z and isometric embeddings f : ξ). Hence, the metric (4.1) is identical to the metric for marked closed subsets and T is a subspace of the space C τ corresponding to simple marked compact subsets (see Proposition 2.33). Since C τ is Polish (it is a G δ subspace of some Polish space by Proposition 2.33) and T is closed in C τ , one obtains that T is also Polish and the claim is proved.
To avoid the issue of non-completeness of T , [14] uses another approach by restricting attention to the subspace T ′ of spatial trees (X, ϕ) in which ϕ is little α-Holder. Then, a metric is defined on T ′ by adding to (4.1) a term addressing the Holder property 4 (Equation (2.5) of [14]). It is proved that T ′ is complete and separable. Similarly to the above proposition, it can be shown that this metric is also a special case of the framework of Section 2 written in a Strassen-type form, and also Polishness follows from the results of Section 2.
The paper [10] studies the set T ′′ of measured rooted spatial trees and shows that T ′′ is a separable (non-complete) metric space. The issue of noncompleteness can be resolved as follows. First, one can rewrite the metric of [10] in the form of (2.4), where the additional structure is a tuple of a point, a measure and a 1-fold marked compact subset. Similarly to the above proposition, T ′′ is a G δ subspace of the resulting Polish space, and hence, T ′′ is also Polish.
Measured rooted spatial trees are also extended in [10] to the case of locallycompact length spaces. This extension is by the same method as [1] with the difference that the resulting metric space is not complete. This issue can be resolved by proving Polishness similarly to the above discussion using the results of Section 3 (see Example 3.32). 4 In fact, [14] assumes that ϕ is a proper function as well (this matters only when X is not compact) and adds another term to (4.1) addressing this property. We omitted this because it is not needed for having Polishness and some modification is needed to represent it in the framework of this paper.
The Spectral Gromov-Hausdorff Metric
Let I ⊂ R be a fixed compact interval. The paper [15] considers the set T of tuples (X, π, q), where X is a compact metric spaces, π is a Borel probability measure on X and q ∈ C(X × X × I, R). A metric on this space is defined in [15] using both isometric embeddings and correspondences and it is shown that a separable (non-complete) metric space is obtained. This metric is called the spectral Gromov-Hausdorff metric in [15]. It is shown below that this is a special case of the framework of Section 2 and, in addition, the issue of non-completeness is resolved.
Note that C(X × X × I, R) is not a functor similarly to the previous subsection. However, the elements of C(X × X × I, R) can be regarded as continuous functions from X × X to Ξ and vice versa, where Ξ := C(I, R) is equipped with the sup metric. The graph of such a function is a simple 2-fold marked compact subset (Example 2.32). So, T is identified with a subset of C τ , where τ is the product of the functor of 2-fold marked compact subsets and the functor of measures. In addition, by the Strassen-type results of Subsection 2.7, one can deduce that the metrics on T and C τ are identical. Now, similarly to the previous subsection, it can be seen that T is a G δ subspace of the Polish space C τ , and hence, T is Polish (it is complete with another metric). This resolves the issue of non-completeness of the metric in [15].
Particle Processes
Roughly speaking, a particle process in a bcm S is a random discrete collection of compact subsets of S. More precisely, let K(S) be the set of nonempty compact subsets of S equipped with the Hausdorff metric. Let ϕ 1 (S) be the set of discrete subsets A of K(S); equivalently, every compact subset of S should contain only finitely many elements of A. It is usually required that every compact subset of S intersects only finitely many elements of A. Let ϕ 0 (S) be the set of such subsets of K(S). Then, a particle process in S is a a random element of ϕ 0 (S). See e.g., [41] for more details. The discussion below allows one to define a particle process in a random environment as well.
To apply the framework, let D 0 (resp. D 1 ) be the space of pointed bcms (S, o) equipped with some a ∈ ϕ 0 (S) (resp. a ∈ ϕ 1 (S)). For all compact metric spaces X, let τ (X) be the set of finite subsets of K(X) equipped with the inclusion partial order and the Prokhorov metric. Then, a truncation functor τ t is defined as follows: For every isometric embedding f : Y → X and a ∈ τ (X), Note that this definition of the pair τ and τ t is exactly the composition of the two functors of compact subsets and finite subsets (Example 3.38). Therefore, all of the assumptions of Section 3 are satisfied except that τ (X) is not complete (verification of Assumptions 3.10 and 3.11 should be done separately and is left to the reader). In addition, the extension defined in Definition 3.5 coincides with ϕ 1 . So, (3.5) defines a metric on D = D 1 which makes it separable.
The completion of D 1 is the space D 2 of pointed bcms (S, o) equipped with a discrete multi-set in K(S). One can proceed similarly to show that D 2 is a Polish space. Also, it can be seen that D 2 contains D 1 and D 0 as Borel subsets. This allows one to define random elements in D 0 or D 1 , as desired. One could also equip τ (X) with the Hausdorff metric, but the topology would become coarser. Here, the completion of τ (X) is K(K(X)) ∪ {∅}, which is a composition of two functors as in Example 3.38 and satisfies all of the assumptions. Also, the completion of D 1 is the space of pointed bcms (X, o) equipped with a closed subset of K(X).
Processes of Closed Subsets and Measures
For a metric space S, let F (S) (resp. K(S)) denote the set of closed (resp. compact and nonempty) subsets of S.
Point Processes of Closed Subsets
Given a bcm S, a point process in F (S) \ {∅} can be called a point process of closed subsets of S. Examples of such processes are line processes and hyperplane processes in R d (see e.g., [41]). Here, it is shown that this gives an instance of the framework of Section 3. As before, this allows one to let (S, o) be random as well.
Let D 0 be the space of pointed bcms S equipped with a discrete subset of F (S) \ {∅}. To use the framework, for compact X, let τ (X) be the set of finite multi-sets in K(X) equipped with the Prokhorov metric. This is just the functor τ 2 in Subsection 4.6, but the following truncation functor and partial order make the story different. For every isometric embedding f : Y → X and a ∈ τ (X), let τ t f (a) := {f −1 (K) : K ∈ a, K ∩ f (Y ) = ∅}. Also, for a, a ′ ∈ τ (X), define a ′ ≤ a if there exists an injective function h : a ′ → a such that ∀K ∈ a ′ : K ⊆ h(K). It can be seen that these definitions satisfy the assumptions of Section 3. The difficult part is to prove assumptions 3.10 and 3.11, but the proofs are omitted since they are identical to the proof of Lemma 4.4 below, except that all measures in the proof should be integer-valued (see Corollary 2.3 of [32] for the integer-valued version of the generalized Strassen's theorem). Therefore, the results of Section 3 imply that the corresponding space D is complete and separable.
Here, D is the space of pointed bcms S equipped with a discrete multi-set in F (S) \ {∅}. It can be seen that D contains D 0 as a Borel subset. This enables one to define a (simple or non-simple) point process of closed subsets in a random environment.
Remark 4.2. The use of multi-sets is necessary due to the nature of the truncation functor. Also, one cannot equip τ (X) with the Hausdorff metric since Assumption 3.10 would not hold.
Closed Subsets of Closed Subsets
For compact X, let τ 0 (X) := K(K(X)). Note that τ 0 is a composition of functors as in Subsection 2.6.6. So the corresponding metric space C τ0 is complete and separable. This allows one to define a random compact metric space X equipped with a random element in K(K(X)). The same hold for the functor K(τ (s) (X)).
For bcms, composition of functors (Example 3.38) gives ϕ(X) = F (K(X)) as mentioned in Subsection 4.6. Here, we would like to use a different truncation to obtain the space D 0 of pointed bcms (X, o) equipped with a closed subset of F (X) \ {∅}. Unfortunately, it seems that D 0 cannot be obtained by the framework of Section 3 5 . In the following, we use the framework for a specific subset of D 0 .
For compact X, let τ (X) be the set of elements a ∈ F (K(X)) which are lower sets; i.e., for every K ∈ a, every closed subset of K belongs to a. Equip τ (X) with the Hausdorff extended metric and the inclusion partial order. For every isometric embedding f : Y → X, define the truncation by τ t f (a) := {f −1 (K) : K ∈ a} \ {∅}. It is easy to see that all of the assumptions of Section 3 are satisfied. For brevity, we only prove the following. Proof. Assume f : X ⊆ a X (if one regards a ′ X as an element of τ (X) by an abuse of notation). Let Y ′ := N ǫ (X) ∩ Y and a ′ Y := {K ∈ a Y : ∃K ′ ∈ a ′ X : d H (f (K ′ ), g(K)) ≤ ǫ}. It is easy to see that a ′ Y is in τ (Y ′ ) and satisfies the assumptions.
Here, D is the space of pointed bcms (X, o) equipped with a lower set a ∈ F (F (X) \ {∅}). So the results of Section 3 define a metric on D which make it a complete separable metric space.
Measures on Closed Subsets
Here, we define a complete metric on the space D f (resp. D lf ) of pointed bcms X equipped with a finite measure on F (X) (resp. a measure on F (X) \ {∅} that is finite on compact subsets of F (X) \ {∅}). For compact X, let τ (X) := M f (K(X)), where M f (·) denotes the set of finite Borel measures. For g : Y → X and a ∈ τ (X), define the truncation of a as follows. Let L := {K ∈ K(X) : K ∩ g(Y ) = ∅} and let τ t g (a) be the push-forward of a L under the function K → g −1 (K), which is a function from L to K(Y ). Let the partial order on τ (X) be a ′ a if there exists a Borel measure α on K(X) 2 supported on {(K 1 , K 2 ) : K 1 ⊆ K 2 } such that π 1 * α = a ′ and π 2 * α ≤ a, where π i denotes the projection onto the i'th component. These definitions are different from the composition of functors in Example 3.38. The following lemma proves that they satisfy Assumptions 3.10 and 3.11. It is easy to verify the rest of the assumptions of Section 3 and to see that D = D lf . Therefore, the results of Section 3 define a metric on D lf that make it a complete separable metric space.
For Assumption 3.11, one should modify the above construction as follows.
Two-Level Measures and Measures on τ 0 (X)
In [37], it is shown that the set of compact metric spaces X equipped with a two-level measure; i.e., a finite measure on the set of finite measures on X, is a Polish space. The metric considered in [37] (Definition 4.1 of [37]) is a GPtype metric. If one considers a GHP-type metric in a similar manner, then the result will be identical to the composition functor τ (X) := M f (M f (X)) and Polishness is implied by Subsection 2.6.6. Note that M f (X) is not compact, but one can still use Remark 2.28 for the composition.
One should be careful for extending this to bcms. The composition of functors in Example 3.38 does not work here, since Assumption 3.10 is not satisfied. The reason is that a small perturbation of a measure might change the support of the measure significantly. If it would have worked, then ϕ(X) would be the set of measures on the set of compactly-supported measures on X (with a specific locally-finiteness condition). It is not clear whether the integral formula (3.1) is useful in this case or not.
To extend to bcms, one can change the partial order and the truncation maps according to the general construction in Example 4.5 below. Then, when X is boundedly-compact, ϕ(X) = M f (M bf (X)), where M bf (X) is the set of boundedly-finite measures on X. In addition, all assumptions are satisfied and the corresponding space D is complete and separable.
Example 4.5 (Measures on τ 0 (X)). Let τ 0 and τ t 0 be functors that satisfy the assumptions of Section 3. Let τ (X) := M f (τ 0 (X)) (or the set of probability measures on τ 0 (X)) equipped with the Prokhorov metric. This is useful for comparing two metric spaces equipped with random additional structure (e.g., in Subsection 4.9). Define the partial order on τ (X) by a 1 a 2 when there is a coupling of a 1 and a 2 supported on {(K 1 , K 2 ) ∈ τ 0 (X) 2 : K 1 ≤ K 2 }. For an isometry g : Y → X and a ∈ τ (X), define the truncation τ t g (a) to be the pushforward of a under the map (τ t 0 ) g : τ 0 (X) → τ 0 (Y ), which makes sense by assuming the following (note that these definitions are different from the composition of functors in Example 3.38).
Assumption 4.6. Assume the following further conditions: (i) τ 0 (X) is always separable, (ii) The relation ≤ is a closed subset of τ 0 (X) 2 , (iii) the truncation maps (τ t 0 ) g are Borel measurable and (iv) the choice of Y ′ in Assumptions 3.10 and 3.11 can be done as a Borel measurable function of X ′ . Proposition 4.7. In Example 4.5, all of the assumptions of Section 3 are satisfied. For a bcm X, the set of additional structures is ϕ(X) = M f (ϕ 0 (X)). Hence, under the assumptions of Theorem 3.16, the corresponding space D is a metric space and is Polish.
This result can be proved similarly to Subsection 4.7.3. Here, we only prove the following lemma and the rest is skipped. Proof. The proof is almost identical to that of Lemma 4.4. Here, we only highlight the differences for brevity. Here, α is a coupling of a ′ and a. Hence, the situation is simpler: π 2 * α = a, a 1 = π 1 * β and β 1 = β. The measure γ is almost supported on the set R of tuples (K 1 , K 2 , K 3 ) ∈ τ 0 (Z) 3 such that K 1 ∈ τ 0 (X ′ ), K 1 ≤ K 2 and d(K 2 , K 3 ) ≤ ǫ. In addition, if a B r (o) ≤ a ′ , one might add the condition K 2 Br(o) ≤ K 1 (this is because α induces a coupling of a Br(o) = a ′ Br (o) and itself that is supported on {(K 1 , K 2 ) : K 1 ≤ K 2 }, and hence, Lemma 4.9 below implies that the latter is the trivial coupling).
To define the map m on R, one needs to use Assumption 4.6 to find K 4 := m(K 1 , K 2 , K 3 ) ≤ K 3 such that K 4 ∈ τ 0 (Y ′ ) and d(K 1 , K 4 ) ≤ d(K 2 , K 3 ) ≤ ǫ. In addition, if K 2 Br (o) ≤ K 1 , then K 3 Br−2ǫ(o) ≤ K 4 . The rest of the proof is identical to that of Lemma 4.4. Lemma 4.9. Let E be a separable metric space and ≤ be a partial order on E which is a closed subset of E 2 . Assume X and Y are random elements of E that have the same distribution and X ≤ Y a.s. Then, X = Y a.s.
Proof. If A is a Borel lower set in E, then P [X ∈ A] ≥ P [Y ∈ A] = P [X ∈ A]. So, P [X ∈ A, Y ∈ A] = 0. Therefore, it is enough to find countably many closed lower sets in E that separate every pair e 1 < e 2 . Let x 1 , x 2 , . . . be a countable dense set in E. Let A m,n be the closure of the set of elements below B 1/n (x m ). Let e 1 < e 2 be an arbitrary pair. For every n, find m = m(n) such that d(e 1 , x m ) ≤ 1/n. It is easy to deduce that one of these sets A m(n),n separates e 1 and e 2 (otherwise, one finds sequences f n ≤ g n such that f n → e 2 and g n → e 1 , which contradicts closedness of the relation). This completes the proof.
Isometries
In this subsection, we apply the framework to metric spaces equipped with an isometry or a group of isometries.
Convergence of Isometries
Gromov defined convergence of pointed bcms (X, o) equipped with an isometry h : X → X (Section 6 of [28]). This is used to prove that the Gromov-Hausdorff limit of a sequence of homogeneous spaces (i.e., the isometry group acts transitively) is homogeneous. Note that the set ϕ(X) of such isometries is not a functor, since an isometric embedding f : X → Y does not induce a natural map from ϕ(X) to ϕ(Y ). However, by identifying every isometry h with its graph, which is a closed subset of X × X, isometries are special cases of 2-fold marked closed subsets. This way, it can be seen that the notion of convergence is the same as that of Example 3.31. In addition, Example 3.31 provides a complete metrization of Gromov's notion of convergence.
Equivariant Hausdorff Convergence
Fukaya [23] defined a metric on the space T of triples (X, Γ, p), where (X, p) is a pointed bcm and Γ is a closed subgroup of the isometries of X. This is called the equivariant Hausdorff distance in [23]. For brevity, we only mention the notion of convergence in T in an equivalent form (after some correction 6 ) and show that this convergence is a special case of the framework of this paper. In addition, a completeness and separability result for T is obtained.
Let X n := (X n , Γ n , p n ) be a sequence in T . Call (X n ) n convergent to X := (X, Γ, p) if and only if they can be isometrically embedded in a common bcm Z such that, after the embedding, (i) p n converges to p, (ii) X n converges to X in the Fell topology, (iii) For every ǫ > 0, for large enough n and every γ n ∈ Γ n , the graph of γ n (regarded as a closed subset of Z 2 ) is ǫ-close to the graph of some γ ∈ Γ in some metrization of the Fell topology (e.g., (3.1) or Example 3.27) and (iv) the same holds by swapping X n and X. The last two conditions can be summarized as d H (Γ n , Γ) → 0, where Γ n and Γ are regarded as closed subsets of F (Z 2 ); i.e., Γ n is close to Γ as elements in τ 0 (Z) := K(F (Z 2 )). It is good to mention that for compact metric spaces, a stronger notion of convergence is obtained by requiring Z to be compact and by equipping F (Z 2 ) with the Hausdorff metric.
To express this convergence in the framework of this paper, we proceed similarly to Subsection 4.7.2. As mentioned therein, we need to focus on the set τ (Z) of closed lower sets in F (Z 2 ), which is smaller than τ 0 (Z). Similarly to Subsection 4.7.2, one can define the truncation and partial order and show that the corresponding space D is complete and separable. Now, for X n and X mentioned above, define a := γ∈Γn F (gr(γ)) ∈ τ (X), where gr(γ) ⊆ X 2 is the graph of γ. Note that a is a closed lower set in F (X 2 ). Define a n ∈ τ (X n ) similarly.
Theorem 4.10. (X n , Γ n , p n ) converges to (X, Γ, p) in the equivariant Hausdorff metric if and only if (X n , p n ; a n ) converges to (X, p; a) in D. In addition, the space T is complete and separable under the metric induced from D.
Sketch of the proof. Assume X n → X in T . The definition of convergence in T , mentioned above, implies that X ′ n := (X n , p n ; a n ) converges to X ′ := (X, p; a) in D. Conversely, assume X ′ n → X ′ . By Lemma 3.28, one can assume that X n and X are subsets of a common bcm Z such that p n → p, X n → X in the Fell topology and a n → a as elements in τ (Z). So, for large n, the graph of every γ n ∈ Γ n is close to some subset S of the graph of some γ ∈ Γ. One has S = gr(γ D ) for some D ⊆ X. Since γ n is defined on the whole X n and X n is close to X, one obtains that D is close to X in the Fell topology. This implies that γ n is close to γ as well. Similarly, every γ ∈ Γ is close to some γ n ∈ Γ n . Therefore, X n → X in T . The second part of the claim is also implied by the fact that T is a closed subset of D, which is straightforward to prove.
Convergence of Metric G-Spaces
Given a group G, let G 1 be the space of pointed bcms (X, o) equipped with an action of G on X by isometries, which are called metric G-spaces. If G is a σ-compact topological group, define G 2 similarly by considering only continuous actions. The papers [25] and [40] define a metric on G 1 and a topology on G 2 respectively. In what follows, after some correction, 7 the topologies on G 1 and G 2 are expressed in the framework of this paper. Let X n := (X n , o n ; π n ), where π n is an action of G on X n by isometries. As in Subsection 4.8.1, we identify every isometry of X with its graph, which is a closed subset of X 2 . Then, π n can be regarded as a function from G to F (X 2 n ). It can be seen that X n converges to X := (X, o; π) in the sense of [25] (resp. [40]) if and only if they can be embedded in a common bcm Z such that, after the embedding, o n → o, X n → X in the Fell topology and π n → π uniformly (resp. uniformly on compact subsets of G). In the latter, π n and π are regarded as functions from G to F (Z 2 ) and the space F (Z 2 ) is equipped with the metrization of the Fell topology in Example 3.27 (note that the choice of any root in Example 3.27 leads to the same notion of convergence here).
To use the framework of this paper, when X is compact, let τ (X) be the set of functions from G to F (X 2 ) equipped with the sup metric (equip F (X 2 ) with the Hausdorff extended metric). If a : G → F (X 2 ) and f : Y → X, define the truncation of a by truncating the sets a(g) separately for all g ∈ G (note that the truncation of an isometry of X is not necessarily an isometry of Y ). Also, define the partial order on τ (X) by a 1 ≤ a 2 if and only if ∀g ∈ G : a 1 (g) ⊆ a 2 (g). It can be seen that the assumptions of Section 3 are satisfied except separability of τ (X) and compactness of the cones. Also, the extension ϕ(X) to bcms X is the set of functions from G to F (X 2 ) and the topology on ϕ(X) is that of uniform convergence w.r.t. the metrization of the Fell topology in Example 3.27. Therefore, Lemma 2.23 implies that the topology of G 1 is just the restriction of the topology of the corresponding metric space D.
For G 2 , one can proceed similarly by equipping τ (X) with a suitable metrization of uniform convergence on compact subsets of G. For instance, let G 1 ⊆ G 2 ⊆ · · · be an exhaustion of G by compact subsets. For (not necessarily continuous) functions π i : G → F (X 2 ) (i = 1, 2), let d(π 1 , π 2 ) := inf{ǫ ≤ 1 : d sup (π 1 G ⌊1/ǫ⌋ , π 2 G ⌊1/ǫ⌋ ) ≤ ǫ} similarly to (3.6). Similar claims hold and the corresponding space D extends G 2 and its topology. However, it is not clear whether G 1 and G 2 are separable (note that we cannot restrict attention to continuous functions π in the above approach, since the truncation of a continuous function is not necessarily continuous).
Càdlàg Curves and Processes
Let X n be a metric space and η n be a càdlàg curve in X n . In Definition 1.3 of [8], it is said that (X n , η n ) converges to (X, η) if they can be embedded in a common metric space such that the images of the curves η n converges to the image of η in the Skorokhod metric. If η n is a random curve in X n , a similar notion is defined by requiring that the images of the random curves converge weakly. This is used in [8] for studying limits of random walks on trees. However, [8] does not define a metrization of this notion of convergence.
Here, we concentrate on bcms and we add the natural condition that the image of X n converges to the image of X after embedding in the common metric space. Also, we consider η(0) as the root. For deterministic curves, this notion of convergence is the same as that of Subsection 3.7.5 (see Lemma 3.28). The case of random càdlàg curves is also obtained by composition with the functor of measures, which is discussed in Example 4.5 (verification of Assumption 4.6 is skipped). Therefore, the framework of Section 3 provides a metrization of these notions of convergence. Note that these metrizations are not complete (the completion can be obtained by adding curves that blow up at a finite time) but the space is still Polish, as explained in Subsection 3.7.5. If one restricts attention to compact metric spaces only, then one can use the simpler setting of Section 2 (discussed in Subsection 2.6.5) and the metrization is complete.
Ends
Ends are defined in [22] for all topological spaces and graphs and, heuristically, are the points at infinity. For simplicity, we only consider the class L of bcms X such that X is either a simple connected graph (equipped with the graph distance metric) or it is locally-connected . In this case, given a point o of X, an end ξ of X can be uniquely described by a sequence of closed sets ξ 1 ⊇ ξ 2 ⊇ · · · , where ξ n is a connected component of X \ B n (o) for each n, where B n (o) is the open ball of radius n centered at o. So the set L of (equivalence classes of) tuples (X, o, ξ), where X ∈ L, o ∈ X and ξ is an end of X, can be regarded as a subset of the space D defined in Section 3. Here, the additional structure is a sequence of closed subsets (see Example 3.37). It can be seen that L is a closed subset of D. Therefore, the metric on D can be used to make L a Polish space. This allows one to define random metric spaces equipped with an end. A similar idea can be used to define random metric spaces equipped with a closed subset of ends, which is skipped here. | 35,245 | 2018-12-10T00:00:00.000 | [
"Mathematics"
] |
Dark Sector Glueballs at the LHC
We study confining dark sectors where the lightest hadrons are glueballs. Such models can provide viable dark matter candidates and appear in some neutral naturalness scenarios. In this work, we introduce a new phenomenological model of dark glueball hadronization inspired by the Lund string model. This enables us to make realistic predictions for dark glueball phenomenology at the LHC for the first time. Our model reproduces the expected thermal distribution of hadron species as an emergent consequence of hadronization dynamics. The ability to predict the production of glueball states heavier than the lightest species significantly expands the reach of long-lived glueball searches in MATHUSLA compared to previous simplified estimates. We also characterize regions of parameter space where emerging and/or semivisible jets could arise from pure-glue dark sectors, thereby providing new benchmark models that motivate searches for these signatures.
Previous collider studies have been limited by the absence of dedicated simulation tools for dark glueball production.Pythia's Hidden Valley module [79,80] is the current state-of-the-art in simulating strongly-coupled dark sector hadronization, but it does not accommodate the qualitatively different pure-glue (N f = 0) case.Recently, the Python module GlueShower [81] was created to address this gap.This package implemented a perturbative gluon shower and exploited only energy conservation and the large pure-glue mass-gap to parameterize the unknown details of glueball hadronization.While this enabled the first quantitative studies including the effects of the shower and multiple glueball species [71], the lack of any realistic hadronization dynamics resulted in very large uncertainties for exclusive quantities, like the production of specific glueball species, that can strongly influence collider signals.
In this work, we present a more sophisticated glueball hadronization model, based on applying Lund string dynamics [82] to the pure-glue regime, and implement it in a customized version of Pythia 8 [83].This enables more theoretically robust collider studies with improved uncertainties compared to the earlier GlueShower approach. 1e find that our hadronization algorithm dynamically realizes certain theoretically expected features, such as the thermal distribution of produced glueball species.These results suggest that the most important pure-glue hadronization dynamics may be captured by our approach.
We apply this implementation of dark glueball hadronization to classify the phenomenology across the parameter space of two specific models, determining which regions could possibly be probed by future emerging or semivisible jet searches.We consider applications to long-lived particle (LLP) searches and semivisible/emerging jet searches.In particular, we update the predicted signal at the proposed MATH-USLA LLP detector [84][85][86] of dark glueballs produced in exotic Higgs decays in Sec.4.1.Compared to earlier estimates based on two-body Higgs decays [44,87], our dark shower and hadronization dynamics lead to a dramatically expanded reach estimate, as the production of various glueball species with different lifetimes generates signals in different parts of parameter space.
Semivisible jets and emerging jets have become targets for LHC searches, see [19,20] and [22,23] respectively.This motivates developing consistent benchmark models that can serve as reference points for designing experimental analyses.In Sec.4.2, we show how glueball production can also realize both signatures and elucidate some properties of the resulting signals.In particular, the parameter r inv (which characterizes the collider-stable component of semivisible jets) can be predicted as a distribution, and we provide a number of examples in the results presented below.
The rest of this paper is structured as follows.We introduce the hadronization model in Sec. 2, first reviewing the Lund string model in Sec.2.1 and then showing our modifications of this approach for pure-glue hadronization in Sec.2.2 (further discussion is provided in App.A).We demonstrate that the expected thermal distribution of glueball species dynamically emerges in Sec.2.3.We provide benchmark values of the hadronization model parameters in Sec.2.4, which span a range of outputs representative of theoretical uncertainties from unknown hadronization details.In Sec. 3, we introduce glueball production and decay mechanisms through the Higgs portal that are relevant for collider signals.We then apply our glueball production and decay simulations to two phenomenology studies: glueball LLP decays in the proposed MATHUSLA experiment in Sec.4.1 and semivisible/emerging jet signatures in Sec.4.2.We conclude in Sec. 5.In App.B, we elaborate on the glueball species and momentum variations from our suggested benchmark parameters.A few additional distributions of interest for the semivisible jet scenario are provided in App. C.
Glueball Hadronization
The non-perturbative nature of hadronization necessitates introducing phenomenological models to make predictions for the collider signatures of confining sectors.This approach has a long history going back to Field and Feynman's "independent fragmentation" [88], where the model is simply that individual quarks fragment into the mesons making up a jet.The modern Monte Carlo event generator Pythia uses the "Lund string model" [82] (described below), while its contemporaries Herwig [89] and Sherpa [90] each use versions of "cluster hadronization" [91,92], where color-singlet clusters of partons that are close together in phase space decay into hadrons.Hadronization models introduce phenomenological nuisance parameters.
For SM QCD, one can perform elaborate tunes to data to constrain these parameters.Of course, we do not have the luxury of data to fit these parameters for a dark sector.Fortunately, as we show in Sec. 4, the observables of interest here are only moderately sensitive to the nuisance parameters.Developing theoretical predictions with error estimates and search strategies for dark sector jets that are less sensitive to nuisance parameters is an area of active interest, see e.g.[37,93].
The rest of this section is devoted to a description of string hadronization.First, we review the Lund string model used in Pythia 8.This provides the context for the description of our dark glueball hadronization model that follows.In all of our analyses, we consider the case where the number of colors N c is 3, but generalization to other values of N c is straightforward (given the glueball mass spectrum and its scaling with the confinement scale from lattice studies).
Lund String Model for Mesons and Baryons
We start by briefly summarizing the Lund string model of hadronization as implemented in Pythia 8.A more detailed explanation can be found in [83] with additional context in [82].Before hadronization, partons undergo a perturbative shower, iteratively splitting until the characteristic energy scale (transverse momentum p T relative to the parent parton in Pythia's implementation) reaches an IR cutoff p T min , which parameterizes the scale where the shower approaches strong coupling and must be matched onto the hadronization model.The shower is executed in the leading color (N c → ∞) approximation, such that each (anti-)quark has a unique (anti-)color label, and each gluon has unique color and anti-color labels.Therefore, for each color label, there is exactly one parton with the compensating anti-color label at each step of the shower.
Partons are grouped into color singlets by "Lund strings."These are simple representations of flux tubes dictating the flow of color charge.Quarks and antiquarks live at the ends of strings, while gluons are represented as kinks in the strings.Strings are therefore comprised of "string pieces," the segments of the string that connect individual quarks and gluons.Each string piece has momentum where p µ 1 and p µ 2 are the momenta of the partons connected by the string piece.This momentum defines a string piece mass m piece via p 2 piece = m 2 piece .Each (anti-)quark effectively donates all its momentum to the string piece that terminates on it, and each gluon donates half its momentum to each of the two string pieces that are connected to it.
In order to account for the fact that QCD has a finite number of colors, Pythia implements a procedure called "color reconnection" between the end of the perturbative shower and the formation of hadrons.Out of the few different options Pythia 8 offers for color reconnection, the so-called "QCD-based" version is the best-motivated Color and anti-color labels are represented by filled and empty (semi-)circles, respectively.Quarks q and antiquarks q form the ends of strings, while gluons g are kinks in the string.String pieces span between the color/anti-color pairs of individual partons and are labeled with displayed colors (colors have numerical labels so that gray-scale versions contain the same information).Each parton is displayed with a fixed location in an abstract color-connection space where the displayed lengths of the string pieces correspond to the string-length λ. Between 1b and 1c, the pairs of blue (1) and green (3) connections are swapped.
for our regime without beam remnants or light quarks. 2Here, color/anti-color pairs are randomly reassigned a new label, which permits more than one possible grouping of partons into color singlets. 3Color reconnection seeks to minimize a Lorentzinvariant effective free energy λ called the string-length where m ref is the mass of some reference hadron.The minimization of λ is performed by swapping which color end of a color/anti-color pair is connected to which anticolor end.We provide a sketch of this procedure in Fig. 1 for a simple system with a few partons.The approach taken in the Lund string hadronization model is to consider these 2 Part of the purpose of color reconnection is to treat states at the end of showers and beam remnants consistently, so Pythia's default implementation was formulated with beam remnants specifically in mind.
3 More precisely, there are nine possible reassignments (with the restriction that gluons cannot be reassigned to have the same color and anti-color) to reflect the 1/9 probability of an SU (3) fundamental being able to form a singlet with an SU (3) anti-fundamental.More detail can be found in [83].
color connections between partons as oscillating classical strings that break up into hadrons.A string with two ends connecting a q q pair is called a "yo-yo mode" and is identified with a meson. 4When a hadron fragments off of a string, it takes away some random fraction z of the string's light-cone momentum p ± = E ± p z (with the z-axis being a preferred direction which Pythia takes to be the string axis), which has convenient Lorentz transformation properties.This z is sampled from the Lund Symmetric Fragmentation Function (LSFF) where a and b are phenomenological parameters, and the hadron's transverse mass m ⊥ appears due to quark tunneling effects explained in [83].Given that Lund fragmentation assumes strings break into pieces ending on quarks, this approach must be modified to accommodate a pure-glue sector.
String Model for Glueball Hadronization
In this section, we provide a qualitative discussion of our glueball hadronization algorithm for N c = 3, which can be easily generalized to other numbers of colors.Our focus is on explaining the role of the adjustable nuisance parameters that parameterize incalculable effects.A more detailed description with further justifications of the choices made here are is given in App. A. We modified Pythia 8 to simulate the branching of a Lorentz-singlet dark gluon pair (produced e.g. in the decay of a heavy scalar) via a leading color, p Tordered, pure-dark-glue parton shower.The shower cutoff scale is parameterized as p T min = c Λ D , where c is an O(1) nuisance parameter, and Λ D is the dark sector confinement scale. 6This cutoff scale parametrizes the onset of strongly-coupled dynamics, where the dark sector coupling α D becomes non-perturbatively large.In practice, the dimensionful scale that determines all of the scales in the pure-glue theory is the lightest glueball mass m 0 , as further described below.
Lattice studies have provided us with many glueball properties in pure SU (3), and in some cases for other values of N c [95][96][97].There are twelve species that are stable in the absence of external couplings, each with their own set of J P C quantum numbers [98].The lightest state is the 0 ++ with mass m 0 .Each heavy state's mass is a multiple of m 0 between ∼ 1.4 and ∼ 2.8, which we take from [96].The masses and spins of this glueball spectrum provide the inputs we will need to select the species of glueballs that are emitted during fragmentation, which will be described below.Lattice results also allow us to specify the boundary condition in the dark strong coupling's renormalization group evolution given a choice of m 0 , since m 0 = 6.28ΛD in pure SU (3) [97].In this way, we derive Λ D from the physical scale m 0 .We set the default value of c so that α D evaluated at the default shower cutoff scale is 1.
Non-default values of c change p T min without affecting the running of α D .Following the termination of the perturbative shower, we implement a version of QCD-based color reconnection.As visualized in Fig. 2, the only color-singlet Lund string topology in the pure-glue model is a closed ring.As in the SM, we swap color connections to minimize the string-length in Eq. (2.2), using the lightest glueball mass m 0 as m ref . 7This leaves us with color-singlet rings of string pieces that will fragment into glueballs.Both color reconnection and our hadronization algorithm are phenomenological models for flux tube rings twisting until they cross themselves and pinch into smaller rings.Without quarks, the strings are unable to break, so this pinching action is the only way the rings can divide into units with smaller invariant mass.
The intuitive picture of glueball rings pinching off the color-singlet flux tube ring in order to most rapidly decrease the total string-length inspires the glueball hadronization algorithm depicted in Fig. 3. First, we select string pieces with sufficient total invariant mass to be converted (or "fragmented") into a glueball.We then determine the species of the glueball by randomly selecting from among the species with mass less than that of the fragmenting string pieces, with probabilities weighted by the number of spin degrees of freedom.The emitted glueball's direction is along the total momentum of the fragmenting string pieces in the ring's rest frame, and its light-cone momentum is a random fraction z of the light-cone momentum of the fragmenting strings.We study the effect of sampling z from one of two fragmentation functions, the first being the LSFF in Eq. (2.3) with m ⊥ replaced by the glueball mass m G , and the second being a beta distribution where α and k β are nuisance parameters.Having specified the glueball's species, direction, and light-cone momentum, its four momentum is fully determined by the on-shell condition.Whatever momentum is left over from the fragmenting string pieces is distributed equally among two new string pieces, and the resulting new ring can emit the next glueball.If emitting a glueball with the selected momentum would result in a new ring that is kinematically forbidden from further fragmentation, the ring instead fragments into two glueballs with the second glueball's species randomly sampled as previously discussed.In summary, our model's nuisance parameters are the shower cutoff factor c, the fragmentation function, and the chosen function's two shape parameters.
Emergence of Thermally Distributed Production Rates
By analogy to the hadron spectra produced in SM QCD fragmentation [99], a motivated expectation for the relative distribution of different glueball species is that they approximately follow a Maxwell-Boltzmann distribution [14]: where P J is the relative rate of producing the species with mass m J and spin J, and T had is some "hadronization temperature."In [14], which analyzed glueball production in a dark matter indirect detection context without separating out the perturbative shower, T had was taken to be related to the center-of-mass energy of the initial hard process.For high enough initial energy, this would result in a power law distribution favoring heavier hadron masses, a behavior quite different from what we are used to in SM QCD.Instead, we would expect that the hadronization temperature is fairly unrelated to the high scale at which the original gluons are produced (provided this high scale is sufficiently greater than any kinematic thresholds), but rather is set by an intrinsic feature of the confining theory.In particular, for N f = 0, N c = 3, the critical or Hagedorn temperature of the QCD phase transition [100][101][102] is T c ≃ 1.2 Λ D [97,103].This motivated the approach taken by GlueShower [81], which explicitly imposed this thermal distribution with T had = dT c for d ∼ O(1).Remarkably, we will show that our hadronization algorithm produces an approximately thermal multiplicity distribution of glueball species with very little dependence on the choice of fragmentation function or its parameters.Furthermore, the hadronization temperature is of the theoretically expected size, T had ≃ Λ D , increasing slowly with increasing shower cutoff scale for reasonable values of c ∼ O(1).
Our algorithm makes the minimal assumption that a local set of string pieces fragmenting into glueballs has no preference amongst the kinematically accessible glueball species, beyond the 2J + 1 spin multiplicity factor.The overall distribution of glueball species must therefore emerge from the kinematics of color-singlet rings.A color-singlet flux tube ring made of only soft string pieces that are close together in momentum space will predominantly produce only the lighter species, since each additional selected string piece will only modestly increase the total invariant mass available for fragmentation until the m 0 threshold is reached.On the other hand, fragmenting string pieces that are heavy compared to m 0 , as well as combinations of color-connected string pieces that are far-separated in momentum space, will produce heavy and light glueballs without preference.The combination of these effects results in a net suppression of the heavy species.This idea of "closeness" in momentum space (as determined by the invariant mass of sums of string piece momenta) elicits an intuitive geometric picture.If we imagine the color-singlet rings as polygons (as in Figs. 1 to 3) whose side lengths are determined by the string-length in Eq. (2.2), but whose angles randomly fluctuate, then combinations of string pieces that are "larger" in this sense have a greater propensity to cross each other and fragment off heavier glueballs.We would expect such a system to fragment in the order that most rapidly decreases its perimeter, which inspires our choice to begin fragmentation by selecting string pieces with the largest string-length. 8This intuitive picture may serve as a good analogy for the dynamics of closed flux tube rings.
This illustrates qualitatively how our hadronization algorithm provides a plausible model of glueball fragmentation, but there is no a priori reason to expect it to quantitatively produce an approximately thermal distribution.Furthermore, the above arguments suggest a significant dependence on the shower cutoff scale p T min = c Λ D , with higher values of c producing fewer gluon splittings and therefore fewer string pieces that each have higher mass, resulting in overproduction of heavy glueball states.Indeed, we observe a modest increase of the corresponding hadronization temperature with increasing c.
We now quantitatively demonstrate how this thermal species distribution emerges, and investigate the extent to which the glueball multiplicity distribution depends on the nuisance parameters of our hadronization model.Recall that these parameters are the shower cutoff scale set by c, the choice of fragmentation function between Eq. (2.3) or Eq.(2.4), and the two shape parameters for each function.Here, we focus on the fragmentation function and therefore set c to its default of 1.8.The discussion will not change for other O(1) values, and when defining hadronization benchmarks in the next section, we will include different choices for c.
The physical interpretation of the numerical values of the fragmentation function parameters is obscure, and there is no obvious correspondence between the parameters of the LSFF and that of the beta distribution.Therefore, we specify the mean µ z and standard deviation σ z of the probability distributions for the 0 ++ species, which fix values for the fragmentation function parameters and are easy to interpret.Another advantage of specifying the mean and standard deviation is that for each possible mean of a finitely-supported probability distribution, there is a maximum possible standard deviation.Thus, the space of all possible fragmentation function parameters is bounded when expressed this way.
In Fig. 4, we present the results of fitting the distributions of species to Eq. (2.5) for many points in the µ z -σ z plane for the fragmentation function of the 0 ++ species.We find the best fit T had by maximizing where y i is the total fraction of the i th species produced by the Monte Carlo, P J (x i ) is the thermal distribution in Eq. (2.5) evaluated at the mass x i of the i th species, and ⟨y⟩ is mean of the y i 's.We chose R 2 to quantify the quality of the fit, rather than χ 2 , because we are interested in the infinite Monte Carlo statistics limit.Using χ 2 would therefore artificially assign greater weight to the smallest species fractions.
The point with the best fit was in the plane of the beta distribution at µ z = 0.6, σ z = 0.008 with R 2 = 0.93 and T had = 0.99Λ D .We show results for shower center-of- mass energy 125 GeV and glueball mass m 0 = 10 GeV, but the results are very similar for center of mass energy of 1 TeV.It is encouraging that the best-fit hadronization temperature lies close to the theoretical expectation, and that both T had and the high quality of fit depend only very little on the choice of fragmentation function, its parameters, or the center of mass energy.This suggests that our hadronization model may represent a good analogy for the true non-perturbative fragmentation dynamics of crossing color strings.
Fig. 5 shows a representative example of these production rates as a function of species, with the corresponding best fit using the default nuisance parameters described in Sec.2.4.Overall, the agreement between the thermal expectation and our model is fairly good.There is, however, a noticeable and consistent overproduction of very heavy glueball states compared to the Boltzmann expectation.
As an instructive comparison, Fig. 6 shows production rates of different SM hadron species produced by Pythia's default hadronization tune.The distribution organizes itself by the heaviest quark flavor in each species, and each of these groups Figure 5: Production rates P J of glueball species in ascending order of mass produced using the default parameters described in Sec.2.4 and the corresponding best fit to the thermal model in Eq. (2.5).The upper and lower plots have identical information, with the upper plot on a logarithmic scale and the lower plot on a linear scale.
appears to follow its own scaling relation as a function of mass.We fitted each group to its own Boltzmann distribution, generally finding good agreement between the fits and Monte Carlo, up to a few outliers.In fact, the heaviest SM hadrons appear to exhibit a mild enhancement compared to the thermal fit, which is consistent with the output of our glueball hadronization algorithm.These fits demonstrate that glueball species production from our algorithm should be approximately Boltzmann-like, but some deviations are to be expected, and the parameters should not necessarily be tuned solely to achieve an optimal Boltzmann fit.Rather, we are encouraged that our model's parameters only mildly impact the fit quality, and we set benchmarks in Sec.2.4 to capture the most extreme possible variations of the model's output.m (GeV)
Benchmark Parameters
In this section, we suggest three benchmarks for setting the shower cutoff and fragmentation function parameters for collider studies.Our analysis of thermal production rates in Sec.2.3 does not strongly favor a particular region in fragmentation function parameter space.Therefore, in addition to a well-motivated default choice, we define two bracketing variations that capture the different plausible outcomes of glueball hadronization.These are "soft" and "hard" scenarios, where the glueballs tend to have smaller and larger momentum in the dark shower rest frame, respectively.First, we investigate how varying the hadronization scale parameter c changes the glueball hardness.As the hadronization scale decreases, the gluons in the perturbative shower branch more often, and the Lund strings are softer, so the glueballs emitted by combining those strings are also softer.Thus, benchmarks for softer scenarios should correspond to smaller values of c.As for the fragmentation function parameters, it is simplest to interpret their effect in the µ z -σ z plane as in Sec.2.3, since parameters corresponding to a larger µ z tend to take more momentum from the fragmenting string pieces, resulting in harder glueballs.It is not obvious a priori which of the two fragmentation functions Eq. (2.3) and Eq.(2.4) would result in harder glueballs, but simulations show that the LSFF leads to harder kinematics by a small margin.See further discussion of glueball hardness in App.B.
With these qualitative effects in mind, we make some concrete suggestions for benchmarks.The default value of c is taken to be 1.8, since this sets our p T min at the scale where α D = 1.Pythia's default settings provide useful guidance in the variation of c because the SM α S evaluated at the default p T min for final state radiation is ≃ 1.6.The value of c for which our α D satisfies the same condition is 1.4, which we therefore adopt as our soft benchmark.We choose our hard benchmark c to be 2.1 so that the default is equidistant from the two variations.For the default fragmentation function, we choose the LSFF because this is what is used in the Lund string model.We choose the default function parameters to satisfy µ z = 0.5 and σ z = 0.3 since this is about as close to a uniform distribution as possible with this fragmentation function, and we do not have any reason to favor large or small z.For the soft and hard scenarios, we want to capture the extremes of the possible variations, so we choose µ z = 0.1 and 0.9, respectively, with σ z = 0.01.These numerical values, and their corresponding fragmentation function parameters, are summarized in Table 1.
Total Multiplicity Distributions
In addition to the relative production rates of different glueball species in Sec.2.3, we can compare distributions of the total number of glueballs per event N from our algorithm to analytical predictions for QCD with zero flavors.In the pure-glue limit with small hadron masses, the average number of hadrons is expected to scale with center of mass energy E CM as [104] ⟨N where C A is the quadratic Casimir factor for the adjoint representation, which is N c for SU (N c ). Fig. 7 shows a comparison of ⟨N ⟩ at various values of E CM between our algorithm with each set of benchmark parameters and the QCD prediction, with the normalization of Eq. (2.7) fixed by matching to the Monte Carlo at the largest E CM .The analytic prediction is slightly larger than our model at low energies, except where E CM is near 2m 0 and the prediction falls below the kinematic threshold of two hadrons.This is an expected consequence of the finite hadron masses, since for smaller E CM and parameters that tend to produce more glueballs, a larger portion of the energy is taken up by glueball masses.The reproduction of this standard result is a useful check on the validity of our algorithm.Notably, our algorithm tends to produce a greater number of glueballs than GlueShower, which generated ⟨N ⟩ ∼ 7 at E CM = 100 m 0 [81].Therefore, our more physically-motivated approach predicts greater discovery potential.
Dark Glueball Decay via Higgs Portal
We now have a concrete numerical method to simulate the production of dark glueballs.In order to connect with phenomenology, we need to specify the portal between the dark sector and the SM that will determine how the dark gluons are produced in a hard interaction and how the dark glueballs decay.We consider a pure-glue dark sector that couples to the SM via the Higgs portal, since this is the lowest-dimension portal that can connect the pure-glue sector to the SM.We compute the resulting glueball lifetimes and show them in the parameter space of two neutral naturalness scenarios.
Dark Glueball Decay Widths
In this section, we briefly summarize the pertinent results of [105] used in our estimation of dark sector glueball lifetimes and decay branching ratios.Strongly-coupled Glueball Mass (m 0 ) Higgs Portal dark sectors that include heavy fermions coupling to the Higgs give rise to the effective dimension-6 Higgs portal operator9 where H is the SM Higgs doublet, G µν (D) is the dark gluon field strength, α D is the dark sector strong coupling, M is the mass scale of the dark sector fermions, and y is an effective coupling that is determined by a model-dependent combination of the dark sector fermion Yukawa couplings with the Higgs (see [105] for explicit expressions).This operator can mediate both dark gluon production at the LHC and subsequent glueball decay to the SM.
The decay channels for each of the twelve glueballs are summarized in Table 2.The 0 ++ species decays into SM states ξ by mixing with the Higgs boson, 0 ++ → h * → ξξ, with the decay width where m h is the Higgs mass, Γ SM h→ξξ (m 0 ) is the decay width for a Higgs-like scalar of mass m 0 , which we calculate using HDECAY [106], and F 0 ++ is the non-perturbative decay constant with mass dimension 3. The heavier species (with the exceptions of the stable 0 −+ and 1 +− ) decay into lighter glueballs via emission of an off-shell Higgs, J → J ′ + h * (→ ξξ).The decay width for a glueball with spin J to a lighter glueball with spin J ′ and the SM is given by where g(x, y; z) = (1−x/z −y/z) 2 −4xy/z 2 , |M J,J ′ | is the averaged non-perturbative transition matrix element, and Γ (i) J,J ′ are dimensionless functions of the glueball masses that depend on the angular momentum transfer associated with each transition, which can be found in [105].The mass splitting of the glueball states can be a few GeV at small m 0 , where perturbative SM QCD breaks down, so we use Γ SM h→ξξ (m 12 ) values calculated from chiral perturbation theory [107] for this range.
The glueball decay widths depend on the theory parameters m 0 and M/y, as well as the non-perturbative decay constants and transition matrix elements.The matrix elements corresponding to the decays of the lightest glueballs have been calculated on the lattice [96], e.g.4π α D F 0 ++ = 2.3m 3 0 , which we use in this work.However, the matrix elements for the heavier states have not been computed.We use dimensional analysis to approximate the remaining heavy species' transition elements up to dimensionless prefactors, thus obtaining the correct scaling with m 0 .We set |M J,J ′ | = m 3 0 for our decay widths, vary each matrix element independently by a factor of two, and marginalize over the variation as part of our hadronization uncertainty.One could in principle also incorporate the dimension-8 operators listed in [105], which render the 0 −+ and 1 +− unstable.However, corrections due to these operators are suppressed by multiple orders of magnitude in the parameter space of interest, and these species only make up a few percent of produced glueballs, so we do not include these decays in our study.
Neutral Naturalness Models
The results of Sec.3.1 can be readily mapped onto parameters in neutral naturalness models because they generate the Higgs portal operator in Eq. (3.1) [44].For the Fraternal Twin Higgs (FTH) [45], where m tFTH is the twin top mass, and θ = tan −1 (m t /m tFTH ).For Folded Supersymmetry (FSUSY) [41], where m t is the SM top quark mass, m tFSUSY is the folded stop mass, and v is the SM Higgs vacuum expectation value.This mapping allows us to predict lifetimes and branching ratios for each glueball species given a choice of m 0 and the mass of the FSUSY or FTH top quark partner.Fig. 8 shows some representative examples.The plots show that 0 ++ state is the shortest lived state for each point in parameter space because it mixes directly with the Higgs.The next few heavy species that can decay via the dimension-6 operator (2 ++ , 2 −+ , 3 +− ) have much longer lifetimes due to only being able to radiate an off-shell Higgs.The remaining heaviest states (3 ++ and above) have slightly shorter lifetimes due to having more available decay channels with larger mass splittings for the off-shell Higgs.
One of the most important characteristics of the LHC signatures of dark glue showers is the distribution of glueball lifetimes.Depending on the fundamental parameters of the model, the predictions range from semivisible jets (all the decays that are visible to ATLAS/CMS are prompt) to emerging jets (the glueball decays occur within the ATLAS/CMS detector) to the long lifetime regime (all glueballs escape the main detectors).For small m 0 and large M/y, all species are sufficiently longlived that a dedicated long-lived particle experiment such as MATHUSLA [84][85][86] can significantly extend sensitivity beyond main detector searches due to its large volume.
There are also regions where one kind of jet signature dominates over another, or a mixture of both strategies is potentially viable.Given that a generic strongly-coupled sector can have a spectrum of many hadrons with a broad hierarchy of lifetimes (as in the SM itself), an optimal search could incorporate methods from the semivisible jet, emerging jet, and external LLP detector strategies simultaneously.
In the remainder of this section, we discuss two production mechanisms for glueballs at the LHC: through the Higgs and through a new heavy Z ′ .For each mechanism, we show the parameter space relevant for semivisible or emerging jet searches, and we discuss predictions for two different classes of glueball collider phenomenology.For Higgs portal production, we make predictions for glueball decays that could be observed in the proposed MATHUSLA experiment, considering glueball production and decays through a Higgs portal within FSUSY and FTH as discussed in Sec.3.2.This will supersede the rudimentary MATHUSLA sensitivity estimates for neutral naturalness presented in [87].
For the Z ′ production, we show that this model could yield a good benchmark for semivisible jet and emerging jet searches.One phenomenological parameter used in the studies of semivisible jets is r inv , the average ratio of the number of dark hadrons that are stable on collider scales compared to the total number of total dark hadrons produced.In current searches, one takes r inv as a simplified model-like input parameter and models the distribution of the invisible fraction of hadrons as Poissonian.Our ability to model hadronization and decay of dark glueballs allows us map parameters in the fundamental description onto a prediction for r inv event by event.Thus, we provide a theoretically motivated range of r inv distributions to consider for future semivisible jet searches.
Dark Glueballs via Higgs Production
In this section, we discuss the signatures of dark glueball showers produced via the Higgs portal, which we outline in Sec.4.1.1.Fig. 9 shows fractions of dark glueball events that could possibly give rise to an emerging jet signature, as well as fractions of events that could possibly have a semivisible jets signature with no displaced decays.These plots reveal how different regions of parameter space motivate different For the emerging jet fractions, events were required to have at least one glueball decay within the CMS tracker with transverse displacement of at least 50 mm [21].For the semivisible jet fraction, events were required to have at least one glueball escape the tracker, at least one prompt glueball decay within the tracker, and no glueball decays within the tracker with transverse displacement > 50 mm.combinations of main detector search strategies depending on the glueball lifetime hierarchy.Therefore, the below sensitivity analysis for MATHUSLA will demonstrate where in parameter space the dedicated LLP strategy has reach beyond the main detectors and where these strategies have potential overlap.
Higgs Production
To model Higgs production of dark glueballs we simulate gluon-gluon fusion and VBF in MadGraph5 amc@nlo [108] + Pythia 8 [83].Gluon fusion is implemented via the effective ggh operator, with jet matching for up to one extra hard jet and slight event reweighting to reproduce the NLO+NNLL Higgs p T spectrum computed by HqT 2.0 [109,110].As discussed in [44], the Higgs-to-dark gluon branching ratio can be found by a rescaling of the SM Higgs-to-gluon branching ratio of 8.5% [111,112].
Dark Glueballs at MATHUSLA
In Fig. 10, we show sensitivity curves for decays within the 100 m × 100 m × 25 m MATHUSLA decay volume as specified in [86], assuming an integrated luminosity of 3 ab −1 at √ s = 14 TeV.The contours we show correspond to 4 decays in MATH-USLA's decay volume, illustrating the exclusion reach in the absence of backgrounds, which is expected for LLP decays to high multiplicities of SM hadrons.The experimental bound on the Higgs-to-invisible branching ratio of 18% [113] excludes the parameter space of top partner masses below the range shown in the plots.We account for uncertainty in the various heavy glueball lifetimes by varying the cor- We take 4 events within the decay volume as the exclusion limit.The top plots show exclusive decays of the two lightest glueball species, and the bottom is inclusive of all species.The dashed contours reflect uncertainties due to variation of both the hadronization benchmark and the decay matrix elements.The inclusive plot also shows the previous estimate from [87] based on the simplifying conservative assumption of two-body exotic Higgs decays h → 0 ++ 0 ++ only.responding decay constants independently by a factor of 2 in each direction.Our uncertainty bands also include the variation obtained by running simulations with the different hadronization benchmarks introduced above in Table 1.
A striking feature of these results is the importance of including the heavier glueball species, and the resulting dramatic increase to MATHUSLA's estimated sensitivity in neutral naturalness parameter space.Since the heavier glueballs have longer lifetimes than the 0 ++ , MATHUSLA is able to probe an entirely complementary mass regime with heavier glueball decays, extending its reach up to m 0 ∼ 50 GeV compared to the ∼ 20 GeV maximum probed by the 0 ++ alone.
Previous studies of dark glueball phenomenology [44,87] made the conservative simplifying assumption that only two glueballs were produced in exotic Higgs decays, some fraction of which was h → 0 ++ 0 ++ , the only channel assumed to be observable.This was necessitated by the absence of a realistic simulation framework for glueball production.Our work significantly improves on these previous sensitiv-ity estimates by including the dark gluon shower and Lund string-inspired glueball hadronization, allowing for both the higher glueball multiplicity in each Higgs decay and the contribution of heavier, more long-lived glueball states to be systematically taken into account.This leads to the improved projections for the inclusive total reach of MATHUSLA to all glueball decays, shown in the bottom panel of Fig. 10.It is interesting to note that this updated inclusive MATHUSLA reach therefore not only includes the long 0 ++ lifetime regime below 20 GeV, but also exceeds, or is at least comparable to, the total projected coverage of main detector searches relying on LLP decays in the tracker or muon system for m 0 ≲ 50 GeV, computed with the above simplifying two-body-decay assumption [44].While the main detector search sensitivities would be expanded due to increased glueball multiplicity in our updated simulations, the inclusion of heavier glueballs would have a much smaller effect than it did for MATHUSLA, since the main detector is most sensitive to short lifetimes.While the detailed study of main detector sensitivities to dark glueballs is an important subject of future study with our updated simulation framework, this nonetheless already suggests that MATHUSLA's LLP sensitivity may dramatically enhance new physics coverage in a large region of dark glueball parameter space.
Our results also motivate further study into the properties of the heavier species.In particular, lattice computations to determine the decay matrix elements would reduce uncertainty in the glueball lifetimes.In the regions of parameter space where the heavier species dominate decays in MATHUSLA, the uncertainty due to lifetime variation is larger than that due to the hadronization benchmark variation.
Note that the final states of 2 ++ decay always include a 0 ++ , and the region of parameter space where the 2 ++ dominates decays in MATHUSLA is also where the 0 ++ has short O(cm) lifetimes, see Fig. 8. Therefore, given the cm-scale tracking resolution of the MATHUSLA experiment, the 2 ++ decay can be treated as a single vertex.This region of parameter space is also interesting because any 0 ++ produced would decay within CMS.These can be searched for with dedicated searches using CMS detector information alone [44,114] (though with significant signal penalty due to trigger limitations) or a combined MATHUSLA-CMS search if MATHUSLA provides a trigger signal to CMS [115].In the latter case, simultaneous reconstruction of the 0 ++ and 2 ++ decay would allow a detailed characterization of the dark sector and provide strong evidence that the newly discovered LLP states are in fact dark glueballs.
Dark Glueballs via Z ′ Production
In some of our parameter space, the lightest dark glueballs can decay promptly while the rest are either stable or very long lived.This would lead to LHC events where the visible jet transverse momentum ⃗ p J T and missing transverse momentum ⃗ p miss T are aligned, which is the characteristic property of so-called semivisible jets [15].To define a benchmark for future semivisible jet searches, we consider the simplified m 0 (GeV) For the emerging jet fractions, events were required to have at least one glueball decay within the CMS tracker with transverse displacement of at least 50 mm [21].For the semivisible jet fraction, events were required to have at least one glueball escape the tracker, at least one prompt glueball decay within the tracker, and no glueball decays within the tracker with transverse displacement > 50 mm.signal model used in the recent CMS semivisible jet search [19].This search assumed the resonant production of a Z ′ mediator that decayed to dark sector quarks, which showered and formed dark hadrons that decayed to SM quarks.We retain the Z ′ mediator, but we work in the region of parameter space that produces dark glueballs, and we introduce the Higgs portal to facilitate the glueball decays.Further details of the production mechanism via a heavy Z ′ are outlined below in Sec.4.2.1.In Fig. 11, we show the fractions of dark glueball events that could give rise to a emerging jet and/or a semivisible jet signature through Z ′ production.Semivisible jet searches may be able to probe the large m 0 regime, while emerging jet search strategies may be able to probe parameter space that includes lower m 0 values.The actual ATLAS or CMS sensitivity to these search strategies requires detailed modeling of the emerging or semivisible jets including SM backgrounds, which is beyond the scope of this paper.
Z ′ Production
The signal model features a Z ′ that couples to both SM quarks and dark sector quarks Q D charged under the dark QCD with confinement scale Λ D .This allows for dark quark pair production in LHC collisions pp → Z ′ → Q D QD .In the parameter regime analyzed by the CMS search, the dark sector quarks have mass M Q < Λ D ≪ M Z ′ , which hadronize into jets of dark mesons (bound states of quark-anti-quark pairs).For the semivisible jet benchmark introduced here, we instead consider the quirk-like regime [116], with Λ D ≪ M Q ∼ M Z ′ /2.This implies that Q D QD pair production via the Z ′ resonance results in a quirk bound state.The Q D QD pair are connected by an oscillating flux tube, which de-excites by radiating glueballs (and angular momentum) before the dark quark pair annihilates into dark gluons.Since the de-excitation sheds angular momentum, the final annihilation is anticipated to be dominated by the s-wave.We also assume that the dark quarks couple to the SM Higgs with a Yukawa coupling y.Integrating out the dark quarks generates the Higgs portal operator, which we assume provides the dominant channel for the dark glueball decays.
The dynamics of quirk de-excitation via glueball emission are not well understood, but as a naïve first guess, we assume the glueball radiation from de-excitation is highly subdominant compared to the glueballs produced in the ultimate s-channel annihilation of the Q D QD pair.This can be guaranteed by setting M Q just below M Z ′ /2, where a tiny mass difference is required to allow emission of a single glueball to shed the quirk's orbital angular momentum.This model technically contains both Higgs and vector portals to the dark sector.In practice however, the vector portal dominates dark quark pair production for M Z ′ up to a few TeV, while the Higgs portal dominates glueball decays with lifetimes shown in Sec.3.2.The vector portal glueball decays are phase space suppressed, since they induce four body decays compared to the two body decays that are induced by the Higgs portal.Additionally, the vector portal decays have lower rates due to the higher dimension of the corresponding effective operator.
The existence of the Higgs portal accommodates the heavy quarks being vectorlike doublets under SM SU (2) L × U (1) Y , but one can also consider the same effective operator in an FTH-like scenario where the dark quarks are SM singlets that couple to a scalar that mixes with the SM Higgs boson, resulting in an analogous M Q /y that sets the glueball lifetimes in combination with m 0 .Whether the UV model has SU (2) L doublet quarks that do not get all of their mass from SM electroweak symmetry breaking, or FTH-like quarks whose M Q /y is not fixed by neutral naturalness considerations, we will simply vary M Q ≃ M Z ′ /2 and y independently for the purpose of studying the semivisible jet signal at the LHC.
Dark Glueball Semivisible/Emerging Jets
For this study, we assume the model described in Sec.4.2.1.We take a benchmark where the Z ′ has mass M Z ′ = 3 TeV, and the dark quarks have M = M Q ∼ M Z ′ /2.We choose M/y = 4.5 TeV, which fixes the dimension-6 glueball lifetimes for any choice of m 0 .To generate events, we use MadGraph5 amc@nlo [108] with a Z ′ model [117,118] to simulate pp → Z ′ production at a 14 TeV proton collider.We run our dark shower and glueball hadronization algorithm as though the Z ′ were a heavy scalar decaying to two dark gluons, which models s-wave quirk annihilation as , where r inv is the fraction of dark hadrons that are invisible to the semivisible jet reconstruction.Solid histograms come from using the default hadronization benchmark, and dashed histograms come from the soft and hard variations.Means µ and standard deviations σ are displayed, with uncertainties corresponding to hadronization variations.discussed in Sec.4.2.1. 10We take events with Z ′ production and decay to glueballs as the hard process and pass them to Pythia version 8.307 [83] to handle SM QCD initial-and final-state radiation and jet clustering with the FastJet version 3.4.0plugin [119].Following the procedure from the CMS search in [19], we use the antik T jet clustering algorithm [120] with jet radius R = 0.8.SM final states in each event are characterized as "invisible" if they are neutrinos or they have a glueball ancestor that decayed outside of the cylinder spanned by the CMS tracker [121].We consider all other SM final states as "visible" and cluster them into jets.This is a highly simplified picture of the detector and semivisible jet reconstruction, but we performed the same analysis using the central hadronic calorimeter as the border between visible and invisible states and found qualitatively similar results.The invisible SM final states, as well as any stable glueballs, contribute to the missing transverse momentum ⃗ p miss T .Most of the glueball species decay by emitting a lighter glueball, resulting in cascade decays.However, only the primary glueballs (i.e.those produced from hadronization) contribute to r inv .In order to understand the role of displaced ver- , where r dec is the distance of glueball decay vertices within the CMS tracker to the IP.Solid histograms come from using the default hadronization benchmark, and dashed histograms come from the soft and hard variations.tices, we tracked the distances r dec between the interaction point and the decay vertices of glueballs that decayed within the tracker.We also computed a few useful observables for semivisible jet searches and describe them further App.C. The distributions of these other observables have the expected qualitative form, so here we focus on the novel results of r inv and r dec shown in Fig. 12 and Fig. 13, respectively.
We see that the average value of r inv ranges from ∼ 0.45 to ∼ 0.82.This spread of average r inv demonstrates that a constraint on r inv from a semivisible jet search could potentially be recast as a constraint on our model's microscopic parameters.It would also be interesting to investigate the extent to which the shape of the r inv distribution predicted here would impact limits set by existing analyses.As m 0 increases, the mean r inv approaches ∼ 0.45, and we expect from Fig. 5 that about half of the glueballs produced are 0 ++ .Therefore, this behavior of r inv shows that as m 0 increases through this range, all the 0 ++ glueballs decay within the tracker while all heavier species tend to escape.The r dec plots emphasize the importance of displaced vertices in this analysis.There are two ways for a dark sector to generate missing momentum aligned with a jet: the jet contains states with long lifetimes compared to the detector scale as well as states that decay promptly, or the jet contains states with lifetimes comparable to the detector scale, allowing a portion of them to decay in the detector and leave displaced vertices.The former case is the prototypical semivisible jets scenario, while the latter is closer to an emerging jets signal.With our dimension-6 glueball decays through a Higgs portal, these two cases overlap.Depending on the region in parameter space, the 0 ++ may decay promptly or have cm to m lifetimes while the heavier states are relatively long-lived.Alternatively, the 0 ++ may decay promptly while only a subset of the heavier species leave displaced vertices.We leave the interesting task of developing an optimal search strategy that takes advantage of this class of signals to future work.
Conclusions
Confining dark sectors appear as a component of a large class of possible BSM scenarios with a wide range of possible signatures and very broad theoretical motivation.The case of a pure Yang-Mills dark sector, corresponding to N f = 0 QCD, is an important representative of this class, but one whose study has been hampered by our ignorance of pure-glue hadronization into dark glueballs.While first steps to constrain the possible range of hadronization outcomes based on the perturbative gluon shower, energy conservation, and the large m 0 /Λ D mass gap were taken in [81], the absence of a realistic hadronization model left large theoretical uncertainties, especially for exclusive production rates of individual glueball species, which determine most collider observables.This motivates developing a more sophisticated phenomenological parameterization of the non-perturbative physics, which allows us to make more quantitative predictions for the final state from dark glue sector showers.
In this work, we present the first implementation of a color string dynamics inspired hadronization model for dark glueball fragmentation.We borrow from the Lund string model to parameterize how color-singlet flux tubes produced by the dark gluon shower fragment into dark glueballs.The specific algorithm is quite simple, and local in the sense that it assumes each combination of fragmenting string pieces chooses democratically from all kinematically available glueball species.This makes one of our main results all the more remarkable: the relative multiplicities of different glueball species approximately follows the theoretically expected thermal distribution with T had ≃ T c ≃ Λ D , independent of the chosen fragmentation function and with a weak dependence on the shower cutoff scale.Also, our algorithm's intuitive geometric picture of self-intersecting color flux rings suggests our approach may capture the relevant dynamics of glueball fragmentation.
Our shower and hadronization model has a handful of parameters beyond the physical glueball mass and initial center of mass energy: the shower cutoff scale, the choice of fragmentation function, and that function's two parameters.We suggest three sets of benchmarks that span a broad space of our model's physically reasonable predictions for different possible values of these nuisance parameters, see Table 1.
We apply our new simulation framework to explore the potential reach of emerging and semivisble jet searches, finding both search strategies would probe distinct but overlapping regions of dark glueball parameter space.We then focus on two important phenomenological demonstrations: the study of glueball decays in the proposed MATHUSLA detector and a realistic benchmark model for semivisible/emerging jets.
For dark glueballs decaying in MATHUSLA, we focus on the simplified glueball parameter space motivated by theories of neutral naturalness like the Fraternal Twin Higgs or Folded Supersymmetry, where the dark QCD sector is coupled to the SM via the Higgs portal.We find that including the multiplicity-enhancing effects of the shower and the realistic full spectrum of glueball species produced from our hadronization model dramatically increase the projected sensitivity of MATHUSLA compared to earlier simplified estimates, see Fig. 10.
We also considered a simplified model of a Z ′ coupled to a dark QCD in the quirklike regime that lead to the production of dark glueballs via resonant Z ′ production.This model has broad and potentially overlapping regions of parameter space that can possibly have emerging jet and semivisible jet signatures.The main result we obtained using our simulation of the pure-glue shower and hadronization in the Z ′ model was finding the distributions of r inv that arise due to the pure-glue theory's multiplicity of glueball states with potentially widely separated lifetimes, see Fig. 12.This demonstrates how a semivisible jet search can yield realistic constraints for pure-glue dark sectors.
We hope that some version of our approach can be incorporated into the Pythia Hidden Valley Module.For future studies, we suggest further lattice calculations of glueball decay matrix elements, which will reduce systematic uncertainties in glueball lifetimes relevant to the long-lived particle regime.Our hadronization model could also be improved or generalized in various ways, such as accounting for parity and charge selection rules, and generalizing the number of dark colors beyond 3 (though fully characterizing the glueball mass spectrum for N c ̸ = 3 would again require additional lattice studies).A more sophisticated implementation might explicitly simulate a closed oscillating classical string in position space.This would improve the IR/collinear unsafety inherent in our approach, which relies on discretizing rings into string pieces in a way that explicitly depends on the number of gluon splittings during the shower.
A reliable glueball Monte Carlo also enables new cosmological studies of these dark sectors.Previous analyses derived constraints from avoiding overproduction of surviving stable glueball states [64,65,73,75,122,123] or late-time decays modifying big-bang nucleosynthesis and the cosmic microwave background [74].These analyses assumed that the glueball relic densities originated in the dark QCD phase transition, which itself is not well understood.However, it is possible for glueball densities to receive important contributions from late-time decays, annihilations, or other entropy injections.For these scenarios, our shower and hadronization model could supply new predictions.The same can be said for models where glueball production plays an important role in the production of cosmic rays [71,124].
The most immediate application of our work will be to enable many new detailed collider studies of N f = 0 QCD dark sectors.For example, including factors such as detector effects is required in order to quantitatively establish the distinction between the emerging and semivisible jet regimes, as well as the realistic sensitivity of the ATLAS and CMS main detectors to dark glueball decays.This work also provides us with a tool we can use to further develop search strategies that are insensitive to dark hadronization uncertainties [93], perhaps relying on some aspects of jet substructure and that could even incorporate machine learning, see e.g.[18,28,[125][126][127][128][129][130][131][132].In general, understanding the detailed phenomenology of these dark sectors will help us design the searches that could lead to the next discovery beyond the Standard Model.
λ is the seed for glueball emission. 11The two string pieces connected by this vertex are (at least) the pieces that will be converted or "fragmented" into a glueball.If the two pieces have an invariant mass less than m 0 , then one of their nearest neighbors (selected arbitrarily) will also be added to the list of fragmenting pieces.If this is still not enough invariant mass, the nearest neighbor in the other direction (still in color-connection space) will fragment as well, and so on until we have a selection of string pieces with invariant mass at least m 0 .
Next, we select the glueball's species.The invariant mass of the fragmenting string pieces is an upper bound on the mass m G of the selected species.We perform a weighted random selection from the kinematically available species, where the weight 2J + 1 accounts for the higher multiplicity of a state with spin J.A similar approach is used for SM meson species selection in Pythia.For example, a u d mode could be either a pion or a ρ meson.The choice is determined in Pythia by incorporating a spin-dependent weight into the random selection.As a correction to better fit the data, Pythia additionally includes suppression of heavier species beyond the naïve 3:1 expectation for the vector-to-scalar weight. 12As an alternative approach, one could plausibly select the species before the fragmenting string pieces and gather string pieces with invariant mass at least m G .However, that approach causes the species distribution to acquire a strong dependence on the ratio of the invariant mass of the shower, which is distinctly different behavior from what we expect in QCD as discussed in Sec.2.3.After determining the glueball species, we must specify its momentum.First, we choose the direction of the three momentum pG to be along the momentum of the fragmenting string pieces in the ring's rest frame.This decision is admittedly not Lorentz covariant, but this pG is the best indication of a preferred direction of the fragmenting system.If all of the string pieces in the ring are fragmenting, then pG is selected randomly and isotropically in the ring's rest frame.Then, again inspired by the Lund string model, the glueball takes a fraction z of the fragmenting pieces' light-cone momentum p ±pieces = E pieces ± |⃗ p pieces |, so that the glueball's light-cone momentum is which is a relation that is invariant under boosts along pG .With the glueball's direction and light-cone momentum fixed, and imposing the on-shell condition, the
B Benchmark Parameter Variations
Here, we show variations in the species production rates and glueball momentum distributions resulting from our different benchmark parameters.The momentum distributions in Fig. 14 provide an intuitive demonstration of what we mean by glueball "hardness."As discussed in Sec.2.4, there is a straightforward relation between our hadronization algorithm's nuisance parameters and the glueballs' tendency to be produced with smaller or larger momentum.In this sense, the soft and hard variations of our suggested benchmarks are meant to provide the extremes of our algorithm's possible sensible outputs.
As seen in Fig. 15, as the shower cutoff scale (parametrized by c) increases, the best-fit T had also increases.This behavior is as expected because a higher shower cutoff scale means the dark gluons have fewer opportunities to branch, leading to higher-mass string pieces during fragmentation and weaker suppression of heavy species production.As in Figs. 4 and 1, measured in the rest frame of the dark gluon shower.Exclusive distributions of the two lightest species are shown, as well as the inclusive distribution.As expected, glueballs from "harder" parameter variations tend to have larger momentum.
C Additional Semivisible Jet Distributions
In addition to r inv and r dec , we computed three observables that [19] and the two highest-p T jets.The m T distribution is essentially cutoff by the mass of the Z ′ , and R T and ∆ϕ min can be used to help cut out background.We found that the ∆ϕ min and R T distributions were fairly consistent across the model parameters we simulated, so we show a few representative examples in Fig. 16.The m T distribution changed more noticeably, so we show more model parameter variations in Fig.
Partons at the end of the shower with N c → ∞ have unique color and anticolor labels.String pieces are randomly reassigned a new color, now restricted to N c = 3 choices.
between color/anti-color pairs are swapped if this reduces the string-length λ.
Figure 1 :
Figure 1: A sketch of QCD-based color reconnection.Color and anti-color labels are represented by filled and empty (semi-)circles, respectively.Quarks q and antiquarks q form the ends of strings, while gluons g are kinks in the string.String pieces span between the color/anti-color pairs of individual partons and are labeled with displayed colors (colors have numerical labels so that gray-scale versions contain the same information).Each parton is displayed with a fixed location in an abstract color-connection space where the displayed lengths of the string pieces correspond to the string-length λ. Between 1b and 1c, the pairs of blue (1) and green (3) connections are swapped.
Gluons at the end of the N c → ∞ shower.
Reassignment of string piece colors for N c = 3.
Figure 2 :
Figure 2: A sketch of QCD-based color reconnection for a system of only gluons, as in Fig. 1. Between 2b and 2c, the pair of blue (1) connections are swapped.
(a) The vertex (green) joining the string pieces with the largest string-length begins the fragmentation.(b) A minimal set of string pieces (blue) with total mass ≥ m 0 nearest to the vertex is selected to fragment into a glueball.(c) The glueball (red circle) takes a fraction of the fragmenting pieces' momentum.The remaining momentum is distributed among two new string pieces (blue).
Figure 3 :
Figure 3: A visual depiction of our glueball hadronization mechanism.Color-singlet rings are shown as polygons whose edges are Lund string pieces.The criterion for selecting the seed vertex (green) is chosen to allow for the most rapid reduction in overall string length with each step.Glueball emission (depicted by the red circle in 3c) is conceptualized as pinching off from the fragmenting string pieces (blue in 3b).
Figure 4 :
Figure4: Thermal model fit quality (top) and corresponding best fit hadronization temperature in units of Λ D (bottom) using the beta distribution (left) and the LSFF (right) for points in the plane of the mean µ z and standard deviation σ z of the 0 ++ fragmentation function.The shower center of mass energy is 125 GeV, the lightest glueball mass is m 0 = 10 GeV, and the shower cutoff parameter is set to the default c = 1.8.The black contours indicate an upper bound on σ z for a given µ z .For the beta distribution, this is the least upper bound for parameters where f β (0) and f β (1) are finite.For the LSFF, σ z does not saturate the bound.
Figure 7 :
Figure 7: Average glueball multiplicity as a function of E CM .The points show the output of our algorithm, and the solid lines show the QCD prediction in Eq. (2.7) normalized to match the Monte Carlo at the largest E CM .
Figure 8 :
Figure 8: Contours show log 10 (cτ /m), where cτ is the mean decay length of the glueball in the space of the lightest glueball mass m 0 and top partner masses assuming folded supersymmetry m tFSUSY or fraternal twin Higgs m tFTH .The top plots show the two lightest species, and the bottom plots show representative examples of heavier species.
Figure 9 :
Figure9: Fractions of dark glueball events for the Higgs production scenario satisfying necessary but not sufficient conditions to produce emerging jet signals (left) or semivisible but not emerging jet signals (right).For the emerging jet fractions, events were required to have at least one glueball decay within the CMS tracker with transverse displacement of at least 50 mm[21].For the semivisible jet fraction, events were required to have at least one glueball escape the tracker, at least one prompt glueball decay within the tracker, and no glueball decays within the tracker with transverse displacement > 50 mm.
Figure 10 :
Figure 10: Sensitivity curves for glueball decays in MATHUSLA in the space of the lightest glueball mass m 0 and top partner masses in the fraternal twin Higgs model m tFTH or folded supersymmetry model m tFSUSY .We take 4 events within the decay volume as the exclusion limit.The top plots show exclusive decays of the two lightest glueball species, and the bottom is inclusive of all species.The dashed contours reflect uncertainties due to variation of both the hadronization benchmark and the decay matrix elements.The inclusive plot also shows the previous estimate from[87] based on the simplifying conservative assumption of two-body exotic Higgs decays h → 0 ++ 0 ++ only.
Figure 11 :
Figure11: Fractions of dark glueball events in the Z ′ production scenario with m Z ′ = 3 TeV satisfying necessary but not sufficient conditions to produce emerging jet signals (left) or semivisible but not emerging jet signals (right).For the emerging jet fractions, events were required to have at least one glueball decay within the CMS tracker with transverse displacement of at least 50 mm[21].For the semivisible jet fraction, events were required to have at least one glueball escape the tracker, at least one prompt glueball decay within the tracker, and no glueball decays within the tracker with transverse displacement > 50 mm.
Figure 12 :
Figure 12: Distributions of r inv for various values of the lightest glueball mass m 0 in the Z ′ production model with m Z ′ = 3 TeV andM Q ∼ M Z ′ /2, where r inv is the fraction of dark hadrons that are invisible to the semivisible jet reconstruction.Solid histograms come from using the default hadronization benchmark, and dashed histograms come from the soft and hard variations.Means µ and standard deviations σ are displayed, with uncertainties corresponding to hadronization variations.
Figure 13 :
Figure 13: Distributions of r dec for various values of the lightest glueball mass m 0 in the Z ′ production model with m Z ′ = 3 TeV andM Q ∼ M Z ′ /2, where r dec is the distance of glueball decay vertices within the CMS tracker to the IP.Solid histograms come from using the default hadronization benchmark, and dashed histograms come from the soft and hard variations.
5, Figs. 14 and 15 were generated with m 0 = 10 GeV and dark shower center of mass energy of 125 GeV.
Figure 14 :
Figure 14: Distributions of |⃗ p |/m 0 for the three sets of benchmark parameters listed in Table1, measured in the rest frame of the dark gluon shower.Exclusive distributions of the two lightest species are shown, as well as the inclusive distribution.As expected, glueballs from "harder" parameter variations tend to have larger momentum.
Figure 16 :
Figure 16: Distributions of ∆ϕ min and R T for various values of the lightest glueball mass m 0 for the semivisible jets scenario.Solid histograms come from using the default hadronization benchmark, and dashed histograms come from the soft and hard variations.
2 T = m 2 JJ + 2|⃗ p miss T | m 2
used in their search.The transverse mass m T is given bym JJ + |⃗ p T,JJ | 2 − |⃗ p T,JJ | cos(ϕ miss JJ ) , (C.1)where the two highest-p T jets have total momentum p JJ with corresponding invariant mass m JJ , and ϕ miss JJ is the azimuthal angle between ⃗ p T,JJ and ⃗ p miss T .The other two observables are R T = |⃗ p miss T |/m T and the minimum azimuthal angle ∆ϕ min between ⃗ p miss T
17
. Since R T depends on m T but has significantly weaker dependence on the model, there must be a compensating change in |⃗ p miss T | as m T changes.All of these plots were generated with M/y = 4.5 TeV.
Figure 17 :
Figure17: Distributions of m T for various values of the lightest glueball mass m 0 for the semivisible jets scenario.Solid histograms come from using the default hadronization benchmark, and dashed histograms come from the soft and hard variations.
Relative production rates of primary SM hadron species, normalized to number of spin degrees of freedom, following decay of a 1 TeV scalar to two gluons in Pythia with electroweak interactions turned off.The grouping is determined by identifying the heaviest valence quark flavor within the hadron, and each group is fit to its own Boltzmann distribution (solid lines) by maximizing the coefficient of determination R 2 .The contribution to the fit from hadron/anti-hadron species pairs are averaged to avoid fitting the same masses twice.The Monte Carlo statistics are sufficiently high that the excesses of heavy hadrons compared to the fits are not due to random fluctuations.
Table 1 :
D (p T min ) µ z σ z T had /Λ D Suggested benchmarks to set the hadronization scale and fragmentation function nuisance parameters.Also shown are the corresponding values of the dark sector coupling α D evaluated at the shower cutoff scale p T min = c Λ D , the mean µ z and standard deviation σ z of the 0 ++ fragmentation function, and the best-fit T had in Eq. (2.5) for the relative species production rates.
Table 2 :
Table of masses and decay channels for each glueball; h * indicates an offshell Higgs. | 16,238.6 | 2023-10-20T00:00:00.000 | [
"Physics"
] |
Gene-Swapping Mediates Host Specificity among Symbiotic Bacteria in a Beneficial Symbiosis
Environmentally acquired beneficial associations are comprised of a wide variety of symbiotic species that vary both genetically and phenotypically, and therefore have differential colonization abilities, even when symbionts are of the same species. Strain variation is common among conspecific hosts, where subtle differences can lead to competitive exclusion between closely related strains. One example where symbiont specificity is observed is in the sepiolid squid-Vibrio mutualism, where competitive dominance exists among V. fischeri isolates due to subtle genetic differences between strains. Although key symbiotic loci are responsible for the establishment of this association, the genetic mechanisms that dictate strain specificity are not fully understood. We examined several symbiotic loci (lux-bioluminescence, pil = pili, and msh-mannose sensitive hemagglutinin) from mutualistic V. fischeri strains isolated from two geographically distinct squid host species (Euprymna tasmanica-Australia and E. scolopes-Hawaii) to determine whether slight genetic differences regulated host specificity. Through colonization studies performed in naïve squid hatchlings from both hosts, we found that all loci examined are important for specificity and host recognition. Complementation of null mutations in non-native V. fischeri with loci from the native V. fischeri caused a gain in fitness, resulting in competitive dominance in the non-native host. The competitive ability of these symbiotic loci depended upon the locus tested and the specific squid species in which colonization was measured. Our results demonstrate that multiple bacterial genetic elements can determine V. fischeri strain specificity between two closely related squid hosts, indicating how important genetic variation is for regulating conspecific beneficial interactions that are acquired from the environment.
Introduction
Environmentally transmitted symbioses occur through the acquisition of bacteria from the environment into a naïve, uncolonized juvenile host [1]. This type of transmission strategy can be complex, since bacteria are obtained anew for each generation of hosts, and is dependent upon the population and type of symbionts present when transmission occurs [2,3]. Both host and environment have strong influences upon symbiont fitness, and it is the interplay between these two forces that determine whether specific symbiotic strains are able to colonize and persist generation after generation [4,5]. One example where both host and environment exert notable selection pressures upon symbiotic bacteria is in the sepiolid squid-Vibrio mutualism [5].
Complex molecular dialogs (including genetic interdependence) exist between sepiolid squid hosts and their Vibrio bacteria, leading to a highly specific association and subsequent cospeciation [5][6][7][8]. The complex processes by which hosts and symbionts find each other (among the tremendous marine bacterial community) in order to initiate a successful mutualism include a myriad of welldefined molecular signaling events that dictate a certain ''conversation'' between partners [9]. Additionally, it has been reported that both bacterial specificity (where Vibrios preferentially colonize particular species of hosts as well as environment [6,10,11] dictate which symbionts are successful in squid light organ symbioses. Studies competing native strains with non-native strains in both allopatric Australian Euprymna tasmanica and Hawaiian Euprymna scolopes indicate the existence of competitive dominance and intraspecific recognition of environmentally transferred symbionts [6,8,11]. Along with host specificity, environmental temperature is also an important factor for colonization and dominance of specific Vibrio strains when colonizing different squid host species living in sympatry [4]. Thus, bacterial specificity is dictated both by host mechanisms of selection (particular Vibrio spp. are host specialists) or the environment (vibrio bacteria as a group are host generalists), but the exact means of this specificity have not been determined [5].
Recent studies have been devoted to defining bacterial mechanisms (for example gene activation, horizontally transmitted elements, mutations, duplications, etc.) for host specificity. Recenty, a study demonstrated that, under laboratory conditions, host specificity between sepiolid squids and one species of monocentrid fish was determined by the presence of a single gene in V. fischeri (rscS), which regulates luminescence and synthesis of the symbiosis polysaccharide locus (syp) that is important for host colonization and biofilm formation [7]. What subtle genetic factors are responsible for the dramatic competitive fitness differences between various isolates of V. fischeri among all sepiolid squids, rather than between squids and a completely different vertebrate host, is the focus of this study.
Two closely related V. fischeri isolates (ETJB1H from the Australian host Euprymna tasmanica, and ES114 from the Hawaiian host E. scolopes) were examined in order to determine whether differences in symbiotic loci were important for strain specificity and host recognition. These two V. fischeri strains were selected because they can each colonize aposymbiotic hatchlings from both species of squid equally well in 48 hour colonization assays so long as they are the only strain of V. fischeri present; and they nevertheless also demonstrate competitive dominance when they are presented together to their native host. That is to say Australian E. tasmanica hosts are preferentially colonized by V. fischeri ETJBH1 when V. fischeri ETJBH1 and V. fischeri ES114 bacteria are both present, and E. scolopes are preferentially colonized by V. fischeri ES114 when V. fischeri ETJBH1 bacteria are also present [6,8,11]. It is likely that subtle differences in specific symbiotic loci are responsible for this complex phenotype. The two particular bacterial strains were also selected because they have full or partial sequenced genomes, allowing easy genetic comparisons between both strains [10].
Materials and Methods
This study was carried out in strict accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health. The protocol was approved by the Institutional Biosafety Committee of New Mexico State University (Permit Number: 1306NMD20103) and under the guidelines of the NMSU's Institutional Animal Care and Use Committee (85-R-009 and OLAW A4022-01 and IACUC license 2013-029). Animals were appropriately handled with care and under appropriate conditions to minimize any suffering [5]. Adult Euprymna tasmanica were collected from Botany Bay, New South Wales, Australia with permits from the Australian Government, Department of Sustainability, Environment, Water, Population, and Communities (Export permit WT2013-10343), the New South Wales Government, Industry and Investment (Collection permit P04/0014-6.0), and the Australian Government Department of Agriculture, Fisheries, and Forestry Biosecurity (AQIS invoice ELS0016507329). Euprymna scolopes (Kane'ohe Bay, Honolulu, O'ahu, GPS coordinates-N 21u269 W 157u479) were not required to have any collection permits at this site. Both species of Euprymna are not endangered or are protected in either location.
Bacterial strains and growth conditions
Two V. fischeri strains were chosen for this study: V. fischeri ETJB1H isolated from the light organ of Euprymna tasmanica from Jervis Bay, Australia and V. fischeri ES114 isolated from the light organ of Euprymna scolopes from Kane'ohe Bay, Hawaii. Both strains were grown in Luria Bertani high Salt (LBS; per liter composition: 10 g tryptone, 5 g yeast extract, 20 g NaCl, 50 mL 1 M Tris pH 7.5, 3.75 mL 80% glycerol and 950 mL dH 2 O) media and shaken at 225 rpm at 28uC overnight.
Mutant construction
Campbell mutations. Luciferase (lux) mutants of both strains (V. fischeri ETJB1H and ES114) were constructed by insertion of the plasmid pEVS122 as described previously (11) and constructs are listed in Table S2. Briefly, the luxA gene was partially amplified with specific primers designed from the sequenced strain V. fischeri ES114 (NCBI accession: NC_006840.2). PCR products were purified and cloned (after double digestion of PCR products and plasmid with XbaI and XmaI, with posterior ligation in a 1:3 plasmid-insert ratio) into the suicide vector pEVS122, and wild type V. fischeri strains were transformed by tri-parental mating via conjugation through a helper strain [12]. Strains that had undergone single homologous recombination events with the native gene were selected on LBS plates enriched with erythromycin (25 mg/mL). Strains constructed were defined as ES114::pACH101 (for the lux mutant of the Hawaiian V. fischeri strain ES114) and ETJB1H::pACH102 (for the lux mutant of the Australian V. fischeri strain ETJB1H). Constructs were verified by Southern blotting.
Allelic exchange. msh and pil mutants (mshINQ and pilABCD) were constructed by allelic replacement of the chromosomal loci as described previously [13]. 500 bp of neighbor genes were amplified and cloned (the first insert was cloned after digestion of plasmid and PCR product with SmaI and BamH1, with posterior ligation in a 1:5 plasmid-insert ratio; the second insert was cloned after digestion of plasmid and PCR product with SpeI and XbaI, with posterior ligation in a 1:10 plasmid-insert ratio) into the suicide vector pSW7848 containing the P BAD promoter and a chloramphenicol resistant cassette (Tables S1, S2). After transformation of ultracompetent cells (NEB 10-beta competent E. coli, New England BioLabs, MA, USA), selection was achieved through antibiotic enrichment (5 mg/mL choloramphenicol). Recipient cells (V. fischeri) were transformed by tri-parental mating as described above. Transformed strains (with respective deletions) were selected through colony patching after inoculation in LBS media enriched with 2% arabinose to allow dismissal of inserted constructs through expression of the toxic gene ccdB by activation of the P BAD promoter after incubation in LBS media with arabinose. To easily discriminate transformants, colonies from the original tri-parental mating that were initially resistant to chloramphenicol and eventually insensitive to CcdB toxicity were selected. Constructs were named by their respective deletion (Table S2) and were verified by PCR.
Complement construction
GAPture or TAR cloning. Complementation of the lux operon with the opposite strain's loci (lux in ETJB1H for ES114::pACH101 and lux in ES114 for ETJB1H::pACH102) was achieved through operon mobilization (''TAR cloning'' or ''GAPture'') as previously described [14]. TAR cloning technique was achieved by using the yeast homologous recombination pathway. 700 bp of neighboring genes (upstream and downstream) from the luxCDABEG operon (with 40 nucleotides of the 59 end that were homologus with vectors pCRG13 and pCRG23) were PCR amplified and purified. Vector pCRG23 was digested with SrfI and pCRG13 was digested with EcoRV. In Saccharomyces cerevisiae transformation, the yeast strain CRY1-2 (containing the genotype ura 2 , leu 2 , cyh2 R , that confers sensitivity to cyclohexamide and cannot grow in media without uracil) was cotransformed with the two digested plasmids and the amplified upstream and downstream genes using lithium acetate transformation. After transformation, yeast colonies were plated on synthetic URA medium (per liter composition: adenine hemisulfate 0.18 g, arginine HCl 0.12 g, glutamic acid 0.6 g, histidine HCl 0.12 g, myo-inositol 0.2 g, isoleucine 0.18 g, leucine 0.18 g, lysine HCl 0.18 g, methionine 0.12 g, p-aminobenzoic acid 0.02 g, phenylalanine 0.3 g, homoserine 0.6 g, tryptophan 0.24 g, tyrosine 0.18 g, valine 0.9 g, Difco yeast nitrogen base without aminoacids 6.67 g, glucose 20 g) and incubated at 30uC for 4 days. After incubation, colonies were suspended en masse with 10 mL of TE and transferred into a 15 mL falcon tube, spun, and the construct (two plasmids + upstream/downstream genes) was extracted with glass beads and 200 mL of glass beading solution (per liter composition: 5 mL 20% sodium dodecil sulfate, 10 mL 1 M NaCl, 1 mL 1 M Tris-HCl pH 8.0, 1 mL 0.1 M EDTA, 2 mL Triton X100) and purified with Phenol/Chloroform. Plasmid DNA was transformed with ultracompetent E. coli cells (NEB 10-beta competent E. coli, New England BioLabs, MA, USA) and incubated for 24 hours at 37uC. Transformed cells (, 10 colonies) were re-inoculated and plasmid DNA was extracted using the Qiagen plasmid Maxi kit (QIAGEN Inc., CA, USA). For lux operon cloning step, CRY 1-2 yeast cells were transformed (CaCl 2 spheroplast transformation procedure) with 1 mg of the plasmid extract and 5 mg of genomic DNA (from either V. fischeri ES114 or ETJB1H). Yeast cells were plated onto TYC1/ Cycloheximide plates (per liter composition: D-sorbitol 182.2 g, Difco yeast nitrogen base without aminoacids 6.75 g, dextrose 0.98 g, adenine 0.2 g, arginine 0.2 g, aspartic acid 1 g, histidine 0.2 g, leucine 0.59 g, lysine 0.53 g, methionine 0.2 g, phenylalanine 0.4 g, threonine 2 g, tryptophan 0.2 g, tyrosine 0.3 g and 3 mg/mL cycloheximide) and incubated at 30uC for 7 days. Plasmids (containing the lux operon) were extracted from yeast spheroplasts using the Stratagene strataprep plasmid miniprep kit (Fisher Scientific, PA, USA). Constructs were verified by PCR and Southern blotting. E. coli ultracompetent cells were transformed and triparental mating was achieved as described previously. V. fischeri ES114::pACH101 was complemented with the lux operon of V. fischeri ETJB1H and strain V. fischeri ETJB1H::pACH102 was complemented with the lux operon of V. fischeri ES114.
Cloning using the conjugal vector pVSV105. Complete copies of the loci for msh and pil operons were amplified with specific primers for the entire locus (Table S1). PCR products and the vector pVSV105 [15] were double digested with XbaI and XmaI digests were ligated in a 1:3 plasmid-insert ratio and transformed into ultracompetent E. coli cells (NEB 10-beta competent E. coli, New England BioLabs, MA, USA). Cells were selected with chloramphenicol enrichment (25 mg/mL) and V. fischeri recipient cells were transformed by tri-parental mating and selected after chloramphenicol enrichment (5 mg/mL). Lastly, we constructed complements that contain each strain's native loci by cloning the respective locus into vector pVSV105. Transformation was then performed as described previously (see Table S2 for complete list of complements). Complemented strains were verified by Southern blot.
Colonization assays
Colonization assays were performed as described previously [16]. Overnight cultures of V. fischeri wild-type strains (ES114 and ETJB1H), mutants and complements were regrown in 5 mL of fresh LBS media until they reached an OD 600 of 0.3. For single and competition infection experiments, cultures were then diluted to approximately 1610 3 CFU/mL in 5 mL of sterile artificial seawater and added to glass scintillation vials where newly hatched juvenile squids were placed (one individual/vial). Seawater was changed with fresh uninoculated artificial seawater every 12 hours over a period of 48 hours. Animals were maintained on a light/ dark cycle of 12/12. After 48 hours, animals were sacrificed and homogenized, and the diluted homogenate was plated onto LBS agar plates for the wild-type V. fischeri, LBS with erythromycin (25 mg/mL) for the V. fischeri mutants, and LBS with chloramphenicol (5 mg/mL) for the V. fischeri complements. A second set of animals were selected for competition studies where juvenile squids were co-infected with the native strain and a respective complement (Table S2), sacrificed after 48 hours, homogenized, and plated onto the various media as reported above. Colony forming units (CFUs) were counted the next day to determine colonization efficiency of each strain. A total of 8 animals/strain were used for each competition assay, and 10 non-infected (aposymbiotic) juveniles were used as negative controls.
Statistical analysis
To compare bacterial populations (wild-type, mutant, and complement constructs), one way ANOVA followed by the Tukey comparison was performed on calculated CFU numbers. Three technical replicates and 10 biological replicates (representing 3 treatments with 10 animals/strain and one set of 10 non-infected or aposymbiotic animals for the negative control).
Results and Discussion
We disrupted loci from three operons that were previously reported to be important for host colonization and persistence: lux (light production), msh (biofilm formation) and pil (attachment to host). First, gene disruption was achieved via single recombinational events and allelic exchange. Secondly, complementation in trans of mutants with copies from the other strain was achieved by the Saccharomyces cerevisiae-based molecular tool (GAPture) for operon manipulation and mobilization (lux) and extrachromsomal maintenance (pil and msh). For detailed information of plasmids and strains constructed and used in this study, see supplementary data (Tables S1, S2). Finally, animal colonization experiments were performed using host-specific (or native) strains and complemented mutants in both squid host species (E. tasmanica or E. scolopes) to determine whether these loci were involved in strain recognition with the purpose of describing how competitive hierarchy is linked to the manipulated symbiotic operons. Using single and competitive colonization experiments for all strains constructed (Table S1), colonization studies were performed in naïve hatchlings of both E. scolopes and E. tasmanica animals (Figures S1-S3). Competition assays between the two wild type V. fischeri strains (ETJB1H and ES114) exhibit the expected host preference for the native strain, where native V. fischeri significantly out-competed non-native strains during colonization, supporting earlier work [5,6].
Infection studies in Hawaiian juvenile E. scolopes competed native Hawaiian V. fischeri ES114 against non-native Australian lux-V. fischeri ETJB1H strain complemented with either the native ES114 lux or the ETJB1H lux genes (Figs. 1, S1). The luxnonnative V. fischeri ETJB1H had equal competitive ability against native V. fischeri ES114 exclusively when its lux mutation had been complemented with native ES114 lux (Fig. 1). That is, luxnonnative ETJB1H behaved like ES114 exclusively when the luxmutation was complemented with the ES114 lux operon. Furthermore, when the luxnative Hawaiian strain (ES114) was complemented with the non-native lux operon from the Australian strain (ETJB1H) and competed against native V. fischeri ES114, the wild type dominated the complemented strain (Fig. 1). That is to say the lux-ES114 strain complemented with the lux operon from non-native ETJB1H behaved like the non-cognate ETJB1H strain.
Results of similar experiments completed in E. tasmanica juveniles (where V. fischeri ETJB1H is native, and V. fischeri ES114 is non-native) produced the expected reciprocal results. For example, when lux from non-native Hawaiian V. fischeri (ES114) was replaced with native lux from Australian V. fischeri ETJB1H (strain -luxES114::luxETJB1H), there was an increase in colonization efficiency of the competitor as if using the native wild type Australian ETJB1H strain. Additionally when native Australian ETJB1H strain was mutated (-lux) and complemented with nonnative Hawaiian ES114 lux (strain -luxETJB1H::luxES114), colonization efficiency was as if the native wild type Australian ETJB1H strain had been competed against itself (Figs. 1, S1). These results indicate that complementary lux genes are equally proficient at determining host preference in both E. tasmanica and E. scolopes squid hosts, indicating that phenotypic plasticity at one locus can give a subtle advantage to a non-native symbiont, even though it may not be the only gene responsible for symbiont recognition and specificity.
The lux operon is responsible for biosynthesis of luciferase, which has a crucial role in V. fischeri bioluminescence and fitness. Light production is used by the squid to avoid predation via silhouette reduction in a behavior known as counterillumination [16,17]. The lux operon is present in V. fischeri as a conserved, contiguous, and coordinately expressed set of genes that have thought to have been acquired through horizontal gene transfer (HGT) among closely related bacterial clones and through vertical inheritance between bacterial families (e.g., Vibrionaceae and Enterobacteriaceae). Results from this part of our study indicate that although both lux operons produce bioluminescence and their structural proteins are similar in primary sequence, host specificity can be obtained through artificial HGT of the lux operon alone [18]. Our cloning method intentionally included 59 and 39 noncoding sequences flanking the operons; perhaps noncoding sequences contribute to the observed host preference. The lux operon might therefore drive evolutionary strain speciation through non-reproductive transmission of lux genes, when lux DNA is available in the environment and there are no other constraints on integration of operons into the recipient cell (e.g. the action of restriction endonucleases). Additionally, natural competence has been previously observed in V. fischeri after expression of the transcriptional regulators tfoX and tfoY (chitin-sensing regulators); this earlier study highlights a conserved mechanism of genetic exchange in the presence of chitin [19].
Multiple genes comprise the entire msh operon (including mshABCDGIJLMNOPQ), which is responsible for the synthesis of type IV pseudopili, important for biofilm formation [20] and attachment (or adherence) to abiotic surfaces [21]. The msh operon has also been reported to be crucial for attachment to certain host tissues, which is an important step for successful colonization and persistence [11]. We specifically targeted mshI, mshQ and mshN, since these proteins exhibit high variability in their primary sequence among multiple strains of V. fischeri, including Hawaiian ES114 and Australian ETJB1H (C. Lostroh, unpublished data). Loci from the msh operon were mutated by means of insertional inactivation and complemented by extrachromosomal maintenance [13,15,22]. Similar to the lux operon experiments, ES114 mutant strains were complemented with the ETJB1H msh gene, and vice versa. Colonization tests using all mutant strains were then completed in both E. tasmanica and E. scolopes juvenile squids. Results of mshI, mshN and mshQ loci after colonization are illustrated in Figure 2. Due to the difficulty of obtaining a large number of animals from one clutch to complete all infection experiments with msh strains, we used three different clutches from E. scolopes and two from E. tasmanica. Inter-clutch colonization variability was observed between groups, and reflected in low numbers in competition experiments; however, animals from the same clutch were used to replicate the same competition experiment to avoid variation in colonization efficiency.
Mutation of the msh genes in Hawaiian V. fischeri ES114 caused a significant reduction in colonization efficiency in E. scolopes (data not shown), demonstrating that the msh operon is important for symbiotic competence. When Hawaiian E. scolopes were infected with non-native ETJB1H complemented with native mshI (-mshIETJB1H::mshIES114), colonization efficiency was equal to the native wild-type (ES114). Results were similar for mshL and mshQ. These observations indicate that mshI, mshL, or mshQ are all important in conferring host specificity between E. scolopes and E. tasmanica squids. Interestingly, colonization in E. tasmanica juveniles did not mirror these results as they did for the lux operon. Overall levels of colonization in this case were very low (Fig. S1). The mshI Infection efficiency data is plotted as the log values of the relative competitiveness index (RCIs), calculated by dividing the ratio of mutant to wild-type by the starting ratio [28]. If the RCI is ,1 the mutant strain was outcompeted by the wild-type, the wild-type strain was outcompeted by the mutant if the value is .1, and a RCI equal to 1 indicates no competitive difference. Data points represent individual animals and the position of the figures on the y axis is merely for spacing. Vertical line represents the median value of each data plot. doi:10.1371/journal.pone.0101691.g001 and mshN ES114 strains complemented with their ETJBH1 msh counterparts were out-competed by wild type ETJBH1, while the mshQ ES114 strain complemented with its ETJBH1 msh counterpart competed slightly better for colonization than wild type ETJBH1. Alternatively, ES114 complemented with native ETJB1H mshQ locus (-mshQES114::mshQETJB1H) outcompeted the wild-type strain. Thus, results for mshQ closely resemble those for lux, whereas mshI and mshN favored one V. fischeri strain (ETJB1H) but not the other (ES114). In our mixed competitions using mshI or mshN mutants, E. tasmanica hosts select against all complemented bacteria, keeping total levels of each symbiont low (Figs. 2, S2). In addition to clutch variability, E. tasmanica hosts may exert stronger sanctions against non-native V. fischeri more than its congener E. scolopes due to the presence of a genetically diverse group of V. fischeri symbionts available for colonization in the E. tasmanica habitat, whereas V. fischeri symbionts from E. scolopes are more homogeneous and host squids sample from only a small set of V. fischeri genotypes [5]. Having the ability to discern amongst a large, genetically diverse pool of V. fischeri may give squids an advantage to also differentiate cheaters to allow for a more successful beneficial symbiosis [23]. Recent work has demonstrated changes in particular symbiotic traits (luminescence, biofilm production, motility, carbon source utilization, growth) of Hawaiian V. fischeri strain ES114 when evolved in E. tasmanica hosts [24]. These traits differ quite dramatically, with the evolved strain gaining traits similar to the native strain over time. Thus, our results indicate that the msh operon is not only important for successful colonization of sepiolid squids, but also determines host range and accommodation from a large pool of available Vibrio symbionts.
We also created null pil mutants, and complemented them in trans to examine host selection. Colonization experiments in Hawaiian E. scolopes hatchlings indicate that pilA, pilB and pilD have important roles in host specificity (Figs. 3, S3). When constructs containing the native complemented gene were competed with either native or non-native wild-type strains, colonization efficiency of the constructed strains was equal or greater than the wild-type strain (Fig. 3). Similar results were observed in the case of E. tasmanica infection studies; however, pilD was the only locus that demonstrated host specificity in E. tasmanica (and not pilA or pilB). Genes from the pil operon (pil ABCD) encode for assembly of type IV pili, and are essential for bacterial attachment to both abiotic surfaces and to host cells [16,19]. In V. fischeri, pilus subunits are synthesized by the pilABCD operon, where pilA contributes to colonization effectiveness and encodes a protein similar to type IV-A pilins (where mshA is a close relative [25,26]. Phylogenetic and molecular differences have also been observed in pilB and pilD loci among multiple V. fischeri strains isolated from different squid hosts [27]. Our study demonstrates that V. fischeri ETJB1C pilC complemented with non-native Hawaiian V. fischeri ES114 pilC (-pilC ETJB1H::pilC ES114) is dominant in E. scolopes, but loses in E. tasmanica, since there is a competitive dominance for the native pilC locus (Fig. S3). Similar results are observed with V. fischeri ES114 pilC complemented with non-native Australian V. fischeri ETJB1H from E. tasmanica. This may be due to PilC being a phase variable protein (with minor differences in 3-5 aminoacids [25], which besides being implicated in type IV pilus biogenesis, mediates cell adherence [26]. Also, the heterogeneity of pili morphology means that multiple minor proteins composed of PilC subunits have evolved to be variable in order to compete for pilus receptors in host cells [25]. The intriguing question of how Pil-dependent binding is modulated and controlled between closely related host species may explain how host-switching can be accomplished through slight variations at this locus. Additionally, we constructed complements containing the native genes and performed single colonization experiments as well as competition studies. Single colonization assays indicated that the complement was able to regain the colonization efficiency observed in the wild-type strain (data not shown), and the competition experiments (where the wild-type strain is used to coinfect the host with the native complement) indicated equivalent colonization efficiency between the two strains (Fig. S4).
To determine whether deletion of the various genetic elements had polar effects, we performed additional experiments to observe Euprymna tasmanica by their respective wild-type (ES114 or ETJB1H), mutant, and complement strains of msh genes for Vibrio fischeri. Infection efficiency data is plotted as the log values of the relative competitiveness index (RCIs), calculated by dividing the ratio of mutant to wild-type by the starting ratio [28]. If the RCI is ,1 the mutant strain was outcompeted by the wild-type, the wild-type strain was outcompeted by the mutant if the value is .1, and a RCI equal to 1 indicates no competitive difference. Data points represent individual animals and the position of the figures on the y axis is merely for spacing. Vertical line represents the median value of each data plot. doi:10.1371/journal.pone.0101691.g002 whether our mutants can affect phenotypes related to the function of downstream genes in the operon. For example, msh and pil influence adhesion and biofilm formation [21], and lux is responsible for light production [9]. We quantified biofilm and light production in both mutants and mutants complemented with the native gene, or in the case of lux, genes. Biofilm production decreased in mutant msh and pil strains, and light production was also impaired in lux mutants. Each phenotype was recovered in the respective native complements (data not shown), indicating that polarity effects may not be present; however, to be certain of this assumption additional studies are planned to determine if there is an influence in additional phenotypes. Future studies include transcriptional profiling and genetic analyses of metabolic pathways that might be affected in the various mutant strains.
Previous work examining experimental evolution of V. fischeri demonstrated polymorphic changes in phenotype (e.g., bioluminescence, biofilm, motility, growth) when strains are evolved in a novel host, allowing greater colonization efficiency of evolved strains when competed against their non-evolved ancestor [5,24]. These results are consistent with our directionally mutated strains reported here, where non-native strains complemented with native loci (in both Hawaiian E. scolopes and Australian E. tasmanica) outcompeted non-native strains and competed favorably over native parental strains during colonization in both host species examined.
Our results indicate that the operons examined here are critical host-specificity factors and sufficient to dictate host recognition among closely related strains of V. fischeri from different geographical origins. Thus, strain specificity between two closely related V. fischeri symbionts from similar hosts is not mediated by a single or few loci, but rather multiple bacterial genetic elements that determine host range in allopatric Indo-west Pacific Euprymna-Vibrio associations.
Colonization of the squid host is multifactorial, and different studies from our laboratory have demonstrated that genes that are responsible for phenotypes associated to colonization are important for successful infection; additionally, experimental evolution of closely related strains does lead to competitive dominance of non-native strains [5,24]. Although these studies suggest that these loci are important for host preference, there is the possibility that compensatory mechanisms could overtake the effect of a mutation and regulatory mechanisms (along with genetic factors) are responsible for colonization efficiency.
This study provides additional support of how bacterial diversity can be maintained through host selection, and key symbiotic loci are just one factor in determining host specificity. Determining whether these loci are acting in concert with one another to further push the selective advantage of beneficial vibrios is crucial for our understanding the evolution of symbiotic associations. How these subtle differences arise in wild populations, and whether they confer a greater selective advantage in bacterial fitness, will give insight into the processes of ecological adaptation in Vibrio bacteria. Competition experiments are represented with two bars (% is the first strain and & is the second strain), and each strain used is indicated below each competition. Wild-type ES114 significantly colonized the host better than non-native ETJB1H. Apo = aposymbiotic or non-infected juvenile squids. Data are plotted as the mean of Colony Forming Units (CFUs) counted for each strain. Multiple comparisons were calculated between groups using the Tukey PostHoc comparison. Different letters indicate significant differences (p,0.05) between groups or infection sets. See Table S1 for a complete description of strains and Table S2 Euprymna tasmanica by their respective wild-type (ES114 or ETJB1H), mutant, and complement strains of pil genes for Vibrio fischeri. Infection efficiency data is plotted as the log values of the relative competitiveness index (RCIs), calculated by dividing the ratio of mutant to wild-type by the starting ratio [28]. If the RCI is ,1 the mutant strain was outcompeted by the wild-type, the wild-type strain was outcompeted by the mutant if the value is .1, and a RCI equal to 1 indicates no competitive difference. Data points represent individual animals and the position of the figures on the y axis is merely for spacing. Vertical line represents the median value of each data plot. doi:10.1371/journal.pone.0101691.g003
Supporting Information
Australian V. fischeri ETJB1H significantly colonized the host better than the non-native Hawaiian V. fischeri ES114. Apo = aposymbiotic or non-infected juvenile squids. Data are plotted as the mean of Colony Forming Units (CFUs) counted for each strain. Multiple comparisons were calculated between groups using the Tukey PostHoc comparison. Different letters indicate significant differences (p,0.05) between groups or infection sets. (TIFF) Figure S2 A) Colonization assays 48-hour post-infection of juvenile Euprymna scolopes by wild-type, mutant, and complement strains of msh genes for Vibrio fischeri. Single strain infection experiments are represented when only a single bar is shown (%). Competition experiments are represented with two bars (% is the first strain and & is the second strain), and each strain used is indicated below each competition. Wild-type ES114 significantly colonized its native host better than non-native ETJB1H. Apo = aposymbiotic or non-infected juvenile squids. Data are plotted as the mean of Colony Forming Units (CFUs) counted for each strain. Multiple comparisons were calculated between groups using the Tukey PostHoc comparison. Different letters indicate significant differences (p,0.05) between groups or infection sets. Competition experiments are represented with two bars (% is the first strain and & is the second strain), and each strain used is indicated below each competititon. Wild-type ES114 significantly colonized the host better than the non-native ETJB1H. Apo = aposymbiotic or non-infected juvenile squids. Data are plotted as the mean of Colony Forming Units (CFUs) counted for each strain. Multiple comparisons were calculated between groups using the Tukey PostHoc comparison. Different letters indicate significant differences (p,0.05) between groups or infection sets. B) Colonization assays 48-hour post-infection of juvenile Euprymna tasmanica by wild-type, mutant, and complement strains of pil genes for Vibrio fischeri. Single strain infection experiments are represented when only a single bar is shown (%). Competition experiments are represented with two bars (% is the first strain and & is the second strain), and each strain used is indicated below each competition. Wild-type ETJB1H significantly colonized the host better than the non-native ES114. Apo = aposymbiotic or noninfected juvenile squids. Data are plotted as the mean of Colony Forming Units (CFUs) counted for each strain. Multiple comparisons were calculated between groups using the Tukey PostHoc comparison. Different letters indicate significant differences (p,0.05) between groups or infection sets. | 7,679 | 2014-07-11T00:00:00.000 | [
"Biology",
"Environmental Science"
] |
Revisiting the Plant CLE Gene Family with a New Method for Predicting and Clustering Short Amino Acid Sequences
Background: The CLV3 / ESR-RELATED ( CLE ) gene family encodes small secreted peptides (SSPs) and plays vital roles in plant growth and development through cell-to-cell communication. The prediction and classification of CLE genes is challenging because of their low sequence similarity. Results: We developed a machine learning-aided method for predicting CLE genes by using a CLE motif-specific residual score matrix and a novel clustering method based on the Euclidean distance of the 12 amino acid residues from CLE motifs in a site-weight dependent manner. In total, 2156 CLE candidates—including 627 novel candidates—were predicted from 69 plant species. The results from our CLE motif-based clustering are consistent with previous reports using the entire pre-propeptide. Characterization of CLE candidates provided systematic statistics on protein lengths, signal peptides, relative motif positions, amino acid compositions of different parts of the CLE precursor proteins, and decisive factors of CLE prediction. The approach taken here provides information on the evolution of the CLE gene family and provides evidence that the CLE and IDA/IDL genes share a common ancestor. Conclusions: Our new approach is applicable to SSPs or other proteins with short conserved domains and hence, provides a useful tool for gene prediction, classification and evolutionary analysis.
Background
Small secreted peptides (SSPs) play vital roles in cell-to-cell communication during plant growth and development [1][2][3][4]. The most well understood plant SSPs are encoded by the CLAVATA3 ( CLV3)/EMBRYO SURROUNDING REGION ( ESR)-RELATED ( CLE) gene family [5,6]. CLE peptides have been widely identified in bryophytes, pteridophytes, gymnosperms and 3 angiosperms [7]. A typical CLE protein contains an N-terminal signal peptide, a nonconserved variable region in the middle, a C-terminal conserved motif (CLE motif) and in some instances, a short C-terminal tail downstream of the CLE motif. CLE motifs are usually composed of 12 to 13 amino acid residues, independent of the flanking sequences.
Artificially synthetic peptides representing the CLE motif domains can mimic the overexpression transgenic phenotypes [8][9][10]. The conserved CLE domains contain hydroxyproline and arabinosylated hydroxyproline residues [11][12][13]. Interestingly, the influence of these post-translational modifications varies in different species. For instance, post-translational modifications are critical for the activity of the CLV3 peptide in tomato but not in Arabidopsis [ 14,15]. Typically, the mature forms of CLE peptides are recognized by plasma membrane-localized leucine-rich repeat receptor-like kinases (LRR-RLK) or receptor-like proteins (LRR-RLP) [16][17][18]. The extracellular domains of LRR-RLK/RLPs bind cognate CLE peptides as ligands and then transduce the extracellular signals by activating the intracellular domain of the LRR-RLKs or plasma membraneassociated kinases. Various methods have been used to investigate the interactions between CLE peptides and LRR-RLK/RLPs, such as genetic and physiological approaches, direct physical interaction and phosphor-proteomics. However, only a small number of possible ligand-receptor pairs have been identified [19,20].
Each amino acid of the CLE motif plays different roles [37,38]. For example, clv3 mutants and plants expressing a CLV3 motif with the Gly residue at the 6th position substituted with Leu, Ile, Val, Phe, Tyr, or Pro are phenotypically similar [38]. Similarly, structural and functional analyses of the TDIF-TDR/PXY (ligand-receptor pair) demonstrate that each amino acid residue of the TDIF motif is important. Indeed, amino acid substitutions at the 1st, 3rd, 4th, 6th, 8th, 9th and 12th positions of the TDIF motif result in reduced or complete loss of function [39]. Although amino acid substitutions at the 2nd, 5th, 10th and 11th sites of the TDIF motif have very little impact on its activity in terms of inhibition of TE differentiation, these sites are important for specifically binding the TDR/PXY receptor [40,41].
Because of the short coding sequences and the generally low sequence similarity of CLE proteins, the identification and classification of CLE genes has always been a challenge, even in the model plant A. thaliana. Originally, using TBLASTN, 39 typical CLE polypeptides were identified-24 of them were from A. thaliana [ 42]. Subsequently, CLE40, CLE41 and a nematode CLE ( HgCLE) gene were identified using the same approach [43].
The latter one emphasized the possibility of ligand mimicry. CLE41 was the first of a novel class of CLE gene, the TDIF and TDIF-like genes [39,44]. A total of 32 CLE genes have been identified in A. thaliana defining 26 unique CLE peptides [45]. The Arabidopsis CLE genes have been used to identify CLE homologues in many other plant species, such as Oryza sativa [ 46], Lotus japonicas [ 47], Selaginella moellendorfii [ 48], Medicago truncatula [ 49,50], Picea abies [ 51], Solanum lycopersicum [ 52], Glycine max [ 53], Raphanus sativus [ 54], and Populus trichocarpa [ 55]. Goad et al. [7] predicted CLE polypeptides from 57 plant species. The classification of CLE gene families has been based on their functions or sequence similarities. Based on the effects of CLE peptides on plant growth, the 22 Arabidopsis CLE polypeptides were classified into two groups [56].
According to their physiological functions, four classes of CLE peptides were proposed [57]. On the other hand, 13 categories of CLE motifs were generated by clustering of the conserved sequences with the CLANS software [7,58].
The objective of this study was to develop a novel approach for efficiently and accurately predicting and classifying CLE proteins. The general substitution matrix was replaced with a modified amino acid substitution matrix that is based on the weight of each position of the CLE motif. Machine learning (ML) was used to improve the accuracy of CLE gene predictions. This study helps to define the characteristics of different groups of CLE genes and therefore, to explore the origin and evolution of the CLE gene family.
Results
Developing a new residual score matrix for CLE motifs To predict CLE genes in plants, we developed a new residual score matrix for CLE motifs 6 by integrating the amino acid substitution matrix, amino acid usage frequency matrix and site weights of the CLE motif.
The amino acid composition of the CLE motif was analyzed in 69 species at different levels that included total proteins, small proteins (≤ 200 residues in length) and CLE precursor proteins (Additional file 1: Figure S1). The amino acid composition of small proteins was similar to total proteins. However, a higher frequency of particular residues was observed in CLE precursors (e.g., proline (P) and histidine (H)) (Additional file 1: Figure S1). The amino acid composition in different regions of CLE proteins was also analyzed (Additional file 1: Figure S1). The frequency of P and H in CLE motifs were both more than fourfold higher than in total proteins, which provides evidence that they are functionally important amino acids for peptide processing or peptide-receptor recognition (Fig. 1A). In contrast, some residues were very scarce in CLE motifs, such as the three aromatic amino acids (phenylalanine (F), tyrosine (Y) and tryptophan (W)) and the two sulfur-containing amino acids (cysteine (C) and methionine (M)) ( Fig. 1A; Additional file 1: Figure S1). This strong bias in amino acid composition encouraged us to try and build a CLE-specific score matrix.
We tested three commonly used substitution matrices-BLOSUM62, BLOSUM80 and PAM250-and found that the performance of each was similar (Additional file 2: Figure S2).
Nevertheless, the BLOSUM80 matrix provided a slightly better resolution of the motif scores and therefore, was used to develop the new score matrix. For the amino acid usage frequency matrix, 1628 reported CLE genes from 57 species [7] were chosen as references (Additional file 12: Table S1). The amino acid usage frequency at each site of the CLE motif was calculated as a percentage (Additional file 3: Figure S3) and was represented as a Weblogo sequence (Fig. 1D). The conservativities of each site were largely different, as previously reported [38]. Sites with higher conservativity were considered to hold higher weight in our new score matrix. Some sites contained two dominant residues, such as the 8th site (50.03% N and 47.06% D) and the 12th site (66.49% N and 31.38% H). Based on the modified method for evaluating site weight, the weight of the 12th site was set at 1.00, and the 1st, 6th -9th, and 11th sites had weights no less than 0.70 (Fig. 1B).
In the new CLE score matrix, each residue of a candidate CLE motif made a contribution to its total score. Residues at the conserved sites contributed more than those at less conserved sites. Dominant residues contributed more than scarce residues. For example, the proline at the 9th site alone had a score of 6.62, which made the most striking contribut in the score matrix (Fig. 1C). It is worth mentioning that the combination of 12 residues with the highest frequency at each site was "RLVPSGPNPLHN", found in CLE9/10 in A. thaliana. The combination of residues with the highest score was "RRVPSGPNPLHN".
The total motif score was 38.00.
Machine learning aided the prediction of CLE genes in plants
In addition to the CLE motif score, we also included protein lengths, motif positions and signal peptide scores to predict CLE genes in 69 plant species. Three machine learning algorithms, C4.5, ANN and SVM, were employed to categorize all candidate genes into CLE genes or non-CLE genes using the reported CLE genes in the training data set. Our analysis of the training data set, based on 53 species, yielded 1709 CLE candidate genes, including the 1529 genes that were predicted using the Hidden Markov Model (HMM) (Goad et al 2017) and 180 novel genes. All three machine learning algorithms supported 1475 (96.5%) of the reported CLEs and 106 (58.9%) of the novel CLEs. In total, 94 (5.5%) of the candidate genes were supported by only one algorithm (Fig. 1E). Additionally, machine learning aided in the prediction of CLE genes. Indeed, machine learning identified 447 novel CLE candidates from the 16 species in the testing data set. Therefore, our method identified a total of 2156 CLE candidates in 69 species (Additional file 12: Table S1).
A new CLE classification method based on the Euclidean distance of CLE motifs in a site-8 weight dependent manner To group the 2156 CLE motifs, the Euclidean distances (d) between each CLE candidate and the 32 Arabidopsis CLE motifs (AtCLEs) were calculated ( Fig. 2 and Fig. 3). Motifs from the top 5% maximum d to AtCLEs were classified into Group "Others". The rest of the CLE motifs were classified with their closest AtCLE. Consequently, all of the CLE motifs were grouped into six groups, Group1-5 and Others. As a comparison, phylogenetic trees constructed using the A. thaliana CLE motifs ( Fig. 2A), CLE proteins without signal peptides (Fig. 2B) and log-normalized rank of all-vs-all BLAST e-values of full-length CLE proteins ( Fig. 2C) were constructed using the NJ method, as previously described [7,59].
The new AtCLE clustering using the HCL method was based on the Euclidean distance between each pair of AtCLE motifs (Fig. 2D). The clustering results were similar to the third phylogenetic tree, except for AtCLE8, AtCLE40 and AtCLE43 ( Fig. 2 and Additional file 13: Table S2). In Group3, the AtCLE8 and AtCLE12 motifs, which are "RRVPTGPNPLHH" and "RRVPSGPNPLHH", respectively, share high sequence similarity. However, clustering of AtCLE40 and AtCLE43 was not consistent among the four methods (Fig. 2D). To determine the reasons for these discrepancies, Weblogos of the appropriate subgroups (Group5A and Group5B) were created. Both subgroups were less conserved relative to other subgroups (Additional file 4: Figure S4 and Additional file 14: Table S3).
A cluster tree of all CLE candidates in 69 species was drawn that includes a heatmap indicating the Euclidean distance between the CLE motifs (Fig. 3). The heatmap demonstrated that the CLE candidates in Group5 and Group "Others" have a higher diversity in residual composition. Based on the cluster tree, the 26 AtCLE subgroups were then combined into 11 subgroups. Weblogos of the final 12 subgroups illustrated the importance of "heavy-weight" sites in the classification of CLE motifs (e.g., the 1st and 8th sites (Additional file 4: Figure S4)). Analysis of tandem CLE genes revealed that Group1 had the highest rate of tandem genes. Besides, candidates from monocots seemed to form clusters with other monocots, and candidates from dicots seemed to form clusters with other dicots. These data indicate a strong specificity among the monocot CLE motifs and the dicot CLE motifs (Fig. 3). Statistical analysis of the different types of CLE motifs showed that monocots and dicots share very few CLE motifs (18 out of the 474 CLE motifs in dicots). Furthermore, there was no common TDIF/TDIF-like motif shared between monocot and dicot species, probably due to the evolution of distinct vascular patterns in monocots and dicots (Additional file 15: Table S4).
Evolution of CLE genes in plants
To understand the evolution of CLE genes in plants, the number of CLE genes in each species was counted ( Fig. 4 and Additional file 5: Figure S5). Although three CLE genes had been detected in algae, including one in Dunaliella salina and two in Coccomyxa subellipsoidea, the algal CLE genes were atypical because of their low motif scores, low signal peptide scores and poor motif positions (Additional file 16: Table S5). In contrast to algae, there were nine typical CLE genes in Physcomitrella patens ( Figure S5). The proportion of CLE genes in different species was not fixed, ranging from 0.015% (Vitis vinifera) to 0.204% (Phaseolus vulgaris). The mean proportion of CLE candidates in dicots was slightly higher than in monocots, which were 0.105% and 0.091%, respectively. Their proportions in the three Bryophytes and the pteridophyte (Selaginella moellendorffii) were 0.027%, 0.041%, 0.041% and 0.036%, respectively, in general lower than in the monocots and dicots.
To further investigate the evolution of CLE genes in different species, the number of CLE genes in each subgroup was counted in each species (Fig. 4). CLE candidates appeared in fewer subgroups in lower plants. For example, the nine CLE candidates in P. patens were all presented in Group3B. Mapoly1011s0001.1 from M. polymorpha was the first candidate identified in Group4. Its motif "HKNPAGPNPIGN" shared high similarity with the CLE motif from Arabidopsis CLE46, a homolog of TDIF. Although none of the Group1 candidates were identified in the bryophytes, two CLE candidates from Group1 were identified in S.
moellendorffii.
In addition, to the finding that CLE motifs are most frequently found in monocots and dicots, the number of each motif was counted (Additional file 6: Figure S6 and Additional file 17: Table S6). Our results indicated that the most frequent CLE motif in monocots was "RRVRRGSDPIH"-the same as CLE45 in A. thaliana; and the most frequent CLE motif in dicots was "HEVPSGPNPISN"-the same as CLE41/44 (TDIF) in A. thaliana. Particular CLE motifs have strong bias in monocots and dicots. For example, although the TDIF motif appeared 83 times in dicots, none were found in monocots. In contrast, only a TDIF-like motif "HEVPSGPNPDSN" appeared in monocots (Additional file 17: Table S6).
Statistics analysis of CLE precursor proteins CLE peptides are derived from nonfunctional precursor proteins by removal of the Nterminal signal peptide from the latter and by enzymatical processing to yield the mature peptide [60]. In order to get a better understanding of CLE protein evolution, various characteristics of different groups were analyzed, including CLE motif score, protein length, relative position of CLE motif, length of the C-terminal tail, signal peptide scores, and correlations among the major variables of the score matrix (Fig. 5, Additional file 3: Figure S3, Additional file 7: Figure S7 and Additional file 8: Figure S8). Group 3 had the highest median CLE motif score, followed by the rest of the groups in the following order: Group 1, Group 2, Group 4, Group 5 and Group "Others" (Fig. 5A and Additional file 18: Table S7). Although about 90% of the CLE precursor proteins are 50-150 amino acid residues long, most groups had more candidates containing 50 to 100 residues, except for Group 4 ( Fig. 5B and Additional file 9: Figure S9). Group 1 to 4, particularly Group 3, had higher values for the relative position of the CLE motifs (i.e., means closer to the C-terminal end). In contrast, the motif positions in Group 5 and "others" were more widely distributed (Fig. 5C). When the number of residues following the CLE motif at the C-terminus was checked, about two thirds of the candidates had a Cterminal tail of 0 to 2 residues. More than 50% of the candidates from both Group 1 and Group 3 did not have a C-terminal tail. The basic amino acids Arginine (R) and lysine (K) dominated at the first amino acid residue position in the short C-terminal tails (1-2 residues), except for the candidates from Group 1 ( Fig. 5D and Additional file 7: Figure S7). The presence of a signal peptide in the CLE precursors was predicted online using the SignalP/TargetP server and illustrated with a violin plot. Most genes in Group 1 had high signal peptide scores (Fig. 5E, F). However, about two-thirds of the genes in Grp. 2B and Grp. 5A had SignalP scores lower than the cut-off value (Additional file 19: Table S8). In general, the lengths of the CLE precursor proteins in the bryophytes and S. moellendorffii were slightly longer than the average. Other variables, including the signalP score, motif position and the CLE motif score, were not significantly different between vascular and non-vascular plants (Additional file 8: Figure S8).
To determine how much each variable contributed to each CLE candidate, correlations between the five variables and the decision to define a candidate as a CLE were calculated ( Fig. 5G-5I). Motif score and motif position were decisive factors when the length of the CLE proteins was between 50 and 150 residues. Protein length was positively correlated with the decision when the candidates were shorter than 100 residues. However, the correlation was negative for the candidates between 100 and 150 residues in length ( Fig. 5G and 5H). For longer candidates (> 150 residues), the correlation between motif position and the decision was less. For these candidates, the motif score was the only decisive factor (Fig. 5I). It is worth mentioning that the correlation between the signal peptide scores and the decision was less than expected. In addition, we analyzed the gene structures of the CLE candidates in A. thaliana and Zea mays. The results provide evidence that alternative splicing may allow particular CLE genes to concurrently encode proteins with or without the CLE motif (e.g., AT5G59305/CLE46 and GRMZM5G875999) (Additional file 10: Figure S10).
Identification of new types of CLE genes
By applying our new approach, 5% (n = 136) of the CLE candidates that are more distantly related to the Arabidopsis CLEs were clustered into Group "others". A total of 31 of these candidates were reported previously [7]. Based on the clustering, a novel subgroup of candidates (n = 26) was identified, with an unusual "serine (S)" at the 12th site of the CLE motif (Fig. 6). This subgroup could be further divided into three types, mainly based on the last three residues of their CLE motifs. All members of this subgroup were from monocots and dicots, consistent with their recent evolution.
Most of the IDA/IDL-like candidates were from the monocots and dicots, except for MA_9094901g0010 and AmTr_v1.0_scaffold00135.62 from M. polymorpha and Amborella trichopoda, respectively. By clustering the IDA/IDL-like candidates together with the Arabidopsis IDA/IDL motifs, using PIP/PIPL motifs [61] as the outgroup, we found that the 13 SVPP-and PVPP-type motifs were grouped with the IDA/IDL family, while the RIPP-type motif was more closely related to the CLV3 motif (Fig. 7A). All of the PVPP-type genes were predicted to encode a potential signaling peptide "PVPPSGPSPCHN" (Fig. 7B).
In addition to the novel CLE candidates from Group "others", small sets of novel candidates were identified in the major groups. The most common residues at the 1st site of a typical CLE motif are arginine (R) and histidine (H). However, candidates with an initial lysine (K) or tryptophan (W) residue in the CLE motif were identified. These K-type and W-type CLE motifs are the most closely related to CLE16 (Group 3C) and CLE45 (Group 2A), respectively (Additional file 11: Figure S11). The 11 K-type candidates were all from monocots. The 13 W-type candidates were exclusively found in dicots.
Discussion
Small secreted peptides (SSPs) (e.g., CLE peptides) are hard to predict in silico because their conserved motifs are short-usually less than 20 residues in length. The commonly used method for predicting SSPs use BLAST (Basic Local Alignment Search Tool) [62].
However, when using BLAST, some thresholds should be defined, such as the S score, which provides a measure of local similarity for any pair of sequences, and the E-value, which is the probability of finding a segment pair with a score no less than the S score. It is difficult to define an appropriate threshold for E-values when using CLE as query because it is too short to achieve a high S score and therefore, yields a much greater Evalue. When using a CLE precursor protein as query, the signal peptide and the nonconserved variable region will interfere with the BLAST result. Another common method for predicting SSPs uses HMMER [63]-the latest version is HMMER3 [64]. The results from HMMER depend on the training set. Although the public database of small proteins is expanding, it still cannot meet the demand for predicting SSPs.
In this study, we retrieved all of the annotated amino acid sequences for small proteins 14 from 69 plant species. A CLE-specific score matrix was developed because of the hidden information for peptide processing and peptide-receptor interactions in CLE motifs ( Fig. 1). Three ML algorithms were applied for predicting CLE genes using multiple variables based on a variety of properties of CLE precursor proteins, in addition to a motif score matrix. A low motif score threshold was set and the union of the ML results was analyzed, in order to keep as many CLE candidates as possible. The "low stringency" strategy allowed us to uncover some candidates that are atypical in that they are less similar to the well-studied AtCLEs. By using our newly developed clustering approach for identifying CLE motifs, we were able to classify the major groups and to identify minor groups of new candidates (Fig. 3, Fig. 4 and Fig. 6). A "high stringency" version of this approach could be developed by simply increasing the threshold of the motif score and changing the ML results from union to intersection.
When a candidate had a low motif score, it probably fell into Group "others" (Fig. 6). Most of the candidates (ca. 78%) in Group "others" have not been previously reported. Several criteria are needed to determine whether a candidate from Group "others" is a CLE, including the number of similar motifs, the number of species containing the candidate, and the number of ML algorithms that support it. Candidate motifs that are identified only in one species are more suspicious than candidate motifs that are identified in more than one species.
Although it is possible to classify CLE genes based on their contributions to particular biological processes, several difficulties impede a comprehensive functional analysis of CLE genes, such as high gene redundancy, specific temporospatial expression patterns and mostly, unknown forms of the mature peptide. Knock-out lines generated using the CRISPR-Cas9 system will shed some light on the biological functions of CLE genes.
However, this approach is time consuming. Moreover, transgenic manipulation remains difficult in particular species. In contrast, our new clustering method is more efficient because it considers only the amino acid compositions and site weights of CLE motifs.
Functional information embedded in the major residues or the heavyweight sites will be reflected in the score matrix and the one-on-one Euclidean distances between the CLE motifs. The clustering results may in turn be helpful for functional analysis of the CLE genes that are closely grouped.
One of the main purposes of this study was to determine how CLE genes evolved in plants.
We were not able to identify any typical CLE genes in the seven species of algae used in this study. The existence of CLE genes in P. patens, S. fallax and M. polymorpha provides evidence that the CLE genes evolved in bryophytes. All of the nine P. patens CLE candidates belong to Group 3B and have a consensus motif sequence of "RXVP(S/T)GPNPLHN". The motif "RLVPTGPNPLHN" found in P. patens is one of the top10 most frequently used CLE motifs in plants, but it is not common in eudicots. A similar motif "RLVPSGPNPLHN", found in Arabidopsis CLE9/10 was identified exclusively in eudicots. The CLE9/10 motif is the second most abundant CLE motif in dicots. The involvement of CLE9/10 in the drought response and primary root development in A.
thaliana [ 27,65] is consistent with the peptide "RLVPTGPNPLHN" helping bryophytes to develop adaptations to survive in more arid environments. Another interesting finding in bryophytes is the evolution of the Group 4 candidate Mapoly1011s0001.1 in M. polymorpha. Its potential motif "HKNPAGPNPIGN" is identical to the Arabidopsis CLE46 motif "HKHPSGPNPTGN" at all of the conserved sites ( Fig. 1B and Additional file 5: Figure S5) [40,41]. CLE46 is highly homologous to CLE41 and CLE44-two TDIF encoding genes in Arabidopsis [ 39]. However, similar to other liverworts, M. polymorpha has neither vascular tissue nor true roots. Therefore, the presence of a CLE46-like gene in M. polymorpha remains mysterious. Nevertheless, the number of candidate genes in Group 4 rapidly increased in vascular plants, especially genes encoding candidates with the TDIF motif "HEVPSGPNPISN". The largest number of candidates in dicots contain the TDIF motif (Additional file 17: Table S6).
Besides the CLE gene family, several gene families have been identified that encode SSPs [3,20]. Among them, the CLEL/GLV/RGF and IDA/IDL motifs share high sequence similarities with the CLE motif [19,66]. However, our knowledge of the evolutional relationship among these peptide-coding genes remains limited. Based on our lessstringent gene prediction strategy, it is possible to compile a list of atypical CLE genes.
We found three types of candidates: true CLE genes, non-peptide-coding genes and novel peptide-coding genes. We identified 21 candidates that belong to three small but conserved groups in Group "others" (Fig. 6). Their potential CLE motifs are highly similar to the IDA/IDAL motifs and thus, appear to represent a transitional type of CLE and IDA/IDL motif. The IDA/IDL genes are involved in floral organ abscission, lateral root emergence and root cap sloughing [67]. Since we have not found any typical IDA/IDL genes in P. This study was based on a global analysis of the annotated genes from 69 plant species, from single-cell green algae to giant trees. Comparative analysis of CLE gene family sequences from multiple species could increase the reliability of gene prediction and characterization and thus, provide information on how these genes have evolved. There are a few challenges remaining for future work. First, the number of lower plant and lower vascular plant species used in this study was limited. The availability of more genome sequences from bryophyte and pteridophyte species will be useful for understanding the origin and evolution of SSP-encoding genes. Second, the quality of genome annotation varies considerably, mainly due to the complexity of each genome and the quality of genome sequencing, assembly and annotation. Thus, high genome complexity or low genomic sequencing quality will increase the frequency of miss counts of SSP-encoding genes. Furthermore, SSP-encoding genes could not be effectively predicted and/or annotated [68]. It is difficult to distinguish them from non-coding sequences because their coding regions are small. More than this, without a reference gene, there is no effective method to predict an SSP-encoding gene when alternative splicing introduces additional complexity. Regarding particular types of SSPs that are variable in length, more research is required for determining how to set a gap penalty for SSP prediction. The in silico prediction of SSPs that are present in single-copy or low copy numbers (e.g., Casparian Strip Integrity Factor (CIF) from Arabidopsis) [69,70] requires a comparative genomics analysis with multiple species. In addition, integration of next-generation sequencing (NGS)-based transcriptomics and mass spectrometry (MS)-based proteomics analyses will provide essential information about SSPs, especially the novel SSPs.
Conclusions
In summary, we developed a novel machine learning-aided method for predicting CLE genes from 69 plant species by using a CLE motif-specific residual score matrix. We found 2156 CLE candidates, including 627 novel CLE candidates. We also developed a novel clustering method based on the Euclidean distance of CLE motifs in a site-weight dependent manner. Our grouping was relatively consistent with the previous reports by Oelkers et al. [58] and Goad et al. [7] Moreover, the advantage of this new clustering method is that it does not require any flanking sequences from the CLE motifs.
Characterization of CLE candidates suggested that ca. 90% of the CLE precursor proteins have a protein length of 50 to 150 amino acid residues, about 30% of the CLE candidates may not have a signal peptide targeting them to the secretory pathway, two-thirds of the 18 CLE candidates we identified have a short C-terminal tail (i.e., 0-2 residues) downstream of their CLE motifs, and the CLE motif score was the only decisive factor for identifying candidates longer than 150 residues. These characteristics are important for classifying novel candidates as CLE genes. The approach taken here not only helps us to investigate the evolution of the CLE gene family, but also allows us to discover a potential evolutionary relationship between the CLE and IDA/IDL gene families. The IDA/IDL-like CLE candidates represent a missing link between the two families and provide evidence that the CLE and IDA/IDL genes probably share a common ancestor. Our novel approach for predicting and clustering CLE genes may also be applicable to other SSPs and, therefore may provide a powerful tool for studying the origin and evolution of SSPs.
Developing a new residual score matrix for CLE motifs in plants
The new residual score matrix for CLE motifs was developed by integrating the amino acid substitution matrix, the amino acid usage frequency matrix of CLE motifs and the site weights of CLE motifs.
To find an optimal amino acid substitution matrix, three commonly used substitution matrices, BLOSUM62, BLOSUM80 and PAM250, were tested using 116 CLE candidates from A. thaliana, O. sativa, S. moellendorfii and P. abies (Additional file 20: Table S9). The scores of these 116 reported CLE genes followed an order from large to small and were fitted to a curve using the Local Polynomial Regression Fitting (LOESS) method. A matrix with the highest sensitivity was chosen to construct the score matrix for the subsequent analyses.
To develop the amino acid usage frequency matrix for CLE motifs, we used the 1628 reported CLE genes as references [7]. The percentage of each amino acid residue S at each of the 12 sites of the CLE motif was calculated as follows: 19 where S ij represents the percentage of amino acid i at site j; a ij represents the number of amino acids i at site j and n represents the number of reported CLE genes.
The weight of each site (w j ) in the CLE motif was based on the Bits value of each site [71].
The modified Bits values (Bits') were used to assign a weight to each site of the CLE motif with the following steps: (1) select amino acids with S ij ≥ 25% as the major amino acids for each site, (2) combine S ij values for these amino acids, and (3) calculate the Bits' values based on the ratio of the amino acids at each site using the following equation: where m represents the types of amino acids (m = 20), k represents the number of amino acids with S ij ≥ 25% at site j, H j ' represents the modified entropy of site j, and e m is the correction number, which was mainly applied when the number of input sequences was less than 20.
A novel residual score matrix N was then constructed by integrating the amino acid substitution matrix M, the amino acid usage frequency matrix S and the site weight w j : 20 where M ik represents the substitution score between amino acid i and amino acid k in the amino acid substitution matrix, S jk represents the frequency of amino acid k at site j in the amino acid usage frequency matrix. The motif score v of each CLE motif was calculated by applying the novel score matrix N: where i represents an amino acid of the CLE motif at site j. where L represents the length of the corresponding protein and l s represents the start position of the CLE motif.
Machine learning aided prediction of CLE genes in plants
The coding sequences of 68 species were extracted at the whole genome level from Phytozome v12 (https://phytozome.jgi.doe.gov/pz/portal.html) [74]. Coding sequences of P. abies were downloaded from PlantGenIE (http://plantgenie.org) [75,76]. First, we filtered out protein sequences with L < 30 and L > 300. For the remaining protein sequences (30 ≤ L ≤ 300), we calculated a motif score for any fragment containing 12 amino acid residues. A motif with the highest score was chosen as a potential CLE motif for this protein. The 1529 reported CLE genes identified using the HMM algorithms from 53 species in the Phytozome v12.1 database [7] were labeled as CLE genes. The number of CLE genes (X) in a particular species was counted. If X ≤ 10, 30 candidates with the highest scores were selected. For a species with X > 10, 3X candidates with the highest scores were selected. All of the CLE genes were removed from the list of candidate genes.
The remaining genes were defined as non-CLE genes. To build the training data set, the CLE and non-CLE genes were combined.
Three machine learning algorithms, C4.5, Artificial Neural Network (ANN) and Support Vector Machine (SVM), were used to analyze the training dataset using the abovementioned five variables. All three algorithms were implemented in the R language (R- The maximum number of iterations was set to 1000 (SVM, e1071_1.6-8 package). The default settings were used for the other parameters. Candidate genes from the remaining 16 species were used for the testing data set. Candidate CLEs were supported by at least one of the three classifiers.
Clustering of CLE genes in plants
The CLE candidates predicted by machine learning were further clustered using a novel protocol based on the Euclidean distance (d). The Euclidean distance between each candidate sequence and each reported Arabidopsis CLE motif was calculated to find its minimum distance (d m in ). The top 5% of motifs with the maximum d m in were categorized 22 into the "others" group. The modified Euclidean distance (d) between every two CLE motifs was as follow: Where a j represents the amino acid at site j of a candidate CLE motif and b j represents the amino acid at site j of A. thaliana CLE motifs. The distance between a j and b j was defined as d j .
For all grouped CLE candidate genes, a hierarchical clustering (HCL) method was applied with R (R-3.4.0) to build a clustering tree. Phylogenetic trees of A. thaliana CLE motifs, full-length CLE proteins without signal peptides and log-normalized rank of all-vs-all BLAST e-values were constructed using the neighbor-joining (NJ) method with MEGA X [77]. The clustering trees and phylogenetic trees were edited using Evolview (http://www.evolgenius.info/evolview/) [78].
Statistical analysis
To find out the bias in amino acid usage in CLE precursor proteins and CLE motifs, the amino acid composition of all proteins, all small proteins (i.e., proteins with lengths between 50 and 200 amino acid residues) and all CLE candidates were analyzed in 69 plant species. To study the evolution of the CLE genes, the numbers of CLE candidate genes were counted in each species and in each group. Characterization of CLE precursor proteins was performed by analyzing the distribution of motif scores, protein lengths, motif positions, lengths of C-terminal tails, SignalP and TargetP scores of each CLE candidate by group. Decisive factors in determining a CLE candidate gene were uncovered using a correlation analysis between each of the above-mentioned variables and the decision in three ranges of protein lengths, 51-100, 101-150 and > 150 amino acid residues. The clustering trees of CLE candidates in Group "others" and IDA-like candidates were built by applying the HCL method-based on Euclidean distance-to every pair of candidate sequences. The lengths of the C-terminal tails and their corresponding amino acid compositions in each subgroup were evaluated using a heatmap that showed the counts of CLE candidates with different lengths of C-terminal tails and using Weblogos to represent the conserved residues. For A. thaliana and Z. mays, the gene structures of the CLE candidates with alternative splicing were obtained from the gff3 files of A. thaliana and Zea mays in Phytozome v12 (https://phytozome.jgi.doe.gov/pz/portal.html).
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Availability of data and materials
All data generated or analysed during this study are included in this published article and its supplementary information files.
Competing interests
The authors declare that they have no competing interests. Blue represents long distances. A shorter Euclidean distance implies a higher degree of motif similarity. CLE motifs were clustered based on the Euclidean distance of each pair of sequences in a site-weight dependent manner. The clustering tree was generated using the HCL method. The information on the classification of the CLE motifs is shown on the top of the heatmap. All CLE motifs were clustered into six major groups: Group 1-5 and Group "others". "TGD" and 38 "Non-TGD" indicate whether the motif was from a potential tandem gene duplication (TGD). "Species" indicates that a motif was from a dicot, monocot or other type of plant species. | 8,794.8 | 2020-01-22T00:00:00.000 | [
"Biology",
"Computer Science"
] |
Glycoprotein Hormone Assembly in the Endoplasmic Reticulum
Glycoprotein hormone heterodimers are stabilized by their unusual structures in which a glycosylated loop of the α-subunit straddles a hole in the β-subunit. This hole is formed when a cysteine at the end of a β-subunit strand known as the “seatbelt” becomes “latched” by a disulfide to a cysteine in the β-subunit core. The heterodimer is stabilized in part by the difficulty of threading the glycosylated end of the α-subunit loop 2 through this hole, a phenomenon required for subunit dissociation. Subunit combination in vitro, which occurs by the reverse process, can be accelerated by removing the α-subunit oligosaccharide. In cells, heterodimer assembly was thought to occur primarily by a mechanism in which the seatbelt is wrapped around the α-subunit after the subunits dock. Here we show that this “wraparound” process can be used to assemble disulfide cross-linked human choriogonadotropin analogs that contain an additional α-subunit cysteine, but only if the normal β-subunit latch site has been removed. Normally, the seatbelt is latched before the subunits dock and assembly is completed when the glycosylated end of α-subunit loop 2 is threaded beneath the seatbelt. The unexpected finding that most assembly of human choriogonadotropin, human follitropin, and human thyrotropin heterodimers occurs in this fashion, indicates that threading may be an important phenomenon during protein folding and macromolecule assembly in the endoplasmic reticulum. We suggest that the unusual structures of the glycoprotein hormones makes them useful for identifying factors that influence this process in living cells.
knot and its carboxyl-terminal cysteine is "latched" by a disulfide to a cysteine in loop 1. This creates a hole in the -subunit that is bordered on one side by the core of the -subunit and on the other side by the seatbelt. The ␣-subunit straddles this hole such that the glycosylated end of loop ␣2 must pass beneath the seatbelt through the -subunit hole for the heterodimer to dissociate. This contributes to the stability of the heterodimer, which dissociates at low pH or in high concentrations of urea (4), but not in the presence of ionic detergents such as 0.1% sodium dodecyl sulfate. If the seatbelt were to be latched before the subunits combine, the glycosylated end of loop ␣2 would also need to pass through the -subunit during heterodimer assembly. This would impede assembly, a notion supported by the finding that removal of this oligosaccharide accelerates assembly in vitro substantially (5), a process that occurs by a threading mechanism (6).
Pulse-chase analyses of hCG assembly in cells led to the suggestion that the seatbelt remains unlatched until after the subunits dock with one another (7). In this pathway, which we term "wraparound" (Fig. 1, upper pathway), formation of the seatbelt latch disulfide is the final step in heterodimer assembly and occurs after the seatbelt has been wrapped around loop ␣2. This pathway circumvents the need for the glycosylated end of loop ␣2 to pass through the hole in the -subunit and explains the abilities of cells to make cross-linked hormone analogs in which the seatbelt is latched to cysteines added to the ␣-subunit (8). Assembly of glycoprotein hormone heterodimers can occur by a threading pathway in vitro at high subunit concentrations (6). Before heterodimer assembly begins in the threading pathway, the seatbelt is latched to a cysteine in loop 1 (Fig. 1, lower pathway).
Studies described here were initiated to learn if threading has a role in the intracellular assembly of the glycoprotein hormones using a strategy that circumvents the need for pulsechase analysis, the most common approach to studying protein folding in cells. Pulse-chase methods require labeling, isolating, and characterizing partially folded intermediates. Important intermediates such as heterodimers that have not yet latched their seatbelts or in which loop ␣2 has not been threaded beneath the seatbelt are unstable and difficult, if not impossible to isolate. As shown here based on the abilities of -subunit analogs to compete for formation of cross-linked and non-cross-linked heterodimers, cells can assemble hCG, hFSH, and hTSH by a threading mechanism. Indeed, it appears as if these human glycoproteins are assembled in the ER primarily by a threading route and that the wraparound pathway is used sparingly, if at all. used to express hCG in cultured cells were produced by polymerase chain reaction and cassette mutagenesis (9) and were sequenced prior to use. Analogs used in this study are listed in Fig. 2 and are readily identified by their names. Thus, ␣-L41C is the natural human ␣-subunit having a codon for cysteine in place of that for ␣Leu 41 . Proteins were produced by transfecting the constructs into COS-7 cells obtained from the ATCC (Bethesda, MD) using a calcium phosphate procedure (10). The amounts of ␣and -subunit constructs used were 20 and 10 g/10-cm culture plates, respectively. Secreted analogs were harvested 3 days after transfection and analyzed in monoclonal antibody sandwich immunoassays (11) employing antibodies A113, B111, B112, B404, B603, and B806, obtained from Dr. William Munroe (Hybritech Inc., San Diego, CA, a subsidiary of Beckman Coulter, Inc.), B101 was obtained from Dr. Robert Canfield (Columbia University, New York), B122 was obtained from Dr. Robert Campbell, and B110 was produced as described (12). The relative binding sites of these conformation-dependent antibodies have been determined and are indicated in Fig. 3. This figure also illustrates the locations of several residues discussed in this study. A113 recognizes a conformation-dependent ␣-subunit epitope in the heterodimer. B101 recognizes a conformation-dependent epitope in loop 2 of hCG and the uncombined -subunit. B110 and B112 recognize conformation-dependent epitopes formed when loops 1 and 3 are adjacent in hCG and the uncombined -subunit. B112 binds hCG and analogs in which Asn 77 is replaced by cysteine but not by aspartic acid or analogs in which a cysteine substitution participates in a disulfide bond. B111 recognizes a conformation-dependent epitope formed when Cys 110 at the end of the hCG seatbelt is latched to Cys 26 in the heterodimer and the uncombined -subunit. B111 can also recognize analogs of hCG in which Cys 26 and Cys 110 are converted to alanine provided the heterodimer is stabilized in another fashion, such as fusing the NH 2 -terminal end of the ␣-subunit to the COOH-terminal end of the -subunit (8). This indicates that B111 does not recognize the Cys 26 -Cys 110 disulfide per se. B111 does not recognize hCG analogs in which the seatbelt is latched to any other residue other than Cys 110 , however, or when residues near Cys 110 are derived from hLH, hFSH, or hTSH. B603 and B806 recognize loops 1 and 3 in the -subunits of hFSH and hTSH, respectively, but the binding sites of these antibodies have not been well characterized. None of the antibodies used in these studies recognize the -subunit prior to formation of the cystine knot, a key step in formation of the -subunit core.
Antibodies used for detection were radioiodinated to a specific activity of ϳ50 Ci/g using IODO-GEN (Pierce) as described (13). The acid stability of the heterodimers was tested in 0.4-ml samples by reducing the pH to 2 by addition of microliter aliquots of 2 M HCl, while monitoring the pH, and incubating acidified samples 30 min at 37°C, readjusting the pH to 7.5 by addition of sufficient microliter aliquots of a mixture of 10 N NaOH, 1 M Tris buffer (pH 7.5) (1:2), and then quantifying them by sandwich immunoassay (11). Material that contained the ER retention signal was isolated from the cells 1 or 2 days after transfection by scraping them from the culture dishes and solubilizing them in 10 mM sodium phosphate buffer (pH 7.5) containing 140 mM KCl, 20 mM EDTA, 1 M leupeptin, 1.5 M pepstatin, 500 M pefablock, and 1% octyl glucoside (Sigma). Following sedimentation at 14,000 ϫ g (10 min at 4°C), the supernatants were diluted 6.7-fold with a phosphate-buffered saline solution (40 mM KCl, 1.5 mM KH 2 PO 4 , 140 mM NaCl, 1.0 mM Na 2 HPO 4 , pH 7.2) and assayed by sandwich immunoassay (11) using the indicated antibodies and pure recombinant hCG as a standard. The hCG -subunit used as a standard was purified from this hCG by high performance liquid chromatography on a C-18 resin using an acetonitrile gradient in water containing 0.1% trifluoroacetic acid as described (6). Standards were dissolved in octyl glucoside extracts of untransfected COS-7 cells for measurements of intracellular -subunits and heterodimers. This minimized the possible influence of detergent and cell extract on the assay. Procedures to monitor assembly in vitro have been described (6). All sandwich assay estimates were determined statistically using Prism (GraphPad Software, San Diego, CA). Most analogs were studied three or more times. Differences in expression relative to that of hCG, which was always included as a standard, are typical despite the fact that some transfections were more efficient and led to the formation of larger amounts of heterodimers than others.
FIG. 1. Pathways of glycoprotein hormone assembly. During assembly that occurs by the wraparound pathway (7,8), the subunits dock before the seatbelt is latched (upper pathway); formation of the heterodimer is completed when the seatbelt is wrapped around loop ␣2 and the latch disulfide is formed (right vertical pathway). In the threading pathway (6), the seatbelt latch disulfide forms before the subunits dock (left vertical pathway); assembly of the heterodimer is completed when loop ␣2 and its attached oligosaccharide traverse the hole in the -subunit beneath the seatbelt (lower pathway). Key: ␣-subunit, light gray; -subunit, black; small rectangle, disulfide that stabilizes the small loop within the seatbelt; large rectangle, seatbelt latch disulfide; C, -subunit cysteines in loop 1 and at the end of the seatbelt; open y-shaped figure on ␣-subunit loop 2, loop ␣2 oligosaccharide. For simplicity, the remaining oligosaccharides are not depicted.
FIG. 2.
Sequences of hCG ␣and -subunit analogs used in this study. The linear amino acid sequences of each hCG subunit are shown in single letter code. The locations of mutations used in these studies are shown in standard nomenclature. In some cases two mutations were present in a single protein and these are identified by the name of the subunit (i.e. hCG) and the mutations (i.e. -C26A,N77C). Several analogs contained four additional residues at the carboxyl-terminal end of the -subunit shown as KDEL. The presence of these residues slowed secretion of the heterodimer, presumably because it caused it to be retained in the ER (18). The presence of this sequence is identified by the term -KDEL appended to the name of the analog. Lines under the amino acid sequence refer to its position in the protein.
RESULTS
Rationale for Our Approach to Distinguish Heterodimer Assembly Pathways-The relative timing of subunit docking and seatbelt latch formation are reversed in the threading and wraparound pathways. Therefore, in principle, the threading and wraparound pathways could be distinguished by pulsechase analysis (7,14,15), the most common method for studying protein folding in mammalian cells. This approach would not be useful for detecting trace quantities of transient unstable folding intermediates such as heterodimers that have not latched their seatbelts (16) or those in which loop ␣2 is only partially threaded through the -subunit hole, however. Furthermore, pulse-chase methods can give undue weight to deadend folding products that appear transient because they are degraded, not because they are folding intermediates. These considerations led us to monitor assembly using methods that depend on the abilities of folding intermediates to compete for the formation of cross-linked heterodimers.
We distinguished the threading and wraparound pathways by measuring the amounts of cross-linked heterodimer formed when ␣-subunit analogs containing an additional cysteine were cotransfected with the native -subunit (Fig. 4, middle and bottom lines). We have found that the hCG seatbelt can be latched to a cysteine added to the ␣-subunit during the wraparound pathway of heterodimer assembly (8). Assembly by this route is efficient and many of the cross-linked heterodimers produced are as active as hCG in receptor binding and signal transduction assays (8). During assembly that occurs by a threading pathway (Fig. 4, lower row), the seatbelt is latched to the cysteine in loop 1 before assembly begins. As a result, the seatbelt would remain latched to loop 1, which would lead to the formation of a heterodimer that would be unstable at pH 2, 37°C. During assembly that occurs by a wraparound mechanism, the seatbelt would have the opportunity to be latched to the cysteine in loop 1 or that had been added to the ␣-subunit. Consequently, the heterodimer would contain an intersubunit cross-link.
An alternative method of distinguishing the threading and wraparound mechanisms depends on the competition between two -subunits (Fig. 4, top and bottom lines). We employed this method to eliminate the possibility that the seatbelt latch site might be rearranged during assembly in the cell. For example, it might be possible for the seatbelt of the native hCG -subunit to be latched to a cysteine in the ␣-subunit during assembly that occurs by a wraparound mechanism. Subsequently, the seatbelt latch site might "migrate" to its native latch site by a disulfide exchange with Cys 26 (Fig. 4, dashed arrow), making it appear that the heterodimer had been formed by a threading pathway. To avoid this possibility, we took advantage of the FIG. 3. Relaxed stereo view depicting the C␣ carbon atoms of hCG, the locations of mutations used in this study, and the relative antibody binding sites. Key: ␣-subunit, white; ␣-subunit mutations, light spheres with black text denoting the amino acid residue number; CHO, location of residue ␣Asn 52 that contains an N-linked oligosaccharide (not shown); -subunit, black; -subunit mutations, dark spheres with white text denoting the amino acid residue number; A113 and arrow, approximate location of the binding site of the ␣-subunit antibody used for capture in sandwich immunoassays; B101, B110, B111, B112, and arrows, approximate locations of the binding sites of the -subunit antibodies used for capture or detection in these studies. The seatbelt latch disulfide is normally formed between -subunit residues 26 and 110. Note, the proximity of ␣-subunit residues 37, 41, and 43 to -subunit residue 26, the normal seatbelt latch site. The small seatbelt loop is stabilized by a disulfide between -subunit residues 93 and 100. B111, an antibody that was essential to distinguish the location of the seatbelt latch disulfide, recognizes a region of hCG near -subunit cysteines 26 and 110, although it does not recognize the seatbelt latch disulfide per se. Although B111 can bind to single chain analogs of hCG in which -subunit cysteines 26 and 110 are converted to alanine, it does not recognize any analog in which the seatbelt is latched to the ␣-subunit (8). B111 can also recognize heterodimers in which -subunit cysteines 26 and 110 are converted to alanine if the heterodimer is stabilized by the presence of an NH 2 -terminal Fos/Jun dimerization domain or if the heterodimer is stabilized by an N-terminal disulfide cross-link (27).
observation that the seatbelts in hCG -subunit analogs such as hCG-C26A, which cannot latch their seatbelts to loop 1 because they contain an alanine in place of Cys 26 , can become latched to cysteines added to the ␣-subunit in place of residues 35, 37, 41-50, 64, 86, 88, and 90 -92, among others (8). Because the seatbelts of these analogs cannot be latched until after the subunits contact one another, heterodimers containing these -subunits can only be assembled by the wraparound pathway. Furthermore, once latched, the seatbelt in these heterodimers cannot migrate to the -subunit unless the heterodimer dissociates. The observation that these heterodimers are secreted efficiently indicates that they do not dissociate.
Before its seatbelt is latched, hCG would be expected to have the same overall conformation as hCG-C26A (Fig. 4). Thus, hCG-C26A and the unlatched form of hCG (i.e. hCG*) would be expected to compete with one another for docking with the ␣-subunit in the wraparound pathway. If most heterodimers became assembled by the wraparound pathway, one would expect to find a significant fraction of the total heterodimer that contained hCG-C26A. In contrast, because hCG-C26A can be incorporated into heterodimers only by the wraparound pathway, it would not be expected to compete with hCG for heterodimers that are assembled after the seatbelt is latched, i.e. by threading (Fig. 4). Therefore, if most assembly occurs by threading, very little of the heterodimer formed would contain hCG-C26A.
The position of the seatbelt latch site in hCG can be determined by the acid stability of the heterodimer and by its ability to be recognized by monoclonal antibody B111. Heterodimers in which the seatbelt is latched to the ␣-subunit contain an intersubunit disulfide cross-link. These are distinguished readily from heterodimers in which the seatbelt is latched to Cys 26 by their resistance to dissociation at pH 2, 37°C, and by their inabilities to bind monoclonal antibody B111 (8). B111 binds a conformational hCG epitope formed when the seatbelt is latched normally, i.e. to Cys 26 . It does not bind heterodimers in which the seatbelt is latched to other cysteines such as those that have been added to either subunit (8,17).
Human Choriogonadotropin Can Be Assembled in the ER by Two Different Routes, but Most Is Made by the Threading
Pathway-The seatbelts of heterodimers produced by co-expressing hCG and each of the ␣-subunit analogs tested became latched primarily to Cys 26 , not to the cysteine added to the ␣-subunit. This was the first indication that hCG is formed in the ER by a threading pathway. An example of this is seen by comparing the properties of heterodimers produced when hCG, was expressed with ␣-L41C (Table I, 1). Most heterodimers secreted by cells that were co-transfected with ␣-L41C and hCG lacked an intersubunit disulfide and were unstable following 30 min at pH 2, 37°C (Table I, 1, row 1). As a result they were detected readily in heterodimer-specific sandwich immunoassays employing an antibody to the ␣-subunit for capture (i.e. A113) and a radioiodinated antibody to the -subunit for detection (i.e. 125 I-B110) before, but not after low pH treatment. These heterodimers were also detected in similar immunoassays employing A113 for capture and 125 I-B111 for detection before treatment at low pH. This indicated that their seatbelts were latched to Cys 26 , not ␣Cys 41 . Both findings are consistent with the conclusion that the heterodimer was formed by a threading mechanism.
To exclude the possibility that the location of the seatbelt in the heterodimer had undergone a disulfide exchange and become latched to Cys 26 in loop 1 after it had been latched to ␣Cys 41 , we repeated the study in the presence of hCG-C26A, an analog that cannot latch its seatbelt to loop 1. When ␣-L41C was expressed with hCG-C26A, the heterodimer that formed was detected in A113/ 125 I-B110 assays before and after acid treatment (Table I, 1, row 2). Furthermore, none of it was detected in A113/ 125 I-B111 assays before or after low pH treatment. These findings showed that seatbelt residue Cys 110 of this heterodimer was cross-linked to the ␣-subunit, a consequence of its formation by a wraparound mechanism. When both -subunits were expressed simultaneously with ␣-L41C, heterodimers secreted into the medium contained hCG and little or no hCG-C26A (Table I, . Rationale for the experiments involving a competition between hCG and hCG-C26A for ␣-subunit analogs that contain an additional cysteine residue. We presume that hCG can exist in two states, one in which the seatbelt is latched (hCG) and another in which the seatbelt is unlatched (hCG*). Because hCG-C26A cannot latch its seatbelt to 1, it can exist only in a state that is comparable with hCG*. As outlined in the top reaction, hCG-C26A can form an intersubunit disulfide cross-linked heterodimer by the wraparound pathway with several ␣-subunit analogs that contain an additional cysteine (8). This heterodimer is stable at low pH and is readily recognized by conformation-dependent monoclonal antibodies A113, B101, B110, B112, and B122. The heterodimer is not recognized by B111, however. This shows that both subunits have folded properly but that the seatbelt is not latched as it is in hCG. hCG* would also be expected to form a heterodimer by a wraparound pathway. Heterodimers in which the seatbelt is latched to Cys 26 and a cysteine added to the ␣-subunit would be readily distinguished by differences in their acid stabilities and their recognition by B111 as indicated. We expect that hCG-C26A and hCG* would compete for docking with the ␣-subunit analogs used in these studies. Because the seatbelt of hCG-C26A can be latched efficiently to several sites on the ␣-subunit (8), some seatbelts of hCG* should also become latched to the ␣-subunit. Theoretically, heterodimers in which hCG* is latched to a cysteine in the ␣-subunit could also undergo an internal disulfide rearrangement such that the seatbelt migrated from the cysteine in the ␣-subunit to Cys 26 . This is indicated by a dashed arrow. A rearrangement such as this cannot occur for heterodimers that contain hCG-C26A. In the fully folded form of hCG, the seatbelt is latched to loop 1 and we anticipate that it would be assembled into a heterodimer only by the threading route. As shown in the text and Table I, we observed that the hCG-C26A seatbelt becomes latched to the ␣-subunit. We did not detect latching of the hCG seatbelt to the ␣-subunit or more than marginal competition of hCG-C26A with hCG for any ␣-subunit analog. These findings support the notions that most hCG is assembled by a threading pathway and little, if any, is formed by the wraparound pathway.
belts in these heterodimers were latched to Cys 26 , not ␣Cys 41 , they were detected readily in A113/ 125 I-B110 and A113/ 125 I-B111 assays before, but not after low pH treatment. The finding that hCG-C26A did not compete with hCG for formation of heterodimers containing ␣-L41C indicated that hCG assembly occurs primarily by threading.
One could argue that heterodimers having their seatbelts latched to ␣Cys 41 were disrupted or degraded during secretion and that this prevented us from detecting them in preparations containing ␣-L41C and hCG. This appeared highly unlikely because heterodimers containing hCG-C26A were found in the medium when it was the only -subunit used in the transfection. Nonetheless, we tested this possibility using analogs of hCG and hCG-C26A that contained four COOH-terminal residues (i.e. KDEL) known to delay the secretion of other proteins from the ER (18). To determine how this affected the secretion of hCG, we transfected COS-7 cells with the native ␣-subunit and hCG or hCG-KDEL and measured the ap-TABLE I hCG -subunit analogs forced to latch their seatbelts to the ␣-subunit compete poorly with those that can latch their seatbelts to Cys 26 This table describes the properties of heterodimers produced by co-expressing the ␣-subunit analog indicated at the top of each block with -subunits capable of participating in wrapping or threading pathways (i.e. hCG and hCG-KDEL), -subunits that are limited to wrapping pathways (i.e. hCG-C26A and hCG-C26A-KDEL), or with both types of -subunits simultaneously. The total amount of heterodimer in 50-l aliquots of unconcentrated culture media (secreted) or 7 l of cell lysate (intracellular) was quantified in an A113 capture/ 125 I-B110 detection sandwich assay using purified recombinant hCG as standard. The fraction of the total heterodimer that was acid stable was determined after treatment at pH 2 for 30 min at 37°C. Data in the first and second columns were determined in A113 capture/ 125 I-B110 detection sandwich assays. Those in the third and fourth data columns are the results of A113 capture/ 125 I-B111 detection sandwich assays. Values in the first to fourth data columns are mean Ϯ S.E. for 3 independent transfection plates. Similar results were observed in at least three other independent studies for each analog. The values in the fifth column, row 1 of blocks 4 and 5 were derived from these means by comparing differences in the B111 assays before and after treatment at acid pH (row 1) (Co-expression of ␣ -subunit analogs having a free cysteine and the native hCG  -subunit can give rise to four populations of heterodimers, i.e. one that does not have a cross-link, one in which tensor cysteine 93 is cross-linked to the cysteine added to the ␣ -subunit, one in which tensor cysteine 100 is cross-linked to the cysteine added to the ␣ -subunit, and one in which the seatbelt is latched to the cysteine added to the ␣ -subunit. We calculated the maximum amount of heterodimer in which the seatbelt is latched to the ␣ -subunit in Table I, rows 1, 4 and 5, as follows. For simplicity, we assign variable x to be the amount of uncross-linked heterodimer, variable y to be the amount of heterodimer in which either tensor cysteine is cross-linked to the ␣ -subunit, and variable z to be the amount of heterodimer in which the seatbelt is latched to the ␣ -subunit. The latter could be formed only by the wraparound pathway. Constants a, b, and c represent the abilities of B111 to bind heterodimers with these configurations relative to B110, respectively. Because B111 does not bind heterodimers in which the seatbelt is latched to the ␣ -subunit, c ϭ 0. Data in the first column (C 1 ) is the total amount of heterodimer detected by antibody B110, namely C 1 ϭ x ϩ y ϩ z. Data in the second column (C 2 ) is the fraction of heterodimer detected by antibody B110 that contains a cross-link. Thus, C 1 C 2 ϭ y ϩ z. Data in the third (C 3 ) and and fourth (C 4 ) columns represent the abilities of B111 to bind the total and cross-linked heterodimers relative to those measured by B110. Note that for all calculations the values shown in C 2 , C 3 , and C 4 were converted to their fractional equivalents by dividing them by 100. The values of C 3 and C 4 can be expressed as: To estimate maximal amount of z, we first divided C 3 by C 4 and rearranged the terms to give: C 3 /C 4 ϭ C 2 (ax ϩ by)/(by). Because the ability of B111 to recognize the cross-linked heterodimer in 4 and 5 in Table I appears to be less than its ability to recognize the total heterodimer, b Յ a and this equation can be written as the inequality: C 3 /C 4 Ն C 2 b(x ϩ y)/(by) ϭ C 2 (x ϩ y)/y, and solved for z by replacing (x ϩ y) with (C 1 Ϫ z) and by replacing y with (C 1 C 2 Ϫ z). These relationships are known from the definitions of C 1 and C 2 noted above. Thus, C 3 /C 4 Ն C 2 (C 1 Ϫ z)/(C 1 C 2 Ϫ z), which can be rearranged to solve for z as: z/C 1 Յ C 2 (C 3 Ϫ C 4 )/(C 3 Ϫ C 2 C 4 ). The value of z/C 1 represents the maximal fraction of the total heterodimer that has its seatbelt latched to the ␣ -subunit. The values of z/C 1 shown in the fifth column, row 1, of 4 and 5, were converted to percentages by multiplying them by 100). Values in the fifth column, row 2 of each data block were determined from the stability of the heterodimer. Values in the fifth column, row 3 of each data block were determined by comparing the amount of acid stable heterodimer in the absence and presence of hCG -C26A or hCG -C26A-KDEL. For example, in the case of block 2, row 3, the fraction of the acid stable heterodimer likely to contain hCG -C26A-KDEL was calculated as (55.78 -35.50)/55.78 or 0.364. This was then used to calculate the amount of this material in the total heterodimer by multiplying it by the fraction of the total that is acid stable (i.e. 0.364 ϫ 18.60%) to give the value of 6.8% shown in the table. The binding site of antibody B111 is shown in Fig. 3 pearance of heterodimer in media and cell lysates. The KDEL tag delayed heterodimer secretion from the cell and caused it to be accumulated in the cells (Fig. 5). Prolonged incubation resulted in release of the KDEL-tagged material from the cells, probably because the ER retention mechanism had been saturated. These studies suggested that assays of KDEL-tagged heterodimers in cell lysates would reflect material located primarily in the ER. The seatbelts of heterodimers measured in lysates of cells co-transfected with ␣-L41C and hCG-KDEL were latched to Cys 26 . As a result, most were unstable at low pH and readily detected by B111 (Table I, 2, row 1). A small fraction (9.7%) of the heterodimer was stable at low pH even though it was detected in A113/ 125 I-B111 assays. Whereas its acid stability suggested that this fraction contained an intersubunit disulfide cross-link, its ability to be recognized by B111 showed that its acid stability was not due solely to the formation of a disulfide between seatbelt residue Cys 110 and loop ␣2 residue ␣Cys 41 . This indicated that ␣Cys 41 can participate in an intersubunit disulfide with -subunit cysteines other than that at the end of the seatbelt (i.e. Cys 110 ). The amounts of the acid stable ␣-L41C/hCG-C26A-KDEL heterodimer in cell lysates were too small for us to attempt identifying this intersubunit disulfide using traditional biochemical methods. Therefore, we modeled each of the 12 intersubunit disulfides that could be formed between ␣Cys 41 and cysteines in the -subunit and excluded those that were likely to disrupt the conformation of the heterodimer to an extent that it would no longer be recognized by antibodies used in these studies. Only two intersubunit disulfides, namely ␣Cys 41 -Cys 93 and, more likely, ␣Cys 41 -Cys 100 appeared to fit these criteria. These -subunit cysteines stabilize a small loop within the seatbelt and are near several residues in loop ␣2, including ␣Cys 41 .
To test the notion that Cys 100 or Cys 93 might participate in the formation of an intersubunit disulfide with ␣Cys 41 without disrupting the B111 binding site, we expressed ␣-L41C with hCG-C93A-KDEL and hCG-C100A-KDEL. These analogs cannot form the small seatbelt loop and have free cysteines at Cys 100 and Cys 93 , respectively. We also expressed ␣-L41C with hCG-C93A,C100A-KDEL, an analog lacking both cysteines. Because the small seatbelt loop has been shown to be essential for the formation of heterodimers containing the native ␣-subunit (16), we expected that these -subunits would form heterodimers with ␣-L41C only if they could form an intersubunit disulfide. This prediction was satisfied by the observation that hCG-C93A-KDEL, the analog having a free cysteine at Cys 100 , formed a heterodimer with ␣-L41C (Table II). The findings that ␣-L41C did not combine stably with hCG-C93A,C100A-KDEL and that the native ␣-subunit did not combine stably with hCG-C93A-KDEL supported the notion that the intersubunit disulfide involved residues ␣Cys 41 and Cys 100 . As had been predicted from modeling studies, the amount of heterodimer formed when ␣-L41C was expressed with hCG-C93A-KDEL was much greater than that formed when it was expressed with hCG-C100A-KDEL (Table II).
Based on this observation and the finding that both the ␣-L41C/hCG-KDEL and ␣-L41C/hCG-C93A-KDEL heterodimers were detected readily by B111 (Tables I and II, respectively), we expect that the acid-stable fraction of ␣-L41C/ hCG-KDEL contains an intersubunit disulfide cross-link between ␣Cys 41 and Cys 100 . Nonetheless, we cannot exclude the possibility that a portion of this material contains a disulfide between ␣Cys 41 and Cys 110 , indicating that it had been formed by a wraparound mechanism. The finding that the seatbelt was latched to Cys 26 in the vast majority of the acid unstable ␣-L41C/hCG-KDEL heterodimer and a substantial fraction of the acid-stable ␣-L41C/hCG-KDEL heterodimer showed that Cys 26 out competed ␣Cys 41 as a seatbelt latch site. Whereas this is consistent with the view that the seatbelt had become latched to Cys 26 before the subunits docked, it does not preclude the possibility that the seatbelt had become latched to Cys 26 by a process of disulfide exchange. We tested this possibility by comparing the abilities of hCG-KDEL and hCG-C26A-KDEL to compete for heterodimer formation.
The heterodimer made by co-expressing ␣-L41C and hCG-C26A-KDEL was acid stable and could not be detected in A113/ 125 I-B111 assays before or after low pH treatment (Table I, 2, row 2). This showed that it contained an intersubunit disulfide, a consequence of its assembly by a wraparound mechanism. hCG-C26A-KDEL barely competed with hCG-KDEL for heterodimer formation, however. Most heterodimers made in the presence of both -subunit analogs were unstable at pH 2, 37°C, and were readily detected in A113/ 125 I-B111 assays (Table I, 2, row 3). These findings are consistent with the conclusions that the seatbelts of most heterodimer molecules were latched to Cys 26 , not ␣Cys 41 and that they had been formed by the threading pathway. Much of the acid-stable fraction was recognized by B111, indicating that its seatbelt was latched normally and that it may have been stabilized by an intersubunit disulfide between ␣Cys 41 and either Cys 93 or Cys 100 . Differences in the ability of B111 to recognize the acid-stable heterodimer made in transfections lacking and containing hCG-C26A-KDEL (i.e. Table I, 2, rows 1 and 3) indicated that a small amount of the acid-stable heterodimer made in the presence of hCG-C26A-KDEL contained an intersubunit disulfide cross-link between ␣Cys 41 and Cys 110 . Based on calculations described in the legend to Table I, it appears as if 6.8% of the heterodimer in cell lysates may have been formed by the wraparound pathway when both -subunits were present. This small amount is consistent with the notion that threading is much more efficient than wrapping, particularly because much more hCG-C26A-KDEL was incorporated into heterodimers containing ␣-L41C in the absence of hCG-KDEL.
We have found that removal of the loop ␣2 oligosaccharide facilitates threading in vitro (5) and considered the possibility that it would also enhance assembly in cells. To test this, we studied assembly of heterodimers that contain ␣-L41C,N52D, an analog of ␣-L41C that lacks the loop ␣2 glycosylation signal. We co-expressed this ␣-subunit analog with hCG-KDEL, hCG-C26A-KDEL, or both -subunit analogs and measured the formation of heterodimer in cell lysates (Table I, 3). The heterodimer formed with hCG-KDEL was acid labile and was FIG. 5. Influence of KDEL sequence on heterodimer secretion. Cells transfected with hCG analogs containing KDEL sequences and materials that were retained within the cell (lysates) and secreted into the media during 3 days of incubation were measured as described in the text. detected readily in A113/ 125 I-B111 assays, showing that its seatbelt was latched to Cys 26 (Table I, 3, row 1). Heterodimer formed with hCG-C26A-KDEL was acid stable and not recognized in A113/ 125 I-B111 assays, indicating that seatbelt residue Cys 110 became bridged to ␣Cys 41 , a consequence of the wraparound pathway (Table I, 3, row 2). Most heterodimers formed when both -subunits were co-expressed with ␣-L41C,N52D contained hCG-KDEL and 80% dissociated during the pH 2 treatment (Table I, 3, row 3). The finding that most of the acid-stable heterodimer was also recognized in A113/ 125 I-B111 assays showed that its seatbelt was latched to Cys 26 , not ␣Cys 41 . Less than 8% of the heterodimer made in the presence of both -subunit analogs appeared to contain hCG-C26A-KDEL. Thus, preventing the glycosylation of loop ␣2 did not affect the route of assembly in cells, most likely because nearly all hCG is assembled by a threading mechanism, even when the loop ␣2 oligosaccharide is present.
Together, these observations suggested that most heterodimers containing ␣-L41C are assembled by a threading route. Whereas it might be argued that the apparent inefficiency of wrapping is because of the possibility that ␣Cys 41 is a poor seatbelt latch site, this seemed unlikely given the finding that ␣-L41C assembled readily with hCG-C26A and hCG-C26A-KDEL. Furthermore, we had chosen this ␣-subunit residue because of its proximity to Cys 26 in the heterodimer. Thus, we expected that seatbelt residue Cys 110 would be latched to ␣Cys 41 readily, a phenomenon observed only when the seatbelt is prevented from being latched to its natural -subunit site (i.e. Cys 26 ).
We tested the abilities of hCG-KDEL and hCG-C26A-KDEL to compete for two other ␣-subunit analogs containing a cysteine in loop ␣2. When ␣-S43C and ␣-T46C were co-expressed with hCG-KDEL, we observed that 18.1 and 14.4%, of the heterodimer that remained in the cells did not dissociate at acid pH even though it was readily detected with B111 (Table I, 4 and 5, row 1). The acid stability of these heterodimers appeared because of the formation of a disulfide between the cysteine that had been added to loop ␣2 and Cys 93 or, more likely, Cys 100 . Both of these ␣-subunit analogs formed significant amounts of heterodimer when expressed with hCG-C93A-KDEL, indicating they are likely to contain an intersubunit disulfide cross-link with Cys 100 (Table II). Because the recognition of the acid-stable forms of these heterodimers by B111 is similar to that of heterodimers in which these ␣-subunit cysteines were cross-linked to Cys 100 , it appeared likely that most, if not all of the cross-linked material contains a disulfide between the cysteine added to the ␣-subunit and either Cys 93 or Cys 100 . Consequently, the threading pathway was expected to be responsible for more than 95% of the het-erodimers formed when hCG-KDEL was expressed with either ␣-S43C or ␣-T46C (Table I, 6 and 7, row 1).
To test the possibility that we were being mislead by our choice of an ␣-subunit latch site, we repeated these studies with ␣-S43C and ␣-T46C, analogs that also formed heterodimers efficiently with hCG-C26A (8). When these ␣-subunit analogs were co-expressed with hCG-C26A-KDEL, nearly all the heterodimer retained within the cell was acid stable (Table I, 4 and 5, row 2). Neither heterodimer was detected by B111, indicating that its seatbelt had become latched to the ␣-subunit. The ample amount of heterodimer formed with either ␣-subunit analog suggested that ␣Cys 43 and ␣Cys 46 are readily bridged to Cys 110 . Thus, these cysteines should have competed effectively with Cys 26 during assembly of heterodimers that formed by the wraparound pathway. The finding that little, if any, intersubunit disulfide between Cys 110 and either ␣Cys 43 or ␣Cys 46 was formed when ␣-S43C and ␣-T46C were expressed with hCG-KDEL is consistent with the notion that most heterodimers are assembled by threading (Table I, 4 and 5, row 1).
To learn if hCG-C26A-KDEL would compete with hCG-KDEL during assembly of heterodimers containing ␣-S43C and ␣-T46C, we co-expressed each ␣-subunit analog with both -subunit analogs. The amounts of heterodimer formed were always similar to those seen when each ␣-subunit analog was co-expressed with hCG-KDEL alone (Table I, 4 and 5, row 3). Furthermore, we often observed that a higher percentage of heterodimers containing ␣-S43C and ␣-T46C were acid stable than when ␣-L41C was used as the assembly partner. For example, 23.9 and 37.5% of the heterodimer appeared to be acid stable when ␣-S43C and ␣-T46C were expressed with both -subunit analogs (Table I, 4 and 5). B111 recognized more of the acid-stable heterodimer containing ␣-S43C than that containing ␣-T46C, an indication that the latter contained a significant fraction of hCG-C26A-KDEL. This difference is correlated with the amounts of heterodimer observed following transfection of the cells with hCG-C26A-KDEL in the absence of hCG-KDEL, showing that hCG-C26A-KDEL can compete with hCG-KDEL when it is present in sufficient excess. The fraction of acid-stable heterodimer in these preparations likely to contain an ␣Cys 43 -Cys 110 or ␣Cys 46 -Cys 110 disulfide was 7.6 and 21.3%, respectively. Note that in both cases, the presence of hCG-KDEL inhibited heterodimer production, indicating that heterodimer assembly occurred preferentially by a threading mechanism.
Observations made using ␣-subunit analogs containing a cysteine in loop ␣2 suggested that most hCG assembly occurred after the seatbelt had been latched. Consequently, the majority of these hCG analogs appeared to be assembled by a threading TABLE II Cross-linking of Cys 93 and Cys 100 to ␣-subunit analogs having an extra cysteine COS-7 cells were co-transfected with constructs encoding the indicated ␣and -subunit analogs. The -subunits employed are unable to form the tensor disulfide and in most instances did not combine stably with the ␣-subunit unless it contained a cysteine at an appropriate location. The free cysteine in hCG-C93A is Cys 100 and that in hCG-C100A is Cys 93 . The values under the heading B111 (% total) refer to the binding of these heterodimers by B111 relative to that of B110. These data show that Cys 100 can be cross-linked to many ␣-subunits containing an additional cysteine and that the resulting heterodimers can be recognized by B110 and B111. A few can also be cross-linked to Cys 93 . Not detectable refers to heterodimer that is less than 0.02 ng/50 l. In many cases we detected the presence of material that is just above this blank value but not enough to quantify accurately. This has been identified by the symbol "Ͻ0. 10 route. To test the notion that cysteines in other regions of the ␣-subunit would permit us to detect hCG assembly by the wraparound pathway, we tested the influence of a cysteine in place of ␣Ser 92 . We have reported that this residue can be readily latched to the seatbelt (8). This cysteine would not be expected to pass beneath the seatbelt during assembly by a threading mechanism and we reasoned that it would be less likely to form a disulfide with either Cys 93 or Cys 100 during assembly even though it can be cross-linked efficiently to either of these cysteines when the other is absent (Table II). Co-expression of ␣-S92C and hCG-KDEL led to the formation of considerable amounts of heterodimer, nearly all of which dissociated at acid pH (Table I, 6, row 1). The acid-stable fraction of this heterodimer was recognized almost as well in A113/ 125 I-B111 assays as it was in A113/ 125 I-B110 assays. Based on the abilities of ␣-S92C to form heterodimers with either hCG-C93A-KDEL and hCG-C100A-KDEL (Table II), we anticipate that this small amount of crosslinked heterodimer contains an intersubunit disulfide between ␣Cys 92 and either Cys 93 or Cys 100 . Both of these are recognized well by B111. Expression of ␣-S92C with hCG-C26A-KDEL also led to the formation of a substantial amount of acidstable heterodimer (Table I, 6, row 2), but this was not recognized by B111, indicating that it was stabilized by the ␣Cys 92 -Cys 110 disulfide and had been formed by a wraparound pathway. Coexpression of ␣-S92C, hCG-KDEL, and hCG-C26A-KDEL resulted in a heterodimer that was acid unstable and recognized well by B111, indicating that it had been formed by a threading mechanism. These data suggested that only 1.6% of the heterodimer formed might contain an ␣Cys 92 -Cys 110 disulfide. Again, this supported the notion that hCG is assembled by a threading pathway.
Human Follitropin and Thyrotropin Also Appear to be Assembled by a Threading Pathway-hFSH and hTSH are structurally similar to hCG and contain the same ␣-subunit. These -subunits formed heterodimers with ␣-subunit analogs containing cysteines added to the ␣-subunit in place of residues 35, 37, 41-50, 64, 86, 88, and 90 -92 (not shown). Unlike the hCG -subunit, however, analogs of hFSH and hTSH -subunits lacking the abilities to latch their seatbelts to -subunit loop 1 (i.e. hFSH-C20A, hFSH-C20A-KDEL, and hTSH-C19A) did not form heterodimers with any of these ␣-subunit analogs (not shown). This suggested that the wraparound pathway makes few contributions, if any, to the assembly of hFSH or hTSH.
Latching the Seatbelt to a Cysteine in hCG -Subunit Loop 1 Occurs Before the Subunits Dock-We began these studies to learn if threading might be capable of making small contributions to glycoprotein hormone assembly, but did not anticipate finding that it was the major route of human glycoprotein hormone assembly in the ER. Indeed, the notion that hCG is assembled by a threading mechanism contradicted earlier suggestions that it was assembled by a wraparound mechanism (7). Efforts to confirm the use of the threading pathway for hCG assembly led us to test this possibility by an alternative strategy. We reasoned that if threading is the main route of hCG assembly, the seatbelt would have a strong tendency to be latched to the -subunit before the subunits dock, even if it were forced to be latched to sites other than Cys 26 . Furthermore, we anticipated that when the seatbelt is latched to an inappropriate site, it would interfere with heterodimer assembly. We tested these possibilities using analogs of hCG and hCG-C26A that contained an additional cysteine as described (Fig. 6).
Adding a cysteine to hCG creates the potential for new disulfide bond arrangements. The structure of the -subunit suggests relatively few of these will be formed, however, without distorting the protein to the extent that it is no longer FIG. 6. Rationale for studies involving a competition between intrasubunit cysteines and intersubunit cysteines for formation of the seatbelt latch disulfide. The presence of an additional cysteine in hCG or hCG-C26A would create a new seatbelt latch site within the -subunit. As shown in the top two rows, the presence of this cysteine in hCG-C26A creates an analog (hCG-C26A,N77C) that can exist in two states. In one of these, the seatbelt remains unlatched because of the difficulty of forming the non-native intrasubunit disulfide. In the other state, the seatbelt becomes latched to the cysteine added to the -subunit before the subunit has time to dock with an ␣-subunit analog such as ␣-L41C. Formation of an acid-stable heterodimer would imply that the seatbelt had been latched to the cysteine added to the ␣-subunit. This would show that it had not become latched to the -subunit before the subunits docked. In contrast, formation of an intrasubunit disulfide prior to docking would prevent the seatbelt from being latched to the ␣-subunit. Consequently, no heterodimer would form unless it were possible for the ␣-subunit to be threaded through the altered -subunit. In the case of hCG-C26A,N77C, latching the seatbelt to Cys 77 would also disrupt the ability of the free subunit to be recognized by B112 as well as by B111. Addition of a cysteine to hCG to create hCG-N77C would provide the seatbelt with a second latch site. If the seatbelt became latched to its native site, this -subunit would be able to form an acid unstable heterodimer by a threading mechanism and both the free subunit and the heterodimer should be detected by B111 and B112. In contrast, latching the seatbelt to the added cysteine would be expected to disrupt assembly by either the threading or the wraparound pathway. As described in the text, the presence of additional cysteines in hCG did not prevent heterodimer formation, suggesting that the seatbelt was more likely to form a stable disulfide with Cys 26 , its natural site. In contrast, the presence of additional cysteines in hCG-C26A prevented this -subunit analog from being incorporated into a heterodimer. measurable by conformation-sensitive antibodies such as those employed in these studies. For example, a disulfide that disrupted the cystine knot would be likely to prevent the protein from folding and being assembled into a heterodimer with the ␣-subunit (16). A cysteine that disrupted the disulfide between Cys 23 and Cys 72 would prevent it from being recognized by B110. As noted earlier, a cysteine that interfered with seatbelt latching would prevent B111 binding. Several cysteines have been added to the hCG -subunit without preventing its assembly into heterodimers or being recognized by monoclonal antibodies (20,21). This shows that adding a cysteine to the native hCG -subunit does not prevent its seatbelt from being latched to Cys 26 .
In contrast, if the seatbelt has a strong tendency to be latched to the -subunit before the subunits dock with one another, addition of a cysteine to hCG-C26A would prevent it from being assembled with ␣-subunit analogs that contain an additional cysteine unless assembly can occur by a threading mechanism. As noted earlier, heterodimers that contain hCG-C26A can form only by a wraparound mechanism. The addition of a cysteine to hCG-C26A in place of Asn 77 to create hCG-C26A,N77C creates a potential latch site in loop 3. Because latching the seatbelt to Cys 77 before hCG-C26A,N77C docks with ␣-L41C would prevent the seatbelt from being latched to ␣Cys 41 , this substitution would block heterodimer formation by a wraparound mechanism. If the latching of the seatbelt to this location also blocked threading, this substitution would also prevent any heterodimer formation (Fig. 6).
Substitution of a cysteine for Asn 77 in hCG did not prevent it from forming heterodimers with ␣-L41C that were recognized by B111 (Table III, Study 1). This showed that the presence of Cys 77 did not block subunit folding or prevent the seatbelt from being latched to Cys 26 . The total amount of heterodimer formed was usually decreased, however, indicating that Cys 77 may have competed with Cys 26 as a seatbelt latch site. Based on the ability of ␣-L41C/hCG-N77C to be recognized by B111, we expect that its seatbelt is latched to Cys 26 , not Cys 77 .
As shown earlier (Table I, 1), ␣-L41C can be assembled with hCG or hCG-C26A to form acid unstable and cross-linked heterodimers, respectively. We observed that addition of a cysteine to hCG to create hCG-N77C did not prevent it from being assembled into heterodimers with ␣-L41C (Table III, Study 1, rows 1 and 3). In marked contrast, addition of a cysteine to hCG-C26A, which created hCG-C26A,N77C, prevented heterodimer formation (Table III, Study 1, rows 2 and 4). This was not because of the inability of the cell to make this -subunit analog. As noted in the legend to Table III, we detected a significant amount of the free -subunit in the culture medium (0.67 ng/50 l) that was not recognized by monoclonal antibodies B111 or B112, indicating that its seatbelt was latched to Cys 77 . This strongly suggested that its seatbelt was latched to Cys 77 before the subunits dock, a phenomenon that would be expected to interfere with threading. Furthermore, because Cys 110 was present in a disulfide with Cys 77 , the seatbelt was unable to be wrapped around loop ␣2 and form an intersubunit disulfide cross-link with ␣Cys 41 .
To minimize the possibility that there was something unique about the presence of a cysteine at -subunit residue 77, we repeated these studies using three different analogs of hCG-C26A. The presence of a cysteine in place of Ala 35 , Phe 64 , and Ala 83 disrupted its ability to form cross-linked heterodimers with ␣-L41C (Table III, Study 2). Thus, we found 1.5 ng of heterodimer containing hCG-C26A in 50 l of culture medium, but almost no heterodimer containing hCG-C26A analogs having cysteines in place of Ala 35 , Phe 64 , or Ala 83 . These observations supported the notion that most seatbelt latching occurred before the subunits docked. Formation of trace amounts of acid-stable heterodimer containing hCG-A35C,C26A (Table III, Study 2) indicated that a small fraction of the seatbelt might remain unlatched until after assembly of this heterodimer.
DISCUSSION
Threading Appears to Be the Major Route of Assembly for the Human Glycoprotein Hormones-The crystal structures of hCG (1, 2) and hFSH (3) show that their seatbelts are latched to a conserved cysteine in loop 1. Because of similarities in the locations of the cysteines of the hLH and hTSH -subunits, the seatbelts of these hormones are also likely to be latched to this site. The efficiency with which the seatbelt can be latched to Cys 26 of hCG suggests that the seatbelts of the other human -subunits are also likely to be latched before their subunits dock. This is supported by our inability to detect heterodimer assembly when any of several ␣-subunit analogs containing an additional cysteine were expressed with hFSH and hTSH -subunits in which Cys 20 and Cys 19 were replaced by ala-
TABLE III
Competition between -subunit cysteines and a cysteine added to ␣2 This table describes the production of heterodimers following co-transfection of COS-7 cells in triplicate with ␣-L41C and the indicated -subunit analog. The total heterodimer in the medium was determined in A113/ 125 I-B110 sandwich assays. Latching of the seatbelt to loop 1 was determined in A113/ 125 I-B111 sandwich assays. The presence of a cysteine in ␣-L41C reduced the binding of B111 to the ␣-L41C/hCG heterodimer to 58.9 Ϯ 7.3% that of hCG (average of 5 independent studies). This ratio was not changed by the presence of the cysteine in the ␣-L41C/hCG-N77C heterodimer. Free hCG-C26A,N77C was readily detected in the medium using antibody B101 for capture and 125 I-B122 for detection (0.67 Ϯ 0.01 ng/50 l medium, Study 1). hCG-N77C is recognized by both 125 I-B111 and 125 I-B112, antibodies that bind the hCG -subunit near residues Cys 110 and Asn 77 , respectively. This showed that the seatbelt of hCG-N77C is latched to Cys 26 nine. Thus, unless the seatbelt becomes unlatched transiently during the assembly process, hFSH and hTSH are also likely to be produced by a threading mechanism. Furthermore, the failure of hCG-C26A,N77C to be assembled into heterodimers with ␣-L41C suggests that the seatbelt latch disulfide is not readily disrupted once it has formed. This argues against the likelihood that the seatbelt becomes unlatched transiently during assembly. Throughout these studies we were concerned by the possibility that we were being misled by our methodology, particularly because we had expected to find that most heterodimer assembly would occur by a wraparound pathway. We were especially cognizant of the possibility that adding a cysteine to the ␣-subunit might alter the route of assembly, which is why we studied several ␣-subunit analogs. We were also concerned that replacing hCG Cys 26 with alanine would disrupt the structure of the -subunit. This is also unlikely based on the finding that hCG-C26A containing heterodimers were readily recognized by all conformation-sensitive antibodies tested except B111, an antibody that recognizes the position of the latched hCG seatbelt. Furthermore, when hCG-C26A or hCG-C26A-KDEL were expressed with cysteine containing ␣-subunit analogs in the absence of hCG or hCG-KDEL, they formed comparable or greater amounts of heterodimers. This indicated that hCG-C26A and hCG-C26A-KDEL were capable of being incorporated into heterodimers at rates that should have enabled them to out compete hCG and hCG-KDEL, if assembly occurs primarily by a wraparound pathway. The finding that only small amounts of hCG-C26A and hCG-C26A-KDEL were incorporated into heterodimers in the presence of hCG or hCG-KDEL suggests that the wraparound pathway is a relatively minor route for formation of the human glycoprotein hormones.
As a final effort to test the notion that threading is the more favored route of assembly, we measured the abilities of cysteines within the -subunit to compete for formation of the seatbelt latch disulfide. The threading pathway predicts that the seatbelt would be latched prior to heterodimer assembly. The finding that addition of a latch site to hCG-C26A disrupted its ability to form heterodimers with ␣-L41C satisfied this prediction. The observation that independent methods led us to the same result, namely that threading is the dominant assembly pathway, strengthens our confidence in this conclusion significantly.
Cysteines Added to the ␣-Subunit Can Become Cross-linked to the -Subunit during Assembly-A fraction of several ␣-subunit analogs became cross-linked to the native hCG -subunit during assembly. This suggests that one or more -subunit disulfides are disrupted during assembly and/or that the proximity of a -subunit disulfide to the cysteine added to the ␣-subunit makes it subject to a disulfide exchange. The presence of the ER retention signal KDEL facilitated cross-linking of analogs ␣-L41C, ␣-S43C, and ␣-T46C (Table I, 2, 4, and 5; data for ␣-S43C and ␣-T46C expressed with -subunits lacking KDEL retention signal not shown), indicating that this phenomenon occurred in the ER. The ability of ␣-S92C to be crosslinked to the native -subunit was as low or lower than that of any other cysteine tested, even though it became cross-linked to hCG-C93A-KDEL and hCG-C100A-KDEL better than any other cysteine that was added to the ␣-subunit. This suggested that cross-linking depended on the proximity of the ␣-subunit cysteine to the seatbelt during threading. As will be described elsewhere (26), the disulfide that stabilizes a small loop within the seatbelt is disrupted during threading, which permits it to form this cross-link. This disulfide is also the only ␣or -subunit disulfide that we found to be disrupted significantly dur-ing -mercaptoethanol catalyzed threading in vitro (6).
We considered the possibility that the cross-linking we observed during assembly of heterodimers that contained hCG and hCG-KDEL might be because of latching of the seatbelt to the cysteine that had been added to the ␣-subunit. Whereas we cannot exclude this possibility completely, the fact that the hCG analogs lacking the abilities to latch their seatbelts to the -subunit competed poorly with those that can latch their seatbelts to Cys 26 in every case is inconsistent with this possibility. This includes more than 30 independent experiments done by different individuals over a period of three years, some of which were performed with 6-fold more hCG-C26A than hCG. Furthermore, the notion that the wraparound pathway is a significant mode of hCG assembly is inconsistent with the finding that the hCG seatbelt has a marked tendency to be latched to the -subunit before the subunits dock productively, even when the seatbelt can be latched only to a site such as Cys 77 (Table III).
The Wraparound Pathway May Be a Salvage Pathway That Is Particularly Useful for Assembling Molecules with Lutropin Activity-The finding that hCG-C26A can be incorporated into heterodimers shows that the wraparound pathway can be used for heterodimer assembly. The observation that it is not as efficient as the threading pathway indicates that it is available as a potential salvage mechanism that would permit natural experimentation with the structure of the seatbelt. The seatbelt is the portion of the -subunit that has the greatest influence on hormone activity (9,(22)(23)(24) and is among the most divergent parts of lutropins, follitropins, and thyrotropins (25). We were not able to detect synthesis of any hFSH or hTSH by the wraparound pathway, a phenomenon that may indicate the seatbelts of these human -subunits are not wrapped around loop ␣2 efficiently. Whereas this precluded us from performing competition studies with these -subunits, as will be discussed in greater detail elsewhere (26), cross-linked heterodimers containing either the hFSH and hTSH -subunits were found in cells that co-express these -subunits with ␣-subunits containing an additional cysteine.
Methods Used Here May Be Suited to Studying the Folding and Assembly of Other Proteins in the ER-Earlier analyses of hCG assembly in vivo employed pulse-chase methods that are less suited to detecting transient intermediates than the competition approach outlined here (7). This may explain why the threading pathway was not seen previously. We suggest that the competition strategies outlined here, which can be tailored to permit the detection of transient intermediates, will be useful adjuncts to pulse-chase methods for studying protein folding in cells. | 13,826.4 | 2004-08-20T00:00:00.000 | [
"Biology",
"Chemistry"
] |
Direct Detection Signals from Absorption of Fermionic Dark Matter
We present a new class of direct detection signals; absorption of fermionic dark matter. We enumerate the operators through dimension six which lead to fermionic absorption, study their direct detection prospects, and summarize additional constraints on their suppression scale. Such dark matter is inherently unstable as there is no symmetry which prevents dark matter decays. Nevertheless, we show that fermionic dark matter absorption can be observed in direct detection and neutrino experiments while ensuring consistency with the observed dark matter abundance and required lifetime. For dark matter masses well below the GeV scale, dedicated searches for these signals at current and future experiments can probe orders of magnitude of unexplored parameter space.
The search for dark matter (DM) is rapidly expanding both theoretically and experimentally. Weakly interacting massive particle (WIMP) DM searches have pushed the limit on the WIMP-nucleon cross-section near the neutrino floor for masses around the weak scale [1][2][3]. These null results have sparked a renaissance in DM model building, in search of alternative thermal histories which predict lighter DM [4][5][6][7][8][9][10][11][12][13]. For masses below the GeV scale, DM which scatters off a target will typically deposit energy below the threshold of the largest direct detection experiments (O(keV)), significantly relaxing the direct constraints.
Particle DM detection strategies can be grouped into two classes: scattering and absorption. Searches for scattering look for a DM particle depositing its kinetic energy onto a target within the detector, typically a nucleus or an electron. In contrast, searches for absorption look for signals in which a DM particle deposits its mass energy. Absorption signals have primarily been considered for bosonic DM candidates with studies of fermionic absorption signals limited to induced proton-to-neutron conversion in Super-Kamiokande [33] and sterile neutrino DM [34][35][36][37][38][39][40][41] (see also exothermic DM [42] and selfdestructing DM [43] for related signals).
In this Letter, we systematically study direct detection signals from the absorption of fermionic DM. We describe novel signals and their corresponding lowest-dimension operators; project the sensitivities of ongoing and proposed DM direct detection and neutrino experiments to these signals; and demonstrate the consistency of these signals with the issues of DM stability and abundance.
Signals and operators. For simplicity, we take DM (χ) to be a Dirac fermion charged under lepton number, and impose only Lorentz, SU(3) C × U(1) EM , CP, lepton and baryon number symmetries. Baryon number conservation is necessary to avoid proton decays while lepton number allows the (Dirac) neutrino to remain light. We enumerate operators in the effective theory with the fields {χ, n, p, e, ν, F µν }, where F µν is the EM field strength tensor. We do not include other QCD resonances as they have no bearing on direct detection.
Consider first dimension-6 operators of the form, [χΓ i ν] ψ Γ j ψ , where ψ ⊃ {n, p, e, ν} and Γ i = {1, γ 5 , γ µ , γ µ γ 5 , σ µν } denotes the different possible Lorentz structures of the bilinear. These "neutral current" operators generate the first class of new signals we consider; (-) χ + T → (-) ν + T , where T is a target nucleus or electron which absorbs a fraction of the DM mass energy. We will focus on nuclear absorption, where the rates may be coherently enhanced, and postpone the study of electron absorption [44].
Next, consider dimension-6 operators of the form, [χΓ i e] [nΓ j p]. These generate a class of "charged current" signals; (-) χ + A Z X → e ± + A Z∓1 X ∓ * , in which DM can induce β ± decay in nuclei which are stable in vacuum. This process potentially has multiple correlated signals: a detectable e ± , a nuclear recoil, a prompt γ decay from the excited final nucleus, and further nuclear decays if the final nucleus is unstable. Induced β + decays have significantly smaller rates relative to β − due to the Coulomb repulsion between the emitted e + and the nucleus, so we focus on DM-induced β − decays and leave the β + decays for future work [45] [46]. The same charged current operators can also shift the endpoint of the β ± distribution for nuclei which already undergo β ± decays in vacuum. While this might be detectable at PTOLEMY [47,48], these kind of experiments have small exposures and large backgrounds, so we defer their study [45].
Finally, DM candidates which have fermionic absorption signals decay. At dimension-5, the operator χσ µν νF µν induces decays of χ as do the dimension-6 operators,χγ ν Γ (5) ∂ µ νF µν , where Γ (5) ≡ {1, γ 5 }. At higher dimensions, there exist operators allowing multiphoton decays. The single photon channel can be detected with the usual line search, while the multiphoton channels are constrained by diffuse photon emission. Detectable fermionic absorption signals, consistent with indirect detection bounds, typically require lighter dark matter as the decay rates scale with a large power of m χ . We include a discussion of decays below for each signal and operator we consider.
Neutral current signals: nuclear recoils We first study the process χ + N → ν + N, where N is a target nucleus. We will focus on two operators: We choose this Lorentz structure for concreteness. However, the neutral current signal is not highly dependent on it as long as there is some amount of vector coupling to the nucleons. These can arise from a theory of a heavy Z coupled to quarks and χ with some mixing between the right handed components of χ and ν. The incoming χ is non-relativistic, so its mass dominates its energy resulting in a momentum transfer (q) and nuclear recoil energy (E R ): where M is the mass of the nucleus. For contrast, elastic scattering off a nucleus yields at most E R = 2v 2 µ 2 /M, where µ is the reduced mass and v is the DM velocity (see [49] for a recent review). This 1/v 2 increase in E R relative to WIMP scattering allows searches for lighter DM with both direct detection experiments and higherthreshold, neutrino experiments. The differential rate of neutral current nuclear recoils from absorbing fermionic DM is; where N T is the number of target nuclei, ρ χ 0.4 GeV/cm 3 is the local DM energy density, E 0 R ≡ m 2 χ /2M , E th is the experiment's threshold, and |M N | 2 is the matrix element squared (at q) averaged over initial spins and summed over final spins. In elastic scattering, the spread in incoming DM velocities causes a spread in recoil energies, but in fermionic absorption, the rate is sharply peaked at E R = E 0 R . Every isotope in an experiment has a distinct peak with width (∆E R ) determined by higher order corrections to Eq. (2), corresponding to ∆E R /E R ∼ 10 −3 . There are no modulation signals or rate uncertainties arising from the DM velocity distribution.
The total rate for absorption by multiple nuclei is where N T,j , A j , E 0 R,j , and F j , are the number, mass number, recoil energy, and Helm form factor [69] (evaluated at q = m χ and normalized to 1) of target isotope j. The cross section per-nucleon is σ NC = m 2 χ / 4πΛ 4 . Absorption has the unique signature of correlated, peaked counts in dR/dE R bins containing E 0 R,j = m 2 χ / (2M j ) for the different target isotopes with masses M j . This can be a powerful discriminator from backgrounds since the relative heights and spacing of the peaks is completely determined. Whether an experiment can resolve these distinct peaks depends on its energy resolution and the mass splitting between the target isotopes.
For m χ MeV, future experiments are necessary to probe the small nuclear recoil energy. Detailed projections are challenging due to the breadth of proposals and possible absorption by collective modes of nuclei. So, we roughly estimate the sensitivity of such future detectors in Fig. 1 (Left) where, for simplicity, we require at least 10 events to set our projections, independent of mass or experiment. The cross sections are smaller than those in typical WIMP searches due to the larger number densities of lighter DM. We consider Hydrogen and Lithium targets with energy thresholds of eV − 100 eV for 1 kg-year and 100 kg-year exposures (see [21] for one possible realization). In the Lithium target, the detection of two correlated signals from both isotopes is possible. For m χ MeV, we project the sensitivity of current experiments in Fig. 1 (Right). Interestingly, which experiments best probe the neutral current absorption signal are not always the same as those which best probe WIMPs (e.g., Borexino). Each experiment can only detect the absorption signal off a target isotope when its distinct nuclear recoil energy is larger than the threshold energy, hence the edges in Fig. 1.
We now address the stability of χ. For concreteness, we consider a model where a heavy Z couples in an isospininvariant way to quarks, with gauge coupling g Z , and to χ and P R ν in an off-diagonal way [70]. Quark loops induce a kinetic mixing, , between the Z and the photon of order ∼ g Z e/16π 2 allowing the decay χ → νe + e − . Without additional Z or Z mass suppressions, the decay χ → νγ is forbidden by gauge invariance while χ → νγγ is forbidden as a consequence of charge conjugation (also known as Furry's theorem). For m χ MeV, the electron channel is kinematically forbidden and the dominant decay is χ → νγγγ, whose primary contribution proceeds through a kinetic mixing and the Euler-Heisenberg Lagrangian, yielding the approximate rate [55,56] (green); CDMSliteR2 [57] and SuperCDMS [58] ("SuperCDMS" in aqua); PICO-60 run with C3F8 [59] and PICO-60 run with CF3I [60] ("PICO" in sky blue); COHERENT [61,62] (blue); LUX [2], PandaX-II [63], and XENON1T [64] ("Xenon expts" in navy blue); and Borexino [65] (purple; see [66] to extract nuclear recoil threshold). Both panels include LHC bounds [67] and the indirect detection constraints from χ decay [68] which require different levels of fine-tuning between the UV and IR contributions to kinetic mixing between the photon and Z for the Z model as described in the text.
Estimating the DM decay rates in this simple UV completion, we find future experiments can quickly probe new parameter space while cross-sections accessible to current experiment are ruled out by indirect detection bounds [68].
However, it is possible to suppress DM decays by finetuning the UV contribution to the kinetic mixing against the IR piece estimated here. Concretely, we define this fine-tuning as F.T. ≡ | UV − | / and we show the finetuning necessary to evade indirect detection constraints with dashed gray lines labeled "F.T." in Fig. 1. We note that the projected direct detection sensitivities in Fig. 1 are insensitive to the details of the UV completion. We study ways to reduce fine-tuning by incorporating flavordependent couplings to suppress in future work [45].
Also shown in Fig. 1 are direct constraints from LHC mono-jet searches on the Z model, which bound new neutral currents below the TeV scale [67]. Dijet constraints are model dependent: in the Z model, dijet bounds are suppressed in the limit where the quark coupling to the Z is much smaller than the χ coupling to Z . The excess neutrino flux emanating from the Sun and Earth due to Eq. (1) is not quite large enough to be seen in neutrino observatories in the near future. Cosmological bounds depend on initial conditions (e.g., the reheat temperature) and the UV completion. While we postpone a detailed study of the dark matter relic abundance, we comment that a simple way to populate such light dark matter is through its thermal production and relativistic decoupling followed by its dilution from the decay of another heavy particle-a mechanism considered for sterile neutrinos [71]. If the dark matter χ decouples while it is relativistic, which with only the quark coupling, will occur at the latest around the QCD phase transition, it will be overproduced. After relativistic decoupling of χ another state becomes non-relativistic leading it to quickly dominate the energy density of the universe. This mechanism can produce and sufficiently dilute DM to achieve its observed relic abundance over the entire DM mass range shown in Fig. 1. While other production mechanisms are possible, one must carefully avoid spoiling Big Bang Nucleosynthesis (BBN) for DM lighter than O(1 MeV) [72], e.g. via freeze-in. Neutron absorption of χ through n + χ → p + e could also spoil BBN, but the number density of χ is substantially less than that of SM neutrinos and the rate of scattering is suppressed relative to that of neutrinos by (m W /Λ) 4 making this negligible.
Charged current signals: DM-induced β − decays Next, consider signals from χ + A Z X → e − + A Z+1 X + * (or at the nucleon level, χ + n → p + e − ), which we refer to as an induced β − decay. This process can cause stable elements to become unstable in the presence of DM if m χ is large enough to overcome the kinematic barrier. Such a signal may proceed through the dimension-6 charged current vector operator, This can be generated by a W which can appear if the electroweak gauge group is embedded in a larger gauge group which subsequently breaks into the SM. We consider the vector operator in Eq. (6) to leverage known results from the neutrino and nuclear physics literature. The vector-vector interaction primarily induces Fermi transitions which are characterized by their conservation of spin (J) and parity (P ) of the nucleus [73], also known as J P → J P transitions. However, we emphasize that the DM induced β − decay signal is more general, with different vertex structures allowing different transitions. We leave a study of additional interactions to [45].
Denoting the mass of a nucleus of mass number A and atomic number, Z, by M A,Z , we focus on isotopes which satisfy M A,Z < M ( * ) A,Z+1 + m e , such that the nucleus is stable against β − decay in a vacuum (the ( * ) is included to emphasize the daughter nucleus may be in an excited state, typically 200 keV − 1 MeV heavier in mass). Then DM induced β − decay is kinematically allowed if In these induced decays, χ is absorbed by the target nuclei and transfers the majority of its rest mass to the outgoing electron. In the limit where m χ − m β th m e , the electron and nuclear recoil energies are analogues to the neutral current case with m χ → m χ − m β th , and are given by; Therefore, the energetic outgoing electron will shower in the detector, and can be searched for. The nuclear recoil energy, as with the neutral current case, is independent of DM velocity, and can be searched for as well. Additional correlated signals result from the possible de-excitation of the daughter nucleus and its subsequent decay (typically many days later). These multiple signals make possible correlated searches to reduce backgrounds. The specific signals depend on the experiment, the particular isotope, and the DM mass. The rate for DM-induced β − decays is; where we sum over all isotopes in a given target material, N T, j is the number of target isotope j, and σv j is an isotope's velocity averaged cross-section where | p e | 2 j = (m β th, j − m χ )(m β th, j − m χ − 2m e ) is the electron's outgoing 3-momentum in the center of mass frame (which is approximately the lab frame), in the limit FIG. 2. Projected sensitivities to m 2 χ /2πΛ 4 from a dedicated search for the charged current induced β − transition at Cuore [74] (red); LUX [2], PandaX-II [63], and XENON1T [64] ("Xenon DM expts" in navy blue); EXO-200 [75] and KamLAND-Zen [76] ("Xenon 0νββ expts" in sky blue); SuperKamiokande [77] (yellow); CDMS-II [78] (aqua); DarkSide-50 [55,56] (green); and Borexino [65] (purple). Also shown are LHC bounds [79] and indirect constraints from χ decays in our simple UV model [68].
that m e , m χ , m β th, j M Aj ,Zj . The amplitude M N is for absorption by the whole nuclei (the momentum transfer is not enough to resolve individual nucleons), which can be related to the nucleon level amplitude M (with the spinors normalized to p µ p µ = M 2 Aj ,Zj ) through the Fermi function, F(Z, E e ) and a form factor, F V (q 2 ): The Fermi function accounts for the Coulomb attraction of the ejected electron and can enhance the cross-section by several orders of magnitude for heavier elements. The form factor is equal to 1 for small momentum transfer relative to the nucleon mass, q 2 m 2 n , while for larger q 2 the dependence can be extracted from the neutrino literature [80]. In principle, (10) must contain a sum over all possible nuclear spin states. The assumption made here is that this sum will be dominated by ∆J P = 0 transitions as is the case of a vector coupling [73]. Excitation of additional final states is possible if q r −1 N , where r N 1.2A 1/3 fm is the nuclear radius [81], however for simplicity we focus on lighter masses such that these do not contribute significantly to the rate for any isotope considered here.
The total rate is found by summing over the contributions from each isotope. Evaluating (10) in the limit where m e , m χ , m β th M A,Z , the total rate is; where we have integrated over all energies with the assumption that such a signal could be detected by most experiments under consideration here given the multitude of correlated high energy signals.
We project the sensitivity of current experiments to the charged current signal in Fig. 2 where we again require at least 10 events to set our projections, independent of isotope mass or experiment. Sensitivities are displayed in terms of the theoretically interesting quantity m 2 χ /2πΛ 4 (to which Eq. (10) reduces in the limit of large M Aj ,Zj and m χ m β th, j , modulo the Fermi function). As with the neutral current case, limits depend on the different isotopes in a given experiment. In particular, the kinks in Fig. 2 occur at m χ ∼ m β th, j for every relevant isotope in a given experiment.
To estimate the DM decay constraints from a typical UV completion, we consider a model with a W coupled vectorially to up and down quarks without any direct couplings to leptons. When kinematically allowed, the dominant decay is χ → e + e − ν which arises from a kinetic mixing between W and the SM W boson of order ∼ g W e/16π 2 . The decay χ → νγ is subdominant since it is at two-loop order, making it roughly (4π) 2 smaller. We estimate the decay rate and show the resulting indirect constraints [68] in gray in Fig. 2. The decay bounds are much weaker than in the neutral current case as they are suppressed by both the weak scale and the W mass.
In addition to decays, there are direct bounds from LHC searches for pp → ν. A search was done by CMS at 8 TeV looking for helicity-non-conserving contact interaction models which have contact operators with vertex structure different than that of the SM [79] which sets a powerful constraint on the charged current operators. For the W model, this constraint corresponds to a scale in Eq. (6) of Λ 3.2 TeV. In the W model, there is also a Z which could lead to direct bounds. However, direct searches for Z are not as stringent as those for the W as the Z can be somewhat heavier than the W and elastic scattering constraints are negligible for the masses and Λ of interest here. We also consider low energy searches for modifications to the V − A gauge structure of the SM [82,83] and for light fermions in charged pion decays: π ± → e ± χ [84], but find they are subdominant to the CMS constraint. Cosmological constraints require detailed assumptions about the initial conditions and the full set of interactions. As for O NC , a simple production mechanism with O CC has the DM decouple from the SM bath while relativistic, followed by late decays of a dominating particle [85][86][87].
Discussion In this Letter, we have introduced a novel class of signals from fermionic DM absorption in direct detection and neutrino experiments. We have studied the sensitivities of future and current experiments to neutral current signals from the process χ + N → ν + N, as shown in Fig. 1. This neutral current causes target isotopes to recoil with distinct energies and correlated rates, enabling significant background reduction in searches. We have also studied the sensitivities of current experiments to induced β − decays from the process χ + A Z X → e − + A Z+1 X + * , as shown in Fig. 2. This charged current enjoys multiple signatures from a sequence of events starting with a nuclear recoil and ejected e − , followed by a likely γ decay and often a final β decay or electron capture event several days later. For both signals, ongoing experiments can probe orders of magnitude of unexplored parameter space by performing dedicated searches.
Without yet knowing the true nature of DM, it is impossible to know how it will appear in an experiment. Perhaps, it has been a fermion, depositing its mass energy into unsuspecting targets all along. | 5,212.2 | 2019-05-29T00:00:00.000 | [
"Physics"
] |
New Insights into Crust and upper Mantle Structure in Guangdong Province, China and Its Geothermal Implications
: Southeast Asia contains significant natural geothermal resources. However, the mechanism for generating geothermal anomalies by the crust–mantle structure still needs to define. In this study, we focused on Guangdong Province, China. We conducted three magnetotelluric profiles to interpret the crust and upper mantle structure beneath the Guangdong Province and its geothermal implications. Based on data analysis results, a two-dimension inversion was conducted on the dataset. The inversion model revealed that there is a presence of upwelling channels, and some channels are connected with shallow crustal fault zone; the thickness of crust and lithosphere in Guangdong Province is relatively thin. Such a special crust and upper mantle structure form high surface heat flow. Merged with previous research, our results imply that massive Late Mesozoic granites, which contain high radioactive heat generating elements, are distributed on the surface and underground of Guangdong Province. Based on the correlation between high radioactive Late Mesozoic granites, crust-upper mantle structure, surface heat flow, and locations of natural hot springs, we established a geothermal conceptual model to visualize the origin of a current geophysical and geothermal anomaly in Guangdong Province.
Introduction
Southeast Asia straddles the boundary between the Pacific/Philippine Plate and Eurasia Plate and locates in the South China fold belt. It is mainly located on the Cathaysian plate. The geology is highly diverse, and the tectonic setting ranges from the amalgamation between the Yangtze block and the Cathaysia Block during the Neoproterozoic [1] to the subduction of the Pacific/Philippine Plate in the Cenozoic [2]. Guangdong Province is located on the Cathaysian plate and has the same tectonic evolution as the Cathaysian plate ( Figure 1). The crust and upper mantle structure of Guangdong Province in this area have shaped by these tectonic impacts, which are mainly manifested as follows: Figure 1. Tectonic map in East Asia and distribution of exposed Late Mesozoic granite in South China (modified from Kuang et al. [3]). The green area is the distribution of exposed Late Mesozoic granite, modified from Zhou et al. [4]. The red line is Guangdong Province.
First, the predominant feature in Guangdong Province is the widespread exposure of Mesozoic granite with an exposed area of 60,000 km 2 , accounting for about one-third of the area, considered the result of the multi-stage emplacement of magmatic rocks [3]. Such spatial-temporal distribution characteristics of the Mesozoic granites have been attributed to the dynamic mechanism associated with subduction and interaction with multiple plates [5,6]. These granites, Late Mesozoic granite, in particular, were formed by the remelting of the Neoproterozoic and Paleozoic crust [7] and extremely rich heat-producing elements (Th, U, and K) with average heat production of more than 5 µW/m 3 [8]. Second, various geophysical methods have led to the thin lithosphere (~80 km) present in South China [9][10][11][12]. Combining with studies on mantle peridotite enclaves/xenoliths in Paleozoic suggested that a lithospheric thinning process has occurred in Meso-Cenozoic [13][14][15]. Furthermore, there are abundant NE-and NW/WNW-trending faults and associated foldand-fault zones in Southeast Asia ( [6]; Figure 1). Consequently, these processes shaped Southeast Asia into a geothermally active region and southeast China into the secondlargest high heat flow region in China, where there are many natural hot springs spanning an unusually large area ( [16,17]; Figure 2). The large area geothermal anomaly constitutes an impressive geothermal utilization prospective area; however, it has not been well exploited due to the deficiency of comprehensive studies of the geothermal anomaly in southeast China.
Recently, a study based on Bouguer gravity data has suggested that the geothermal anomalies in Guangdong Province originated from the combined effect of asthenosphere upwelling and granite, which emplaced along the faults [18]. Another study based on heat flow data and tectonic setting stated that the high surface heat flow values correspond to the lithosphere's thinning [17]. However, these results do not fully explain the crust structure, geothermal anomalies, and their interrelationships. These results do not fully account for the crust structure, geothermal anomalies, and their interrelationships, which hinders the subsequent utilization of geothermal resources, the implementation of relevant simulation work, and analysis of the geothermal polygeneration system [19][20][21].
To solve these problems, the primary goals are to constrain the crust-mantle structure and to establish the association between geothermal anomalies and the crust-mantle structure. In this study, we conducted three magnetotelluric profiles in Guangdong Province, China, where these areas are abundant in the geothermal resource. Further, the granitic intrusions and faults are available for analyzing the effects of different factors on the generation of hot springs. We present new imaging results of the crust and upper mantle structure across a major portion of Guangdong Province and establish a geothermal conceptual model to decipher geothermal formation in Guangdong Province.
Geological Setting
The Guangdong Province has narrowed due to three major convergent tectonic plates since the Mesozoic, which are the subduction of the Pacific Plate to the east, the subduction of the India Plate beneath the Eurasia Plate to the southwest, and the convergence between North and South China Blocks to the north ( Figure 1). As a response to this tectonic event multi-plate interaction, this region underwent a widespread tectonic thermal event and intracontinental deformation. These events are characterized by massive magmatic emplacement, widespread shortening, thrusting, and decollement in the Mesozoic [4,6]. Specifically, these events could be evidenced by the widespread granitoid belts of different ages and large-scale fault zones. Such features were mainly caused by the multi-plate interaction [7] or by the advance and retreat of the Pacific Plate [6,22]. Later on, during the Cenozoic, a basin and range-like region and widely distributed basalt were generated in the coastal areas [23,24]. These tectonic events have been suggested to be formed by asthenospheric convection-driven extension and thinning of continental crust. Such asthenospheric convection is controlled by the collision between India Plate and Eurasia Plate (for a review, see [3]).
MT Data Acquisition
From July to August 2013, three MT profiles (L100, L200, and L300) with 440 km and 103 stations were established to obtain the electrical structure of crust and mantle in southeast China ( Figure 2). The L100 is divided into two parts. The east part has a length of 40 km with an interval of 1 km. The west part has a length of 100 km with a station spacing of 5 km. L200 has a length of 100 km with a station spacing of 5 km. The L300 has a length of 200 km with a station spacing of 10 km. The L100 and L200 cross the Wuchuan-Sihui fault zone and the Enping-Xinfeng fault zone ( Figure 2). The L300 crosses the Enping-Xinfeng fault zone, Heyan fault zone, Zijin-Boluo fault zone, and Lianhuashan fault zone (south section of the Zhenghe-Dapu fault zone) ( Figure 2). Extending direction of the MT profiles is designed to be east-west trending.
MT data were collected with Phoenix MTU-5 instruments. All 5 orthogonal components of the electromagnetic field (Ex, Ey, Hx, Hy, and Hz) were recorded. The x-axis and the y-axis are magnetic N-S trending and magnetic E-W trending, respectively. The horizontal electric (E) and magnetic (H) fields are measured in the time domain and converted to the frequency domain by Fourier transform to receive the MT response function. Before the field data collection, we performed calibration and consistency experiments on all the instruments and equipment used to ensure that the instruments invested during the construction process work properly. The first and second Supplementary Figures (Supplementary Figures S1 and S2) show the calibration results of the V5 system 2000 equipment box and probe, respectively. With a recording time no less than 18 h, MT data were obtained in an average period of 0.003-2000 s. The MT time-series were transformed into frequency domain with fast Fourier transform, and the frequency-dependent transfer function elements were calculated by standard remote reference [25], robust routines [26].
MT Data Analysis
In magnetotelluric analyses, the regional structure's response can be concealed by the galvanic distortion caused by small-scale inhomogeneities near the surface. In this work, the multi-site multi-frequency distortion decomposition, which is based on the Goom-Bailey (GB) decomposition method [27], was used to estimate the galvanic distortion of the MT response and the regional strike and dimension of magnetotelluric data before two-dimensional inversion and obtained the best electrical principal axis information of the three profiles in the study area according to this method (Supplementary Table S1). Under the assumption that the surface layer is partially covered by 3D on 2D structural paper, the observed impedance tensor (Z) was decomposed [27], the formula is as follows: C is the frequency-independent local distortion matrix, g is a scalar factor, R is the rotation matrix, R T is the transpose matrix of R, T is the torsion matrix, S is the shear matrix, A is the decomposition tensor, and Z 2-D is the actual 2D impedance tensor of the region. T can be expressed as: t is the torsion factor, θ is the strike angle, e is the shear factor, and s is the splitting scale factor. gAZ 2-D is solved as a whole due to its nonuniqueness: There are 8 equations and 7 unknowns when the impedance tensor is expanded in the form of a real part and an imaginary part. The parameters of regional impedance, strike, and distortion can be obtained by using the least-squares method. Furthermore, the whole frequencies of the MT data are rotated to the respective strike directions before inversion. The GB strike directions of all sites for whole frequencies were depict using the rose diagram ( Figure 3). As shown in Figure 4, the calculated structural strike almost coincides with the strike of the large-scale fault in Guangdong Province, China. The main electrical axes of the three profiles are mainly NE, which are consistent with the large structural trend of southeast China [6].
MT Data Inversion
Using the nonlinear conjugate gradient algorithm developed by Rodi and Mackie [28], two-dimensional inversion analysis of the rotated data is carried out, and the algorithm is implemented in the data interpretation package WinGLink. Before calculating the final model, several inversion parameters should be set to fit the data.
The collected magnetotelluric data can be divided into two parts, which includes data with a magnetic field direction perpendicular to propagation direction (TM) and data with the electric field direction perpendicular to propagation direction (TE), and the inversion modes include TM mode, TE mode, and TE and TM joint inversion mode. For TM mode it is more sensitive to the low-resistance structure in the shallow part and is susceptible to the influence of static displacement, which mainly produces current-type distortion; the TE mode well reflects the deep and high-resistance structure and is less affected by the static displacement, which is prone to inductive distortion. For measured data, it is generally preferred to use TM model data for two-dimensional inversion [29,30]. Consequently, to select the inversion results more suitable for the geological parameters, TE model inversion, TM model inversion, and TE and TM joint model inversion were carried out for the L300, respectively ( Figure 5). The TE model inversion has a good reflection on the shallow high-resistance layer. However, the low-resistance layer is missing, and it is impossible to analyze the fracture characteristics of the underground structure. The TM model highlights the low-resistance layer well and has a perfect correspondence with the deep-seated fault in the Guangdong Province. There is a certain similarity between TE and TM joint inversion model and the TM model. However, the result of joint inversion is not ideal due to the large fitting difference between the TE and TM joint model and TM model. Accordingly, in this study, the TM model of nonlinear conjugate gradient (NLCG) two-dimensional was selected for inversion. The NLCG inversion method has the advantages of fast operation layer speed, less memory occupation, multimode inversion, avoiding the single inversion mode and multi-solution of inversion results. The results are more comprehensive and selective, and the inversion model is more intuitive, reflecting the underground problems clearly.
To obtain the best regularization parameter (τ) values, we selected different τ values (τ = 1, 3, 5, 10, 20, 50) for the L300, and carry out inversion, respectively. In the inversion process, the other parameters remain unchanged with the weighted parameter is 1.5 and the error range is 5%. Meanwhile, the fitting difference root-mean-square (RMS) value of each inversion is discriminated (Supplementary Table S2). Figure 6 displays that, τ = 1, it can be seen from the figure that its reflection effect on the shallow part is better, however, for the deep information, the overall performance is low resistance, which does not achieve good results; τ = 3, both the shallow part and the deep part have a good reflection effect; τ = 5 and τ = 10, it can be seen from figures that there is no significant difference in the whole, and it also has a large similarity with τ = 3. However, it does not obviously reflect the highly conductive upper mantle layer; τ = 20 and 50, the inversion results are much smoother than that in others. Although it reflects well on deep electrical characteristics, it does weakly on shallow formation information. Therefore, 3 is the best τ value, and it is used in the later inversion. Moreover, the initial resistivity was set as 100 Ω·m; the homogeneous half-space initial model was adopted; the WinGLink data inversion software was used for inversion.
Inversion Results
The most notable feature of the 2D inversion result is the large area of low resistance area along with these profiles (Figure 7). Each profile's conductivity has a three-layered structure in vertical, and the low conductors are inserted between the high conductors across these profiles. The overall RMS of the L100, L200, and L300 are 4.4, 4.7, and 5.2, respectively. As demonstrated in Figure 7, the RMS value of most of the stations of the three profiles is below 4.5, and the RMS value of 90% of the station is less than 6. The 190 and 195 stations of the L100, which are located near Yangjiang City and Yangdong County, have a relatively large RMS value and may be greatly disturbed by human activity, resulting in poor data fitting in two-dimensional inversion. Similarly, the 225 station of the L200, which is located near Enping City, has a relatively large RMS value. The overall RMS of the L300 is much large than that of L100 and L200, and 20% of the L300 stations have high RMS values (>6). However, there is no significant human disturbance near these stations with high RMS values. Thus, we speculate that there are complex fault systems near these stations, and the RMS is affected by a three-dimensional inhomogeneous geological body near the surface.
Interpretations of the Model
As can be seen from Figure 8, the resistivity increases with the depth in vertical profile, which contains three layers: crust sedimentary caprock in the top, middle and lower crust in the middle, and mantle to the bottom.
The top layer's thickness gradually thins from west to east in L100 and L200 profiles ranging from 9 km to 2 km thickness, while it is about 4 km thickness in the L300 profile. Similarly, crust thickness gradually thins from west to east in all profiles with an average of~30 km even though the crust's thickness is various with 22 km in local. The highresistance layer in the entire crust is cut into several blocks by the low-resistance bodies, forming a discontinuous spatial distribution of the high-resistance layer. A large area of low resistance layer has a resistivity value of 0.4-100 Ω·m in the lower layer of L100 and L200 profiles, and it tends to extend to −120 km or deeper. Furthermore, there is a large area of low resistivity in the upper mantle with a depth below 90 km, which is supposed to be asthenospheric. The presence of a discontinuous low resistivity layer in the range of −10 to −30 km suggests multiple channels for upwelling of the mantle sources or recommends a high-conductor formed by the alteration or melting of wall rocks caused by mantle materials. Specifically, Figure 8 shows the F 3 (Heyuan Fault) adjacent to Heyuan City is connected with the asthenospheric upwelling in the L300. Our previous geophysical exploration in the Heyuan Basin confirmed that the Heyuan Fault controls Cenozoic basalt occurrence [3]. Moreover, all the regional fault zones are well reflected in the inversion model, and the low resistance zone near the surface matches with the actual location of fracture exposure. The lithosphere thickness of the study areas and adjacent areas is around 80 km, as shown in this study. This result is similar to other geophysical observations in South China. For example, the ambient noise tomography work indicated that the lithosphere thickness in the Cathaysia Block is 60-70 km [9]. The receiver function results implied a lithosphere thickness of~65 km in southeast China [11,31]. Deng and Levandowski proposed that the depth of the lithosphere-asthenosphere boundary (LAB) is ranging around 100 km, which is estimated by the final density model and receiver functions [12]. A joint inversion of Rayleigh wave dispersion data, topography, geoid height, and terrestrial heat flow with a probabilistic Monte Carlo method predicts the recent lithosphere in South China is ranging from 80-105 km [10].
Notably, the depth of LAB in South China observed by different complex and commendably geophysical methods seems variable. The presence of multichannel of asthenosphere upwelling in the coastal area and adjacent area may well explain the variable depth of LAB as these upwelling channels interfered with geophysical interpretation to some extent. As shown in Figure 8, each profile has several asthenospheric upwelling channels along deep-seated faults whose influence width is tens of kilometers. Similarly, using the magnetotelluric method to detect the crust/mantle thermal structure shows that the asthenospheric upwelling is common in southeast China, including Fujian Province, Guangdong Province, etc. [32,33]. The impact of these widespread distributed multichannel asthenospheric upwelling on the lithosphere mainly reflects in the following two points. For one, the rigid lithosphere turns into a plastic state under the underplating of hightemperature materials. It is gradually eroded by the asthenosphere, resulting in thinning of the lithosphere. Additionally, the lithosphere undergoes partially melting due to the underplating of the asthenosphere with meltable material separate out from the lithosphere to the asthenosphere. The lithosphere's remaining rigid material undergoes rigid rupture under gravity and sinks into the asthenosphere [34,35]. These two mechanisms coexist in the upwelling process of the asthenosphere, and all have a significant impact on lithospheric thinning. Furthermore, Compared with other ancient cratons, U-Pb zircon geochronology dates the Cathaysian block where southeast China locates as Neoproterozoic in age [36] indicate the lithosphere is more vulnerable to erosion and destruction [32]. In summary, the asthenosphere's upwelling has completely modified the lithospheric structure, resulting in different thicknesses of the lithosphere and crust-mantle structures in Guangdong Province.
Guangdong Province straddles the boundary between three energetic tectonic domains: the Pacific subduction zone to the east, the collision zone between the Philippine Sea and the Eurasian plate to the southeast, and the spreading of the South China Sea to the south (Figure 1). Specifically, for the Pacific plate, previous receiver function images of mantle transition zone [37][38][39] and tomographic studies [40,41] indicate that the slab front extends into the area beneath the South China block (~105 • E). Various geophysical and geochemical evidence has indicated that the Pacific plate stagnant in the mantle transition zone and has continuously released fluid material to destruct and reform the overlying lithospheric mantle [40,42,43]. The collision zone between the Philippine Sea and the Eurasian plate forms compressional uplifting and orogeny along the southeast coast area and Taiwan [44,45]. The evolution of the South China Sea has a significant impact on the surrounding continents, which is reflected in the formation of crustal uplifting or depression [2,46,47]. The interaction of these plates affects the activity of the asthenosphere in Guangdong Province and adjacent areas. For example, the force driven by the Pacific plate's subduction triggers the mantle convection, inducing the eastward asthenospheric flow beneath South China in the big mantle wedge. For one, during the flow process, the positive buoyancy causes asthenospheric upwelling accompanied by decompression melting and melt extraction [48]. This process will erode the overlying lithosphere. On another side, fluid released by the stagnant Pacific plate is added to the asthenosphere to promote the partial melting of the Upper mantle and Mantle transition zone [49][50][51].
Moreover, geophysical results imply that the present lithospheric thickness (~80 km) is much less than that of the Paleozoic lithosphere. Geochemistry and P-T studies on mantle peridotite enclaves/xenoliths entrained by Paleozoic kimberlite and basalt have indicated that there was a thick lithosphere (110-230 km) at that time beneath South China [13,15]. However, the study on Mesozoic Ningyuan mantle xenoliths implies a thin lithosphere (<80 km) [52] and that on Cenozoic Xinchang mantle xenoliths intimate the mantle replacement and accretion is a common process in South China since the Mesozoic [14]. These pieces of geological evidence present a process of incessant lithospheric thinning and asthenospheric intrusion.
In summary, for a given tectonic domain mainly affected by subduction or collision, the evolution of the continent plate depends on the fluid (primarily water) content and forms of the subducting or colliding plate and the intrinsic properties of the continental block [32]. The structure of the upper mantle and thickness of the lithosphere in southeast China are affected by different motion types of different plates, fluid addition, and its crust-mantle properties, leading to regional large-scale asthenosphere upwelling, causing the South China lithosphere to be destructed and reformed by mantle-derived hot materials. As a consequence, a thin lithosphere (<80 km) is commonly present beneath southeast China and is consistent with the high heat flow (Q) [17].
Structure of the Crust
MT results thoroughly document the crustal electrical structure, the characteristics of deep-seated faults, and the variation of crustal thickness. As mentioned in previous (Section 5.1), numerous low electric resistance geological body is present in the crust where couples with deep-seated faults. The asthenosphere uplift's top interface corresponds well with the position of the fault zone in the crust. For example, the asthenospheric material can uplift to a shallow position where there are deep-seated faults in the superficial (Figure 8). In other words, deep-seated fault zones play an important role in controlling the upwelling of the asthenosphere. The thickness of the crust is generally around 30 km and tends to thin eastward.
The same geological structure feature was also reported in most other southeast China areas by different geophysics observations or numerical simulations. The MT results in other southeast China regions presented a similar crustal electrical structure, the characteristics of deep-seated faults, and the variation of crustal thickness of that in this study [33]. Based on deep seismic-sounding data, Zhang and Wang inferred that the crust thickness in the Cathaysia Block is around 33 km, and the crustal thickness tends to thin eastward [53]. Deep seismic-sounding data also displays such a thin eastward trend of crustal thickness and the crustal thickness ranging from 30 to 34 km; the result from receiver function analysis with teleseismic wavefield reconstruction suggested that Moho surface depth in southeast China ranges from 25-35 km [54]. Based on the numerical simulation in South China, Zhang et al. proposed the Moho temperature, and the Moho depth is ranged from 500 to 650 • C and from 27 to 32 km, respectively [55]. The joint inversion of receiver functions and surface wave dispersion indicated a crust thickness in southeast China is approximately 30 km [56]. These studies all show a relatively thin and electrical heterogeneity crust in Guangdong Province.
Interpretation of the Geothermal Anomalies in Guangdong Province
Heat flow is considered as one of the direct surface geothermal manifestations of subterranean thermal energy and is a key parameter used to interpret the crust-mantle structure and geodynamics [17,57,58]. Guangdong Province is located in the second-largest geothermal anomaly area in China, where surface heat flow ranges from 61.6 to 97 mW/m 2 with a mean average of 73 mW/m 2 [17]. The values of surface heat flow are greater than the mean heat flow of continental China (60 mW/m 2 , [17]), and the globe means heat flow of continental crust (65 mW/m 2 , [57]). High heat flow has formed many "hot" basins in Guangdong Province ( Figure 2) and developed with numerous natural hot springs (recorded natural hot springs more than 300, Figure 2). However, the surface heat flow for Guangdong Province is limited by the small number of measurement sites (only 24 sites have been reported in the literature up to 2019 in Guangdong Province, Figure 2) and are affected by the local geothermal fluid convection [59]. Therefore, we use the surface heat flow and the natural hot spring, which is a direct indicator to interpret the geothermal anomalies in Guangdong Province.
The high ratio of mean Q mantle /Q crust (~1.33) in southeast China implies that mantle heat causes surface geothermal anomalies in Guangdong Province [17]. As mentioned above, the thin lithosphere, which accompanies by multichannel asthenospheric upwelling, determines a high terrestrial heat flow in Guangdong Province. The upwelling channel of mantle-derived material is connected with the fault system of shallow crust in Guangdong Province. Source waters penetrate the fault system and reach deep into the places where the mantle-derived material is affected. These places have a high temperature, warming the cold water and resulting in fluid convection in the fault system. Fluid convection causes heat upwelling and the development of natural hot springs along with the fault system or adjacent areas (Figure 2).
It should be noted that many natural hot springs in Guangdong Province and its surroundings are distributed along with the faults system and the exposed areas of the Late Mesozoic granite. This is attributed to the high radioactive heat-producing elements (HPE, such as 238 U, 232 Th, and 40 K) of the Late Mesozoic granites in South China. These Late Mesozoic granites in Guangdong Province are widely distributed with an exposed area of 60,000 km 2 , accounting for more than one-third of the area (Figure 2). These granites in Guangdong Province and adjacent areas were formed in a typical continental arc setting and were considered to associate with the advance of the Paleo-Pacific Plate in the Early Middle Jurassic and the retreat of the Paleo-Pacific Plate in the Late Jurassic to Cretaceous [2,5,22]. Importantly, subduction plate-derived materials and the decompression melting caused by stress relaxation promoted the reworking of terrane in South China [7,60]. Two-stage model age of Jurassic and Cretaceous granite Hf isotope ranges between 1.6 and 1.8 Ga, suggesting Late Mesozoic granites in Huizhou area were generated by remelting of Proterozoic crust [61]. This result is consistent with the two-stage model age of detrital zircons Hf isotope in Oujiang River, eastern Cathaysia, Fogang granites, and Nankunshan granites [7,60]. The remelting of differentiated crust material leads to redifferentiation occur. Consequently, the Late Mesozoic granites inevitably have high large ion lithophile elements. Statistics and calculation of the Th, U, and K content of Mesozoic granites in South China show an extremely high heat production with average values of 6.29 µW/m 3 for the Late Mesozoic granite in Guangdong [8,62]. The radioactive heat reservoirs calculated based on the heat production show the Mesozoic granite intrusions contain abundant radioactive heat production ( Figure S3). As shown in Figure S3, compared with the Mesozoic granites in Guangdong Province and its surrounding areas, the Late Mesozoic granites in Nanling Range have the highest heat production (heat production more than 9 µW/m 3 of some granites, radioactivity heat reservoirs more than 10 16 J/a of some granite intrusions) and radioactive heat reservoirs and couple with numerous high-temperature (>80 • C) natural hot spring. This finding reveals Late Mesozoic granite has a marked contribution to the regional geothermal anomaly.
The previous study inferred, based on low gravity anomalies, that there are massive concealed granitic bodies under the exposed Mesozoic granite and adjacent areas [18]. However, our previous study in the Huiyang-Meixian depression between Huizhou and Heyuan City revealed a continuous concealed granite under the depression [3] where Xi et al. [18] deduced there was an absence of concealed granite. Thus, we speculate that the scale of concealed granite under the Guangdong Province is larger than Xi et al. [17] suspected. In other words, due to the extremely high heat production of the Late Mesozoic granite, the Late Mesozoic granite under the Guangdong Province turned into a high-temperature geothermal reservoir. Large quantities of heat released from persistent radioactive decay are one of the most significant geothermal mechanisms in Guangdong Province.
By integrating the results and discussions above, a geothermal model is proposed to visualize the origin and evolution process of geothermic in Guangdong Province (Figure 9). For one, the arc tectonic setting in Guangdong had gradually changed into an intraplate rift setting since Mesozoic [2,22], forming large-scale basins includes Heyuan Basin, Sanshui Basin, Lianping Basin, etc. [3,4,23], and accompanying with upwelling of mantle material. The thin lithosphere superimposed upwelling of mantle-derived material determines the high heat flow background in Guangdong Province. For another, voluminous Late Mesozoic granite generated by remelting of the Neoproterozoic and Paleozoic crust [7,61] contains an extremely high content of heat-producing elements. Large quantities of heat are released from the persistent radioactive decay of these heat-producing elements. Consequently, the special crust-upper mantle structure in Guangdong Province has led to the formation of numerous natural hot springs. These hot springs can be divided into two types ( Figure 9). The first is type A, hot springs distributed near the fault of granite area, the Late Mesozoic granite is the key heat source. Typical examples are the hot springs in the Nanling Range. The second is type B, hot springs distributed along fault zones with mantle-derived material upwelling, the mantle material and the Late Mesozoic granite are the key heat source. Typical examples are the hot springs along the Heyuan fault, where noble gas evidence shows the upwelling of mantle material [63].
Conclusions
In this study, we focused on the crust and upper mantle structure and its geothermal implications in Guangdong Province. The main results and conclusions are as follows:
1.
Three new MT profiles with a total of 440 km long across the major portion of Guangdong Province were acquired to reconstruct crust and upper mantle structure. The TM model of the nonlinear conjugate gradient (NLCG) two-dimensional inversion with τ = 3 was determined by data analysis; 2.
Inversion results show that the low resistance zone on the shallow surface matches the actual location of the fault; there is the presence of multi upwelling channels of asthenosphere mantle, and some channels are connected with shallow crustal fault zone; the thickness of the crust and the lithosphere in Guangdong Province are relatively thin. The crust and upper mantle structure in Guangdong Province is the result of long-term (from Proterozoic to Cenozoic) tectonic magmatism, especially the intense tectonic magmatism caused by multi-plate interaction since the late Mesozoic. Such special crust and upper mantle structure forms high surface heat flow and is one of the key factors for generating anomalies; 3.
Massive Late Mesozoic granites, which contain high radioactive heat-producing elements, are distributed on the surface and underground of Guangdong Province. Large quantities of heat released from persistent radioactive decay of Late Mesozoic granite are another significant geothermal mechanism in Guangdong Province.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/en14082236/s1, Figure S1: Calibration results of V5 system 2000 equipment box, Figure S2: Calibration results of V5 system 2000 equipment probe, Figure S3: Radioactive heat reservoirs and radioactive heat production rate of the late Mesozoic exposed granite and the distribution of the hot springs in Guangdong province and adjacent area. | 7,424.2 | 2021-04-16T00:00:00.000 | [
"Environmental Science",
"Geology"
] |
Structural changes during water-mediated amorphization of semiconducting two-dimensional thiostannates
The amorphization of semiconducting two-dimensional thiostannates was studied using X-ray total scattering and pair distribution function analysis. The local structure and light absorption properties are retained, while the amorphization is associated with disorder of the thiostannate nanosheet stacking.
AEPz-SnS-1: a=b=13.3037(3) Å, c=19.2195(5) Å, R F =0.24. trenH-SnS-1: a=b=13.2457(4) Å, c=19.0860(8) Å, R F =0.10. 1.2 PXRD data of AEPz-SnS-1 and trenH-SnS-1 dispersed in ethanol PXRD patterns of samples dispersed in ethanol for 1 h were collected on a STOE STADI P diffractometer using CuK α1 radiation (1.54056Å) at room temperature. Ground powder samples were distributed on a piece of sticky tape, and data were collected in transmission geometry. 2. Synchrotron total scattering data of water-mediated samples Figure S3: Synchrotron total scattering data of pristine and water-treated all data (left) and low Q (right). Figure S4: Synchrotron total scattering data of pristine and water-treated trenH- all data (left) and low Q (right). (Baur & Khan, 1971, Filsø et al., 2017, compared with the experimental PDF of trenH-SnS-1. The isostructural thiostannate layers in AEPz-SnS-1 and trenH-SnS-1 has P6 3 /mmc symmetry and contains four atoms in the asymmetric unit. Refinement details are shown in Table S1 Table S3: Refinement parameters of trenH-SnS-1 fits using anisotropic atomic displacement parameters. (5) 13.285 (12) 18.97 (7) (2) Total scattering patterns of pristine, non-stirred and stirred samples (in water 24 h) of trenH-SnS-1 (Fig. S10a). As the non-stirred sample contains a larger amount of precursor SnO 2 (different trenH-SnS-1 batches) and thus some peaks related to this phase, we will only compare I(Q) at Q < 1.8 Å -1 , where no SnO 2 peaks are present (Baur & Khan, 1971). Evidently, more peaks remain in the non-stirred sample compared to that of the stirred sample, indicating a higher degree of order remaining in the non-stirred sample. The PDFs of the two samples ( Fig. S10b) show retention of the local [Sn 3 S 7 2-] n structure. In the PDF of the nonstirred sample, peaks related to the SnO 2 impurity is mainly observable in the high-r region (r > 10 Å), where the thiostannate correlations are weak in the water-treated sample.
Correlation sorting script
A correlation-sorting MATLAB script was written as a tool to visualize refined correlations against the experimental PDFs. Output from refinements in PDFgui is used as input for the visualization script.
When using a cif-file in PDFgui as a structural starting model for PDF data analysis, an expansion of the structure from the original space group (here P6 3 /mmc) to P1 is made, such that each atom in the unit cell is given a unique index. There are two thiostannate layers in one unit cell of AEPz-SnS-1 and trenH-SnS-1, and the unique atomic ID (e.g. "SN (#1)") allows identifying in which layer an atom in question is placed. This allows distinguishing between bonds/correlations within the layers ("intralayer correlations") and between different layers ("interlayer correlations").
The bond correlation output from PDFGui has the format: SN (#1) -S (#18) = 2.40104 (0.0975516) Å From the PDFgui expansion it is known that the atoms "SN (#1)" and "S (#18)" are in the same layer, and that the distance between the atoms is 2.40104 Å, with an error of 0.098 Å. By a "string compare", the script recognizes a correlation between Sn(1) and S(18), and that both atoms are within the same layer. In addition to identifying (1) the correlation length and (2) whether the bond is intralayer or interlayer, we (3) apply a weighting to the correlation reflecting the scattering power of the two atoms in the correlation pair. Thereby, a Sn-Sn correlation will be weighted higher than an S-S correlation in the histogram. In the above example, a weighting is added by: Z(Sn) * Z(S) = 50 * 16 = 800. An S-S correlation will use the weighting of 16 2 , where Sn-Sn uses 50 2 . Each weighted correlation length is saved in a list for plotting in a histogram.
A bar in the resulting histograms is a sum of the weighted multiplicity of different correlations within the distance interval defined as one bar. The script identifies and sorts all correlations between 0-14.5 Å, while it (in its current form) is unable to extend beyond 14.5 Å. At larger distances, there is a risk of mixing intraand interlayer correlations, as the atomic ID system will start to repeat itself, as layer n and n+2 are equivalent in the structure (as there are two thiostannate layers in one unit cell).
Debye refinements and simulations
In addition to the data analysis methods presented in the manuscript we performed Debye refinements of the PDF data in the program Diffpy-CMI by using the structure file obtained from the refinements in PDFgui. By doing so, we aimed at obtaining information on the crystallite shape and size. Only one Atomic Displacement Parameter (ADP) of S and Sn was varied (i.e. all Sn and all S atoms, respectively, were treated identically). The crystallite size was altered by introducing a supercell, and the shape and size were changed by varying the length along the a, b and c unit cell axes. The best refinement was evaluated from the lowest R w factor. This method suggested crystallite sizes of 1-4 unit cells. As this result is unphysical (e.g. PXRD of the pristine samples reveal microsized crystallites), the method was not explored further.
In a different approach to describe the data, PDFs were calculated in Diffpy-CMI by varying the crystallite sizes and comparing the resulting PDFs to the experimental data. We calculated a series of PDFs where only the layer size (dimension in the ab-plane) was changed (while the size along c was fixed). This series was complemented by a series of simulated PDFs in which only the number of layers along c was changed. By comparing the two series of patterns, we aimed at identifying peaks that only changed in either case. The calculated PDFs were compared to the experimental data. However, both data series presented changes in the PDF intensities at similar distances, which complicated the peak assignment for both samples.
TEM
TEM images were acquired on a Tecnai Spirit electron microscope equipped with a TWIN lens system operating at 120 kV, and using a Veleta CCD side mounted camera. TEM reveals formation of small particles in addition to larger particles identified by SEM (manuscript Fig. 4).
XPS -spectra and atomic concentrations
Representative XPS spectra are shown in Fig. S15-S18. The relative atomic concentrations were determined using a Shirley background and deconvolution.
In the S 2p spectra of both pristine samples ( Fig. S15c and S17c, respectively) an additional peak is observed besides the sulfide peak from the [Sn 3 S 7 2-] n layers. The additional peak corresponds to oxidized sulfur (possibly sulfate) (Moulder & Chastain, 1992) and disappears by water treatment. The two Sn 3d peaks arise from the spin-orbit coupling (3d 5/2 and 3d 3/2) and are assigned to Sn 4+ , as confirmed by literature (Price et al., 1999, Hyeongsu et al., 2018, He et al., 2013. All N is spectra present multiple components, indicative of multiple nitrogen sites. In Fig. S15e and S16e, the spectra of pristine and a water treated sample of trenH-SnS-1 are seen. Two components have been fitted, at binding energies of 399.8 and 401.7 eV (area ratio of 2.3:1 for the pristine sample) assigned to primary and tertiary amines, respectively, of the tren molecule. In the post water treatment, the primaryto-tertiary amine ratio has decreased to 1.3:1. Conversely, the N peaks (tertiary and primary/secondary amine) from AEPz, in Fig. S17 and S18, almost retains the same area ratio of 1:1.8 for the pristine sample and 1:1.7 for the water treated sample.
In all C spectra three components are found at binding energies of 285.5, 286.4 and 288.3 eV, which we suggest to arise from the C sp 3 , C-N/C-O and carbonyl groups, due to the tren/AEPz molecules and surface contaminants.
The O 1s spectra have not been deconvoluted owing to the high contamination of the sample surface.
In Table S5-8 the areas of the integrated peaks are tabulated along with their respective binding energies. Table S9 displays the averaged composition of the samples. The composition presented in the manuscript is based on the values in Table S9. 1.24 ± 0.14 0.60 ± 0.14 1.17 ± 0.01 0.57 ± 0.09 | 1,960 | 2019-07-05T00:00:00.000 | [
"Chemistry"
] |
Islam and the ASEAN Economic Community (Aec): a Perspective of Islamic Economy in Building a Multicultural Society in Indonesia
Problems faced by society in general now is the emergence of a view that places the material aspect which is free of the dimension value in the dominant position. View of life that is based on the ideology of materialism which then push human behavior into economic principals hedonistic, materialistic and secularistic. Indonesia as the country with the world's largest Islamic community, as well as the role of Muslims in a bid for independence is one proof that Islam teaches morality and responsibility in defending the homeland. Economic role is as the main street permanence in the life of the state. Infact, Islam teaches its followers to be a lot of the individuals who are experts in economic development as a means contributive to realize the vision of building a multicultural Indonesia.
Introduction A.
Civilization is often associated with the material, so it is not uncommon that the mark of a civilization is usually LGHQWLÀHG ZLWK PDJQLÀFHQW EXLOGLQJV RU EXLOGLQJV ZLWK D particular artistic style and pattern. It is part of the product of civilization. Indonesia towards the MEA (ASEAN Economic Community) already in front of the eyes, of course Need the readiness of the competency in the competitive power of SURÀW 7KH H[SHULHQFH RI HFRQRPLF GHYHORSPHQW LQ WKH QHZ order that is run with the market system does not run fairly and evenly, cover the community had to swallow bitter-a bitter reality in which Government is more in favor of the economic elite have big capital, so more ease of support. 1 Although LQLWLDOO\ H[SHFWHG WR IDYRU WR FRPPXQLW\ HFRQRPLF PHGLXP WKH fact that the issue of the economy also poses various problems due to interference with the condition of interest.
7KH PHWKRGRORJ\ XVHG LQ WKLV SDSHU LV D TXDOLWDWLYH PHWKRG XVLQJ GHVFULSWLYH DQDO\VLV DQG OLWHUDWXUH UHYLHZ 7KH data used is the publication of Law No. 10 of 1998, Law No. 3 of 2006 on the Amendment of Law No. 7 of 1989 About the Religious Courts which authorizes the Religious Courts to resolve disputes sharia economy is a political move marvelous law in completing the institutional "law" to realize the economy movement syariah in Indonesia, so that now the real Islamic economic movement gained support from YDULRXV SDUWLHV 7KXV ,VODP LV EHOLHYHG WR EH WKH UHOLJLRQ RI the "comprehensive" provides settlement of problems in the economic order in the face of the impartiality of the public, submitted bids is a concept that was born and is based on WKH VRFLR HFRQRPLF V\VWHP RI ,VODP ZKLFK LV H[SHFWHG WR SURYLGH VROXWLRQV WR H[LVWLQJ SUREOHPV ZLWK SROLFLHV WKDW IDYRU FRPPXQLW\ EHQHÀW DQG HFRQRPLF MXVWLFH 2 7KH FDSLWDOLVW economic system has failed to solve the problems of humanity, social and economic. It is capable of prospering capitalist individual or a particular country materially. But keep in mind the welfare and prosperity are built on the suffering of people or other countries. Capitalists are not able to resolve economic LPEDODQFHV DQG VRFLDO LQHTXDOLW\ RQ WKH FRQWUDU\ LW FUHDWHV DQG SHUSHWXDWHV WKH JDS WR PDLQWDLQ LWV H[LVWHQFH 7KLV LV ZKHUH ,VODP WR FULWLFLVP RI WKH FDSLWDOLVW HFRQRPLF system that is responsible for the change in direction, pattern DQG VWUXFWXUH RI WKH ZRUOG HFRQRP\ WRGD\ 7KHUH VKRXOG EH DQ intensive study to provide an alternative view, the formulation and development strategies, multicultural society with Islamic economic system.
B.
Build Concept of Islamic Economics 1.
Step change in the economy of Muslims, especially in Indonesia should begin with the understanding that economic activity in the Islamic views the demands of life dimension of ZRUVKLS ,W LV OLVWHG LQ 4 6 DO $UDI > @ ZKLFK PHDQV ´Indeed, we have put all our earth and put upfront for you on earth that was the source of livelihood very little you are grateful." Also mentioned in Q.S. DO 0XON > @ 4 6 DQ 1DED· > @ DQG 4 6 DO -XPX·DK > @ ,VODPLF HFRQRPLF DFWLYLWLHV DUH QRW SXUHO\ PDWHULDO EXW DOVR DLPV WR PHHW WKH QHHGV RI RQH·V OLIH LV VLPSOH *UHHG\ IRU wealth and attitude that emphasizes the sheer material, highly FULWLFL]HG $OWKRXJK LQ WKH 6KDUL·DK UHFRJQL]HG WKH ULJKWV RI WKH LQGLYLGXDO QDWXUH RI DQ REMHFW LW GRHV QRW PHDQ DQ\WKLQJ DW LWV top, one can act arbitrarily. Because of economic activity in the Islamic view, in addition to meeting the needs of life itself is still attached to the rights of others.
Islam is a religion that is concerned with the afterlife, and therefore the life of the world really needs to be carried on sharia rules with the goal of happiness of the world and the KHUHDIWHU 7KLV GHPDQG LQFOXGHV DOO DVSHFWV RI FRPPXQLW\ OLIH including the implementation of the Islamic economic system VXFK DV ,QGRQHVLD ZLWK WKH PDMRULW\ RI WKH DGKHUHQWV RI ,VODP ,VODP KDV RXWOLQHG WKH UXOHV RI JHQHUDO SULQFLSOHV DQG VSHFLÀF to humans in seeking grace of God so that the harmony of life is always maintained. In other words, Islam ordered its followers to get gift of God with sincerity.
Islamic economic development has become the center of a long study, because of its scope to collide directly with the public. Basically, the concept of economic development of Islam departed from the human resource development itself, because the Islamic economic development is inseparable IURP EXLOGLQJ D VXPPDU\ RI WKH ÀQDQFLDO V\VWHP JRYHUQDQFH HFRQRPLF MXVWLFH DQG VRFLDO HTXDOLW\ 'HYHORSPHQW LQ ,VODP encapsulates the spectrum of values in the Islamic system, the social system that protects the rights of the Ummah. According WR +DEDNNXN Economic development is an immensely complicated process. ,W LV QRW MXVW PDWWHU RI QDWXUDO FDSLWDO DQG ODERU UHVRXUFHV It is part of the whole social development of a society; it is not merely depend on economic circumstances but on social structure and the attitudes of people to life as a whole. 3 At the same time the overall development of a country cannot be separated from the three key factors. Firstly, awareness about the deterioration in all the factors. Secondly, important awareness about trying to get up and remove setbacks. Third, step and action to remove erase setbacks. Although it is not denied thet the most important element in the economic development of Islam is the human element. Economic development in the perspective of Islam has always optimized the factors of community welfare, morals, property ownership, the value of the vertical and social Islam. Ibrahim argues that the main concern of economic development in the Islamic economic system is the well-being of humans (human welfare). 4 7KH SURFHVV RI HFRQRPLF GHYHORSPHQW LQ ,VODPLF thought should humanely as possible. He should be concerned with education, promoting social integration and conservation of the environment. For him, economic development must be sustained (continuous) and not forgetting the generations to come (future generation).
Economic System of Islam vs Capitalist Economic 2. System
Islamic Economics is the embodiment of the Islamic paradigm. Economic development of Islam, is a form of UHVLVWDQFH DJDLQVW WKH HFRQRPLF FDSLWDOLVW V\VWHP DV LW H[LVWV today. With the aim of formulating and looking for an economic V\VWHP WKDW KDV WKHVH DGYDQWDJHV WR FRYHU GHÀFLHQFLHV ZKLFK are not capitalist economic system in favour of people.
According to Hussin Salamon, there are a number of principles underlying the process of distribution in the HFRQRP\ RI ,VODP ERUQ IURP WKH 4XU·DQ 5 The Prohibition of Riba a.
,Q WKH 4XU·DQ WKH ZRUG ULED XVHG ZLWK YDULRXV PHDQLQJV DV it grows, add, fertilize, develop and become great and numerous. ,Q JHQHUDO WKH ULED PHDQV LQFUHDVHG ERWK TXDOLWDWLYHO\ DV ZHOO DV TXDQWLWDWLYHO\ 6 7KH SURKLELWLRQ RI ULED LV D YHU\ IXQGDPHQWDO problem in the economy. First because of the riba is prohibited E\ WKH 4 6 DU 5XP > @ ´$QG VRPHWKLQJ ULED DGGLWLRQDO that you gave her to grow human treasures, then the Riba does not add it on the side of God. And what you give in the form of tithes who you meant to reach, then God means (which doing so) that those who fold the duplicate (a reward)." An Islamic economic system must be free of interest (riba ULED LV H[WRUWLRQ WR WKH VKRUWQHVV RI KLV OLIH KDUG SUHVVHG by necessity.
Prohibition of b.
at- Tanajusi gabn al-fahisy $V IRU WKH 6KHLNK 7DTL\XGGLQ DQ 1DEKDQL H[SODLQV ghabn is selling/buying something at a price more than comparable or less than a comparable, if any of these LWHPV DUH GRQH LQWHQWLRQDOO\ DV D ZD\ WR FKHDW WR SURÀW it is forbidden in Islam, whether it is performed by the buyer or seller (receiver or contract bidder). However, if in accordance with market demand and supply so he does not become a mistake.
Al-Ghallat 5)
Al-Ghallat is an error or the recipient contract that makes a response or misunderstanding of a contract ZKHUH LI WKH FRPPXQLW\ ZKR NQRZ WKH WKLQJV VKH ZRQ·W do the contract. Ghallat not only prohibited by Islamic MXULVSUXGHQFH KRZHYHU DUH IDEULFDWHG LQ ,VODPLF ÀTK Prohibition of 6) al-maysir (gambling system) Al-maysir is a business activity in which clearly are chancy or speculation that irrational, illogical, obscure stuff WKDW RIIHUHG ERWK TXDQWLWDWLYHO\ DV ZHOO DV TXDOLWDWLYHO\ Business activities containing the activities of maisyir are the business activities carried out in order to get something with a chancy or pitted fate. Islam forbids all forms of crime, the anything does all acts that give ULVH WR UHJDUG IRU VHOI DQG RWKHUV (YHQ LQ WKH 4XU·DQ al-maysir principals with the offender drank alcohol (Q.S. DO 0D·LGDK > @ Economic Capitalism was born of the motives of individual interests, with familiar liberalism with the onset of free markets. Milton H. Spancer wrote in his book contemporary economic "capitalism is a system of economic organisation in the private property rights attributed by (individual) over the means of production, and the distribution of land and its utilization is XVHG HQWLUHO\ IRU WKH EHQHÀW RI PDJQLWXGH LQ YHU\ competitive conditions".
Limitations of Contemporary Theories of Justice d.
7KH TXHVWLRQ RI WKH LPSRUWDQFH RI WKH UROH WKH FRXQWU\ cannot be removed in the discussions of the contemporary HFRQRP\ 7KLV SUREOHP LV UHODWHG WR KRZ WKH 6WDWH WRRN LQ HQVXULQJ PDLQWDLQ DQG UHJXODWH D YDULHW\ RI RZQHUVKLS 7KLV LV one of the decisive issues in a range of contemporary economic systems and becomes an element of difference between one system with another system. Economic Secondly, on the issue of resources, principles of Libertarianism asserts that this world was originally no one has. If so, how this world is to be treated is not an important problem of Justice.
Third WKHUH DUH VHYHUDO WKHRULHV RI MXVWLFH DUH WRR HPSKDVL]HG RQH DVSHFW RI IDFW DQG WKH VKHHU HFRQRPLF MXVWLFH problems resulting in less able to give precise answers to the SUREOHP RI -XVWLFH LWVHOI 3ULQFLSOH %DVHG 5HVRXUFHV VLJQLÀFDQWO\ does not provide a place for social responsibility over those less fortunate, and no subsidies for those less revenues; Principlebased Welfare (Utilitarianism), based on the great happiness for WKH JUHDW QXPEHU VDFULÀFLQJ D VPDOO JURXS RI SHRSOH RQ EHKDOI RI WKH LQWHUHVWV RU ZHOIDUH RI WKH PDMRULW\ DQG SULQFLSOH EDVHG 5HSO\ ZDV DOVR XQDEOH WR SURYLGH DQVZHUV WR TXHVWLRQV when everyone must receive a reply or wages in accordance with the actual effort and contribution to the community, and who is responsible for the condition of those less fortunate in society?
Fourth, in the principle of Radical Egalitarianism, when everyone should have the same level of in need of goods and services, where recognition of the difference of antarorang per person and for those who are economically more productive?
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7KH SXUSRVH RI WKH DSSOLFDWLRQ RI WKH SULQFLSOHV RI IDLUQHVV in economic activity was to prosper at both the individual and FROOHFWLYH OHYHOV 7KH HIIRUW RI PDLQWDLQLQJ D ´VHQVH RI MXVWLFHµ and applying ethical principles in order toward the welfare (sense of happiness) spawned a number of implications in WKH SURFHVV WKH DJHQF\ V\VWHP WKURXJK WKH HVWDEOLVKPHQW RI the values of Justice as the motives acting (motive of action) in economic activity the embodiment of "religious obligations and virtues" in economic activity, the establishment of a "socioeconomic management systemµ WKDW DUH HTXLWDEOH KXPDQH DQG environmentally friendly and the implementation of the *RYHUQPHQW·V UROH role of state) in running the political system and the policy fairly and prosper for all.
7KH IXWXUH RI WKH FRXQWU\ GHSHQGV RQ KRZ WKH HIIRUWV RI the concept of a more integrated economic development which puts the interests of the community, have the competitiveness and the capacity of the ASEAN Economic Community market penetrated. It also depends on the system and the management RI 6WDWH DQG VRFLDO HTXLW\ ÀUP DQG IUHH IURP XQQDWXUDO SROLWLFDO interventions and interests. A system and a culture that is free RI FRUUXSWLRQ DQG QHSRWLVP LQ DGGLWLRQ WR DEXVH SHRSOH·V mandate for a particular party or group interests. | 3,882.2 | 2016-11-03T00:00:00.000 | [
"Economics",
"Political Science"
] |
Reducing Side Effects of Hiding Sensitive Itemsets in Privacy Preserving Data Mining
Data mining is traditionally adopted to retrieve and analyze knowledge from large amounts of data. Private or confidential data may be sanitized or suppressed before it is shared or published in public. Privacy preserving data mining (PPDM) has thus become an important issue in recent years. The most general way of PPDM is to sanitize the database to hide the sensitive information. In this paper, a novel hiding-missing-artificial utility (HMAU) algorithm is proposed to hide sensitive itemsets through transaction deletion. The transaction with the maximal ratio of sensitive to nonsensitive one is thus selected to be entirely deleted. Three side effects of hiding failures, missing itemsets, and artificial itemsets are considered to evaluate whether the transactions are required to be deleted for hiding sensitive itemsets. Three weights are also assigned as the importance to three factors, which can be set according to the requirement of users. Experiments are then conducted to show the performance of the proposed algorithm in execution time, number of deleted transactions, and number of side effects.
Introduction
With the rapid growth of data mining technologies in recent years, useful information can be easily mined to aid mangers or decision-makers for making efficient decisions or strategies. The derived knowledge can be simply classified into association rules [1][2][3][4][5], sequential patterns [6][7][8], classification [9,10], clustering [11,12], and utility mining [13][14][15][16], among others. Among them, association-rule mining is the most commonly used to determine the relationships of purchased items in large datasets.
Traditional data mining techniques analyze database to find potential relations among items. Some applications require protection against the disclosure of private, confidential, or secure data. Privacy preserving data mining (PPDM) [17] was thus proposed to reduce privacy threats by hiding sensitive information while allowing required information to be mined from databases. Privacy information includes some personal or confidential information in business, such as social security numbers, home address, credit card numbers, credit ratings, purchasing behavior, and best-selling commodity. In PPDM, data sanitization is generally used to hide sensitive information with the minimal side effects for keeping the original database as authentic as possible. The intuitive way of data sanitization to hide sensitive information is directly to delete sensitive information from amounts of data. Three side effects of hiding failure, missing cost, and artificial cost are then generated in data sanitization process but most approaches are designed to partially evaluate the side effects. Infrequent itemset is, however, not considered in the evaluation process, thus raising the probability of artificial itemsets caused. Besides, the differences between 2 The Scientific World Journal the minimum support threshold and the frequencies of the itemsets to be hidden are not considered in the above approaches.
In this paper, a hiding-missing-artificial utility (HMAU) algorithm is proposed for evaluating the processed transactions to determine whether they are required to be deleted for hiding sensitive itemsets by considering three dimensions as hiding failure dimension (HFD), missing itemset dimension (MID), and artificial itemset dimension (AID). The weight of each dimension in evaluation process can be adjusted by users. Experimental results showed that the proposed HMAU algorithm has good performance in execution time and the number of deleted transactions. Besides, the proposed algorithm can thus generate minimal side effects of three factors compared to the past algorithm for transaction deletion to hide the sensitive itemsets.
This paper is organized as follows. Some related works are reviewed in Section 2, including the data mining techniques, the privacy preserving data mining, and the evaluated criteria of PPDM. The proposed HMAU algorithm to hide the sensitive itemsets for transaction deletion is stated in Section 3. An illustrated example of the proposed HMAU algorithm is given in Section 4 step by step. Experiments are conducted in Section 5. Conclusion and future works are mentioned Section 6.
Review of Related Works
In this section, privacy preserving data mining (PPDM) techniques and evaluated criteria of PPDM are respectively reviewed.
Privacy Preserving Data Mining
Techniques. Data mining is used to extract useful rules from large amounts of data. Agrawal and Srikant proposed Apriori algorithm to mine association rules in two phases to firstly generate the frequent itemsets and secondly derive the association rules [3]. Han et al. then proposed the Frequent-Pattern-tree (FP-tree) structure for efficiently mining association rules without generation of candidate itemsets [18]. The FP-tree was used to compress a database into a tree structure which stored only large items. It was condensed and complete for finding all the frequent patterns. The construction process was executed tuple by tuple, from the first transaction to the last one. After that, a recursive mining procedure called FP-Growth was executed to derive frequent patterns from the FP-tree.
Through various data mining techniques, information can thus be efficiently discovered. The misuse of these techniques may, however, lead to privacy concerns and security problems. Privacy preserving data mining (PPDM) has thus become a critical issue for hiding private, confidential, or secure information. Most commonly, the original database is sanitized for hiding sensitive information [19][20][21].
In data sanitization, it is intuitive to directly delete sensitive data for hiding sensitive information. Leary found that data mining techniques can pose security and privacy threats [22]. Amiri proposed the aggregate, disaggregate, and hybrid approaches to, respectively, determine whether the transactions or the items are to be deleted for hiding sensitive information [23]. The approaches considered the ratio of sensitive itemsets to nonsensitive frequent itemsets to evaluate the side effects of hiding failures and missing itemsets. Oliveira and Zaïane designed the sliding window algorithm (SWA) [24], in which the victim item with the highest frequency in the sensitive rules related to the current sensitive transaction is selected. Victim items are removed from the sensitive transaction until the disclosure threshold equals 0. Hong et al. proposed a lattice-based algorithm to hide the sensitive information through itemset deletion by a lattice structure to speed up the sanitization process [25]. All the sensitive itemsets are firstly used to build the lattice structure. The sensitive itemsets are then gradually deleted bottom-up form the lowest levels to the highest ones until the frequencies of the sensitive itemsets are lower than the minimum support threshold. Different strategies for hiding sensitive itemsets are still designed in progress to find better results considering of side effects and the dissimilarity of database [21,[26][27][28][29][30].
Evaluation Criteria.
In data sanitization, the primary goal is to hide the sensitive information with minimal influences on databases. Three side effects of hiding failures, missing itemsets, and artificial itemsets are used to evaluate the performance of data sanitization. for data distortion [28,31,32] of sensitive itemsets in PPDM. The relationships between the side effects and mined itemsets of the original database and sanitized one are shown in Figure 1.
In Figure 1, represents the frequent itemsets mined from the original database, represents the frequent itemsets mined from the sanitized database, and represents the sensitive itemsets that should be hidden. The part is concerned as hiding failures that fail to hide the sensitive itemsets. Thus, is the intersection of and (= ∩ ). part is concerned as missing itemsets that mistakenly to delete the nonsensitive frequent rules. Thus, is the difference between , , and (= − − ). part is concerned as artificial itemsets which is unexpectedly generated. Thus, is The Scientific World Journal 3 the difference between and (= − ). In PPDM, it is intuitive to delete transactions with sensitive itemsets in the sanitization process. In this paper, , , and with adjustable weights are considered to evaluate whether the processed transactions are required to be deleted. Besides the above side effects, the number of deleted transactions or items is also a criterion to evaluate the data distortion [32,33].
Proposed Hiding-Missing-Artificial
Utility Algorithm
Definition of Formulas.
Data sanitization is the most common way to protect sensitive knowledge from disclosure in PPDM. To avoid the side effects of hiding failures, missing itemsets, and artificial itemsets, minimal distortion of the databases is thus necessary. In this paper, a hiding-missingartificial utility (HMAU) algorithm is proposed to hide sensitive itemsets through transaction deletion. Three dimensions of hiding failure dimension (HFD), missing itemset dimension (MID), and artificial itemset dimension (AID) are thus concerned to evaluate whether the transactions are required to be deleted for hiding the sensitive itemsets. The transactions with any of the sensitive itemset are first evaluated by the designed algorithm to find the minimal HMAU values among transactions, The transaction with minimal HMAU value will be directly removed from the database. The procedure is thus repeated until all sensitive itemsets are hidden. In order to avoid exposing the already hidden sensitive itemsets again, the minimum count is dynamically updated during the deletion procedure. The value of each dimension is set from 0 to 1 (0 < value ≤ 1). In the proposed formulas, the differences between minimum support threshold and the frequencies of the sensitive itemsets are thus considered to evaluate whether the transactions are required to be deleted instead of only the presence of the itemsets in the transactions.
First, the HFD is used to evaluate the hiding failures of each processed transaction in the sanitization process. When a processed transaction contains a sensitive itemset ℎ , the HFD value of the processed transaction is calculated as where is defined as the percentage of the minimum support threshold, sensitive itemset hs is from the set of sensitive itemsets HS, MAX HS is the maximal count of the sensitive itemsets in the set of sensitive itemsets HS, | | is the number of transactions in the original database , and freq(hs ) is the occurrence frequency of the sensitive itemset hs . Second, the MID is used to evaluate the itemsets of each processed transaction in the sanitization process. When a processed transaction contains a frequent itemset fi , the MID value of the processed transaction is calculated as where an itemset fi is a frequent itemset from the set of large (frequent) itemsets FI, MAX FI is the maximal count of the large itemsets in the set of FI, and freq(fi ) is the occurrence frequency of the large itemset fi . Third, the AID is used to evaluate the artificial itemsets of each processed transaction in the sanitization process. In AID, only the small 1-itemsets are considered in the sanitization process since it is a nontrivial task to keep all infrequent itemsets. When a processed transaction contains a small 1-itemset si , the AID value of the processed transaction is calculated as where a small 1-itemset si is from the set of small 1-itemsets SI 1 , MIN SI 1 is the minimal count of the small 1-itemsets in the set of SI 1 , and freq(si ) is the occurrence frequency of the small 1-itemset si .
In this paper, a risky bound is designed to speed up the execution time of the proposed HMAU algorithm by avoiding the evaluation of all large itemsets and small 1itemsets by considering MID and AID. A parameter is set as the percentage used to find the upper and lower boundaries of the minimum support threshold. Only the large itemsets and infrequent 1-itemsets within the boundaries are used to determine whether the processed transactions are required to be deleted. For the large itemsets, the minimum support threshold is set as the lower boundary, and the upper boundary is set as where | | is the number of transactions in the original database , is the minimum support threshold, is the risky bound, and freq(fi ) is the occurrence frequency of the large itemset fi . For small 1-itemsets, the minimum support threshold is set as the upper boundary, and the lower boundary is set as where freq(si ) is the occurrence frequency of the small 1itemset si . The flowchart of the proposed HMAU algorithm is depicted in Figure 2. Table 1.
Notation. See
Details of the proposed HMAU algorithm are illustrated as follows.
Proposed HMAU Algorithm.
Input. This includes an original database , a minimum support threshold ratio , a risky bound , a set of large (frequent) itemsets FI = {fi 1 , fi 2 , . . . , fi }, a set of small Output. This includes a sanitized database * with no sensitive information.
Step 1. Select the transactions to form a projected database , where each transaction in consists of sensitive itemsets hs within it, where 1 ≤ ≤ .
Step 2. Process each frequent itemset fi in the set of FI to determine whether its frequency satisfies the condition freq(fi ) ≤ ⌈⌈| | × ⌉ × (1 + )⌉, where | | is the number of transactions in the original database and freq(fi ) is the occurrence frequency of the large itemset fi . Put the fi that do not satisfy the condition into the set of FI tmp .
Step 3. Process each small 1-itemset si in the set of SI 1 to determine whether its frequency satisfies the condition freq(si ) ≥ ⌊⌈| | × ⌉ × (1 − )⌋, where freq(si ) is the occurrence frequency of the small 1-itemset si . Put the si that do not satisfy the condition into the set of SI 1 tmp .
Step 4. Calculate the maximal count (MAX HS ) of the sensitive itemsets hs in the set of HS as where freq(hs ) is the occurrence frequency of the sensitive itemset hs in the set of HS.
Step 5. Calculate the HFD of each transaction . Do the following substeps. Step 6. Calculate the maximal count (MAX FI ) of the large itemsets fi in the set of FI as The Scientific World Journal 5 The temporary set of sensitive itemsets outside the boundary FI tmp The temporary set of large itemsets outside the boundary SI The occurrence frequency of the large itemset fi MIN SI 1 The minimal count of the small 1-itemsets in the set of SI 1 freq(si ) The occurrence frequency of the small 1-itemset si The weights for HFD, MID, and AID, in which 0 < ≤ 1 HMAU The utility value used to determine whether the processed transactions should be deleted Step 7. Calculate the MID of each transaction . Do the following substeps.
Substep 7.3. Normalize the MID for all transactions in .
Step 8. Calculate the minimal count (MIN SI 1 ) of the small 1itemsets si in the set of SI 1 as Step 9. Calculate the AID of each transaction . Do the following substeps. Substep 9.1. Calculate the AID of each small 1-itemset within as Substep 9.2. Sum the AIDs of small 1-itemsets si within as 6 The Scientific World Journal Step 10. Calculate the HMAU for HFD, MID, and AID of each transaction as (15) where 1 , 2 , and 3 are the predefined weights by users.
Step 13. Update the occurrence frequencies of all sensitive itemsets in the sets of HS and HS tmp . Put hs into the set of HS tmp if freq(hs ) < minimum count (= ⌈| | × ⌉), and put hs into the set of HS otherwise.
Step 14. Update the occurrence frequencies of all large itemsets in the sets of FI and FI tmp . Put fi into the set of FI tmp if freq(fi ) < minimum count (= ⌈| | × ⌉), and put fi into the set of FI otherwise.
Step 15. Update the occurrence frequencies of all small 1itemsets in the sets of SI 1 and SI 1 tmp . Put si into the set of SI 1 tmp if freq(si ) ≥ minimum count (= ⌈| | × ⌉), and put si into the set of SI 1 otherwise.
Step 16. Repeat Step 2 to Step 15 until the set of HS is empty (|HS| = 0).
An Illustrated Example
In this section, an example is used to illustrate the proposed algorithm step by step. Consider a database with 10 transactions (tuples) and 6 items (denoted as to ) shown in Table 2. Each transaction can be considered a set of purchased items in a trade. The minimum support threshold is initially set at 40%, and the risky bound is set at 10%. A set of sensitive itemsets, HS = { : 6, : 4}, is considered to be hidden by the sanitization process.
Based on an Apriori-like approach [3], the large (frequent) itemsets and small 1-itemsets are mined. The results are, respectively, shown in Tables 3 and 4.
The proposed algorithm then proceeds as follows to sanitize the database for hiding all sensitive itemsets in HS.
Step 1. The transactions in are selected with any of the sensitive itemsets in HS. In this example, the transactions 1, 3, 6, 7, 8, and 10 are selected to form the database shown in Table 5.
Step 4. The maximal count (MAX HS ) among the sensitive itemsets in the set of HS is then calculated. In this example, the maximal count of the sensitive itemsets { } and { } is calculated as MAX HS = max{6, 4} = 6.
Step 5. The HFD of each transaction is calculated to evaluate the side effects of hiding failures of the processed transaction.
The HFDs for all transactions are then normalized as shown in Table 7.
Step 6. The maximal count (MAX FI ) among the large itemsets in the set of FI is then calculated. In this example, the large itemsets are { , , , , }, and the MAX FI is calculated as MAX FI = max{5, 5, 4, 5, 5} (=5).
Step 7. The MID of each transaction is calculated to evaluate the side effects of missing itemsets of the processed transaction. The frequent item { } in transaction 7 is used as an example to illustrate the steps. According to formula (2) Table 8.
The MIDs for all transactions are then normalized as shown in Table 9.
Step 8. The minimal count (MIN SI 1 ) among the small 1itemsets in the set of SI 1 is then calculated. In this example, the small 1-itemset has only { }, and the minimal count of the small 1-itemset is calculated as MIN SI 1 = min{3} =3.
Step 9. The AID of each transaction is calculated to evaluate the side effects of artificial itemsets of the processed transaction. Small 1-itemset { } in transaction 7 is used as an example to illustrate the steps. According to formula (3), the AID of the small 1-itemset { } is calculated as AID 7 ( ) = (3 − 3 + 1)/(4 − 3) = 1; since there is only one itemset in the set of SI 1 , no other calculations are necessary. The AID of transaction 7 is calculated as AID 7 = 1/(1 + 1) = 0.5. The other transactions are processed in the same way. The results are shown in Table 10.
The AIDs for all transactions are then normalized as shown in Table 11.
Step 10. The three dimensions for evaluating the selected transactions are then organized as in Table 12. The weights of hiding failures, missing itemsets, and artificial itemsets are, respectively, set to 0.5, 0.4, and 0.1. Note that these values can be defined by users to decide the importance among the dimensions. In this example, the HMAU of transaction 7 is calculated as HMAU 7 = 0.5 × 0.57 + 0.4 × 1 + 0.1 × 0.5 (= 0.735) . (16) The other transactions are processed in the same way. The results are shown in the last column of Table 12.
Step 11. The selected transactions in Table 12 are then evaluated to find a transaction with the minimal HMAU value.
8
The Scientific World Journal In this example, transaction 8 has the minimal value and is directly removed from Table 12.
Step 13. The occurrence frequencies of all sensitive itemsets in the sets of HS and HS tmp are, respectively, updated. Since the original database with transaction 8 consisted of the sensitive itemsets { , }, which was deleted in Step 11, the counts of { , } in the set of HS are, respectively, updated as { } (= 6 − 1) (= 5) and { } (= 4 − 1) (= 3). In this example, the set of HS tmp is empty, so there is nothing to be done in this step. After the updating process, the itemset { } is put into the set of HS tmp since its count is below the minimum count (3 < 4).
Step 14. The occurrence frequencies of all large itemsets in the sets of FI and FI tmp are, respectively, updated. . After the updating process, the itemset { } is put into the set of FI tmp since its count is below the minimum count (3 < 4).
Step 15. The occurrence frequencies of all small 1-itemsets in the sets of SI 1 and SI 1 tmp are, respectively, updated. Since the original database with transaction 8 did not consist of any of the small 1-itemsets in SI 1 and SI 1 tmp , nothing is done in this step.
Step 16. In this example, the sensitive itemset { } is already hidden, but the occurrence frequency of sensitive itemset { } is larger than the minimum count. Steps 2 to 15 are repeated until the set of sensitive itemsets HS is empty (|HS| = 0). After all Steps are processed, the sanitized database is obtained as shown in Table 13.
Comparing the original database and the sanitized one, transactions 1, 3, 6, and 8 are removed from the original database, and the minimum count is updated as 3. The updated frequent itemsets of the sanitized database are shown in Table 14.
Comparing the large itemsets in Table 3, the sensitive itemsets { } and { } are hidden and no artificial itemset is generated. Three itemsets, { , , }, are, however, missing itemsets of the sanitized database. In this example, the side effects of hiding failures, missing itemsets, and artificial itemsets are 0, 3, and 0, respectively.
Experimental Results
Experiments are conducted to show the performance of the proposed HMAU algorithm compared to that of the aggregate algorithm [23] for hiding sensitive itemsets through transaction deletion. The experiments were coded in C++ and performed on a personal computer with an Intel Core i7-2600 processor at 3.40 GHz and 4 GB of RAM running 64bit Microsoft Windows 7. The real database BMS-WebView-1 [34] and a synthetic database (T7I7N200D20K) [35] from IBM data generator in which symbolizes the average length of the transactions, symbolizes the average maximum size The Scientific World Journal 9 of frequent itemsets, symbolizes the number of differential items, and symbolizes the size of database were used in the experiments. The details of the two databases are shown in Table 15.
For the BMS-WebView-1 database, the minimum support thresholds were, respectively, set at 1% and 2% to evaluate the performance of the proposed approach, and the percentages of sensitive itemsets were sequentially set from 5% to 25% of the number of frequent itemsets in 5% increments. In the experiments, the weights of HFD, MID, and AID in the proposed algorithm were, respectively, set at 0.5, 0.4, and 0.1.
For the T7I7N200D20K database, the minimum support thresholds were, respectively, set at 1.5% and 3%, and the percentages of sensitive itemsets were sequentially set at 2.5% to 12.5% of the number of frequent itemsets in 2.5% increments. In the experiments, the weights of HFD, MID, and AID in the proposed algorithm were, respectively, set at 0.5, 0.4, and 0.1. Figure 3 shows the execution time of two algorithms in BMS-Web-View-1 database. Different minimum support thresholds of two algorithms are then compared in various sensitivity percentages of the frequent itemsets.
Comparisons of Execution Time.
The execution time of the proposed HMAU algorithm is faster than those of the aggregate algorithm whether the minimum support threshold is set at 1% or 2%. Experiment is then conducted in T7I7N200D20K database and the results are shown in Figure 4.
From Figures 3 and 4, it is obvious to see that the proposed HMAU algorithm is faster than those of the aggregate method in two different databases.
Comparisons of Number of Deleted Transactions.
Experiments were also conducted to evaluate the number of deleted transactions of the proposed algorithm in two different databases. For the BMS-WebView-1 database, the results are shown in Figure 5.
From Figure 5, it is obvious to see that the proposed HMAU algorithm deletes fewer transactions than the aggregate algorithm whether the minimum support threshold is set at 1% or 2% in BMS-WebView-1 database, thus achieving lower data distortion. For the T7I7N200D20K database, the results are shown in Figure 6.
From Figure 6, it is obvious to see that when the sensitive itemsets were set at 10% of the frequent itemsets with 1.5% minimum support threshold in T7I7N200D20K database, the proposed HMAU algorithm produced more transactions to be deleted for hiding sensitive itemsets. Since the proposed HMAU algorithm considers the three dimensions together, the selected transactions for deletion may consist of fewer large transactions rather than many sensitive itemsets.
Comparisons of Side Effects.
Three side effects are then compared to show the performance of the proposed algorithm in two different databases. The side effects of hiding failures, missing itemsets, and artificial itemsets are, respectively, symbolized as , , and . In Table 16, it can be seen that when the minimum support threshold was set at 1%, the proposed HMAU algorithm produces no side effects whereas the aggregate algorithm produces some artificial itemsets since the criteria of artificial itemsets are not considered in aggregate algorithm. Both the two algorithms produce no side effects when the minimum support threshold was set at 2%. The results to evaluate the side effects of the proposed HMAU algorithm in T7I7N200D20K database are shown in Table 17.
From Table 17, it is obvious to see that when the minimum support threshold was set at 1.5%, the proposed HMAU algorithm produces fewer artificial itemsets and missing itemsets than the aggregate algorithm for various sensitivity percentages of the frequent itemsets. The proposed HMAU algorithm produces no side effects at 3% minimum support threshold whereas the aggregate algorithm produces some artificial itemsets.
To summarize the above results for BMS-WebView-1 and T7I7N200D20K databases, the proposed HMAU algorithm outperforms the aggregate algorithm in terms of the execution time, the number of deleted transactions, and the number of side effects.
Conclusion and Future Works
In this paper, the HMAU algorithm is proposed for hiding sensitive itemsets in data sanitization process by reducing the side effects through transaction deletion. The formulas of three dimensions as HFD, MID, and AID are defined to In the future, the sensitive itemsets to be hidden can be extended to the sensitive association rules to be hidden. More considerations are necessary to be concerned to decrease not only the supports of sensitive itemsets but also the confidence of sensitive association rules. Other distortion approaches such as the noise addition and data modification are also the important issues to hide the sensitive information in PPDM. | 6,328 | 2014-04-10T00:00:00.000 | [
"Computer Science"
] |
A progression of pre-service teachers towards deep curricular knowledge (the Pieces model in Open Source Tutorials)
, we aim to equip our pre-service teachers (PSTs) with “curricular knowledge” about instructional materials, knowledge about the “theory” underlying the curriculum and the reasons behind particular choices such as conceptual flow, use of individual vs. group work, and so on. This study presents two case studies grounded in of our attempts to teach nuanced curricular knowledge about differences between two fairly similar sets of curricular modules. Our analysis centers on two Masters of Science (MS) students who had various experiences involving Open Source Tutorials (OSTs), guided worksheets developed by the University of Maryland. A theoretically nuanced (and hence deep) component of curricular knowledge regarding OSTs is that they are based upon the “Knowledge in Pieces” (in contrast to a “Misconceptions” or unspecified) model of student ideas. The Pieces model maintains that student ideas are not always robustly intact and inherently incorrect cognitive structures, but rather, that student ideas are often temporary coherences of thought assembled from finer-grained pieces of knowledge that can productively be drawn upon and refined in instruction. In our courses, PSTs read research literature about OSTs, conduct mock lessons using existing OSTs, improve existing OSTs, design and teach their own OSTs to real students, and reflect upon the process to further improve the curriculum. Our analysis focuses upon case studies of Brock and Saki, MS students at our institutions. In addition to one-on-one interviews with these PSTs, we will draw upon data from in-class observations and written coursework to discuss how PSTs progressed in their understanding of nuanced curricular knowledge about OSTs and
I. INTRODUCTION
"Curricular knowledge" [1], including "knowledge of the purpose of particular questions" within research-based curricular materials [2], is a valuable component of preservice teacher (PST) education. Curricular knowledge helps teachers implement the materials in coherent ways [3] and make modifications (if needed) consistent with the underlying approach, rather than following the materials too tightly, failing to deviate in response to unexpected student ideas [4]. Although curricular knowledge is an attainable PST instructional target, it is often not a trivial one [2,5].
In our experience, PSTs come to terms fairly easily with some curricular knowledge, such as why research-based curriculum carves out time for students to articulate and discuss their own ideas. Other curricular knowledge, by contrast, is harder to learn deeply. In this paper, we present an example of such a form of "deep" curricular knowledge and what scaffolding we provided to our PSTs to help them acquire this knowledge. Our aim was to have PSTs come to understand the "Pieces model" of student ideas and how it undergirds Open Source Tutorials.
I.1 Overview of the Pieces model and Open Source Tutorials
Historically, much of PER has focused on diagnosing and "treating" incorrect ideas and ways of thinking that interfere with student learning (e.g., [6]). Researchers have often considered (at least implicitly) these ideas to be stable and almost always considered these ideas to be hindrances to attaining the target content knowledge (e.g., [7][8][9]); consequently, it has often been argued, instruction should draw these ideas out so that they can be scrutinized and then rejected in favor of the target material (e.g., [10,11]). In 2007, Scherr, building on the work of Hammer [12], contrasted this "Misconceptions model" of student ideas with the "Pieces model", which explicitly considers student ideas as having the potential to be fluid, with knowledge pieces assembling and disassembling in response to contextual shifts [13]. This distinction is relevant for teachers because it informs instruction (e.g., [14]). Whereas the Misconceptions model typically calls for a confrontation strategy like "elicit, confront, resolve" (ECR) [10,11], the Pieces model calls for instruction where teachers guide students in rearranging the knowledge pieces that they already have-"refining" their intuitive ideas. Many Open Source Tutorials (OSTs) [15] explicitly rely on a "Pieces"based, intuition-refinement approach. By contrast, many Tutorials in Introductory Physics (TIPs) [16] utilize an ECR approach consistent with the Misconceptions model.
At the University of Vienna (UV) and Tokyo Gakugei University (TGU), we have been instructing our PSTs in the use of OSTs and how they are similar to and different from TIPs. Recently, we have begun collecting data to investigate the degree to which our PSTs understand and appreciate the difference between the Misconceptions and Pieces models. We conceptualize OSTs' underlying assumption of student ideas being Pieces-like as a type of curricular knowledge [2]. Since the Pieces model and accompanying strategies (like refining intuitions) differ in subtle ways from Misconceptions-based materials employing ECR, we expect this curricular knowledge to be relatively challenging to inculcate in PSTs, and our research questions for this paper are "to what extent is the Pieces model of student ideas an attainable instructional target for pre-service teachers? In what ways can teacher educators support pre-service teachers in coming to understand the model?"
II. STUDY DESIGN AND METHODOLOGY
Our qualitative study draws upon video and audio recordings from in-class discussions in courses for PSTs and from one-on-one interviews with PSTs. Our focal participants come from two cohorts of PSTs, one instructed by the first author at UV and the other instructed by the second author at TGU. At TGU, the second author teaches the large-enrollment course "Physics Exercises" for undergraduate PSTs. OSTs serve as the core to "Physics Exercises" and TA's who facilitate the OSTs are often upper-classmen PSTs or PSTs in the MS program. TAs meet weekly with the second author to prepare for the next week's OST, and they meet again after the OST to reflect on the experience. We present below a case study of Saki (all names are pseudonyms), a MS student who took the "Physics Exercises" course as an undergraduate PST in 2018 and then went on to become a TA for the next generation of PSTs in 2021. For her MS thesis advised by the second author, Saki made significant modifications to the Pressure OST and investigated the effects of these modifications. She was interviewed by the second author in May 2022. She was presented with a gift certificate worth $10 to the bookstore as compensation.
In the winter semester of 2021-2022, the first author taught a low-enrollment OSTs-based seminar for PSTs in a MS program at UV. Like at TGU, PSTs at UV experienced a different Tutorial every week, but it was generally done in a mock lesson format. That is, one PST took on the role of "teacher" for the lesson while the other 4 PSTs were "students". Feedback was provided to the "teacher" after the Tutorial, and the "teacher" then wrote a reflection about the mock lesson. In this seminar, PSTs were also assigned as homework reading about the theory underlying OSTs (including the Pieces model), and the seminar culminated in each PST creating his or her own OST and arguing how it is consistent with the "spirit" of OSTs in that it "expects and utilizes the fact that student reasoning is often fluid (in accordance with the "Pieces model)". Each PST taught their own OST in a high school, usually with about 20 students to instruct alone, wrote a reflection, and improved the OST.
Three of these PSTs (Brock, Arnold, and Sean) were interviewed by the first author in February and March 2022 (after the seminar had concluded and final grades had been assigned). As compensation, the first author donated money to treenation.org for trees that the PSTs had chosen to be planted in their honor. Brock, who serves as our second case study below, had been one of 16 PSTs to take an undergraduate version of the OSTs seminar (which did not include the creation of an OST) from the first author in the summer semester of 2018. In between the two seminars, Brock had experienced teaching with OSTs in his own classroom during a year-long internship. All interviews were video and audio recorded with interviewee consent. At UV, each class was also audio and video recorded, and PSTs were assured that the first author would not share this data with the other authors without consent, and that consent forms would only be checked after final grades had been assigned. Interview questions for Brock were based in part on things Brock had said and done in class, in order to further draw out his thinking about the Pieces model and OSTs.
After the course ended, the first author made an outline of the interview with Brock, highlighting and transcribing points that related to Brock's understanding of and views about the Pieces model. Consistent with the constant comparative method (e.g., [17]), the first author drew upon the transcribed text as well as Brock's written coursework and in-class utterances to draft an account that was shared with the other two authors. Claims about Brock were scrutinized by looking for consistency across the interview as a whole, and modifications were made until agreement between the three authors was reached. A similar process was carried out in creating Saki's case study.
III. PSTS CAN LEARN THE PIECES MODEL
At both the undergraduate and MS seminars at UV, the Pieces model is taught to PSTs by contrasting OSTs with TIPs. Since Brock had completed the undergraduate seminar, the first author asked Brock on the first day of the MS seminar what, if anything, he remembered that he could tell his classmates about OSTs. He recalled that they are worksheets originating from research on student ideas that are completed in groups. Brock did not recall any contrast between OSTs and TIPs, nor did he mention ECR or refining intuitions. From this and other evidence, we infer that Brock had learned curricular knowledge about tutorials in general, such as the use of small-group work to elicit student ideas, but had not learned (or at least, not retained) knowledge about "Pieces" and the nuanced characteristics of OSTs.
At the end of the semester, however, Brock demonstrated more nuanced understandings. When asked how he would explain the differences between TIPs and OSTs, Brock responded "TIPs use the elicit, confront, resolve method explicitly, and OSTs don't use that, and it's more about epistemology as well, that's what I would say are the key elements, the key differences." Before the interviewer explicitly mentioned it, Brock brought up the Pieces model in the interview: I think these intuitive ideas… will remain with you almost forever, because they are intuitive… it kind of relates to the Pieces model… more about restructuring them maybe, or adding new pieces to that piece, to previous information or previous intuitions.
Furthermore, Brock demonstrated in the interview that he saw the value in thinking about student ideas as being something that can be "worked with" instead of "removed": I think it is not worth the time, even if it is, even if [emphasis his] it is possible, to remove all these ideas, but it is better to add additional ideas and to teach students how to, how to work with their intuitions and new physics … We see these statements as indicating understanding of the Pieces model, not merely because Brock is able to produce the technical jargon ("Pieces model") on his own, but because he is able to describe the model without support from the interviewer. He discusses "restructuring" instead of "removing", a key characteristic of the Pieces model. Brock could articulate that eliciting and confronting misconceptions is not always the best thing to do.
By the end of the seminar, Brock had succeeded in creating his own OST that the first author judged to be consistent with the Pieces model. Figure 1 shows a translation of an explicitly-labeled "intuition refinement" part of Brock's OST on Heat and Temperature.
FIG. 1. An excerpt from Brock's OST that he explained came from the "recipe" of refining intuitions.
The difference between the two models is something that Brock came to understand in the MS seminar. When asked "Is there anything specific that you can remember that like, sank in more, or that you understood better the second time around that you had not really picked up the first time?", Brock quickly responded with "I think the difference between OSTs and TIPs. That wasn't... or it wasn't so clear to me in the first round, yeah. Definitely." Like Brock, Saki also advanced her understanding of the Pieces model from the first to second "round". In the interview conducted by the second author, Saki said that she now finds the approach of refining intuitions to be "really interesting" but that when she was an undergraduate PST learning from OSTs, that she had "probably not really understood it at all." Now, however, when prompted by the interviewer, Saki was able to identify the process of refining intuitions in the Pressure OST she was modifying, even though it is not explicitly labeled as such in the OST.
Like, a lot of students catch this rough idea that the magnitude of water pressure has something to do with height or displacement from the water surface… There is where that ambiguity comes in, but when you go through experiments and solve problems, you will find that it is not the amount [of water on top] … or distance to the ceiling, but the height from the water surface … that is close to refining intuitions.
Nowhere in the interview did Saki deliver an explicit contrast between the Pieces and Misconceptions models as Brock did, nor did she refer to the ECR process. Nevertheless, in the above quote, Saki discussed how the Pressure OST uses experiments and "problem solving" to make less "ambiguous" the idea that students already have about pressure. The fact that she was able to specify how the OST refines student ideas like this demonstrates understanding of an element of the Pieces model.
Our case study includes only two PSTs, so we aim only to generate hypotheses about whether the Pieces model is a feasible instructional target. Nevertheless, evidence suggests that Brock and Saki were not unique. The other four PSTs in the MS seminar, like Brock, all succeeded in creating a "Pieces"-like OST.
In their interviews, both Sean and Arnold (two of Brock's classmates) demonstrated an understanding that OSTs see student ideas as containing valuable knowledge pieces that can productively be drawn upon in learning 1 . As such, in answer to our first research question, "to what extent is the Pieces model of student ideas an attainable instructional target for pre-service teachers?", we have presented an existence proof that it is indeed attainable, but that it requires more investment than the relatively superficial curricular knowledge about OSTs being group-based interactive engagement materials. While this existence proof is an important first step, future work should investigate what percentage of PSTs deepen their curricular knowledge if they receive scaffolding like Brock and Saki did.
IV. FACTORS THAT MAY HAVE CONTRIBUTED TO PSTS LEARNING THE PIECES MODEL
As discussed above, at the start of the MS seminar, Brock did not demonstrate an understanding that OSTs are designed upon the assumption that student reasoning can shift fluidly from moment to moment. This indicates that merely being exposed to OSTs, reading the teacher's guide, and teaching with the OSTs (which is what Brock did in the first seminar and what most TA's go through when they receive TA training) might not be sufficient to comprehend the more subtle aspects of curricular knowledge associated with OSTs. What then, led to the growth that we observed in Brock in the MS seminar? Was it simply a second semester of exposure? Indeed, he credited that as giving him "a huge advantage compared to [his] peers" in the seminar.
… I knew most of the Tutorials … so I could look into them in more detail, and I did know some of the concepts before, so that maybe helped me to deepen my knowledge … Immediately prior to this point in the interview, Brock had been talking about the role of models in learning physics and about how people often misapply those models in trying to make sense of their world. After saying the above quote, Brock would next say that he came to understand the difference between OSTs and TIPs in the MS seminar (see transcript in previous section). Based on this context, we think that his saying "I did know some of the concepts before" is not about his understanding of physics content knowledge, like Newton's laws. Rather, we interpret his statement to be referring to his previous well-developed understanding of tutorials in general, including both OSTs and TIPs, as engaging small groups of students in guided inquiry in order to help them reconsider their ideas. We find Brock's explanation very plausible: it is likely that Brock's prior understanding set him up to focus more narrowly on nuances about what "reconsider their ideas" can entail. In addition, Brock gave much credit to the process of creating his own OST. When asked at the beginning of the interview if he felt the seminar would help his future teaching, he spontaneously brought up the creation of his own OST: …I was thinking on my way here, that… especially, the part of creating materials by yourself I think is really really beneficial for your future practice as a teacher… I think it is kind of the key element of the whole course… kind of the difficult part is thinking about, "ooh, … how do I deal with misconceptions 2 in general? Is that such a strong relevant misconception that I have to confront it using 'confront, resolve'?" The first author then asked Brock if, even were he never to use the OST he created or teach that specific topic again, he still felt that "it would have been beneficial to have gone through the process of creating this thing." He responded with "yeah, definitely" and continued with the following explanation, including his recollection of his own OST (see Figure 1): … it is kind of a recipe… you need to find out whether that recipe works for that different topic, so, like with the boxes model [see Fig. 1], so you are refining an intuition, I used two boxes as well… it is still useful if you know about the methods.
In contrast to just seeing the methods used in other OSTs, Brock emphatically said that "doing it yourself is on a different conceptual level", and he ascribed to it the greater depth that is generally obtained when actually doing something yourself instead of just being shown how to do it.
Taken together with the preceding transcript, we see Brock as saying that creating one's own curriculum in a given style builds expertise in understanding the "recipe" of that style.
As discussed above, Brock came to understand the difference between OSTs and TIPs in this MS seminar. In particular, in the interview, Brock could articulate the Pieces-based approach of OSTs, and he valued this approach. The process of creating an OST involved receiving feedback multiple times, both from the first author and from Brock's classmates throughout the creation process, and hence occupied a significant portion of the seminar. Brock described making his own OST as being the "key element" of the course, and it is plausible that this helped him come to better understand the Pieces model as he had to answer carefully "how do I deal with [student ideas] in general?" Unlike Brock, Saki did not create an OST from scratch. Instead, she modified an existing OST. Saki credited not her creative process of modifying the Pressure OST, but rather, her teaching of existing OSTs for helping her come to value the OST-style of instruction. In the interview, she said that she would have more than half of her class time be groupbased, and she showed her support for the type of discussion that is emphasized in OSTs: A lot of students ask me if something is correct or not, but… [it should not be] "the teacher says it is correct so it is correct", but rather, I think it is more important whether that will convince someone or not. … I want to recognize "ah, there is also that way of thinking about it, I see!", or, yeah, with incorrect ways of thinking, I want to observe where it is that a contradiction is taking place… When asked if Saki always felt that way, she responded that it was a change that had taken place as a result of being a TA for OSTs. She specified that while doing her best to follow the fast thinking of the students, she would come to wonder how the students were coming up with the ideas that they voiced, and she came to recognize the importance of answering that question. We acknowledge, though, that here and elsewhere in the data, Saki didn't articulate a Pieces perspective as fully as Brock did. We revisit this point below.
V. CONCLUSION
We have investigated progress that two MS students made in coming to understand the Piece model. To be clear, we do not conceptualize understanding of the Pieces model in a binary (understand or not) sense. Rather, the model has many facets about which learners can understand to varying degree. Saki demonstrated awareness of the importance of having students make sense of the material in their own terms but did not explicitly connect that awareness to the Pieces model. Brock, on the other hand, connected specific instructional strategies like intuition refinement diagrams to the underlying Pieces model.
As an undergraduate, Brock took a seminar on OSTs where he read and heard that OSTs are premised on the assumptions that student ideas are comprised of smaller knowledge pieces that can fluidly rearrange in response to contextual cues. Despite this, and despite having taught with OSTs for a year after the seminar, Brock did not articulate this characteristic of OSTs at the start of the MS seminar. This suggests that the Pieces model and its relationship to OSTs is nuanced curricular knowledge, challenging for PSTs to attain. Nevertheless, we have presented an existence proof that PSTs can reach a deeper understanding of the Pieces model. At the start of the MS seminar, Brock already understood why small-group discussion of conceptual issues is helpful, indicating existing curricular knowledge about active-learning Tutorials. Through his experiences in the seminar, Brock was able to build upon this existing curricular knowledge to develop the more nuanced curricular knowledge demonstrated later in the semester.
By focusing on case studies of Brock and Saki, we have also addressed our second research question: "In what ways can teacher educators support pre-service teachers in coming to understand the model?" Specifically, Brock credited his learning about the difference between OSTs and TIPs (and, by extension, about the Pieces model) particularly to 1) having taken the course as an undergraduate, and 2) creating his own OST. From these two points, we hypothesize that educators wishing to instruct PSTs in the Pieces model should expect to allocate substantial class time to do so, and that devoting time to the process of creating an OST may be time well spent. Saki's experiences suggest that being an instructor of OSTs plays a key role, too. Scaffolded by weekly TA training, Saki came to recognize the importance of listening to student ideas to find "where it is that a contradiction is taking place" in student reasoning so that students can become personally convinced of the material instead of just memorizing it because "the teacher says it is correct." Although Saki, unlike Brock, did not explicitly contrast the Pieces and Misconceptions models or discuss ECR, she was able to recognize-on her own-how the Pressure OST refines student ideas about "depth" and pressure, as discussed in Section III. We expect that a PST who is thinking of student ideas only in terms of Misconceptions would have great difficulty doing this, and we find it plausible that listening carefully to students discussing their ideas about pressure contributed to Saki's awareness of this point.
In this paper, we have chosen to focus on the features of the support we provided that the PSTs identified as salient. Other factors likely played a role as well, and our data greatly underdetermine the fine-grained learning pathways. Still, our case studies suggest that understanding about the importance of eliciting and attending to student thinking is a helpful knowledge base upon which to build more nuanced curricular knowledge about (in our cases) the Pieces model and its curricular implications. | 5,691 | 2022-09-22T00:00:00.000 | [
"Education",
"Computer Science"
] |
The CoREST complex regulates multiple histone modifications temporal-specifically in clock neurons
Epigenetic regulation is important for circadian rhythm. In previous studies, multiple histone modifications were found at the Period (Per) locus. However, most of these studies were not conducted in clock neurons. In our screen, we found that a CoREST mutation resulted in defects in circadian rhythm by affecting Per transcription. Based on previous studies, we hypothesized that CoREST regulates circadian rhythm by regulating multiple histone modifiers at the Per locus. Genetic and physical interaction experiments supported these regulatory relationships. Moreover, through tissue-specific chromatin immunoprecipitation assays in clock neurons, we found that the CoREST mutation led to time-dependent changes in corresponding histone modifications at the Per locus. Finally, we proposed a model indicating the role of the CoREST complex in the regulation of circadian rhythm. This study revealed the dynamic changes of histone modifications at the Per locus specifically in clock neurons. Importantly, it provides insights into the role of epigenetic factors in the regulation of dynamic gene expression changes in circadian rhythm.
Introduction
Studies in recent decades have revealed the core molecular mechanism that controls biological rhythms.The first molecular clock gene, Period (Per), was identified through a genetic screen of mutants generated in Drosophila melanogaster [1].In Drosophila clock neurons, the protein complexes composed of CLOCK/CYCLE (CLK)/(CYC) and PERIOD/TIMELESS (PER)/(TIM) form a negative feedback loop [2].Studying the regulatory mechanisms of the core clock genes within this regulatory loop is of great significance for improving our understanding of the molecular mechanisms of the biological clock.
Histone modification plays an important role in the regulation of circadian rhythm.H3K9me3 and H3K27me3 have been found to modify mammalian clock genes and their downstream genes [3][4][5].Moreover, histone acetylation and ubiquitination are also important in circadian rhythm regulation [6][7][8][9][10].However, most studies investigating the interplay between histone methylation/acetylation and clock regulation have been conducted in liver tissue or mammalian cell lines.The roles of histone methylation/acetylation in the core clock regulatory circuit of clock neurons are still unclear.
The analysis of the molecular features of clock neurons shows that they possess a unique pool of expressed genes.In a previous study, clock neuronspecific expressed genes were analysed using microarray technology [11].However, the epigenetic characteristics of clock neurons remain unknown.Recently, the development of the mini-INTACT (isolation of nuclei tagged in specific cell type) method has provided a rapid way to isolate neurons for
Drosophila activity monitor-based method for circadian rhythm measurement
For all activity measurements, flies were kept in a 12 h light/12 h dark (12:12 LD) cycle at 25°C.Flies (3−5 days old) were individually loaded into detection tubes (length, 65 mm; inner diameter, 5 mm) containing standard cornmeal fly food at one end and a cotton stopper placed at the other end.The circadian rhythm was measured using the DAM (Drosophila activity monitor) System (Trikinetics, MA), which counted the infrared beam crossings of individual flies in each tube every 1 min.All circadian rhythm tests were carried out on male flies unless otherwise specified.Flies were entrained in the detection tube at 25°C for 72−96 h in a 12 h light/12 h dark cycle.Subsequently, data were collected in dark conditions for at least 5 days using the DAM System.The analyses of circadian rhythm were carried out using faasX software (obtained from the website https://trikinetics.com) and MATLAB (MathWorks, Natick, MA).
Circadian behaviour assessment of temperature-mediated phase shift
The temperature cycle (TC) experiment was conducted following the method described by Gentile et al. [23].Initially, flies were synchronized to three light/dark (LD) cycles at 25°C.Subsequently, the temperature was reduced to 16°C for 6 h, followed by 12 h at 25°C and 12 h at 16°C TC for 6 days.The initial TC was then modified by delaying the temperature rise by 6 h, and flies were tested to resynchronize with the shifted TC for another 6 days.The entrainment index (EI) was calculated as the ratio of total activities occurring during a 6 h window to the activities occurring during the entire warm phase [23].A value close to 1 indicates that most of the activity occurred within the specified window, indicating entrainment.Based on the inspection of the average activity profiles of the control flies, a 6 h window for the main temperature-synchronized activity was defined as ZT15-ZT20.5 (displayed as a red dotted line in figure 1a,b; ZT, zeitgeber time) [23].
Quantitative real-time PCR
Total RNA was extracted from 30 heads using TRIzol Reagent (TIANGEN, no.DP4−02).Reverse transcription and real-time PCR (RT-PCR) were performed using the PrimeScriptTM RT reagent Kit with gDNA Eraser (Perfect Real Time; TakaRa, no.RR047A) and SuperReal PreMix Plus (SYBR Green; TIANGEN, no.FP205−02) following the manufacturer's instructions.All experiments were performed using the StepOne Real-Time PCR system (Applied Biosystem, Foster, CA).Quantification was 2 royalsocietypublishing.org/journal/rsob Open Biol.14: 230355 performed using the ΔΔCT method.Unpaired two-tailed Student's t-test (Prism GraphPad) was used to compare the differences between genotypes.All primers used are listed in electronic supplementary material, table S1.All quantitative RT-PCR analyses were performed with three biological replicates.
Cell culture and transient transfection
S2 cells were cultured in serum-free insect cell culture medium (HyClone, no.SH30278.02) at 25°C.Transient transfection was performed using X-tremeGENE HP DNA Transfection Reagent (Roche, no.06366236001), following the manufacturer's protocol.
Plasmid constructions 2.7.1. Cloning of pAC-CN fusion plasmids
The N-terminal part of mCerulean (CN) was amplified via PCR from the pGWAAV-CMV-PSD95-mCerulean using the forward primer EcoRI-CN F and reverse primer NotI-CN R [24].Plasmid pAC-mGFP was digested with EcoRI-NotI, and the CN fragment was inserted, resulting in pAC-CN.The CoREST-RF (CoREST long form) was amplified via PCR from the cDNA of fly heads using the forward primer NotI-CN-CoREST-RF F and the reverse primer HindIII-CN-CoREST-RF R. Plasmid pAC-CN was digested with NotI-HindIII, and the CoREST-RF fragment was inserted, resulting in pAC-CN-CoREST-RF.LSD1, HDAC1 and KDM4A were also cloned into the pAC-CN vector using the same procedure, respectively.All primers used are listed in electronic supplementary material, table S1.
Cloning of pAC-CC fusion plasmids
The C-terminal portion of mCerulean (CC) was amplified via PCR from the pGWAAV-CMV-PSD95-mCerulean using the forward primer NotI-CC F and reverse primer HindIII-CC R [24].Plasmid pAC-mGFP was digested with NotI-HindIII, and the CC fragment was inserted, resulting in pAC-CC.The CoREST-RF was amplified via PCR from the cDNA of fly heads using the forward primer EcoRI-CoREST-RF-CC F and reverse primer NotI-CoREST-RF-CC R. Plasmid pAC-CC was digested with EcoRI-NotI, and the CoREST-RF fragment was inserted, resulting in pAC-CoREST-RF-CC.E(Z), HDAC1 and KDM4A were also cloned into the pAC-CC vector using the same procedure, respectively.All primers used are listed in electronic supplementary material, table S1.
Bimolecular fluorescence complementation
The bimolecular fluorescence complementation (BiFC) analysis was performed following the method described by Bischof et al. [24].Briefly, the mCerulean partial sequences encoding amino acid residues 1−173 (CN) or amino acid residues 173−238 (CC) were used to construct plasmids containing fusion genes.Fusion gene plasmids were transfected into S2 cells.After 48 h of transfection, cells were washed three times with phosphate-buffered saline (PBS).The samples were analysed using confocal microscopy (Leica SP8).
Chromatin immunoprecipitation to detect clock binding
Chromatin immunoprecipitation (ChIP) of adult heads was performed as previously described [25], with minor modifications.Twenty-five heads were collected in 450 µl PBS on ice.For cross-linking, 6.02 µl 37% formaldehyde was added, followed by incubation at room temperature for 10 min.Chromatin was sonicated for 2.5 min on ice (settings were 10 s on, 30 s off, high power).The sheared chromatin had an average length of 0.1-0.5 kb.Rabbit anti-GFP (Invitrogen, no.G10362) was used for immunoprecipitation.Fold enrichment was calculated by the ΔΔCT method.All ChIP analyses were repeated three times as independent biological replicates (refer to electronic supplementary material, table S1 for primer sequences).
CoREST long isoform was required for the regulation of circadian rhythm
In a candidate screen aimed at identifying epigenetic regulators of circadian rhythm, we discovered that mutations of CoREST resulted in circadian rhythm defects.The two insertional mutations of CoREST, CoREST MI08173 and CoREST EY14216 , resulted in a decrease in rhythmicity percentages to 62.8% and 60.6% respectively, compared with w 1118 control (figure 2a,d).Moreover, both mutants exhibited significantly reduced power values (figure 2e).Female flies carrying CoREST MI08173 and CoREST EY14216 mutations also exhibited identical circadian rhythm defects as observed in male flies (figure 2f,h,j).Furthermore, the weak enhancement of circadian phenotypes in the CoREST MI08173 /CoREST EY14216 double mutant (female; both genes are on the X chromosome) (figure 2i,k) suggested that these two alleles likely share similar mechanisms in causing circadian phenotypes.Hence, these results support the role of CoREST as a regulator of circadian rhythm.
A previous study has shown that CoREST has two major splicing forms with different functions, which are represented by RC and RF (figure 2l) [20].the long form of CoREST was referred to as CoREST-RF.While, the N-terminus truncated isoform was CoREST-RC, which contains an extra sequence at the 5′UTR (figure 2l).CoREST EY14216 and CoREST MI08173 alleles are insertional mutations of CoREST, inserted in the 5′ and 3′ of the CoREST coding region, respectively (figure 2l).As a result, CoREST EY14216 only affects RF instead of RC (figure 2m).On the other hand, CoREST MI08173 affects both the RF and the RC isoforms (figure 2m).
To determine which splicing form was crucial in the circadian phenotypes caused by CoREST MI08173 and CoREST EY14216 alleles, we conducted genetic interaction experiments.Our findings revealed that the expression of RF driven by tim-Gal4 was able to rescue the circadian phenotypes caused by both alleles (figure 2n,o).In contrast, the expression of RC driven by tim-Gal4 failed to rescue the phenotypes caused by CoREST MI08173 and CoREST EY14216 (figure 2n,o).Consistently, specific RNAi knockdown of RC did not result in noticeable circadian phenotypes (figure 2p,q).The knockdown of CoREST RF in clock neurons using tim-Gal4 resulted in a decrease in the percentage of rhythmicity to 77.1% (figure 2p).Moreover, the power value was also significantly reduced in tim-Gal4/UAS-CoREST RF RNAi (figure 2q).These results indicated that the long-form RF was the major isoform responsible for the circadian phenotypes.
In conclusion, CoREST long isoform was essential for regulating the circadian rhythm.In our subsequent experiments, we primarily used the CoREST MI08173 allele as it exhibits stronger effects compared to the other allele.
CoREST regulates circadian rhythm by modulating the expression of Per
Previous studies have reported that CoREST mediates the binding of epigenetic factors on chromatin [16,17,26].To investigate the mechanism of CoREST function in circadian rhythm, we examined the binding profile of epigenetic factors on core clock regulators, Per, Clk, Tim and Cyc.In modENCODE database (http://www.modencode.org/),we identified significant binding of KDM4A, LSD1 and HDAC1 on the Per locus (electronic supplementary material, figure S1A) [27].Previous data have shown that LSD1 and HDAC1 are binding proteins of CoREST [16,17,26].It has also been observed that LSD1 interacts with E(Z) [28,29].Moreover, previous studies have shown that mutation and overexpression of Per result in strong and weak rhythmic phenotypes, respectively [1,30].Therefore, we hypothesized that CoREST regulates circadian rhythm by controlling the activity of these factors at the Per locus.
To test our hypothesis, we examined the effects of CoREST mutation on the expression of Per.First, we detected the relative expression level of Per in CoREST MI08173 .We found that under constant darkness (CT) conditions, the peak of Per expression in w 1118 was located at CT12, while this peak was shifted to CT16 in CoREST MI08173 (figure 3a).Compared with the w 1118 , the overall oscillation pattern of Per expression in CoREST MI08173 was significantly enlarged (figure 3a; w 1118 JTK_amplitude = 0.449, p < 0.0001; CoREST MI08173 JTK_amplitude = 1.500, p = 0.0008) [31].Under the LD condition, the peaks of Per expression of w 1118 and CoREST MI08173 were at ZT16 (figure 3b).Compared with the w 1118 , the overall oscillation pattern of Per expression in CoREST MI08173 was also significantly enlarged (figure 3b; w 1118 JTK_amplitude = 4.631, p < 0.0001; CoREST MI08173 JTK_amplitude = 5.460, p = 0.0001).Consistently, the variation of Per expression level from ZT8 to ZT16 was steeper compared with the w 1118 (figure 3b).The protein level of Per was also influenced by CoREST.The detection of PER protein at various time points demonstrated alterations in its protein level (figure 3c,d).These results imply that CoREST influences the expression pattern of Per.In addition, we also constructed CoREST MI08173 /Per 01 double mutant (female) to reduce the amplitude of Per and performed behavioural assays.The results showed that the CoREST MI08173 /Per 01 double mutant could partially rescue the circadian phenotype caused by CoREST MI08173 (figure 3e,f).Based on these results, we concluded that CoREST regulates circadian rhythm by modulating Per expression.
Identification of genetic and physical interactions between CoREST and histone modification factors KDM4A, LSD1, E(Z) and HDAC1
To further validate the hypothesis that CoREST regulates the circadian rhythm by recruiting epigenetic factors (including KDM4A, LSD1, E(Z) and HDAC1) at the Per locus, we conducted genetic interactions tests between CoREST and these histone modification factors.We examined the circadian rhythm phenotypes of various mutants and double mutants.The results showed that the mutations in KDM4A and HDAC1 resulted in mild rhythmic defects, respectively (with the percentage of rhythmicity at 88.5% in KDM4 KO /+ and 96.6% in HDAC1 303 /+) while, the mutation in E(Z) did not result in any rhythm defects (percentage rhythmicity in E(Z) 63 /+ was 100%) (electronic supplementary material, figure S1b, f).We deduced that the weaker rhythm phenotype occurred because none of these mutants could be homozygous, and only a subset of them could fulfil the organism's required function.Consistently, the knockdown of LSD1, KDM4A and HDAC1 in clock neurons resulted in mild defects in the percentage of rhythmicity (electronic supplementary material, figure S1e).In contrast, the power value significantly decreased, thereby confirming our conjecture (electronic supplementary material, figure S1f).These results suggest that HDAC1, KDM4A and LSD1 are all involved in the regulation of circadian rhythm.
CoREST MI08173 ; KDM4A KO /+double mutant (percentage of rhythmicity was 75.9% in the double mutant compared to 62.8% in CoREST MI08173 ) did not significantly rescue or enhance the percentage of rhythmicity of CoREST MI08173 (figure 4a,e).However, CoREST MI08173 ; E(Z) 63 /+double mutant (percentage of rhythmicity was 85.3% in the double mutant compared to 62.8% in CoREST MI08173 ) showed the rescued phenotypes of CoREST MI08173 in the percentage of rhythmicity (figure 4b,e).There was also a clear enhancement in the power value (figure 4f).
CoREST MI08173 ; HDAC1 303 double mutant (percentage of rhythmicity was 47.8% in the double mutant compared to 62.8% in CoREST MI08173 ) showed an enhanced phenotype of CoREST MI08173 in the percentage of rhythmicity (figure 4c,e).CoREST MI08173 ; tim-Gal4/+; UAS-LSD1 RNAi/+ (percentage rhythmicity of 48.4% compared with 54.8% in CoREST MI08173 ; tim-Gal4/+) showed a trend towards an enhanced phenotype of CoREST MI08173 in the percentage of rhythmicity and power value (figure 4d,f).These results indicate that these factors are potential circadian regulators that mediate the function of CoREST in clock neurons.
In clock neurons, multiple histone modifications at the Per locus were affected by CoREST
We deduce that if CoREST recruits these epigenetic factors at Per locus to regulate the circadian rhythm, the relevant histone modifications should rely on CoREST.Therefore, we conducted ChIP experiments in the context of clock neurons to investigate whether the histone modifications at the Per locus were altered owing to CoREST mutation.We analysed H3K27me3, regulated by E(Z) [32,33], H3K4me2 regulated by LSD1 [34], H3K27ac regulated by HDAC1 [35], H3K9me3 regulated by KDM4A and LSD1 [34,36] and H3K36me3 regulated by KDM4A [36,37] in the clock neurons of w 1118 and CoREST MI08173 using CNS-ChIP (see §2) (figure 5a).
We found that at the Per locus, the negative control IgG showed no change.In contrast, H3K27me3 significantly increased at ZT16 compared with ZT8 in the control group (electronic supplementary material, figure S3b, d).After the CoREST mutation, there was a significant increase in the level of H3K27me3 (figure 5b,c), indicating that CoREST negatively regulates this modification.E(Z) is a positive regulator of H3K27me3 at both ZT8 and ZT16 (electronic supplementary material, figure S3c , d).These results suggest that the CoREST negatively regulates E(Z) in clock neurons, which is consistent with the results of the genetic interaction between CoREST and E(Z) mutants (figure 4b,e, f).
H3K4me2 levels were found to be higher at ZT16 than at ZT8 in the Per locus in the control group (figure 5d,e).The level of H3K4me2 was significantly higher in the CoREST MI08173 mutant (figure 5d,e), indicating a negative regulation by CoREST.The core of the CoREST complex contains LSD1, a histone modification enzyme that demethylates histone H3K4-me2 and -me1 residues [14][15][16][17].Therefore, these results suggest that the CoREST positively regulates LSD1 in clock neurons.
The levels of H3K27ac showed little change at the Per locus between ZT16 and ZT8 in control (electronic supplementary material, figure S3E and F).After CoREST mutation, the level of H3K27ac significantly increased (figure 5f,g), indicating a (q) Summary of the interactions between the proteins that make up the CoREST complex.'+' indicates physical interaction between two proteins.'−' indicates that there is no physical interaction between two proteins.
negative regulation by CoREST.HDAC1 was the negative regulator of H3K27ac at both ZT8 and ZT16 (electronic supplementary material, figure S3e , f).Consequently, CoREST positively regulates HDAC1, which is consistent with the results of genetic interaction between CoREST and HDAC1 mutants (figure 4c,e,f).
At the Per locus, H3K9me3 levels were significantly higher at ZT16 compared with ZT8 in the control group (electronic supplementary material, figure S3G and H).After the CoREST mutation, H3K9me3 levels decreased significantly at ZT8, indicating that CoREST positively regulates H3K9me3 (figure 5h).However, there was no effect on H3K9me3 levels at ZT16 when the CoREST function was lost (figure 5i), indicating that the CoREST regulation of H3K9me3 was time dependent.To further explore whether the temporal specificity was owing to the time-dependent function of KDM4A, we examined H3K9me3 in KDM4A mutants.The results showed that KDM4A primarily acts as a negative regulator of H3K9me3 at ZT8, while it had no effect on H3K9me3 at ZT16 (electronic supplementary material, figure S3G and H).In addition, it has been reported that LSD1 facilitates H3K9me3 modification [34].These results suggest that CoREST negatively regulates KDM4A, but positively regulates LSD1 in clock neurons, which is consistent with the results of genetic interaction analysis between CoREST, KDM4A and LSD1 mutants (figure 4e,f).
H3K36me3 levels are higher at ZT16 than at ZT8 in the Per promoter in the control group (electronic supplementary material, figure S3I and J).After the CoREST mutation, there was a significant increase in H3K36me3 levels at ZT8 and a significant decrease at ZT16 (figure 5j,k).For H3K36me3, KDM4A acted as a positive regulator at ZT8 but a negative regulator at ZT16 (electronic supplementary material, figure S3i, j).Consequently, at both ZT8 and ZT16, CoREST negatively regulates KDM4A, which is consistent with the situation observed with H3K9me3.Similar to H3K9me3, the temporal-specific function of CoREST may be attributable to the time-dependent role of KDM4A.This conjecture is supported by the rescue of the CoREST MI08173 power value by the CoREST MI08173 ; KDM4A KO /+double mutant (figure 4a,e,f).
To investigate whether CoREST regulates the cycling of histone modifications at the period locus in the clock neurons, we examined the H3K27me3 levels in clock neurons of both CoREST mutants and the controls.Consistent with the mRNA levels, we observed oscillations with a much higher amplitude in the mutants, reaching a peak at ZT16 (electronic supplementary material, figure S3k).
In conclusion, these results demonstrate that CoREST regulates circadian rhythm.This regulation was to some extent dependent on histone-modifying factors, such as KDM4A, LSD1, E(Z) and HDAC1, along with their corresponding histone modifications.Moreover, the temporal-specific regulation of H3K9me3 and H3K36me3 by CoREST can be attributed to the temporal-specific function of KDM4A.
CoREST complex regulates CLK binding at the Per locus
A previous study has shown that CLK is the main transcriptional factor of Per [38].Epigenetic modifications often regulate gene expression through transcription factors.Therefore, we investigated whether CoREST regulates the binding of CLK to the Per gene locus.The expression level of Per at CT16 or ZT16 was significantly higher than that at CT4 or ZT8 (figure 3a,b).Consistent with this, the CLK binding at the Per locus of CT16 or ZT16 was more abundant compared to that at CT4 or ZT8 (figure 6a,b).In CoREST mutants, compared to the control group, the CLK binding at the Per locus of CT16 or ZT16 increased, while it decreased at CT4 or ZT8 (figure 6a,b), indicating that the presence of the CoREST complex inhibited CLK binding at CT16 and ZT16 while enhancing CLK binding at CT4 and ZT8.Therefore, the overall effect of CoREST complex regulation on the Per locus is to maintain the variation of CLK binding and the oscillation of Per expression within a narrow range.
In conclusion, we have a model illustrating the regulation of the CoREST complex on histone modification at the Per locus (figure 6c).Through direct interactions between CoREST-RF and HDAC1, CoREST-RF and LSD1, LSD1 and E(Z), HDAC1 and KDM4A, CoREST positively regulates LSD1 and HDAC1, while negatively regulates E(Z) and KDMA.Under the influence of these histone-modifying factors, CoREST interactively regulates multiple histone modifications in a time-dependent manner.At ZT8, the absence of CoREST led to a substantial elevation in H3K4me2 and H3K27ac, a significant decrease in H3K9me3, and an increase in H3K27me3 and H3K36me3, ultimately resulting in a decrease in Per expression (figures 3b and 6c).While, at ZT16, the loss of CoREST resulted in a significant elevation in H3K27me3, a mild decrease in H3K36me3, a significant increase in H3K4me2 and H3K27ac, and no significant change in the repressive mark H3K9me3.These combined effects contributed to an increase in Per expression (figures 3b and 6c).Notably, at ZT16, both the gene body and promoter of Per exhibited a substantial repressive modification, H3K9me3, which likely accounted for the subsequent trough in Per expression (figures 3b,5i and 6c).
The ability of Drosophila to be entrained by environmental changes is limited by CoREST mutation
To further investigate the function of CoREST-dependent epigenetic regulatory machinery in Drosophila, we examined the adaptation of the circadian rhythm of the CoREST mutant and the control group to changing conditions.Specifically, we tested the temperature entrainment condition at 16°C for 12 h followed by 12 h at 25°C TCs.The results revealed a significant reduction in the entrainment index for the CoREST mutations (figure 1a,c), indicating a decreased ability to adapt to environmental changes.It has been previously reported that synchronization to low TCs in DD requires Per in ventral lateral neurons [23].The altered expression pattern of Per caused by CoREST mutations may explain the inability of CoRESTMI 08173 to adapt to environmental changes.In conclusion, these data collectively indicate that CoREST mutation limits the ability of Drosophila to be entrained by temperature.
Discussion
In this study, we investigated the mechanism of CoREST regulation in circadian rhythm.By studying the regulation of the CoREST complex on circadian rhythm, we revealed that CoREST regulates HDAC1, LSD1, E(Z) and KDM4A and their corresponding histone modifications at the Per locus specifically in clock neurons.Interestingly, we found dynamic changes in histone modifications at different time points of the Per locus, suggesting that histone modification plays an important role in regulating gene expression oscillation.More importantly, we found differential effects of the same factor on the Per locus at different time points, such as the effect of KDM4A on H3K9me3 and H3K36me3 at ZT8 and ZT16.Understanding the mechanism behind this time dependence poses an intriguing problem.
The regulatory relationships identified in this study are consistent with or provide an explanation for phenotypes previously reported in the literature.The discovery of CoREST's function on E(Z) explains the previous report that CoREST negatively regulates H3K27me3 in Drosophila follicle cells [19].The discovery of CoREST's role on LSD1 and E(Z) also explains its involvement in regulating the H3K4me2, H3K9me3 and H3K27me3, as reported in a previous study [18].Previous reports have indicated that H3K36me3 levels increase alongside transcription to inhibit repeated transcription [39].Specifically, H3K36me3 on the gene body correlates with transcriptional activity.Conversely, the presence of H3K36me3, along with H3K9me3, at the regulatory region maintains a repressive state of gene expression [40].Our study demonstrates a positive correlation between H3K36me3 on the gene body of the Per locus and transcriptional levels, while a negative correlation is observed between H3K36me3 at the regulatory region and transcriptional levels (figure 5j,k).All of these pieces of evidence support the effectiveness of the techniques employed in this study.
Histone modifications, as a feedback regulation mechanism, maintain the dynamic expression of Per in a relatively narrow range.Transcription is mainly driven by CLK.This study shows that the level of inhibitory histone modification is closely related to the Per transcriptional level in w 1118 flies.There is a time delay between the mRNA level and the levels of epigenetic modifications.This phenomenon is similar to what we observe for the mRNA level and protein level of clock genes.At ZT8, when the expression level is relatively low, the inhibitory histone modifications are also low.This low level of inhibitory histone modifications at the Per locus facilitates the subsequent enhancement of the transcriptional level.On the contrary, at ZT16, when the expression level is relatively high, the inhibitory histone modifications are high.This high level of inhibitory histone modifications at the Per locus dampens its subsequent transcription.The function of CoREST complex is to maintain histone modifications of Per locus.Our data indicate that except for H3K9me3 at ZT16, the other four modifications can be altered by CoREST mutation.Other mechanisms are involved in maintaining H3K9me3 at ZT16.The collective effects of multiple histone modifications at the Per locus can influence the recruitment of CLK and transcription.The increase in activating histone modifications promote CLK binding and transcription, and vice versa (figure 6c).The question then remains: how is the initial state established with both a relatively high level of H3K9me3 and a relatively high CLK binding and transcription level?Feedback mechanisms are probably involved in this process.
One interesting discovery in this study is the temporal-specific role of CoREST in regulating H3K9me3 and H3K36me3.Further evidence from our study demonstrates that this is attributed to the temporal-dependent function of KDM4A.Regarding H3K9me3, the lack of impact from KDM4A or CoREST loss at ZT16 may be owing to high levels of H3K9me3 at this stage or the involvement of other mechanisms maintaining its level.Additionally, other similar mechanisms have been observed to maintain H3K9me3 levels in mammals [3].As for H3K36me3, the contrary effects at ZT8 and ZT16 resulting from KDM4A or CoREST loss could be a consequence of different histone modification states, diverse expression patterns of interacting factors, or varying responses from redundant homologues during these time points.Investigating the underlying mechanism behind this phenomenon would be of great interest, although we are currently lacking the necessary reagents to conduct further experiments.This study serves as yet another example highlighting the involvement of the CoREST complex in timely dynamic transcriptional regulation.A previous report by Y.H.'s lab demonstrated the role of CoREST in activity-dependent transcription regulation in memory [20].
The tests of physical interactions among the factors mentioned in this study have limitations.The lack of an in vivo context means that the results shown here only provide evidence of the possibility of interaction, rather than the actual states of the protein complexes.As previously mentioned, the CoREST complex may exhibit dynamic behaviour at different time points in terms of temporal-specific regulation.The model in figure 6c may only capture a limited state of the CoREST complex.The inclusion of certain components, particularly E(Z) or KDM4A, could be subject to dynamic regulation by other factors.The genetic relationship discovered in this study is limited in this regard.It would be intriguing to further investigate the components and functions of the CoREST complex at various time points in clock neurons.
Figure 1 .
Figure 1.CoREST is required to synchronize with low temperature cycles in DD. (a,b) Actograms.Flies were initially synchronized to 3 LD cycles at 25°C, followed by two at 16°C and 25°C temperature cycles (TCs) in DD, each TC was delayed by 6 h compared to the previous regime, and subsequently released to DD at 25°C.Cyan and pink areas indicate 16 and 25°C, respectively.n = 16.Red dots indicate activity peaks.The red rectangle frames a 6 h window for the main temperature-synchronized activity.(c) Plotting of the EI.Data information: Statistical differences were measured using unpaired two-tailed Student's t-test.
Figure 5 .
Figure 5. CoREST regulating histone modification on the Per genomic locus in clock neurons.(a) Primers used in (b)-(k).(b,c) ChIP experiments showing the relative enrichment (% Input) of H3K27me3 on the Per gene locus in CoREST MI08173 and w 1118 .(b) H3K27me3 was weakly upregulated in CoREST MI08173 at ZT8. (c) H3K27me3 was strongly upregulated in the CoREST MI08173 mutant at ZT16. (d,e) ChIP experiments showing the relative enrichment (% Input) of H3K4me2 on Per gene locus in CoREST MI08173 and w 1118 .(d) H3K4me2 was strongly upregulated in CoREST MI08173 at ZT8. (e) H3K4me2 was also strongly upregulated in the CoREST MI08173 mutant at ZT16. (f,g) ChIP experiments showing the relative enrichment (% Input) of H3K27ac on Per gene locus in CoREST MI08173 and w 1118 .(f) H3K27ac was upregulated in the CoREST MI08173 mutant at ZT8. (g) H3K27ac was also upregulated in the CoREST MI08173 mutant at ZT16. (h,i) ChIP experiments showing the relative enrichment (% Input) of H3K9me3 on the Per gene locus in CoREST MI08173 and w 1118 .(h) H3K9me3 was downregulated in the CoREST MI08173 mutant at ZT8. (i) H3K9me3 was invariant in the CoREST MI08173 mutant at ZT16. (j,k) ChIP experiments showing the relative enrichment (% Input) of H3K36me3 on the Per gene locus in CoREST mutant CoREST MI08173 and w 1118 control.(j) H3K36me3 was upregulated in Per promoter but downregulated in Per gene body in the CoREST MI08173 mutant at ZT8. (k) H3K36me3 was weakly downregulated in the CoREST MI08173 mutant at ZT16.Data information: Statistical differences were measured using unpaired two-tailed Student's t-test.The significance levels were represented as *p < 0.05, **p < 0.01, ***p < 0.001 and ****p < 0.0001.If the p-value was greater than 0.05, it was not displayed in the figures. | 6,892.2 | 2024-07-01T00:00:00.000 | [
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The great revolution of technology and its fast growth have led to a cyber space increasingly vulnerable to cyber-attacks. For this reason, cyber security becomes paramount to protect our cyber space by presenting and implementing important solutions to protect sensitive data from malicious persons. Thereby various measures of protection have been developed and aim to minimize the risks and damages of attacks. Among them, cryptography plays a vital and crucial role in protecting sensitive transmissions and electronic exchanges through complex networks. Numerous scientific studies have emerged with the advent of the cloud and the Internet of Things (IoT); all of them have expressed a strong need for building secure, efficient and fast cryptosystems targeting confidentiality, integrity and authentication. The last two objectives are essentially built on hash functions which are the main components of many applications and secure networks. The purpose of this paper is to give recent advances of lightweight cryptographic solutions that meet the requirements of constrained systems, and to present a study, in terms of security, energy-consuming and efficiency, of the main hash functions standardized by NIST (National Institute of Standards and Technology). In the end, the paper will give a comparison between the studied hash functions aiming to come up with a recommendation of good lightweight hash functions suitable for implementation in an IoT framework.
Introduction
The impressive technological revolution and its rapid growth have greatly changed our way of life; we are living in a connected world in which we handle daily binary data transiting through a complex ecosystem, smart devices communicating through a multitude of networks, etc. Most of the internet activities concern the exchange of different types of data; some of them are critical such as login, passwords, credit card numbers, etc. Exchanged data are facing different hazards; they can be intercepted, deleted, changed/encrypted, or sold for money, etc. Thus, almost all sectors such as transport, energy, e-commerce, hospitals, health industry, and education or government institutions are vulnerable to cybercrime; the injection of viruses, the spread of malware constitutes a threat that can damage or paralyze vital sectors. Otherwise, we can note that hackers techniques constantly evolve with technology, and types of attacks are constantly mutating and adapting to defense mechanisms. Therefore, strengthening and innovating security mechanisms is of great importance for the survival of the digital world.
To avoid or to minimize the risks of attacks, various solutions of protection have been developed as for instance access policy, firewalls, anti-viruses, anti-malwares, IDS (Intrusion Detection Systems). These solutions are not sufficient because some existing systems, applications, and protocols present often weaknesses likely to be exploited by cybercriminals. Cryptography plays a vital and crucial role for protecting sensitive transmissions and reinforcing existing solutions [1]. Furthermore, cryptography owes its strength from important mathematical areas such as arithmetic, number theory, algebra with Galois Fields, etc. [2]. This force is often based on mathematical conjectures difficult to be demonstrated, namely discrete logarithm problem, or factorization of very large integers into a product of prime numbers. Since the past decades, scientists community expresses a strong need for building cryptosystems satisfying: efficiency, speed, security, and resistance against cryptanalysis coming essentially from active attacks; the need has greatly increased with the advent of IoT [13]. These cryptosystems are often targeting confidentiality, authentication; and integrity [3]. Integrity ensures that data are not corrupted during their transmission and it is essentially built on hash functions which are the main components of many security applications and communication protocols on Ipv4/Ipv6 [4,5] like SSL (Secure Sockets Layer), TLS (Transport Layer Security) and IPSec (IP Security). The present work aims to present an analysis of lightweight block ciphers and lightweight hash functions suitable for implementation on resource-limited computational devices. A focus will be done on some selected hash functions qualified as lightweight, essential for building authentication and integrity solutions needed for securing constrained environments.
The rest of the paper is organized as follows: Section 2 presents an overview on lightweight cryptography including a discussion on the most important lightweight block ciphers essentially those standardized by the NIST; a discussion on security aspects is given. Section 3 is devoted to a review on hash functions, including conventional and cellular based hash functions. Section 4 is dedicated to the description of our proposed solution. We end this paper with a conclusion and some outlines.
Lightweight Cryptography
To ensure the confidentiality and integrity of data, a list of cryptosystems has been released in modern cryptography. The most important ones are of two categories. The first category concerns symmetric algorithms using the same secret key for encrypting and decrypting data as for instance DES (Data Encryption Standard), AES (Advanced Encryption Standard), 3DES etc. [3]. Their role is to encrypt and to decrypt data into blocks through a number of iterations/rounds; these iterations use transformations versus some sub keys generated from the chosen single secret key. The second category is asymmetric algorithms using public keys to cipher texts and secret keys to reconstruct plaintexts; the well-known algorithms are RSA, El Gamal, and elliptic curve-based ciphers, [3].
With the advent of IoT and smart citie applications, a great need is to secure small and smart devices, but conventional cryptography standards know some limits making them difficult to be implemented on constrained devices including embedded systems deployed in various industrial installations, smart cards, RFID and sensor networks. Another type of cryptography has emerged within a new subfield of cryptography named lightweight cryptography setting the challenge to build secure solutions on hardware and software, and tailored for each constrained device. The properties of lightweight cryptography are presented in ISO/IEC JTC 1/SC 27 and in ISO/IEC 29192. On software, smaller code and RAM size are recommended for lightweight applications in ISO/IEC 29192, while chip size and energy consumption constitutes important measures in lightweight solutions on hardware. More details can be found in NIST report [6] which presents a study demonstrating the performance of lightweight block ciphers over conventional block ciphers taking into account, smaller block sizes, smaller key sizes, simpler rounds, simpler key schedules, and minimal implementations of only necessary functions for consuming minimal resources.
Lightweight block ciphers and security analysis
This section discusses the performance of some selected lightweight block ciphers: AES-128, DESL, PRESENT, SIMON, SPECK, RC5, TEA and XTEA; it may be possible to apply them for protecting data on constrained environments as we will see here after.
A number of lightweight block ciphers have been proposed targeting good performance as for instance AES, standardized by NIST and more precisely AES-128. The DES algorithm has also been adapted for lightweight cryptography applications. For example, DESL (DES lightweight extension) is a variant of DES where initial and final permutations are excluded, and where a single S-box is used instead of eight; the omission of permutations is for improving the size of the hardware implementation. Concerning DESL/DES security, a brute force attack is able to break the entire 56-bit key. Linear, differential and hybrid differential-linear cryptanalysis applied on DES/DESL can led to breaking the 16 rounds of the algorithm. PRESENT is one of the first lightweight block cipher built for constrained hardware environments. The 4-bit S-box used in PRESENT requires 28 GEs (Gate Equivalence) whereas the AES S-box required 395 GEs. For this reason, PRESENT is about 2.5 times smaller than AES: Thanks to this performance, the International Organization for Standardization and the International Electrotechnical Commission introduced PRESENT in the new international standard for lightweight cryptographic methods. Concerning the security, PRESENT is threatened by a differential cryptanalysis. SIMON and SPECK are families of lightweight block ciphers designed by the NSA (National Security Agency) to be simple, flexible, and perform well in hardware for SIMON, and in software for SPECK. The two ciphers are expected to operate well on various IoT devices. We note that Speck is vulnerable to differential and side-channel attacks, and SIMON is vulnerable to differential and linear Hull cryptanalysis. Otherwise, some old algorithms like RC5 (symmetric-key block cipher), TEA (Tiny Encryption Algorithm) and XTEA (eXtended TEA) are suitable for constrained software environments because they are built on simple round structures [6].
Hash functions
To begin this section, it would be preferable to remind the concept of hash function. Definition 3.1. Let Σ * be a set of alphabetic strings. We define a hash function h as an application from Σ * to Σ n , n ∈ N such that it associates images strings of a fixed length to strings of any length in Σ * . The function h cannot be injective. • The argument x can be of arbitrary length and the image h(x) has a fixed length of n bits.
• For a given y image of the hash function, it is almost impossible to find a message x such that h(x) = y. Given x and h(x), it is very difficult or impossible to find an arguement x = x such that h(x ) = h(x).
Brief review on conventional hash functions
A cryptographic hash function can be applied to verify data integrity, message authentication and digital signatures; it corresponds to a one-way function where the input is an arbitrary block of data and where the output is of fixed size. The encoded data is called the message, and the hash value is the message digest [8]. The most known cryptographic hash functions are MD5 (Message Digest 5), SHA-1 (Secure Hash Algorithm 1), SHA-256, SHA-512, RIPEMD-160, and HAVAL; all these functions are based on the so-called MD4, [9].
In 1991, Ron Rivest developed MD5, a 128-bit hash function more secure than the initial hash function MD4. MD5 knew some difficulties in 1993 related to its compression operation; it suffered vulnerabilities due to collision attacks; the attacks were also applied to several other hash functions built on MD4 like HAVAL and RIPEMD [10].
SHA-1 successor of MD4 was designed by the NSA and produces a 160-bit hash value. Due to its vulnerabilities against collision attacks, many organizations have recommended to replace SHA-1 by SHA-256. [24]. Keccak was the winner of the NIST hash function Competition held on 2012 [11]. In 2013, two sets of lightweight implementations of all SHA-3 were presented. The final selection, implemented on Xilinx devices are BLAKE-256 followed by Grostl [12].
Cellular automata-based hash functions
Cellular automata (CA) were first invented by Ulam and Von Neumann in 1940; afterwards, the CA theory was developed by Stephen Wolfram author of many reference studies in the field of CA [26]. CA is a dynamical system of a network of cells evolving versus given rules and according to specific neighborhoods. CA can be applied in many fields as biology, transport, biomathematics, cryptography, network security, etc. For example, CA are a useful tool to design IDS (Internet Detection Systems) and can led to interesting schemes for malware propagation modelling [26]. In Cryptography, CA were applied to design secure and fast cryptosystems to guarantee confidentiality, integrity or authentication in electronic transmissions [15,28,29].
Definition 3.3. A cellular automaton (CA) is a dynamic system considered as a discret model equal to a regular grid of cells defined by its dimension, a set of finite states, a neighborhood and a set of rules. If
A is a cellular automaton, then A can be expressed by the set {S, Z d , V, f} where S is a finite set of states, d is the size of the automaton, Z d is the space of the automaton, and f is the rule also called transition function defined from S n to S with n = card(V), and V is the set of neighborhood.
Cryptographic hash functions based on CA are suitable for applications where data must to be authenticated and where CPU time of transmission can be very important as for instance applications related to secure transmissions between smart devices on IoT. Damgard in [23] built a fast and collision free one way hash function based on CA. And in [16], authors presented a study demonstrating that based on CA, a new one-way hash function providing authentication and data integrity is suitable for fast implementation in hardware; and it is secure against all known attacks. The characteristics of this function make it useful for securing smart cards and electronic cash payment protocols. In 2013, a detailed study demonstrated that CA based schemes are able to define hash functions for low hardware complexity on small silicon area [10]. In 2014, a new CA hash function called CASH was presented and a comparison with some CA based hash functions has been given and demonstrated that the proposed hash function preserved all good characteristics of the previous CA based hash function guarantying improvement of security and complexity, The results show that CASH is better than SHA-3 with respect to throughput [14]. A more recent study published in 2017 presented a fast new CA based hash function compared to the well-known hash functions SHA2-512, MD5 and keccak. Numerical tests were performed on simple configuration machine (Intel Core i5, 64-bit, 4 GB, 1.8Ghz). The results meet the integrity and authentication requirements and show that the new hash function is resisting against forgery attacks [17]. Following the previous scientific contributions, we can conclude that CA based hash function can perform well than MD5, SHA-512 and SHA-3 when implemented for specific requirements. CA can lead to interesting solutions of authentication and integrity on constrained environments.
Analysis and comparison of the well-known lightweight hash functions
The expected usage of conventional and lightweight hash functions differs in various aspects such as smaller internal state, output sizes and smaller message size. Conventional hash functions may not be suitable for constrained environments, mainly due to their large internal state sizes and high-power consumption requirements. The most interesting lightweight hash functions are: PHOTON, SPONGENT, Lesamnta-LW, Quark, Keccak, Gluont, Neiva, Armadillo, BLAKE, SHA-1, SPECK, SHA-3; MD5. An analysis of these functions is given here after. Firstly, following a study on [18], we can notice that PHOTON is recommended for constrained devices like passive RFID tags. Otherwise, SPONGENT [19] is a family of lightweight hash functions with hash sizes of 88,128, 160, 224, and 256 bits based on a sponge construction. The importance of these functions lies in the fact that it leads to fast algorithms.
Hirose et al. defined a lightweight 256-bit hash function under the name of Lesamnta-LW respecting security against collision, preimage, and second preimage attacks and using AES as the compression function [20].
In [22], authors presented the hash function family Quark based on the sponge construction. It was demonstrated that Quark is resisting against well-known attacks, and gave satisfactory performance when implemented on hardware with minimal memory requirements. In 2017 [21], a classification of lightweight cryptographic hash algorithms has been presented and aimed to select a lightweight cryptographic primitive ensuring security and respecting resource constraints. A performance comparison of Photon, Quark, Keccak, Gluont, Spongent, Neiva, Armadillo and Lesmanta has been presented considering specific metrics such as throughput, power, and, hardware efficiency. This study did not ended to a clear classification between the analyzed functions. However, this study could be useful in making a compromise between security and environment constraints. More recently, in 2019, authors presented software implementation benchmarks for various hash functions: MD5, BLAKE, SHA-1, SPECK, and SHA-3. The implementation was performed for resource limited devices [27]. The benchmarks were evaluated on a batteryless RFID device and revealed that MD5 produces the best performance when compared to BLAKE, SHA-1, SPECK, and SHA-3.
Definition of a lightweight cryptography based solution to secure resource-constrained environment communications
In this section, we define a global lightweight solution protecting resource-constrained environments, targeting confidentiality, integrity and authentication. This solution includes: • A confidentiality mechanism to protect exchanged data using AES-128 associated to a secret key K of 128-bits (a lightweight block cipher implemented with block sizes of 128-bits); • A secure mechanism to share the secret key K using the algorithm RSA-1024 which is considered as a lightweight algorithm; • A lightweight hash function as for instance Quark function to enhance the security process guaranteeing integrity and authentication.
Let consider two communicating entities A as a sender and B as a receiver. Firstly, using for example MQTT (Message Queuing Telemetry Transport) protocol, B sends to A his couple of public keys (e, n) ∈ N × N; the private key d ∈ N is kept on B server. The sender A encrypts the plaintext text M using AES-128 with the key K producing the cipher text C. After this step, the system call RSA algorithm to encrypt the key K using the equation 4.1: Thereafter, the lightweight function Quark is called to hash C and to produce hash(C). Following this step, the entity A sends to B the block: (C, hash A (C), K ). From the other part, the receiver executes the following steps: -Deduction of the key K from K using RSA with the equation : where d is the private key of B.
-Decryption of C using the algorithm AES and deduction of a plaintext text M 1 .
-Call of Quark function to hash C and to produce hash B (C).
-Comparison of hash B (C) and hash A (C) : If hash B (C) = hash A (C), then accept the data and confirm that M 1 = M; and if hash B (C) = hash A (C), then reject the data.
Note that the proposed solution is a global one as it offers data protection, verification of integrity and authentication.
To summarise, the proposed solution is illustrated in figure 1.
Conclusion and some directives for a future work
In this work, we presented and discussed the most relevant lightweight block ciphers and lightweight hash functions including those based on cellular automata. The work covered performance analysis of the most known block ciphers. A particular focus was accorded to the main hash functions, qualified as lightweight, and suitable for building authentication and integrity solutions essential to secure constrained environments. As we noticed above, MD5 produced the best performance when compared to BLAKE, SHA-1, SHA-3, and SPECK. Otherwise, Quark can be considered as a good candidate for integrity and authentication solutions since it is resisting against well-known attacks, and presents good performance when implemented on hardware with minimal memory requirements. Regarding CA applications, we can affirm that CA based hash function can perform well than MD5, SHA-512 and SHA-3 when implemented for specific requirements. In a future work, we will carry out more simulations on the proposed secure solution that could represent a model implemented on a network including different layers as smart devices, gateway, and servers on the cloud. The model can be applied for many applications as for instance the protection of sensitive data exchanged through a health architecture. | 4,349.8 | 2021-06-01T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Design and Implementation of a New Automatic Charging System for Metal Round Tubes
This paper took the automatic charging process of metal round tubes as the research object. A traditional manual charging method was researched and an automatic charging system was designed in this paper. The system improved the existing enterprise processing mode significantly and the overall production efficiency of metal round tubes. This article introduced the composition of the automatic charging system for metal round tubes, and further analyzed the structural design features and operation principles of each component; in order to realize the automatic production of the charging system, a complete set of automatic control system was designed in the paper, enabling the orderly connection between the round tube cutting and edge chamfering processing procedures. The automatic charging design was used to replace the original cut round tube manually transported to the chamfering process and then manually load to the chamfering slot, thereby reducing the cost of enterprise labor, improving productivity and ensuring production safety.
1.Introduction
In order to meet different production requirements, it is necessary to cut the long metal round tube into a shorter tube. After the metal round tube is cut, burrs will generally appear at the corresponding position, which affects the quality of the round tube. The processing of such products mainly relies on the traditional processing mode. Generally, workers operate the cutting machine to cut the long tube into short tubes, and then transport them to the next station for chamfering by a forklift, which is represented by a schematic diagram of the processed product. Pain points of the existing method lie in the efficiency of charging and chamfering, and the expensive labor cost, and the shape burrs after cutting, which easily threatens the safety of the operator. To improve production efficiency and reduce labor costs, enterprises are eager to develop an automatic charging system [1][2][3][4] . A device with both deburring and loading and uploading functions was studied in this paper. It can receive cut round tubes, align the placement of those tubes, and remove the burrs generated after cutting, and complete the process of charging and baiting, thereby supplying materials for the chamfering. The device can operate and charge materials at a speed of 40-60 pieces per minute when chamfering. A single automatic loading and uploading system can save the labor of 4-5 people. The design can improve the operating efficiency of the metal round tube production line, reduce labor costs and labor intensity of workers, and provide a safer working environment.
The Composition of the Automatic Loading and Uploading System
The automatic charging system for metal round tubes designed in this paper includes the baiting device, material storage tank, deburring device and charging device arranged in sequence, and also includes a transition line between the storage tank and the charging device; The tank and the transition line are inclined downward along the conveying direction of the round tube, while the charging device is inclined upward along the tube; the line passes through the deburring device, connecting the end of the storage tank and the end of the charging device respectively. The overall assembly drawing of the device is shown in Figure 2 The workflow: the cut round tube first falls on the conveyor belt of the uploading device. When it falls on the conveyor belt, the products are out of order and some products are even upright. Therefore, the uploading device ensures that the products are uniformly lying flat when conveying the products. Then products fall into the tank through the charging device, and enters the transition line in an upright state after falling; Since the line is designed with a certain inclination angle, products roll to the next procedure due to gravity; when a certain amount of products passes through the deburring device, the burrs are squeezed to the end of the inner circle by the cylinder positioning and squeezing burr mechanism; after the extrusion is completed, the cylinder and deburring device, then the products continues to roll to the next chamfering and charging station. The slots on the conveyor belt of the charging device can only hold each product. Finally, the products are sent to the charging platform of the end chamfering equipment. After this single process, the next process is followed.
Operation analysis of automatic uploading device
The uploading device is mainly composed of driving mechanism, chain conveyor belt, motor, height limiting rod, conveying plate, shell and frame and other parts. among them There are two outer shells, which are respectively fixed on both sides of the upper end of the bracket; the driving mechanism is fixed on one side of the bracket, and its output end is connected with the chain conveying mechanism; the chain conveying mechanism is arranged between the two shells, and the conveying direction is set along the length of the shell ; The two ends of the Frame Figure 3 Assembly drawing of automatic Baiting device
Operation Analysis of Transition Line and Deburring Device
After the product is output from the baiting device, it first falls into the storage tank, and the product is in an upright state; the storage tank and the transition line are installed on a bracket with a certain inclination angle, and then the product depends on its own weight along the inclined transition line rolling in the direction of the upward charging device; in the rolling process, the burr is removed through the squeezing and deburring device, and the burr is placed on the inner circle side to facilitate the removal of the burr in the chamfering process. As shown in Figure 4, a schematic diagram of the assembly of the transition line and the deburring device. (1) The transition line mechanism is composed of storage tank, inclined bracket, frame, flow plate, air cylinder and push plate, as shown in Figure 4(a). The storage tank is installed on the end frame of the uploading device. In order to ensure that the products lying flat in the uploading device stand upright when entering the storage tank, it is bent at a certain angle on one side of the storage rack groove to realize the smooth sliding and upright status of the product, see Figure 4 (a) an enlarged view of the deburring device. The flow plate that plays a guiding role is installed on the inclined bracket. In the area of deburring device, the flow plate allows products to pass, and the two aligning posts are symmetric. Since the posts guide and align the round tubes, so the cylinder cannot be too large.
(2) The deburring device includes a second support, a first stopper cylinder, a second stopper cylinder, and a squeezing push cylinder arranged on the second support; the second support is installed from top to bottom; the first stopper The air cylinder and the second stopper cylinder are respectively arranged on opposite sides of the first mounting part of the second bracket along the conveying direction of the circular tube, the squeeze push cylinder is arranged between the first stopper cylinder and the second stopper cylinder, and on the top of the second bracket, with its working end downward.
For the squeezing and pushing cylinder in the deburring device, it includes a connector, a cylinder body, a guide post, a spring guide post, a scraper, and a pressure plate; the lower end of the cylinder body is connected with the connector through the guide post; the guide post and the spring guide post pass through There are two connecting pieces, spring guide posts, which are arranged symmetrically on both sides of the guide posts along the length direction of the connecting piece, and their lower The length of the scraper along the conveying direction of the circular tube is shorter than the distance between the two stopper cylinders; the length of the pressure plate along the conveying direction of the circular tube is no longer than the length of the scraper along the conveying direction of the circular tube.
Operation analysis of chamfering charging device
How to transport products to the chamfering process in an orderly and stable manner is a key technical indicator reflecting the feasibility of the equipment, which is also the core content of the research and development device in this article. In this paper, innovative design is carried out in accordance with the existing charging methods of the products to be chamfered. As shown in Figure 5. 1. Frame; 2. Drive mechanism; 3. Shell; 4. Transport plate slot;5. Slot body; 6. Baffle plate; 7.
Protection net Figure 6 Assembly drawing of chamfering charging device The designed chamfering charging device includes a frame, a drive mechanism fixed on the frame, a shell and a transport plate slot set between the two shells. One end of the drive mechanism rotating shaft is connected with the transport plate slot, and the conveying direction is along the side of the shell. It is set in the length direction; the power source of the transport plate groove is provided by the drive mechanism to drive the gear chain transmission to ensure the stable charging of the transport plate groove. The shells located on both sides can protect the round tubes in the transport plate slot and prevent the round tubes from falling from the side.
The transport plate trough in the charging device is composed of several troughs. The troughs and the round tubes are of the same specifications. Each trough can only transport one round tube to prevent the round tubes from squeezing each other and falling due to the influence of gravity during the ascent. If the specification of the tank is adapted to the round tube, the round tube will not shake in the tank, avoiding the round tube falling during the ascending process. The charging device also includes a baffle plate and a protection net. The baffle plate is arranged at the end of the charging device close to the conveying transition line, and is fixed between the two shells so that the round tubes entering the transport plate slot fall into different slots; the protection net is arranged on the shell to prevent the round tube in the tank from falling from the side.
Equipment Operation Control System Design
In order to ensure that each mechanism of the equipment can perform as expected, it is necessary to design and produce a complete set of automated control systems: the core control unit module of the control system of the whole set of equipment chooses Siemens CPU314C-2PN/DP as the controller. The PLC control module can meet the need of the IO points required for the operation of a single or multiple sets of equipment. It supports Ethernet communication or PROFIBUS DP communication protocol; the inverter module uses Siemens MM440 to achieve the purpose of speed adjustment of the chain conveyor; Siemens TP177B series touch screen is used to detect the operating status of the equipment, display the production process data, and display alarms, data information management and equipment debugging and operation, etc. [5][6][7] .
The equipment studied in this paper has been successfully adopted in the production of metal round tubes and innovatively designed for the existing production mode. The operation status of the original single process sheet equipment has been integrated into an automated production line mode. It can complete receiving and cutting round tubes and pairings according to requirements. The burrs on the edge of the round tube are removed into the inner edge and the material is charged to the chamfering process. Practice has proved that the automatic charging system of the designed metal round tube can meet the expected functional requirements. With stable overall operation, the automation and efficiency of the entire production line are improved, the labor cost is reduced, and the operational safety of workers is guaranteed. This also solves the problems of slow charging of metal round tubes and a large number of labors.
Conclusion
The automatic charging system of metal round tube designed in this paper is an integration and innovative design of the existing traditional production equipment, and can achieve the technical index of charging at a speed of 40-60 pieces/min for the chamfering process. At the same time, it can meet the automatic charging of products of the same specification and different sizes, and has certain technical promotion value among similar products.
The designed system can not only complete the above technical indicators, but also has the following characteristics: (1) Change the previous manual loading, manual transportation and manual charging modes. All the actions of the entire charging system are controlled by PLC, which saves the labor cost of the enterprise while monitoring and commanding the operating status and data of the system, etc.; (2) The modular design is easy to ensure the continuous and stable operation of the equipment, and the maintenance is simple and convenient, thereby reducing the cost of the enterprise; (3) Advocate low-carbon and environmentally friendly operation. Most of the system adopts air cylinder and mechanical transmission technology, which has high operational reliability. It can make the equipment stay in the best operating condition and realize zero-emission production. | 3,063.2 | 2021-01-01T00:00:00.000 | [
"Engineering",
"Materials Science"
] |
Abnormal road surface detection using wheel sensor data
In this manuscript we investigate methods for abnormal road surface detection using 3D force sensors implanted into the wheels of a vehicle. This research is realized as a collaboration between the Hungarian Institute of Technical Physics and Materials Science (MFA), Institute for Computer Science and Control (SZTAKI) and the department of Numerical Analysis of Eötvös Lóránd University (ELTE). The sensor in question was created by researchers at MFA. The hardware’s technical description will not be discussed here in detail, rather we focus on the sensor’s applications and the signal processing methods needed to implement them. Nevertheless we provide a basic overview of the sensor and the measurements that it produces below. A single sensor has four output bridges, which measure a change in resistance when the sensor is subjected to some outside force. A simple (albeit not perfect) relationship between the forces acting on the sensor and the produced outputs is described by
Introduction
In this manuscript we investigate methods for abnormal road surface detection using 3D force sensors implanted into the wheels of a vehicle.This research is realized as a collaboration between the Hungarian Institute of Technical Physics and Materials Science (MFA), Institute for Computer Science and Control (SZ-TAKI) and the department of Numerical Analysis of Eötvös Lóránd University (ELTE).
The sensor in question was created by researchers at MFA.The hardware's technical description will not be discussed here in detail, rather we focus on the sensor's applications and the signal processing methods needed to implement them.Nevertheless we provide a basic overview of the sensor and the measurements that it produces below.
A single sensor has four output bridges, which measure a change in resistance when the sensor is subjected to some outside force.A simple (albeit not perfect) relationship between the forces acting on the sensor and the produced outputs is described by where F x , F y and F z are the different forces acting on the sensor and the ∆V directions denote the measured changes in resistance at each bridge.It is important to emphasize, that the forces in (1) refer to the forces acting on the sensor itself, the relationship between the forces acting on the tyres of the vehicle and the sensor's output is much more complicated.
The wheel sensors are located on the inner wall of the two front tires of the test vehicle (one sensor on each side).Because of this, the output signals are produced in response to tyre deformation.When the vehicle is in motion, the forces acting on a single point of the tyre (and causing deformation) depend on the wheel angle, thus the produced output signals are quasi-periodic.Figure 1 illustrates the signals generated at each bridge of the sensor.
A single period corresponds to a full rotation of the tyre.Since the sensor is most-excited when it is close to the ground, the resulting periods produce quasi-compact signals.The quasi-periodic and quasi-compact behavior of the wheel sensor signals make them very similar to many biological signals such as ECG.This similarity will be later exploited in the introduced signal processing algorithms.
The discussed sensor is well suited for the detection of road surface abnormalities, because of the direct relationship between tyre deformation and the output signals.The detection and subsequent classification of road abnormalities is a well researched [3] and important topic.Gathering and sharing information about road quality can decrease maintenance costs and several recent information sharing frameworks [2, 1, 3] have been proposed for this purpose.
In this report, we show through experiments that the investigated wheel sensors are indeed well suited to detect road surface abnormalities.We propose, discuss in detail and compare several abnormality detecting algorithms.
The rest of this report is organized as follows.In section 2.1 we discuss the preprocessing steps applied to the output signals of the wheel sensor.We then describe naive approaches with well-known classification schemes in 2.2.The main findings of this manuscript can be found in sections 2.3 to 2.5.We discuss an appropriate way to model the output of the wheel sensor using socalled adaptive Hermite-functions [8] in 2.3.Through an experiment, we then demonstrate how adaptive Hermite-functions can be applied for road surface abnormality detection in 2.4.Finally, in section 2.5, we combine the previous findings into a robust classification scheme utilizing a state-of-the-art neural network architecture called VP-NET [7].The conducted tests, their results and subsequent discussion can be found in sections 3 and 4.
Road Surface Abnormality Detection with Wheel
Sensor Data In the following sections we detail several approaches for road abnormality detection based solely on wheel sensor measurements.
Preprocessing and data description
In the first section of this report we observed the quasi compact and quasi periodic nature of the wheel sensor data.In order to use wheel sensor based signals for surface abnormality detection, we analyze the properties of each full period (corresponding to a full rotation of the tyre), thus we need to segment the measurements.The segmentation algorithm used to produce the below results is based on the ECG-segmentation method described in [9], however new steps and various new parameters had to be introduced to adapt the method to wheel sensor data segmentation.The specifics of the segmentation algorithm will not be detailed here, as currently the test vehicle is being equipped with accurate wheel-angle measuring sensors, making any subsequent segmentation obsolete.
Once the data from the different bridges of the wheel sensor (see Figure 1) has been segmented, we can label each period as "normal" or "abnormal" using our ground truth data.That is, if some acceleration data which has been detected as caused by surface abnormality occurred during the current period, the entire period is labeled "abnormal".Ground truth generation is described in section 3.
Because of the imperfect nature of the segmentation algorithm and noise present in the measurements, the first and last points of a period of wheel sensor data may not be equal.In order to preserve the quasi-compact property of each period, we subtract the line connecting the first and last values of the period.
The number of data points which make up a period changes with the vehicle speed.For the easier handling and storage of the data, zero padding is applied to each segmented period.The maximal length of a period is identified as 500 data points, any periods longer than this (for example if the vehicle stood still for sometime) are disregarded.Periods of fewer than 500 data points, are zero padded to match this length.An example period after the above preprocessing steps labeled "normal" and another one labeled "abnormal" are given in Figure 2.These preprocessed periods will be referred to as "samples" henceforth.The samples are then standardized and their order is randomized.Finally, the samples are split into training and test sets.The properties of these sets are discussed in section 3.
Road abnormality detection with well-known classifiers
Once the wheel sensor signals have been preprocessed, we can utilize classification schemes to identify the samples corresponding to abnormal road conditions.In order to provide a benchmark result for more sophisticated classification approaches, an SVM classifier using Gauss-kernel was trained and tested with the samples.
Well known classifiers such as fully connected neural networks and convolutional neural networks were also implemented and used to classify the wheel sensor data.The networks considered here all used the binary cross-entropy loss function and were trained using the powerful ADAM optimizer [10].The exact number of layers and neurons per layer was determined through a grid search of the hyper-parameter space.The best performing network architectures are detailed for each case in section 3.
Modeling wheel sensor data using adaptive Hermitefunctions
The main assumption for wheel sensor based road abnormality detection is that samples corresponding to abnormal road conditions will contain more noise than those measured on a normal surface.Comparing noise levels on the preprocessed samples however is problematic, because (especially at high velocity) the signals from the wheel sensor contain high frequency components.One way to measure noise levels would be to model the samples using smooth functions, subtract the approximation from the measured sample and check the noise levels of the residual.Below we briefly describe adaptive Hermite-functions as introduced in [4] and provide insight into why this function system is especially well-suited to model wheel sensor data.
Let us denote the m-th Hermite-polynomial by h m (x), (m ∈ N).These polynomials are orthogonal on the weighted Lebesgue-space L 2,w (R), where ( Using the Hermite-polynomials we can acquire the so-called Hermite-functions These functions provide a (complete) orthonormal function system on L 2 (R) and so Next we detail some properties of the Hermite-functions, which make them particularly suitable for the approximation of quasi-compact signals.The first few Hermite-functions are depicted on figure 3.
• Hermite-functions tend quickly to zero as the argument increases: • Hermite-functions can be calculated with a (stable) second order recursion: • The derivative of Φ m can be expressed with Φ m and Φ m−1 : Taking the affine transformations of Hermite-functions yields further complete orthonormal systems which retain the useful above properties.Specifically, consider the functions Then, the function system √ λΦ t,λ m , (m ∈ N) is also orthonormal and complete on L 2 (R), thus for the partial sums S t,λ m f holds.We refer to these functions as adaptive Hermite-functions [4] henceforth.The m-th partial sum, S t,λ m f can also be thought of as the projection of f onto the subspace spanned by the first m adaptive Hermite-functions.This subspace is fully determined by the dilation and translation parameters λ > 0 and t ∈ R. For a fixed function f ∈ L 2 (R), and a fixed dimension m ∈ N, the error functional always has a local minimum [4].In order to get the best possible approximation for a fixed m, we need to minimize (7) with respect to t and λ.
In applications the function f , (in our case a preprocessed sample, see Figure 2) is given as a vector of discreet values.We can approximate such an f ∈ R N , N ∈ N with the linear combination of the first m discretely sampled adaptive Hermite-functions by where the components of c ∈ R m are referred to as linear parameters and the k-th column (ψ t,λ k ) of Ψ t,λ ∈ R N ×m is the discretized version of the adaptive Hermite-function Φ t,λ k (x), (x ∈ R, k = 1, . . ., m).Since the approximation depends on the λ dilation and t translation parameters in a nonlinear way, we will refer to these as nonlinear parameters.For fixed nonlinear parameters, the linear parameters can be expressed as where Ψ + t,λ denotes the Moore-Penrose pseudo inverse, and thus the projection of f onto the subspace spanned by the first m discretely sampled adaptive Hermite-functions can be expressed by We note that if we choose the sampling points as the (N real) roots of Φ t,λ N (x), then the resulting sampled adaptive Hermite system will have discrete orthogonality.The difference between the signal f and its approximation P t,λ f is called the residual and can be expressed by Similarly to (7), our goal is to find the nonlinear parameters λ > 0 and t ∈ R, such that the error functional e(c, t, λ) assumes a local minimum, where the operator P ⊥ t,λ := (I − Ψ t,λ Ψ + t,λ ) projects onto to the otrhogonal complement of the subspace spanned by the columns of Ψ t,λ .The operator P ⊥ t,λ is referred to as a variable projection operator [5] and since (for fixed nonlinear parameters) the linear parameters can be expressed via the pseudoinverse, the optimization task can be simplified by min c∈R m ,t∈R,λ>0 e(c, t, λ) = min t∈R,λ>0 Such optimization problems are called separable nonlinear least squares (SNLLS) problems.In [5] it is shown that the gradient of e(c, t, λ) can be given explicitly if the partial derivatives of the adaptive Hermite-functions are known with respect to the nonlinear parameters.We note that one could use any linearly independent function system instead of adaptive Hermite-functions, however because of the reasons highlighted above these functions are suitable for modeling wheel sensor data.
We can now acquire the so-called residuals ("flattened" wheel sensor samples) with the following steps: 1. Solve (13) to determine the optimal dialation λ * and translation t * parameters for the given sample f using a gradient based optimization method, 2. Approximate f with P t * ,λ * f , (10), 3. Acquire the residual f − P t * ,λ * f , (11).
Finally we note that adaptive Hermite-functions can be further generalized by adding new parameters to the weight function w(x) := e −x 2 [8].We would like to explore approximations of wheel sensor data with these so-called weighted Hermite-systems in a future work.
Road abnormalities and the residual signal
As stated in 2.3, our main assumption regarding road abnormality detection using data from the wheel sensor was that samples corresponding to abnormal road conditions will contain more noise than those measured on a normal surface.In order to empirically verify this hypothesis, we randomly selected and examined 100 samples from each class (normal and abnormal).To estimate noise levels, we looked at the standard deviation of each sample.That is, for a sample f ∈ R N , (see figure 2), we calculated where µ is the mean of the sample f .In order to justify modeling the samples using adaptive Hermite-functions and examining the noise levels in the residuals (11), we also measured the standard deviation of the residuals acquired from the same samples.The results of the investigation can be seen on figure 4. On the figure, the standard deviation of samples recorded on normal road surfaces are colored blue, while the abnormal samples are colored red.Even though noise levels of normal samples seem to be generally less than those of abnormal samples, when the deviation is compared on the samples themselves (top of figure 4), the classes cannot be separated by a simple noise threshold.On the other hand, when noise levels were compared on the residuals (bottom of figure 4), the standard deviations of normal and abnormal cases can be easily separated using a threshold.A possible explanation as to why the noise levels of residuals can be separated more easily than the noise levels of the samples themselves follows the intuition that at high speeds, (which would occur more often on normal road surfaces), higher frequency noise-like components appear in the samples.This increases their standard deviation thus causing an overlap in the classes' noise levels.On the other hand, the residuals are created by subtracting a smooth approximation from the samples ( 11) which (if the approximation is precise enough) removes any high frequency components appearing in the signal, but has little effect on the noise.
Even though the above experiment empirically verified our main assumption on the noise levels of the different classes, comparing the standard deviation of residuals does not lead to a perfect result as can be seen on figure 4. To overcome this a more sophisticated, machine learning based approach is utilized.
Classification with VP-NET
In this section we describe the application of VP-NET to the road abnormality detection problem.VP-NET is a special neural-network architecture introduced in [7] containing so-called variable projection layers.These layers are capable of solving SNLLS problems (13) and passing the results to a conventional neural network.VP-layers have several modes of operation.They are capable of passing linear parameters, nonlinear parameters, approximations, or residuals to lower layers.
Formally, the different versions of VP-layers can be expressed by the below equations.Let f ∈ R N , N ∈ N be an input sample and m ∈ N. Furthermore let Ψ µ ∈ R N ×m , µ ∈ R p , p ∈ N be a matrix whose columns contain some discretized version of a linearly independent function system, where the system depends (in a nonlinear fashion) on the parameter vector µ.Then, a VP-layer solving the SNLLS problem and passing the optimal linear parameters can be given as These parameters can then be used to solve classification problems.This use case can be regarded as a dimension reduction and automatized feature extraction step.For regression tasks it might be more appropriate to pass the approximation (projection onto the column space of Ψ µ ) of f to the lower layers: When detecting road abnormalities, the experiments detailed in 3 show that the VP-layers performed best, when they passed on the residual signal: These results were in line with the reasoning given in 2.4.A visual representation of VP-NET is given on figure 5.
Input Hidden layers
Output layer In theory, convolutional layers equivalent to VP-layers could be constructed [7], however as can be seen in section 3, the application of VP-NET is more appropriate for the detection of road abnormalities.The reasons behind this could be traced back to several important differences between VP-NET and convolutional networks.Firstly, the optimization task is usually a lot simpler when using VP-NET.Instead of having to learn the appropriate kernel weights (which could be numerous), the VP-layer only has to optimize the nonlinear parameter vector µ.In our case for example, when the columns of Ψ µ contain discretized adaptive Hermite-functions, the parameter vector µ only contains only two components: µ := (t, λ) ∈ R 2 .By contrast the best performing convolutional network used a kernel size of 25 making the training process and the network more complicated.Another advantage of using VP-layers is that unlike the the kernel weights, the nonlinear parameters of a VP-layer can contain interpretable information.In our case for example, the dilation parameter is related to the speed of the vehicle.
Tests and Results
In order to verify the results of any wheel sensor based abnormality detection algorithm, we need to establish some ground truth data.In other words, we need to label the timestamps of the measurements which correspond to times when the vehicle encountered abnormal road conditions.This can be done by creating measurements in a controlled environment, where road surface abnormalities and the timestamps when they occur are known in advance.Although there are plans to conduct such measurements using our test vehicle in the future, in this report we relied on automatically labeled measurements.Automatizing ground truth generation can have several benefits, including access to more data for training and testing purposes.Recently many successful road surface abnormality detection approaches have been proposed [1,6,11,3].Most of these approaches rely either solely on acceleration data (along the X and Z axes), or on various sensor fusion strategies.The acceleration based algorithms usually utilize some version of the so-called Gaussian background model in order to detect road surface abnormalities.In this work we use the algorithm introduced in [3] for automatic ground truth generation.The robustness of the method is well reflected in the fact, that it is even suitable for use when the vibration acceleration is measured by a mobile device.
Two measurements were used for our experiments.They were acquired using a modified Nissan Leaf test vehicle provided by SZTAKI.The measurements were recorded on the public roads of Budapest, with one measurement having been recorded on a newly built road and the other in an old parking lot. Figure 6 shows the labeled vertical acceleration data from the measurements.For the experiments described below we used the signals from the second bridge of the wheel sensor in the front right tyre of the vehicle, however preliminary investigations show similar results for all of the available signals.The measurements used contained roughly the same amount of normal and abnormal samples.The results show that each of the examined classifiers was successful in identifying abnormal road conditions from the wheel sensor measurements.The neural network based classification schemes required a fine tuning of hyperparameters, such as the number of layers and the number of neurons present in each layer.Finding the optimal hyperparameters was done via grid search.In order to ensure a "fair contest", the hyperparameters present in each of the classifiers were evaluated over the same search space.The convolutional networks and VP-NET configurations each contained a single convolutional/VP-layer.The specifics of each best performing network type are given in the below tables.The notation [a, b, c] means that the network consisted of 3 fully connected layers, with a, b and c neurons respectively.Based on the above results, VP-NET provides the most accurate wheel sensor based road abnormality detection.Furthermore the use of VP-NET is preferred because of the simplicity of the VP-layer compared to a convolutional layer, which makes it more suitable for low-level implementations.
Conclusion and future plans
In this manuscript we successfully demonstrated that accurate road abnormality detection based on signals from MFA's 3D force measuring sensor is possible.We presented an experiment that showed the connection between abnormal road conditions and the level of noise present in the residual signal (11).We then experimented with different classification schemes and found that VP-NET classifiers outperform the other candidates in both accuracy and simplicity.
There are several proposed next steps to continue this research.For example, ensemble methods could be created to further increase the accuracy of the classification.A VP-NET classifier could be used on signals from each bridge of the wheel sensor to identify road abnormalities, then some ensemble classification scheme could be applied to the output of the classifiers.A low level implementation of the classification schemes could also be created enabling on-line testing of the methods.
Figure 1 :
Figure 1: Signals produced by the wheel sensor.
Figure 3 :
Figure 3: The first few Hermite-functions.Their shapes closely resemble wheel sensor data.
Figure 4 :
Figure 4: Noise levels in the samples (top), and in the residuals (bottom).
Figure 6 :
Figure 6: Abnormal road surfaces detected in the acceleration data (red markings).Newly built road (left), old parking lot (right).
Table 1
shows the number of samples in each class.
Table 1 :
Sample numbers and ratio in each class.The different classification algorithms were trained on identical training sets and were evaluated on identical test sets.The training set contained 413 (80%) randomly selected samples, the remaining 104 (20%) samples were assigned to the test set.The examined algorithms were evaluated based on classification accuracy given as a percentage.The results are shown in table 2
Table 2 :
Examined classification schemes and their accuracy.
Table 3 :
Best performing convolutional network and training specifics.
Table 4 :
Best performing fully connected network and training specifics.
Table 5 :
Best performing VP-NET network and training specifics. | 5,206.6 | 2021-01-01T00:00:00.000 | [
"Computer Science"
] |
Permeation of Therapeutic Drugs in Different Formulations across the Airway Epithelium In Vitro
Background Pulmonary drug delivery is characterized by short onset times of the effects and an increased therapeutic ratio compared to oral drug delivery. This delivery route can be used for local as well as for systemic absorption applying drugs as single substance or as a fixed dose combination. Drugs can be delivered as nebulized aerosols or as dry powders. A screening system able to mimic delivery by the different devices might help to assess the drug effect in the different formulations and to identify potential interference between drugs in fixed dose combinations. The present study evaluates manual devices used in animal studies for their suitability for cellular studies. Methods Calu-3 cells were cultured submersed and in air-liquid interface culture and characterized regarding mucus production and transepithelial electrical resistance. The influence of pore size and material of the transwell membranes and of the duration of air-liquid interface culture was assessed. Compounds were applied in solution and as aerosols generated by MicroSprayer IA-1C Aerosolizer or by DP-4 Dry Powder Insufflator using fluorescein and rhodamine 123 as model compounds. Budesonide and formoterol, singly and in combination, served as examples for drugs relevant in pulmonary delivery. Results and Conclusions Membrane material and duration of air-liquid interface culture had no marked effect on mucus production and tightness of the cell monolayer. Co-application of budesonide and formoterol, applied in solution or as aerosol, increased permeation of formoterol across cells in air-liquid interface culture. Problems with the DP-4 Dry Powder Insufflator included compound-specific delivery rates and influence on the tightness of the cell monolayer. These problems were not encountered with the MicroSprayer IA-1C Aerosolizer. The combination of Calu-3 cells and manual aerosol generation devices appears suitable to identify interactions of drugs in fixed drug combination products on permeation.
Introduction
Inhaled medicines compared to oral medication have the advantage of shorter onset times and increased therapeutic ratio due to reduced first pass effect and higher permeation across the epithelium [1]. Active pharmaceutical ingredients (APIs) can be delivered to the lungs by nebulizers, metered dose inhalers and dry powder inhalers, as single compounds or in a fixed dose combination [2]. Currently, most formulations are designed for local therapy of common respiratory diseases, such as asthma, chronic obstructive pulmonary disease (COPD), and cystic fibrosis (CF). However, systemic delivery of insulin has already entered the market, Afrezza is available for treatment of diabetes mellitus types I and II, and several types of molecules and peptides are in preclinical development.
For the development of new formulations it would be helpful to estimate permeation, metabolism and potential drug interference at the epithelium by in vitro screening systems. A recent study showed that the presence of salmeterol decreased the transport of fluticasone across Calu-3 cells [3], suggesting that interaction at the cellular level could partly explain the variable efficacy of fixed dose combinations in clinical trials compared to the same doses applied by single inhalers.
Permeation of drugs for oral delivery is assessed by application of the dissolved APIs to Caco-2 monolayers. Other types of cells, usually cell lines are used for pulmonal drug delivery [4]. For physiologically representative exposure, these cells are cultured at an air-liquid interface where cells are supplied with medium only from the basolateral side while the apical side is exposed to air. Calu-3 cells are most commonly used for the assessment of pulmonary permeability because they reached higher TEER values than measured in the rabbit airways and showed good correlation of permeability values with drug absorption from the rat lung in vivo [5][6][7][8]. Furthermore, drug release from disodium cromoglycate (DSCG)/polyvinyl alcohol (DSCG/PVA) microparticles in Calu-3 cells showed good correlation to suitable models [9]. Calu-3 cells are good models because they show similar transporter expression to respiratory cells [10,11]; protein expression of human lung tissue is highest for the organic cation transporter OCTN1, followed by multidrug resistance protein 1 (MRP1), breast cancer resistance protein 1 (BCRP1), ATP-binding cassette sub-family G member 2 (ABCG2), and organic anion transporter OATP2B1. Many inhaled compounds, for instance beclomethasone, budesonide, flunisolide, fluticasone, mometasone, salbutamol, and ipratropium, interfere with efflux pumps (MDR1/P-glycoprotein, MRP1, etc.) and organic cation transporters (OCT1-3, OC TN1, and OCTN2). OCTN1 and OCTN2 are expressed at high levels, OCT1 and OCT3 at moderate levels, and OCT2 at low levels in whole lung tissue [12]. Expression of MDR1/P-glycoprotein, OCTN1, OCTN2, PEPT2 was specifically documented in alveolar epithelial cells [6]. Calu-3 cells express OCT1, OCT3, OCTN1 and OCTN2 and peptide PEPT1/PEPT2 transporters, as well as MDR1/P-glycoprotein [13][14][15]. All proteins have been detected in Calu-3 cells in submersed culture and in air-liquid interface culture [13,16].
In order to mimic realistic transport and toxicity studies, air-liquid interface culture should be combined with application of aerosols [17]. A variety of elaborate exposure systems have been described for cellular exposure to nebulized and dry aerosols, for instance CULTEX [18,19] and ALICE CLOUD system [20]. However, these systems need specialized equipment and know-how, may lead to particle-dependent differences in deposition, and cannot easily be adapted to the different forms of aerosol applications [21]. Animal studies are the gold standard in the preclinical evaluation of pharmaceutical formulations and intratracheal instillation is the most commonly used application method because delivered doses by whole body exposure or nose-only inhalation vary due to differences in breathing, deposition on the furs, and oral uptake by licking [22]. The use of the same delivery devices as for animal experimentation might allow a better comparison of in vitro data and results obtained in animals because particles that are being delivered are of comparable sizes in both exposures. High local drug concentrations are a problem but occur also in intratracheal instillation [23]. MicroSprayer IA-1C Aerosolizer for liquid aerosols and DP-4 Dry Powder Insufflator for powder aerosols have been used for intratracheal delivery of nanoparticles and toxicants to mice and rats [24][25][26][27]. The MicroSprayer has also been used in cellular studies [21,[28][29][30][31][32][33][34][35][36].
In order to find out whether these devices could be used in cellular experiments we compared different exposure models based on Calu-3 cells regarding transport of APIs in different aerosol formulations. Sodium fluorescein was chosen as paracellular transport marker with no distinct directionality while rhodamine 123 served to assess the effect of the MDR1/P-glycoprotein efflux pump. As examples for relevant drugs, budesonide and formoterol fumarate were chosen. The glucocorticoid budesonide and the long-acting beta-adrenoreceptor agonist formoterol fumarate are routinely used drugs in the treatment of obstructive lung diseases. Budesonide as well as formoterol fumarate are sold as single drugs in various pressurized metered dose inhalers and dry powder inhalers. The fixed dose combination product is marketed by AstraZeneca under the trade name Symbicort.
Cell culture
Calu-3 cells were obtained from the American Type Culture Collection (ATCC, HTB-55, LGC Standards GmbH, Wesel, Germany). Cells were cultured in 90% Minimum Essential Medium (MEM) with Earle's salts, 10% fetal bovine serum, 2 mM L-glutamine and 1% penicillin-streptomycin (PAA Laboratories and Lifetechnologies, Vienna, Austria) at 37°C in humidified air atmosphere containing 5% CO 2 in 175 cm 2 cell culture flasks (Greiner Bio-One GmbH, Rainbach, Austria). 0.5 x 10 6 cells (passage 32-38) were seeded per 12-well Transwell insert. To study the influence of material properties on the system, membranes made from different materials (polycarbonate, polyester, polyethylene terephthalate) in pore sizes of 0.4 μm and 3 μm obtained from Corning (Szabo-Scandic, Vienna, Austria) and Greiner Bio-One GmbH, were used. Cells were cultured in submersed conditions with 500 μl medium in the apical compartment and 1500 μl in the basolateral compartment. Medium was changed every 2 or 3 days. For air-liquid interface culture, the cell culture medium was removed either one day post-seeding or for 3 days after the cells had reached a transepithelial electrical resistance value >700 O Ã cm 2 in submersed culture. In air-liquid interface culture, medium (600 μl) in the basolateral compartment was changed every 2-3 days. For safety reasons, exposures with the compounds were performed in a HERAsafe KS 9 clean bench (Thermo Scientific, Vienna, Austria) equipped with UPLA filters of both filter grades U15 and H14.
Transepithelial electrical resistance (TEER)
TEER values were determined for all cultures every 2-3 days with an EVOM STX-2-electrode (World Precision Instruments, Berlin, Germany). 0.5 ml MEM were added to the apical and 1.5 ml MEM to the basolateral compartment for TEER measurements. Prior to the reading cells were equilibrated for 30 min in the incubator. TEER values were calculated as follows: TEER ðO Ã cm 2 Þ ¼ ðSample À blank resistance; given in OÞ Ã membrane area; given in cm 2 Blank resistance is defined as the resistance of the membrane without cells and the membrane area for 12-well inserts is calculated to be 1.12 cm 2 /well. TEER values were also determined at the beginning and the end of the transport studies using Krebs-Ringer buffer instead of medium. When Krebs-Ringer buffer was used TEER values were~80 O Ã cm 2 lower than for cell culture medium.
Cytotoxicity by formazan bioreduction
Bioreduction to formazan was used as an indication for viable monolayers. CellTiter 96 Aqueous Non-Radioactive Cell Proliferation Assay (Promega, Mannheim, Germany) was used according to the manufacturer's instructions. To all wells the combined MTS/PMS solution (200 μl + 1 ml medium) was added. Plates were incubated for 2 hours at 37°C in the cell incubator. Absorbance was read at 490 nm on a plate reader (SPECTRA MAX plus 384, Molecular Devices, Biberach, Germany).
Membrane damage according to lactate dehydrogenase release
The CytoTox-ONE Homogeneous Membrane Integrity Assay (Promega, Mannheim, Germany) was used according to the instructions given by the producer and fluorescence was recorded with an excitation wavelength of 544 nm and an emission wavelength of 590 nm. After subtraction of the blank value the average fluorescence from the samples was normalized to the maximum LDH release (lysis control). Transport studies 0.5 x 10 6 Calu-3 cells (passage 32-38) were seeded per membrane and different exposure systems were used (Fig A in S1 File). To discriminate between the different exposures, the following terminology is used. Cultures with cells supplied with medium only from the basolateral side are termed air-liquid interface culture. In submersed liquid exposure (SLE) cells are cultured in submersion and exposed with compound dissolved in buffer. In the air liquid exposure (ALE) cells are cultured at an air-liquid interface and the compound dissolved in buffer is applied to the cells. For air-liquid interface deposition (AID) cells are cultured at an air-liquid interface and exposed to the compound applied as liquid aerosols by MicroSprayer IA-1C Aerosolizer (AID_M) or as powder aerosols by DP-4 Dry Powder Insufflator (AID_D). For comparison of the different exposure systems Calu-3 cells cultured for 11 days on 3 μm 12-well insert (Greiner Bio-One) were used.
Compounds were applied in Krebs-Ringer buffer (142 mM NaCl, 3 mM KCl, 1.2 mM MgCl 2 , 1.5 mM K 2 H 4 PO 4 , 4.2 mM CaCl 2 , 25 mM NaHCO 3 , 4 mM glucose, 10 mM Hepes, pH 7.4). For SLE and ALE exposures the apical compartment was filled with 500 μL and the basolateral compartment with 1500 μL. Concentrations were 10 μg/ml (26 μM) fluorescein sodium, 100 μg/ml rhodamine 123 (262 μM), 100 μM budesonide and 1 mM formoterol fumarate. For AID studies the basal compartment was filled with 700 μl, and 200 μl of drug dissolved in Krebs-Ringer buffer were sprayed on each Transwell insert using the MicroSprayer IA-1C Aerosolizer (AID_M exposure). 1 mg (2.66 μmol) fluorescein sodium, 1 mg (2.63 μmol) rhodamine 123, 1 mg (2.3 μmol) of budesonide, 1 mg (2.9 μmol) formoterol fumarate as single compound or 1 mg Symbicort 160/4.5 Turbuhaler powder (AstraZeneca GmbH) consisting of 0.46 μmol budesonide and 0.017 μmol formoterol were sprayed on the Transwell Inserts using the DP-4 Dry Powder Insufflator (AID_D exposure). To identify cytotoxicity by high compound concentrations in the exposures with DP-4 Dry Powder Insufflator, 100 μl of a suspension (1 mg in 200 μl Krebs-Ringer buffer) of the respective compounds was applied to the cells. The dose was chosen based on delivery rates in animals [37] with the limitation that no complete dissolution could be obtained. Viability assessed by MTS assay (cytotoxicity) did not show a significant decrease of viability, release of LDH or significant decrease of TEER values after 2h (data not shown). 100 μl samples from the basolateral compartment were taken at 0-30-60-90-120 min and replaced with pre-warmed Krebs-Ringer buffer. Well plates were shaken using an orbital shaker at stirring rate 200 rpm and 37°C for the entire exposure time. At the end of the SLE and ALE studies the content of the basolateral compartment and 10 μl of the apical compartment were collected. After the AID studies 100 μl of Krebs-Ringer buffer for the fluorescent dyes and 100 μl DMSO for budesonide and formoterol was added to the apical chamber. The total volume of this solution was determined and this value minus the added 100 μl used for calculations of drug concentrations. The entire content of the basolateral compartment and 10 μl of the apical compartment were collected. In the initial experiments, after the last sample was taken, cells were lysed with 20 μL Triton-X 100 and 70% ethanol (50:50) for 30 min under agitation using an orbital shaker. The contents of the basolateral and the apical compartments were pooled, filtered and either determined immediately by fluorescent detection or stored at -20°C in HPLC vials until measurement by HPLC. Lysis was omitted in subsequent experiments because the amount of budesonide in the cells was very low (0.96 μg) related to the total recovered amount of 19.3±0.7 μg. It was not expected that these amount would strongly affect P app values, which are based on the time dependency of the transport across the monolayer.
For the determination of the permeability coefficient (P app ) the following equation, where dQ/dt is the flux across the cell monolayer (ng/sec), A the surface of the monolayer (cm 2 ) and C the initial concentration in the apical compartment (ng/ml), was used: In the case of AID where the drug was applied as powder no P app values were calculated because of non-linear transport of the compounds and unknown initial volume in the apical compartment.
Application devices
The MicroSprayer IA-1C Aerosolizer (PennCentury Inc., Wyndmoor, PA) was used to mimic nebulization of the compounds. The device consists of a thin, flexible, stainless steel tube measuring 0.64 mm in diameter and 50.8 cm in length attached to the light, hand-operated, highpressure syringe FMJ-250. A unique patented atomizer at the very tip of the tube generates the aerosol with a mass median diameter of 16-22 μm (http://www.penncentury.com/products/ IA_1C.php). The device was fixed at a distance of 11 cm between tip of the MicroSprayer and the rim of the exposure plate. Inserts were transferred to a separate (exposure) plate to avoid contamination of the adjacent inserts and 200 μl of the aerosol were applied per well (Fig B, a in S1 File). After the treatment the insert was replaced into the original plate for transport studies. The device was cleaned with 70% ethanol and aqua dest. at the end of the experiments and dried at 60°C overnight.
The DP-4 Dry Powder Insufflator (PennCentury Inc., Wyndmoor, PA) was used to simulate the deposition by a dry powder inhaler and was fixed at a distance of 3-10 cm between tip of the tube and the rim of the exposure plate. Two delivery tube lengths were tested; one 52.3 cm and the other 7.3 cm long. In contrast to the delivery tube used for in vivo application, the delivery tube had a straight form. The shorter delivery tube produced more reproducible results and was used for the subsequent experiments (Fig B, b in S1 File). Inserts were transferred to a separate plate to avoid contamination of the adjacent inserts and 1 mg of the powder weighted into the sample chamber was applied. After the treatment the insert was returned to the original plate. In pilot experiments the influence of the distance between the end of the delivery tube and the cells as well as the role of repeated actuation of the syringe was studied. Damage of monolayer integrity was interpreted as difference between TEER values before and after the experiments > 100 O Ã cm 2 . For the experiments the set-up with shorter tube and longer distance between tip and cells was chosen. Between the applications the device was cleaned with a compressed air cleaner spray and in addition by piercing with a fine wire. After the experiments it was cleaned with 70% ethanol and aqua dest. in addition and dried at 60°C overnight.
Particles that were delivered by the DP-4 Dry Powder Insufflator were analyzed by brightfield microscopy. The particles were applied to a glass slide instead of an insert and viewed at an upright microscope (BX-51, Olympus, Vienna, Austria) at magnification x10 to demonstrate the particle distribution pattern and at x40 to determine particle sizes. Sizes were measured using Cell^D Imaging software (Olympus).
Quantification
Fluorescent samples were detected at excitation wavelength of 485 nm and emission wavelength of 520 nm for sodium fluorescein and rhodamine 123. Samples were diluted with Krebs-Ringer buffer and measured with a FLUOstar Optima (BMG Labtech, Graz, Austria). Linearity was proven for 0.12-10 μg/ml sodium fluorescein and for 1.25-100 μg/ml rhodamine 123.
Budesonide and formoterol fumarate were quantified by high-performance liquid chromatography electro spray ionization mass spectrometry (HPLC-ESI-MS) using an Acquity UPLC H-Class system (Waters, Vienna, Austria) equipped with a photodiode array detector and a single quadrupole detector. As stationary phase a Superspher 100 RP-18e column (125mm x 4mm i.d, 4 μm particle size) was used. Mobile phase was composed of acetonitrile (A) and 10 mM ammonium acetate buffer pH 3.0 (B) using the following gradient program: 2% A (0-0.5 min), 2-95% A (0.5-6.0 min), 2% A (6.1-10.0 min).) At a flow rate of 0.6ml/min, retention times were 7.1 min and 5.6 min for budesonide and formoterol, respectively. Mass spectrometric detection was operated in single ion recording (SIR) mode using m/z 345.1 for formoterol and m/z 431.2 for budesonide. Capillary voltage was set to 0.5 kV and 2.5 kV and cone voltage to 25 V and 20 V, for formoterol and budesonide respectively. The limit of detection for both, budesonide and formoterol fumarate was determined with 20 ng/ml; linearity was proven for budesonide and formoterol fumarate in the range of 20 ng/ml to 500 ng/ml. Krebs-Ringer buffer did not interfere with the measurements.
Immunocytochemistry
For detection of mucus production, the membranes were excised from the plastic insets and washed 3 x 5 min with PBS. Subsequently, membranes were fixed with 4% paraformaldehyde for 20 min at RT and washed again 3 x 5 min with PBS. After permeabilization with PBS containing 0.2% Triton X-100 for 2h at RT, blocking with 10% normal goat serum (Zymed Medical Product GmbH, Vienna, Austria) for 30 min at RT, incubation with mouse anti-mucin 5AC ([45M1], Abcam, 1:200, Cambridge, UK) or normal mouse Immunglobulin G (DAKO diagnostic, Hamburg, Germany) for negative controls was performed at 37°C for 60 min followed by goat Alexa Fluor 488-labelled anti-mouse IgG antibody (1:400, Life technologies, Vienna, Austria) again at 37°C for 60 min. Nuclei were counterstained with 1 μg/ml Hoechst 33342 (Life technologies) for 15 min at RT. Incubations were performed under light protection and between the antibody incubations the membranes were rinsed 3 x 5 min in PBS. Subsequently, all membranes were mounted in fluorescence mounting medium from DAKO and stored in the dark. Cells were viewed at a 510 LSM Meta (Zeiss, Vienna, Austria) using excitation at 405 nm and detection with a BP 420-480 nm filter for the nuclear stain. Binding of the anti-mucin antibody was recorded at excitation at 488 nm and detection with a BP 505-550 nm filter.
For quantification of mucus production after different duration of air-liquid interface culture images of anti-mucin 5AC staining were taken with the same settings at the LSM510 Meta and mean intensities in the different channels (blue, green) determined using Image J 1.49v software. For each condition, 11 days and 3 days of air-liquid interface culture and antibody negative control, 800 cells were evaluated. Representative images that were analyzed are shown in Fig C in S1 File.
Statistics
Data from ! three independent experiments were subjected to statistical analysis. These values are represented as means ± S.D. and have been analyzed with a one-way analysis of variance (ANOVA), followed by a Tukey-HSD post hoc test for multiple comparisons (IBM SPSS statistics 19 software). Independent t-test and Levine's Test for equality of variances analyzed the differences between two mean values. The results with p-values of less than 0.05 were considered to be statistically significant.
Results
To allow the comparison of our data with the Calu-3 models used in other studies the influence of the duration of the air-liquid interface culture and of different membranes was determined ( Table 1). Characteristics of the Transwell inserts from Corning and Greiner Bio-One (product information) are provided in S1 Table. Aerosols generated by MicroSprayer IA-1C Aerosolizer and DP-4 Dry Powder Insufflator were assessed for deposition rate, effects on the Calu-3 monolayer, and particle size (dry powder). (Table 1). Since the time to reach these TEER values was also more variable for 0.4 μm, in the transport studies membranes with 3 μm pore size were used. TEER values were not influenced by differences in membrane materials (not shown), and different protocols of air-liquid interface culture (3 versus 11 days prior to the experiments) did not result in significantly different TEER values (538±105 vs. 461±99 O Ã cm 2 ). Mucin production after submersed culture and culture at an air-liquid interface for 11 days and for 3 days was visualized by anti-mucin5AC staining. Secretory granules located at the apical side of Calu-3 cells were seen in air-liquid interface culture (Fig 1A and 1B) but not in Calu-3 cells in submersed culture (Fig 1C). Tile scans of confocal images showed considerable differences in the intensity of the anti-mucinAC staining between cells but image analysis of anti-mucin 5AC stained cells showed no differences in mean intensities between cells cultured at an air-liquid interface for 3 days versus 11 days prior to the experiments Fig D in S1 File). Means (RFU) in the green channel were 3629.88 ± 691.92 for 11 days air-liquid interface culture vs. 3695.33 ± 501.51 for 3 days air-liquid interface culture. Negative controls (background) showed an intensity of 0.28 ± 0.01. When normalized to intensity of the nuclear stain (blue channel) ratios of 0.54 ± 0.04, 0.53 ± 0.18, and 0.00 ± 0.00 were obtained for 11 days airliquid interface culture, 3 days air-liquid interface culture and negative control. Virtual serial sections of Calu-3 cells grown on the 3 μm membranes obtained by laser scanning microscopy as well as stained cryosections of cells on membranes confirmed that cells formed a monolayer and grew only on one side of the membrane (Fig D in S1 File). Similar to data by Zhang et al. [38] TEER values without cells (blank) did not differ between membranes with different pore sizes (125 ± 8 O Ã cm 2 for 0.4 μm and 116 ± 8 O Ã cm 2 for 3 μm).
Aerosol generation devices
Aerosols generated by MicroSprayer IA-1C Aerosolizer were deposited with an efficacy of 27 ± 3%, as shown previously [21]. The application of aerosolized medium did not induce significant decreases in TEER values of Calu-3 cells cultured at an air-liquid interface (Fig 2). The amounts of the compounds delivered by DP-4 Dry Powder Insufflator and applied as solution for ALE and SLE according to recovery at the end of the transport studies are listed in Table 2. Efficiency of delivery by DP-4 Dry Powder Insufflator was compound-specific and ranged from~3% to 28%. A variable part of the powder did not leave the sample chamber. When the sample chamber was weighed before and after application around 50% of the initial dose for fluorescein, but only 10-20% of Symbicort powder had been retained. Moreover, powder was lost during the spraying and did not deposit on the cells. Total amounts of compounds applied as dry powder in the apical compartment (μg) were lower for fluorescein, rhodamine 123 and formoterol (alone and as Symbicort 160/4.5). Conversely, considerably higher amounts of budesonide were applied as dry powder than as solution. The calculated drug concentration (μg/ml) was in the same order of magnitude only for the fluorescent dyes, the concentrations of the budesonide and of formoterol alone were much higher when applied with DP-4 Dry Powder Insufflator than as solution. This caused different ratio of budesonide and formoterol (in μg delivered); in ALE and SLE the Bud/Form ratio was 1:10.9 compared to 27.7:1 in the Symbicort formulation applied by DP-4 Dry Powder Insufflator. Sizes of the particles delivered by the DP-4 Dry Powder Insufflator are formulation dependent and have to be determined experimentally [37]. The visualization by bright-field microscopy (Fig E in S1 File) indicated that, in general, powders were well dispersed with agglomerates preferentially seen for fluorescein. Delivered single particles of fluorescein (1.1±0.3 μm), budesonide (3.2± 1.3 μm), and Symbicort (6.9±1.4 μm) presented a roughly spherical shape and formed agglomerates. These agglomerates were largest (up to 18 μm) for Symbicort. Rhodamine 123 and formoterol deposited as elongated crystals of 8.6±1.9 x 14.7±3.8 μm and 9.1±3.5 x 17.1±1.2 μm, respectively. Larger agglomerates were rarely seen.
Cellular compatibility was assessed for the DP-4 Dry Powder Insufflator by using clean air as negative control in syringe-based dry powder aerosol exposure systems as suggested by Garcia-Canton et al. [39]. This exposure induced significant decreases of TEER values in the exposed cells (Fig 2). On the other hand, no decrease in cell viability according to bioreduction to formazan or release of lactic dehydrogenase as indication for plasma membrane damage was seen.
Transport of dissolved compounds
When applied in solution P app values of all compounds were higher upon ALE than upon SLE (Table 3). P app values were highest for budesonide and lowest for the fluorescent dyes. Differences of P app values between SLE and ALE were much less pronounced for budesonide.
Co-incubation of budesonide and formoterol did not show changes in budesonide transport neither in SLE nor in ALE (Fig 3). However, formoterol, which was transported only at low rates across the Calu-3 monolayers, showed higher transport rates when applied together with budesonide in ALE but not in SLE. The effect was significant after 2 hrs (Fig 4).
Transport of aerosolized compounds
Since these parameters are difficult to control the amount of recovered sample (start concentration in apical compartment à volume + amount in the samples + concentration in both compartments à volume) was set as 100%. The transport rates of the fluorescent dyes, fluorescein and rhodamine 123, applied by MicroSprayer IA-1C Aerosolizer was lower than after application by DP-4 Dry Powder Insufflator (Fig 5) and an initial delay in the transport (lag phase) was seen only upon application by MicroSprayer IA-1C Aerosolizer, (Fig 5A). Dye transport
Lung Permeation of Drugs in Different Formulations
Transport of formoterol in the fixed dose combination Symbicort was significantly higher than when applied alone by DP-4 Dry Powder Insufflator (Fig 6). For budesonide no differences between application alone and in combination with formoterol were seen.
Discussion
This study demonstrated that, with some limitations, an exposure system consisting of manual devices for animal studies and Calu-3 cells in air-liquid interface culture could be used as screening tool for drug permeation in the preclinical assessment of formulations for oral inhalation. . TEER values in submersed culture reported elsewhere ranged between 500-1200 O Ã cm 2 [40][41][42][43][44][45][46], while they were 300-700 O Ã cm 2 in air-liquid interface culture [45,[47][48][49][50][51][52]. Consistent with data available in the literature [53] the membrane material did not influence TEER values in this study. Our Calu-3 cells also had similar TEER values when cultured on 3 μm pores and on 0.4 μm pores. This is in contrast to data published by Geys et al. who measured higher TEER values of Calu-3 cells on membranes with 0.4 μm pores than on membranes with 3 μm pores [46]. These differences, however, disappeared when cells were cultured for >5 days. The majority of studies [41,48,52], including this study, reported mucus production of Calu-3 cells only when cultured at an air-liquid interface, while only a minority of studies has demonstrated mucus production in Calu-3 cells in submersed culture [54,55]. Calu-3 cells have been switched from submersed culture to air-liquid interface culture after 24-48h in some studies and 2-5 days prior to the experiments in others [8,35,48,[56][57][58]. Our comparison between 11d of air-liquid interface culture and 3 days of air-liquid interface culture showed that 3d were sufficient to induce the phenotype reached after 11 days based on TEER values and induction of mucus production. The short time to switch from submersed to air-liquid interface condition is not surprising given that transcriptional changes of protein expression are generally observed 48h after stimulation (e.g. [59]). Furthermore, human bronchial epithelial cells showed different basal levels of cytokines at three days of submersed and air-liquid interface culture [60].
Aerosol generation device
As reported previously, delivery rates by the MicroSprayer IA-1C Aerosolizer in the selected set-up showed low dependency from the material that has been aerosolized; conventional Abbreviations: Form mix: formoterol when applied as Symbicort powder; Bud mix: budesonide when applied as Symbicort (n = 3). The total amount of drug applied to the cells was set as 100% and the transport rate normalized to a membrane area of 1 cm 2 . Asterisks indicate differences between application as single substance and as combination. compounds and nanoparticles in the size range from 20 nm to 200 nm showed similar deposition rates [29]. Aerosols generated from aqueous sodium fluorescein solutions were deposited with an efficacy of 27 ± 3%, of fluorescent polystyrene nanoparticles with an efficacy of 28 ±1.96% and of carbon nanotubes with an efficacy of 25±2.5% [21]. In contrast, delivery by DP-4 Dry Powder Insufflator showed considerable variations in delivery to the cells. These differences are linked to the properties of the aerosolized powders and are also seen in dry-powder inhalers. For instance, 80% of the metered dose in Symbicort Turbuhaler is delivered to the mouthpiece of the device. Particle size, shape, surface texture, contact area, surface energy, hygroscopy, relative humidity, and electrical properties are known to influence the delivery rate [61]. Furthermore, in our study also the distance between tip of the device and cells had an impact on aerosol delivery. It is known that emitted fractions of the DP-4 Dry Powder Insufflator are independent of the loaded amount but influenced by physicochemical properties of the formulation [37,62]. The observed differences are, therefore, not unexpected. Delivery of high amounts of APIs and potential cell damage by shear stress may cause concerns in the delivery by manual aerosol generation devices. For permeation studies traditionally relatively high drug concentrations are used in order to detect the drug in the basolateral compartment [63]. Due to the handling of the device even higher concentrations were used for the applications with DP-4 Dry Powder Insufflator. While no obvious cytotoxicity was seen by bioreduction to formazan and LDH release, TEER values were decreased when the DP-4 Dry Powder Insufflator was used. TEER values in these samples were below 300 O Ã cm 2 and might not guarantee an intact barrier function of Calu-3 cells [64]. Choosing a greater distance between device and cells could prevent decreases of TEER values. However, the detection threshold of the compound in the basolateral compartment limits the distance between cells and device. This problem is particularly relevant when formulations contain drugs in highly different amounts and with different permeability. In this study the low amount of formoterol in Symbicort was the limiting factor for the distance between device and cells.
Permeability and transport
P app values of fluorescein reported in this study are similar to values published by other groups (0.1 x 10-6 cm/s for SLE and 0.1 x 10 −6 cm/s or 0.94 x 10 −6 cm/s for ALE [8,41,49,[65][66][67][68][69]). The same applies for P app values of rhodamine 123, which were reported as 0.49 x 10 −6 cm/s in SLE and 2.27 x 10 −6 cm/s for ALE [68,70]. The difference in the time-dependent permeation of drugs applied as solution (linear) and as aerosol (saturation) is consistent with the study by Bur et al. [35]. The non-linear transport curves suggest that sink conditions are not maintained. Although absorption of APIs in the lung usually is fast, non-sink conditions have also been suspected to occur in the deep lung [71,72]. Therefore, the culture model might mimic the situation in vivo where the small amount of lung lining fluid could be too low to completely dissolve the deposited particles.
The shape of the time-dependent transport curve for rhodamine 123 differed between the two aerosol applications, MicroSprayer IA-1C Aerosolizer and DP-4 Dry Powder Insufflator. While a lag phase in the transport was seen for application by MicroSprayer IA-1C Aerosolizer this delay was absent upon exposure by DP-4 Dry Powder Insufflator. Total amounts (in μg, Table 2) of rhodamine 123 were higher with the Aerosolizer (13.23 μg) than with Insufflator application (4.7 μg). Concentrations, on the other hand were similar (93.3 vs. 98.0 μg/ml). The delay in transport could be explained by the fact that rhodamine 123 is transported by MDR1/ P-glycoprotein transporter [73]. The lack of delay upon application by DP-4 Dry Powder Insufflator might be caused by locally higher concentrations due to dissolution of the particles.
In view of the observed decreases in TEER values in this exposure model, increased paracellular transport resulting from an impaired barrier function also cannot be excluded.
The effect of higher transport of formoterol across the monolayer in this study upon coexposure with budesonide was observed when the compounds were applied as solution and as dry powder (Figs 4 and 6). It was specific for formoterol and could not be explained by differences in TEER values after application alone and in combination with budesonide. Single particles of Symbicort powder were smaller than formoterol particles but dissolution is very unlikely to be an important contributing factor because formoterol alone was used in a very high concentration. Interaction of budesonide with MRP1, MDR1/P-glycoprotein, OCT1, OCT2, and OCT3 and of formoterol with OCT3 and OCTN2 has been reported [74]. According to studies by Koepsell et al. budesonide can inhibit OCT2 activity [75], but this effect is not relevant in this model because Calu-3 cells do not express OCT2 [13]. Unexpected effects of OCT inhibitors (and high concentrations) on formoterol transport across Calu-3 layers have already been reported [13] and hypothesized to be linked to the bidirectionality of OCT mediated transport across the cell membrane.
As summarized in Table 4 the combination of Calu-3 cells and manual aerosol generation devices might provide more information on the interaction of different compounds on permeation. Main imitations of this study are that high powder concentrations of some APIs (budesonide) were used and that concentrations were not identical for all exposure models. The fact that similar findings were obtained in the different exposure conditions suggests that the differences in concentrations did not influence the observed effect. Studies for determination of P app values in general use relatively high concentrations of APIs [63], and the observed effects on transporters might be different from effects at the lower concentrations invivo.
Conclusions
Calu-3 cells are suitable for permeation studies because the desired phenotypes can be obtained largely independent from material and pore size of the transwell membranes and the duration of air-liquid interface culture when longer than 3 days. The use of manual aerosol generation devices for the assessment of transport and drug interaction at the cellular layer was more sensitive in identifying interactions of APIs but application of dry powders by DP-4 Dry Powder Insufflator presented problems due to compound-specific efficiency of delivery, high drug concentrations at the cell surface, and potential disruption of the cell monolayer. Conversely, MicroSprayer IA-1C Aerosolizer appears to be suitable for the testing of permeability of drug formulations for inhalation because TEER values did not decrease after the application and delivery was not compound-specific. Table 4. Limitations and advantages of the manual devices for permeability testing.
Advantage Limitation
Formulated (fixed dose) product can be tested to identify interaction between drugs using a relatively simple exposure system The detection limit of one compound in the fixed dose combination limits the distance between DP-4 Dry Powder Insufflator and cells, and exposure can decrease TEER values of the exposed cells Table. (PDF) | 8,520.4 | 2015-08-14T00:00:00.000 | [
"Biology"
] |
Self-Excited Acoustical Measurement System for Rock Mass Stress Mapping
This paper presents the results of a preliminary study of a self-excited acoustical system (SAS) for nondestructive testing (NDT). The SAS system was used for mine excavation stresses examination. The principle of operation of the SAS system based on the elastoacoustical effect is presented. A numerical analysis of the excavation was carried out considering the stress factor. An equivalent model based on a two-degree-of-freedom system with a delay has been developed. This model allowed to determine the relation which relates the frequency of the self-excited system to the stress level in the studied ceiling section. This relationship is defined by the elastoacoustic coefficient. The test details for anchorages in laboratory conditions and Wieliczka Salt Mine were presented. This research details of a method for creating actual stress maps in the ceiling of a mine excavation. The results confirmed the possibility of using the new measurement system to monitor the state of stresses in the rock mass.
Introduction
In mining, one of the most important aspects is to ensure human safety in changing environmental conditions [1,2]. The risk may result from both mining operations [3,4], as well as movements of the rock mass itself [5,6]. Although there are methods of protection such as anchor bolt [7] it is still essential to know the state of stress in the mine excavation in order to prevent death and severe injury to miners. For coal mining, stress monitoring systems have been shown in [8]. The authors present the primary indicators for the quantitative assessment of stresses in the excavation. The classical methods of measuring the roof displacement are used. An indicator for the strength assessment of anchors is also given. The following parameters are measured: arch strength, geostress, lateral pressure coefficient, and surrounding rock mechanical parameter. However, all of these methods require destructive testing in rock drilling or mechanical tearing of the anchors. An analytical approach to stress propagation using the method of tension is presented in [9]. The results were compared with experimental destructive test results in the existing rock mass. Test results for a combination of numerical simulations and destructive experimental tests were presented for investigating the failure behavior of rock massif in [10]. An interesting solution is the measurement of acoustic emission used in [11]. The authors show the correlation between the stress state of the specimens and the change in the acoustic emission coefficient for coal. In ore mining, methods related to the measurement of the anchorage itself are widely used [7]. It is due to the different dynamics of rock mass stress changes than in coal mining [12]. In the vast majority of cases, the change is of an impact nature. In salt mining, another fascinating measurement aspect has been claimed in the form of fatigue testing. The authors in [13] present laboratory fatigue test results for salt from a salt chamber that is used as compressed air storage for wind energy conversion. The salt chamber is used as an air tank. The self-healing capacity of salt achieves air-tightness due to viscoplastic deformation of the grains. New measurement methods and new sensors are constantly being explored to improve the miners' safety. The new methods based on wireless sensors are presented in [14,15]. The hydraulic fracturing test was conducted, and the results were presented in [16][17][18]. The test proved it was difficult to make artificial fractures because of water leaking between the rock layer. The primary purpose of [19] was to establish the relationship between measured in situ stress data by a neural network. The electromagnetic radiation of rock to perform the internal stress distributions was done by [20]. The self-excited acoustic SAS system is an indirect structural stress measurement system based on the elastoacoustic effect [21]. It has been successfully applied to measure stresses in metal [22] and concrete [23]. Attempts have also been made to implement it for single anchors [24]. Artificial intelligence was also used in the articles [25]. The fuzzy logic was used for the interpretation of the results. In each case, however, the system was attached to materials made of a single material. This paper presents an attempt to implement it as a sensor placed on two composite anchors to determine the stresses in the rock mass, which is located between these two anchors. A numerical analysis of the anchored rock mass model was carried out, and a 2-DOF model of the measuring system was made. The presented measuring system is a key element in monitoring the stresses state in the excavation and thus contributes to improving the safety of people in the salt mine.
Methodology
The conceptual scheme of the SAS system application is to monitor the stress state of the roof over the entire mining roadway and create a dynamic stress map of the excavation is shown in Figure 1. In this case, the transmitting head is the entire anchor. The receiving antenna can be attached to any other anchor. The measurement transducer works in a heterodyne system. The receiver and transmitter of the acoustic wave are located at a certain distance. In an autodyne system, both heads are located in the same place. The exciter and receiver axes are perpendicular to the axes of the anchors to which they are attached. It ensures the best transmission of the acoustic wave through the rock mass. The proposed system works on a principle very similar to a radio network. The transmitting antenna, i.e., the anchor on which the inductor is placed, vibrates and emits acoustic waves. The waves flowing through the roof reach the receiving antenna, i.e., the anchor on which the receiver is placed. In this case, the receiver and inductor create a closed circuit with positive feedback. The signal from the receiver is amplified appropriately using an external power source and then routed back to the inductor. The resulting induced waves have a specific frequency that depends on the strain of the rock mass and the type of rock between the two anchors. Open systems, i.e., those in which modal frequencies of free vibrations are measured, have fundamental problems related to wave phenomena occurring at the media boundary. There are simple problems with the interpretation of the obtained frequency spectra. In the case of a closed, positive feedback loop, the amplification of a particular frequency of the limit cycle of the self-excited system is obtained. No limit cycle phenomenon appears in open systems. Therefore, it is necessary to loop the entire system.
The proposed system may consist of a single transmitting anchor, multiple receiving anchors, and an appropriate switching system. A schematic of such a system is shown in Figure 2a. By causing cyclic switching of the receiving antennas, a measurement system can be created that continuously monitors the excavation condition over a large area. In Figure 2a, the blue color indicates the area where the initial conditions have not changed. The red color indicates that there has been a change in the heterodyne frequency in the inductor E-receiver R8 system due to a change in stress in the direction determined by the straight line passing between the heads. Figure 2b shows the reference position of heads R1-R8 and emitter E showed in Figure 2a on the actual mine roof. A schematic of the SAS system, which is an example of an auto-oscillator, is shown in Figure 3. The system can be broadly divided into two parts. The first part is the test object. The second part of the system is the actuator part, which has two main components: the exciter (E)-a piezoelectric actuator and the receiver (R)-a piezoelectric accelerometer sensor. The system uses an IMI 623C01 piezoelectric accelerometer with a VibAMP PA-3000 conditioner. The parameters of the accelerometer are given in Table 1, and the actuator in Table 2. The amplifier, actuator (E), conditioner, and accelerometric sensor (R) realize positive feedback. The accelerometer signal is conditioned to a voltage signal by a conditioner. The measurement system is implemented by the Field Programmable Gate Array (FPGA) system. The FPGA has two functions. The most important is to pass the signal to the amplifier directly, from where it goes to the exciter (E). It creates the feedback loop. The second function is to prepare a buffer of measurement data for the Real-Time Operating System (RTOS), which can then be processed or archived. By using the electrical loop, non-extinguishable oscillations with a specific limit cycle frequency are generated. The main factor affecting the self-excited system frequency is the change in the propagation velocity of the wave, and hence the change in the time for the wave to pass through the test object. Changes in stress cause changes in the speed of propagation of the acoustic wave. Measuring the frequency of the limit cycle indicates the level of stress in the excavation.
System Modelling
Two masses represent the dynamic model with spring rates. The scheme shown in Figure 4 corresponds to the scheme of the SAS system. Mass m 1 represents the transmitting anchor, mass m 2 represents the receiving anchor. The elasticities k 1 ,k 2 ,k 3 represent the elasticities of the rock mass surrounding the anchorage. (1) and (2). x 1 and x 2 are the respective displacements of the transmitting head and the receiving head.
The signal from the receiving bolt goes to the transmitting bolt using positive feedback. Hence, the forcing force u(t) can be determined by the control law given by Equation (3): where: A steady-state solution is given by Equation (4) for mass m 1 and by Equation (5) for mass m 2 .
x 1 = A 1 sin ωt (4) where: A 1 ,A 2 -Amplitudes of vibration for corresponding bolting, ω-SAS frequency. After substituting Equations (4) and (5) into Equations (1) and (2) and ordering, the polynomial Equation (6) is obtained from which the system frequencies can be calculated as a function of delay assuming equal system masses m 1 = m 2 = m.
The relation between the stresses and the total delay time in the system is given in [21]. This relationship is expressed by Equation (7). where: β-Elastoacoustic coefficient, σ-Stress, E-Young modulus, t 0 -Time of acoustic wave propagation in no-stress state.
Relationships (6) and (7) may allow for direct determination of stresses in the investigated rock mass considering the measured frequency of the SAS system. Nevertheless, this method requires further research to identify individual elasticities and masses for different types of roofs and anchors. Such studies will be performed at a later stage under actual mine conditions.
Stress Modeling in a Mine Roof
The numerical studies were performed in the Phase2D computer program based on the finite element method. The method allows for the approximate solution of physical problems, generally defined by a system of differential equations with appropriate boundary conditions. As a result of solving complex systems of differential equations, we obtain specific function values at selected points. In this method, the considered area is discretized into an equivalent system of a finite number of sub-areas of a simple shape (triangle) called finite elements. This set of elements is connected at points called nodes. Several elements can be connected at each node. A finite element mesh thus replaces the area under consideration. As a result of solving the system of equations at the nodes of the finite element mesh, the values of displacements and forces (reactions) caused by the loads or displacements (deformations) acting on the area are obtained. By having the displacements of the nodal points, the deformations, and then the stresses are calculated. The primary objective of this study was to determine the state of stress, strain, and rock failure zone around the Vernier excavation on level IV at Wieliczka Salt Mine. In addition, the maximum axial force in the excavation anchors was determined for the excavation with shoring. Numerical modeling was performed for the excavations with anchor bolt shoring fixed along their entire length. The strength and elastic parameters of the rock mass were selected based on the geological documentation of Wieliczka Salt Mine, whereas the material constants were calculated using RocLab software. The results of calculations conducted in Phase2D software are presented in the form of Table 3 and Figures 5-12 showing, among others: average stress, total strain, range of rock stress in roof and maximum axial force in roof anchors. The Hoek-Brown criterion, Coulomb-Mohr criterion, and Strength Factor strain rate were used in the study. The Hoek-Brown strength condition defines an empirical relationship between standard stresses and the compressive strength of rocks and parameters m b , s and a (characterizing the rock mass quality) selected using Rocklab software or based on tables. The general form of the Hoek-Brown condition, as determined by testing rock samples, is expressed by Equation (8). where: where: m i -constant for unruptured rock, depending on the type of rock, determined using a triaxial compression test or from tabular data, GSI-Geological Strength Index, D -the factor of weakening of the rock mass resulting from the mining method.
In the case when GSI > 25, then the parameters s and a of the Hoek-Brown condition are determined using relations (10) and (11).
The Coulomb-Mohr criterion describes the linear relationship between normal and tangential stresses (or maximum and minimum normal stresses) in the damaged zone. The quantities needed to determine the relationship are defined by Equations (12) and (13) By using expression (14) that defines the stresses σ and τ in the boundary condition equation at the slip surface: Equation (15) was obtained: where: The Strength Factor (SF), which expresses the ratio of rock strength to reduced stress at a given point, was used to analyze and determine the failure zones of the rock mass around the workings in the numerical model. If the SF value is less than 1, it means that the reduced stress exceeds the strength of the rock mass at the point, and material failure may occur (plastic analysis). Assuming that the system is elastic, material failure does not occur.
The following parameters were adopted in the numerical modeling: compressive strength Cs = 31.14 MPa; tensile strength Ts For the Hoek-Brown criterion and unanchored gallery, the results of numerical analysis are presented for the mean stress ( Figure 5), total strain (Figure 6), and SF ratio (Figure 7). The white rectangle illustrates the cross-section of the mine roadway. It can be seen that there is a high concentration of stresses above the excavation. For the Hoek-Brown criterion and the sidewalk anchored along its entire length, the results of the numerical analysis are presented for the mean stress (Figure 8), total strain (Figure 9), and SF coefficient (Figure 10).
The presence of anchors reduced the stresses and strains above the excavation. Figure 11 shows the distribution of mean stress, and Figure 12 the total strain for the unanchored heading obtained using the Coulomb-Mohr criterion. The strength criterion used shows the same maximum stress values but is located significantly higher above the sidewalk. The proposed Hoek-Brown criterion was also used to calculate the force distribution along the entire length of the modeled anchor. The simulation results are shown in Figure 13.
Results
The research on stresses in the composite anchor bolt casing type J64-27 was conducted on the laboratory test stand and the Wieliczka Salt Mine. The view of the laboratory model station is shown in Figure 14. The highest stress in the tested excavation model had to occur in the direction of the force application. Measurements were performed ten times for each SAS configuration. The comparative results are shown in Table 4. The frequency difference for the direction of the main force application was the largest concerning the second pair of anchors. The table should be interpreted as follows: For the K1-K2 load application direction, the reading from the SAS system setup on the K1-K2 anchors was 51.2 ± 0.1 Hz greater than for the K3-K4 configuration, with the same load configuration (on the K1-K2 direction). The oblique directions K1-K5 and K2-K5 reached a frequency value 16.7 ± 0.3 Hz more than the side direction K3-K4. A similar relationship was seen for every other load configuration. The preliminary laboratory tests confirmed that it is possible to quantify the stress increase in the tested anchored material using the SAS system. As a general rule, the SAS system indicates higher frequencies for a head application direction consistent with the normal stress direction.
In the following part of the task, preliminary investigations were carried out in the transmitting-receiving casing system, which created the first stress maps of the mine excavation. These tests confirmed that an acoustic wave generated at one anchor could be received at another anchor. As part of the research, an experiment was conducted in the mine excavation at Wieliczka Salt Mine. A gallery was prepared in which 25 of J64 anchors with complete bonding were previously anchored. These anchors were arranged in five rows and five columns, whose mutual distance was 1 m (Figure 14). In order to facilitate the experiment description, each anchor was marked with two coordinates: the x-index and the y-index. Figure 15 shows the mounting directions of the receiving head (position 33) and the sample transmitting anchor (E51). The tests were conducted under different load application arrangements. All anchors were not tightened through the nut. For the tests, individual anchors or anchor assemblies were tightened to a torque of 200 Nm, causing local compression of the excavation. A transmitting head was then applied to each anchor, and the limit cycle frequency for a given head position configuration (E x y − R) was read. Each frequency was then entered into a matrix (x, y, f ) where x, y are the coordinates of a given anchor, and f is the frequency value for a given emitter position. An example of the stress field is shown in Figure 16. In the position projection, where frequency values are represented by color change, interpretation of the results is even easier (Figure 17). In the presented case, only the anchor with coordinates 4.4 was tightened with the nut. The frequencies were measured only in the nodes. The coordinate intersections and the space between them were interpolated. Nevertheless, it is easy to see that the highest frequency is achieved for the exact coordinates as the compressive stress is applied.
Conclusions
The paper presents a proposal for the new ultrasonic stress monitoring system for a mine excavation. It also presents results of preliminary tests in a laboratory system and undermining conditions. The measurement system is based on the self-excitation effect. It brings the system to the limit cycle, where the frequency depends on the stresses in the tested space between anchors. The elastoacoustic effect pairs the stress change and the frequency of the limit cycle. This effect determines that as the stress changes, the propagation speed of the acoustic wave in the test material changes. It changes the wave transmission time between the transmitting and receiving antenna, which directly affects the limit cycle frequency.
The proposed 2-DOF model, which is equivalent to the real system, allowed to determine the relation that relates the frequency of the self-excited system to the stress level in the studied ceiling section. This relationship is determined by the elastoacoustic coefficient. This relationship was formed by considering the acceleration form of the feedback signal and the effect of signal delay on the limit cycle frequency of the SAS system.
The laboratory and in situ tests performed allowed to conclude for the SAS system: • The proposed reduced model can be used in the future to determine the absolute value of stress between anchors based on the measured frequency of the SAS system. • It is possible to quantify the stress increase in the tested anchored specimen with the SAS system. As a general rule, the SAS system indicates higher frequencies for a head application direction consistent with the predominant stress direction. • The presented results of preliminary tests at the Wieliczka Salt Mine allowed confirming the applicability of the measurement system in the conditions of a real mine.
The main advantage of the proposed method over the other mentioned methods is the simplicity. On the one hand it is the simplicity and speed of the measurement method itself. Neither roof of the excavation nor anchors have to be specially prepared and do not require long lasting preparations. The limit cycle is reached in less than 1 s and in principle this moment is sufficient to end the measurement itself, although it can also be continued. Such a system can be used for dynamic measurement of stress changes between anchors. The proposed system is also easy in the results interpretation. A change in limit cycle frequency which indicates a change in ceiling stress is easy to find in the frequency spectrum. This is due to the fact the limit cycle frequency has an amplitude of oscillations significantly larger than the amplitude of the disturbance. Hence, in contrast to other measurement systems, it requires less expert knowledge to analyze the results.
The system requires further research work, especially in applying it to the anchoring of less heterogeneous materials. It will be essential to confirm the possibility of interpreting the results for anchoring in multilayer ceilings with different fractions of rock materials.
Conflicts of Interest:
The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript: | 4,984 | 2021-10-01T00:00:00.000 | [
"Materials Science"
] |
Axon Injury-Induced Autophagy Activation Is Impaired in a C. elegans Model of Tauopathy
Autophagy is a conserved pathway that plays a key role in cell homeostasis in normal settings, as well as abnormal and stress conditions. Autophagy dysfunction is found in various neurodegenerative diseases, although it remains unclear whether autophagy impairment is a contributor or consequence of neurodegeneration. Axonal injury is an acute neuronal stress that triggers autophagic responses in an age-dependent manner. In this study, we investigate the injury-triggered autophagy response in a C. elegans model of tauopathy. We found that transgenic expression of pro-aggregant Tau, but not the anti-aggregant Tau, abolished axon injury-induced autophagy activation, resulting in a reduced axon regeneration capacity. Furthermore, axonal trafficking of autophagic vesicles were significantly reduced in the animals expressing pro-aggregant F3ΔK280 Tau, indicating that Tau aggregation impairs autophagy regulation. Importantly, the reduced number of total or trafficking autophagic vesicles in the tauopathy model was not restored by the autophagy activator rapamycin. Loss of PTL-1, the sole Tau homologue in C. elegans, also led to impaired injury-induced autophagy activation, but with an increased basal level of autophagic vesicles. Therefore, we have demonstrated that Tau aggregation as well as Tau depletion both lead to disruption of injury-induced autophagy responses, suggesting that aberrant protein aggregation or microtubule dysfunction can modulate autophagy regulation in neurons after injury.
Introduction
Autophagy is a lysosome-mediated intracellular catabolic process that is a central component in stress response [1]. It plays a conserved role in maintaining cellular homeostasis by degrading dysfunctional proteins, lipids, and organelles through an autophagosome-lysosome pathway [2]. In response to increased energy demands of cells, autophagy provides metabolic substrates, making autophagy a cytoprotective mechanism [3]. Autophagy was first discovered in conditions of starvation, which activates autophagy [4]. Autophagy is initiated with the formation of a double membrane structure around cellular substances, followed by the formation of autophagosome that then fuses with a lysosome. The engulfed substances are then degraded and recycled back to the cell as amino and fatty acids [5].
Connections between autophagy and human disease or physiology have been active research topics. It has become apparent that autophagy plays a central role not only in cancer and aging but also in neurodegeneration. As neurons become terminally differentiated post-mitotic cells early in development, they are unable to dilute out misfolded proteins and damaged organelles through cell division like replicating cells [6]. The mice lacking the essential autophagy-related geneAtg7 in the central nervous system showed massive neuronal degenerations in the cerebral and cerebellar cortices [7]. Ineffective autophagic lysosomal clearance, resulting in toxic protein accumulation, is found in various neurodegenerative diseases [3]. Tauopathies in particular share a commonality in their aggregation of either wild-type or mutant, phosphorylated Tau. A key role of autophagy in tauopathies is the removal of aggregated Tau [8][9][10]. Autophagy activators have been shown to reduce the levels of misfolded and aggregated proteins, mitigating the spreading of tau and neuronal loss [11][12][13][14][15][16][17], although whether autophagy impairment is a contributor or a consequence of tauopathy remains unclear [18,19].
Accumulating evidence also supports that proper function of autophagy is critical for the maintenance of normal axonal function by supporting local axon homeostasis and protecting against axonal degeneration under stress conditions [20][21][22][23]. An explicit acute neuronal stressor is axonal injury with extreme responses involving calcium influx, axonal membrane sealing, injury signaling and transcriptional changes [24]. Previous studies in rodent models reveal that autophagy is among the cellular process altered after axon injury [25][26][27]. Axon injury has been shown to up-regulate essential autophagy genes, including Ambra, Atg5, Beclin 1 and LC3 in both CNS and PNS [28,29]. Activating autophagy after spinal cord injury lesion attenuated axonal retraction and promotes axon regeneration by stabilizing microtubules [28]. Using a reporter that monitors autophagosomes and autolysosomes, we have recently reported that axon injury triggers autophagy activation, which declines with age, and that the injury-induced autophagy activation is critical for axon regeneration by limiting NOTCH [30]. However, the injury-induced autophagy response has not been previously investigated in the context of neurodegeneration.
In this study, we monitor the dynamics of autophagosomes and autolysosomes in response to axon injury in a C. elegans model of tauopathy that expresses pro-aggregant F3∆K280 Tau fragment [31]. We found that pro-aggregant Tau abolished axon injury-triggered autophagy activation and reduced axon regeneration capacity. In addition, axonal trafficking of autophagic vesicles were significantly reduced in the tauopathy model. The autophagy activator rapamycin failed to rescue the defects in autophagy activation or trafficking caused by Tau aggregation. Loss of PTL-1, the sole Tau homologue in C. elegans, also led to impaired injury-induced autophagy activation, with an increased basal level of autophagic vesicles. Therefore, like in aged neurons, injury-triggered autophagy induction is impaired in neurons with Tau aggregation or Tau depletion, suggesting a negative impact of aberrant protein aggregation and MT dysfunction on neuronal autophagy response to injury.
Axon Injury-Triggered Autophagy Induction Is Abolished in a Transgenic Tauopathy Model
Previous studies have suggested that autophagy dysfunction contributes to the toxic aggregation in neurodegenerative diseases. Conversely, increasing evidence also implicates the protein aggregation itself in affecting autophagy regulation [32]. We have recently reported that axon injury activates autophagy, which is required for effective axon regeneration through limiting Notch signaling [30]. To test whether injury-induced autophagy is affected by protein aggregation, we investigated autophagy dynamics in a transgenic Tau aggregation model that expresses chromosomally integrated versions of the amyloidogenic F3DK280 fragment of human Tau derived from the repeat domain of TauDK280 [31,33,34]. We expressed a dual-fluorescent mCherry::GFP::LGG-1 protein under the control of a touch neuron-specific promoter ( Figure 1A) in the strains carrying integrated transgene of the pro-aggregant F3∆K280 (BR5270 byIs161) or the anti-aggregant F3∆K280-PP control (BR5271 byIs162). The dual-fluorescent reporter has been previously used to monitor both autophagosomes and autolysosomes, and has been shown to be functional as it was able to rescue an embryonic lethal lgg-1(tm3489) mutant [35,36]. In cells expressing this reporter, autophagosomes are positive for both GFP and mCherry, while autolysosomes are only positive for mCherry, as GFP is quenched due to the low pH in autolysosomes. LGG-1. PLM axon was axotomized on Day 1 of adulthood. Images were taken immediately before axotomy (Uninjured) and 24 h post axotomy (injured). AP, autophagosome; AL, autolysosome. Scale bar: 10 µm. Statistics: one-way ANOVA; mean ± SEM; * p < 0.05; ** p < 0.01; ns, Not significant.
As we previously reported [30], we observed significantly increased numbers of mCherry/GFP double-positive autophagosome puncta and mCherry single-positive autolysosome puncta in injured PLM neurons compared to uninjured neurons in wild-type animals ( Figure 1B,C), indicating that axon injury induces autophagic vesicle formation and promotes autophagy flux. This injury-induced autophagy activation was completely abolished in the BR5270 strain expressing pro-aggregant Tau, although we were able to detect a significantly enhanced number of autolysosomes puncta in the control strain BR5271 ( Figure 1B,C). These aforementioned findings suggest that Tau aggregation impairs the autophagy response to axon injury.
Transgenic Expression of Pro-Aggregant Tau Leads to Reduced Axon Regeneration after Injury
Our previous studies implicated only autophagic activation in response to injury, as opposed to basal autophagy itself, is correlated with the regeneration capacity of axons [30]. In addition, this response is reduced with age [30]. This age-related diminishing of autophagic induction correlates to the gradually reduced axon regeneration in PLM neurons [37]. In dlk-1 mutant, in which PLM axon regrowth is completely inhibited, axotomy fails to induce autophagy, although loss of DLK-1 does not affect the basal autophagy level in non-injured neurons [30]. Similarly, blocking internal calcium release is sufficient to inhibit axon regrowth [38] and block autophagy induction after injury [30]. As transgenic expression of pro-aggregant Tau abolished injury-triggered autophagy response, we hypothesized that it would also diminish axon regeneration. Indeed, PLM axon regrowth in BR5270 was significantly less than that in wild-type control, while regrowth in BR5271 was comparable to wild-type (Figure 2A,B). This supports our claim that injury-induced autophagy activation correlates with axon regeneration capacity.
Injury Induces Autophagic Vesicles Trafficking in Wild-Type Neurons but Not in Neurons Expressing Pro-Aggregant Tau
Autophagic vesicles have been shown to move bidirectionally in axons of primary neurons [39]. We observed very few moving autophagic vesicles labeled by GFP::LGG-1 in intact PLM axons in wild-type young adult animals. Remarkably, the portion of moving vesicles significantly increased in regenerating axons 24 h post injury, with majority of the puncta moving retrogradely ( Figure 3A,B). This observation is consistent with previous studies showing that autophagosomes move bidirectionally along MTs and ultimately concentrate around the centrosome in the perinuclear region MT minus-end-directed motor dynein [40]. However, when we examined the vesicle trafficking in BR5270 strain, we did not detect this injury-associated movement of autophagic puncta ( Figure 3A,B), possibly due to the inhibited autophagosome formation by pro-aggregant Tau.
Autophagy Activator Rapamycin Failed to Rescue Autophagy Defects in the Tauopathy Model
Autophagy activators, such as rapamycin, have been shown to reduce the levels of aggregated Tau proteins, mitigating the Tau aggregation-induced neurodegeneration phenotypes [11][12][13][14][15][16][17]. Given this, we explored whether rapamycin was able to rescue the defects in both autophagy induction and trafficking in neurons expressing pro-aggregant Tau. As we have previously reported [30], rapamycin treatment was able to significantly enhance the numbers of autolysosome puncta in intact PLM neurons, although it was not sufficient to further increase autophagic vesicles in injured neurons ( Figure 4A). This is possibly due to the already high basal level of autophagy in injured young neurons, as rapamycin treatment was sufficient to elevate the number of autophagic vesicles in injured old neurons, which had shown diminished autophagic response to injury [30]. Like aged neurons, neurons expressing pro-aggregant Tau failed to activate autophagy in response to axon injury (Figures 1 and 4A). We therefore predicted that rapamycin would at least partially restore the autophagic response to injury in the tauopathy model. However, rapamycin treatment was found to not increase autophagic vesicles in the presence of pro-aggregant Tau, despite the low basal level. We next examined the effect of rapamycin on autophagic vesicle trafficking. Rapamycin treatment greatly enhanced the percentage of moving autophagic vesicles in uninjured PLM axons of wild-type animals. Either rapamycin or axotomy alone was sufficient to promote the trafficking of autophagic vesicles, whereas combining both treatments did not further enhance trafficking ( Figure 4B). We also examined rapamycin effect on trafficking in BR5270 strain. No change was observed treated and untreated neurons in both intact and injured neurons ( Figure 4B), consistent with the inability of rapamycin in promoting autophagic vesicle formation.
Loss of PTL-1 Blocks Injury-Induced Autophagy Activation
Like many other membrane-bound organelles and vesicles, autophagosome dynamics rely in part on their interactions with the cytoskeleton and especially with microtubules (MTs) [41]. Tau is a MT-binding protein that promotes MT assembly and stability. In Tau-induced neurodegeneration, Tau aggregation is often associated with Tau hyperphosphorylation and loss of Tau-MT interaction [42]. These prompted us to examine how Tau depletion affected injury-triggered autophagy induction using a genetic mutant allele of ptl-1 gene, which encodes the sole ortholog of human MAPT in C. elegans [43,44]. Interestingly, we observed a higher number of autolysosomes in uninjured PLM neurons of ptl-1(ok621) mutants ( Figure 5A,B). It has been proposed that MTs are not involved in autophagosome formation under basal conditions, as several studies have reported that acute treatment of a MT destabilization drug, nocodazole, as well as a MT stabilization drug, Taxol, did not affect basal autophagosome formation [45][46][47]. The high basal autophagy level of autophagy in ptl-1 mutant might be due to prolonged loss of function of PTL-1 in the mutant, possibly resulting in a stress-like condition. We found that both axotomy and rapamycin treatment failed to promote autophagic vesicle formation in ptl-1 mutant ( Figure 5A,B), thus indicating the important role of MTs in autophagy regulation. We also observed higher basal level of autophagic vesicle trafficking in intact PLM axons in ptl-1 mutants ( Figure 5C,D). Unlike in the wild-type animals, rapamycin treatment did not significantly enhance trafficking in intact axons in ptl-1 mutants. Axotomy also failed to promote trafficking in the absence of PTL-1 ( Figure 5C,D). Therefore, these findings suggest that loss of PTL-1 leads to diminished autophagic response to axon injury, despite the enhanced basal level of autophagy.
The High Basal Level of Autolysosomes in Ptl-1 Mutant Is Resistant to Autophagy Inhibitor BA1
Bafilomycin A1 (BA1) is a wildly used inhibitor of the late phase autophagy. BA1 blocks vacuolar type H + -ATPases and prevents maturation of autophagic vacuoles by inhibiting fusion between autophagosomes and lysosomes. As we previously reported [30], BA1 treatment by injection into the body cavity resulted in an increase in mCherry/GFP double positive puncta (indicating an increase of autophagosomes) and a decrease in mCherry single positive puncta (indicating a decrease of autolysosomes) in injured neurons of wild-type animals ( Figure 6A,B). Ample evidence from previous studies has shown that MTs are involved in the formation and motility of autophagosomes, but not in the process of autophagosome fusion with lysosomes [48]. We found that BA1 treatment did not significantly affect the numbers of autolysosomes in injured neurons in ptl-1 mutant ( Figure 6A,B). The reduced sensitivity of autolysosomes in ptl-1 mutant to BA1 suggests that fusion events between autophagosomes and lysosomes might be reduced in ptl-1 mutants.
Discussion
Accumulation of misfolded proteins is a common pathology shared by various neurodegenerative diseases. Since autophagy is a conserved mechanism that maintain cellular homeostasis by degrading damaged organelles and misfolded proteins, autophagy activity can affect the onset and progression of neurodegenerative diseases, with which Autophagy dysfunction is often associated. However, it remains unclear whether autophagy impairment is a contributor or consequence of neurodegeneration. In this study, we examined the autophagic response to axon injury in a C. elegans model of tauopathy that expresses pro-aggregant Tau fragment. We showed that injury-triggered autophagy induction is impaired in neurons with Tau aggregation, demonstrating the detrimental effect of Tau aggregation on autophagy regulation.
This impaired neuronal autophagy response to axon injury is also found in aged neurons [30]. Numerous studies have reported that, as the organism ages, regulation of protein homeostasis becomes disrupted, resulting in accumulation of misfolded proteins. In C. elegans, a sharp decline in chaperone expression correlates with the end of the reproductive phase and leads to the aggregation of misfoled mutant proteins [49]. In mammals, the ER stress-induced unfolded protein response is impaired with age [50]. Similarly, lysosomal chaperone-mediated autophagy activity is reduced in old-aged rat livers and senescent human fibroblasts [51]. It's also known that physiological age-related aggregates resemble disease aggregates in several aspects [52]. Therefore, the impaired autophagic response in aged neuron could be partially due to age-related protein aggregation. However, our data on rapamycin treatment suggest that Tau aggregation and aging might impact autophagy through different mechanisms. We have previously shown that treating young adult animals with autophagy-inducing agents leads to elevated autophagosome and autolysosome numbers in un-injured neurons. However, in injured young neurons, which have high level of autophagy activity in response to injury, autophagy-activating drugs do not further activate autophagy. Additionally, these autophagy activating agents were sufficient to increase autophagic vesicle number in aged wild-type neurons. These summarized observations suggest that axonal injury maximally activates autophagy in young wild-type neurons. This may explain the failure of autophagy-inducing agents to further augment autophagy. However, in neurons with defective injury response, such as those in aged animals, autophagy activity is not at the maximal level and therefore can be elevated by autophagy-activating agents. Interestingly, in neurons expressing pro-aggregant Tau, rapamycin treatment was not sufficient to enhance the number of autophagy vesicles, despite the low level in these neurons.
Tau aggregation is often associated with Tau hyperphosphorylation and loss of Tau-MT interaction in Tau-related neurodegeneration [42]. The involvement of MTs in different steps of autophagic process has been a debatable topic over the past years, but it becomes clear that MTs play essential roles in regulating autophagy dynamics. In this study, we found that loss of PTL-1/Tau lead to enhanced basal level of autophagy, inconsistent with previous reports that acute treatment of nocodazole or Taxol did not affect basal autophagosome formation [45][46][47]. We suspect that the high basal autophagy level of autophagy in ptl-1 mutant might be due to a stress-like condition caused by the loss of PTL-1 function in MT assembly and stabilization. Although it is generally believed that basal autophagosome formation does not involve MT, stress-induced autophagosome formation requires proper MT function [48]. WIPI1-positive pre-autophagosomal structures move along MTs upon starvation of the cells and such movements are highly sensitive to nocodazole treatment [53]. MTs and MT motors are also known to regulate mTORC1 and the class III PI3-kinase complex, the two major complexes required to initiate the autophagic response [54]. We found that either axotomy stress or rapamycin was sufficient to promote autophagic vesicle formation in ptl-1 mutant ( Figure 5), indicating the important role of MTs in neuronal autophagy regulation in response to axon injury. Furthermore, the high level of autolysosomes in ptl-1 mutant is relatively more resistant to BA1, which inhibits the fusion of autophagosomes with lysosomes. This suggests that fusion events might be reduced in ptl-1 mutants, despite the high basal autophagy level. This is consistent with the important role of MTs in regulating the movement of autophagosome toward the perinuclear region, where autophagosomes fuse with lysosomes [55]. We showed that injury-triggered autophagy induction is negatively impacted by both Tau aggregation and PTL-1/Tau deletion. However, elevated basal autophagy level is only observed in ptl-1 mutant, but not in Tau transgenic animals, suggesting that Tau aggregation and PTL-1/Tau loss-of-function might affect autophagy regulation through distinct mechanisms. Extensive studies have demonstrated that Alzheimer's disease is associated with defects in different steps of autophagy, including initiation, autophagosome transport and lysosomal fusion [56]. These defects are likely due to a combined effect of protein aggregation and abnormal MT function.
In summary, we employed a dual reporter to monitor the dynamics of autophagosomes and autolysosomes in response to axon injury. We found that this injury-induced autophagy response was abolished in neurons expressing pro-aggregant Tau and neurons with PTL-1/Tau depletion, and that rapamycin was not sufficient to restore these defects in autophagy response, suggesting that aberrant protein aggregation or abnormal MT function can modulate autophagy regulation in neurons after injury through distinct mechanisms.
C. elegans Genetics
C. elegans strains were maintained at 20 • C using standard procedures on nematode growth medium (NGM) agar plates with OP50 E. coli. Mutant C. elegans strains carrying ptl-1(ok621) alleles and transgenic Tau strains carrying byIs161, and byIs162 alleles were provided by the C. elegans gene knockout consortium (CGC). This consortium is funded by the NIH Office of Research Infrastructure Programs (P40 OD010440). Microinjection was utilized to generate transgenic animals. PCR was used for genotyping.
Transgene Construction
To construct the Pmec-4::mCherry::gfp::lgg-1 vector, mCherry::gfp::lgg-1 sequence was amplified by PCR from the lysate of MAH215 (Chang et al., 2017) and PCR product was inserted into TOPO TA vector to generate entry vectors. The expression vectors were generated using LR gateway recombination between the entry vectors and the Pmec-4 gateway cloning destination vector.
Laser Axotomy
Axotomy was performed as previously described by Wu et al. [57], with slight modification. Batches of 12 adult day 1 animals, unless otherwise indicated, were first immobilized using either 0.7% phenoxypropanol (484423, MilliporeSigma, St. Louis, MO, USA) or muscimol (M1523, MilliporeSigma, St. Louis, MO, USA). An Olympus IX83 microscope using 100× objective was then used to visualize GFP labeled PLM axons. Axotomies were performed with a Micropoint UV laser (Andor Technology, Oxford Instrument, Belfast, United Kingdom) at 50 µm from the cell body. Animals were then recovered in agar plates for 24 h prior to remounting, unless otherwise indicated, for scoring. A minimum of 20 animals were axotimized. ImageJ was used to measure 10 axons of each genotype. All experiments performed with a matched control in parallel.
Rapamycin and Bafilomycin A1 treatment
Rapamycin (AG-CN2-0025, AdipoGen, San Diego, CA, USA) was first dissolved in DMSO at a final concentration of 100 nM. This mixture was then added to standard NGM agar plates. Administration of rapamycin was performed by culturing on rapamycin NGM plates for 24 h prior to imaging, unless otherwise indicated. Bafilomycin A1 (BA1; BBVT-0252-C100, BioViotica, Dransfeld, Germany) was suspended in 0.2% DMSO and 0.1% phenol red solution at a final concentration of 50 µM and administered via injection into body cavity at tail position. This was done as BA1 is not cuticle permeable. Injections were performed 24 h before imaging. For axotomy experiments involving BA1 treatment, animals were cultured on NGM plates for 2 h post injection prior to axotomy.
Quantification of Autophagic Vesicles
Live animals were first immobilized with either 0.7% phenoxypropanol or 30 mM muscimol on a 5% agarose pad for quantitative analysis of both vesicles and puncta. Fluorescence images were taken on either an Olympus IX83 fluorescence microscope or a Zeiss LSM780 confocal microscope at 100× or 63× oil objectives. Confocal Z-stack images were generated with 0.5 µm slice intervals. Autophagic vesicle puncta in PLM neuron cell bodies were manually counted. Puncta were labeled by GFP::LGG-1 and mCherry::LGG-1. In neurons with the tandem sensor, total puncta were counted of either only mCherry-positive, only GFP-positive, or mCherry and GFP double-positive. Autolysosome puncta, indicated by mCherry-only, were counted subsequent to merging separate red and green channel images. Autolysosome puncta was verified by substracting the total number of GFP-positive puncta from the total number of mCherry-positive puncta.
Live imaging of Autophagy Dynamics
Live imaging of autophagic vesicles was performed 24 h after axotomy. Videos were taken with an Olympus IX83 microscope. Each video was 5 min in duration. Kymographs were generated with the software Kymograph of the Olympus IX83. The kymographs were utilized to determine autophagic vesicle trafficking. Kymographs are two-dimensional displays of a video with the x-axis is a line-scan of each video frame at a particular time, representing space along the process, and the y-axis representing time. This sequential assembly visualizes autophagic vesicle behavior over time.
Statistical Analysis
The software GraphPad PRiSM (version 8, San Diego, CA, USA) was utilized for all statistical analysis. Student's t tests were utilized for all two-way comparisons. ANOVA tests were performed for comparisons involving multiple groups in the design. Funding: This work was supported by funds from the San Antonio Nathan Shock Center (NIA grant 3P30 AG013319-23S2) to L.C. and Voelcker Fund Young Investigator pilot award to L.C. | 5,203.8 | 2020-11-01T00:00:00.000 | [
"Biology",
"Medicine"
] |
Money holding and budget deficit in a growing economy with consumers living forever
I examine the problem of budget deficit in a growing economy in which consumers hold money as a part of their savings in the case where consumers live forever. For simplicity and tractability I use a discrete time dynamic model and Lagrange multiplier method. In the appendix I briefly explain the solution using a discrete time version of the Hamiltonian method. I will show the following results. 1) Budget deficit is necessary for full employment under constant prices. 2) Inflation is induced if the actual budget deficit is greater than the value at which full employment is achieved under constant prices. 3) If the actual budget deficit is smaller than the value which is necessary and sufficient for full employment under constant prices, a recession occurs. Therefore, balanced budget cannot achieve full employment under constant prices. I do not assume that budget deficit must later be made up by budget surplus.
Introduction
This paper is an attempt to present a simple theoretical model for the following statement by J.M. Keynes."Unemployment develops, that is to say, because people want the moon; -men cannot be employed when the object of desire (i.e.money) is something which cannot be produced and the demand for which cannot be readily choked off.There is no remedy but to persuade the public that green cheese is practically the same thing and to have a green cheese factory (i.e. a central bank) under public control."(Keynes(1936), Chap. 17) In Japan and many other countries, fiscal deficits and accumulated government debt have become a problem, and it is argued that fiscal soundness must be improved.Is this really the case?Even if the goal of achieving a balanced budget will worsen the economy, impede growth, and create unemployment, does it still make sense to improve fiscal soundness?These questions are the starting point for this study.
In recent some researches I have examined the role of the budget deficits in a growing economy when consumers get utility from money holding as well as consumptions of goods.In these studies I have used an overlapping generations model in which consumers live over two periods, the younger period and the older period.They work in the younger period and retire in the older period.They consume goods in the older period by the savings carried over from the younger period.About the overlapping generations model I referred to Diamond (1965), J. Tanaka (2010Tanaka ( , 2011aTanaka ( , 2011bTanaka ( , 2013) ) and Otaki (2007Otaki ( , 2009Otaki ( , 2015)).Such a model may be reasonably realistic, but it may not be very general.In this study, therefore, I would like to examine the same issue under the assumption that people will live forever.I assume the exogenous growth by population growth1 .I do not assume that a new generation is born, but rather that the population of the current generation multiplies in the next period.About a model in which consumers infinitely live I refer to Weil (1987Weil ( , 1989)).However, although he used a continuous time model, I use a more tractable discrete time model.My another reference is Tachibana (2006).
The main results of this paper are as follows.
(1) We need budget deficit for full employment under constant price in a growing economy.(2) If the actual budget deficit is greater (smaller) than the value which is necessary and sufficient for full employment under constant price, an inflation (a recession) occurs.Balanced budget cannot achieve full employment under constant price.We should not assume that budget deficit must later be made up by budget surplus.There is a persistent belief that accumulated government debt must eventually be repaid by running budget surpluses, but such a move would lead to a severe recession.It should be recognized that even if a certain level of budget deficit continues under steady-state conditions, it will not cause inflation unless it is excessive, and that it is essential to maintain full employment at stable prices2 .
In the next section, I present the model of this paper and prove the above main results.In Section 3 I calculate the explicit values of the savings and money holding3 .In Section 4 I present a brief numerical example.
The proofs of each proposition are largely contained in the appendices.
Money holding and budget deficit in a growing economy
32
Consumers' behavior
I introduce money demand or money holding by consumers into a simple exogenous growth model in which consumers infinitely live.Consumers use wages and profits earned from firms and savings left over from the previous period to consume a homogeneous good in each period and save for the next period.The savings include capital as well as money holding.The consumer's utility depends on the consumption and the real money holding.The population of consumers grows by constant rate from a period to the next period.This does not mean that a new generation will be born, but rather that the population of the current generation will multiply at a constant rate.
The consumer's utility over an infinite period of time is expressed as follows.
Specifically, the utility function is and are the (real value of ) consumption per capita and the price of the good in Period . +1 is the nominal value of the money holding of the consumer at the end of Period .It will be carried over to the next period. Therefore, is the real value of the money holding. is the discount rate. is the parameter of the utility function.Let +1 be the savings of the consumer at the end of Period , and +1 be its value in Period + 1.
Then, we have (2) +1 − +1 represents the portion of savings that is invested in productive capital, which generates interest in the next period. +1 is the interest rate of the capital in Period + 1.Similarly, The budget constraint for the consumer in period is is the nominal wage rate, and is the indicator that represents whether the consumer is employed or not. is the tax rate, 0 < < 1 .If we assume full employment, = 1 for all consumers. > 0 is the population growth rate.The savings at the end of Period are distributed equally among consumers in Period + 1.From this, we obtain and It is rewritten as Further, By Lagrangian method we obtain the following consumption and money holding of the consumers (please see Appendix 1). and Let be labor supply or population in Period .Under full employment the employment equals .Since it grows at the rate of , The total consumption in Period is is the employment in Period . +1 is the value of the total savings in Period + 1.The total nominal consumption is On the other hand, the total nominal money holding is The total nominal savings is The real value of the capital in Period + 1 is Similarly, the real value of the capital in Period is The relationships between the total values of the variables and the per capita values are Similarly, for the values in Period , we have
Firms' behavior
Let be the output, be the capital, be the employment of firms in Period .Then, the production function is written as follows.
I assume the constant returns to scale property for the production function. is the real capital per labor.The number of firms is normalized to one.Each firm maximizes its profit in each period.The profit of a firm is The first order conditions for profit maximization are This is the total nominal supply of the good.
Market equilibrium
In this subsection I will show the main result of this paper.The total nominal consumption demand is Let be the fiscal expenditure in Period .The total nominal demand is The market clearing condition is Taking as given, if full employment has been achieved until Period − 1, then it is necessary and sufficient to create the budget deficit shown in (A.8) to achieve inflation-free full employment in Period .
Inflation and recession
About inflation and recession we can get the following results.Proposition 2 If the budget deficit is larger than the value which is necessary and sufficient to achieve full employment under constant price, inflation is triggered.On the other hand, if the budget deficit is smaller than the value which is necessary and sufficient to achieve full employment under constant price, a recession occurs.Proof: If the actual budget deficit is larger than the value which is necessary and sufficient for full employment under constant price (expressed by (A.7) in Appendix 2 with = −1 , or (A.8)), should be larger.Therefore, inflation is triggered.On the other hand, if the actual budget deficit is smaller than that value, +1 should be smaller.This will be realized through a decline in income and production.(Q.E.D.)
Explicit values of the savings and money holding
The equations of individual consumption and money holding expressed in (4) and ( 5) include savings and are not in closed form.Therefore, I consider the explicit values of some variables, savings and money holding, in this section.I will show the following proposition.Proposition 3 The explicit solutions of the value of the savings in Period and the value of the money holding at the end of Period are and ̃ is the equilibrium value of the capital-labor ratio.It is determined by the growth rate and the discount rate.Proof: Appendix 3. Let us consider the steady state in Period .From (7), ≈35.87 .The consumption demand is
Numerical example
The invest demand is ̃ = 1 .The supply minus tax is If the budget deficit is 0.33, we have = 1 and full employment is realized under constant price.If it is larger than 0.33, > 1 and an inflation is triggered.On the other hand, with downward price rigidity, if the budget deficit is smaller than 0.33, a recession occurs.
Conclusion
In recent years, I have been interested in the issue of budget deficits and government debt, not specifically as a policy to recover from recession, but to prove that budget deficits are necessary to achieve full employment without inflation nor deflation in a steady state.The key to this is to consider a growing economy and the fact that people hold money for liquidity and other reasons.This paper develops the argument not in the overlapping generations model in which people live for a finite period, but in a model in which people live for an infinite period.If similar conclusions can be reached in various models, a model in which people live forever may be easier to handle than a model in which generations overlap.
A3. Proof of Proposition 3
From (A.2) in Appendix 1 for Period and + 1 we have Similarly, From the costate equation, (A.5) in Appendix 1, In the steady state under full employment with constant price, since = −1 , = −1 , = +1 , Then, we obtain This is the explicit solution of the value of the money holding at the end of Period .By (A.7), (A.13) and (A.14) for +1 and , we can explicitly get the steady state values of the budget deficit.(Q.E.D.)
A4. Hamiltonian method
Although the Lagrange multiplier method is used in the text, analysis by Hamiltonian method is also possible, which is briefly discussed below.(A.1) is rearranged as follows.
are the marginal productivity of capital and that of labor.From them, we have = [( ) − ′( ) ] , and ) + − 1 1 + +1 +1 ] + ( +1 − ) = + .(6) ( +1 − ) is the investment in Period which is the nominal value of the increase in the capital from Period to Period +1.I will show the following proposition.Please see Appendix 2 for the proof of this proposition.Proposition 1 In a growing economy, if consumers get utility from money holding, in the steady state under full employment with constant price, we need positive budget deficit.
Denote the steady state value of the interest rate by ̃= + + .If this relation holds, the capital-labor ratio, , which is constant in the steady state, satisfies ′ () = .Denote this value of by ̃.Then, the steady state value of the capital in Period and + 1 are | 2,836.4 | 2023-09-14T00:00:00.000 | [
"Economics"
] |
Molecular characterization of the sequences of the 16S-23S rDNA internal spacer region (ISR) from isolates of Taylorella asinigenitalis
Background Sequence information on the 16S-23S rDNA internal spacer region (ISR) exhibits a large degree of sequence and length variation at both the genus and species levels. A primer pair for the amplification of 16S-23S rDNA ISR generated three amplicons for each of isolates of Taylorella asinigenitalis (UCD-1T, UK-1 and UK-2). Findings Following TA cloning and sequencing, the three isolates of T. asinigenitalis were demonstrated to possess three ISR units of different lengths. Although the three corresponding ISRs (A, B and C) were identified to be identical to each other (UK-1 and UK-2 isolates), the ISRs shared approximately 95.3–98.9% nucleotide sequence similarities between the UCD-1T and UK-1/-2 isolates. A typical order of two intercistronic tRNA genes (5'-tRNAIle-tRNAAla-3') with the different nucleotide spacers [44 through 51 base pairs (bp)] in length was identified among the isolates. The consensus sequences of the antiterminators of boxB and boxA were also identified in all ISRs. Thus, three ISRs were identified for each isolate, and therefore, at least three distinctly different ribosomal RNA operons were suggested to occur in the genome of T. asinigenitalis. This was also confirmed by Southern hybridization procedure. Conclusion The present study represents a dendrogram constructed based on the nucleotide sequence data of 16S-23S rDNA ISR for T. asinigenitalis, which may aid in the phylogenetic positioning of T. asinigenitalis within the genus Taylorella, and in the molecular discrimination of T. asinigenitalis.
In late 1997 and in early 1998, three bacterial isolates were isolated from donkey jacks (Equus asinus) in the USA and a new second species of the genus Taylorella, T. asinigenitalis, was established for these atypical organisms [5,6]. Additional T. asinigenitalis isolates (Bd3751/05 and 115/04) were obtained more recently and were identified from the genital tract of stallions in Sweden (GenBank accession No. DQ099547) and in Spain (DQ 393780). Sequences of the nearly full-length 16S rDNA from all these five isolates of T. asinigenitalis have already been deposited in DDBJ/EMBL/GenBank (AF297174 for UK-1, AF297175 for UK-2, AF067729 for UCD-1 T , DQ099547 for Bd3751/05 and DQ393780 for 115/04). It was demonstrated that the sequences were almost identical (> 99.8% similarity) among the three isolates obtained in the USA [6]. However, no sequence information on the 16S-23S rDNA internal spacer region (ISR), which exhibits a large degree of sequence and length variation at both the genus and species levels [7,8], of T. asinigenitalis have yet been reported.
Therefore, the aim of the present study is to clone, sequence, and analyze the 16S-23S rDNA ISRs of three isolates of T. asinigenitalis (UCD-1 T , UK-1 and UK-2) and to compare the ISRs sequence data.
Methods
In the present study, three isolates of T. asinigenitalis (UCD-1 T , UK-1 and UK-2; [5,6]) were analyzed. The conditions for cell culturing have previously been described by Matsuda and colleagues [9,10]. Genomic DNA preparation for the PCR amplification was carried out, as described already [11,12].
The primer pair used for the 16S-23S rDNA ISR amplification of T. asinigenitalis isolates in the present study was ISR-Tef (5'-CTGGGGTGAAGTCGTAACAAG-3') for the forward primer and ISR-5r (5'-GCCAAGGCATCCACC-3'; the sequence of region 5 reported by Gurtler and Stanisich (1996) [7,12] for the reverse primer. The ISR-Tef primer was designed in silico in the present study for PCR amplification of full-length ISR of the genus Taylorella.
PCR mastermix contained 10 mM Tris-HCl (pH 8.3), 50 mM KCl, 1.5 mM MgCl 2 , 40 mM of each dNTP, 1 μM of each primer and 0.5 unit of EX Taq™ DNA polymerase, which possesses 3'-5' exonuclease activity (Takara BioInc. Shiga, Japan). PCR was performed in a 50 μl volume, for 25 cycles at 94°C for 1 min, 65.4°C for 30 sec, 72°C for 30 sec and finally 72°C for 7 min. Purification of the amplified PCR products and TA cloning of the PCR amplicons were carried out, as described previously [12]. Dideoxynucleotide sequencing and sequence analysis were also performed, as described previously [12]. For accurate sequencing, multiple TA-cloned PCR products were sequenced. The sequence data of the 16S-23S rDNA ISR of T. asinigenitalis determined in the present study have been deposited in DDBJ/EMBL/GenBank (AB264283-AB264291).
Southern blot hybridization analysis of the ISR was carried out using digoxigenin (DIG) labeled fragment of the ISRA (nucleotide position 452-761:AB264283) prepared from the T. asinigenitalis UCD-1 T , as a probe with Pst I digested whole genome DNAs, respectively, according to the procedure described by Sambrook et al. (2001) [11].
Random primer extension was performed in order to prepare the fragment using a DIG-High Prime kit (Roche Applied Science, Penzberg, Germany).
Nucleotide sequences of the ISRs from the isolates of the genus Taylorella were compared to each other using CLUS-TAL W software [13], which was incorporated in the GENETYX version 9 (GENETYX Co., Tokyo, Japan) computer software. Following this, a phylogenetic tree was constructed by an unweighted pair group mean average (UPGMA) method available on the GENETYX (version 9).
Results and discussion
The PCR primer pair (ISR-Tef and ISR-5r) used for the amplification of the segments containing the 16S-23S rDNA ISRs of the three T. asinigenitalis isolates produced three amplicons of approximately 930 to 1,050 bp in length for the three isolates, respectively (data not shown). This may imply that T. asinigenitalis possesses at least three ISR units of different lengths. Subsequently, nine purified and cloned fragments, containing the ISRs, were subjected to TA cloning and sequencing. The sequences corresponding to the PCR primers (ISR-Tef/-5r) were excluded from the sequence data and further analysis in the present study. The sequences containing the two 16S-23S rDNA ISRs from T. equigenitalis NCTC11184 T (AB113653 and AB113656) were also compared. The genetic relatedness of the ISRs is shown in Figure 1.
The sequence corresponding to the CCUCCU sequence, a highly conserved sequence close to the 3' end of the mature 16S rRNA that is complementary to the Shine-Dalgarno sequence on mRNA [14,15], was identified in the sequences of the amplicons of T. asinigenitalis isolates [nucleotide position 31-36; AB264283-AB264291], as well as T. equigenitalis isolates (AF408197, AB066372, AB069660, AB113653-AB113658). Thus, in the present sequencing study of the ISRs of T. asinigenitalis, CCTCCT sequences were observed in all isolates examined, where the 3' end of some bases downstream of the CCTCCT sequence may represent the probable 3' end of the 16S rRNA gene.
In relation to the 3' end of the ISR of T. asinigenitalis isolates, the probable 3' end of the ISR may represent the nucleotide position 989 of the NISR-A of T. equigenitalis NCTC11184 T , since the nucleotide position 990 of the NISR-A of T. equigenitalis NCTC11184 T [12] was previously deduced to be the possible 5' end of the 23S rDNA sequence of T. equigenitalis by the nucleotide sequence alignment and analysis of the ISR sequences, with the 5' end sequences of the 23S rDNA from several bacterial species (see Figure 2 in the paper described by Kagawa et al. (2006) [12].
Consequently, the 16S-23S rDNA ISRs (A, B and C) from the three isolates of T. asinigenitalis were estimated to be approximately 837 to 955 bp. The ISR sequence data characteristically indicate that the three corresponding ISRs (A, B, and C) were identified to be identical to each other (UK-1 and UK-2 isolates). In addition, the ISR sequences shared nucleotide sequence similarities of approximately 95.3-98.9% between UCD-1 T and UK-1/UK-2 isolates, respectively.
In addition, as shown in Figure 1, a dendrogram constructed, based on the nucleotide sequence information of the ISRs, demonstrated that T. asinigenitalis isolates formed a major cluster separating from T. equigenitalis isolates (Fig. 1). Thus, nucleotide sequence divergence with 16S-23S rDNA ISR for T. asinigenitalis could be useful to discriminate among the isolates and between species within the genus Taylorella.
A typical order of intercistronic tRNA genes with 44 through 51 nucleotide spacers of 5'-16S rDNA-tRNA Ile (nucleotide position 202-278 of the ISR-A of UCD-1 T ) -tRNA Ala (nucleotide position 325-399 of the ISR-A of UCD-1 T ) -23S rDNA-3' was identified in all three kinds of ISRs from the three T. asinigenitalis isolates. Figure 2 clearly demonstrates, that both genes for tRNA Ile and tRNA Ala were almost identical among the ISRs from T. asinigenitalis, as well as T. equigenitalis (Fig. 2). The consen-sus sequences of the antiterminators of boxB (a stem-loop structure with no apparent sequence conservation at nucleotide position 486-500) and boxA (a conserved sequence, TGTTCTTTAACA, at nucleotide position 576-587 in AB264283 for the ISR-A of UCD-1 T ) were also identified in all three kinds of ISRs (Fig. 3). As illustrated in Figure 3, boxA occured with sequences among the 11 ISRs from the genus Taylorella examined. Although the nucleotide sequence differences in the boxB were demonstrated at two loci between the UCD-1 T ISR-A and -B/-C in the 15-16 nucleotide sequence, boxB of UCD-1 T ISR-A was identical to those of UK-1 and -2. In addition, the two ISR-A and -B from T. equigenitalis NCTC11184 T were relatively divergent with respect to boxB (nucleotide position 487-509 in AB113653 for the ISR-A) from those of T. asinigenitalis isolates, respectively, as shown in Figure 3.
When Southern blot hybridization analysis was carried out in order to clarify how many ISRs occur in the genome of the three T. asinigenitalis isolates, the occurrence of the three was identified in all the three isolates, respectively (Fig. 4).
Consequently, in the present study, it was demonstrated that three isolates of T. asinigenitalis possess three kinds of ISRs with different length, respectively. Thus, the present results may possibly indicate that T. asinigenitalis isolates carry at least three distinctly different ribosomal RNA operons in the genome. Jang et al. (2001) previously demonstrated that pulsedfield gel electrophoresis (PFGE) profiles after digestion with Not I of the genomic DNAs from the two isolates (UK-1 and UK-2) of T. asinigenitalis were the same, but they differed from the other isolate (UCD-1 T ) [6]. The present sequencing results of the 16S-23S rDNA ISR (A, B and C) clearly identified that the three ISRs were quite identical to each other [UK-1 and UK-2], but they were different from those of the UCD-1 T , respectively. Thus, our present sequence informations of the ISRs are consistent with the result of PFGE analysis by Jang et al. (2001) [6]. The two isolates (UK-1 and UK-2) of T. asinigenitalis obtained from donkey jacks in Kentucky, USA, in 1998 [6] gave the quite identical profiles of the PFGE and the 16S-23S rDNA ISR sequences. Therefore, these two isolates may possibly be identical.
Overall, this study is the first report of 16S-23S rDNA ISR sequences and tRNA genes from T. asinigenitalis. This is also first molecular comparison of the ISRs from T. asinigenitalis with those from T. equigenitalis.
A phylogenetic tree constructed based on the nucleotide sequence information of the ISRs, by using the UPGMA method Nucleotide sequence alignments of the reagion including two intercistronic tRNA genes in the ISRs from the three isolates of T. asinigenitalis Nucleotide sequence alignments of the region including the consensus sequence of the antiterminators of boxB and boxA in the ISRs from the three isolates of T. asinigenitalis and T. equigenitalis NCTC11184 T isolate | 2,606.8 | 2009-03-03T00:00:00.000 | [
"Biology"
] |
NCSU_SAS_SAM: Deep Encoding and Reconstruction for Normalization of Noisy Text
As a participant in the W-NUT Lexical Normalization for English Tweets challenge, we use deep learning to address the constrained task. Specifically, we use a combination of two augmented feed forward neural networks, a flagger that identifies words to be normalized and a normalizer, to take in a single token at a time and output a corrected version of that token. Despite avoiding off-the-shelf tools trained on external data and being an entirely context-free model, our sys-tem still achieved an F1-score of 81.49%, comfortably surpassing the next runner up by 1.5% and trailing the second place model by only 0.26%.
Introduction
The phenomenal growth of social media, web forums, and online reviews has spurred a growing interest in automated analysis of usergenerated text. User-generated text presents significant computational challenges because it is often highly disfluent. To address these challenges, we have begun to see a growing demand for tools and techniques to transform noisy usergenerated text into a canonical form, most recently in the Workshop on Noisy User Text at the Association for Computational Linguistics. This work describes a submission to the Lexical Normalization for English Tweets challenge as part of this workshop (Baldwin et al., 2015) Motivated by the success of prior deep neural network architectures, particularly denoising autoencoders, we have developed an approach to transform noisy user-generated text into a canonical form with a feed-forward neural network augmented with a projection layer (Collobert et al., 2011;Kalchbrenner, Grefenstette, & Blunsom, 2014;Vincent, Larochelle, Bengio, & Manzagol, 2008). The model performs a character-level analysis on each word of the input. The absence of hand-engineered features and the avoidance of direct and indirect external data make this model unique among the three topperforming models in the constrained task.
This paper is organized as follows. In Section 2 we describe each component of our model. In Section 3 we describe the specific instantiation of our model, and in Section 4 we present and discuss results.
Architecture and Components
Our model consists of three components: a Normalizer that encodes the input and then reconstructs it in normalized form, a Flagger that determines whether the Normalizer should be used or if the word should be taken as-is, and a Conformer that attempts to smooth out simple errors introduced by quirks in the Normalizer.
In this section we will use the simple example transformation of "u" to "you" where "u" is the input text and "you" is the gold standard normalization. In our example we use a maximum word size of three. Figure 1 shows the flow of our example through the model. In broad overview, the input is preprocessed and sent to both the Nor-malizer and the Flagger. The Normalizer computes a candidate normalization, and the Flagger determines whether to use that candidate or the original word. The Normalizer's output is passed to the Conformer, which conforms it to a word in the vocabulary list, and then the candidate, the flag, and the original input word are passed to a simple decision component that either keeps the original word or uses the normalized version based on the output of the Flagger. While it may seem inefficient that the normalized version is always computed, even if it is not used, this approach is used so that the Normalizer and Flagger can be run in parallel on many inputs at once.
Deep Feed-Forward Neural Networks
As the central element of the Flagger and the Normalizer, the deep feed-forward neural network forms the basis of our model. A deep feedforward neural network takes a vector of numbers as input. This vector is known as a layer and each value within it is a neuron. The network multiplies the input layer by a matrix of weights to return another vector. This new vector is then transformed by a non-linearity. A number of functions can serve as the non-linearity, including the sigmoid and the hyperbolic tangent, but our model uses a rectified linear unit, given by the following expression.
= max , 0 The rectified linear unit has been successful in a number of natural language tasks such as speech processing (Zeiler et al., 2013), and it was effective in an unpublished part-of-speech tagging model we developed.
The transformed vector is referred to as a hidden layer because its values are never directly observed in the normal functioning of the model. A deep feed-forward neural network can contain any number of hidden layers, each going through the same process, multiplying by a matrix of weights and transforming via a non-linearity. Hidden layers may also be of any size. Multiple applications of learnable weight matrices and non-linear transformations together allow a deep neural network to represent complex relationships between input and output (Bengio, 2009).
Deep feed-forward neural networks are trained by backpropagation. Backpropagation is a training method by which the gradient of any given weight in a network can be calculated from the error between the output of the network and a gold standard. It is described in more detail in (Rumelhart, Hinton, & Williams, 1986).
The Normalizer
Our use of deep feed-forward neural networks for the task of normalization is inspired by the success of denoising autoencoders. (Vincent et al., 2008). Denoising autoencoders are neural networks whose output is the same as their input. That is, they specialize in developing a robust encoding of an input such that the input can be reconstructed from the encoding alone. The denoising aspect refers to the fact that to encourage robustness, denoising autoencoders are given inputs that have been deliberately corrupted, or "noised" and are expected to reconstruct them without the noise. It is this "denoising" aspect that makes denoising autoencoders so interesting for text normalization.
The main component of our model, the Normalizer, uses a feed-forward neural network that functions on a similar principle to that of a denoising autoencoder. It reads the character sequence that describes the word and encodes it internally, outputting the denoised (normalized) version. It accomplishes this in three sets of layers. First the character projection layer takes a string and represents it as a fixed-length numeric vector. Next, a feed-forward neural network converts the data into its internal representation and, with a special output layer, into a denoised version of the input. Figure 2 shows a diagram of the Normalizer's architecture.
The first step of the Normalizer is performed by the character projection layer (Collobert et al., 2011). The character projection layer learns floating point vector representations of characters, which it concatenates into one large floating point vector word representation. In our example, the letter "u" is represented by n floating point numbers. For example, if n = 3 the representation for "u" might be [0.1, -1.2, -0.3]. This vector was chosen arbitrarily, but in the actual model, values are learned in training. The representations allow more information to be associated with a character than a simple numeric index.
In this simple example, the word "u" is composed of one character, but if it were longer, each letter would be separately represented. A key challenge at this point is that a feed-forward neural network cannot handle an arbitrary number of inputs. Because each position in the vector is a neuron matched directly to a set of weights, changing the size of the vector would require changing the size of the learned weights, and the model would have to be retrained.
To accommodate this, we use a fixed window. Before we send our input to the Normalizer, we preprocess it to meet a specified length, filling in unused spaces with a sentinel padding "character" that projects to its own set of learned weights like the other characters. Since the maximum word size in our example is 3, we use a window of size 3. Therefore, our input "u" be-comes [u, _, _] and then is projected and concatenated and becomes something like [0.1, -1.2, -0.3, 1.3, 0.0, -1.1, 1.3, 0.0, -1.1]. Notice that we have nine values now in our input. That is the three values from "u" and then the three values for "_" ([1.3, 0.0, -1.1]) twice, once for each "_". After this step, the system has a numeric vector representation of a word that is always the same length. It now sends it to the first layer of the feed-forward neural network. We deliberately select a large enough window that only in a small minority of cases does a word have to be reduced to fit into the window.
The last hidden layer's values go through one final matrix multiplication to output a list of values wv in size, where w is the size of the window and v is the number of possible characters including the padding character, that is, the number of characters in the alphabet, which is shared between the input and output layers. In this last layer the nonlinear transformation is a special version of the softmax operation.
The softmax operation transforms a vector such that each of its values is between zero and one and the new vector sums to one. Mathematically, it is given as: Where K is the number of values in the vector. In our model, K = v, the size of the alphabet. These individual values can alternately be considered posterior probabilities for each of the possible decisions. If each value is mapped to a character, one can simply take the highest value to select the most likely character. In this case, we are predicting a window of w characters rather than a single character, so we perform softmax separately on each of the w sets of v values in the layer. In prediction, we simply take the index of the highest value in each of the w sets, but in training we take the whole prediction distribution and try to maximize the likelihood of each correct letter. We do not attempt to predict character embeddings because we are learning them, and the model would be likely to learn a trivial function with character embeddings that are all equal.
Training the Normalizer as a whole relies on generating posterior distributions and attempting to minimize the total negative log likelihood of the gold standard. Mathematically, our objective function is Where p is an element in P, the vector of the probabilities of each gold standard letter. So, if our model predicts "y" as 75% likely for character 1, "o" as 95% likely for character 2, and "u" as 89% likely for character 3 in our window of size 3, the negative log likelihoods calculated as (.29, .05, .12) are summed to get the error. This sum error gives a simple measurement of performance to optimize, which backpropagates through the model to learn all the weights described above (Rumelhart et al., 1986).
The Flagger
The Flagger identifies what does and does not require normalization. The vast majority of the training data (91%) does not require normalization, so returning the reconstructed encoding of every word would risk incorrectly regenerating an already canonical token.
The Flagger has the same general structure as the Normalizer itself except for the final layer. Instead of generating text at the last layer, a softmax layer predicts whether the token should be normalized at all. Thus, the Flagger's output layer is two neurons in size, one representing the flag "Do Normalize," and another representing the flag "Do Not Normalize." In the construction of the gold standard for the task, there were three reasons a token would not be normalized: firstly, the token is already correct, second, the token is in a protected category (hashtags or foreign words), or third, it was simply unrecognizable such that the human normalizer could not find the correct form. The Flagger accounts for but does not distinguish between these three possibilities.
The Conformer
Even when a token should be corrected, it is possible that the normalizer will come very close to correcting it without succeeding. Reconstructing the word "laughing," for instance, the normalizer can fail completely if it predicts even one letter wrong. An early analysis of validation data found that the normalizer had predicted "laugling" instead of laughing. These off-by-one errors are a frequent enough occurrence to merit a module to deal with them. The Conformer is also useful for correctly normalizing rare words whose correct normalization is too long for the window to represent. In particular "lmfao" expands to an impressive 27 characters, but if the Normalizer predicts only the first 25 characters, the Conformer can easily select the correct token.
To correct these small normalizer errors we construct the Conformer by collecting a dictionary from the gold standard training data. The dictionary is simply a list of all the unique words in the gold standard data. Then at runtime, whenever the Normalizer runs and predicts a word that is not present in the dictionary, we replace it with the closest word in the dictionary according to Levenshtein distance (Levenshtein, 1966). Ties are resolved based on which word comes first in the dictionary. Because Python's set function, which does not guarantee a specific order of its contents, is used to construct the dictionary, the dictionary's order is not predictable and thus ties are resolved unpredictably.
Settings and Evaluation
The model was implemented in Theano, a Python library for fast evaluation of multidimensional arrays using matrix operations (Bastien et al., 2012;Bergstra et al., 2010). We used Theano's implementation of backpropagation to train our model. For our window size, we selected 25 characters, which is large enough to completely represent 99.9% of the tokens in the training data while remaining computationally feasible. There are also a number of hyperparameters: the number and size of hidden layers, the size of character embeddings, and the dropout rate. We tried various combinations of values between 50 and 6000 for the size and 1 and 4 for the number of hidden layers in both our Normalizer and Flagger. Some combinations we tried can be seen in the results section. Especially large sizes and numbers of layers proved to require more memory than our GPU could support, and training them on our CPU was exceptionally slow. We also tried 50% and 75% dropout, meaning that during training we randomly excluded hidden nodes from consideration at each layer. Dropout has been shown to improve performance by discouraging overfitting on the training data, and 50% and 75% are common dropout rates (Hinton, 2014).
We found the highest F1 score on the validation data for the Normalizer with two hidden layers of size 2000 each and 50% dropout. This was close to the maximum size our GPU could support without reducing the batch size to be too small to take advantage of the parallelism. The Flagger's highest score was found at two hidden layers of size 1000 each and 75% dropout. Attempts to provide hidden layers of different sizes consistently found inferior results. For the size of each embedding in the character projection layer, 10 had proven effective earlier in a simpler unpublished Twitter part-of-speech task. We selected 25 for our character embedding size to account for the greater complexity of a normalization task.
We separated the provided training data into 90% training data, 5% validation data and 5% was held out as test data. In order to construct a useful model on the small amount of available data, we iterate training over the same data many times. Our model stopped training after 150 training iterations in which there was no improvement on the validation set. We chose 150 iterations as the smallest value that did not lead to ending the training at a clearly suboptimal value. The training also stops at 5,000 iterations but in practice it converged before reaching this value.
Early in development we found that the Normalizer had exceptional trouble reconstructing twitter-specific objects, that is, hash-tags (#goodday), at-mentions (@marysue) and URLs (http://blahblah.com). Generally its behavior in all three cases was to follow the standard marker characters (@, #, http://) with a string of gibberish unrelated to the word itself. Because these are protected categories that should not be changed, we removed them from the training data and rely on the Flagger to flag them as not to be corrected.
We used layer-wise pre-training, meaning we first trained with zero hidden layers (going directly from the character projection to the softmax layer) to initialize the character embeddings, then we trained with one hidden layer, initializing the character embeddings with their previously trained values. When we trained the full model using two hidden layers, we initialized both the character projection layer and the weights from the projected input to the first hid-den layer with the values learned before. The model continued to learn all the weights it used. Pretrained weights continued to be trained in the full model, although "freezing" some pretrained weights after pretraining and only training later weights in the full model has shown success when working with large amounts of unsupervised data and may be worthwhile to consider in future work (Yosinski, Clune, Bengio, & Lipson, 2014).
Running on an NVIDIA GeForce GTX 680 GPU with 2 GB of onboard memory, training the Normalizer took about six hours. We do not include CPU and RAM specifications because they were not heavily utilized in the GPU implementation. The Flagger was considerably faster to train than the Normalizer, taking only a little over half an hour.
Results and Discussion
The model earned third place in the competition, with scores very close to the second place model. The model's results in the competition compared to the first, second, and fourth place models is shown in Table 1. The precision scores are much higher than the recall scores for all models because in this task precision measures the capability of the model to not normalize what does not need normalizing while recall requires that a model both correctly identify what needs to be normalized and correctly normalize it.
In addition to the challenge results, we performed a more in-depth analysis on our own held-out validation and test data. Our analysis of the scores is shown in Table 2.
Initial data on the Flagger is in Table 3. We further analyzed the different errors made on the validation data. Our findings can be found in Table 4. Given the large proportion of errors mistakenly marked "Do Not Normalize," we looked at these errors. A few examples can be found in Table 5. Although the Flagger was not trained with Normalizer confidence in mind, it does an impressive job of only cancelling a normalization when the normalization is either unnecessary or would fail. In no case did the Flagger prevent the Normalizer from making a correct normalization.
An analysis in Figure 3 shows some early results from using only the Normalizer without a Conformer or Flagger. To fit this many runs in a reasonable time span, we used only ten percent of the training data. In this analysis, error rate is measured by token. To put the error rates in perspective, our final error rate was close to three percent. We show this graph to illustrate a number of points. Particularly, we wish to illustrate the challenge of encoding and reconstructing every item in a massive vocabulary, the value of additional iterations of layer-wise pre-training, and the large spikes in the error rates at certain points in the model.
Model
Precision The Normalizer demands much more representational power when not assisted by the Flagger. Before we added the Flagger, we saw continual improvement of results going up to four layers of six thousand nodes each. We saw greater improvements from adding more nodes per layer than from adding more layers. The cluster of three lines near the top all have layers of 1500 or 2000 nodes each, and the next cluster down is the models we tried with 4500 and 6000 nodes. Incidentally, all but the smallest of these models were too large for our GPU's 2GB of onboard memory. As a reminder, after we added the flagger, we only required two layers of 2000 nodes each to get competitive results. In each case we used a dropout rate of 50%.
The default models pre-trained each layer for 250 iterations and we also trained models with the same structure for 500 iterations. We find a noticeable improvement in the error rate for the models that were pre-trained for more iterations. In the graph, the models with more pre-training make up the cluster of lines near the bottom of the graph.
Looking at the graphs, one may notice that some lines have brief spikes multiple percentage points in size. Because it only takes a one-letter mistake for a word to be misnormalized, we expect that at these times a small error arose that affected a large number of words. It is worth pointing out that each model continues to improve while in its spike, eventually dropping back to pre-spike levels.
The model is unique among the three topperforming models in that it avoids external data both directly and through indirect sources. The constrained task does not allow external data, but it does allow the use of off-the-shelf tools trained on external data. Our model does not use any such tools. Without the assistance of tools such as part-of-speech taggers, attempts to use context proved ineffective, likely because of increased sparsity. A given word that appears in the training set three hundred times may only appear three times after another particular word, and may not occur more than once with a particular prior word and following word, so it is more difficult to find patterns in limited data. Future work could either attempt to use tools to provide additional information or could simply take advantage of large amounts of data to learn directly the relationships such tools traditionally abstract for the benefit of conventional machine learning.
There is one other point: the human graders often made different decisions about whether or what a term should be normalized to. For exam-ple, sometimes the word "pics" used to refer to pictures was normalized to "pictures" but other times it was left as "pics". These inconsistencies in the gold standard make it difficult to accurately judge the quality of the models submitted. Occasionally when we examined mistakes the model made, we found that the model's prediction was correct according to the gold standard, but that the gold standard was wrong. An inter-rater reliability measure would help us to gauge not only how well our models compare to each other but how they compare to agreement between human coders.
Conclusions and Future Work
Normalization of Twitter text is a challenging task. With a direct application of simple deep learning techniques and without relying on any sources of external data, direct or indirect, we built a model that performed competitively with the other models in the task. Our method shows the ability of deep learning to tackle complex tasks without labor-intensive hand-engineering of features.
An important direction for future work is simplifying the normalization pipeline. The need for a Conformer in particular suggests that there is room for improvement in the model. Although constructing the normalized form rather than selecting from a list leaves the possibility open that a system could normalize to a correct word that did not appear in the training data, in practice this happened much less often than having the system normalize incorrectly. A model that predicts words from a vocabulary instead of reconstructing them would be faster to train and would not require a Conformer, and, considering the top two models were vocabulary based, might outperform our reconstruction-based model.
A second direction for future work centers on leveraging external data. With more time and greater computing power, it may be the case that it is possible to learn sophisticated language models in an unsupervised fashion from both standard conversational text and twitter data.
With this additional data, a model may be able to effectively use context in distinguishing between multiple possible normalizations of a word. Denoising autoencoders in particular are known to make good use of unsupervised data.
A third direction for future work is to investigate more challenging normalization tasks that include correction of syntax and do not present the text already tokenized. These will give us an opportunity to attempt tasks closer to the challenges our normalization systems will face in the real world.
Finally, it will be important to investigate the overall utility of normalization of text as a preprocessing step for other analysis. While many tasks will only benefit from cleaning the data, it is not clear that the canonical forms of words retain the same connotations that the original "noisy" versions held. For a simple example, if we were to normalize "cooooooool" to "cool" we would lose the emphasis implied by the elongation of the vowel. For some tasks, it may be important to retain the information contained in such non-canonical forms. | 5,804.4 | 2015-07-01T00:00:00.000 | [
"Computer Science"
] |
Classification of Traces and Associated Determinants on Odd-Class Operators in Odd Dimensions
To supplement the already known classification of traces on classical pseudodifferential operators, we present a classification of traces on the algebras of odd-class pseudodifferential operators of non-positive order acting on smooth functions on a closed odd-dimensional manifold. By means of the one to one correspondence between continuous traces on Lie algebras and determinants on the associated regular Lie groups, we give a classification of determinants on the group associated to the algebra of odd-class pseudodifferential operators with fixed non-positive order. At the end we discuss two possible ways to extend the definition of a determinant outside a neighborhood of the identity on the Lie group associated to the algebra of odd-class pseudodifferential operators of order zero.
Introduction
From the connection between the trace of a matrix with scalar coefficients and its eigenvalues, one can derive a relation between the trace and the determinant of a matrix, namely det(A) = exp(tr(log A)).
At the level of Lie groups, a trace on a Lie algebra is the derivative of the determinant at the identity on the associated Lie group. Using the exponential mapping between a Lie algebra and its Lie group, one recovers in this setting the relation (1). This exponential mapping always exists in the case of finite-dimensional Lie groups, and in the infinite-dimensional case its existence is ensured by requiring regularity of the Lie group. On trace-class operators over a separable Hilbert space one can promote the trace on matrices to an operator trace. Further generalizing to classical pseudodifferential operators one can consider traces on such operators. In the case of a closed manifold of dimension greater than one, M. Wodzicki proved that there is a unique trace (up to a constant factor) on the whole algebra of classical pseudodifferential operators acting on smooth functions on the manifold, namely the noncommutative residue [31]. As S. Paycha and S. Rosenberg pointed out [23], this fact does not rule out the existence of other traces when restricting to subalgebras of such operators. In fact, other traces such as the leading symbol trace, the operator trace and the canonical trace appear naturally on appropriate subalgebras. The classification of the traces on algebras of classical pseudodifferential operators of non-positive order has been carried out in [17] (see also [12]).
After the construction of the canonical trace on non-integer order pseudodifferential operators, M. Kontsevich and S. Vishik [8] introduced the set of odd-class operators, which is an algebra that contains the differential operators. They also defined a trace on this algebra when the dimension of the manifold is odd, and it has been proven that this is the unique trace in this context [14,22,26]. In [21], M.F. Ouedraogo gave another proof of this fact based on the expression of a symbol of such an operator as a sum of derivatives of symbols corresponding to appropriate operators on the same algebra.
Odd-class operators are one of the rare types of operators in odd dimensions on which the canonical trace is defined, this fact serving as a motivation to investigate the classification of traces on the algebra of odd-class operators of order zero. The noncommutative residue is not of interest here since it vanishes on odd-class operators (Lemma 2). This contrasts with the algebra of ordinary zero-order operators where the only traces are linear combinations of the leading symbol trace and the noncommutative residue (see [13]). We supplement that classification of traces, showing that when restricting to odd-class zero-order operators, the only traces turn out to be linear combinations of the leading symbol trace and the canonical trace (this is the particular case a = 0 in Theorem 3).
In this article we present the classification of traces on algebras of odd-class pseudodifferential operators acting on smooth functions on a closed odd-dimensional manifold. The methods we implement combine various approaches used in the literature on the classification of traces. However, a detailed analysis is required here because of the specificity of odd-class operators (see Proposition 3). We recall the one to one correspondence between continuous traces and determinants of class C 1 on regular Lie groups 1 , and as in [13] we use this correspondence to give the classification of determinants on the Lie group associated to the algebra of odd-class operators of a fixed non-positive order. At the end we discuss two ways to extend the definition of determinants outside a neighborhood of the identity.
In Section 2 we recall some of the basic notions of classical pseudodifferential operators, including that of symbols on an open subset of the Euclidean space and odd-class operators on a closed manifold. Inspired by [14], we use the representation of an odd-class symbol as a sum of derivatives up to a smoothing symbol (Proposition 1), to express an odd-class operator in terms of commutators of odd-class operators (Proposition 3), a fact that helps considerably in the classification of traces.
In Section 3 we give a classification of traces on odd-class operators of non-positive order. For that we recall the known traces on classical pseudodifferential operators. The noncommutative residue vanishes on the algebra of odd-class operators in odd dimensions, whereas the canonical trace is the unique linear form on this set which vanishes on commutators of elements in the algebra (see [14]). Then using the fact that any odd-class operator can be expressed in terms of commutators of odd-class operators (Proposition 3), we prove that any trace on an algebra of odd-class operators of fixed non-positive order can be expressed as a linear combination of a generalized leading symbol trace and the canonical trace (Theorem 3).
In Section 4 we classify determinants on the Lie groups associated to the algebras of oddclass operators of non-positive order. We follow some of the work done in [13], concerning the one to one correspondence between continuous traces on Lie algebras and C 1 -determinants on the associated regular Lie groups (this is also discussed in [2] in specific situations). Then, we combine this correspondence with the classification of traces given in Section 3.3, to provide the classification of determinants on Lie groups associated to algebras of odd-class operators of fixed non-positive order (Theorem 4). This classification is carried out for operators in a small neighborhood of the identity, where the exponential mapping is a diffeomorphism.
At the end of this section, we give two possible ways to extend the definition of a determinant outside a neighborhood of the identity on the Lie group associated to the algebra of odd-class pseudodifferential operators of order zero; the first one (see (22)) using a spectral cut to define the logarithm of an admissible operator; in this case, for some traces this definition of determinant depends on the spectral cut; the other one (see (24)) via the definition of the determinant of an element on the pathwise connected component of the identity, using a path that connects the element with the identity. Both the first and the second extension of the definition of a determinant, provide maps which do not depend on the spectral cut and which satisfy the multiplicativity property, under the condition that the image of the fundamental group of invertible odd-class pseudodifferential operators of order zero is trivial.
Preliminaries on pseudodif ferential operators
Here we recall the basic notions of classical pseudodifferential operators following [29].
Symbols
Let U be an open subset of R n . Given a ∈ C, a symbol of order a on U is a complex valued function σ(x, ξ) in C ∞ (U ×R n ) such that for any compact subset K of U and any two multiindices α = (α 1 , . . . , α n ), β = (β 1 , . . . , β n ) ∈ N n there exists a constant C K,α,β satisfying for all (x, ξ) ∈ K × R n , where ∂ α x = ∂ α 1 x 1 · · · ∂ αn xn , |β| = β 1 + · · · + β n , and (a) stands for the real part of a. Let S a (U ) denote the set of such symbols. Notice the space of smoothing symbols on U . Given σ ∈ S m 0 (U ), The product on symbols is defined as follows: if σ 1 ∈ S a 1 (U ) and σ 2 ∈ S a 2 (U ), In particular, σ 1 σ 2 ∈ S a 1 +a 2 (U ).
Classical symbols
A symbol σ ∈ S a (U ) is called classical, and we write σ ∈ CS a (U ), if there is an asymptotic expansion Here σ a−j (x, ξ) is a positively homogeneous function in ξ of degree a − j: for all t ∈ R + , |ξ| = 0, and ψ ∈ C ∞ (R n ) is any cut-off function which vanishes for |ξ| ≤ 1 2 and such that ψ(ξ) = 1 for |ξ| ≥ 1.
We denote by the algebra generated by all classical symbols on U for the product .
Odd-class symbols
The homogeneous components in the asymptotic expansion of a classical symbol may satisfy some other symmetry relations additional to the positive homogeneity on the second variable. Now we recall the definition of odd-class symbols introduced first in [8] (see also [5]).
Definition 1 (see [8]). A classical symbol σ ∈ CS a (U ) with integer order a is odd-class if for each j ≥ 0, the term σ a−j in the asymptotic expansion (3) satisfies In other words, odd-class symbols have the parity one would expect from differential operators.
Let us denote by CS a odd (U ) the set of odd-class symbols of order a ∈ Z on U . We set Lemma 1 (see [3,8]). The odd-class symbols satisfy the following: 1. The product of two odd-class symbols is an odd-class symbol, therefore CS odd (U ) is an algebra.
2. If an odd-class symbol is invertible with respect to the product , then its inverse is an odd-class symbol.
The noncommutative residue on symbols
As before, we consider U an open subset of R n .
Definition 2 (see [6,31]). The noncommutative residue of a classical symbol σ ∼ where µ is the surface measure on the unit sphere S * x U over x in the cotangent bundle T * U .
The noncommutative residue clearly vanishes on symbols of order strictly less than −n and also on symbols of non-integer order.
Lemma 2. In odd dimensions, the noncommutative residue of any odd-class symbol vanishes.
The function b −n is smooth on U × R n and is homogeneous of degree −n + 2 in ξ for |ξ| ≥ 1. As σ −n (x, ξ) vanishes for x outside a compact set, so does b −n (x, ξ). In particular, b −n is a symbol of order −n + 2 on U . Let us define τ i,−n+1 := −∂ ξ i b −n . Since h is odd so is b −n and therefore, Moreover, we have for r = |ξ| ≥ 1
Pseudodif ferential operators
Let U ⊂ R n be an open subset, and denote by C ∞ c (U ) the space of smooth compactly supported functions on U . To the symbol σ ∈ S(U ), we associate the linear integral operator Op(σ) : where u(ξ) = U e −iy·ξ u(y) dy is the Fourier transform of u and dξ := (2π) −n dξ. In this expression k(x, y) = e i(x−y)·ξ σ(x, ξ)dξ is seen as a distribution on U × U that is smooth outside the diagonal. We say that Op(σ) is a pseudodifferential operator (ψDO) with Schwartz kernel given by k(x, y). An operator is smoothing if its Schwartz kernel is a smooth function on U × U . If ψσ a−j is a classical symbol of order a, then A = Op(σ) is called a classical pseudodifferential operator of order a. The homogeneous component σ a of σ is called the leading symbol of A, and will be denoted by σ L A . A ψDO A on U is called properly supported if for any compact K ⊂ U , the set {(x, y) ∈ supp(k A ) : x ∈ K or y ∈ K} is compact, where supp(k A ) denotes the support of the Schwartz kernel of A. Any ψDO A can be written in the form (see [29]) where P is properly supported and R is a smoothing operator. A properly supported ψDO maps C ∞ c (U ) into itself. The product on symbols defined in (2) induces a composition on properly supported ψDOs on U . The composition AB of two properly supported ψDOs A and B is a properly supported ψDO with symbol σ(AB) = σ(A) σ(B).
The notion of a ψDO can be extended to operators acting on manifolds (see Section 4.3 in [29]). Let M be a smooth closed manifold of dimension n. A linear operator A : C ∞ (M ) → C ∞ (M ) is a pseudodifferential operator of order a on M if in any atlas, A is locally a pseudodifferential operator. This means that given a local coordinate chart U of M , with diffeomorphism ϕ : U → V , from U to an open set V ⊆ R n , the operator ϕ # A defined by the following diagram is a pseudodifferential operator of order a on V : is the natural embedding, and r U : Let C a (M ) denote the set of classical ψDOs of order a on M , i.e. operators whose symbol is classical of order a in any local chart of M . We will also denote by the space generated by classical ψDOs on M whose order is non-integer or less than −n. A classical operator A ∈ C a (M ) of integer order a is odd-class if in any local chart its local symbol σ(A) is odd-class. We denote by C a odd (M ) the set of odd-class operators of order a ∈ Z and we define As in Lemma 1, the following lemma implies that C odd (M ) is an algebra: The algebra C odd (M ) contains the differential operators and their parametrices.
Remark 1.
Even though the definition of odd-class pseudodifferential operators makes sense on any closed manifold, in this paper we restrict ourselves to odd-dimensional closed manifolds. The reason is that the canonical trace (which will be explained below in Section 3.1.2) is well defined only in that case. So, from now on, the notation C odd (M ) will be used only when the dimension n of the manifold M is odd.
Fréchet topology on pseudodif ferential operators
For any complex number a, we equip the vector space C a (M ) with a Fréchet topology as follows. Let us consider a covering of M by open neighborhoods {U i } i∈I , a finite subordinated partition of unity (χ i ) i∈I and smooth functions ( χ i ) i∈I on M such that supp( χ i ) ⊂ U i and χ i = 1 near the support of χ i . By (5)
any ψDO A can be written in the form
a−j (A), and R i is a smoothing operator with smooth kernel k i which has compact support in U i × U i .
We equip C a (M ) with the following countable set of semi-norms: for any compact subset K ⊂ U i for any j ≥ 0, N ≥ 1 and for any multiindices α, β
The logarithm of a classical pseudodif ferential operator
An operator A ∈ C (M ) with positive order has principal angle θ if for every (x, ξ) ∈ T * M \ {0}, the leading symbol σ L A (x, ξ) has no eigenvalues on the ray L θ = {re iθ , r ≥ 0}; in that case A is elliptic.
Definition 3 (see e.g. [18]). An operator A ∈ C (M ) is admissible with spectral cut θ if A has principal angle θ and the spectrum of A does not meet L θ = {re iθ , r ≥ 0}. In particular such an operator is invertible and elliptic. The angle θ is called an Agmon angle of A.
Let A ∈ C (M ) be admissible with spectral cut θ and positive order a. For (z) < 0, the complex power A z θ of A is defined by the Cauchy integral (see [28]) where λ z θ = |λ| z e iz(argλ) with θ ≤ arg λ < θ + 2π. Here Γ r,θ is a contour along the ray L θ around the (non-zero) spectrum of A, and r is any small positive real number such that Γ r,θ does not meet the spectrum of A. The operator A z θ is an elliptic classical ψDO of order az; in particular, for z = 0, we have A 0 θ = I. The definition of complex powers can be extended to the whole complex plane by setting for k ∈ N and (z) < k; this definition is independent of the choice of k in N and preserves the usual properties, i.e.
Complex powers of operators depend on the choice of spectral cut. Indeed, if L θ and L φ are two spectral cuts for A outside an angle which contains the spectrum of σ L (A)(x, ξ) then where the operator is a projection (see [25,32]). Here Γ θ,φ is a contour separating the part of the spectrum of A contained in the open sector θ < arg λ < φ from the rest of the spectrum. The logarithm of an admissible operator A with spectral cut θ is defined in terms of the derivative at z = 0 of its complex power: Logarithms of classical ψDOs of positive order are not classical anymore since their symbols involve a logarithmic term log |ξ| as the following elementary result shows.
be an admissible operator with positive order and spectral cut θ. In a local trivialization, the symbol of log θ (A) reads: where σ A 0 is a classical symbol of order zero. Remark 2. If A is a classical ψDO of order zero then A is bounded, and if it admits a spectral cut, then complex powers and the logarithm of A are directly defined using a Cauchy integral formula, and they are classical ψDOs (see [18] and Remark 2.1.7 in [21]).
Just as complex powers, the logarithm depends on the choice of spectral cut. Indeed, given two spectral cuts θ, φ of the operator A such that 0 ≤ θ < φ < 2π, differentiation of (6) with respect to z and evaluation at z = 0 yields
Pseudodif ferential operators in terms of commutators
In this subsection we use the ψDO analysis techniques similar to the ones implemented in [14]; we assume that M is an n-dimensional closed manifold and n is odd. Given a function f ∈ C ∞ (M ), we also denote by f the zero-order classical ψDO given by multiplication by f .
odd (M ) and a smoothing operator R A such that Proof . Let us consider a covering of M by open neighborhoods {U j } N j=1 and a finite subordinated partition of unity {ϕ j } N j=1 , such that for every pair (j, k), both ϕ j and ϕ k have support in one coordinate neighborhood. We write (see Subsection 2.2.1) Each operator ϕ j Aϕ k may be considered as an odd-class ψDO on R n with symbol σ in CS a odd (R n ). By Proposition 1, there exist odd-class symbols τ l of order a + 1 such that For any symbol τ we have, As in (5) we write ϕ j Aψ j = Op(σ j ) + R j for some σ j ∈ CS a odd (R n ) and some smoothing opera- where α k is a smooth function on M (and represents the operator in C 0 odd (M ) of multiplication by α k ), B k lies in C a+1 odd (M ), and R A is a smoothing operator.
, and a smoothing operator R such that
Classif ication of traces on odd-class operators
The classification made in this section is essentially based on Proposition 3, namely the decomposition of an odd-class operator in terms of commutators of odd-class operators. Let us first recall the definition of a trace. Let M be a closed connected manifold of dimension n > 1, and linear in the sense that for all a, b ∈ C, whenever A, B and aA + bB belong to A we have τ (aA + bB) = aτ (A) + bτ (B), and such that for any A, B ∈ A, whenever AB, BA ∈ A it satisfies
Examples of traces on pseudodif ferential operators
Interestingly by Lemma 2, the noncommutative residue, which is the only trace on the whole space C (M ) (see [4,10,31]), vanishes on odd-class operators when the dimension of the manifold is odd. In this section we review the traces which are non-trivial on this class of operators.
The L 2 -trace
A ψDO A whose order has real part less than −n is a trace-class operator. The L 2 -trace (also called operator trace) is the functional Tr : where k A is the Schwartz kernel of the operator A. This trace is continuous for the Fréchet topology on the space of ψDOs of constant order less than −n. This is the unique trace on the algebra of smoothing operators C −∞ (M ), since we have the exact sequence (see [7]) More precisely we have Theorem 1 (Theorem A.1 in [7]). If R is a smoothing operator then, for any pseudodifferential idempotent J, of rank 1, there exist smoothing operators S 1 , . . . , S N , T 1 , . . . , T N , such that Therefore, any smoothing operator with vanishing L 2 -trace is a sum of commutators in the space Proposition 4 (see e.g. Introduction in [10] and Proposition 4.4 in [11]). The trace Tr does not extend to a trace functional neither on the whole algebra C (M ), nor does it on the algebra C 0 (M ).
The canonical trace
We start with the definition of the cut-off integral of a symbol, as in [22]. Let U be an open subset of R n .
Proof . We write Using the fact that σ a−j is positively homogeneous of degree a − j we have It follows that the integral B * x (0,R) σ(x, ξ) dξ admits the asymptotic expansion where α x (σ) is given by which may depend on the variable x.
For N sufficiently large, the integral B * x (0,R) σ N (x, ξ)dξ is well defined, so the term α x (σ) given by (11) converges when R → ∞, and taking this limit we define the cut-off integral of σ by where S * x U stands for the unit sphere in the cotangent space T * x U . This definition is independent of N > a + n − 1. Moreover, if a < −n, then − R n σ(x, ξ)dξ = R n σ(x, ξ)dξ. According to Proposition 4, there is no non-trivial trace on C (M ) which extends the L 2 -trace. However, the L 2 -trace does extend to non-integer order operators and to odd-class operators. Indeed, M. Kontsevich and S. Vishik [8] constructed such an extension, the canonical trace where the right hand side is defined using a finite covering of M , a partition of unity subordinated to it and the local representation of the symbol, but this definition is independent of such choices.
As we already stated in Remark 1, the canonical trace is well defined on C odd (M ) only when the dimension n of the manifold is odd (see [5,10]), which is always our case.
If A ∈ C a (M ), B ∈ C b (M ) and if a, b / ∈ Z, then ord(AB) = a + b may be an integer, so the linear space C / ∈Z (M ) is not an algebra; in spite of this, the canonical trace has the following properties (see [8], Section 5 in [10], and [20,22,24]
Generalized leading symbol traces
In [23], S. Paycha and S. Rosenberg introduced the leading symbol traces defined on an algebra of operators C a (M ) for a ≤ 0; in this section we follow [17] and consider a trace which actually coincides with a leading symbol trace when a = 0. Let a be a non-positive integer and consider the projection map π a from C a (M ) to the quotient space C a (M )/C 2a−1 (M ): One can see in Remark 3. For a < 0, a leading symbol trace is the particular case of a generalized leading symbol trace when ρ a−i ≡ 0 for all i = 1, . . . , |a|.
Generalized leading symbol traces are continuous for the Fréchet topology on the space of constant order ψDOs, since they are defined in terms of a finite number of homogeneous components of the symbols of the operators.
Trace on C odd (M )
The canonical trace is the unique trace (up to a constant) on its domain. This result was proved in [14] (which goes back to 2007 but it was published in 2008) using the fact that the operator corresponding to the derivative of a symbol is, up to a smoothing operator, proportional to the commutator of appropriate operators. The latter idea was considered in [22] to show the equivalence between Stokes' property for linear forms on symbols and the vanishing of linear forms on commutators of operators. In [26] the author uses the Schwartz kernel representation of an operator to express any non-integer order operator and any operator of regular parity class as a sum of commutators up to a smoothing operator, and then to give another proof of the uniqueness of the canonical trace. The following proof, that we find in Proposition 3.2.4 of [21], is done in the spirit of [14]. Proof . By (9) any operator A in C odd (M ) can be written in the form where α k are smooth functions on M that can be seen as elements of C 0 odd (M ), B k belong to C a+1 odd (M ), and R A is a smoothing operator. By Theorem 1, we can express R A as where J is a pseudodifferential projection of rank 1 and S j , T j are smoothing operators. Summing up, the expression for A becomes Applying the canonical trace TR to both sides of this expression, since TR vanishes on commutators of operators in C odd (M ), we infer that TR(A) = Tr(R A ).
Thus (13) reads
If τ is a trace on C odd (M ), applying τ to both sides of (14) we reach the conclusion of the theorem.
Traces on C a odd (M ) for a ≤ 0
In this section we assume as before, that the dimension n is odd, and we prove that any trace on the algebra of odd-class operators of non-positive order is a linear combination of a generalized leading symbol trace and the canonical trace. We can adapt Lemma 4.5 in [12] (see also Lemma 5.1.1 in [17]) in the case of odd-class operators: Lemma 5. If a ∈ Z is non-positive, then there exists an inclusion map Proof . By Lemma 3, integer powers of an invertible differential operator are odd-class operators. Hence we proceed as in the proof of Lemma 4.5 in [12] as follows: Let A ∈ C 0 odd (M ), B ∈ C 2a odd (M ). Consider a first-order positive definite elliptic differential operator Λ. For any a ∈ R, Λ a and Λ −a are operators of order a and −a, respectively, and therefore AΛ a , Λ a A, Λ a , BΛ −a , Λ −a B, ABΛ −a , Λ −a BA are operators in C a odd (M ). Moreover, Adding up the expressions in (15) As in (12), for a non-positive integer a we also denote by π a the projection with corresponding splitting θ a : C a odd (M )/C 2a−1 odd (M ) → C a odd (M ), so that for any A ∈ C a odd (M ), A − θ a (π a (A)) ∈ C 2a−1 odd (M ). The following result adds to the known classification of traces on pseudodifferential operators, the classification of all traces on odd-class operators with fixed non-positive order in odd-dimensions.
We fix a non-positive integer a, and describe any trace on C a odd (M ) (see Section 5.1.4 in [17]).
Theorem 3. If a ∈ Z is non-positive, any trace on C a odd (M ) can be written as a linear combination of a generalized leading symbol trace and the canonical trace.
So we conclude that τ is a linear combination of a generalized leading symbol trace and the canonical trace.
Determinants and traces
We use the classification of traces on algebras of odd-class operators given in Theorem 3 to classify the associated determinants on the corresponding Fréchet-Lie group. Well-known general results in the finite-dimensional context concerning determinants associated with traces generalize to the context of Banach spaces (see [2]) and further to Fréchet spaces (see [13]).
Definition 4 (Definition 36.8 in [9]). A (possibly infinite-dimensional) Lie group G with Lie algebra Lie(G) admits an exponential mapping if there exists a smooth mapping Exp : Lie(G) → G such that t → Exp(tX) is a one-parameter subgroup, i.e. a Lie group homomorphism (R, +) → G with tangent vector X at 0.
The existence of a smooth exponential mapping for a Lie group is ensured by a notion of regularity [9,16] on the group. Following [9], for J. Milnor [16], a Lie group G modelled on a locally convex space is a regular Lie group if for each smooth curve u : [0, 1] → Lie(G), there exists a smooth curve γ u : [0, 1] → G (which is unique: Lemma 38.3 in [9]) which solves the initial value problemγ u = γ u u with γ u (0) = 1 G , where 1 G is the identity of G, with smooth evolution map For example, Banach Lie groups (in particular finite-dimensional Lie groups) are regular. If E is a Banach space, then the Banach Lie group of all bounded automorphisms of E is equipped with an exponential mapping given by the series In [19] a wider concept of infinite-dimensional Lie groups called regular Fréchet-Lie groups is introduced. In this paper we will consider the regular Fréchet-Lie groups of classical ψDOs of non-positive order (see [33]).
If G admits an exponential mapping Exp and if a suitable inverse function theorem is applicable, then Exp yields a diffeomorphism from a neighborhood of 0 in Lie(G) onto a neighborhood of 1 G in G, whose inverse is denoted by Log.
For our purpose in this section, we assume that the Lie group G is regular.
Definition 5 (see Definition 2 in [13]). Let G be a Lie group and letG be its subgroup of elements pathwise connected to the identity of G. A determinant on G is a group morphism i.e. for any g, h ∈G, We also say that Λ is multiplicative. A trace on the Lie algebra Lie(G) is a linear map λ : Lie(G) → C, such that for all u, v ∈ G, In our examples below [u, v] = uv − vu.
The following lemma gives the construction of a locally defined determinant on G from a trace on Lie(G).
Lemma 6 (see Proposition 2 and Theorem 3 in [13] which is based on [2]). A continuous trace λ : Lie(G) → C gives rise to a determinant map Λ : Exp(Lie(G)) ⊂G → C * def ined on the range of the exponential mapping by Λ(g) := exp(λ(Log(g))), where locally Log = Exp −1 , making the following diagram commutative, for any small enough neighborhood U 0 of zero in Lie(G):
Conversely, following [13] we give a construction of a trace from a determinant. Our proof here is different from the one in loc. cit.
Lemma 7 (See Proposition 2 and Theorem 3 in [13]).
A determinant Λ : Exp(Lie(G)) → C * , which is of class C 1 on G, yields a continuous trace λ : Lie(G) → C in the following way: for all u ∈ Lie(G) which makes the following diagram commutative:
Exp
Proof . Let u 1 , u 2 ∈ Lie(G). Then Here we use the fact that Λ is multiplicative, which implies that Λ(g −1 ) = Λ(g) −1 . The linearity of λ can be proved using the commutativity of the diagram. In the following we assume that M is an n-dimensional closed manifold and n is odd. We are going to classify determinants on a neighborhood of the identity in the space of invertible pseudodifferential operators (I + C a odd (M )) * , for a non-positive integer a. For that, let us first single out the Fréchet-Lie groups and Fréchet-Lie algebras we use.
The following proposition can be found in Proposition 3 in [13] for the case (C 0 (M )) * . See Proposition 6.1.4 in [21] for the case of odd-class operators. We give here an exhaustive proof of this result since we did not find it in the literature. On the other hand (see [29]), the inclusion C 0 (M ) → L(L 2 (M )) is continuous so that the inclusion i : C 0 odd (M ) → C 0 (M ) → L(L 2 (M )) is also continuous and the inverse image i −1 (V ) yields an open neighborhood of A in C 0 odd (M ) * . It follows that C 0 odd (M ) * is canonically equipped with a manifold structure which makes it a Lie group. Let us now construct an exponential mapping on C 0 odd (M ). Given any operator B in C 0 odd (M ), the differential equation has a unique solution in C 0 (M ) * given by where Γ is a contour around the spectrum of B. Note that A t is bounded since B has zero order. Let us check that A t belongs to C 0 odd (M ) * . The homogeneous components of the u which solves the initial value problem γ −1 uγ u = u, γ u (0) = I.
Inspired by Corollary 5.12 in [19], and [33] we have the following Proposition 7. If a < 0, the space of invertible odd-class ψDOs G := (I + C a odd (M )) * = ({I + A : A ∈ C a odd (M )}) * is a Fréchet-Lie group with Fréchet-Lie algebra C a odd (M ), which admits an exponential mapping from C a odd (M ) to (I + C a odd (M )) * . Explicitly this exponential mapping is given by This map restricts to a diffeomorphism from some neighborhood of the identity in C a odd (M ) to a neighborhood of the identity in G. The inverse is given by 4.1 Classif ication of determinants on (I + C a odd (M )) * for a ≤ 0 As before we consider a non-positive integer number a. From the classification of traces on C a odd (M ) derived in Theorem 3, we infer a description of the determinants defined on the range of the exponential mapping in (I + C a odd (M )) * . The following theorem supplements the known classification of determinants on classical pseudodifferential operators. Det c 1 ,c 2 (·) = exp c 1 ρ • π a (Log(·)) + c 2 TR(Log(·)) .
Proof . By Theorem 3, any trace τ on C a odd (M ) is a linear combination of the canonical trace and a generalized leading symbol trace: for some c 1 , c 2 ∈ C, and for some linear map ρ : Cl a odd (M )/Cl 2a−1 odd (M ) → C. Moreover, τ is continuous for the Fréchet topology of C a odd (M ). Then, applying Lemma 6 to G = (I + C a odd (M )) * and Lie(G) = C a odd (M ), it follows that a determinant map on G is of the form exp c 1 ρ • π a (Log(·)) + c 2 TR(Log(·)) .
The determinants given in Theorem 4 differ from the ones sometimes used by physicists for operators of the type I+Schatten-class operator [15,30] which in contrast to these are not multiplicative but do extend the ordinary determinant (Fredholm determinant) for operators of the type I+trace-class operator.
Extension of determinants
Now we consider determinants constructed from a trace as above, by defining both sides of Equation (21), not only on a neighborhood of the identity in the range of the exponential mapping, but also on a set of admissible operators and on the pathwise connected component of the identity.
Remark 5. In this section, the word "extension" is in the sense that the determinants can be defined on operators which not necessarily lie in the range of the exponential mapping. See Remark 6 below for the other sense of this word.
First extension
The first way to define these determinants is carried out by considering the right hand side of (21). In the case of G = C 0 odd (M ) * the logarithm can be defined provided one chooses a spectral cut θ thereby to fix a determination log θ of the logarithm. We set Recall that if the operator A lies in the odd-class and has even order, then the logarithm log θ A lies also in the odd-class. If φ is another spectral cut of A such that 0 ≤ θ < φ < 2π, by formula (8) we have where P θ,φ (A) is an odd-class projection as in (7).
Proposition 8 (Proposition 6.2.3 in [21]). Let λ be any continuous trace on C 0 odd (M ). Suppose that λ takes integer values on the image of P θ,φ (A) for all θ, φ and A, where A is an admissible operator with spectral cuts θ and φ as in (8). Then λ gives rise to the map Det λ θ in (22), on admissible operators, independent of the choice of the spectral cut θ.
Let us consider this construction for the traces given in Section 3: Let A be an admissible operator in C 0 odd (M ) with spectral cut θ. With the notation of Subsection 3.1.3, the determinant associated to the leading symbol trace λ = ρ • π 0 is defined by Det λ θ (A) := exp (ρ • π 0 (log θ A)) .
In Example 2 of [13], it is shown that if P is a zero-order pseudodifferential idempotent, then its leading symbol p is also an idempotent so that the fibrewise trace tr x (p(x, ·)) is the rank rk(p(x, ·)). Hence It follows that Det λ θ (A) is independent of the choice of the spectral cut θ for any linear map ρ : Cl 0 odd (M )/Cl −1 odd (M ) → Z. Observe that if A is a zero-order odd-class operator so is log θ A. Hence, the canonical trace extends to logarithms of admissible odd-class operators of order zero with its property of cyclicity in odd dimensions. The determinant associated to the canonical trace is defined by Det TR θ (A) := exp(TR(log θ A)).
In contrast to the leading symbol trace, the canonical trace does not satisfy the requirement of Proposition 8 so that the associated determinant depends on the choice of spectral cut.
Second extension
An alternative way to define these determinants is by considering the left hand side of (21) and the expression for a determinant given in the proof of Lemma 6: where γ : [0, 1] → G is a C 1 -path with γ(0) = 1 G and γ(1) = g.
Such an approach was adopted in [2] by P. de la Harpe and G. Skandalis in the case of a Banach Lie group. In her thesis [3], C. Ducourtioux adopted this point of view to construct a determinant associated to a weighted trace with associated Lie algebras C 0 (M ) and C (M ). In [13], J.-M. Lescure and S. Paycha showed that such a construction extends to Fréchet-Lie groups with exponential mapping.
As in Definition 5, let G denote the pathwise connected component of the identity 1 G of G and P(G) the set of C 1 -paths γ : [0, 1] → G starting at 1 G (γ(0) = 1 G ) in G. On P(G) we introduce the map: Det λ : P(G) → C * defined by where ω = g −1 dg is the Maurer-Cartan form on G.
Since λ satisfies the tracial property, Det λ has the multiplicative property: Lemma 8. Let γ 1 , γ 2 be two C 1 -paths in P(G). Then Proof . The same proof applies as in Lemma 6.
In general the Maurer-Cartan form ω = g −1 dg is not exact on G so that for a C 1 -path c : [0, 1] → G with c(0) = c(1), the integral c ω = independently of the choice of path γ.
3. If g lies in the range of the exponential mapping Exp then Det λ (g) = exp (λ(Log(g))) , where Log = Exp −1 is the inverse of the exponential mapping.
Remark 6. Item 3 of this proposition shows that Det λ is an extension of the determinant map defined in Lemma 6.
Proof . 1. We want to show that two homotopic loops c 1 and c 2 have common primitive. Let us first recall the following general construction of a primitive: for ω a differential form on G, let γ : [0, 1] → G be a C 1 -path and F : [0, 1] → G be such that for any t ∈ [0, 1], F (t) = ω(γ(t))γ (t).
If ω is an exact form i.e. w = df for some f ∈ G, then F (t) = f (γ(t)) is a primitive of F . If the form ω is closed, then ω is locally exact. In this case, let 0 = t 0 < t 1 < · · · < t k = 1 be a subdivision of the interval [0, 1] such that γ([t i−1 , t i ]) is a subset of G, and there exists f i defined on [t i−1 , t i ] such that df i = ω. We can construct a function F (t) on [0, 1] in the following way: F (t) = f 0 (γ(t)) on [t 0 , t 1 ], F (t) = f 1 (γ(t)) − h 1 on [t 1 , t 2 ] where h 1 = f 1 (γ(t 1 )) − f 0 (γ(t 1 )) and for i = 3, . . . , k, F (t) = f i (γ(t)) − h i on [t i−1 , t i ] where h i = f i (γ(t i )) − f i−1 (γ(t i )) + h i−1 . Now let F (t) and G(t) be primitives of c 1 and c 2 respectively. Since c 1 and c 2 are homotopic, there exists a family of C 1 -paths (α i ) 0≤i≤k defined in a neighborhood of 1 G such that c 1 = c 2 k i=0 α i . Each path α i is closed so that c ω vanishes on α i . It follows that F (t) = G(t), and therefore the map Φ is well-defined on Π 1 (G).
From Proposition 8 we can see that in the first extension of the definition of a determinant, the non-dependency on the spectral cut is controlled by the image of the projection P θ,φ by the trace λ. From Proposition 9, the map Det λ is well defined if the image of the fundamental group of C 0 odd (M ) * is trivial. The following theorem shows that in both definitions (Subsec- Theorem 5 (see Section 4.5 in [8] and Lemma A.5 in [3]). The fundamental group of C 0 odd (M ) * is generated by the homotopy classes of loops {Exp(2iπtP )} 0≤t≤1 , where P is a projector in C 0 odd (M ).
Remark 7. Let us give some comments for the case C odd (M ). As seen in Theorem 2, any trace in C odd (M ) is proportional to the canonical trace. For the subalgebra C 0 odd (M ) in (23) we defined the determinant associated to the canonical trace of an operator A with spectral cut θ. Unfortunately, this definition cannot be extended a priori to positive order elements of C odd (M ). Indeed, as we said before (see Subsection 4.2.1), if the order of A is even, for any spectral cut θ of A, the logarithm log θ A is also odd-class, so the canonical trace extends to logarithms of odd-class operators with even order and one can extend the determinant by: Det TR θ (A) := exp(TR(log θ A)). This is no longer true if the order of A is odd. M. Braverman in [1] introduced the notion of symmetrized trace to define a symmetrized determinant on oddclass operators. It was shown in [20] that this symmetrized trace is in fact the canonical trace. The idea is to compute the average of the usual terms given by two spectral cuts of A, namely θ and θ − aπ, where a is the order of A; one obtains the following definition of symmetrized logarithm: log sym θ A := 1 2 (log θ A + log θ−aπ A).
This symmetrized logarithm is also odd-class and, once again, one can use the canonical trace to define a determinant by setting: DET sym θ (A) := exp TR log sym θ A .
Notice that if a = 0, DET sym θ (A) = Det TR θ (A). However this symmetrized determinant also depends on the spectral cut θ and under suitable assumptions it is multiplicative up to a sign (see [1]). | 11,009.6 | 2011-11-29T00:00:00.000 | [
"Mathematics"
] |
MIED : An Improved Graph Neural Network for Node Embedding in Heterogeneous Graphs
.
Introduction
Graph data, utilizing nodes and edges to represent entities and their relationships, is a powerful structure for modeling complex real-world data [1,2], including social networks [3] and academic citation networks [4,5].Computing the embedding vectors of the nodes of the graph in the low-dimensional space is an important work.Compared to other types of data, graph data provides flexibility and expressive power for handling intricate relationships [6].To take advantage of this, a variety of graph embedding techniques [7] have been developed, such as HOPE [8] and GraRep [9] that use matrix factorization [10], DeepWalk [11] and Node2Vec [12] that rely on random walks.Powerful models like Graph Neural Networks (GNNs) [13] can also be used to calculate embedding.These methods are carefully designed and demonstrate strong embedding capabilities and primarily focus on homogeneous graph data [14].
However, in the face of real-world data, these techniques encounter difficulties.Often, data in many cases presents not as homogeneous graphs but as heterogeneous structures [15].These diverse entities and relationships reflect the complexity of real-world systems such as movie recommendation systems [16].Recognizing these complexities, researchers propose many heterogeneous graph embedding algorithm and metapath-based [17] methods are widely used in this area.Metapaths are predefined sequences of node types that encapsulate high-order semantic relationships within a heterogeneous graph.By simplifying complex relationships into homogeneous subgraphs, we can apply the homogeneous graph embedding algorithms that were previously discussed.
MAGNN [17], for instance, is one of best methods that integrate metapaths and attention mechanism to achieve efficient node representation learning for heterogeneous graph.Firstly, it uses dense layers to transform the features of different type of nodes into the same dimension.Then it uses metapaths to connect two same type nodes which are not directly connected in the original graph and aggregates the features of the metapaths.When combining results of different metapaths or their instances, it uses attention mechanism to find appropriate weights.This method has strong adaptability.Through the metapaths, the efficient aggregation of information in various heterogeneous graphs can be realized, and the attention mechanism is used to assign appropriate weights to different metapaths, so as to extract as much information as possible from the graph.
Despite these advantages, metapath-based methods still have room for improvement.Current models often neglect important adjacency relationships between nodes during feature alignment.To address these limitations, we propose a novel model called Metapath-Infused Exponential Decay graph neural network (MIED) for heterogeneous graph embedding.The model includes three parts: GCN-based node feature alignment, exponential decay encoder and metapath aggregation.Specifically, MIED first utilizes GCN to align the node features in the heterogeneous graph, enabling the aligned features to have the same dimension and reside in a unified feature space.Additionally, GCN effectively utilizes the neighborhood information based on metapaths during feature alignment, resulting in improved graph embeddings for downstream tasks.Next, when encoding features on metapath instances we introduce an exponential decay encoder to aggregate the features of nodes on the metapath with varying importance due to their distance to starting node.Finally, MIED employs the attention mechanism for metapath aggregation, fusing latent vectors obtained from multiple metapaths into the final node embeddings.
In summary, this work makes the following major contributions: (1) We propose a novel GCN-based node feature alignment method for metapath-based heterogeneous graph node embedding.
(2) We design an effective encoder function for metapath instances called exponential decay encoder which reasonably encode the features on the metapath according to the node importance.
(3) We conduct extensive experiments on the IMDb [18] and DBLP datasets [19] for node classification and node clustering, demonstrating that the node embeddings learned by MIED consistently outperform those generated by other state-of-the-art baselines.
Related works
This chapter will focus on heterogeneous graph representation learning methods relevant to our research.Through a comprehensive analysis of these methods, we will uncover their characteristics in practical applications and gain valuable insights for our research.
Graph Neural Networks
GNN [13,20] is a kind of specialized machine learning models designed for processing graph data.Graph Convolutional Networks (GCNs) extend convolution operation to GNN field.However, GCN suffers from "over-smoothing" [21][22][23] where its performance decreases with an increasing number of layers.Several algorithms have been proposed to address this problem or extend the GCN model.For example, Simplified Graph Convolution (SGC) [24] simplifies GCN by removing non-linear activation functions to enhance the propagation mechanism.
GCN requires that all nodes of the graph are present during training and do not naturally generalize to new added nodes.GraphSage [25] is designed to learn aggregators that samples and aggregates features from a node's neighbors.Therefore, it allows for efficiently generate node embeddings for previously unseen data.
Graph Attention Networks (GAT) [26] introduced attention-based neighborhood aggregation, allowing each node to attend to its neighbors and update its representation.GATv2 [27] modifies the order of internal operations in its attention function, working better in some cases.
Heterogeneous Graph Embedding
The distinct structures and properties of heterogeneous graphs make the direct application of homogeneous algorithms unsuitable [28][29][30].To address these limitations, researchers have introduced heterogeneous graph embedding techniques.
In this area, early algorithms like Metapath2Vec [31] utilized metapaths to generate node sequences in heterogeneous networks, capturing complex semantic relationships.However, they primarily focused on local structures, neglecting global information.To rectify this, Heterogeneous Graph Attention Networks (HAN) [32][33][34] and ESim [35] were introduced.HAN incorporates node types and neighbor data through a hierarchical attention mechanism, enhancing the capture of node attributes and topological data, and ESim provides a embedding-based similarity search framework for heterogeneous information networks, enabling effective handling of large-scale networks and capturing rich semantics.
In the domain of analyzing heterogeneous graph networks, MAGNN [17] has demonstrated promising performance.This method leverages a multi-head attention mechanism to adaptively allocate weights during the learning process, enabling a more comprehensive exploration of node data.MAGNN enhances graph embedding by aggregating neighbor features via combining node content transformation, intra-metapath and inner-metapath aggregation.
Furthermore, the application of knowledge graphs in online learning frameworks has been explored, with a focus on access control decision-making [36,37].Another notable work is SMiLE, which presents a schema-augmented multi-level contrastive learning approach for knowledge graph link prediction [38].
Definition
When describing the symbolic definition of heterogeneous graph embedding, we first need to clarify the symbolic representations of concepts.To facilitate the understanding of the symbols used throughout the discussion, Table 1 provides a comprehensive list of symbols and their respective descriptions.
Heterogeneous Graph.A heterogeneous graph is represented as G = (V , E), where V and E represent the sets of nodes and edges.T and R represent the sets of node types and edge types.ψ V : V → T and ψ E : E → R denote the node type mapping function and the edge type mapping function with |T | + |R| > 2.
Metapath.In the context of heterogeneous graphs, a metapath is a sequence defined by alternating nodes and edges.A metapath P is formally defined by the Equation ( 1), where t i and r i respectively represent the node types and edge types in the graph.
Metapath-based Neighbor.For a given metapath P and a node v ∈ V , the metapath-based neighbors of node v, denoted as N P (v), are defined as nodes that can be reached from node v through the metapath P .
Metapath-based Subgraph.For a node type t and a given metapath P , we can derive a homogeneous subgraph G t P = (V t , E t P ) from graph G.We define the adjacency matrix A t P = [a i,j ] ∈ R n t ×n t , where n t represents the number of nodes of type t.If node v i is adjacent to node v j with respect to metapath P , then a i,j = 1 else a i,j = 0.The node feature matrix for node type t is represented as X t ∈ R n t ×d t , where d t represents the dimension of the original node features.
Heterogeneous Graph Embedding: For a node type t in heterogeneous graph G, X t ∈ R n t ×d t denotes its feature matrix, in which d t represents the dimension of node features.Heterogeneous graph embedding aims to learn d-dimensional node representations H t ∈ R n t ×d (usually d ≪ d t ) which captures structural information for all nodes of type t.
Methodology
Our model MIED consists of three main parts: GCNbased node feature alignment, exponential decay encoder and metapath aggregation.It is outlined in Figure 1.The calculation process of heterogeneous graph embedding is illustrated in Algorithm 1.
GCN-based node feature alignment
In heterogeneous graphs, different types of nodes may have different feature dimensions.Even with the same dimension, different structures may have different feature distributions, demanding feature space alignment.In order to take into account the structural information of the graph, we propose node feature alignment using GCN.
If the adjacency matrix of a homogeneous graph is denoted as A, and I is its corresponding identity matrix, the output of (l + 1)-th GCN layer H (l+1) is calculated in the form of Equation ( 2), where à = A + I, H t P (0) = X t , Di,i = j Ãi,j is a diagonal matrix and W (l) is the weights of l-th layer.φ is used to denote the activation function, such as ReLU (x) = max(0, x) or sigmoid(x) = 1 1+e x .
For a heterogeneous graph G and a node type t, if given a metapath P , we can derive a homogeneous subgraph from G by using P and denote its adjacency matrix as A t P .We can apply GCN for each homogeneous subgraph and can get the transformed hidden states as in Equation ( 3).
If given a set of metapaths P t = {P 1 , P 2 , ..., P n } for node type t, We can apply GCN to each metapath according to the above method.Then we sum the hidden states computed by each metapath and get the final hidden states for each node of type t, as shown in Equation (4), where H t P represents the final output of GCN layers.
During the alignment process, the features of each node type are transformed into the same dimension, and feature space and graph information from neighbor nodes is aggregated, enriching the information contained in the aligned results.Output of the l + 1-th GCN layer W (l) Weights of the l-th GCN layer α Decay parameter in the exponential decay encoder Regarding computational complexity, in comparison to the baseline MAGNN, the addition of GCN-based node feature alignment involves GCN aggregation for each node type.Consequently, the increased computational complexity can be expressed as , where |T | represents the number of node types, N i denotes the number of nodes of the i-th type, M i signifies the mean number of neighbors for the i-th type, and K i represents the number of features for the i-th type.In many real-world graph data, the mean number of neighbors and the number of features for different node types may be constrained by a constant.Therefore, if we denote the maximum number of neighbors and features by M and K respectively, the total computational complexity increased by GCNbased node feature alignment compared to MAGNN is O(M • K • N ), where N corresponds to the total number of nodes in the graph.
Exponential Decay Encoder
After feature alignment, feature aggregation on the metapath must consider that nodes farther from the starting point have less relevance.Some proposed methods use average encoder, linear encoder or RNNbased encoder, but they lack effectiveness in capturing node weight decay on a metapath because of a long path of gradient backpropagation.MAGNN's relational rotation encoder [39] mitigates this to some extent but increases computational complexity and has potential for improvement.
We propose an exponential decay encoder (EDE) for better feature aggregation on a metapath.Given a metapath P for node type t, the encoder function is f θ (P (v, u)), where P (v, u) denotes the metapath from target node v to a neighbor instance u ∈ N P (v).The aggregation process is in Equation (5), with h (i) P ∈ R d as the aligned feature vector of the i-th node on P (v, u) from v to u and α as the decay parameter.The length of for i = 1, 2, .., I do for node type t ∈ T do 12: for metapath P ∈ P t do 13: for v ∈ V t do 14: Calculate h l P (v,u) for all u ∈ N P (v) using EDE refer to Equation (5); 15: Calculate β P (v,u) refer to Equation (7); 16: Combine extracted metapath instances of multi-head attention: 17: end for end for 20: Calculate γ P for each metapath P ∈ P t refer to Equation ( 12) and get : 21: [ end for
23:
Layer output projection: In order to reduce the impact of different magnitudes of features on EDE, techniques such as normalization can also be used to normalize the aligned features.Many normalization methods can be used, such as Min-Max normalization and Z-score normalization [40].During actual training, these methods can be set as a hyperparameter to let the model choose the most suitable normalization method.
The computational complexity of EDE on a metapath instance with n nodes is n i=1 where K represents the number of aligned features.
In contrast, for a similar method, the relational rotation encoder of the baseline model has a computational complexity of K EDE has an increase of O(n 2 ), but n represents the length of a metapath, which is usually not large and much smaller than K. Additionally, EDE reduces data storage space from O(K • n) to O(1) compared with relational rotation encoder.
Metapath Aggregation
Upon aggregating features of nodes on each metapath instance to h P (v,u) , we seek to aggregate all metapath instances linking node v. Appropriate weights must be assigned to each metapath instance's vector representation, as they influence the target node v differently.A graph attention layer is applied to metapath instances related to v, allowing the model to find optimal weights.The process uses ∥ for vector concatenation.
s∈N p (v) exp(e P (v,s) )) ( 7) Similarly, this method can be extended to incorporate a multi-head attention mechanism, as shown in Equation (9).Here, K represents the number of attention heads and β k P (v,u) represents the relative contribution value of the k-th attention head.
After aggregating the instances of the metapath P for node v, we need to further aggregate the information about the metapath set P t = {P 1 , P 2 , ..., P n } for node type t.For a node v, we denote {h v P 1 , h v P 2 , ..., h v P m } as the aggregated representation of each metapath, where m represents the number of metapaths corresponding to its node type t.Therefore, considering the different contributions of metapaths, we can apply an attention mechanism to find the weights of these metapaths.
Firstly, we average the representations of all nodes of type t with each metapath P ∈ P t , as shown in Equation (10).Here, |V t | represents the number of nodes of type t, M t ∈ R d m ×d and b t ∈ R d m are the weight parameters and bias vector.We denote the dimension of parameterized attention vector as d m .
Then the attention mechanism can be represented as follows, where q t ∈ R d m is the parameterized attention MIED : An Improved Graph Neural Network for Node Embedding in Heterogeneous Graphs vector.By summing all the weighted vectors, we calculate the aggregation of information for node v.
e P = (q t ) T • s P (11) γ P = exp(e P ) exp(e P i ) ( 12) Finally, we use a linear layer followed by a nonlinear activation function to map the aggregation of information for node v into the desired dimension of the vector feature space.This can be represented by Equation ( 14), where σ is the activation function and W o ∈ R d o ×d is the weight matrix.The entire equation can be seen as the output layer that connects to downstream tasks.
Training
After obtaining the embedding representation h v for each node, using the node labels, we perform backpropagation and gradient descent to minimize the cross-entropy and optimize the model weights.The loss function can be expressed by Equation (15), where C represents the number of classes, y v [c] represents the one-hot vector of the node label c, and log(h v [c]) represents the predicted vector for the node label c.
The MIED forward propagation algorithm, as delineated in Algorithm 1, is meticulously designed to produce node embeddings from a heterogeneous graph G with its nodes and edges.
Starting with the inputs, the algorithm receives the heterogeneous graph G, node types T , metapaths P t for each node type t, initial node features X t , the number of attention heads K, the number of layers L, the number of GCN layers I, and the exponential decay weight α.The end goal is to compute the node embeddings h v for every node v in G.
For every node type t, the algorithm, in lines 1-9 of Algorithm 1, initializes the feature matrix for each related metapath P using X t and subsequently refines it over I GCN layers.The formula H t P (i) (line 5 of Algorithm 1) depicts the GCN transformation, which incorporates adjacency and degree matrices with the node features to capture the graph structure.After iterating over all metapaths, the aligned node feature matrix is produced in line 8 by summing the outputs.
Delving deeper, lines 10-24 of Algorithm 1 iterate over L layers.Within each layer, for every node v of type t, the algorithm calculates features for all its neighbors using the metapath and the Exponential Decay Encoder (EDE) as detailed in line 14 of Algorithm 1.The attention mechanism is then invoked in lines 15-17 to aggregate these features into a single representation for the node.This ensures that more significant neighboring nodes, as described by the metapath, have a stronger influence on the node's representation.
Subsequent to aggregating features for each metapath, the algorithm, in line 20 of Algorithm 1, computes weights γ P for every metapath.This information is then employed in line 21 to combine embeddings across metapaths, forming a complete representation for each node type.Lastly, line 26 of Algorithm 1 applies a dense layer to refine these embeddings, making them suitable for downstream tasks.
By intertwining information from various metapaths in a heterogeneous graph, and leveraging the power of GCN and attention mechanisms, this algorithm efficiently derives rich and informative node embeddings.
Experiment
In this section, we apply MIED on two datasets to compare MIED with baselines on node classification task and node clustering task.We also try different normalization strategies and different hyperparameters α for exponential decay encoder to further explore their impact.Dataset.We experiment with two heterogeneous graph datasets, similar to the base model MAGNN.The detailed information of the two datasets is shown in Table 2 and the schemas of the datasets are shown in Figure 2. IMDb is a database about movies and television programs and has three kinds of labels: [41] and we use a subset of the dataset extracted by [17].The authors in DBLP have three kinds of labels: Database, Data Mining, Artificial Intelligence and Information Retrieval.We divide the DBLP dataset into training, validation, and testing sets with 400, 400 and 3257 nodes, respectively.We use one-hot id vectors as input features for nodes with no features in these datasets.We conduct node classification and node clustering tasks on these two datasets to evaluate the performance of our model.
Experimental Settings
Baselines and Hyperparameters.We compare MIED with various types of graph embedding models including MAGNN.These models include homogeneous models such as node2vec, GCN and GAT, as well as heterogeneous models such as ESim, metapath2vec, HERec and HAN.For MIED, we use the same settings and metapaths with MAGNN, if applicable.We set dropout rate to 0.5 and learning rate to 0.005.The number of attention heads is set to 8 and the dimension of attention vectors is set to 128.We set the dimension of the aligned features to 64 for MAGNN and MIED.For exponential decay encoder, we conduct a grid search on the weight decay parameter, using both original and Zscore normalized inputs to find the optimal model.
Node Clustering
We use the same split method of training, validation and testing sets and use K-Means [42] algorithm to cluster embeddings of labeled nodes into the number of classes for each dataset.Normalized mutual information (NMI) [43] and adjusted rand index (ARI) [44] are used as the evaluation metrics.MIED is tested over 10 runs, and we report the average results in Table 3.We can see that MIED outperforms MAGNN and other baselines in all metrics.When compared with the base model, MIED has improved by a maximum of 7.23% and a minimum of 1.27%.For the IMDb dataset, the best result is attained when using a decay value of 2/3 on original input.For the DBLP dataset, the best result is attained when using a decay value of 2/3 on Z-score normalized input.
Node Classification
To evaluate the embeddings of labeled nodes generated by each model, we use a linear support vector machine (SVM) [45] to classify them with varying training proportions.We test MIED over 10 runs and report the averaged Macro-F1 and Micro-F1, as shown in Table 4.We can see that MIED performs best across all metrics.When compared with base model, MIED has improved by 1.97% at most when the dataset is IMDb and the training proportion is 20%.For the IMDb dataset, the best result is attained when using a decay value of 1/2 on original input.For the DBLP dataset, the best result is attained when using a decay value of 1/3 on original input.
Module Analysis
To further explore the effect of two modules, we train a model that only applies the GCN module to MAGNN on the same data in 5.2 and 5.3, and collect results for comparison and analysis.We average the scores of node classification in different training proportions and show them in Table 5.
As shown in the table, after incorporating GCN method in MAGNN, the model performs better across all metrics.This shows that replacing the dense layer with GCN is effective.After implementing the EDE, the performance of the model is further improved.Among the 8 sets of comparative data, 7 sets of data have shown further improvement, which shows EDE is also effective.This table shows that our methods enhance metapath based heterogeneous graph embedding.
Parameter Analysis
We also try to inspect the influence of hyperparameters in the two modules.For GCN, we use one layer in our best result.We also experiment with using two layers of GCN, but the performance of the model get worse.We think the reason is when using two (or more) layers of GCN, the model will consider neighbors that are two (or more) hops away in the homogeneous graphs derived from metapaths, which are actually much far away in the original heterogeneous graph.
For the exponential decay encoder, an important parameter is α, and data normalization is also an important factor.So more experiments are done to inspect the influence of these two factors.We search best α in a set of {1/3, 1/2, 2/3, 1} on both original input and Z-score normalized input when that the model works relatively well in the middle part of the curves.Therefore, when selecting α we recommend selecting an α in [1/2, 2/3] or performing a grid search on (0, 1).
Conclusions and future work
In this paper, we propose MIED which contains two modules to enhance the node embeddings of heterogeneous graph.These two modules are: (1) using metapath-based GCN in the feature alignment to include graph information; (2) proposing EDE to distinguish the importance of different nodes when aggregating features on the metapath.Our comparative experiments demonstrate the effectiveness of our methods.
We also analyze the computational complexity of two proposed methods.They increase in computational complexity, but are controllable compared to their effects.Meta-path based methods have some scalability challenges when applied to large-scale graphs.But this can be effectively controlled by controlling the number and length of metapaths.After all, the value of information along very long metapaths is rapidly diminishing.
As heterogeneous graphs play an important role in fields such as multi-mode heterogeneous graph recommendation, we will apply our methods to graphs in these fields in the future, with the aim of further improving the performance of these models.MIED : An Improved Graph Neural Network for Node Embedding in Heterogeneous Graphs
Figure 1 .
Figure 1.Framework of MIED (GCN feature transformations for yellow and blue nodes are executed but not illustrated for clarity).
Figure 2 .
Figure 2. Schemas of the two heterogeneous graph datasets used in experiment.
Figure 3 .
Figure 3. NMI and mean Macro-F1 of IMDb and DBLP with different settings.
EAI
Endorsed Transactions on Scalable Information Systems 2023 | Volume 10 | Issue 6
Table 1 .
Symbols and Descriptions.
t Aggregated information representation of node v for node type t à Adjusted adjacency matrix D Diagonal matrix corresponding to à H (l+1) Algorithm 1 : MIED forward propagation.Output: The node embeddings {h v , ∀v ∈ V } 1: for node type t ∈ T do Input: The heterogeneous graph G = (V , E) , node types T = {t 1 , t 2 , ..., t |T | }, metapaths P t = {P 1 , P 2 , ..., P |P t | } for node type t , node features {X t , ∀t ∈ T }, the number of attention heads K, the number of layers L, the number of GCN layers I, the exponential decay weight α 4:
MIED : An Improved Graph Neural Network for Node Embedding in Heterogeneous Graphs EAI Endorsed Transactions on Scalable Information Systems 2023 | Volume 10 | Issue 6
Table 3 .
Experimental results (%) on the datasets for the node clustering task (n2vec is short for node2vec and m2vec is short for metapath2vec in the table).
Table 4 .
Experimental results (%) on the datasets for the node classification task (n2vec is short for node2vec and m2vec is short for metapath2vec in the table).
Table 5 .
The effect of the two modules on the model. | 6,165.6 | 2023-09-27T00:00:00.000 | [
"Computer Science"
] |
Positioning a Bank Service in Nigeria : A Conceptual Framework
The study looks at positioning of bank service in a competitive environment like Nigeria. Positioning was examined from the various definitions in the literature and the major components and strategies of positioning were discussed. The bank service in Nigeria was seen to be best positioned through non-functional and functional benefits. The non-functional benefits involve the bank’s corporate identity and brand image, this were seen to be well suited for old banks with high public acceptance, and positioning through functional benefits, which involve developing new attributes for the product or altering the old attributes of the product was found to be well suited for both old and new banks, and a framework for this was also developed.
Introduction
A bank service helps to distribute resources of a nation from a high concentrated area to a low concentrated area, to facilitate national growth and development.But numerous external forces shape the market of bank service (Zeithaml, Bitner, and Gremler, 2009)).The service is affected by economic, technological, demographic, socio-cultural, political and legal factors.
The level of prosperity, changing levels of disposal income, inflation rates, stock market performance, the rate of unemployment, shortages of raw material -all these affect the packaging and delivery of a bank service.The combination of interest rates, consumers' short term and long-term expectations concerning its direction as well as the general level of competition create marketing challenges for the bank service.
Education and occupation have a definite relationship with social class and consumer banking behavior and government exerts some amount of influence on bank service in order to protect consumers, the economy and other related entities through different regulatory frameworks.All of these put together affect the bank service.Most of prudential regulation of banking was predominant in United States in the mid -70s emanating as a result of the single-office banking system and traumatic experience of bank failures, particularly during the great depression of the 1980s.And when addressing the Lombard Association in April 1987 on the Central banking origins of the bank's supervision, the deputy governor of the Bank of England said he never remembered hearing that word 'supervision' used in the bank before 1974.The traumatic experiences of the fringe banking crises and bank failures of 1973/74 in the United Kingdom and the similar crisis and failure in the highly regulated banking system of Europe and America further enhance bank regulation all over the world, thus banks regulation becomes a prominent factor to envisaged and build into banking operations in order to survive.Nigeria is not different, the bank failure of 1990 -1994 and recapitalization policy of December, 2005 and the toxic loans saga of 2009 have affected the practice of banking.
Adding to this is the fact that banks have gradually realized that due to the presence of globalization and changing technology there is dire need to overhaul their payment and service delivery systems and operations so as to prosper in the new millennium.
Based on the foregoing, it becomes paramount to advance a conceptual framework that would serve as a guide to position the bank service in this turbulent environment of operations.
Literature Review
Positioning: Definitional Approach Kotler (2003) defines positioning as the act of designing a firm's offering and image to occupy a distinctive place in the mind of the target market with concomitant effect of creating a customer-focused value proposition that would facilitate patronage.Ries and Trout (1986) see positioning as a collection of creative activities that manipulates the consumers' mind in favour of the brand.They emphasize that positioning starts with a product and ends up creating a space and occupying it in the consumers' minds.They argue that a well-known brand only holds a distinctive position in consumer's mind which may be difficult for the competitors to claim, and that this position would only be maintained with well-articulated strategies concerning product, price, place, and promotion.Treacy and Wiersema (1994) view positioning as a collection of activities that instills value disciplines such as product leadership, operational excellence or customer-intimacy.This is based on the notion that in every market, there is a mix of three types of customers; some that prefer firm that is technologically inclined (product leadership); others that favour a highly reliable performance (operational excellence) and still, others want high responsiveness in meeting their individual needs (customer intimacy).They argue that no firm is best in any two of these ways as each value disciplines requires different managerial mind-sets and investments that often conflict.Treacy and Wiersema (1994) thus propose that for a business to be successful in positioning its brand there are four major things it must do in this light, first it must become best at one of the three value disciplines, second, it must also achieve adequate performance level in the other two disciplines, third, it must keep improving its superior position in the chosen discipline so as not to lose its position to competing firms and finally, it must not lose sight of the relevance of the other two disciplines as competing firms raise customers' expectations.Sengupta (1997) sees positioning as an act of identifying a vacant space in the consumers' mind space and occupying it for periods that varies according to the quality and quantity of marketing efforts behind the brand.He views it as a deliberate attempt to create a perception for a brand in the prospects' mind so that it stands apart from competing brands and approximates much more closely to what the consumers want.It is a matter of finding a strong position in that mind and sit on it, which means the same brand, in the same pack, with the same formulations can seek different positions in the consumer's mind space.He argues that positioning is less of what we do to the product and more of what we do to the customer's perception of the product.He further emphasizes that positioning is thus the fountain head decision, from which flows all other marketing and advertising decisions and that it provides the direction and thrust to marketing and advertising planning and also fuse them and the marketing mix into a cohesive whole.He finally submits that the position of a brand is its perception among target consumers based on its functional attributes and benefits, as well as on the non-functional or emotional associations it has acquired from its advertising.The colouration of these different perceptions by consumers' own attitudes, beliefs and experience, make different consumers segments to perceive the brand differently, and secondly the brand's position is perceived in relation to competitive brands.This position concurs with the opinions of Perreault Jr. et al (2009) and Kerin et al (2010).
However, Etzel, Walker and Stanton (2007) see it as fitting the product to the segment where product performances and appeals most correspond.It infers that there is a point where the appeal of a product corresponds with its performance.That is, the point where the quality that makes the product attractive or interesting must equate to its performance, such that, the customers are not disappointed, and thus fulfilling the unspoken promises made to the customers.Etzel et al (2007) recognizes this point as the positioning of the brand.This sounds vague and divergent from earlier thoughts of image creation and mind space as postulated by Kolter (2003), Ries and Trout (1982) and Segupta (1997) but tend to align with Treacy and Wiersena (1994)'s idea of product leadership.Smith and Lusch (1976) define positioning as a brand's objective or (functional) attributes in relation to other brands; it is a characteristic of a physical product and its functional features.They see 'position' as brand's subjective or perceived image which belongs not to the product, but rather, it is a mental picture, which could differ from the true physical picture of the brand.The definition emphasizes attributes analysis and estimation that positions the brand in the mind of the consumers, which makes the definition to align with the views of Kotler (2003) and Segupta (1997) but specific issues pertaining to product leadership, operational excellence or customer intimacy are not mentioned but may be inferred.
Rosser Reeves as cited by Sacco (1986) sees positioning as the art of selecting, out of a number of unique selling propositions, the one which will get you maximum sales.This definition looks at positioning superficially, it lacks the depth that the earlier definitions carry, because positioning is more than framing a set of words, the definition also plays down on the opinion of Crawford (1987) who believe that positioning is meant to drive the entire marketing programme of the organization, which aligns with Aaker (1984)'s view that product positioning is so central and critical that it should be considered at the level of a mission statement because it comes to represent the essence of a business.
From the foregoing, it is obvious that what 'positioning' represents seems to be ambiguous as the meaning varies from one researcher to another.However, positioning from the literature reviewed could thus be said to be, the perception of a brand that the consumers hold which makes it to occupy a space in the mind of the consumer as a brand leader, or operationally excellent brand, or customer intimated brand.Sengupta (1997) advances four components of positioning, which are product class, consumer segmentation, consumer perception and brand benefits.The product class denotes the set of products and brands which are perceived as substitute to satisfy some specific needs, it helps to identify the practical space in the mind of the consumer to occupy and the brands that are occupying such space presently.The particular brand that is occupying such space must be a close substitute of the intending brand for it to fit in to the space thus knowing the space gives the picture of the structure of the market.
Components of Positioning
The choice of product class could be used to secure competitive advantage for the brand through identifying the profile of the consumers and their needs, and directing all marketing efforts like promotional and media efforts toward these sets of consumers patronizing the brand in this product class.So, consumer segmentation is another component of positioning, identifying the consumers' characteristics, needs and expectations often makes one to know that segments do exist amidst consumers.Most leading brands with very large market shares often position themselves across several segments (Kerin, Hartley, and Rudelius, 2010).Sengupta (1997) says there is inseparable relationship between the position of a brand and its target segment.The more similar a brand is to other brands the more difficult it is to have a definite and distinct positioning, that is, there is need to be unique amongst the similar, thus carving out a niche for the brand.
The third component of positioning deals with the need to see where the brand is positioned in the mind of his prospects in relation to other brands, this is done with two-dimensional space called perceptual mapping.It helps to make positioning as a concept to be operational, the judgments of managers, sales staff or channel members are used to plot the brand position in the perceptual space of the consumers, and the customers may also be asked to rate the brand along attributes or benefits or they may be asked to judge by pairs, how similar or dissimilar the brands are (Urban, Hauser and Dholakia, 1987).So, the perceptual mapping gives a picture of the level of similarity and competitiveness among different brands by using measure of preferences between brands and ratings of brands on various attributes.
The final component of positioning is brand attributes and benefits, for the brand to occupy a space in the consumer's perceptual map; it must be in consumer's frame of reference, which requires that the brand attributes (which are the manufacturer's claim) be translated into consumer benefits.For a brand to be positioned with reference to an attribute, such attribute must be reinterpreted as measuring consumer benefit.So, it is important to search for vacant positions in the market with reference to preferred benefits and the preferred importance of such benefits.
The customer often evaluate the brand (both physical and emotional benefits) to know where it fits into their framework of needs and wants, since 'position' denotes the consumer's perceived distance from one another.When the perception of the brand has stimulated the consumer's interest, then the consumer gives it a space in her mind, then relates it with other competing brands, which may also have earned positions in her mind, the consumer then patronizes the brand, if he finds it to be better than others.. Consumers are able to form a mental picture of a given brand based on its functional attributes, performance and advertising because brand position is supported by its attribute and these attributes must be communicated in a special way, e.g. consumers may be made to perceive the product in different way without doing anything to the product by emphasizing one attribute of the brand over another because there is a link between the position of the brand as perceived by the target consumer and some of the brand's functional and non-functional attributes.Cravens and Piercy (2009) say that positioning strategy of looking at the world of the product through the consumers eyes and locating a promising vacant position in their minds must come first while articulation of the fitting attributes of the product must come next at the planning stage.
Positioning Strategies
Positioning strategies are needed to locate a niche in the market where the brand is perceived by the target audience as unique, which would invariably help to achieve competitive advantage.
The different types of positioning are thus stated:
(i). Positioning by Corporate Identity
This is only relevant where the organization has become a household name, such corporate identity can be used to position the product for acceptability and patronage.
(ii). Positioning by Brand Endorsement
This is a positioning used in growing a brand out of an existing successful brand, thus helping the new brand to key into the perceptual space of the old brand in the mind of the consumers.
(iii). Macro-Positioning
It relates to positioning the brand in a less-crowded category provided the attributes of the product can match consumer expectations from that category.This will make the brand to be seen differently.However, suitable modifications in the brand functional features and other elements may be needed to communicate it to the new market because new distribution, pricing, as well as competition may need to be defined.
(iv). Benefit -Related Positioning
This is a positioning of a brand through a unique combination of benefits, which may need to flow from feature or attribute, because consumers buy benefits not features.Attribute is important to consumers only when it leads to the special benefits, which the consumers seek, when the attribute provides the convincing reason of how the brand delivers the benefits.Atimes when the functional attributal differences amongst brands are obvious, marketer could use unique selling proposition to communicate this to the target market, but where the attributes of brands in the same product class are the same, the only option left for the marketer is to position such brand through benefit positioning, so that the position, which the consumer gives it in the her mind represents her perception of the brand in terms of the tangible or functional benefit and non-functional or emotional benefits.
(v). Positioning by Usage Occasion and Time of Use
It is important to pre-empt a particular usage, this is a strategy of creating and dominating a specific usage occasion.This is a more specific positioning strategy of having to identify a usage situation and sitting on it.It helps to attract adequate number of consumers, when a brand wishes to expand its market by creating and occupying other usage positions.However, competitive credibility is important if the usage of a brand has to be expanded, it must be credible enough in the intended segment to deliver the promise before it can succeed.
(vi). Price-Quality Positioning
Consumers have different expectations for quality at a particular level of price at different levels of socioeconomic status; this offers a greater opportunity for marketer to position their product through price-quality positioning.Varying levels of price-quality relationship of products often attract different segments of consumers.However, when the price of a brand goes up mainly because of cost and the quality remains the same, marketer often try to use Advertising and Repackaging to create a "quality" difference to shore up the quality of the brand against the price, this may create a credibility gap that may negatively affect the brand's patronage.But the right thing is that consumers get satisfied when there is actual value for money, and Advertising and Repackaging of such brand give a subjective added value that will go further to create an image that places it above its perceived rank on the price-quality ladder.So it is important to first and foremost ensure that price-quality ratio is balance, an imbalance in this ratio must be corrected by either increasing the benefits of the product through quality enhancement or increase price to meet with quality offered because usage for a 'value' brand can be enhanced to the level where it reinforces the users purchase decision but not to the point of the where it stretches the credibility of the brand.
(vii). Positioning by Target Segment
It involves positioning the brand to a set of consumers with similar needs and expectations from the brand and such consumers have similar characteristics in Demography (i.e.Age, income, sex, occupation, education, geographic location, etc.), Behaviour (e.g.volume of usage) Benefit or satisfaction desired, and Psychography (e.g.personality, lifestyle, social class, etc.).When a brand is positioned through any of the above, the segment tend to be strongly identified with it and thus give a distinct and unique identity to the brand.
For behavioural positioning particularly for heavy users of the brand, it gives that advantage of allowing small group of people to represent large percentage of the brand's patronage, that is; though the number of users is few but the volume of brands sold is high.It makes a lot of sense to position for heavy users when it is needful for resources to be economized.
The marketer can also find out the consumers that are linked together by benefit or satisfaction they derive from the brand, he then develops or modifies the brand and positions it to fit into this set of definite needs.
(viii). Positioning by Unique Attribute and Competitor
It is important atimes to position the brand by unique attribute of feature that makes it superior to competition.This attribute must be able to translate into benefit to give it a differential advantage at the market place.
And the brand could also be positioned against the competing brands.This is an offensive strategy that involves comparing the brand with other brands and showing why the brand should be preferred.
(ix). Positioning with Non-functional Values
Products are bought not only for their physical benefits but also for their symbolic or non-functional ones.Atimes customers are ready to pay twice for the symbolic meaning of a brand than for the physical attribute.This work for products that have conspicuous consumption as well as product whose identity is known only to the user.Others will see the result from the use of the product but they may not know until they ask of the name -this also has an implication for word -of -mouth publicity effect.The symbolic meaning that a brand commands is often called the brand image.
The consumption of a brand may be more important to the individual consumer than the functional benefits provided by the brand; actually advertising communicates the symbolic and indirect meanings that the brand represents.And the brand name is always a complex symbol that represents a variety of ideas and attributes, and the consumer buys when the symbolism fits.And the brand takes it up from there by creating strong bonding with emotions between itself and the consumer.The importance of symbolism in brand choice goes up when 'rationality' of the buying decision goes down (Sengupta, 1997).Brand symbolism has been established to have conceptual strength and operational utility (Arens, Weigold and Arens, 2010).Some researchers have also shown a high congruency between owners' perception of himself and the brand products he buys (Budwell, 1968;Belch and Belch, 2009;Arens et al, 2010) The self-Image of the consumer is the combination of its person's basic physical and emotional characteristics of the image of his 'real' self and of his 'ideal' self (i.e. the self he would like to be, this includes his aspirations).It is thus rational to feel that the consumer would buy products consistent with self-Image, and avoid products inconsistent with self-image, and engage in more transactions of products that facilitate his self-image.Therefore, in positioning a brand with its symbolic meaning, such symbolism must support the self-concept of the consumer.In many markets there are no real difference among the competitors, the major difference is in the degree of emotional attachments of the customers, this explains why people prefer a particular brand to another even though there is no physical difference between them.However, though this is important but this non-functional attributes must be adequately blended with the physical and functional values to form an integrated brand personality that can command patronage.
Materials and Methods
Positioning components and strategies as well as bank service in Nigeria were investigated.Also an investigation was carried out on how the bank service could be positioned as a competitive advantage in a turbulent business environment like Nigeria through a thorough examination of the inherent features of each of the bank products.And a conceptual framework for this was sought.
Result and Discussion
The Bank Service in Nigeria Banks are financial institutions that accept deposits and channel them into lending activities.Banks provide financial services that are collection of deposits and lending of such deposits to others that may be in need of them at a price.The bank service thrives on the difference between interest paid on all deposits, which ranges from savings, current to fixed deposits, and the interest received from these deposits when lend out to borrowers.So the bank service is a dichotomous service of two types customers i.e. the depositor and the borrower, as shown in figure 1.There will be no service to render by the banks if they cannot attract depositors whose money they will use to establish their relationship with the borrower apart from buying and selling of foreign currencies.
Figure 1 here
The attraction of these two types of customers are essential for the survival of the bank because if the depositors are attracted and no one is borrowing the money, there would be excess/idle funds in the bank whose cost will be on the bank, the attraction of the two types of customers is imperative for banks survival.
Three major accounts could be said to be existing in every bank, these are savings, current and deposits accounts.These three accounts differ on the basis of requirements, benefits, level of risk and maximum balance.These four variables also determine the proportion of the products that exist in every bank.The savings account has a low level of requirement (for example with any form of identification and a definite place of residence one can open the account); the interest paid on the savings account is the lowest amongst all deposits in most countries); It has high level of risk to the to the bank; (advent of electronic banking has revealed a high level of fraud being perpetrated by holders of this accounts, as it has been discovered that most of the forms of identification used to open such accounts are fake), maximum balance is restricted, (to mitigate this level of risk, banks have set a maximum balance that must be in such account, this is done to reduce the level of risk that is borne by the banks in event of fraud.
The saving account differs in requirement and benefits depending on the type.The average interest rate on it ranges from 1-3% per annum.The higher the interest rate paid to customer the higher the requirements; examples of such requirements are; compulsory savings overtime, little form of insurance, no withdrawal except by termination, where withdrawal are allowed it must not be more than three times in a year or the customers forfeits the interest.
Table 1 here
For current account the requirement for opening the account is high because of the different demands placed on the customers e.g. the customer must be a working class whose salary must be paid into the account i.e. salary current account and all identifications to prove this are required, or customer must have a company that he intends all financial transactions pass through i.e. corporate account/Enterprise account, or a customer wishes that all his financial benefits should be deposited and allocated appropriately after death, i.e. trustee account.All these accounts have high benefits relative to costs, low risk to the bank and unrestricted value to depositors.And the domiciliary account is one that the customer makes deposits and withdrawal of foreign currency depending on the type of the currency e.g.Dollar, Pounds, Euros, etc.
The deposits accounts' requirements are generally low; the period of deposits in most cases distinguishes the different types.It is fixed deposit if it is deposited for a period of one month or less, it is called call deposit when the period is more than one month but less than 1year, it is called a bankers' acceptance when bigger value is involved for a longer time.The benefits enjoyed differ with time and value of the money deposited, for example while with-holding tax and VAT is charged on the fixed deposit, it is not charged on the Bankers' acceptance.The level of risk is low and the maximum deposit is not restrictive.However, the risk of collecting deposits may be high when the bank does not have borrowers to use such monies, because while the bank may be required to pay the customer who deposited the money an interest of about 5 to 8% per annum, when no customer comes forth to borrow such money the only option for the bank is to deposit it with the Central bank of Nigeria that will pay an interest of only 1% per annum.This is a loss of about 4 to 7 percent to the bank.This further lay credence to the importance of the borrowing customers.But when there is a borrowing customer, the bank lends out such money at the rate of 20 percent per annum or more, thus making a gain of 17-20 percent on any money deposited.
Positioning a Bank Service in Nigeria: A Conceptual Framework
Service as a form of offering has unique characteristics such as intangibility, inseparability, variability, and perishability (Perreault Jr., Cannon and McCarthy, 2010).The service industry is a complex, dynamic and competitive environment.Banks in Nigeria witness increased competition that makes it necessary for a bank to position her service effectively to gain competitive advantage.
Positioning by corporate identity is possible for banks that have acquired high market acceptance over the years; most banks that are big and reliable, especially banks that have sufficiently survived the era of Nigerian banks failures of 1990 -1994, the recapitalization era of December, 2005 and the recent toxic loan saga of 2009.Amongst this set, some of the banks cannot still position their service in this manner because their market acceptance has decreased over the years even though they have not totally failed.So, very few banks can afford to position their service in this category.
Positioning by Brand endorsement can also be done by banks that have had a successful offering or brands, using the new brand to occupy the perceptual space of the old brand in the mind of the consumers will not be difficult.
Figure 2 here
Macro positioning of bank service requires an in-depth research of the needs of the customers, then these specific needs are either encapsulated into a new product offering or the old product is modified to fit into it.For example, the savings account could be modified to specifically serve the retirees, or students or teachers who have specific needs that could be incorporated into the offering.Such modification or new product must be well communicated to the target audience using the appropriate medium and all organizational framework that will support the implementation must be put in place aside the need to modify other Ps of marketing that are supposed to provide the necessary complements.
The current and the fixed deposits of banks could be best positioned as Benefit related positioning where more benefits would be attached to these accounts because these two accounts give the banks separate advantages, while the bank benefits from the charges on current account, they pay for the funds of the fixed deposits through interest but such deposits are used as loanable funds to borrowers who pay higher interest.It is important therefore for every bank to distinguish these services from competitors by attaching additional benefits to it, which may alter their attributes, but allows it to be positioned in a new perpetual space in the customers' mind.For example, the current account holder could enjoy more ease of bank transfer, notice of deposits and withdrawals, greater representation of his bank in business transaction, etc., while the fixed depositor may enjoy facilities that would lessen the effect of his money being fixed e.g.unfix the fixed by issuance of cheque books to such persons who fix with the intention that they may require their monies before maturity, thus allowing for an arrangement that makes them to withdraw without totally losing their "fixed" status.Cost of this service will be deducted from the naira value of the interest rate at the end of deposit period.This service relaxes the fixed nature of the fixed deposit account without the bank incurring any loss.
Bank service could also be positioned by usage occasion and time of use through identification of a particular target audience's needs that is attached with occasion or time e.g. for students during collection of University entry forms, West African Examination Council's forms, etc, payment of school fees etc, special services during these time would enhance the patronage of such banks apart from being an avenue of establishing new relationships.As shown in figure 1, the impact of these positioning is often reflected in increase in patronage or market share.
Conclusion
Positioning denotes identifying a vacant space in the consumers' mind space and occupying it.The major components of positioning are product class, consumer segmentation, consumer perception and brand benefits.It is noted that bank service in Nigeria could be positioned through non-functional and functional means.The non-functional means involves making use of the corporate identity and the brand image of the bank where such bank has had high market acceptance, and functional positioning involves making use of the benefits derivable from the product attributes, which may be new attributes or modified attributes and when the product is rightly positioned in the right context it would lead to increase in patronage and enhanced market share for the bank.Urban, Glen, Hauser, John, and Dholakia, Nikhilesh. (1987).Essentials of New Product Management.New Jersey: Prentice-Hall.Zeithaml, Valerie, Bitner, Mary Jo., and Gremler, Dwayne. (2009) Fig. 2. Conceptual frame work of positioning a bank Service
Table 1 .
. Services Marketing: Integrating Customer focus across the firm.New York: McGraw Hill.Analysis of Bank Product | 7,246.4 | 2010-07-21T00:00:00.000 | [
"Business",
"Economics"
] |
Large-$N$ limit of the gradient flow in the 2D $O(N)$ nonlinear sigma model
The gradient flow equation in the 2D $O(N)$ nonlinear sigma model with lattice regularization is solved in the leading order of the $1/N$ expansion. By using this solution, we analytically compute the thermal expectation value of a lattice energy--momentum tensor defined through the gradient flow. The expectation value reproduces thermodynamic quantities obtained by the standard large-$N$ method. This analysis confirms that the above lattice energy--momentum tensor restores the correct normalization automatically in the continuum limit, in a system with a non-perturbative mass gap.
Introduction
The Yang-Mills gradient flow or the Wilson flow [1] is a powerful method to construct renormalized composite operators in gauge theory (see Ref. [2] for a recent review). This follows from the fact that a local product of bare fields evolved by the gradient flow possesses quite simple renormalization properties [3,4]: The multiplicative renormalization factor of the local product is determined simply by the number of fermion (or generally matter) fields contained in the local product; the flowed gauge field requires no multiplicative renormalization. Furthermore, no infinite subtraction is needed. Since such a renormalized operator is independent of regularization (after the parameter renormalization), the gradient flow is expected to be quite useful in relating physical quantities in continuum field theory and operators in lattice theory.
On the basis of this very general idea, a possible method to construct the energymomentum tensor on the lattice through the gradient flow was proposed in Ref. [5]. This method was further investigated from a somewhat different perspective in Ref. [6] and also generalized in Ref. [7]. As well recognized [8,9], the construction of the energy-momentum tensor on the lattice is quite involved because lattice regularization breaks the translational invariance. The intention of Refs. [5,7] is that the constructed lattice energy-momentum tensor restores the correct normalization and the conservation law automatically in the continuum limit.
The construction in Refs. [5,7] is based on very natural assumptions, such as the existence of the energy-momentum tensor and the renormalizability of the gradient flow in the nonperturbative level. Also, the validity of the construction has been tested for thermodynamic quantities in quenched QCD by using a Monte Carlo simulation [10]. See also Ref. [11] for updated numerical results. However, whether the conservation law is really restored in the non-perturbative level is still to be carefully examined.
Under these situations, it must be instructive to consider a simpler system that would allow a similar construction of the lattice energy-momentum tensor. Mainly with this motivation, the gradient flow for the 2D O(N ) nonlinear sigma model was investigated in Ref. [12]; an identical flow equation has also been studied in Ref. [13]. In Ref. [12], it was proven to all orders of perturbation theory that the N -vector field evolved by the gradient flow requires no multiplicative renormalization, a quite analogous property to the 4D gauge field. Because of this renormalizability of the gradient flow and because of the asymptotic freedom, one can imitate the construction of the lattice energy-momentum tensor in Refs. [5,7]. Then, since the 2D O(N ) nonlinear sigma model is solvable in the 1/N expansion (see, e.g., Ref. [14]), one naturally expects that the property of the lattice energy-momentum tensor constructed through the gradient flow can be investigated by utilizing this analytical method, without any systematic errors associated with numerical study. This is the main intention of the present paper: We test the construction of the lattice energy-momentum tensor in Ref. [12] by using the 1/N expansion. For this, we first recapitulate the well known large-N solution of the 2D O(N ) nonlinear sigma model that exhibits a non-perturbative mass gap (Sect. 2). Next, we solve the gradient flow equation in the leading order of the 1/N expansion (Sect. 3). We could not find a solution in the sub-leading order of the 1/N expansion. This is unfortunate, because in the leading order of the 1/N expansion all correlation functions factorize into one-point functions, while the test of the conservation law of the energy-momentum tensor requires nontrivial multi-point functions. Still, we can exactly compute one-point functions in the large-N limit. For example, we can obtain a non-perturbative running coupling constant by computing the vacuum expectation value of a composite operator analogous to the "energy density" defined in Ref. [1] (Sect. 4). The one-point function of our energy-momentum tensor is trivial in vacuum, but it becomes nontrivial if one considers the system at finite temperature, as in Ref. [10]. In Sect. 5, we compute the expectation value of the energy-momentum tensor at finite temperature in the large-N limit. This expectation value is directly related to thermodynamic quantities (the energy density and the pressure) of the present system. We observe that the expectation value correctly reproduces thermodynamic quantities directly computed by a standard statistical large-N method given in Appendix A. In Appendix B, we illustrate how a "naive" construction of the energy-momentum tensor on the lattice fails to reproduce the correct answer. The present analytical test confirms that the lattice energy-momentum tensor in Ref. [12] restores the correct normalization in this system with a non-perturbative mass gap, at least in the large-N limit. The last section is devoted to the conclusion.
Leading large-N solution of the 2D O(N ) nonlinear sigma model
The partition function of the 2D O(N ) nonlinear sigma model is given by where λ 0 is the bare 't Hooft coupling constant, which is held fixed in the large-N limit. Throughout this paper, repeated Latin indices i, j, . . . , are assumed to be summed over the integers from 1 to N . In Eq. (2.1), we assume lattice regularization with the lattice spacing a and ∂ µ denotes the forward difference operator. To apply the 1/N expansion (see, e.g., Ref. [14]), one first integrates over the N -vector field n i (x), to yield where ∂ * µ denotes the backward difference operator. Then, since the exponent is proportional to N , for large N , the integral over the auxiliary field σ(x) can be evaluated by the saddle point method. Assuming that the saddle point is independent of x, σ(x) = σ, it is given by the gap equation, In the present problem, we may equally adopt dimensional regularization (DR), by setting the spacetime dimension D = 2 − ǫ. With this regularization, the associated bare coupling 3 constant λ DR 0 is renormalized as with the renormalization scale µ. The gap equation is obtained as Eq. (2.3) and one has where γ is the Euler constant. From this expression, we can deduce the exact renormalization constant in the minimal subtraction (MS) scheme, and correspondingly the exact beta function, Then, from Eq. (2.7), we have
Leading large-N solution of the gradient flow equation
Following Refs. [12,13], we consider the flow equation in the O(N ) nonlinear sigma model defined by 1 where t is the flow time and the initial value at t = 0 is given by the N -vector field in the original O(N ) nonlinear sigma model, that is subject to the functional integral (2.1). In this expression, again, we are assuming lattice regularization in the x directions. To make the counting of the order of 1/N easier, 1 Note that the normalization of the N -vector field is different from that of Ref. [12] by the factor 1/ √ N .
4
we render the flow equation (3.1) linear in n i (t, x) by introducing a new variable σ(t, x) as, Note that the second relation does not contain the flow-time derivative. Then Eq. (3.3) can be formally solved as is the heat kernel with lattice regularization. The heat kernel satisfies By iteratively solving Eq. (3.5), we can express the flowed field n i (t, x) in terms of the initial value n i (y) and σ(s, z) at intermediate flow times as (3.7) Diagrammatic representation of the above elements and expressions is useful. 2 In Eq. (3.7), the heat kernel K t (x) (3.6) connecting two spacetime points is represented by an arrowed solid line as Fig. 1. An open circle denotes the interaction between the flowed N -vector field and the auxiliary field σ(t, x), which is represented by a short dotted line. A typical term in the solution (3.7) is thus represented as We may now substitute the solution (3.7) in the equality (3.4) to express the auxiliary field σ(t, x) in terms of the initial value n i (y). This process can be diagrammatically represented as Fig. 4.
So far, everything concerns the solution to the deterministic differential equation (3.1). Let us now take into account the quantum effect, i.e., the fact that the initial value n i (y) is subject to the quantum average (2.1). In the leading order of the 1/N expansion, the integration over the auxiliary field σ(x) in Eq. (2.1) is approximated by the value at the saddle point, σ(x) = σ. Then, since the action is quadratic in n i (x), the quantum average produces contractions of n i (x) fields by the free massive propagator with the mass σ. In terms of the diagrammatic representation above, this amounts to taking the contraction of all crosses in all possible ways. Let us consider these contractions for σ(t, x) in Fig. 4. In this diagram, recalling that the vertex in Fig. 3 carries the factor 1/N and noting that each closed loop of the N -vector field gains the factor N , it is obvious that the leading large-N contribution to the quantum average of σ(t, x), denoted by σ(t, x) , is given by a diagram such as Fig. 5 in which each closed loop contains only one vertex in Fig. 3; overall, this is a quantity of O(N 0 ). 3 The topology of diagrams in the leading order in the 1/N expansion is thus identical to that of the leading order diagrams in the conventional 1/N expansion of the N -vector model (the so-called "cactus" diagrams). To calculate sub-leading orders of 1/N , we have to find not only the one-point function but also the (connected) higher-point functions of σ(t, x), whose systematic treatment is left as a future subject. In a similar manner, it is easy to see that, in the leading order in the 1/N expansion, a correlation function of generic operators containing σ(t, x) and n i (t, x) fields factorizes into the product of the expectation value σ(t, x) and correlation functions of the n i (t, x); this is nothing but the large-N factorization. Then, since σ(t, x) is independent of the spacetime position x (the external momentum in Fig. 5 is zero), we can set σ(s, z) in Eq. (3.7) constant in spacetime, σ(s, z) → σ(s) . 4 Then, noting the relation we have a compact expression for Eq. (3.7), where we have written σ(s) ≡ σ(s) for notational simplicity. The propagator between the flowed N -vector fields is then obtained by contracting n i (y) in Eq. (3.9) by the propagator in the large-N limit: This yields In terms of this "dressed propagator", the expectation value σ(t) is given from Eq. (3.4) by This self-consistency condition is schematically represented as Fig. 6. As far as lattice regularization is understood, the momentum integration in the right-hand side is regular even at t = 0 and we may integrate both sides of the above relation over t from t = 0 to some prescribed value. In this way, we have As far as t > 0, the integrals are well convergent and we may send a → 0 to have a definite continuum limit. Thus, for t > 0, we obtain where Γ (z, p) is the incomplete gamma function. Here, the order of the two limits is very important. Our construction of the energy-momentum tensor on the basis of the gradient flow relies on a universality, which is ensured if the flow time is fixed and ultraviolet regularization is removed. Thus, we should first take the continuum limit while keeping the flow 8 time finite; we then consider the small flow-time limit. Also, using Eqs. (3.12) and (3.16), for t > 0 we have The dressed propagator (3.11) with this prefactor provides the solution of the gradient flowed system at the leading order in the large-N limit.
Non-perturbative running coupling in the large-N limit
Since the expectation value, is a renormalized quantity [12] that possesses the perturbative expansion, 16πt E(t, x) = λ 0 + · · · , it can be used as a non-perturbative definition of the running coupling constant at the renormalization scale 1/ √ 8t [12]. This is analogous to the non-perturbative running gauge coupling defined through the "energy density operator" [1].
From our large-N solution in the previous section, we have This is a monotonically increasing function of t being consistent with the fact that the exact beta function (2.9) is negative definite.
Thermal expectation value of the lattice energy-momentum tensor
Following the general idea in Refs. [5,7], a possible method using the gradient flow to construct a lattice energy-momentum tensor for the O(N ) nonlinear sigma model has been proposed [12]. The intention in Ref. [12] is to construct a lattice operator that restores the correct normalization and the conservation law automatically in the continuum limit. It is thus quite interesting to examine if the idea works (or not) by using the above exact large-N solution of the gradient flow. Unfortunately, at the leading order of the 1/N expansion, any correlation function factorizes into one-point functions of O(N ) invariant quantities. Thus, in the present paper, we can consider only the one-point function of the energy-momentum tensor. Since we define the energy-momentum tensor by subtracting the vacuum expectation value, the one-point function is trivial in the vacuum. The one-point function of the energymomentum tensor is quite interesting, however, if we consider the system at finite temperature, as in Ref. [10]. Thus, let us consider the expectation value of the energy-momentum tensor at finite temperature. The construction in Ref. [12] adopted in the present large-N limit reads where the coefficients are given by is the running coupling constant at the renormalization scale q. From the expressions in Ref. [12] (with the normalization change n i (t, x) → n i (t, x)/ √ N ), these expressions are obtained by setting g 2 = λ/N and taking N → ∞.
The expectation value of the energy-momentum tensor at finite temperature, where β is the inverse temperature, is then obtained by contracting n i (t, x) by the dressed propagator (3.11) with the periodic boundary condition in the Euclidean time direction x 0 ; the time component of the momentum in Eq. (3.11) is thus quantized to the Matsubara frequency: Thus, for instance, we have where σ β (s) is the flow-time-dependent auxiliary field at finite temperature that fulfills a finite temperature counterpart of Eq. (3.18): On the other hand, σ β is the saddle point value of the auxiliary field at finite temperature which is given by 1 λ 0 = 1 β −π/a<ωn<π/a π/a −π/a dp 1 2π Now, in expressions such as Eqs. (5.7) and (5.8), the sum and the integral are well convergent for t > 0 because of the Gaussian damping factor. Thus we may simply remove lattice regularization in those expressions to yield regularization-independent expressions such as .
(5.12)
These clearly illustrate the "UV finiteness" of the gradient flow: Any correlation function of the flowed N -vector field in terms of the renormalized coupling is UV finite without the wave function renormalization [12]. 5 It is the basic idea for the construction of the lattice energy-momentum tensor in Refs. [5,7,12] that the continuum limit a → 0 of a lattice composite operator of the flowed field reduces to a regularization-independent expression. Thus, we have observed that the continuum limit a → 0 in Eq. (5.2) can be almost trivially taken. Next, to consider the small flow-time limit t → 0 in Eq. (5.2), we estimate the sum and the integral appearing in the above expressions for t → 0. This can be accomplished by noting the Poisson resummation formula, and, after some calculation, we have the following asymptotic expansions for t → 0: where K n (z) denotes the modified Bessel function of the nth kind. At this stage, we note the following relation: (5.20) It is now straightforward to obtain the t → 0 limit in Eq. (5.2). Noting that β → ∞ and σ β → σ on the vacuum, we have
22)
{T 01 } R (x) β = 0. (5.23) In this calculation, one finds that 1/t singularities are canceled between the expectation value at finite temperature and the vacuum expectation value, and a finite small flow-time limit results. The thermodynamic quantities, the energy density ε and the pressure P , are related to these expectation values of the energy-momentum tensor as In Appendix A, we compute these thermodynamic quantities by the standard large-N method. We find that Eq. (5.24) with Eqs. (5.21) and (5.22) correctly reproduces those large-N results.
Conclusion
In the present paper, we solved the gradient flow equation for the 2D O(N ) nonlinear sigma model in the leading order of the large-N expansion. By using this solution, one can nonperturbatively compute one-point functions of O(N ) invariant composite operators made from the flowed N -vector field in the large-N limit. We computed a non-perturbative running coupling from the expectation value of the "energy density operator" in which the flow time gives the renormalization scale. We also computed the thermal expectation value of the lattice energy-momentum tensor, which is defined by a small flow time limit of composite operators of the flowed field [12]. We found that the small flow time limit can be taken as expected and the lattice energy-momentum tensor correctly reproduces the thermodynamic quantities obtained by the standard large-N approximation. This result for the present system with a non-perturbatively generated mass gap strongly supports the correctness of the reasoning for the lattice energy-momentum tensor in Refs. [5,7,12]. Quite unfortunately, in the present work, we could not find the solution for the gradient flow equation in the next-to-leading order of the large-N expansion. If this solution is obtained, it will make possible the examination of the conservation law of the lattice energy-momentum tensor. We hope to come back to this problem in the near future.
We would like to thank Kengo Kikuchi for the discussion. F.S. would like to thank the members of KIAS, especially Hyeonjoon Shin, for their warm hospitality during his visit. The work of F.S. and H.S. is supported in part by Grants-in-Aid for Scientific Research 25400289 and 23540330, respectively.
Note added
In a recent paper [15], some of the results presented in this paper have been obtained independently.
A. Thermodynamics at large N In the large-N limit, the free energy density of the 2D O(N ) nonlinear sigma model at finite temperature is given by, as a natural generalization of the zero-temperature expression (2.2), where σ β denotes the saddle point value of the auxiliary field σ(x) at finite temperature which is given by the solution of the finite temperature gap equation: We regularize the formal expressions (A1) and (A2) by using dimensional regularization. For this, we note the identity and regularize Eq. (A1) as where λ DR 0 is the bare coupling constant in dimensional regularization appearing in Eq. (2.7), and Eq. (A2) as In the second term of the right-hand side of Eq. (A4), only the n = 0 term requires regularization because the n = 0 terms are Fourier transformations and UV convergent. After the momentum integration, we have Similarly, the integration in Eq. (A5) yields Plugging this into Eq. (A6), by noting the identity K 0 (z) − K 2 (z) = −(2/z)K 1 (z), we have where we have shifted the origin of the free energy density by −β(N/8π)σ, so that it vanishes at zero temperature as lim β→∞ f (β)/β = 0; note that lim β→∞ σ β = σ and lim β→∞ ∞ n=1 K 2 (β √ σ β n) = 0. Since the pressure P is related to the free energy density as P = −f (β)/β in the thermodynamic limit, we have On the other hand, the energy density is given from the free energy density by ε = ∂f (β)/∂β. The derivative of Eq. (A8) with respect to β contains ∂σ β /∂β, which can be deduced from the β derivative of Eq. (A7) as where we have used the relation K ′ 0 (z) = −K 1 (z). Using this expression and noting the identity zK ′ 2 (z) + 2K 2 (z) = −zK 1 (z), we finally obtain Comparing Eqs. (A9) and (A11) with Eq. (5.24) given by Eqs. (5.21) and (5.22), we find that our lattice energy-momentum tensor in the continuum limit correctly reproduces those thermodynamic quantities.
B. Naive lattice energy-momentum tensor
It is interesting to see how the following "naive" energy-momentum tensor, 6 T naive when used in conjunction with lattice regularization, fails to reproduce the correct answer. Using the propagator (3.10), the thermal expectation value of Eq. (B1) is given by may potentially be UV divergent for a → 0, but actually this term vanishes because of the hypercubic symmetry. Other n = 0 terms are UV convergent and we may remove the lattice regulator. In this way, we have (B5) This reproduces the expectation value of the traceless part {T 00 } R (x) − {T 11 } R (x) β correctly, but it misses the trace part {T 00 } R (x) + {T 11 } R (x) β = −N/(4π)(σ β − σ). This failure for the "trace anomaly" is expected, because the naive expression (B1) is traceless for D = 2 and it cannot reproduce the trace anomaly when lattice regularization in D = 2 is used. Our universal formula (5.2) can, on the other hand, incorporate the effect of the trace anomaly correctly, even with lattice regularization. | 5,153.4 | 2014-12-28T00:00:00.000 | [
"Physics"
] |
INVESTIGATING THE PERFORMANCE OF RANDOM FOREST AND SUPPORT VECTOR REGRESSION FOR ESTIMATION OF CLOUD-FREE NDVI USING SENTINEL-1 SAR DATA
The current study focuses on the estimation of cloud-free Normalized Difference Vegetation Index (NDVI) using the Synthetic Aperture Radar (SAR) observations obtained from Sentinel-1 (A and B) sensor. South-West Summer Monsoon over the Indian sub-continent lasts for four months (mid-June to mid-October). During this time, optical remote sensing observations are affected by dense cloud cover. Therefore, there is a need for methodology to estimate state of vegetation during the cloud cover. The crops considered in this study are Paddy (Rice) from Punjab and Haryana, whereas Cotton, Turmeric, and Banana from Andhra Pradesh, India. We have considered, observations of Sentinel-1 and Sentinel-2 sensors with the same overpass day and non-cloudy pixels for each crop. We used Google Earth Engine to extract surface reflectance for the Sentinel-2 and Ground Range Detected (GRD) backscatter for Sentinel-1. The Red and NIR bands of Sentinel 2 were used to estimate NDVI. Sentinel-1 based VV, and VH backscatter was used for estimation of Normalized Ratio Procedure between Bands (NRPB). Regression analysis was performed by using NDVI as an independent variable, and VV, VH, NRPB, and radar incidence angle as dependant variables. We evaluated the performance of Linear regression with tuned Support Vector Regression (SVR) as well as tuned Random Forest Regression (RFR) using the independent data. Results showed that the RFR produced the lowest RMSE for all the crops in the study. The average RMSE using the RFR was 0.08, 0.09, 0.11, and 0.10 for Rice, Cotton, Banana, and Turmeric, respectively. Similarly, we have obtained R values of 0.79, 0.76, 0.69, and 0.71 for the same crops using the RFR. A model with 80 trees produced the best results for Rice and Cotton, whereas the model with 90 trees produced the best results for Banana and Turmeric. Analysis with NDVI threshold of 0.25 showed improved R and RMSE. We found that for grown crop canopy, SAR based NDVI estimates are reasonably matching with the optical NDVI. A good agreement was observed between the actual and estimated NDVI using the tuned RFR model.
INTRODUCTION AND STATE OF THE ART
Continuous regional crop mapping and monitoring is essential especially in countries like India to keep a track on spatio-temporal coverage of various crops. This information can be consumed by various stakeholders like the government for the planning of various import-export activities, agri-input companies for facilitation of various fertilizers/chemicals, farmers to get the status of their crop in real-time (Mohite et al. (2018)). Satellite based remote sensing sensors are being effectively used over the years for continuous crop mapping and monitoring. Such methods are always preferred over manual surveys due to efficiency in terms of time, accuracy, spatial coverage, etc. Space exploration agencies such as the Indian Space Research Organization and international agencies such as the National Aeronautics and Space Administration (NASA), European Space Agency (ESA) have launched multiple Optical (IRS, Landsat 5,7,8, MODIS Terra, Aqua, Sentinel 2) as well as Synthetic Aperture Radar (RISAT-1, Sentinel 1) satellites. These satellites are extensively being used for crop mapping and monitoring.
Optical satellites provide rich spectral information in multiple wavelength bands which offer advantages for various agriculture applications such as crop type identification (Mohite et al. (2018)), crop monitoring, crop loss assessment (Sawant et al. * Corresponding author (2019)), yield estimation ), etc. Various methods based on the vegetation indices have been proposed in the past for agricultural applications. The Normalized Difference Vegetation Index (NDVI) is one of the widely used vegetation index (Rouse et al. (1974)). NDVI is derived using the Red and Near Infrared (NIR) bands of optical satellites such as Sentinel-2, Landsat-8, MODIS Terra and Aqua, etc. However, loss of information due to the presence of clouds in the optical dataset restricts its utilization to its maximum extent. In India, Kharif season is the main cropping season which starts in mid-June with the onset of the Indian Summer Monsoon (ISM) and extends upto November. During this season Indian sub-continent is mostly covered with the dense clouds.
Numerous attempts have been made for the cloud removal and cloud induced gap filling in the optical data using the time-series information and information available in the neighborhood pixels (Roerink et al. (2000); Padhee and Dutta (2019); Adam et al. (2018)). Nonetheless, the cloud removal process is useful in the presence of thin clouds and can be performed effectively but such process can not be considered successful in the case of thick clouds. Also, these methods can not be very useful in India during the Kharif season (June-October) when there is thick cloud cover over most of the season. Alternatively, the Synthetic Aperture Radar (SAR) sensor can collect continuous data in cloudy conditions as well as during day/night. Hence, synergistic use The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLIII- B3-2020, 2020XXIV ISPRS Congress (2020 of optical and SAR sensor observations can generate the continuous stream of NDVI time-series for vegetation monitoring. Studies have attempted to estimate the NDVI using SAR observations (Capodici et al. (2013); Davidse (2015); Filgueiras et al. (2019); Mazza et al. (2018); Navarro et al. (2016); Vreugdenhil et al. (2018)). Capodici et al. (2013) have shown that temporal changes of HV backscatter acquired with off-nadir angle greater than 40 degree best correlates with variations in the vegetation index from optical data. The study has a dependency on historical optical and SAR observations. Frison et al. (2018) showed a strong relationship between Sentinel-1 backscatter and vegetation phenology derived from Landsat-8. Mazza et al. (2018) have developed a CNN based model to derive NDVI from SAR data. Filgueiras et al. (2019) established the regression-based relationship between Sentinel-1 SAR and NDVI from Sentinel-2 to derive the continuous cloudless NDVI for Soybean and Maize (Corn). The study was focused on adjacent fields from a small area. Limitations of the research studies are a) the dependency on data from optical sensors for model development, b) methods are limited to certain incidence angles, c) heterogeneity in the spatial and temporal resolution of the SAR and Optical observations and d) geographical coverage for the model development.
The current study focuses on the estimation of cloud-free NDVI using the SAR observations obtained from Sentinel-1 sensor. The proposed method explores the Linear Regression (LR), Support Vector Regression (SVR) and Random Forest Regression (RFR) for estimation of NDVI using SAR observations. The study was conducted during the Kharif season of the year 2019 for two regions of India.
Study Area
The analysis was performed over two Indian regions namely, Andhra Pradesh and Punjab-Haryana. The study regions are situated in India's southern and northern parts respectively. The crops considered in this study are Paddy from Punjab and Haryana state.
Punjab and Haryana are one of the major paddy producing belt in India. Cotton, Turmeric and Banana crops considered from Andhra Pradesh, India. Figure 1 shows the two locations where the geotagged field data has been collected.
Datasets Used
In this study we have used Sentinel-1 and Sentinel-2 satellite imagery, ground truth data collected from the field visits.
Sentinel-2 Data and Preprocessing
ESA launched the constellation of optical satellite Sentinel-2 A and B which provides the earth observation in 10, 20 and 60 meter spatial resolution at five days repeat period (ESA (2020b)). Observations provided by Sentinel 2 are available in the 13 spectral bands mainly visible and NIR at 10 meters, red edge and SWIR at 20 meters, and atmospheric bands at 60 meters spatial resolution, respectively. For research purposes, Google Earth Engine cloud platform (Gorelick et al. (2017)) provides the collection of time-series Sentinel 2 Level-2A orthorectified atmospherically corrected surface reflectance data. In the present study, the data in Red and NIR bands was accessed from GEE to estimate the NDVI. Table 1 shows the location specific availability of Sentinel-2 data overlapping (or 1 day difference) with the Sentinel-1 overpass date. First number in the pair (1) shows the Sentinel-1 overpass date, however second number represents Sentinel-2 overpass date. Pixels with no cloud cover were considered for model development. NDVI threshold is used for obtaining the cloud-free pixels.
2.2.2 Sentinel-1 Data and Pre-processing Sentinel-1 satellite mission launched by ESA also has a constellation of two satellites 1-A and 1-B (ESA (2020a)). Data has been captured in dual-polarization by C-band Synthetic Aperture Radar. Satellite provides the observations at 5 meter in range and 20 meter in azimuth direction with 6 days repeat period. GEE (Gorelick et al. (2017)) has a collection of S1 Ground Range Detected (GRD) scenes, processed using the Sentinel-1 Toolbox to generate a calibrated, ortho-corrected product. The GRD product has been generated by pre-processing the scenes for thermal noise removal, radiometric calibration and terrain correction (Filipponi (2019)). Sentinel-1 C-band SAR has all weather, day-night capability hence all the observations available during the growing season are useful for the analysis. We have accessed backscatter information in VV, VH polarization along with local incidence angle. Normalized Ratio Procedure between Bands (NRPB) was estimated using VV and VH backscatter using equation 1 and used in the analysis as one of the variables.
2.2.3 Ground truth data from field visits We have developed an android mobile application RuPS (Mohite et al. (2015)) for collection of field geo-coordinates and reporting various agricultural activities and events. For the current research, geo-tagged locations of the fields, crop cultivated on the field, its sowing or planting date and estimated harvest date were collected using the RuPS. Table 2 shows the number of plot boundaries collected for each crop and the total number of pixels associated with those crops.
Overall Approach
Each crop has a different crop season length therefore based on crop sowing and estimated harvest date concerning the region, we have considered NDVI and SAR data. For each crop and plot, we have identified the same satellite overpass dates and data with 1 day difference for Sentinel-1 and 2 and only that data was considered in the analysis. Data on all other dates were ignored to avoid noise and have the same reference. Plots were scattered all over the region to account for the regional variations of crop growth. The problem was devised as a regression analysis to establish the relationship between NDVI as an independent variable using
RESULTS AND DISCUSSION
To carry out the regression analysis, we have extracted the data of NDVI, VV, VH, incidence angle and NRPB for all the pixels associated with individual crops. Crop-wise models are developed for NDVI estimation. For each crop, data was divided into 80% data for model training and 20% data for independent validation of the developed model. We evaluate the performance of Linear Regression (LR), Support Vector Regression (SVR) and Random Forest Regression (RFR). For models such as SVR, RFR there are hyperparameters which could be tuned to obtain the optimum performance. Hence we carried out 3 fold cross-validation on the training data to obtain the best parameters for SVR and RFR.
SVR is tuned for C at 0.1,1,10,100, Sigma at 1, 0.1, 0.01, 0.001 and type of kernel tried were Linear and Radial Basis Function. The model with best parameters (out of 32 models) was determined using 3 fold cross validation. Performance of the best model was evaluated using a 20% validation dataset. RMSE was used as a performance measure to decide the best model. Model with the lowest RMSE was considered as the best model. The same strategy was applied for RFR by tuning the parameters such as number of Trees. The number of trees were varied from 10 to 100 with an interval of 10. A total of 10 models were evaluated to find out the model with optimum trees. In the case of LR, we simply train the model on a random 80% dataset and tested of remaining 20% dataset. To avoid the bias in the random selection of dataset and noise, we ran the LR model 10 times and averaged the RMSE. Overall modeling was repeated considering NDVI values greater than 0.25. This is to verify whether there is any influence of soil background on the overall model performance. Table 5 shows the performance of various models for the data with NDVI greater 0.25.
We can clearly see the improvements across all the models (both linear as well non-linear) when considering the NDVI greater than 0.25. We observed decrease in the RMSE and improvement in R 2 values for all the crops using the RFR models. Such results show that, the soil background available during initial crop growth period was responsible for poor relationship between NDVI and SAR data.
Temporal analysis of few pixels
For continuous monitoring of vegetation, it is important to get the temporal and continuous data of NDVI. To check the temporal feasibility of the developed models, we applied the best models (Linear, SVR, RFR) on unknown fields for each crop. We did not consider this field for model development as well as for validation. For each crop, we have chosen one field and plotted the time-series of NDVI estimated using the best model and actual time-series of median NDVI for that field. Figure 3 shows the time-series pattern for cotton where we can see the RFR model predicts the NDVI which closely matches the actual NDVI for almost all the dates. Also, there was a cloud during the month of July, August and September so there was a drop in the actual NDVI but RFR model predicted NDVI which closely follows the actual temporal NDVI pattern. In the case of Banana crop time-series (Figure 4), although the crop is present throughout the year, we have plotted the time-series between July to Dec 2019. The banana field was mostly affected by clouds during July-September. RFR model predicted NDVI which is closely following the pattern of actual NDVI wherever the actual cloud-free NDVI values are available. Figure 5 shows the time-series pattern for Turmeric. The field is covered by clouds towards the end of August and September. However, RFR predicted NDVI was in good agreement with actual NDVI and predicted the values at cloudy dates which followed the pattern of actual NDVI. Figure 6 shows the time-series of actual and predicted NDVI for rice. All the models were good to follow the actual NDVI however, RFR followed the actual NDVI pattern more accurately among all.
SUMMARY AND CONCLUSIONS
We have attempted to establish a relationship between NDVI derived from Sentinel-2 and Sentinel-1 based VV, VH backscatter, it is observed that the model with 90 trees produced best results for Banana and Turmeric. Further, we have considered data with NDVI greater than 0.25 and carried out a similar analysis. We observed a decrease in the RMSE and improvement in R 2 values for all the crops using the RFR models. We found that, RMSE was decreased to 0.05, 0.06, 0.10 and 0.09 for Rice, Cotton, Banana and Turmeric respectively. Moreover, R 2 was increased to 0.83, 0.78, 0.71 and 0.77 respectively for these crops. We found that the estimation of NDVI was good for high canopy density compared to crop in the early stages with soil background. Further, we have also plotted the time-series of actual vs estimated NDVI using all the models for various crops. NDVI predictions made by the RFR model were closely matching with actual NDVI for almost all temporal instances. This was followed by SVR and LR.
FUTURE WORK
As a part of future work, we plan to implement the method on every cloudy pixel with respective crop and generate the cloudless NDVI images. This will basically help us to carry out the comparison between the actual and generated NDVI images on a spatial level. In addition to this, we plan to collect more data on other crops cultivated during Kharif season and develop models for those crops. | 3,680.6 | 2020-08-22T00:00:00.000 | [
"Environmental Science",
"Mathematics"
] |
Laning, Thinning and Thickening of Sheared Colloids in a Two-dimensional Taylor-Couette Geometry
We investigate the dynamics and rheological properties of a circular colloidal cluster that is continuously sheared by magnetic and optical torques in a two-dimensional (2D) Taylor-Couette geometry. By varying the two driving fields, we obtain the system flow diagram and report the velocity profiles along the colloidal structure. We then use the inner magnetic trimer as a microrheometer, and observe continuous thinning of all particle layers followed by thickening of the third one above a threshold field. Experimental data are supported by Brownian dynamics simulations. Our approach gives a unique microscopic view on how the structure of strongly confined colloidal matter weakens or strengthens upon shear, envisioning the engineering of rheological devices at the microscales.
Understanding the dynamics of confined particulate systems under external deformations is relevant for many industrial and technological processes [1]. A classical yet versatile approach is based on the use of the Taylor Couette (TC) geometry, where complex fluids are confined and sheared between two coaxial cylinders [2,3]. The possibility to independently rotate these cylinders has made this geometry a powerful tool to investigate the emergence of centrifugal instabilities, and how these flow perturbations lead to turbulence in a wide variety of soft matter systems, including foams [4,5], granular materials [6][7][8], micellar [9] or polymeric solutions [10][11][12].
Equally appealing are the rheological properties of colloidal suspensions, complex viscoelastic fluids where the individual particles can be directly observed by optical means, and their interactions tuned by external fields [13]. As such, confocal microscopy of sheared bulk samples has revealed rich dynamics, including the emergence of thinning [14], thickening [15] or shear banding instabilities [16] in crystals [17] and glasses [18]. When confined by gravity to a two-dimensional (2D) plane, an ensemble of colloids is more difficult to shear, since particles tend to escape to the bulk due to compression or thermal fluctuations. Thus, the use of alternative driving methods, such as magnetic fields [19,20] or optical tweezers [21,22], may help creating compact clusters that can be confined and deformed by the applied drive. Recent experiments with optically confined microspheres have addressed the pressure exerted to the boundary [23] and the transmission of torque from the boundary to the center [24], while the rich and complex rheological properties of these systems remain unexplored. In addition, the interplay between shear and confinement gives rise to a host of new phenomena including buckling instabilities, transport via density waves, heterogeneities and defects that (a) Scheme of the experimental system where a cluster of 48 microspheres is confined by 21 time-shared optical traps. The three inner particles are paramagnetic colloids that are subjected to an in-plane rotating magnetic field of amplitude B0. Red (blue) arrow indicates the rotation direction induced by the optical (magnetic) field. (b) Microscope image of one colloidal cluster. Scale bar is 5 µm, see also VideoS1 in [25].
In this Letter we investigate the dynamics and deformations of a circular colloidal cluster composed by interacting microspheres that are assembled and sheared via two independent driving fields. Even in the absence of shear, the particles arrange into four concentrical layers, a generic effect in strongly confined systems [29]. Here, we use time-shared optical tweezers to assemble and rotate the outer particle layer. The other driving mechanism is a rotating magnetic field, which independently imposes a torque on a triplet of particles (trimer) located at the center of the system. In this 2D TC geometry, we observe non-Newtonian velocity profiles where neighboring layers of particles slide with each other cre- ating localized shear zones. By fixing the outer layer, we use the inner paramagnetic trimer as a microrheometer and thereby provide a realization of the original Couette experiment [30] on the colloidal length scale. Further, we observe that for a large magnetic torque, the fast spinning of the inner trimer generates a strong hydrodynamic flow and exerts a radial pressure pushing the third layer against the outer one. The corresponding change in the local densities of the layers manifests as a simultaneous shear thinning of the second layer and thickening of the third one. We use numerical simulations to calculate the local viscosities and the components of the stress tensor, obtaining consistent results with the experimental observations for the whole range of parameters explored. The system geometry is schematically shown in Fig.1(a) for the counter-rotating case, see also VideoS1 in [25]. We use a binary mixture composed of polystyrene particles (diameter 4µm, carboxylate modified from Invitrogen) and paramagnetic colloids (diameter 4.5µm, M-450 Epoxy from Dynabeads). The iron oxide doping of the paramagnetic particles makes them slightly darker under brightfield microscopy, which allows us to distinguish them from the other particles when assembling the cluster. The particles are dispersed in highly deionized water (MilliQ, Millipore) and placed on a capillary chamber where they sediment due to a density mismatch. We assemble a circular cluster composed of 48 microspheres and radius R = 14.1µm, by trapping the outer 21 particles with an infrared laser (λ = 1064nm) that is deflected with an acousto optic device (AOD). More details of the setup can be found in Ref. [25]. The AOD allows scanning the 21 traps in 0.45ms, i.e. much faster than the typical self-diffusion time of the particles, τ B = 40s. Thus, the optical traps can then be considered as 21 independent harmonic potentials placed along the circle. The outer colloidal layer is either rotated with a constant an-gular velocity ω 4 ∈ ±[0.1, 0.6]rads −1 when used in the TC geometry, or kept fixed (ω 4 = 0 rads −1 ) when using the inner trimer as a microrheometer. This trimer is created by placing three paramagnetic colloids at the cluster center and subjecting them to a rotating magnetic field with amplitude B 0 and angular velocity Ω, The applied modulation induces the assembly of the paramagnetic particles due to time-averaged attractive magnetic interactions [31], and also induces a finite torque T m that forces the trimer to rotate at an angular velocity ω 1 . This torque results from the internal relaxation of the particle magnetization [32,33] and can be calculated for the whole trimer as is the volume of the trimer, and χ ef f = 0.18 is the effective dynamic magnetic susceptibility, see Fig.1(b) in [25]. Thus, at a constant driving frequency of Ω = 20πrads −1 , T m ∼ B 2 0 , the amplitude of the rotating magnetic field is used to vary the rotational motion of the inner trimer.
Using video-microscopy, we measure the polar coordinates (r i , ϕ i ) of each particle i with respect to the center of the cluster. We then obtain the average angular velocity per layer n as ω n = <N −1 n Nn i ω (r i ) >, where the summation counts only the N n particles within the respective layer, Fig.1(b). From these data, we calculate the azimuthal flow velocity, v ϕ (r) = <ω(r)> r and the corresponding shear rate,γ(r) = ∂(v ϕ (r))/∂r.
In the central panel of Fig. 2 we show the complete flow diagram of our system obtained by varying the angular velocity ω 4 of the outer shell and the amplitude B 0 of the applied magnetic field. We classify the different dynamical phases in terms of the velocity profiles and corresponding shear rates as they vary along the radial direction. Due to the strong confinement of our colloidal cluster, we never observed particle exchange between the layers. Thus, our system does not display swirls and large scale rearrangements as observed in other sheared granular systems in two and three dimensions [6,[34][35][36]. However, the colloidal layers generate periodic corrugations that slide past each other during their relative motion. The strong confinement favors the fitting of particles of one layer in the interstices generated by the colloids of the neighboring layers. The size difference between the magnetic and non magnetic particles and the circular confinement frustrates ordering, and incommensurability effects between the different colloidal layers become important. Thus, depending on the directions and amplitudes of the shearing torques, the system may show layers that slip and others that temporary lock to each other, resulting in a non-Newtonian velocity profile. In order to characterize the different dynamical regimes, we plot the time-averaged azimuthal velocity per layer and the corresponding jump in the shear rate, some examples are shown in the left and right panels of Fig.2. In particular, we classify as "smooth" (blue regions in Fig.2) velocity profiles that lead to a jump in the shear rate smaller than a given threshold, in this case |(γ i −γ i+1 )/(minγ − maxγ)| ≤ 0.15. On the contrary, in the red and orange regions the system displays velocity profiles with a strong discontinuity, leading to a pronounced jump (> 0.15) in the shear rate. This shearinduced breakage is usually observed when there is no dominant driving mechanism, as opposed to when either the driving of the inner or outer layer is much stronger than the other. The breakage can be localized either between the first and the second layer (r = 6µm) or the second and third layer (r = 10µm). The first case occurs in the counter-rotating situation, when the inner trimer is able to drag the second layer of particles in opposite direction than the outer layer, and the cluster inevitably breaks in pairs of counter-propagating colloidal domains (VideoS1 in [25]). In the co-rotating case, the breakage rather localizes close to the outer layer, as this colloidal shell has a stronger capability to drag nearest layers. The third layer is mainly driven by the fourth one, while the second has a reduced angular speed as it also tries to follow the rotating magnetic triplet. When the first and fourth layer have the same angular velocity (ω 1 = ω 4 ), the system displays a Poiseuille like flow profile.
We will now focus on the central region of the flow diagram in Fig.2, where we keep the outer layer fixed (ω 4 = 0) and continuously rotate only the inner trimer. In Fig.3(a) we show experimental measurements of the average angular velocities of the four colloidal layers versus the square of the magnetic field up to B 2 0 = 20mT 2 . Above a depinning threshold B 0 = 0.6mT, below which all particles are at rest, the trimer starts rotating and shows an angular velocity that increases linearly with B 2 0 , up to a threshold field strength B c = 3.3 mT. At B c we can see a sharp jump in the angular velocity of the trimer, where the mobility, i.e. slope of ω 1 , remains constant. Further, we observe that the slope of ω 3 reveals an abrupt decrease as the magnetic torque applied to the trimer increases, inset in Fig.3(a). As we will show later, this behaviour is related to a transition from "thinning" to "thickening" at B c . Above B c the fast spinning of the trimer generates a strong hydrodynamic flow that lubricates the region between the first and the second layer, see also VideoS5 in [25], . Thus, we find an overall thinning of the trimer viscosity for B 0 > B c . This flow also pushes the third layer of particles towards the outer one, increasing the local packing density and reducing the effective mobility of this layer. This leads to an abrupt transition to thickening as seen in the third layer at a critical field strength B c .
In order to access the viscosity of all the layers and the system shear stresses, we perform 2D Brownian dynamics simulations of a binary mixture of charged colloids partially confined by harmonic potentials and paramagnetic colloids [25]. Taking into account hydrodynamic effects on the Rotne-Prager level, the overdamped equation of motion for the position r i of each colloid i is given by where µ T T ij and µ T R ij are the mobility matrices due to translation-translation (TT) and translation-rotation (TR) couplings. The total force on the particle j is given by F j = k =j F pp (r kj ) + F T (r j , t), and is due to the particle-particle interaction (F pp ) and the optical traps (F T ), see [25] for more details. The torque acting on the paramagnetic particles is given by T j , Γ i is a random force, stemming from random displacements with zero mean and variance 2D 0 δt, and D 0 ≈ 0.4µm 2 /s is the experimentally measured diffusion constant. The simulation time scale is set to the Brownian time τ B = d 2 /D 0 ≈ 40s, while the discrete time step is δt = 10 −6 τ B .
The results of our theoretical model are shown in Fig.3(b), and placed on the same axis as the experimental data in Fig.3(a). We find that the model allows to qualitatively capture the dynamic features observed in the experiments. From the simulation results, the threshold field strength is observed earlier at B c = 1.96 mT, which is of the same order of magnitude as in the experiment. Moreover, the simulations allow us to access all the rheological quantities of interest such as the shear viscosity of each layer, η n = σ rϕ /γ n and the components of the stress tensor, σ rr , σ ϕϕ and σ ϕr = σ rϕ . The shear viscosities of each inner colloidal layer are plotted as a function of B 2 0 in Fig.3(d), and illustrate the continuous thinning of the first three layers as well as the thickening of the third one above B c . We note that, being fixed by the optical tweezers (ω 4 = 0), the viscosity of the outer layer diverges and thus it is not reported in Fig.3(d). The same hold for the inner layers for B 0 → 0, being pinned to the outer one. The transition at B c is also reflected in all components of the stress tensors shown in Fig.3(c). In particular, the shear stress (σ rϕ ) displays an increase in the slope at B 2 c , and subsequent decrease at high magnetic field strengths, corresponding to the shear thinning and thickening respectively. The two diagonal components of the stress tensor decrease as the field increases, corresponding to an increase of the radial-P r = −σ rr and azimuthal pressure P ϕ = −σ ϕϕ . The shear thickening at B c is accompanied by a steep increase of P r , which is resolved subsequently.
While the dynamic transition at B c appears to be sharp in terms of the different rheological quantities, we find in the experiments that the cluster shows a continuous decrease in the amplitude of the radial distortions induced by the rotating trimer. Given the noncircular shape of the trimer, the particles from the second layer are forced to periodically enter and exit its interstitial regions. The induced deformation thus appears in form of a threefold tidal wave as shown in the small polar plot in Fig.4. To characterize these elastic deformations, we measure their amplitude as a function of the magnetic field strength in the Fourier space and in the reference frame of the trimer as, is the distance of the N 2 particles composing the second layer and located at an angle ϕ j in the reference frame of the trimer. In Fig.4 we plot the measured peak of u r (Ω ), namely u p = max[u r (Ω ), Ω ∈ IR], as a function of B 2 0 and in the upper left inset the corresponding u r (Ω ) for one exemplary B 0 . For small field strengths (B 2 0 < B 2 c ), the radial path of the particles in the second layer is deformed by the rotating trimer. After a transient regime, the amplitude of the deformation stabilizes to a stationary value where the relative speed between the N 2 composing particles approaches zero. We further note that, being in the Stokes regime, the decoupling of the dynamics along the radial and azimuthal directions is effectively possible, and thus the emergence of two different types of dynamic transitions sharp and continuous, along either direction, respectively.
To conclude, we have realized a colloidal microrheometer based on the combined action of magnetic and optical torques. When sheared in a TC geometry, the inner col-loidal layers show different dynamical regimes with velocity profiles that deviate from the simple Newtonian case, and reflect the discrete, granular-like nature of the system. By fixing the outer ring, the inner trimer allows exploring the rheological properties of the system inducing solidification and liquefaction of closed particle rings. The present approach may be used as an effective microrheological tool to explore the viscoelastic properties of complex fluids. This could potentially include biological media confined between the magnetic trimer and the optically trapped colloidal ring. In addition, the optical tweezers may be programmed to periodically shear the outer layer of particles and thus to explore the frequencydependent properties of complex fluids, which represents an exciting future avenue. | 4,022.2 | 2017-10-30T00:00:00.000 | [
"Physics"
] |
Market Based Mergers- Study on Indian & Saudi Arabian Banks
This paper analyses the efficiency and performance of post merger using CRAMEL–type variable of selected banks in India & Saudi Arabia which are initiated by the market forces. The results suggest that the mergers did not seem to enhance the productive efficiency of the banks as they do not indicate any significant difference. The financial performance suggests that the banks are becoming more focused on their retail activities (intermediation) and the main reasons for their merger is to scale up their operations. However, it is found that the Advances to total Assets and the profitability are the two main parameters which are to be considered since they are very much affected by mergers. Also, the profitability of the firm is significantly affected after merger.
Introduction
Mergers and Acquisition are not unknown phenomena in Indian Banking.It started way back in 1920 when the Imperial Bank of India was born out of three presidency banks and several Mergers and Acquisitions (M&A) activities were reported in pre-independence period.In 1949, proper regulation was passed by the regulator to control the banking activities which provided a relief to investors and improved the depositor confidence in the banking system.The first half of the sixties witnessed 45 forced mergers under Section 45 of Banking & Regulation Act.Interestingly, all the M&A activities were of failed private banks with one of the public sector banks.After 1980, the consolidation fever started in both commercial and rural banks.There were about 196 rural banks in 1989 which got consolidated into 103 by merging themselves into commercial banks within the state and in 2000 about 17 urban co-operative banks got merged within the state owned commercial banks.Since about 75% of the Indian banking system consists of public sector banks, there were more consolidations started happening in the late 2000.
Saudi Arabia witnessed only one merger that was between Cairo Saudi Bank and the United Saudi Bank.This was further merged with Saudi American Bank in 1999 and the merged entity was called as SAMBA Bank.
Evolution of SAMBA
SAMBA was formed in accordance with a program adopted by the Kingdom in the mid-1970s and it was forced to sell majority equity interests to Saudi nationals.SAMBA commenced business on February 12, 1980 and closed its first fiscal year on December 31, 1980.Saudi nationals held 60% of the total share capital and Citibank acquired the remaining 40% of the equity in exchange for assets of its Riyadh and Jeddah branches.Citibank entered into a Technical Management Agreement under which it agreed to manage the new bank.This agreement provided that Citibank would second staff to the new bank and provide technical support, and that it would not receive compensation for these services other than as a shareholder (except for reimbursement of actual expenses).Towards the end of 1991, Citibank sold part of its equity ownership in SAMBA to two Saudi national agencies for social welfare.As a result, 70% of the share capital of SAMBA was held by Saudi nationals and institutions while Citibank retained 30% ownership of the share capital of Samba.On July 3, 1999, SAMBA merged with the United Saudi Bank (USB) by exchanging 1 new share in SAMBA for each 3.25 existing shares in the USB.The merged bank retained SAMBA name and there was no change in the composition of the Board of Directors.The merger did not affect the Technical Management Agreement with Citibank.This resulted in Citibank holding 22.83% of the merged bank shares.However, near the end of 2002, Citibank sold 2.83% of its shareholding to a Saudi agency.As a result, Citibank held 20% of the share capital of Samba.On September 14, 2003, SAMBA moved to a full local management, culminating a transition plan previously agreed with Citigroup.On December 14, 2003, the Extraordinary Shareholders Meeting was held and resolved to amend several of the company's Articles of Association including changing the name of the company to "Samba Financial Group".On May 26, 2004, Citibank sold its 20% share capital to a Saudi agency.On March 9, 2005, the Extraordinary Shareholders Meeting decided to increase the share capital of the company from SR 4.000.000.000 to SR 6.000.000.000divided into 600.000.000 of equal nominal value of fifty Saudi Riyals cash shares, all of which will be ordinary and as one class in all respects.
Materials and Methods
The literature that will be surveyed addresses the question of whether or not under what conditions bank mergers have the potential to produce real efficiency gains.Adel, KabirHassan & Shari Lawrence (2008) investigates the cost and profit efficiency effects of bank mergers on the US banking industry.He used non-parametric technique of Data Envelopment Analysis (DEA) to evaluate the production structure of merged and non-merged banks.The empirical results indicate that mergers have improved the cost and profit efficiencies of banks.Further, evidence shows that merged banks have lower costs than non-merged banks because they are using the most efficient technology available (technical efficiency) as well as a cost minimizing input mix (allocative efficiency).Ahmad Ismail, Ian Davidson & Regina Frank (2009) concentrates on European banks and investigates post-merger operating performance and found that industry-adjusted mean cash flow return did not significantly change after merger but stayed positive.Also find that low profitability levels, conservative credit policies and good cost-efficiency status before merger are the main determinants of industry-adjusted cash flow returns and provide the source for improving these returns after merger.Anthony (2008) investigates the effect of acquisition activity on the efficiency and total factor productivity of Greek banks.Results show that total factor productivity for merger banks for the period after merging can be attributed to an increase in technical inefficiency and the disappearance of economies of scale, while technical change remained unchanged compared to the pre-merging level.
Benjamin Liu & David Tripe (2002) used accounting ratios and DEA (Data Envelopment Analysis) to explore the efficiency impacts of 6 bank mergers in New Zealand between 1989 and 1998.Acquiring banks were found to be generally larger than their targets, although they were not consistently more efficient.In a majority of cases the merger led to an increase in efficiency, consistent with a trend observed for the banking sector as a whole.Bisceglio (1995) studied the merger-related cost savings and found that No evidence for economies of scale was found.A wide dispersion of average costs was found for banks of similar size.X-efficiency, or managerial, differences were found to be very large relative to scale efficiency differences.Carl Felsenfeld (2008) studied the Antitrust Aspects of Bank Mergers conference --Banking and the Antitrust Laws --has received insufficient attention in the legal literature.
Elena Carletti, Philipp Hartmann & Giancarlo Spagnolo (2007) modelled the impact of bank mergers on loan competition, reserve holdings, and aggregate liquidity.The merger also affects loan market competition, which in turn modifies the distribution of bank sizes and aggregate liquidity needs.Mergers among large banks tend to increase aggregate liquidity needs and thus the public provision of liquidity through monetary operations of the central bank.
George E Halkos & Dimitrios (2004) applied non-parametric analytic technique (data envelopment analysis, DEA) in measuring the performance of the Greek banking sector.He proved that data envelopment analysis can be used as either an alternative or complement to ratio analysis for the evaluation of an organization's performance.Marc J Epstein.(2005) studied on merger failures and concludes that mergers and acquisitions (M&A) are failed strategies.However, analysis of the causes of failure has often been shallow and the measures of success weak.
Morris Knapp, Alan Gart & Mukesh Chaudhry (2006) research study examines the tendency for serial correlation in bank holding company profitability, finding significant evidence of reversion to the industry mean in profitability.The paper then considers the impact of mean reversion on the evaluation of post-merger performance of bank holding companies.The research concludes that when an adjustment is made for the mean reversion, post-merger results significantly exceed those of the industry in the first 5 years after the merger.
Ping-wen Lin (2002) findings proves that there is a negative correlation and statistical significance exist between cost inefficiency index and bank mergers; meaning banks engaging in mergers tend to improve cost efficiency.However, the data envelopment analysis empirical analysis found that bank mergers did not improve significantly cost efficiency of banks.In another study, he found that (1) generally; bank mergers tend to upgrade the technical efficiency, allocative efficiency, and cost efficiency of banks; however a yearly decline was noted in allocative efficiency and cost efficiency.
(2) In terms of technical efficiency and allocative efficiency improvement, the effect of bank mergers was significant; however, in terms of cost efficiency improvement, the effect was insignificant.
Robert DeYoung (1997) estimated pre-and post-merger X-inefficiency in 348 mergers approved by the OCC in 1987/1988.Efficiency improved in only a small majority of mergers, and these gains were unrelated to the acquiring bank's efficiency advantage over its target.Efficiency gains were concentrated in mergers where acquiring banks made frequent acquisitions, suggesting the presence of experience effects.SU WU (2008) examines the efficiency consequences of bank mergers and acquisitions of Australian four major banks.The empirical results demonstrate that for the time being mergers among the four major banks may result in much poorer efficiency performance in the merging banks and the banking sector.Suchismita Mishra, Arun, Gordon and Manfred Peterson (2005) study examined the contribution of the acquired banks in only the non conglomerate types of mergers (i.e., banks with banks), and finds overwhelmingly statistically significant evidence that non conglomerate types of mergers definitely reduce the total as well as the unsystematic risk while having no statistically significant effect on systematic risk.Xiao Weiguo & Li Ming (2008) paper uses DEA (Data Envelopment Analysis) for analyzing commercial banks' efficiency, top five American banks and four Chinese banks and concluded that merger and acquisition (M&A) has greater impact on banking efficiency of Chinese banks than that of American banks.Ya-Hui Peng & Kehluh Wang (2004) study addresses on the cost efficiency, economies of scale and scope of the Taiwanese banking industry, specifically focusing on how bank mergers affect cost efficiency.Study reveals that bank merger activity is positively related to cost efficiency.Mergers can enhance cost efficiency, even though the number of bank employees does not decline.The banks involved in mergers are generally small were established after the banking sector was deregulated.
Data and Methodology
This paper seeks to analyze the efficiency of the banks which are merged due to market forces (not forced by the regulator) and a comprehensive study was undertaken to investigate the performance of those banks.For this research we have considered three private banks and four nationalized banks in India (only 7 banks have merged due do market forces with in 2000) and one bank in Saudi Arabia (since only one merger has been witnessed during this period) has been taken to have a comprehensive study of the framework of entire banking industry.After considering various efficiency techniques, we have used CRAMEL model to assess the firms and also we have used Factor Analysis using Kaiser Normalization method to find out the parameters that we should look for after merger.
The data used in this study is gathered from the annual reports of banks for the post merger period 2000 to 2007.Post Merger financial Performance of the banks was taken in to consideration.The analysis is divided into two parts; namely, Regression Analysis & Factor analysis using Kaiser Normalization method was used with CRAMEL variables as the basic input.An entity specific analysis of the risk profile is done through qualitative cum quantitative approach following a structured methodology called the "CRAMEL" model.Based on the rating criteria, relative strengths and weakness of each entity in comparison to its peer group are evaluated.Liquidity: Current Ratio, Solvency Ratio (%), Liquid Asset / Deposits, Liquid Asset / Total Advances An examination of the impact of the CRAMEL model variables is done by data reduction using Factor analysis.By performing Regression analysis and t tests on the CRAMEL variables it can be determined whether there are significant relationship of those variables during the post-merger periods.Detailed description of the variables will be provided in the following section when the empirical findings are discussed.An examination of the impact of the CRAMEL -type variables is done by data reduction using factor analysis.
Empirical Findings
The results of the regression analysis conducted on CRAMEL type variables (Table1) infers that, out of 16 variables considered for the study only five variables such as cost efficiency, Advances to Total Assets, interest earning ratio, Profit margin, current ratio, solvency ratio were found to be highly significant, which is evident from (table no.1) the t test.Also from the analysis of variance (ANOVA) conducted on those significant variables infers that there is a significant relationship between those variables.The regression equation infers that there is a positive relationship between ROCE and Advances to Total Assets & Current Ratio and there is negative relationship with CE, PM and IER.
Factor Analysis on the CRAMEL Variables
Factor analysis attempts to identify underlying variables, or factors, that explain the pattern of correlations within a set of observed variables.Factor analysis is often used in data reduction to identify a small number of factors that explain most of the variance observed in a much larger number of manifest variables.Factor analysis can also be used to generate hypotheses regarding causal mechanisms or to screen variables for subsequent analysis (for example, to identify collinearity prior to performing a linear regression analysis).The table No.2 shows the factor analysis undertaken on the CRAMEL-type variables before bank merger.The variables are rotated through varimax with Kaiser Normalization method and extracted using principal component analysis.Three factors are evolved through this factor analysis.
Table 2: Factor Analysis of CRAMEL-type variables on Post merger performance of Indian and Saudi Banks From the factor analysis on the post merger performance of the Indian and Saudi banking institutions, it is found that three major factors are identified and they are interlinked.In the first factor variables like capital adequacy, Debt-equity, Cost to total Asset , Cost Efficiency and all liquidity ratios join together to form this factor.In the second factor variables like, Total advances to deposits, Capital Buffer Ratio, Loans to deposits, EPS, Return on share holders fund and interest earning ratios joined together.In the last group variables like, Advances to Total Assets, and Profit Margin ratios are joined to-gether which interprets again the profitability is majorly linked with advances and deposits.
To summarize the factors, the CRAMEL type variables appropriately combine together to and clearly indicate us which are the variables that we should closely monitor.Variables such as advances to total assets, profit margin, which are grouped together is found to be highly significant variables identified through T-test.So the banks that tend to merge have to carefully analyze those two variables after merger, since they are closely associated with the performance of the banks.
Conclusion
This paper attempts to analyze the parameter which affects the post merger performance of the banks.The analysis of CRAMEL-type variables using t test and further by factor analysis tends to identify the important variables such as CBR, EPS, capital adequacy and profit margin which significantly affect the performance of the mergers after the bank mergers.Also the PROXSCAL multi dimensional analysis confirms the same.
In conclusion, the results on the post merger performance of Indian and Saudi banking Institutions suggests that banks are becoming more focused on their high net interest income activities and the main reason for their mergers are to scale up their operation.Also the performance of various CRAMEL type variables suggests that those banks tend to improve on various variables after the merger.
So from the analysis of CRAMEL variables on the post merger performance of banks suggest that the profitability is in stake after the merger.Even though the banks tend to improve their operational efficiency, the banks have to concentrate on their profits which must be one of their merger objectives.
Table 1.Regression Analysis on CRAMEL-type variables From the Regression analysis of CRAMEL type variables keeping return on shareholders funds (ROSF) as constant since performance is assumed to be based on the return on the funds employed.From the t values we find that out of 16 CRAMEL type variables considered for the study only 5 variables seems to be significant.Also the adjusted R Square (0.995) and Durbin-Watson Score (2.266) were found to be highly significant.Also the F test signifies that there is a significant relation between the variables.From the Factor Analysis on the CRAMEL-type variables it is found that 3 major factors are evolved.In the first factor variables like capital adequacy, Debt-equity, Cost to total Asset , Cost Efficiency and all liquidity ratios join together to form this factor.In the second factor variables like, Total advances to deposits, Capital Buffer Ratio, Loans to deposits, EPS, Return on share holders fund and interest earning ratios joined together.In the last group variables like, Advances to Total Assets, and Profit Margin are joined together.The Factors are grouped based on certain significance and we find that the ADTA and PM have formed a factor which is the important finding of the study, since those two variables are seemed to highly significant in regression.
The
on mean differences for the CRAMEL variables it can be determined whether there are significant differences in the average values of those variables during the post-merger period.Based on the CRISIL (Credit Rating Information Services of India Limited) methodology, the following variables are taken into consideration for this current study: Capital Adequacy: Capital Adequacy, Debt-Equity, Advances to Total Assets, Capital buffer Ratio Resources: Cost efficiency (CE), Cost/Total Asset Asset Quality: Loans/ Deposits Management Quality: Total Advances / deposits Earnings Quality: Earnings per share, Interest Earning Ratio, Profit Margin (%), Return on Shareholders Funds (%)
Table 1 :
Regression AnalysisA regression equation has been developed on the significant variables which are shown below:
Table 2 .
Factor Analysis of CRAMEL-type variables on Post merger performance of Indian and Saudi Banks | 4,134.2 | 2010-01-12T00:00:00.000 | [
"Business",
"Economics"
] |
Predicting the Future Manufacturing Cost of Batteries for Plug-In Vehicles for the U . S . Environmental Protection Agency ( EPA ) 2017 – 2025 Light-Duty Greenhouse Gas Standards
In developing the U.S. 2017–2025 Light-Duty Vehicle Greenhouse Gas Emissions Standards, the U.S. Environmental Protection Agency (EPA) modeled lithium-ion battery packs for future electrified vehicles to estimate their direct manufacturing costs through 2025. As part of the 2016 Midterm Evaluation of the standards for model years (MY) 2022 to 2025, the analysis was revised to account for developments in battery design since the 2012 rulemaking. This paper describes the methodology that was used for estimating battery capacity, power, and cost, and compares the projected cost estimates to other sources. An empirical equation is derived for specifying motor power as a function of target acceleration time, and suggested factors for converting cell-level costs to pack-level costs are developed.
Introduction
The 2017-2025 Light-Duty Vehicle Greenhouse Gas Emissions Standards [1] were finalized in 2012 and represent a significant action to reduce greenhouse gas emissions.The rulemaking process included an accounting of the cost of meeting the standards.EPA studied the incremental cost of many advanced automotive technologies, including plug-in electric vehicles (PEVs), a category that includes battery electric vehicles (BEVs) and plug-in hybrid electric vehicles (PHEVs [2][3][4].Because much of the cost of a PEV is in the cost of the battery, it was necessary to develop a robust and transparent methodology for projecting battery costs for these vehicles.Battery costs have many drivers, and regardless of the methodology, future projections are subject to uncertainty.It is, therefore, important to consider the methodology and assumptions when assessing the validity of cost projections as conditions evolve over time. At the time of the EPA final rulemaking (FRM) in 2012, the task of specifying plug-in vehicle batteries for arbitrary combinations of vehicle size, power, and range was a difficult task.At the time, few production vehicles were available either to establish the current state of technology or to suggest the rate of its future advancement.Accordingly, our methodology employed a wide variety of simplifying assumptions and estimation methods to conduct the effort in a practical way while using calculation tools that are easily accessible to external reviewers [3].This paper details the methodology by which we projected future battery performance specifications and costs for MY 2025, including key input assumptions derived from ongoing study of the emerging industry from 2012 through 2016.
Structure of Analysis
The battery cost analysis described here was only one component of a much broader analysis that modeled the cost and effectiveness of many efficiency-improving technologies, including not only electrification but also advanced internal combustion engine, transmission, and road load reduction technologies, among others.Potential penetrations of these technologies were projected across 29 different vehicle types (as described at page 1-37 of [3]) to demonstrate how a cost-minimizing compliant fleet could be achieved at various points in the timeframe of the rule and at what cost.The technology packages considered included several types of PEVs having various targets for range, power, and mass reduction.The battery cost analysis was one step in assigning cost to these vehicles through MY 2025.
As shown in Figure 1, the battery cost analysis began by defining an array of PEVs for which lithium-ion battery packs would be specified and costs determined.This included five PEV types of various ranges (75-mile BEV75, 100-mile BEV100, 200-mile BEV200, 20-mile PHEV20, and 40-mile PHEV40), six baseline vehicle classes having different power and curb weight targets, and five levels of target curb weight reduction (0, 2, 7.5, 10, and 20 percent).This resulted in a total of 150 PEV instances [3].A battery sizing spreadsheet converted each vehicle's range target and mass-reduced curb weight to a target battery and motor power (kW) and a target gross battery capacity (kWh).The sizing spreadsheet was dynamically linked to the Battery Performance and Cost (BatPaC) model developed by Argonne National Laboratory (ANL) [5], which provided specific energy (kWh/kg) estimates for use by the sizing algorithm and direct manufacturing costs for each battery pack.For more detail on the sizing algorithm see pp. 2-359 of [3].
World Electric Vehicle Journal 2018, 9, x FOR PEER REVIEW 2 of 14
Structure of Analysis
The battery cost analysis described here was only one component of a much broader analysis that modeled the cost and effectiveness of many efficiency-improving technologies, including not only electrification but also advanced internal combustion engine, transmission, and road load reduction technologies, among others.Potential penetrations of these technologies were projected across 29 different vehicle types (as described at page 1-37 of [3]) to demonstrate how a costminimizing compliant fleet could be achieved at various points in the timeframe of the rule and at what cost.The technology packages considered included several types of PEVs having various targets for range, power, and mass reduction.The battery cost analysis was one step in assigning cost to these vehicles through MY 2025.
As shown in Figure 1, the battery cost analysis began by defining an array of PEVs for which lithium-ion battery packs would be specified and costs determined.This included five PEV types of various ranges (75-mile BEV75, 100-mile BEV100, 200-mile BEV200, 20-mile PHEV20, and 40-mile PHEV40), six baseline vehicle classes having different power and curb weight targets, and five levels of target curb weight reduction (0, 2, 7.5, 10, and 20 percent).This resulted in a total of 150 PEV instances [3].A battery sizing spreadsheet converted each vehicle's range target and mass-reduced curb weight to a target battery and motor power (kW) and a target gross battery capacity (kWh).The sizing spreadsheet was dynamically linked to the Battery Performance and Cost (BatPaC) model developed by Argonne National Laboratory (ANL) [5], which provided specific energy (kWh/kg) estimates for use by the sizing algorithm and direct manufacturing costs for each battery pack.For more detail on the sizing algorithm see p. 2-359 of [3].
Calculation Method
The battery cost analysis is a spreadsheet-based methodology.An important first step in the analysis is to estimate battery energy capacities and power requirements for the vehicles to be modeled.Because capacity and power requirements are strongly influenced by vehicle weight, and battery weight is both a function of and a contributor to vehicle weight, sizing the battery requires an iterative solution.This problem is well suited to the iteration function available in common spreadsheet software [3].The use of a spreadsheet also makes the analysis easily accessible to public inspection.To this end, further detail on the choice of inputs to this analysis [3] and access to spreadsheets used in the analysis [6] are available.
BatPaC [5] is a spreadsheet-based lithium-ion battery costing model developed by ANL.It employs a rigorous, bottom-up, bill-of-materials approach to battery cost analysis.User inputs to BatPaC include performance goals (power and energy capacity), choice of battery chemistry (for example, Lithium Manganese oxide (LMO) or several varieties of Nickel Manganese Cobalt oxide (NMC)), the vehicle type for which the battery is intended (e.g.PHEV or BEV), the desired number of cells and modules and their layout in the pack, and the volume of production.BatPaC then designs the electrodes, cells, modules, and pack, and provides a complete, itemized cost breakdown [3].From this perspective, the main task in specifying a PEV battery pack is to determine the energy storage capacity (kWh) and power capability (kW) that are needed to provide a desired driving range and level of acceleration performance [3].
The battery cost model upon which BatPaC was based was described in a paper presented at EVS-24 [7].ANL later extended the model to include detailed analysis of manufacturing costs for many types of PEVs [8].EPA arranged for an independent peer review of the BatPaC model in 2011 [9].We used Version 3.0 of BatPaC, provided to EPA on 17 December 2015.EPA continues to work closely with ANL to test new versions of BatPaC and to guide the development of new features [3].
BatPaC models stiff-pouch, laminated prismatic format cells, placed in double-seamed, rigid modules.The model supports liquid-and air-cooling, accounting for the resultant structure, volume, cost, and heat rejection capacity.It takes into consideration the cost of capital equipment, plant area and labor for each step in the manufacturing process and places relevant limits on electrode coating thickness and other limits applicable to current and near-term manufacturing processes.It also considers annual pack production volume and economies of scale for high-volume production [3].
Basis of Battery and Motor Power Specification
An initial step was to assign targets for peak powertrain power based on desired acceleration performance.A commonly cited metric for acceleration performance is the time needed for a vehicle to accelerate from zero to 60 miles per hour, also known as "0-60" time.At the time of the FRM in 2012, EPA's annual Trends Report [10] had customarily used an equation by Malliaris et al. [11] to estimate 0-60 time as a function of the ratio of rated engine power to equivalent test weight (ETW).Because this relationship was derived from the behavior of internal combustion powertrains, we investigated its applicability to the torque-delivering behavior of electric drive by surveying the peak motor power ratings and acceleration performance of electrified vehicles present in the market between 2012 and 2017 and capable of pure electric 0-60 acceleration.As shown in Figure 2, comparing the empirical data for PEVs (shown by the thin orange line) to the Malliaris equation (heavy black line) showed that use of the Malliaris equation would have resulted in much higher power specification than necessary, and would have led to overestimation of the cost of the motor and the battery pack.We used an empirical fit of the PEV data plotted in Figure 2 to derive a new Equation (1) to relate more accurately the ETW and rated peak power of an electric powertrain (kW) to 0-60 time (t, in sec).While the exact relationship of rated power to acceleration would also depend on the gear ratio of the final drive, the basis of the equation on empirical data suggests that suitable ratios exist and could be chosen accordingly by the manufacturer.
Motor power for each vehicle was assigned using this equation, beginning with the baseline ETW and a target 0-60 time between 8.35 and 11 s depending on vehicle class.Because the needed power of the motor and battery interacts with battery and vehicle weight, the power calculation must be performed iteratively by the spreadsheet as part of the overall battery sizing process [3].Because PHEV20 was modeled as a blended architecture with engine assist, the motor power for these vehicles was set to half of the total required power to represent the availability of engine assist, although we acknowledge that vehicle designs may vary in this regard.Battery power was derived from motor power as described later in Section 2.5.1.
Basis of Battery Energy Capacity Assignment
The next step was the specification of battery capacity needed for a given driving range.Range was modeled as a real-world, EPA-label, 5-cycle fuel economy range by applying a derating factor to an estimated EPA 2-cycle range.For BEVs, range was considered a beginning-of-life criterion, in accordance with EPA range labeling practice.For PHEVs, however, manufacturers are likely to consider mitigating loss of electric range because it will affect the utility factor, a component in the calculation of CO2 emissions over useful life.The PHEV sizing algorithm therefore reserves a buffer to be used as the battery ages, as described later in Section 2.5.1.
Battery capacity also depends on the vehicle energy consumption rate.This depends largely on vehicle weight, road load, component efficiencies, and other factors.The process for estimating energy consumption for each PEV was as follows.First its curb weight was estimated as equal to the curb weight CWbase of the corresponding baseline conventional vehicle, modified by any applicable curb weight reduction WRtarget (representing a curb weight reduction of 0, 2, 7.5, 10, or 20 percent), and further modified by deletion of the weight of conventional powertrain components (for BEVs) and addition of electric content (for BEVs and PHEVs), as shown in Equations ( 2) through ( 5) [3].We used an empirical fit of the PEV data plotted in Figure 2 to derive a new Equation ( 1) to relate more accurately the ETW and rated peak power of an electric powertrain (kW) to 0-60 time (t, in sec).While the exact relationship of rated power to acceleration would also depend on the gear ratio of the final drive, the basis of the equation on empirical data suggests that suitable ratios exist and could be chosen accordingly by the manufacturer.
Motor power for each vehicle was assigned using this equation, beginning with the baseline ETW and a target 0-60 time between 8.35 and 11 s depending on vehicle class.Because the needed power of the motor and battery interacts with battery and vehicle weight, the power calculation must be performed iteratively by the spreadsheet as part of the overall battery sizing process [3].Because PHEV20 was modeled as a blended architecture with engine assist, the motor power for these vehicles was set to half of the total required power to represent the availability of engine assist, although we acknowledge that vehicle designs may vary in this regard.Battery power was derived from motor power as described later in Section 2.5.1.
Basis of Battery Energy Capacity Assignment
The next step was the specification of battery capacity needed for a given driving range.Range was modeled as a real-world, EPA-label, 5-cycle fuel economy range by applying a derating factor to an estimated EPA 2-cycle range.For BEVs, range was considered a beginning-of-life criterion, in accordance with EPA range labeling practice.For PHEVs, however, manufacturers are likely to consider mitigating loss of electric range because it will affect the utility factor, a component in the calculation of CO 2 emissions over useful life.The PHEV sizing algorithm therefore reserves a buffer to be used as the battery ages, as described later in Section 2.5.1.
Battery capacity also depends on the vehicle energy consumption rate.This depends largely on vehicle weight, road load, component efficiencies, and other factors.The process for estimating energy consumption for each PEV was as follows.First its curb weight was estimated as equal to the curb weight CW base of the corresponding baseline conventional vehicle, modified by any applicable curb weight reduction WR target (representing a curb weight reduction of 0, 2, 7.5, 10, or 20 percent), and further modified by deletion of the weight of conventional powertrain components (for BEVs) and addition of electric content (for BEVs and PHEVs), as shown in Equations ( 2) through ( 5) [3].
The curb weights CW base of conventional baseline vehicles were assigned based on average weights for each of the six vehicle classes defined in the EPA baseline fleet that was generated for the broader analysis.The divisions among the classes, being based in part on power-to-weight ratio, are referred to here as "P2W class".The P2W classes thereby establish target baseline curb weights and power requirements as inputs.
The weight of conventional powertrain components that would not exist on a battery electric vehicle (called "weight delete", or W ICE_powertrain ) were estimated for each of the six vehicle classes, as an approximate function of power.The weight of electric components (W electric_content ) included an estimated weight for the electric drive (motor and power electronics) as well as the weight of the battery.The weight of this content is computed iteratively by the spreadsheet, because it is strongly influenced by the total weight of the vehicle as well as several other factors.Electric drive weight was based on the targets established by US DRIVE [12] for the specific power of traction motors and power electronics in the 2020-2025 timeframe, at 1.4 kW/kg combined.An additional weight of 50 pounds was added to BEVs to account for the gearbox.
Battery weight was computed from an estimated battery specific energy (kWh/kg).Specific energy is not a fixed value but will vary depending on the power-to-energy (P/E) ratio of the battery and its gross capacity.Specific energy was provided by a dynamic link to ANL BatPaC, which computes specific energy as one of its outputs.
The "raw" PEV curb weights represented by Equations ( 4) and ( 5) are typically significantly larger than the curb weights of the conventional baseline vehicles on which they are based, because the added weight of the battery is typically greater than the weight delete.However, the potential battery cost savings may make PEV mass reduction more cost effective than that represented in the conventional baseline vehicle [13].As an approximate but straightforward way to directionally account for this effect, we further constrained the iteration process by forcing CW BEV or CW PHEV for each vehicle to match the curb weight of the corresponding baseline vehicle (CW base_reduced ) [3].To do so, we solved for the percentage of mass reduction that must be applied to the glider (a vehicle exclusive of powertrain) to offset the additional curb weight.In cases where more than 20 percent glider mass reduction would be needed to fully offset the difference, it was capped at 20 percent and only in these cases was the curb weight of the PEV allowed to be larger than that of its baseline counterpart [3].The degree of applied mass reduction is tracked for each vehicle and its cost is included when estimating the total vehicle cost.
In theory, a similar result might have been attained by applying each mass reduction percentage to the glider itself and allowing the resulting total curb weights to be unconstrained.A different set of data points would have resulted, skewed toward cases with little or no mass reduction applied.However, because we expect that mass reduction in PEVs is attractive to manufacturers for its potential to reduce battery cost, data points representing little or no mass reduction are of limited interest.Generating a greater density of points at greater percentages of mass reduction would therefore align better with expected industry practice.
After determining the PEV curb weight (constrained in most cases to match the baseline curb weight, but with a specific degree of applied mass reduction to do so), the method then computes the loaded vehicle weight (also known as inertia weight or ETW) by adding 300 pounds to the curb weight [3]: The method then uses this test weight to develop an energy consumption estimate.First, it estimates the fuel economy (mi/gal) for a conventional light-duty vehicle of that test weight by a regression formula derived from the relationship between 2-cycle fuel economy and inertia weight.
Compiled data on fuel economy vs. test weight from the EPA Trends Report [10] provided the primary data source.From this data, we derived a polynomial regression formula for fuel economy (mi/gal) as a function of ETW, as shown in Equation ( 7) [3].
An estimate of gross Wh/mile was then computed, assuming 33,700 Wh of energy per gallon of gasoline, as shown in Equation ( 8): A series of adjustments was then applied representing assumed differences in energy losses between conventional vehicles and electrified vehicles (this effectively brings the figure into electrified vehicle space) [3].Several powertrain efficiencies were estimated to assist in this conversion, including battery discharge efficiency, inverter and motor efficiency, transmission efficiency and other losses (such as wheel bearing, axle, and brake drag losses), and the percentage of energy delivered to the wheels that is used to overcome road loads (that is, the portion of wheel energy that is not later lost to friction braking) [3].These efficiencies were selected based on engineering judgement and then optimized in a model calibration step to yield battery capacity estimates in line with the capacities seen in production PEVs of similar specifications.
Estimated road loads appropriate for PEVs were derived from those for conventional vehicles by accounting for reductions in aerodynamic drag and rolling resistance.It was assumed that PEVs would support drag and rolling resistance reductions of 20 percent relative model year 2008 baseline conventional vehicles.Based on simulation models used in the broader analysis, we estimated that a 20 percent reduction in each would reduce PEV road loads to approximately 90.5 percent of the baseline.The effect of reductions in curb weight were inherently represented by use of the ETW regression formula to convert curb weights into base energy consumption estimates [3].
The combined effect of these steps means that the estimated energy consumption of each PEV is derived from the energy consumption of a corresponding baseline conventional vehicle by applying a ratio of the road loads of the PEV (%Roadload P/EV ) to those of the baseline vehicle (%Roadload conv = 1) and a ratio of the assumed efficiencies (η) of the respective powertrains, as shown in Equation ( 9) [3].
Equation ( 9) yields an unadjusted (laboratory), weighted, combined two-cycle (55% FTP, 45% HFET) estimate of energy consumption.To convert this to an estimated real-world energy consumption figure, the analysis applies a derating factor.Derating factors are discussed in a later section.As seen in Equation (10), where the derating factor is illustrated with a value of 70 percent as an example, applying the derating factor results in the PEV on-road energy consumption estimate that the method uses to determine the required battery pack capacity for the vehicle [3].
Finally, as shown by Equation (11), the required battery energy capacity (BEC) is calculated as the on-road energy consumption (Wh/mile) multiplied by the desired range (mi), divided by the usable battery capacity (the usable state-of-charge (SOC) design window).As discussed later, the assumed SOC design window (SOC%) varied appropriately between BEVs and PHEVs [3].
The iterative nature of the battery sizing problem means that all the preceding calculations are constructed in a spreadsheet as circular references and performed iteratively by the spreadsheet software until the estimated weights, sizes, and energy consumption figures converge [3].
Selection of Primary Inputs
Figure 1 (left of Figure ) depicts the role of battery sizing assumptions and battery design assumptions in the model.Battery sizing assumptions include parameters that determine necessary battery power and capacity, such as vehicle weight, energy efficiency, usable capacity, specific energy, mass of motor and power electronics, motor power, allowances for power and capacity fade, and similar factors.Battery design assumptions include factors such as cell capacity, pack topology, cells per module, thermal medium, electrode aspect ratio and coating thickness, and manufacturing volume.These assumptions are reviewed in detail here.
Inputs Influencing Battery Sizing
One important input to the battery sizing process is the usable SOC design window.Based on observation of existing vehicles, we chose 90 percent for BEV200 and 85 percent for other BEVs.For PHEVs, a smaller window was assigned to beginning-of-life (BOL) and a somewhat larger window to end-of-life (EOL).Battery capacity was specified using the BOL figure, which effectively provides a buffer that can be used as the vehicle ages.The BOL SOC window for PHEV20 was placed at approximately 65 percent while the EOL window was placed at 75 percent.For PHEV40, the BOL window was 67 percent and the EOL window 77 percent.These figures were chosen by engineering judgement and by considering their effect on the ability of the sizing method to reproduce battery capacities of production PHEVs [3].
Another important input to the battery sizing process is the required power capability of the battery.Target battery power (10 s pulse) was set to 32 percent greater than the peak motor power, to account for losses in the motor (10%) and EOL power fade (20%).In the case of BEVs and many longer-range PHEVs, target capacity drove the design more than target power, such that the battery is sufficiently large that its natural power capability exceeds the target power.These batteries therefore would have enough power capability to support moderate levels of fast charging and provide a buffer against power fade [3].
In the analysis, PHEV40 was assumed to operate as a range-extended electric vehicle, which meant that the motor and battery would be sized to provide all-electric operation in all driving situations, and hence the PHEV40 range is all-electric.The battery and motor for PHEV20 were sized for blended-operation where it was assumed the engine could assist the motor during the charge depletion phase.All PHEVs were configured with a single propulsion motor, in contrast to some production PHEV designs that split the total power rating between two motors.While we acknowledge that most PHEVs include a second motor used primarily as a generator, the analysis did not assign a separate weight to this component but considered it as part of the weight of the conventional powertrain [3].Although a PHEV application may allow some downsizing of the conventional portion of the powertrain, the analysis did not consider potential weight reductions from this source.
The derating factor also plays a role in determining battery size.The EPA range labeling rule allows manufacturers to determine the label range value either by applying a default 70 percent derating factor to a 2-cycle range test result, or to derive a custom derating factor by an optional process.According to EPA vehicle certification records for MY 2012-2016 BEVs, the vast majority of BEV models used the default 70 percent derating factor.The same data shows that Tesla Motors has elected the optional process for its BEV200+ vehicles resulting in a factor of nearly 80 percent for the standard Model S (60 to 90 kWh), and from 73 to 76 percent for higher-performance and all-wheel-drive versions of the S and X.We therefore adopted a derating factor of 75 percent for BEV200 and 70 percent for all other PEVs.
Inputs Influencing Battery Design
User inputs to BatPaC were chosen as follows.For performance, battery power and energy requirements were derived from the battery sizing analysis described previously.Other considerations were battery chemistry, cell and module layout, and production volumes.The pack voltages, electrode dimensions, cooling capacity, and cell capacities that were output from BatPaC were confirmed to ensure consistency with current and expected industry practice.Because the overall analysis accounted for warranty costs separately, the warranty costs computed by BatPaC were deducted from the output costs.
For chemistry, we selected NMC622 cathode for BEV and PHEV40 packs, and a blended cathode (25 percent NMC333 and 75 percent LMO, the BatPaC default value) for PHEV20 packs, both with graphite anode.These selections were based on the known characteristics of the chemistries and their representation in current and near-term production vehicles.
Pack topology was optimized by choosing values for cells per module and number of modules to target a preferred cell capacity (in Ampere-hours).Since the number of modules per pack must be a whole number, varying the number of cells per module allows the number of cells per pack and their capacities to be better targeted.The number of cells per module were varied between 20 and 36 as needed to achieve target pack voltages and maximum cell capacities [2].
BEV cells were limited to a maximum capacity of 90 A-hr.Most were significantly smaller as only the larger BEV packs approached this limit.The BMW i3 94 Ah provides an example suggesting this can be an effective cell capacity in a BEV application.PHEV cells were limited to 60 A-hr.Electrode coating thickness was limited to 100 microns, which again was only approached by the largest BEV batteries.All packs were modeled with liquid glycol-water cooling.Pack voltages were limited to the approximate range of 300 V to 400 V. Electrode aspect ratio was 3:1, supported by recent developments in pack design that suggest a movement toward low-profile packs that are mounted in the floor.BatPaC computed costs for a range of manufacturing volumes from 50,000 to 450,000 packs per year.
Battery Sizing and Cost Projections for Model Year 2025
Table 1 shows projected curb weight and gross battery capacity for MY 2025 vehicles for the various PEV types and P2W classes.P2W classes are distinguished by relative power and weight, with Class 1 representing the smallest, least powerful vehicles.The two figures reported for each class represent the extremes of the range of values resulting from 0 to 20% target weight reduction.In comparing these figures to current production vehicles, it should be noted that these future vehicles in many cases reflect improvements in road load and efficiency that may not be present in some current vehicles.Table 2 shows the range in projected cost per kWh for each MY 2025 PEV type and P2W class at a production volume of 450,000 packs per year.It is well known that battery cost, when expressed on a cost per kWh basis, is sensitive to total pack capacity and power-to-energy (P/E) ratio.Accordingly, the costs for these packs, for which designs and costs were determined by BatPaC, reflect these trends, with the highest specific cost per kWh projected for smaller PHEV20s and the lowest specific cost for larger BEV200s.
Validation of Battery Sizing
Here we assess the effectiveness of the battery sizing methodology by comparing the battery capacities in production vehicles to those that would be predicted by the methodology for their respective curb weights, driving ranges, and derating factors used in certification.As shown in Table 3, the methodology predicts capacities quite close to those seen in several existing BEVs.One uncertainty affecting the comparison is the true usable capacity of each vehicle, as compared to our assumptions of 90 percent for BEV200 and 85 percent for other BEVs.Manufacturers do not consistently publish usable capacity and it is difficult to verify the accuracy of reported values.Another uncertainty is the true gross capacity, for which reported values may be similarly imprecise.Differences in vehicle efficiency from our assumptions may also affect the comparison.
Figure 3 illustrates another perspective aggregated over a larger population of examples.The battery capacities of actual and projected vehicles are normalized to curb weight, which more directly expresses the efficiency with which a vehicle of a given weight converts gross battery capacity to miles of label range.In the figure, the battery capacity per unit curb weight (kWh/kg) of comparable production BEVs is compared against that of comparable MY 2016-2017 production BEVs.A 75 percent range derating factor is assumed for BEV200+ vehicles (the plotted range of production vehicles that certified with a different derating factor was adjusted to represent what their range would have been if they had certified using a 75 percent factor.It can be seen that the predicted BEV battery capacities closely follow the trend line established by comparable MY 2016-2017 BEVs.Results for PHEVs were similar.On close examination of the plot, it can be seen that for vehicles with shorter ranges, such as BEV75, BEV100, and PHEV20 (not shown), the trend line for projected capacity runs slightly below the trend line of production vehicles, as the methodology is tuned to predict future capacities for these vehicles somewhat smaller (on average) than are currently found in MY 2012-2017 production vehicles.This reflects our expectation that vehicles from that time frame that were marketed with a short range (which in the figure are represented largely by relatively low-production examples from a diversity of manufacturers) may tend to embody a lesser degree of optimization than the longerrange data points which represent higher-production examples from a smaller group of other manufacturers (Tesla and General Motors).In other words, we expect a slightly greater potential for future powertrain efficiency improvement to remain for these shorter-range vehicles than for longerrange vehicles, relative their current state.
Validation of Cost
It is important to reiterate that battery costs are affected by many influences, and future projections are subject to uncertainty.Comparing one set of projections to those from other sources requires a full understanding of the factors considered by each source.As a first-level comparison, here we compare our projected costs to two widely reported sources that are commonly cited in similar comparisons in the literature.
Estimating Pack Costs from Cell Costs
One way to validate cost estimates is to compare them to examples of actual costs.Cost at a pack level is rarely disclosed publicly but is sometimes encountered at the cell level.Here we develop a basis for comparing cell costs to pack costs to enable a comparison to the pack costs estimated here.
We collected several sources that suggest a ratio of total pack cost to constituent cell cost, or that allow such a ratio to be derived [14][15][16][17][18][19][20].Further detail on our use of these sources is provided at pp. 5-124 of [2].As seen in Table 4, most of these sources suggest a ratio of about 1.25 to 1.4.
To further inform this issue, we derived pack-to-cell ratios from costs estimated by BatPaC for a pack configured similarly to that of the Chevy Bolt.The Bolt pack is 60 kWh, arranged 96S3P in ten modules with a varying number of cells per module.Because BatPaC requires a fixed number of cells per module, we modeled 100S3P in ten modules of 30 cells using NMC622-G chemistry at annual production of 100,000 packs and a target 10 s pack power of 100 kW. Figure 4 shows the ratio of pack cost to cell cost for various pack capacities of this construction and suggests a factor of about 1.3 would apply to a 60-kWh pack.On close examination of the plot, it can be seen that for vehicles with shorter ranges, such as BEV75, BEV100, and PHEV20 (not shown), the trend line for projected capacity runs slightly below the trend line of production vehicles, as the methodology is tuned to predict future capacities for these vehicles somewhat smaller (on average) than are currently found in MY 2012-2017 production vehicles.This reflects our expectation that vehicles from that time frame that were marketed with a short range (which in the figure are represented largely by relatively low-production examples from a diversity of manufacturers) may tend to embody a lesser degree of optimization than the longer-range data points which represent higher-production examples from a smaller group of other manufacturers (Tesla and General Motors).In other words, we expect a slightly greater potential for future powertrain efficiency improvement to remain for these shorter-range vehicles than for longer-range vehicles, relative their current state.
Validation of Cost
It is important to reiterate that battery costs are affected by many influences, and future projections are subject to uncertainty.Comparing one set of projections to those from other sources requires a full understanding of the factors considered by each source.As a first-level comparison, here we compare our projected costs to two widely reported sources that are commonly cited in similar comparisons in the literature.
Estimating Pack Costs from Cell Costs
One way to validate cost estimates is to compare them to examples of actual costs.Cost at a pack level is rarely disclosed publicly but is sometimes encountered at the cell level.Here we develop a basis for comparing cell costs to pack costs to enable a comparison to the pack costs estimated here.
We collected several sources that suggest a ratio of total pack cost to constituent cell cost, or that allow such a ratio to be derived [14][15][16][17][18][19][20].Further detail on our use of these sources is provided at pp. 5-124 of [2].As seen in Table 4, most of these sources suggest a ratio of about 1.25 to 1.4.
To further inform this issue, we derived pack-to-cell ratios from costs estimated by BatPaC for a pack configured similarly to that of the Chevy Bolt.The Bolt pack is 60 kWh, arranged 96S3P in ten modules with a varying number of cells per module.Because BatPaC requires a fixed number of cells per module, we modeled 100S3P in ten modules of 30 cells using NMC622-G chemistry at annual production of 100,000 packs and a target 10 s pack power of 100 kW. Figure 4 shows the ratio of pack cost to cell cost for various pack capacities of this construction and suggests a factor of about 1.3 would apply to a 60-kWh pack.
Source Ratio
Kalhammer et al. [14] 1.24-1.4Element Energy [15] 1.6-1.85Konekamp [16] 1.29 USABC [17] 1.25 Tataria/Lopez [18] 1.26 Keller [19] 1.2 UBS [20] 1.32-1.44 World Electric Vehicle Journal 2018, 9, x FOR PEER REVIEW 11 of 14 [15] 1.6-1.85Konekamp [16] 1.29 USABC [17] 1.25 Tataria/Lopez [18] 1.26 Keller [19] 1.2 UBS [20] 1.32-1.44analysis described in this paper generated costs only for the year 2025 and only for the six P2W classes modeled.These costs acted as inputs to a downstream analysis (not described in this paper) that generated costs for intervening years by applying a reverse learning curve based on a range of production volumes, for a group of specific PEV technology packages corresponding to the 29 vehicle classes considered in the broader analysis.The yearly estimates resulting from these curves were ultimately used to project PEV vehicle costs in the broader analysis and are somewhat more conservative on a cost per kWh basis as compared to the raw 2025 costs reported in Table 2.
Figure 5 compares the yearly cost estimates for the various P2W classes of BEV200 to the packconverted GM costs.Our estimates appear consistent with or somewhat conservative relative the trend established by the estimated GM cost (converted to pack-level cost).
Comparison of Projected Costs to Other Sources
In October 2015, General Motors (GM) publicly commented on its cell costs for the Chevy Bolt BEV [21].These costs have been widely reported in the literature and are frequently cited in comparison to future projections.GM reported a cell cost of $145 per kWh for 2015 to 2019, dropping to $120 per kWh in 2020 and to $100 per kWh in 2022.Assuming cell-to-pack factors of 1.3 and 1.5, the 2015-2019 figure would translate to $190 to $220 per kWh on a pack level, while the figures for 2020 and 2022 would translate to $156-$180 and $130-$150 per kWh, respectively.Our estimates for BEV200 pack cost, which range from approximately $120 to $150 per kWh and which we attribute to 2025, compare well to the 2022 pack-converted costs of $130-$150 per kWh.
The analysis described in this paper generated costs only for the year 2025 and only for the six P2W classes modeled.These costs acted as inputs to a downstream analysis (not described in this paper) that generated costs for intervening years by applying a reverse learning curve based on a range of production volumes, for a group of specific PEV technology packages corresponding to the 29 vehicle classes considered in the broader analysis.The yearly estimates resulting from these curves were ultimately used to project PEV vehicle costs in the broader analysis and are somewhat more conservative on a cost per kWh basis as compared to the raw 2025 costs reported in Table 2.
Figure 5 compares the yearly cost estimates for the various P2W classes of BEV200 to the pack-converted GM costs.Our estimates appear consistent with or somewhat conservative relative the trend established by the estimated GM cost (converted to pack-level cost).As a further comparison, Figure 6 plots our estimated costs for larger packs (PHEV40 to BEV200) against the survey of published future cost estimates reported by Nykvist and Nilsson [22].Our estimated costs for these packs also lie within the range of future cost trends suggested by this survey.
Conclusions
We outlined a spreadsheet-based method to project battery gross capacities, motor and battery power ratings, and battery costs for an array of future PEVs.A relationship between 0-60 time and the power rating of the electric drive motor was derived from empirical data.A range of cost ratios between total pack cost and constituent cell cost was derived from published sources and BatPaC output data to assist in the comparison of cell costs to pack costs.The projected battery capacities appear to align well with trends established by production PEVs in the market.Projected costs for BEV200 appear consistent with widely cited cell costs for a production BEV, and projected costs for PHEV40 and BEVs appear consistent with trends described in the literature.
Supplementary Materials: Supporting data is available online at Regulations.gov, in EPA Docket EPA-HQ-OAR-2015-0827.For chart data, search for Docket Item "EPA-HQ-OAR-2015-0827-5788" titled Data and Charts for Selected Figures in Electrification Chapters of Proposed Determination TSD and see Microsoft Excel attachment to that entry.For BatPaC modeling data, search for "EPA-HQ-OAR-2015-0827-5824" and follow the instructions given therein to locate and examine the source data.As a further comparison, Figure 6 plots our estimated costs for larger packs (PHEV40 to BEV200) against the survey of published future cost estimates reported by Nykvist and Nilsson [22].Our estimated costs for these packs also lie within the range of future cost trends suggested by this survey.As a further comparison, Figure 6 plots our estimated costs for larger packs (PHEV40 to BEV200) against the survey of published future cost estimates reported by Nykvist and Nilsson [22].Our estimated costs for these packs also lie within the range of future cost trends suggested by this survey.
Conclusions
We outlined a spreadsheet-based method to project battery gross capacities, motor and battery power ratings, and battery costs for an array of future PEVs.A relationship between 0-60 time and the power rating of the electric drive motor was derived from empirical data.A range of cost ratios between total pack cost and constituent cell cost was derived from published sources and BatPaC output data to assist in the comparison of cell costs to pack costs.The projected battery capacities appear to align well with trends established by production PEVs in the market.Projected costs for BEV200 appear consistent with widely cited cell costs for a production BEV, and projected costs for PHEV40 and BEVs appear consistent with trends described in the literature.
Supplementary Materials: Supporting data is available online at Regulations.gov, in EPA Docket EPA-HQ-OAR-2015-0827.For chart data, search for Docket Item "EPA-HQ-OAR-2015-0827-5788" titled Data and Charts for Selected Figures in Electrification Chapters of Proposed Determination TSD and see Microsoft Excel attachment to that entry.For BatPaC modeling data, search for "EPA-HQ-OAR-2015-0827-5824" and follow the instructions given therein to locate and examine the source data.
Conclusions
We outlined a spreadsheet-based method to project battery gross capacities, motor and battery power ratings, and battery costs for an array of future PEVs.A relationship between 0-60 time and the power rating of the electric drive motor was derived from empirical data.A range of cost ratios between total pack cost and constituent cell cost was derived from published sources and BatPaC output data to assist in the comparison of cell costs to pack costs.The projected battery capacities appear to align well with trends established by production PEVs in the market.Projected costs for BEV200 appear consistent with widely cited cell costs for a production BEV, and projected costs for PHEV40 and BEVs appear consistent with trends described in the literature.
Supplementary Materials: Supporting data is available online at Regulations.gov, in EPA Docket EPA-HQ-OAR-2015-0827.For chart data, search for Docket Item "EPA-HQ-OAR-2015-0827-5788" titled Data and Charts for Selected Figures in Electrification Chapters of Proposed Determination TSD and see Microsoft Excel attachment to that entry.For BatPaC modeling data, search for "EPA-HQ-OAR-2015-0827-5824" and follow the instructions given therein to locate and examine the source data.
Figure 1 .
Figure 1.Analysis structure for vehicle battery sizing and cost estimation.Key: P2W, power-to-weight class; CW, curb weight; WR, curb weight reduction; MR, glider mass reduction.
Figure 1 .
Figure 1.Analysis structure for vehicle battery sizing and cost estimation.Key: P2W, power-to-weight class; CW, curb weight; WR, curb weight reduction; MR, glider mass reduction.
Figure 2 .
Figure 2. Relationship between peak-power-to-ETW ratio and acceleration performance for MY 2012-17 PEVs capable of pure electric acceleration.
Figure 2 .
Figure 2. Relationship between peak-power-to-ETW ratio and acceleration performance for MY 2012-17 PEVs capable of pure electric acceleration.
Figure 3 .
Figure 3. Projected BEV gross battery capacity per unit curb weight compared to comparable production BEVs [3].
Figure 3 .
Figure 3. Projected BEV gross battery capacity per unit curb weight compared to comparable production BEVs [3].
Figure 4 .
Figure 4. Ratio of pack cost to cell cost computed by BatPaC for pack topology similar to Chevy Bolt.
Figure 4 .
Figure 4. Ratio of pack cost to cell cost computed by BatPaC for pack topology similar to Chevy Bolt.
Figure 5 .
Figure 5.Comparison of Estimated Pack-Converted Chevy Bolt Costs to Post-Processed BEV200 estimates.
Figure 5 .
Figure 5.Comparison of Estimated Pack-Converted Chevy Bolt Costs to Post-Processed BEV200 estimates.
Figure 5 .
Figure 5.Comparison of Estimated Pack-Converted Chevy Bolt Costs to Post-Processed BEV200 estimates.
Table 1 .
Projected gross battery capacity for MY 2025 by vehicle type, power-to-weight class, and range.
Table 2 .
Projected pack-level direct manufacturing costs for MY 2025 by vehicle type and range ($/kWh, 2015$).
Table 3 .
Comparison of projected capacities to those of selected production vehicles.
Table 4 .
Ratios of total pack cost to cell cost suggested by information in published sources.
Table 4 .
Ratios of total pack cost to cell cost suggested by information in published sources. | 10,283 | 2018-10-06T00:00:00.000 | [
"Engineering"
] |
Intrusion Detection of NSM Based DoS Attacks Using Data Mining in Smart Grid
: In this paper, we analyze the Network and System Management (NSM) requirements and NSM data objects for the intrusion detection of power systems; NSM is an IEC 62351-7 standard. We analyze a SYN flood attack and a buffer overflow attack to cause the Denial of Service (DoS) attack described in NSM. After mounting the attack in our attack testbed, we collect a data set, which is based on attributes for the attack. We then run several data mining methods with the data set using the Waikato Environment for Knowledge Analysis (WEKA). In the results, we select the decision tree algorithms with high detection rates, and choose key attributes in high level components of the trees. When we run several data mining methods again with the data set of chosen key attributes, the detection rates of most data mining methods are higher than before. We prove that our selected attack attributes, and the proposed detection process, are efficient and suitable for intrusion detection in the smart grid environment.
Introduction
The promotion and industrial development of smart grid technology is accelerating worldwide.However, service construction and research on intrusion detection, one of the most important security considerations in the smart grid, is lacking.Moreover, generality and security by applying standards is required.
The smart grid industry, which is a fusion between traditional industries and emerging industries continues to grow with other technologies.At this time, the security of data transmission and application of standard technology is an indispensable element.In addition, compared to the existing power grids, the smart grid environment is a new business platform fused with information and communication technology.Security problems in information technology still exist in smart grids, and without guarantee of security the impacts are more serious than in the existing information technology.Cyber vulnerabilities and violations are actually increasing, and causing cases of damage.In particular, various types of attacks including physical attacks continue to increase, and intrusion detection methods for this are needed.
IEC 62351-7 [1] is a developing standard in International Electrotechnical Commission (IEC) Technical Committee (TC) 57 on security that is focused on developing standardized Network and System Management (NSM) object definitions for monitoring and controlling the information infrastructure.What is needed is the promotion of generality, extendibility and security through NSM, so that these international standards are applied to the smart grid intrusion detection service.
In this paper, we analyze the security requirements of NSM data objects, which are defined by IEC 62351-7 for intrusion detection, and analyze detection of SYN flood attacks and buffer overflow attacks as a Denial of Service (DoS) attack.For this, we construct a smart grid environment, and select attributes for analysis of those attacks.We then collect data of each attribute actually used in the trial attack.Subsequently, we make a comparative analysis of the data mining algorithms, to detect the attack efficiency.We prove that our selected attack attributes and the proposed detection process are efficient.The overall detection rate is enhanced after selection of key attributes.The rest of this paper is organized as follows: Section 2 presents the network and system management.Section 3 presents the attack method.Section 4 illustrates the system environment, and presents the proposed modeling and detection process.Section 5 analyzes the experimental results, to evaluate the effectiveness of our scheme.Finally, we conclude this paper in Section 6.
Network and System Management
The IEC smart grid standardization roadmap is based on the recent work of IEC SG3.IEC 62351 [2] addresses power systems management and associated information exchange-data and communication security.The scope of IEC 62351-7 focuses on network and system management (NSM) of the information infrastructure.The goal of this standard is to provide a service related to security requirements, of confidentiality, integrity, availability, and non-repudiation.As a protocol approach, it provides a security service in terms of two aspects.First, it protects information, using encryption from the origin point to the target point, or a secure electronic communication system by means of a protected power distribution system.Second, it provides end-to-end security.
Denial of Service Attack
The NSM requirements in IEC 62351-7 deal with detecting resource exhaustion as a DoS attack, for example, a SYN flood attack and a buffer overflow attack.
SYN Flood Attack
A SYN flood is a form of DoS attack, in which an attacker sends a succession of SYN requests to a target's system, in an attempt to consume enough server resources to make the system unresponsive to legitimate traffic [3].
The passive intrusion detection system (IDS) can detect rapidly increasing SYN flooding, based upon time and/or bandwidth consumption.The NSM is required to detect resource exhaustion attacks [1]: -Exceeding the maximum number of connection permitted over the network; -Count of number of connections actually in place over the network; -Exceeding the maximum number of connections which can be in use simultaneously; -Count of the number of connections in use simultaneously; -Exceeding minimum/maximum idle time; -Actual idle time over a specified time period; -Exceeding CPU load limits; -Exceeding memory usage limits; -Below low level battery power limits or too high rate of change.
Buffer Overflow Attack
A buffer overflow is an anomaly where a program, while writing data to a buffer, overruns the buffer's boundary and overwrites adjacent memory [4].The passive IDS is not intrinsically able to determine whether a buffer overflow attack is underway.This is especially true for IEC 61850 [5] and IEC 60870-6 TASE.2 [6] where the application buffer size is negotiated at runtime.However, the application/communication stack could be aware of such overruns [1].The NSM is required to detect buffer overflow attacks: -Number of buffer over runs; -Number of buffer under runs; -Audit ability to detect which source caused the buffer overflow/underflow.
Attack Method
In recent smart grid attack trends, the false data injection attack [7] proposed in 2009 has taken center stage as a new type of attack, and relevant work to respond to this treat is being proposed continuously [8][9][10].
Other attack papers are as follows.Chen et al. [11] investigate the use of Petri nets for modeling coordinated cyber-physical attacks on the smart grid.Yuan et al. [12] propose a Smart Grids Distributed Intrusion Detection System (SGDIDS), by developing and deploying an intelligent module-the Analyzing Module (AM)-in the multiple layers of smart grids.Xie et al. [13] are the first ones attempting to formalize the economic impact of malicious data attacks on real-time market operations.Mohsenian-Rad and Leon-Garcia [14] propose a cost-efficient load protection strategy, which minimizes the cost of the load protection.Lu et al. [15] use experiments to quantitatively evaluate the impact of DoS attacks on a power substation network with a distributed network protocol (DNP3).They prove that long DNP3 packets are more vulnerable to DoS attacks than are short DNP3 packets, and that the performance of the power network does not degrade gradually with the increase of the DoS attack intensity.Kundur et al. [16] propose an impact analysis framework, based on a graph-theoretic dynamical systems approach, for modeling the cyber-physical interactions.Little research exists on the topic of DoS attacks on smart grids.In particular, research of a similar type to a SYN flood attack and a buffer overflow attack has not been conducted.
Intrusion Detection
This section covers the system environment for our experiments, and the modeling and detection process to find an efficient detection rate.
System Environment
We try a SYN flood attack and a buffer overflow attack to cause a DoS attack on a smart grid environment, and experiment to find an efficient data mining mechanism for intrusion detection.The attack test bed is as shown in Figure 1.Our attack test bed consists of the substation and local area network.The substation originally divides into three levels: process level including the I/O devices, intelligent sensors and actuators, bay level including the protection and control IEDs, and station level including the substation computer, operators desk, and the interfaces with outside the substation [15,17,18].However, we depict only two levels: bay level and station level because our attack experiments only need two levels.We use a personal computer (PC) that is similar to an intelligent electronic device (IED)-CPU: 550 MHz, Memory: 256 MB-that is a target, and transmit an attack message using a general object oriented substation event (GOOSE) [19] data format.An IED is a microprocessor-based controller of power system equipment.IEDs receive data from sensors and power equipment, and can issue control commands, such a tripping circuit breakers if they sense voltage, current, or frequency anomalies, or raise/lower voltage levels in order to maintain the desired level.
IEC 61850-7-2 [19] is a standard for communication between IEDs, and defines GOOSE communication stacks.GOOSE transmits trip commands and interlocking information with high priority frames, and ensures that these frames are handled with priority within all participating IEDs [20].Figure 2 depicts a GOOSE communication stack.
Figure 2. GOOSE communication stacks [20] (Copyright ABB).
An attacker tries a SYN flood attack and a buffer overflow attack using a GOOSE message through a router.We use a publish/subscribe communication model as a routing mechanism in this test system.The publish/subscribe communication model is designed for serving this special GOOSE communication requirements of the IEC 61850 standard.The publish/subscribe communication model is basically an added feature to the normal TCP/IP client/server model, any GOOSE message can be multicast by the sender (so called publisher) to the receiver(s) [so called subscriber(s)].The main difference is that multicast group addresses are used instead of IP addresses [21].The attacker tries a SYN flood attack and a buffer overflow attack by simultaneously sending a number of point to point GOOSE message through a router.
We analyze those attacks, and select data attributes for the use of data mining methods, and then collect data based on these attributes.Next, we run several data mining methods with collected data, using the Waikato Environment for Knowledge Analysis (WEKA) [22], and derive data mining methods showing the highest detection rate.
Modeling and Detection Process
We therefore implement a possible DoS attack in a smart grid environment, to experiment to find data mining methods with a better detection rate.Figure 3 depicts the experimental process.
Data Attribute Selection
We analyze attacks, and select data attributes for collection and detection.In this experiment, we analyze a SYN flood attack and a buffer overflow attack, and select data attributes for better detection of the SYN flood attack.First, we analyze the NSM requirements for each attack and select data attributes.After that, we monitor each attack with our monitoring tool during each attack experiment and select additional data attributes.
Attack Trial
We construct an attack test bed as shown in Figure 3, run a SYN flood attack and a buffer overflow attack, and then collect data related to data attributes.
Data Gathering
Before the attack attempts, we collect data related to data attributes in the normal status.After the attack attempts, we create a data set collected by the relevant data attributes.
Data Mining
The normal state data and attack state data are input into the WEKA program, all of the mining algorithms that are automatically selected are run, and the results are compared with the detection rate.
Mining Algorithm Selection
After all mining algorithms in the previous step are compared and analyzed, decision tree algorithms with the best detection rate are selected.
Key Attribute Selection
Selected decision tree algorithms in the previous step show the decision tree with attributes as a result.We select key attributes in the top levels of the tree.
Data Mining
All mining algorithms are run with selected key attributes.After that, we compare and analyze between results, with key attributes, and results with all attributes.
Experimental Results
In this section, the proposed experiments and the results of this experiment about two attacks show respectively depending on the process.
SYN Flood Attack
The SYN flood attack is a classic means of DoS attack.The SYN flood attack exploits the TCP's three-way handshake mechanism and its limitation in maintaining half-open connections.When a server receives a SYN request, it returns a SYN/ACK packet to the client.Until the SYN/ACK packet is acknowledged by the client, the connection remains in a half-open state for a period of up to the TCP connection timeout, which is typically set to 75 s.If a SYN request is spoofed, the victim server will never receive the final ACK packet to complete the three-way handshake.Flooding spoofed SYN requests can easily exhaust the victim server's backlog queue, causing all incoming SYN requests to be dropped [3]. the percentage that the packet occupied ; the packet length between 40 and 79 320-639 packets count the count of packets which packet length is between 320 and 639 320-639 rate average count of packets per ms; the packet length is between 320 and 639 320-639 percent the percentage that the packet occupied ; the packet length between 320 and 639 CPU percent the usage of CPU when traffic stopped Memory used (kB) the memory used when traffic stopped Buffer size (kB) the buffer used when traffic stopped
Attack Trial and Data Gathering
The attacker tries 100 times to attack the victim IED.The attacker continually transmits a SYN packet to the victim IED.When the attack trial starts, the data relevant attributes are captured three times, once every minute, so a total of 300 data are collected.Normal data is also captured once every minute, so 300 normal data are captured.As a result, 300 normal state data and 300 attack state data are collected.
Data Mining
The 300 normal data and 300 attack data generated in the previous step are input into the WEKA, and then the available data mining algorithms are run to obtain the detection rate.The results are show in Table 2.A total of 64 mining algorithms are performed and 30 algorithms including a tree.NBTree shows a 99.833% detection rate, followed by 11 algorithms that show a detection rate of 99.667%, four algorithms show 99.5%, three algorithms show 99.333%, one algorithm shows 98.833%, one algorithm shows 98%, one algorithm shows 96.833%, one algorithm shows 96.333%, two algorithms show 95.5%, thus 54 mining algorithms show a good detection rate.However, tree.SimpleCart and tree.BFTree show 54.833%, and eight algorithms including rules.ZeroR show the lowest detection rate of 50%.WEKA classifies the data mining algorithms as follows.
Mining Algorithm Selection and Key Attribute Selection
The Decision tree algorithms with the best detection rate in the above procedure are selected, and those algorithms show the decision tree as a result.Tree.ADTree and tree.LADTree are chosen.
An alternating decision tree (ADTree) [23] is a machine learning method for classification.It is a class for generating an alternating decision tree.The underlying learning algorithm for ADTrees is AdaBoost.LADTree [24] is a class for generating a multi-class decision tree, using LogitBoost strategy.
Traffic count, memory used, time of round trip (s), average packets size, average B/s, average packets/s are chosen as key attributes, as shown in Figure 5.When LADTree is performed, traffic count, average packets/s, memory used, 40-79 packets count, time of round trip (s), 320-639 percent, and average B/s are chosen as key attributes.Figure 6 depicts the results of LADTree.
Data Mining
All possible mining algorithms are performed with selected key attributes, using ADTree in the previous procedure.The results are as shown in Table 3.Three algorithms show a 100% detection rate, 29 algorithms show 99.833%, 10 algorithms show 99.667%, two algorithms show 99.5%, one algorithm shows 99.333%.The overall detection rate is better than before.Figure 7 depicts the result after key attributes selection using ADTree.Next, all possible mining algorithms are performed with selected key attributes, using LADTree in the previous procedure; traffic count, average packets/s, memory used, 40-79 packets count, time of round trip (s), 320-639 percent, and average byte/s.
As Figure 8 shows, the results are similar to the results of ADTree.Three algorithms show a 100% detection rate, 29 algorithms show 99.833%, 11 algorithms show 99.667%, two algorithms show 99.5%, two algorithms show 99.167%, one algorithm shows 98.833%, one algorithm shows 98%, one algorithm shows 96.833%, one algorithm shows 96.5%, one algorithm shows 95.5%, and one algorithm shows 87.333%.The overall detection rate is better than before.The results of two algorithms are 54.833%, and the results of eight algorithms are 50%.The results of 10 algorithms are significantly low.
Buffer Overflow Attack
A buffer overflow is an attack that could be used by a cracker to overruns the buffers boundary and overwrites adjacent memory while writing data to a buffer.Buffer overflow attacks can be triggered by inputs that are designed to execute code, or alter the way the program operates.This may result in the DoS to undermine the availability, including a modification of data to compromise the integrity and confidentiality.In this experiment, we focus on the denial of service attack causing the buffer overflow.An attacker transmits a malicious code to a target intelligent electronic device (IED) system that randomly writes oversize data due to insufficient bounds checking.We collect the data necessary for the detection of attacks.
Data Attribute Selection
The following details the selected attributes after we analyze the buffer overflow attack.
Two kinds of attributes, buffer used (kB) and transmission payload size (bytes), are added when compared with the SYN flood attack.
Attack Trial and Data Gathering
The attacker tries 100 times to attack the victim IED.The attacker transmits a malicious code to the victim IED that randomly writes oversize data due to insufficient bounds checking, and run the malicious code.When the attack trial starts, the data relevant attributes are captured one time, once every minute, and thus a total of 100 data are collected.Normal data is also captured once every minute, and thus 100 normal data are captured.As a result, 100 normal state data and 100 attack state data are collected.
Data Mining
The 100 normal data and 100 attack data generated in the previous step are input into the WEKA, and then the available data mining algorithms are run to obtain the detection rate.The results are show in Table 4.
A total of 70 mining algorithms are performed and 40 algorithms including a tree.RandomForest show a 100% detection rate, followed by four algorithms that show a detection rate of 99.5%, two algorithms show 99%, two algorithms show 98.85%, three algorithms show 97.5%, three algorithms show 97%, five algorithms show 96.5%, one algorithm shows 96%, one algorithm shows 90%, thus 61 mining algorithms show a good detection rate.However, nine algorithms including rules.ZeroR show the lowest detection rate of 50%. Figure 9 depicts all detection rates of the buffer overflow attack.
Mining Algorithm Selection and Key Attribute Selection
The Decision tree algorithms with the best detection rate in the above procedure are selected, and those algorithms show the decision tree as a result.Tree.ADTree, tree.RamdomTree, tree.REPTree, tree.J48, tree.J48graft, and tree.LADTree are chosen.
RandomTree [25] is a class for constructing a tree that considers K randomly chosen attributes at each node.REPTree [26] is a fast decision tree learner.It builds a decision/regression tree using information gain/variance and prunes it using reduced-error pruning (with backfitting).J48 [27] is a class for generating a pruned or unpruned C4.5 decision tree.C4.5 is an extension of Quinlan's earlier ID3 algorithm.The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a statistical classifier.J48graft [28] is a class for generating a grafted (pruned or unpruned) C4.5 decision tree.
Figure 10 depicts the result after key attributes selection-average packets size-using ADTree, RandomTree, and REPTree.Figure 11 depicts the result after key attributes selection-total transmission packets-using J48 and J48graft.The key attributes of LADTree are selected with average packets size and total transmission packets.The result is as shown in Figure 12.
Data Mining
All possible mining algorithms are performed with average packets size, selected key attributes, using ADTree, RandomTree, and REPTree in the previous procedure.The results are as shown in Table 5. 57 algorithms show a 100% detection rate, 14 algorithms show 50%.The overall detection rate is better than before.After selection of key attributes bayes.NaiveBayesSimple is run in addition.Figure 13 depicts the results of this execution.Next, all possible mining algorithms are performed with total transmission packet, selected key attributes, using J48, J48graft the previous procedure.The results are as shown in Table 5. Fifty seven algorithms show a 100% detection rate, 14 algorithms show 50%.The overall detection rate is better than before.Finally, all possible mining algorithms are executed with average packet size and total transmission packet size.The results are similar to those in Table 5.
Discussion for Scalability Issue
This paper's main contribution is to propose a way to make a detection model using two mining algorithms to improve the efficiency and performance.The first algorithm selects key attributes among candidate attributes.Next, the second algorithm actually makes the detection model with data for selected key attributes outputting from the first algorithm.The final detection model improves detection performance because it is made with data for only a few key attributes, and modeling time reduces through modeling with data for a few key attributes.After that, detection can be performed through detection model in real time.
In our methodology also, the scalability issue is related.The more attacks that are considered to be detected, the more candidate attributes are input in the first algorithm.However, as shown in the experimental results, our methodology can reduce modeling time that can take a lot of time, through selecting a few key attributes among candidate attributes.As experimental results, the average three key attributes of the average 16 candidate attribute was selected.Moreover, this modeling is irrelevant to the detection time because of performing in the offline.If the detection model is made, the detection is performed in real time.As a result, our proposed methodology is not strongly influenced by scalability problem.
Conclusions
This work analyzed Network and System Management (NSM) requirements and NSM data objects for intrusion detection in power systems.We analyzed a SYN flood attack and a buffer overflow attack to cause a DoS attack, as described in NSM.We proposed the data attributes for the SYN flood attack and the buffer overflow attack, and the detection process to find efficient data mining methods for those attacks.In our experiments, several data mining methods showed good detection rates.Moreover, after key attributes selection, the overall detection rate is better than before.
In case of SYN flood attack, a total of 64 mining algorithms are executed with the selected key attributes.Thirty algorithms show 99.833% detection rate and 54 algorithms show more than 90% detection rate.Next, the decision tree algorithms with the best detection rate are selected, and those algorithms show the decision tree as a result.Sixty four algorithms are performed with selected key attributes using result of decision tree.Three algorithms show a 100% detection rate, 29 algorithms show 99.833%.
As similar with SYN flood attack, a total of 70 algorithms are executed with selected key attributes, and 40 algorithms show 100% detection rate.Sixty one algorithms show more than 90% detection rates.Again, the decision tree algorithms with the best detection rate are selected, and key attributes also selected as a result.A total of 71 algorithms are performed, and 57 algorithms show 100% detection rate, 14 algorithms show 50%, the overall detection rate is enhanced after selection of key attributes.We prove that our selected attack attributes and the proposed detection process are efficient, and suitable for intrusion detection in smart grid environments.
Figure 4 depicts all detection rates of the SYN flood attack.
Table 1
details the selected attributes after analysis of the SYN flood attack. | 5,390 | 2012-10-19T00:00:00.000 | [
"Computer Science",
"Engineering",
"Environmental Science"
] |
Synthesis and characterisation of microcapsules for self-healing dental resin composites
Aim The purpose of this study was to i) synthesise TEGDMA-DHEPT microcapsules in a laboratory setting; ii) characterise the resultant microcapsules for quality measures. Materials & methods Microcapsules were prepared by in situ polymerization of PUF shells. Microcapsules characterisation include size analysis, optical and SEM microscopy to measure the diameter and analyse the morphology of PUF microcapsules. FT-IR spectrometer evaluated microcapsules and benzyl peroxide catalyst polymerization independently. Result Average diameter of TEGDMA-DHEPT microcapsules was 120 ± 45 μm (n: 100). SEM imaging of the capsular shell revealed a smooth outer surface with deposits of PUF nanoparticles that facilitate resin matrix retention to the microcapsules upon composite fracture. FT-IR spectra showed that microcapsules crushed with BPO catalyst had degree of conversion reached to 60.3%. Conclusion TEGDMA-DHEPT microcapsules were synthesised according to the selected parameters. The synthesised microcapsules have a self-healing potential when embedded into dental resin composite as will be demonstrated in our future work. Graphical Abstract Graphical abstract showing the microcapsule components. The shell contains poly(urea-formaldehyde), and the core consists of TEGDMA-DHEPT healing agents.
Introduction
Dental resin restorations have been shown to encounter two main downsides: secondary caries and bulk fractures [1].They frequently fail due to the accumulation of microcracks generated from masticatory forces and thermal stresses [2].Self-healing composites and polymers involving microencapsulated healing liquids demonstrate the capability for providing long-life structural materials, with the potential to repair crack damage and recover mechanical performance in polymeric materials [3].
Microencapsulation is defined as "a technology of packaging solids, liquids or gaseous materials in miniature, sealed capsules that can release their contents at controlled rates under the influence of specific conditions" [42].This is a promising approach to increasing the durability of resin composites as the microcapsules will rupture and release of polymerisable healing agents to seal and stop crack propagation when the composite is subjected to fracture [3,14,22].
Technological advances in microencapsulation methods have been introduced; allowing a higher level of standardisation in microencapsulation process.Published reports of lab-based microcapsules synthesis vary but include microfluidic (micro-channels) encapsulation method, mostly used in biological substances, controlled drug release and pharmaceuticals [43][44][45].Although a higher precision can be achieved with microfluidics system, the microchannels are at a higher risk of clogging by PUF shell polymerization during microencapsulation which might be a limiting factor.
Studies have reported the incorporation of poly(ureaformaldehyde) PUF microcapsules encapsulating triethylene glycol dimethacrylate (TEGDMA) monomer and N,N-dihydroxyethyl-p-toluidine (DHEPT) tertiary amine accelerator as healing agents in self-healing dental composite [21][22][23].Also, benzoyl peroxide (BPO) catalyst is an essential part of the resin matrix, functioning as a self-healing initiator, facilitating the chemical polymerization of the healing agents involved in the microcapsules [21][22][23].A successful self-healing efficacy and recovery of the virgin fracture toughness (K IC ) of approximately 65% have been reported [22].The materials involved in self-healing dental composite have proven biocompatibility for dental use [22], however, further investigation is necessary before any in vivo studies in order to rule out the risk of cytotoxic unreacted free formaldehyde [46].
In the present study, the aims were to synthesise and characterise TEGDMA-DHEPT microcapsules, including optimisation of in situ emulsion polymerization of PUF shells, size analysis, optical and SEM imaging, and FT-IR of crushed microcapsules with BPO catalyst.
Synthesis of microcapsules
Microcapsules were prepared by in situ polymerization in an oil-in-water (O/W) emulsion (Fig. 1).At room temperature, 100 mL of distilled water and 26 mL of 2.5 wt% aqueous solution of poly (ethylene co-maleic anhydride) (EMA) copolymer were mixed into a 400 mL beaker flask.The beaker was held in a water bath on a hotplate with a digital display of temperature (Carousel tech stirring hotplate, Radleys, UK).A mechanical stirrer was used to agitate the solution, driving a four-bladed PTFE (40 mm) low-shear mixing propeller positioned just above the bottom of the beaker (Eurostar, IKA Ltd., UK).The stirring speed was set to 400 rpm.Then, 2.50 g urea, 0.25 g ammonium chloride and 0.25 g resorcinol were added into the flask.After dissolution of solids, the pH was checked and adjusted to 3.5 via drop-wise addition of 1 M NaOH solution.
Afterwards, the stirring speed was increased to 500 rpm.The healing liquid consisted of TEGDMA monomer and 1 wt% DHEPT amine.A slow stream of 60 mL of TEGDMA-DHEPT liquid was introduced to the reaction flask.After 10 min of stirring, a stabilised emulsion of fine TEGDMA-DHEPT droplets was formed.Then, 6.30 g of 37% aqueous solution of formaldehyde was added, and the flask was sealed with aluminium foil to prevent evaporation.The target temperature in the flask was 55-60 °C; an external temperature probe was placed in the bath for further confirmation.
The shell materials of the microcapsules were isothermally polymerised under continuous agitation.After 4 h, the suspension of microcapsules was left to cool to ambient temperature.Then, filtration through centrifugation and sedimentation were employed.The microcapsules suspension was centrifuged with distilled water.This process was repeated 5 times, for each 5 min cycle the solution was replaced with fresh distilled water in order to remove the remnant surfactant.Sieving of the microcapsules was undertaken with rinsing with distilled water repeatedly throughout the sieving process, microcapsules were then left to dry for 24 h.
Sizing of microcapsules
In order to separate the microcapsules according to size, a vibratory sieve shaker (Retsch ® AS 200 digital, Retsch Limited, UK) was used.Four different sieves were used Fig. 1 Encapsulation process of in situ emulsion polymerization of TEGDMA-DHEPT microcapsules (45,90,150 and 300 μm pores sizes).The suspension of microcapsules was poured into the sieves and left for 30 min in the shaker (amplitude of 70% -2.1 out of 3 mm).The microcapsules were allowed to dry overnight.Microcapsules were then collected with a plastic spatula into four glass bottles according to the sieve size and weighed.
Imaging analysis
An optical microscope (Leica DMI6000 B, Germany) was used to assess the encapsulation process, and to confirm the diameter of the microcapsules by image processing software (ImageJ, NIH Image).Following that, microcapsule surface morphology and further size analysis were conducted using a scanning electron microscope (Zeiss EVO60, Germany).A small number of microcapsules were spread onto adhesive tape and sputter-coated with gold (7 nm).
Degree of conversion of the microcapsules with the catalyst
An FT-IR spectrometer has been used to measure the degree of polymerization of TEGDMA-DHEPT healing agents with benzoyl peroxide catalyst (Avatar 360, Nicolete Analytical Instrument, Thermo Electron Corp., Cambridge, UK).A mixture of microcapsules and 0.5 wt% of BPO were broken in an agate mortar and pestle grinding bowl then placed and pressed in a PTFE disc mould (4 mm internal diameter, 0.5 mm height).Another PTFE disc mould (4 mm internal diameter, 2 mm height) was also used to test the polymerization of this mixture in 2 mm depth.The spectra were recorded over the range of 4000 to 400 cm −1 with 32 scans at a resolution of 4 cm −1 , the degree of conversion (DC) of TEGDMA monomer was calculated from the peak intensity ratio of C=C at 1637 cm −1 against the internal standard peak of C=O at 1715 cm −1 immediately post-curing and 24 h after polymerization [47].
Size analysis
Synthesis of TEGDMA-DHEPT microcapsules was achieved by in situ polymerization to form poly(ureaformaldehyde) capsular shells.The distribution of microcapsule showed, a small number of microcapsules had a diameter between 45 μm to 90 μm.The size range of most microcapsules was 150 μm to 300 μm (Fig. 2).
Microcapsules imaging
After the filtration process, microcapsules presented as a white powder (Fig. 3, A).However, a number of the synthesised microcapsule batches showed as agglomerated and clustered particles (Fig. 3, B).Optical imaging further confirmed microcapsule sizes (as quantified in two dimensional planes of the sphere and averaged for each microcapsule); this revealed a diameter average of 120 ± 45 μm (n: 100).It is also showed an outer black ring that indicates shell formation and a moderately brighter area interiorly representing the encapsulated healing agents (Fig. 3, C and D).
SEM showed a uniform external surface without voids detectable.The microcapsule diameter (Fig. 4, A), was estimated to be around 150 ± 50 μm (n: 100).The smooth external wall forms a rough surface morphology with the presence of PUF nanoparticles.(Fig. 4, B).
Degree of conversion of the microcapsules with the catalyst
The healing agents TEGDMA-DHEPT successfully polymerised in both 0.5 mm and 2 mm specimens after 24 h, showing a degree of conversion of 60.3 and 34.8% respectively.The analysis of the final polymer spectra confirmed the reactivity of the microcapsules after being crushed and mixed with BPO catalyst.
Discussion
Self-healing composites and polymers, which incorporate microencapsulated healing liquids, have shown great promise in providing durable structural materials.These materials have the ability to repair crack damage and restore mechanical performance in polymeric materials, offering the potential for Fig. 3 Self-healing TEGDMA-DHEPT microcapsules prepared via polymerization in situ;(A) Microcapsules presented as a free-flowing white powder, (B) poor quality microcapsules batch showing agglomerated and fused microparticles, (C and D) Optical microscope images presenting capsular shells as a dark outer ring, encapsulating the healing agents of a lighter shade opacity Fig. 4 (A) SEM image of ≤150 μm microcapsules, also a ruptured microcapsule can be seen.(B) A higher magnification SEM image of the capsular shell, demonstrating a smooth outer shell with deposits of poly(urea-formaldehyde) nanoparticles long-lasting functionality [3].In the present work, TEGDMA-DHEPT microcapsules were successfully synthesised via emulsion polymerization to achieve polymeric capsular shells [36,48].Microcapsules were prepared by in situ polymerization; EMA acts as a surfactant, which helps to form an O/W emulsion, the oil being TEGDMA-DHEPT liquid.The microcapsules consisted of poly(urea-formaldehyde) shells with TEG-DMA monomer and 1 wt% DHEPT amine as healing agents.
The final product of microcapsules was a free-flowing white powder, however, some agglomerated microcapsules were also found.Clustered or fused microcapsules are not ideal, but upon microcapsules dispersion into resin matrix, even distribution was achieved.One of the key factors for the creation of free-flowing microcapsules is the filtration process, which is a very sensitive and delicate procedure [36].Poor filtration can result in an over-dryness of the microcapsules and may affect the permeability of the capsular shells by opening the shell pores.As a result, the microcapsules can become yellowish with time, due to healing liquid leaking through the shells resulting in the agglomeration and fusion of the microcapsules together.
Microcapsule size is an important factor to allow the encapsulation of sufficient healing agents to achieve self-healing capability in resin-based matrix.Smallersized microcapsules ≤70 μm will not be able to fill a crack due to the small amount of healing liquid.However, larger-sized microcapsules ≥300 μm will negatively impact the polymer matrix strength which may lead to voids following microcapsules rupture, resulting in deterioration of the mechanical properties of the polymeric material [49].Microcapsule diameter can be controlled by stirring speed; an average diameter of 10-1000 μm was obtained by 200-2000 rpm [36].A stirring speed of 500 rpm was set to obtain an average diameter of 150 μm microcapsules.Then, microcapsules were sieved using different sieves according to their capsular size, and showed the range was more of 150-300 μm microcapsule sizes.This technique was found to be a reliable and repeatable method for size sorting according to the anticipated application in resin-based materials.Optical or SEM microscopy can also be used to quantify microcapsule surface diameter although is time-consuming and requires the examination of several hundreds of particles to obtain statistically representative data.Optical and SEM imaging have also confirmed the microcapsules diameter ranging from 120 ± 45 μm to 150 ± 50 μm.Previous studies manufactured microcapsules with a similar diameter of 150-200 μm [36], or a smaller diameter of ≤70 μm microcapsules by using a higher stirring speed [22,36].
Shell thickness of microcapsules is of a vital importance; it has been reported that if too thin, shells are more prone to breakdown during resin paste mixing, handling and packing [22].However, if too thick, shells are more resistant to rupture upon composite fracture, which will prevent the delivery of healing liquid to the crack.Previous studies have reported an average shell thickness of 160-230 nm with DCPD or TEGDMA-DHEPT microcapsule, and showed that microcapsules ruptured upon composite fracture and self-healing capability was achieved [3,22,36].
SEM imaging showed that PUF nanoparticles existed on the external surface of the capsular shells.Deposition and aggregation of higher molecular weight pre-polymer on the outer PUF capsular surface during in situ polymerization resulted in a rough and porous surface morphology [36].The inner shell surface was a smooth non-porous wall as a result of low molecular weight pre-polymer deposition.PUF nanoparticles on the outer surface of the microcapsules can facilitate mechanical interlocking interface (micromechanical retention) to the host resin polymer matrix upon photo activation (light-curing) [22].This retention interface will allow the microcapsules to break when subjected to cracking.If the outer surface of the microcapsules had a smooth, non-porous morphology, the interlocking interface will be missing and the crack may bypass the microcapsules without breaking them, resulting in no healing liquid to fill the crack [22].
The ability of TEGDMA-DHEPT microcapsules to polymerise when crushed and mixed with 0.5 wt% benzoyl peroxide (BPO) catalyst was reported.BPO within the host polymeric material promotes the chemical reaction by free radical polymerization when it reacts with tertiary aromatic amine DHEPT in the healing liquid inside the ruptured microcapsules.An FT-IT spectral analysis was conducted within the range of 4000 to 400 cm −1 , utilizing 32 scans at a resolution of 4 cm −1 .To determine the degree of conversion (DC) of TEG-DMA monomer, the peak intensity ratio of C=C at 1637 cm-1 was compared to the internal standard peak of C=O at 1715 cm-1.This comparison was done both immediately after curing and 24 hours after polymerization.In another study involving TEGDMA-DHEPT microcapsules, similar findings were observed [47].A degree of conversion of 60.3% (in 0.5 mm depth) and 34.8% (in 2 mm depth) were obtained after 24 h self-cure at room temperature.Similar findings were reported by a recent study involving TEGDMA-DHEPT microcapsules crushed with 1 wt% BPO; a DC of 67.2% was reported [22].In general, dimethacrylate resins have residual unsaturated monomers in the final polymerised resin matrix which can reach up to 43% [50].In service, it is important to investigate how the reparative resin is released, rate of release, and the extent of mixing with BPO initiator.Also, the consequences of homopolymerization of TEGDMA as a reparative resin should be addressed, along with reaction kinetics of low molecular weight, high mobility resins and cyclisation reaction.
The current study used dental materials including TEG-DMA monomer and DHEPT amine in the microcapsules and BPO catalyst within the resin composite matrix.The materials used have been approved by the Food and Drug Administration, and are available in commercial resin-based dental composites.Human gingival fibroblast cytotoxicity tests in vitro have shown that TEGDMA-DHEPT microcapsules exhibit an acceptable biocompatibility, hence the incorporation of microcapsules in resin does not drastically compromise cell viability [22], although the possibility of leakage of unreacted free formaldehyde from PUF shells should be taken under consideration for cytotoxicity testing.
Conclusion
TEGDMA-DHEPT microcapsules were successfully synthesised by in situ polymerization of an O/W emulsion.The microcapsules have the ability to polymerise when they are ruptured and triggered by a BPO catalyst in the host composite.Microcapsule sizes ranged between 150 and 300 μm with an average of 120 ± 45 μm (n: 100).The morphology analysis showed a rough outer shell due to the presence of PUF nanoparticles.Microcapsules and BPO mixture showed a degree of conversion reached up to 60.3%, which confirms encapsulation of the healing agents and proves functionality of the microcapsules.
The incorporation of TEGDMA-DHEPT microcapsules in a self-healing dental composite model will be presented in our future studies.As yet, cytotoxicity testing should be conducted, considering the unreacted free formaldehyde in the PUF shells of microcapsules.
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On unitary reconstruction of linear optical networks
Linear optical elements are pivotal instruments in the manipulation of classical and quantum states of light. The vast progress in integrated quantum photonic technology enables the implementation of large numbers of such elements on chip while providing interferometric stability. As a trade-off these structures face the intrinsic challenge of characterizing their optical transformation as individual optical elements are not directly accessible. Thus the unitary transformation needs to be reconstructed from a dataset generated with having access to the input and output ports of the device only. Here we present a novel approach to unitary reconstruction that significantly improves upon existing approaches. We compare its performance to several approaches via numerical simulations for networks up to 14 modes. We show that an adapted version of our approach allows to recover all mode-dependent losses and to obtain highest reconstruction fidelities under such conditions.
I. INTRODUCTION
Linear optical quantum computing has attracted major attention since Knill, Laflamme and Milburn have introduced a scheme for efficient quantum computation in 2001 [1]. Notwithstanding tremendous technological progress, the experimental realization of such computers is still challenging with steep requirements for the generation, manipulation and detection of the quantum states of light. In the last decade, integrated quantum photonics [2] has become central to the technological progress by providing the means to miniaturize and mass fabricate vital components, such as quantum light sources [3][4][5][6], quantum storage devices [7,8] and highly efficient photon detection on chip [9][10][11][12]. Of particular importance is the manipulation of the quantum states of light via linear optical networks (LONs). Here, integrated quantum photonics enabled the fabrication of LONs with unprecedented levels of interferometric complexity. The inventory includes optical elements, facilitating either fixed [13][14][15][16][17] or tunable [18][19][20][21] single-qubit transformations but also novel hybride elements [22]. Arranging several of these elements allows fabrication of miniaturized versions of logic gates which are essential in quantum information processing. Those gates resemble small to medium scale interferometers and are either tailored to perform a particular task or can be reconfigured for a variety of tasks [13,15,20,21]. Here, the physical encoding scheme, e.g. a dual-rail polarization encoding, determines how these gates, unitary matrices acting on logical qubits, must be compiled from different optical elements. Hence, the overall transformations of these LONs are required to be unitary, too. This poses a challenge for experimental realizations which are inevitably afflicted by imperfections. Here, the major contributors are on one hand losses, which render these devices non-norm preserving. On the other hand fabrication imperfections stemming from the production itself cause deviations between an initially targeted transformation and the implemented one. Obtaining precise knowledge of an optical transformation at hand therefore is important and serves multiple purposes: It allows theoretical modelling of an experiment and allocation of the error budget to different sources of error. More important, identifying deviations or even defective optical elements is essential for troubleshooting experiments and improving future versions of an optical circuit. The ability to construct high-fidelity gate operations becomes a stringent requirement when circuits are scaled up beyond proof of principle implementations [23]. Since all waveguides are embedded into a bulk material, only the input and output ports and therefore the overall transformation is directly accessible. To acquire knowledge of such an overall transformation one can use different approaches relying on quantum resources [24][25][26][27][28] or classical resources [29][30][31][32]. The majority of these techniques fall in the category of quantum process tomography ('QPT'). While QPT is well established in quantum science, it faces challenges when applied to large networks due to quickly growing resource costs. Alternative techniques, reconstructing a transition matrix [31] or a unitary matrix description [28] of a LON, became prominent in the context of BosonSampling [33][34][35][36][37]. These methods scale more favourably with respect to the required measurements when compared to QPT, and reconstruct matrix descriptions of LONs omitting global phases at the input and output ports. Methods which rely on light that is scattered out of the LON are not further considered as the technique relies on loss that compromises the guiding properties of the whole structure [35]. Here, we present a new approach to characterize the transformation implemented by LONs. We choose to enforce unitarity from the start by parametrizing the LONs as interferometers composed of beam splitters and phase shifters [38]. The reconstructed unitary matrices are then obtained by optimizing the beam splitting ratios and phase shifts to best explain a set of data sensed via probe states injected into the network. We utilize a data set composed of two-photon interference visibilities [39], rendering the procedure insensitive to input and output loss. In this way both afore mentioned purposes of network reconstruction are fulfilled simultaneously; generating a description to model experimental data and gathering knowledge about the transformation of individual optical elements. Our method is a departure from the strategy of related approaches [27,31], which aim to reconstruct transition matrices, or do so in a first step [28,40]. Whereas transition matrices are sufficient to characterize a LON and to model experimental results, they do not allow to identify deviations of individual elements directly. Here a indirect route via a polar decomposition [28,40] and subsequent decomposition into individual elements must be chosen. The identification of faulty elements through a decomposition procedure requires LONs exhibiting a non-redundant layout, e.g. Reck et al. type networks.
II. DIFFERENT APPROACHES TO RECONSTRUCTION
In the following we will compare three approaches to LON characterization. 'Brisbane' [31] and 'Bristol' [28] 1 were chosen for their frequent usage in experiments relying on integrated LONs. Our approach, subsequently labelled 'Vienna', is formalizing ideas developed in [36,41]. Similar to [40,42], an over-complete set of primary data can be used to increase reconstruction fidelities, although we find the effect to be minor (see figure 2). In the following, primary data is referring to data sensed for reconstruction purposes in any of the approaches. The three compared approaches differ in their strategy to characterize a LON. 'Bristol' and 'Brisbane' first reconstruct the individual matrix entries of a scattering description and then require a polar decomposition step to recover the closest unitary matrix. Both utilize a sufficient set of data for this purpose and in the following we refer to this strategy as a passive approach. In contrast 'Vienna' follows an active approach utilizing a larger set of primary data in a global optimization routine which already implements the unitary constrains from the beginning. The approach 'Brisbane' aims to reconstruct a description of a black-box linear optical network from a sufficient set of primary data generated with coherent probe states. This data is then mapped one to one unto a scattering matrix representation M without the need to apply any further algorithms. The scattering matrix M represents a submatrix of a larger unitary matrix U, where the additional modes of U correspond to loss modes. Hence, the task of loss modelling translates to the task of finding a loss matrix that couples the interferometer modes of M to the loss modes of U. This necessarily includes input and output loss terms, as the approach processes transition amplitude data. 'Brisbane' covers the case of mode-dependent input loss in the following way: the loss term for each input mode k is directly given by the ratio between the total power exiting the LON and the power injected into mode k. Subsequently the input loss is modelled by virtual beam splitters, where the square root of the loss terms corresponds to the transmittivity of the virtual beam splitters. Note that such a loss modelling works only in the case when the mode-dependent output loss of the network is zero. In general, loss inside a network cannot be parametrized this way and thus it remains unclear how a more evolved loss modelling can be included in 'Brisbane'. Hence, only a partially loss modelling scattering description M , which is closer to the unitary description U than the matrix M, can be found via this method. Experimental environments exhibiting loss as detailed above cause M to be noticeably non-unitary and necessitate a polar decomposition if the closest unitary descriptionŨ is to be obtained. This polar decomposition can introduce further error dependent on the size of the interferometer under test [43]. Up to the deviations introduced by the polar decomposition the entries ofŨ reconstructed via this procedure are identical to the primary data generated. This self-consistency proves to be challenging when assessing the fidelity and the uncertainty of a reconstructed matrix in the presence of measurement errors. The complete set of single-input data and phase data is already used to fix the real entries and phases of M. To obtain realistic error estimations for the individual entries of M orŨ, the various error sources need to be studied in detail, including calibration uncertainty of the detector efficiencies and uncertainties introduced by fiber mating and coupling to a waveguide. Opposed to more complex algorithmic approaches like 'Bristol' or 'Vienna', the sensed data cannot be used to generate a quantifier for reconstruction success. An additional set of data generated by different means than coherent states is required for this purpose, e.g. a set of two-photon interference visibilities as done in [31]. The approach 'Bristol' aims to reconstruct a unitary description of a black-box linear optical network from a set of primary data, which in this case is generated via quantum probe states. The magnitude of each phase is sensed via a visibility of a non-classical two-photon interference but the sign of the phase needs to be calculated in relation to the other phases such that unitary constraints are obeyed. Note that a phase sensed this way is not a direct phase measurement like in the approach 'Brisbane'. Furthermore the visibility of each non-classical interference is also modified by the four contributing real entries τ jk of the scattering matrix, with j and k labelling the output and input modes, respectively. These transition amplitudes are calculated in a fashion insensitive to mode-dependent input and output loss: the loss terms drop out by relating all input and output single-photon count rates to each other. Therefore each entry of the reconstructed matrix, M jk = τ jk e iθ jk , becomes dependent on the whole set of primary data. All τ jk and θ jk are recovered by solving a linear system of non-linear equations. Again the closest unitary matrix,Ũ, can be found by applying a polar decomposition. Whereas the method is insensitive to loss at the input and output ports of a LON, it is sensitive to mode-dependent propagation loss. The latter introduces systematic error in the algorithm, already before applying the polar decomposition (Further detail on the influence of mode-dependent propagation loss for all three reconstruction approaches is given in Appendix D). Ultimately, the combination of the non-linear dependencies in the algorithmic approach with just a sufficient set of data leads to a lower performance of 'Bristol' with respect to 'Brisbane' and 'Vienna'. . Primary dataṼ,τ ,θ from a LON described by the unitary matrix U (p) is measured. In general this data will be error afflicted denoted by the tilde. The layout and initial parameters p are either known from fabrication (dashed arrow) or are obtained by a reconstruction step, e.g. 'Brisbane'. These initial parameters are now subjected to a global optimization using an, in the best case over-complete, set of primary data. Here the output yields both, the reconstructed unitaryŨ (p ) 'Vienna' and the parameters of the individual building blocksp .
Our new approach 'Vienna' aims to reconstruct the unitary matrix descriptions U (p) of a LON via a global optimization of optical element parameters, p, which is visualized in figure 1 as a flowchart. For purpose-built networks, e.g. quantum logic gates, the physical layout of the optical elements and their target parameters are defined by the encoding scheme and type of gate. If they are sufficiently precise, these target parameters can serve as initial guesses for p and therefore as the starting parameters in the optimization routine. Black-box m × m LONs can be represented by an arrangement of n = m 2 beam splitters and n − 1 phase shifters [38] (see the Appendix for a sketch). In our approach it is sufficient to obtain just one representation of the physical network decomposed in such a way. However, without any knowledge of the starting values the minimization of the pdimensional landscapes is prone to converge into some local minimum only. Hence the starting values need to be obtained by different means. Here we utilize one of the passive reconstruction approaches and find that the approach 'Brisbane' is better suited for this purpose than the approach 'Bristol'. Note that both approaches lead to reconstructed unitaries that are equivalent to the unitary decomposed via the Reck et al. scheme modulo diagonal phase matrices. These diagonal phase matrices do not affect the extraction of the starting parameters [44]. To reconstruct U(p) a set of primary data,Ṽ,τ ,θ, is recorded, whereṼ denotes the full set of two-photon interference visibilities andτ andθ denote the full set of normalized transition amplitudes and relative phases sensed via coherent states, respectively 2 . This data will be in general error afflicted indicated by the tilde.τ ,θ are only used in the case of black-box networks to obtain the initial starting parameters for the global optimization. Finally, a global cost function using an overcomplete set of two-photon interference visibilities,Ṽ, is minimized to obtain optimal reconstructed parameters p . These automatically yield the reconstructed unitarỹ U (p ) 'Vienna' . Optimizing a global cost function comes with an additional advantage: the minimum of that function can act as an direct estimator for the success of the reconstruction and is in our case identical to the χ 2 [45], allowing further statistical interpretation. We choose to utilize just two-photon interference visibilities for the reconstruction ofŨ (p ) 'Vienna' . These visibilities are insensitive to input and output loss, thusŨ (p ) 'Vienna' represents a unitary description modulo loss matrices at the input and output. The parameters of these loss matrices can be easily recovered by using loss sensitive data such as transition amplitude data,τ , and solving a system of linear equations utilizing the reconstructed descriptioñ U (p ) 'Vienna' .
III. RESULTS
We compare the reconstruction results for the different approaches 'Brisbane', 'Bristol' and 'Vienna' numerically for fully coupled m × m networks in the presence of per-2 Throughout the numerical evaluation the transition amplitude data is normalized such that m j=1 |τ jk | 2 = 1. turbance on the primary data. To quantify the performance of the different approaches the fidelity between the initially generated Haar-random unitary matrix, H m,j , and the reconstructed unitary matrixŨ m,j,σ,µ is calculated. We consider m × m networks with m = 4, . . . , 14, where µ labels the reconstruction approach and σ denotes the level of perturbance on the primary data (see Appendix A for further details). Losses are kept zero to allow for a fair comparison between loss sensitive and insensitive approaches. For each network size, 120 Haarrandom unitary matrices are generated (labelled by j) 3 to ensure that random properties of a jth unitary, e.g. symmetry, do not lead to biased results. The unitary descriptions are calculated via a Monte Carlo method drawing the data required for each reconstruction approach, µ, randomly from the set of perturbed data, (Ṽ,τ ,θ) m,j,σ . An average unitary description,Ũ m,j,σ,µ , is obtained after 120 iterations with σ(Ũ m,j,σ,µ ) denoting its standard deviation. We use the fidelity measure, which is normalized by the number of modes, m, such that it is insensitive to the network size. Here, . denotes the trace norm. For given m, σ, µ the resulting fidelity histograms are fitted with Weibull distributions centred around the most probable value,F m,σ,µ (see Appendix A). As an error measure, σ 1 e (F m,σ,µ ), the distances between the most probable fidelity and the two fidelities where the maximum probability decreased to 1 e are used. The most probable fidelities and their respective uncertainties for 200 different combinations of network size and perturbance on the primary data are recovered for each of the reconstruction approaches. Figure 2 shows a representative example, once for 12 × 12 networks and variable error on the primary data, σ, and once for an error of σ = 2.5% and variable network size. Clear differences between the approaches can be observed with respect to the overall performance, the scaling and the dispersive behaviour. Such differences must be attributed to specifics of the reconstruction algorithms as all approaches reconstruct the same unitaries H m,j .
The approach 'Brisbane' shows high reconstruction fidelities with low dispersion which scale linearly with the error, σ, on the primary data (figure 2(a)). Here, an upper bound to the deviation of the reconstructed unitaries, U m,j,σ , from the initial one, H m,j , in the Frobenius norm can be even given analytically: Where M and κ(M ) = M −1 · M denote the reconstructed matrix before applying a polar decomposition and its condition number, respectively. Hence the deviation, = M − H , stems from the polar decomposition, which in turn is due to the errors of the primary data that contribute in first order approximation as . The data shown in figure 2(b) indicates, that the performance of the approach 'Brisbane' is only slightly affected by the network size. The reconstruction fidelities yielded with the approach 'Bristol' are dominated by a (sub)exponential decay, both as a function of the error on the primary data and the network size. This also leads to a highly dispersive behaviour which is reflected in the comparably large error bars in figure 2. While the exponential decay is already observed in the original publication [28], this just represents a phenomenological fit to the data. We conjecture that on one hand this scaling originates from the additional matrix inversion that has to be taken into account when the transition amplitudes are calculated. On the other hand, the primary data undergoes a more complex algebraic transformation, which, dependent on the noise of the primary data, can cause unfavourable amplification of perturbations. Reconstructing the unitary description of unknown m×m networks via the approach 'Vienna' or 'Vienna reduced' works with highest fidelity and minimal uncertainty. Here, 'Vienna reduced' denotes a variant of 'Vienna' utilizing a smaller set of primary data (see Appendix C for further information). This behaviour can be primarily attributed to the natural implementation of the unitary constraints in the algorithm. The statistical advantage of a full over-complete set of primary data as used in 'Vienna' over a smaller set of primary data as used in 'Vienna reduced' is noticeable, albeit being small. For both approaches we find that errors on the starting parameters are of greater impact than errors on the primary data sets of two-photon visibilities. This was tested via a separate numeric evaluation. All starting parameters are extracted using the approach 'Brisbane' and as a consequence the scaling with the error on the primary data, σ, is inherited for large σ. A better scaling is found for small σ, as more precise starting parameters increase the chance that the optimization routine will converge into the global minimum. Both, 'Vienna' and 'Vienna reduced', exhibit negligible dependence on the size of the m × m networks.
IV. DISCUSSION
Precise knowledge about the optical transformation of LONs is a requirement for the validation of experimental results against theoretical predictions in numerous experiments [20,[46][47][48]. For this purpose, the optical transformations can be given either in terms of scattering descriptions or unitary transformations, where the latter allow a decomposition into individual building blocks. Hence the element parameters for each optical element in the LON can be obtained. From a technological point of view this is beneficial as it enables the localization of erroneous elements. Here we present a new approach, 'Vienna', and compare it to two prominently used approaches, 'Brisbane' and 'Bristol'. We investigate all approaches for the regime of zero mode-dependent loss and quantify the differences in reconstruction performance of unitary descriptions via an extensive numerical evaluation: more than 10 5 m × m black-box networks are sampled for distinct m from primary data exhibiting various levels of perturbance. The results substantiate that the direct implementation of the unitary constraints, as done in the approach 'Vienna', are of advantage for highest reconstruction fidelities. Two-photon interference visibilities play a unique role as they are a priori insensitive to input and output loss and allow to obtain over-complete sets of primary data, which are beneficial for highest reconstruction precision. To quantify the performance of the different reconstruction approaches a fidelity between the initially generated Haar-random unitary matrix, H m,j , and the reconstructed unitary matrixŨ m,j,σ,µ is calculated. Here µ denotes the reconstruction approach and σ the level of perturbance on the primary data. For each network size, 120 Haar-random unitary matrices are generated (labelled by j) to ensure that random properties of a jth unitary, e.g. symmetry, do not lead to biased results. For 'Bristol' always j = 1000 matrices are sampled due to the dispersed results. Subsequently the full set of primary data, (V, τ , θ) m,j , is computed from each H m,j , where V, τ , and θ denote the sets of two-photon visibilities, transmission intensities and phases sensed via coherent states, respectively. Under experimental conditions the primary data sets would be afflicted by statistic and systematic noise. We mimic this by perturbing the primary data sets with noise drawn from a normal distribution N (0, σ 2 ) of standard deviation σ centred around zero. The perturbed primary data distributions are given as (Ṽ,τ ) m,j,σ = (1 + N (0, σ 2 )) (V, τ ) m,j and 20 different values of σ are sampled in 0.5% steps from σ = 0.5% to σ = 10%. Note that for the phase data ,θ m,j,σ = θ m,j + N (0, σ 2 ), absolute perturbances were chosen. Eventually the unitary descriptions are calculated via a Monte Carlo method drawing the data required for each reconstruction approach, µ, randomly from (Ṽ,τ ,θ) m,j,σ . An average unitary description,Ũ m,j,σ,µ , is obtained after 120 iterations with σ(Ũ m,j,σ,µ ) denoting its standard deviation. This way errors are estimated via an identical procedure, independent of whether an analytic error propagation method is available or not. Finally the fidelity (see eq. 1) for each of the ≈ 10 5 reconstructed unitaries is computed. A subset of the computed data is shown in Figure 3b), visualized as a two dimensional histogram for m = 4 and µ = 'Brisbane'. Here the data points along one row, i.e for a given perturbance σ, are composed of j = 1000 instead of j = 120 fidelities, for visualization purposes only. The absolute frequencies for a given σ can be associated with a probability distribution of a certain width, where the highest peak represents the most probable fidelity. For small perturbances σ those distributions will be in general sharp but asymmetric, whereas for larger σ dispersed and more symmetric distributions are found. To capture all but the most dispersed results we chose to fit them with a Weibull distribution centred around the most probable value,F m,σ,µ . As an error measure, σ 1 e (F m,σ,µ ), the distances between the most probable fidelity and the two fidelities where the maximum probability decreased to 1 e are used. Figure 3. a) Flowchart for the numerical method used to evaluate the different reconstruction approaches. b) Frequency histogram of fidelities obtained in the case that the reconstruction approach 'Brisbane' is applied to 4 × 4 networks. The fidelity axis is divided into 50 bins ranging from 0.95 to 1, whereas the perturbance on the primary data, σ, ranges from 0.5% to 10% in 0.5% steps. For illustration purposes the sampling size is increased from 120 to 1000 4 × 4 Haar random unitaries for each σ.
Probability distributions
For the lossless case discussed above, Weibull distributions are used to extract the most probable fidelity, F m,σ,µ , and the 1 e errors of the fidelity, σ 1 e (F m,σ,µ ). The Weibull distribution is given as with λ and k the scale and shape parameter, respectively.
APPENDIX B: THE GENERATION OF PRIMARY DATA
An m-mode linear optical scattering network can imprint new amplitude and phase information on an impinging light field (see figure 4). Whereas a large class of classical and quantum light fields can be used with the integrated optical networks considered here, their main application lies in the manipulation of coherent states or single photon Fock-states. Likewise, both states of light are suited as probe states to sense the transition-amplitudes or phases imprinted by the network. In the case that the light source used for characterization differs from the light source used in an experiment care has to be taken that the physical properties, especially the frequency and frequency bandwidth, are kept identical. When injected into a single input port k of a network, both coherent-and single-photon Fock-states allow to sense the transition amplitude τ j,k of a specific matrix entry U j,k with j denoting an output mode 4 . However, intensities measured in this way will be affected by loss, coupling and detection efficiencies. Rudimentary techniques to directly measure input loss [31] work only in the case of zero output loss. Alternatively input and output loss can be traced out during the reconstruction process [28]. While this procedure is under ideal conditions loss-insensitive, the required algebraic transformations may even amplify error stemming from the primary data. Thus loss still presents a major problem when sensing transition-amplitudes and is best dealt with by careful calibration of e.g. detector efficiencies. This way a complete and reasonably accurate set of m 2 real entries of any m × m unitary can be sensed if modedependent propagation loss plays a secondary role. To sense the phases of a linear optical network coherent states can be distributed among two input modes k and l, |α 1 k |e iϕ α 2 l [31]. It is sufficient to choose l = 1 and subsequently measure the different input combinations k = 2 . . . m. Modulating the phase ϕ of this two-mode state at a frequency ω results in output intensities in all coupled output modes that are subjected to the modulation frequency ω albeit featuring a relative phase shift γ j,k between output modes. These relative phase shifts correspond to the phases γ j,k of the unitary matrix entry U j,k with all γ j,k = 0 for j ∨ k = 1 and an arbitrary sign for γ 2,2 . Omitting the intensities and only recording this relative phase renders the measurement insensitive to mode-dependent input and output loss. Experimentally the modulation ω can be realized through a piezo actuated mirror, a delay line or similar devices. Since coupling to integrated devices is predominantly implemented with fiber arrays the phase ϕ and modulation with frequency ω will be affected by fluctuations caused by temperature or vibrations [49,50]. Care has to be taken that such noise is kept below a threshold which still allows to identify a ω-periodicity in the output signal. In general the error can be largely minimized by utilizing a modulation frequency ω that is well separated from the frequency of the noise in the laboratory. An alternative technique to sense the phase information utilizes the non-classical interference of two photons [39]. It can be shown [28,42] that the extend of this quantum effect, the visibility of the resulting interference curve, is sensitive to the phases γ j,k of the interferometric network. Only the special case of a 2 × 2 device is phase-insensitive, owed to the unitary scattering submatrix. In general phase-sensitive probe states are also transition-amplitude sensitive and are therefore sufficient to generate all primary data needed to reconstruct the unitary description of a linear optical network. Remarkably, the visibilities obtained via two-photon interferences are insensitive to input and output loss. In contrast, sensing transition-amplitudes with two-mode coherent states generates the same problems as measuring transition amplitudes directly. Experimentally, non-classical interference visibility measurements are ideally implemented using a pure, separable bi-photon state, where each photon is injected into its own interferometer mode. Subsequently the distinguishability of the two photons is scanned, e.g. by altering the relative temporal delay ∆τ between the photons. Given that coupling to waveguides and propagation in waveguides is not lossless and that detection efficiency of e.g. avalanche photo diodes is limited, measurement times exceed those of coherent probe-states. Imperfections in the probe-state generation are the major contributes to systematic errors and affect the quality of the measured visibility. Using an involved modelling contributions from spectral mismatch and spectral correlations, background noise and drift in the coupling can be taken into account. Thus the accuracy of the extracted visibilities can be increased and errors minimized to ≈ 10 −2 . Complete sampling of all accessible visibilities, N V is = m 2 2 for a m × m network has several algorithmic and statistic advantages and can be reduced to N V is red = m 2 measurement runs if a sufficient number of detectors is available. In many quantum optical experiments generating the data via the non-classical interference of two photons has the additional benefit that the apparatus required for characterization of the network is a subset of the whole experimental apparatus and the procedure works 'in-situ'. single-photon Fock-states injected into one mode of the network allow to measure the transmission and reflection intensity I1(τ1,1) and I2(τ1,2) (shown in red). Repeating the measurement via a second input port (shown in blue) allows to derive a loss-insensitive splitting parameter. Probing of non-global phases relies on interferometry which allows to extract such phases from intensity measurements. c) A coherent state is distributed among two input modes and the relative phase ϕ is e.g. linearly modulated with frequency ω. Here the phase γ1,2 of the interferometer manifests as the relative phase of the recorded intensity pattern. d) In the case of 2 × 2 scattering submatrices the Hong-Ou-Mandel Dip can be utilized to sense the phase γ1,2 via the visibility V is(γ1,2) of the two-photon interference curve, as these 2 × 2 scattering submatrices are in general non-unitary. In contrast, monolithic 2 × 2 blocks, i.e. a beam splitter, are unitary and hence the visibility is only affected by the splitting ratio.
APPENDIX C: SIZE OF THE PRIMARY DATA SET AND RESOURCE COST
Through technological progress the number of fully coupled modes supported by integrated circuits is growing and consequently, so is the size of the primary data sets required to characterize their unitary transformations. Thus a manageable size of these data sets is becoming an important criterion for evaluating different reconstruction approaches. Here, fully coupled interferometers represent the most general case. The lower bound of required data points is quantified by the number n min = 2 m 2 of spherical coordinates that parametrize such a m × m network, with the spherical coordinates corresponding to the beam splitting ratios and phase shifts of Reck et. al [38]. Note that both, 'Bristol' and 'Brisbane' aim to reconstruct the 2m 2 matrix entries directly, hence a set of n min data points is insufficient. The approaches 'Bristol' and 'Brisbane' utilize sufficient data sets that are close to this lower bound and consist of m 2 transition amplitudes and (m − 1) 2 data points to recover the non-trivial phases. In the case of 'Bristol' additional (m − 1) 2 − 1 two-photon visibilities are required to determine the sign of the phases. We chose the upper bound of primary data to be the over-complete set of all two-photon interference visibilities, n full = m 2 2 . This set of data can be efficiently recorded given todays bright single photon sources [51] but can be in principle expanded to even higher order correlation functions. Likewise the m 2 transition amplitudes represent a non-redundant set of data to expand n f ull . Since the transition amplitudes are loss afflicted they are not used in the global optimization routine of 'Vienna'. Only in the case that 'Vienna' is applied to black-box networks the m 2 transition amplitudes and (m−1) 2 relative phases are needed to extract the starting parameters for the global optimization. Furthermore this global optimization allows for an adaptive strategy; best reconstruction accuracy is achieved using the full over-complete set of data. Alternatively, a reduced set of data, the set of all possible two-photon interference visibilities that can be generated when one photon is always inserted into input port one and the second photon into input port 2, . . . , m, can be used. This results in a reduced set of n V iennamin = (m − 1) m 2 visibilities which always suffices to reconstruct m × m networks with m ≥ 3 modes. In the following we will refer to the reconstruction approach 'Vienna' utilizing a reduced set of primary data as 'Vienna reduced'. A second number, the required measurement runs to generate the primary data set, can be regarded as the experimentally more relevant parameter. We list this parameter for the reconstruction approaches compared here in the limit that every output mode is coupled to an individual detector in table I. Now, all output events for a given input combination can be recorded in parallel, thus the number of required measurements corresponds to the required input combinations that need to be consecutively aligned in a laboratory. For instance, the m 2 transition amplitude data can be acquired in m measurement runs and the m Table I. Size of the primary data set and minimal number of measurements for different reconstruction approaches. The three compared unitary reconstruction approaches differ significantly in the minimal and maximal set of primary data available for the reconstruction algorithms. For 'Brisbane' the minimal and maximal set of data are identical. Whereas a larger primary data set is more costly to generate experimentally this expense is justified if the data can be used to increase the accuracy of the reconstructed description. The required number of measurement runs is given in the limit that each output mode is covered by its own detector and can be regarded as the experimentally more relevant quantity. Here 'Vienna' is referring to a reconstruction of a structure with known layout and starting values, while 'Vienna black-box ' refers to a black-box network. The minimal primary data set required for the approach 'Bristol' presents a special case. Here the amount of data is constituted by the m 2 transition amplitudes and the (m − 1) 2 and (m − 1) 2 − 1 two-photon visibilities to recover the absolute values and signs of the phases, respectively. In the case of sufficient detectors the transition amplitudes can be sensed in m measurement runs and the two-photon visibilities to recover the absolute value of the phases in m − 1 measurement runs.
To fix the sign of the phases additional m − 2 measurement runs are necessary.
APPENDIX D: THE INFLUENCE OF LOSS
Loss can be a major factor in experiments using integrated optical circuits. In the case of direct laser-written networks propagation loss of −0.3 dB cm and coupling loss of −2dB are typical values [22,52]. If these losses are mode-independent, however, they just represent a global loss term that commutes with the optical transformation of a LON. In contrast, mode-dependent losses cause deviations in a targeted optical transformation. Characterizing mode-dependent losses thus becomes important when reconstructing the optical transformation of a LON. Here, we distinguish between the case of mode-dependent loss at the input and output ports and the case of mode-dependent propagation loss. In the first case, loss can always be separated from the transformation of a LON and be described by loss matrices containing virtual beam splitters. For a m × m LON this translates to m additional parameters modelling input loss and m additional parameters modelling output loss, the α i and α o of figure 5, respectively. The unitary matrix of the LON expanded by the 2m loss modes now reads as with L denoting the 3m × 3m loss matrices. Still, only the original m input and output modes are experimentally accessible. Note that the data set for relative phases sensed via coherent states, θ, and the the data set composed of two-photon interference visibilities, V, are insensitive to these losses and hence directly reveal information about U m×m . Whereas θ just contains information on the non-trivial phases of the interferometer but not on the transition amplitudes, the set of two-photon interference visibilities contains information on both. This is a unique feature of the latter data set and owed to the quantum nature of the interference. In comparison, a direct measurement of the transition amplitudes τ is always afflicted by mode-dependent input and output loss. As a consequence, the latter set of data only reveals information on a m × m submatrix of U 3m×3m . In our notation this submatrix corresponds to the upper left m × m submatrix of U 3m×3m , that is spanned by the m accessible input and output ports. In general, the size of the transition amplitude data set τ is insufficient to reconstruct all the 2m loss terms in addition to the m 2 real entries directly. Therefore, the strategy used in 'Brisbane' only works if m loss parameters, either all α i or all α o , can be neglected (see also body text). Alternatively, the transition amplitude data can be subjected to a reconstruction algorithm in which the loss terms drop out, as done in 'Bristol', however this necessitates unitary constraints. Although the strategy of 'Bristol' seems to be of advantage, figure 2 gives a indication that the algorithm reacts fragile to measurement error on the primary data. In comparison 'Brisbane' achieves higher reconstruction fidelities. This may change in the presence of mode-dependent input and output loss. It is an open question where the threshold of measurement error on the sensed data opposed to the level of of input and output loss lies, that would favour one over the other algorithm. Due to the processing of just two-photon interference visibilities, 'Vienna' is insensitive to input and output losses. Hence, U m×m is directly reconstructed and the α i and α o can be obtained in a separate step by solving a system of linear equations using loss afflicted data, e.g. the set of transition amplitudes τ . In the case of black-box networks, however, some dependence is carried over if initial starting parameters, p, are obtained via, e.g. 'Brisbane'. In contrast to input and output loss, mode-dependent propagation loss cannot be separated from the unitary description of a LON, as it does not commute with the optical elements that constitute the network's fundamental transformation. Instead, the unitary description needs to be expanded by additional in-circuit loss modes, subsequently labelled l. This is illustrated in figure 5b) with m the number of accessible network-modes, r = 3m + l the total number of modes and L denoting the r × r input and output loss matrices. All data sets sensed for reconstruction purposes, τ , θ , V reveal information about an in general non-unitary submatrix of U r×r . In our notation, this submatrix corresponds to the upper left m × m submatrix of U r×r . Now, the above mentioned strategies to model loss fail. The loss terms cannot be assessed directly and error is introduced by applying unitary constrains to the non-unitary m × m submatrix. We numerically evaluate the exemplary case of m = 4 LONs to investigate how severe the reconstruction performance of the various approaches is offset by mode-dependent in-circuit loss. The general layout of these networks is shown in figure 5b). Here, the input and output losses are kept zero to ensure that they do not influence the results. Thus the networks are just expanded by l = 8 in-circuit loss modes. The approaches 'Brisbane' and 'Bristol' are constructed to obtain 4 × 4 descriptions which prevents the use of the fidelity measure defined in equation 1. Hence we use an alternative measure which is experimentally motivated and constructed as the mean deviation between a point of primary data and its prediction obtained via one of the reconstructed descriptions. Q t quantifies the mean deviation for the normalized transition-amplitude data and Q vis the mean deviation for the two-photon interference visibilities (see definition below). In the limit of Q t = Q vis = 0, perfect reconstruction is achieved, a result only expected if in-circuit loss is either zero or if it can be fully recovered by an approach. One option to achieve the latter is a reconstruction of the complete (4 + 8) × (4 + 8) unitary description, which we investigate for the approach 'Vienna'. The required starting parameters for the λ i and φ i used to initialize to optimization routine are extracted via the approach 'Brisbane'. All β i are initialized at zero. The data presented in figure 6 is sampled for different levels of loss by drawing the transmittances of the loss beam splitters, β 1 , . . . , β 8 , randomly from a uniform distribution [cos( ), 1]. In the worst case of = 0.1, the maximum loss per beam splitter thus is sin 2 (0.1) ≈ 1%. To sample the unitary space representative, j = 500 different 12 × 12 starting matrices are generated for each loss-interval. The general perturbance on the primary data was set to σ = 1%. All reconstructed descriptions are computed in the same way as in section III via a Monte Carlo method with a sampling size of i = 100 (see also Appendix A). The resulting frequency histograms for Q t , Q vis and the fidelity histograms in the case of 'Vienna' were fitted with Burr type XII distributions [53], as these show good overlap with the numerical data. The data points and error bars contained within figure 6 are given as the most probable value of the distributions and the distance between the most probable value and those values to the left and right where the maximum probability decreases to 1 e , respectively. Already for the small levels of mode-dependent propagation loss considered here, all three approaches struggle to reconstruct precise unitary descriptions. This result is to be expected in the case of 'Brisbane' and 'Bristol' as the sets of data used for the reconstruction procedures originate from a non-unitary submatrix. Hence only closest unitary descriptions are reconstructed, which in turn cannot fully explain the original data sets. The results obtained in the case of 'Vienna' need to be interpreted in a different way. Whereas the global optimization of just two-photon interference visibilities converges, as can be seen by the values for Q vis in figure 6b), the values obtained for Q t show a scaling similar to the other two approaches. This indicates that the original optical element parameters for the beam splitters, phase shifters and loss beam splitters cannot be recovered with high accuracy. As a result the fidelities of the reconstructed 12 × 12 unitary matrices decrease rapidly with growing . It is an open question whether a larger set of primary data including relative phase shiftsθ would yield improved reconstruction results. In light of the above results mode-dependent propagation loss still presents a fundamental problem when reconstructing unitary descriptions of LONs.
Quality measure for the case of mode-dependent propagation loss The quality measure Q vis introduced in above is constructed as the difference between the full set of sensed two-photon interference visibilities and the set of predicted visibilities, obtained via a reconstructed unitary matrix. It is normalized by the maximum amount of two-photon interference visibilities, m 2 2 , that can be obtained.
Similarly, the measure Q t quantifies the difference between the set of measured transition-amplitudes and the predicted ones via a reconstructed unitary matrix. It is normalized by the maximum amount of transition-amplitude data, m 2 , that can be obtained. Figure 6. The influence of mode-dependent propagation loss on the reconstruction performance for 4 × 4 LONs and the different approaches 'Brisbane', 'Bristol', and 'Vienna'. The data for 'Brisbane' and 'Bristol' is offset from the data in the case of 'Vienna' for visualization purposes only. Here the general perturbance on the primary data, σ, was chosen to be 1% and input and output loss to be zero. The transmittances, β1, . . . , β8, of the eight beam splitters modelling the mode-dependent loss were drawn uniformly from the interval [cos( ), 1]. Several intervals were sampled in discrete steps ranging from zero loss to sin 2 ( ) = 1% loss and 500 random matrices were reconstructed for each interval. The histograms were fitted with Burr type XII distributions and the error bars are given as the distance between the most probable value and those values to the left and right where the maximum probability decreases to 1 e . a) Qt quantifies the mean deviation of the normalized transition amplitudes between the initial values and the ones obtained from the reconstructed descriptions. b) Analogously Qvis quantifies the mean deviation of the two-photon interference visibilities. Only data from the experimentally accessible 4 × 4 submatrices is considered. c) Reconstruction fidelities for the U (4+8)×(4+8) unitary matrices reconstructed via 'Vienna'.
In the case of Q t , we normalize the transition-amplitude data for each of the m measured inputs over all outputs to m unit vectors, to allow for comparison between the loss sensitive and insensitive approaches. This normalized transition amplitude data is labelled τ * and defined as | 10,693.2 | 2015-12-15T00:00:00.000 | [
"Physics"
] |
A Frequency Model of Vibrational Processes in Gas-Turbine Drives of Compressor Stations of Main Gas Pipelines
At compressor stations, systematic measurements of noise and vibration of power equipment - gas compressor units - are carried out. The article presents basic equations for calculating natural and forced frequencies at which the main defects appear. According to the studied dependences, results of calculations are obtained on the following types of drives for gas-compressor units GTK-10-4, Avon-1534, DG-90.
Introduction
If vibration levels exceed the allowable, breakage of parts and components may occur, leading to failures of power equipment. The presence of excessive vibration and noise indicates the presence of various defects, which are one of the reasons for the accelerated wear and fatigue failure of parts. Measuring vibration and noise during operation can detect many defects at their early stages, prevent possible failures of equipment, as well as put it into operation and repair according to its actual state, instead of conducting planned preventive maintenance.
Methods of vibroacoustic diagnostics provide ample opportunities. They are based on the use of information contained in the oscillatory processes that accompany operation of machines and mechanisms. Vibroacoustic diagnostics is one of technical diagnostics sections. As a source of information, it uses not a series of static parameters characterizing the state of a mechanism, but a number of dynamic parameters causing the occurrence of vibration and acoustic waves. Vibration signal providing capacious enough information on the work of the unit and its components can be a good indicator of its status.
Research
Vibration and noise of the axial compressor (AC) of gas compressor units (GCU). The vortex noise of the compressor and the high-pressure turbine (HPT) arises from vortices occasionally shedding from the blades, the turbulent flow, and the turbulent jet. The spectrum of the vortex noise caused by periodic vortex shedding is determined from the equation [1,2,3] , d where Re=Vd/-the Reynolds number; d -the determining linear dimension; V -the linear flow velocity, -the viscosity of the medium.
The level of wideband noise can be determined according to the equation: where -the sound pressure level, В -the flow of steam through the HPT or air through the AC, Т -the temperature differential in the HPT or AC, z-the number of blades, k -the coefficient determined from the experimental data on the measured noise level and the geometric characteristics of the AC or HPT.
The level of noise of the discrete components [1,2,3]: where D Р -the impeller diameter, d В -the hub-tip ratio, -the efficiency of the first stage, kthe coefficient determined experimentally.
For multistage compressors, the acoustic power is determined by summing the power of each stage. During operation, the AC rotates in a pulsating flow, whereby each blade transfers momentum to the working fluid that is a multiple of the number of blades. When summing these impulses and subsequently transmitting to the body a vibration is excited with frequencies that are multiples of the number of blades [1,2,3]: where i -the harmonic number, i=1,2…n, f Р -the rotor rotational frequency. The amplitude of the blading vibration depends on the steam or air density (the ratio of expansion or compression pressures) and some other factors; the smaller the density, the smaller the aerodynamic imbalance of the working fluid flow. The vibration frequency during a developed shedding is determined by the equation [1,2]: Vibration of the rotor. The vibration state of the AC rotor can best be determined by the speed characteristics when accelerating or running down the rotor.
The oscillatory system rotor-body may be in a certain critical condition in the presence of a number of critical rotational frequencies of the rotor. These frequencies can be higher, lower or within the range of the operating frequency, which is highly undesirable. Reducing the vibration amplitude in this case is achieved by using different damping devices or by balancing.
The critical rotational frequencies of the rotor are calculated by the equation [4]: where К -the coefficient obtained as a result of calculating the system of equations of small oscillations of the rotor, Е -the modulus of elasticity, I -the reduced moment of inertia, L -the rotor length. For the axial compressor blades, the range of static natural frequencies of the first three bending forms of vibrations in the plane of its least stiffness is determined by the equation of I.M. Meerovich: where ibend , ibend , i , i , i -for each waveform there is a wedge, curvature and radial function, a к , к -the maximum curvature and thickness of the blade profile at the root section, 0 -the feather twist (the angle between the chords of the root and peripheral sections), l -the length of the blade feather.
The spectrum of the natural frequencies of torsional oscillations of the axial compressor rotor blades is determined by the equation [1,2]: where icr , icr -the coefficients determined by [1,2], b ср -the width of the blade chord in the middle part, G -the shear modulus.
The rotor unbalance, bending by the first form, the thermal instability of the rotor occur at a frequency [1, 2, 3]: The uneven stiffness of the rotor cross-section, the resonant oscillations of the rotor blades due to loose connections, the misalignment of couplings, the rotor bending by the second form occur at a frequency [1,2]: Rotor elements touching the stator, separation of supports from the foundation [1,2]: Vibration and noise of the bearings. This noise is an indication of a malfunction, since it is not possible to determine it if the bearings are serviceable. The main defects of the bearings are the waviness on the bearing races, the increase in the radial clearance, oval balls and rings, the unroundness of rolling elements, increasing clearances in the sockets of separators, which we denote by (b). Then the forced frequency of faults is determined by the general equation: The value (b) is determined by the geometric dimensions of bearings. Specific equations are given in [1,2,3].
The frequency content of the vibration spectrum of the defective bearing depends on the type of defect. Working with defective bearings we connect the five main bearing frequencies: 1 -F rthe rotor rotational frequency; 2 -F sep -the separator rotational frequency; 3 -F o.r -the ball (roller) frequency of passing the outer ring; 4 -F i.r -the ball (roller) frequency of passing the inner ring; 5 -F r.b -the frequency of natural rotation of the ball, roller. The frequency of natural ball rotation is excited when the defect on the ball or roller meets the race track. The frequency may equal 2FТК, since its defect meets both rings. Excited frequencies seldom reach such high values as: 1. the ball is not always in the loading zone when the defect meeting the rings, and 2. the energy is lost when the signal passes through additional structural joints, when the defect meets the inner ring. The frequency of natural rotation is also excited when the balls are pressed against the separator or the separator is broken. The separator rotational frequency is equal to the rotational speed of a set of balls or rollers and the separator around the axis of the shaft.
Noise of the reduction box gear wheels. This noise occurs when the gears collide in the shortterm contact during operation. The short-term contact leads to the appearance of stress that is cyclical in nature and in turn causes stress wave propagation along the gear wheel and the emergence of noise. The level of noise of gear wheels depends on their residual imbalances, compression of air and oil, torsional oscillations of shafts, irregular shock loads, and uneven teeth surface.
The frequency of contact meshing noise is determined by the equation [1,2] f z = i z f p where z -the number of teeth. The natural oscillation frequency is determined by the formula [1,2]: where -the factor considering the system flexibility; c -the teeth stiffness, m -the reduced gear wheel mass.
Vibration and noise of the combustion chamber. Due to the fact that the combustion chamber is located behind the air intake in the GTU and AC, its noise is the resultant noise caused not only by the combustion process, but also by the previous process. The combustion chamber noise, as well as the AC, is continuous in nature and has a wideband range. The most dangerous is the vibrating combustion that occurs as a result of strong vortices in the flow of gas mixture.
A stable combustion mode gives the maximum value of amplitudes in the low frequency zone of 40 60 s -1 , and during the vibrating one the amplitude shifts to the zone of 200 300 s -1 and above. Flame tubes of the combustion chamber of the investigated GCU are a cylindrical shell simply supported at the ends, so the approximate value of frequencies of natural oscillations is described by the equation [1,2] where -a dimensionless frequency of the normal mode of vibration supported at the ends of the cylindrical shell; R -the radius of shell curvature; E, the modulus of elasticity, the Poisson's ratio and the density of the shell material.
Vibration and noise of the GCU turbine rotor. The first form of static natural bending vibrations for turbine blades is determined by the equation of A.E. Shneydman where х -a function depending on the area and moments of inertia of the cross sections of the blades.
The relationship between the static and dynamic (f d ) natural oscillation frequency of the blades [1, 2]: where -the dynamic frequency coefficient determined from the literature data [1,2]. Table 1 shows the results of the calculation of natural and forced oscillation frequencies of main units of the gas generator Avon-1534 at f p =125 Hz.
In addition to the abovementioned fundamental frequencies excited on the body of a product by rotors, blades, bearings, a gearbox and drive units, the occurrence of combination frequencies is possible, the general formula of which is given by: where n i and n j -fundamental frequencies, K i and K j -integer-valued coefficients. A combination frequency corresponds to a certain physical model of excitation, different for each individual case. Table 1. An example of calculation of the frequency components of vibration processes in the main units of the gas generator Avon-1534. | 2,419.2 | 2016-10-01T00:00:00.000 | [
"Materials Science",
"Physics",
"Engineering"
] |
Osmosensitivity of Transient Receptor Potential Vanilloid 1 Is Synergistically Enhanced by Distinct Activating Stimuli Such as Temperature and Protons
In animals, body-fluid osmolality is continuously monitored to keep it within a narrow range around a set point (∼300 mOsm/kg). Transient receptor potential vanilloid 1 (TRPV1), a cation channel, has been implicated in body-fluid homeostasis in vivo based on studies with the TRPV1-knockout mouse. However, the response of TRPV1 to hypertonic stimuli has not been demonstrated with heterologous expression systems so far, despite intense efforts by several groups. Thus, the molecular entity of the hypertonic sensor in vivo still remains controversial. Here we found that the full-length form of TRPV1 is sensitive to an osmotic increase exclusively at around body temperature using HEK293 cells stably expressing rat TRPV1. At an ambient temperature of 24°C, a slight increase in the intracellular calcium concentration ([Ca2+]i) was rarely observed in response to hypertonic stimuli. However, the magnitude of the osmosensitive response markedly increased with temperature, peaking at around 36°C. Importantly, the response at 36°C showed a robust increase over a hypertonic range, but a small decrease over a hypotonic range. A TRPV1 antagonist, capsazepine, and a nonspecific TRP channel inhibitor, ruthenium red, completely blocked the increase in [Ca2+]i. These results endorse the view that the full-length form of TRPV1 is able to function as a sensor of hypertonic stimuli in vivo. Furthermore, we found that protons and capsaicin likewise synergistically potentiated the response of TRPV1 to hypertonic stimuli. Of note, HgCl2, which blocks aquaporins and inhibits cell-volume changes, significantly reduced the osmosensitive response. Our findings thus indicate that TRPV1 integrates multiple different types of activating stimuli, and that TRPV1 is sensitive to hypertonic stimuli under physiologically relevant conditions.
Introduction
Mammals have a set of homeostatic mechanisms that work together to maintain body-fluid osmolality at near 300 mOsm/kg through the intake or excretion of water and salt [1,2]. This homeostatic osmoregulation is vital, because changes in cell volume caused by severe hypertonicity or hypotonicity can lead to the irreversible damage of organs and cause lethal neurological trauma [3][4][5]. However, the mechanisms for the detection of these fluctuations have not been fully elucidated.
TRPV1 was suggested to be involved in the detection of hypertonicity based on physiological studies with TRPV1knockout (TRPV1-KO) mice [6]. The mice showed pronounced serum hypertonicity under basal conditions and highly compromised vasopressin (VP) production in response to osmotic stimulation in vivo [7]. They also showed a significantly attenuated water intake in response to systemic hypertonicity compared with wild-type (WT) controls [8]. However, another group recently claimed that TRPV1-KO mice displayed normal thirst responses and central Fos activation during hypernatremia [9]. According to the former group, cells in the supraoptic nucleus (SON) or organum vasculosum of the lamina terminalis (OVLT) of TRPV1-KO mice lacked sensitivity to hypertonicity [7,8]. In this study, a putative N-terminal variant of the TRPV1 channel was postulated as a sensor for hypertonic stress in vivo [7]. On the other hand, the osmosensitivity of the full-length form of TRPV1 has not been demonstrated to date by using cell-based expression systems.
As its counterpart, TRPV4 has been reported to be the sensor for the detection of systemic hypotonicity [10][11][12]. A similar discrepancy in results exists for TRPV4-KO mice. One group reported an impairment in the stimulation of Fos expression in OVLT neurons, as well as in thirst and VP production, in response to hypertonicity [13]. However, another group detected no difference in water intake, but excessive production of VP in response to hypertonicity [14]. The response of the TRPV4 channel to hypotonic stimuli is sensitive to temperature [10]: Interestingly, the peak sensitivity of the gating of chick and rat TRPV4 was recorded at the core body temperature of the respective animals. TRPV1 was originally cloned as an endogenous sensor responding to noxious heat (.43uC), in addition to capsaicin and protons [15]. In the present study, we attempted to figure out why the osmosensitivity of the full-length TRPV1 has not been (upper right) perfusion with a hypertonic solution (350 mOsm) at 36uC. The temperature was maintained throughout the respective recording. Representative single cell traces of the fluorescence ratio at a temperature of 24, 30, 36, or 40uC (lower graph). The line on the top indicates the timing of the change from 300 mOsm (gray) to 350 mOsm (black). The response of HEK293-TRPV1 cells to hypertonic stimuli increased noticeably with the experimental temperature up to 36uC. Bar, 40 mm. (D) Summary of the change in the fluorescence ratio during the perfusion with the hypertonic solution at various temperatures in HEK293-TRPV1 (filled bars) and HEK293 (open bars) cells. Data are differences between fluorescence ratios 2 min before and 4 min after the change of the solution. The maximal sensitivity of the HEK293-TRPV1 cells to the hypertonic stimulation was observed at 36uC. Values are the mean 6 SEM. HEK293-TRPV1: n = 147 (24uC), n = 121 (30uC), n = 249 (36uC), n = 106 (40uC). HEK293: n = 110 (24uC), n = 132 (30uC), n = 109 (36uC), n = 101 (40uC). doi:10.1371/journal.pone.0022246.g001 detected so far, by using a heterologous expression system. Here, we demonstrate for the first time that TRPV1 shows clear sensitivity to hypertonic stimuli when ambient temperature is around the mammalian body temperature. Moreover, the osmosensitivity of TRPV1 is potentiated also by other stimuli such as protons and capsaicin.
TRPV1-Expressing Cells Show a Temperature-Dependent Response to Hypertonic Stimulation
First of all, the expression of the full-length form of the TRPV1 channel in the human embryonic kidney (HEK) 293 cells stably expressing rat TRPV1 (HEK293-TRPV1; see Materials and Methods) was verified by RT-PCR using primer sets for rat TRPV1 mRNA (Fig. S1, HEK293-TRPV1), immunostaining with anti-TRPV1 antibody (Fig. 1A, HEK293-TRPV1), and calcium imaging with a TRPV1 agonist, capsaicin (1 mM; Fig. 1B, HEK293-TRPV1). Native HEK293 cells were deficient in the endogenous expression of TRPV1, and used for control experiments ( Fig. 1A and B; HEK293; see also [15]). Changes in the intracellular calcium concentration, [Ca 2+ ] i , was examined by ratiometric calcium imaging with Fura-2.
To test our idea that the osmosensitivity of the TRPV1 channel is triggered by an increase in ambient temperature, a hypertonic solution (350 mOsm) was applied to HEK293-TRPV1 cells at various temperatures (24,30,36, and 40uC) ( Fig. 1C and D, HEK293-TRPV1). When the extracellular environment was changed from an isotonic (300 mOsm) to hypertonic (350 mOsm) solution at 24uC, [Ca 2+ ] i increased only slightly in HEK293-TRPV1 cells, but did not change in HEK293 cells ( Fig. 1C and D, 24uC). Surprisingly, the sensitivity of HEK293-TRPV1 cells to the osmotic stimulation increased markedly with a rise in temperature ( Fig. 1C and D, 30, 36, and 40uC): The baseline showed a considerable difference between 30uC and 36uC, partly because of the temperature dependence of fura-2 fluorescence [16]. The sensitivity of the rat TRPV1 was maximal at 36uC, which is close to the normal mammalian body temperature (,37uC): The [Ca 2+ ] i increase (DF 340 /F 380 ) induced by 350 mOsm was approximately a half of that induced with 1.5 nM capsaicin (see below). In contrast, control HEK293 cells did not respond to the hypertonic stimulus at any temperature. This indicates that TRPV1 is responsible for the osmosensitivity.
TRPV1-Expressing Cells Show Relatively Small Sensitivity to Hypotonicity
Next, we examined the responsiveness of HEK293-TRPV1 cells to a hypotonic stimulus at various temperatures. When the extracellular environment was changed from an isotonic (300 mOsm) to hypotonic (250 mOsm) solution at 24, 30, 36, and 40uC, [Ca 2+ ] i showed a slight decrease (Fig. 2). The amplitude of [Ca 2+ ] i decrease is small but significant. When osmolality was returned to 300 mOsm, [Ca 2+ ] i gradually recovered to the basal level (see, 8 min to 12 min in Fig. 2A). This suggests that some influx of Ca 2+ occurs at a physiologically normal osmolality (,300 mOsm) at 30-40uC and this entry is suppressed under hypotonic conditions. Of note, maximal sensitivity to the hypotonic stimulus was again observed at 36uC (Fig. 2B).
Osmosensitive Responses Are Antagonized by TRPV1 Blockers
Subsequently, we pharmacologically verified that the responses to osmotic stimuli observed in the HEK293-TRPV1 cells were mediated by TRPV1 channels. Application of capsazepine (10 mM), a specific inhibitor of TRPV1, and ruthenium red (10 mM), a nonspecific inhibitor of TRP channels, reduced the response to the basal level (Fig. 3A, CPZ and RuR), indicating that the osmosensitive responses of HEK293-TRPV1 cells were mediated by TRPV1. When hypertonic stimuli were applied with the Ca 2+ -free hypertonic solution, [Ca 2+ ] i did not change (Fig. 3A, Ca-free). Together, these results clearly indicate that the increase
Inhibition of Aquaporins Reduces the Osmotic Response of TRPV1
As cell membranes are highly permeable to water compared with ions, an increase or decrease in extracellular osmolality leads to the shrinkage or swelling of cells. Here, water channels, aquaporins (AQPs), are considered to contribute to the cellular shrinkage and swelling [17]. To test the possibility that the sensing of hypertonicity by TRPV1 is dependent on cell shrinkage through AQP activity, we examined the effect of HgCl 2 , which blocks AQPs and prevents a change in cell volume [18,19]. Upon exposure to hypertonic solutions in the presence of 1 mM HgCl 2 at 36uC, the response was significantly reduced (Fig. 3A, HgCl 2 ). We also specified the expression of the AQP family in HEK293-TRPV1 cells by RT-PCR using primers for AQP members which are known to be expressed in the kidney (AQP1, 2, 3, 4, 6, 7, and 11; see [20]), because HEK293 cells are derived from human kidney. Among them, AQP1 and AQP3 were detected as main AQPs expressed in HEK293-TRPV1 cells (Fig. 3B).
The Response Increases with a Rise in Osmolality
Because HEK293-TRPV1 cells showed a maximal response at 36uC, we further investigated the response to the transfer from the physiological level (300 mOsm) to various osmotic levels at 36uC (Fig. 4A). The response of [Ca 2+ ] i upon the shift in extracellular osmolality is shown in Fig. 4B. The increase in [Ca 2+ ] i is clearly pronounced in a considerably hypertonic range (.330 mOsm).
Hypertonic Response of TRPV1 Is Enhanced by Protons
Because protons are known to potentiate the response of TRPV1 to capsaicin [21] and heat [15,21], we next examined the effect of acidification on the hypertonic response at 36uC (Fig. 5). As previously reported, a reduction in the extracellular pH itself induced an increase of [Ca 2+ ] i at 36uC from pH 6.6 in HEK293-TRPV1 cells, but not in control HEK293 cells ( Fig. 5A and C). The [Ca 2+ ] i increase induced by pH 6.3 was far more large (DF 340 / F 360 was ,15.0; data not shown).
When a hypertonic solution (350 mOsm) at different pH levels (pH 7.8 to pH 6.6) was applied to HEK293-TRPV1 cells, [Ca 2+ ] i showed proportional increases according to the acidity ( Fig. 5B and C). Studies with antagonists again indicated that the response was mediated by TRPV1 channels (Fig. 5D).
These results indicate synergism between the osmo-sensitive and proton-sensitive responses. The small decrease in [Ca 2+ ] i by the hypotonic stimuli was changed to a small increase in [Ca 2+ ] i by the acidic pH shift (Fig. S2). This suggests that opening of TRPV1 by protons overcomes the closing of TRPV1 by hypotonicity under these conditions.
Hypertonic Response of TRPV1 Is Enhanced by Capsaicin
Finally, we examined the relationship between hypertonicity and capsaicin as activating stimuli for TRPV1 at 36uC. We found that the response to capsaicin was potentiated as the osmolality increased, and vice versa (Fig. 7A). The osmotic response was markedly enhanced by costimulation with capsaicin ( Fig. 7B; compare osmotic stimuli capsaicin with osmotic stimuli in HEK293-TRPV1). Studies with antagonists demonstrated that the response was mediated by TRPV1 channels (Fig. 7C).
Discussion
The present study demonstrates that the full-length form of the TRPV1 channel responds to hypertonic stimuli in a temperaturedependent manner. Rat TRPV1 showed peak sensitivity at around the body temperature (36uC) of mammals. In this study, we also demonstrated that the osmosensitivity of TRPV1 at 36uC is further enhanced by another activating stimulus, such as protons (pH) or capsaicin. Inhibition of the water channels significantly decreased the hypertonic response of TRPV1. This suggests that a reduction in cell volume or the tension of the plasma membrane is important for the osmosensitive gating mechanism of TRPV1, as in TRPV4 [22].
Sensitivity of TRPV1 to Hypertonic Stimuli
To our knowledge, only one protein, stretch-inhibitable cation channel (SIC), has been shown to have hypertonicity-sensitive properties in a heterologous expression system [23]. However, it was later found that SIC was an artificial chimeric channel composed of partial fragments of TRPV1 and TRPV4: the core is derived from an N-and C-terminal-deleted TRPV1 containing all of the membranespanning regions, and the C-terminal domain is derived from TRPV4 [24]. However, the response of TRPV1 itself to hypertonic stimuli has not been demonstrated with heterologous expression systems so far, despite the intense efforts of several groups. Our finding that the osmosensitive response of TRPV1 is very small at room temperature (24uC) may explain why it has not been identified previously, because researchers used to employ room temperature for the experiments. Further study will be required to confirm whether the peak sensitivity of TRPV1 to hypertonic stimuli occurs at the particular body temperature of the individual animal species.
Liu et al. recently demonstrated that osmolality potentiates the response to capsaicin of trigeminal sensory neurons [25]. Moreover, the responsiveness of TRPV1 to protons and chemical agonists including capsaicin was markedly enhanced above room temperature in a heterologous expression system like ours [21,26]. These results are in line with our findings that osmosensitive activity of TRPV1 is enhanced by not only temperature but also protons and capsaicin. Here it should be noted that the [Ca 2+ ] i increase induced by hyperosmolality (350 mOsm) at 36uC (see Fig. 1D) is comparable to that induced by capsaicin (1.5 nM) at 36uC (see Fig. 7B; 300 mOsm). All these findings should be further confirmed by using endogenous cells expressing TRPV1.
Physiological Role of the Osmosensitivity of TRPV1
Channels mediating osmosensory transduction in the magnocellular neurons in the SON are reportedly permeable to calcium and can be blocked by the extracellular application of gadolinium (a non-selective cation channel inhibitor) or ruthenium red [8,27,28]. The response of osmosensitive neurons in the OVLT and SON to hypertonic stimulation was abolished in brain slices obtained from TRPV1-KO mice [7,8]. These findings suggested that a TRPV1 gene product plays an important role in osmosensory transduction. Our present study clearly demonstrates that the full-length form of TRPV1 is sensitive to extracellular hypertonic stimuli at around the normal core body temperature of mammals. Although it is not yet clear whether the sensitivity is sufficient to detect the osmotic change within the physiological range in vivo, our findings would be an important contribution to understanding the mechanism for the osmotic homeostasis of body fluids. The discrepancies above noted among experimental results with TRPV1 or TRPV4 gene-KO animals might be attributable to differences in the protocols used for osmotic stimulation. Further research employing more solid experimental techniques might be required to clarify the physiological role of TRPV1 and TRPV4 in body-fluid regulation.
Pathological Meaning of Integration of Multiple Stimuli in TRPV1
Our finding that TRPV1 is synergistically regulated by distinct stimuli for activation may contribute to our pathological understanding of several diseases. Because acidification potentiated the response of TRPV1 to hypertonic stimuli, it is presumable that control of body-fluid osmolality is affected by acidosis. Diabetic acidosis is an acute metabolic complication of diabetes, and dry mouth and excessive drinking are major symptoms of diabetes [29]. Because TRPV1 underlies thirst responses in mammals, the drinking response induced by a hypertonic state is considered to be enhanced by acidosis in diabetic patients, as a result of the integration of hypertonic and acidic stimuli in TRPV1.
Another physiological situation involving the integration of distinct stimuli in TRPV1 may occur in pain sensation. It has been postulated that TRPV1 senses a reduction of pH in tissues caused by infection, inflammation, or ischemia, which produces pain in mammals [15,21]. Presumably, osmolality is also increased in damaged tissues [30,31]. It is known that the injection of a hypertonic solution into skin or muscle causes pain [32]. TRPV1 is thus considered an integrator of the physicochemical noxious signals derived from inflammatory injuries. Taken altogether, our findings provide a novel view of TRPV1 that this sensor integrates multiple combinations of distinct physiological stimuli.
TRPV1-Expressing Cells
To explore the properties of the full-length form of TRPV1, HEK293-TRPV1 cells were used [33]. The cells were plated on glass cover slips (CS-12R, Warner) and cultured in Dulbecco's Modified Eagle Medium (DMEM, Nissui Pharmaceutical) containing 10% fetal calf serum (FCS, Invitrogen) under 5% CO 2 at 37uC for at least 24 h before imaging. For the detection of TRPV1 expression, cells were fixed with 2% (v/v) neutralized formalin (Wako) for 15 min and washed three times with PBS containing 0.5% Triton X-100 (Nacalai Tesque). They were then incubated with anti-TRPV1 antibody (1:1200; RA14113, Neuromics) in PBS containing 10% normal goat serum (Cosmo Bio) for 1.5 h, and subsequently with the secondary antibody, Alexa488-conjugated anti-rabbit IgG antibody (1:1200, Invitrogen), for 40 min. Reverse Transcription (RT)-PCR Total RNA was isolated from HEK293-TRPV1 cells by the Trizol (Invitrogen) method. Oligo(dT)-primed cDNA was synthesized with the SuperScript III reverse transcriptase (Invitrogen). RT-PCR was performed for 40 cycles, with each cycle consisting of 94uC for 30 sec, 60uC for 30 sec, and 72uC for 30 sec with the primer sets to detect expression of rat TRPV1 (TRPV1(59) and TRPV1(39)), human aquaporins (AQPs), and Actin ß (Actin) mRNAs. The sequences of the primers were shown in Table S1. The PCR products were sequenced for confirmation.
During the experiments, the cells were perfused with the imaging buffer at 0.5 ml/min. Before the start of the imaging, cells were placed in the chamber for at least 15 min of perfusion with the isotonic imaging buffer (300 mOsm) to stabilize the basal level of the intracellular Ca 2+ concentration ([Ca 2+ ] i ). The perfusate was changed to a test imaging buffer of different osmolality and/or pH using two peristaltic pumps controlled with a controller (Gradicon III, Atto). The ambient temperature of the cells was maintained with a chamber heater and in-line heater adjusted with a dual heater controller (TC-344B, Warner). All the experiments were performed at temperatures below the activation threshold of TRPV1 (.43uC).
For the experiments to examine the dependency on osmolality of the response to capsaicin, the perfusion was stopped and the remaining fluid in the chamber was replaced with 200 ml of solutions at various osmotic levels. After the Ca 2+ imaging was started, capsaicin was added to the chamber at 1.5 nM (final concentration).
The fluorescence at excitation wavelengths of 340 and 380 nm was measured using a microscope equipped with a cooled charge coupled device (cooled CCD) camera (ORCA-ER, Hamamatsu Photonics). Data were collected every 15 sec, except for experiments on the response to capsaicin (2.5 sec), and analyzed using image-analysis software (AQUACOSMOS version 2.5, Hamamatsu Photonics). Elevated relative calcium concentrations are indicated by an increased ratio of Fura-2 emission at 340 versus 380 nm (F 340 /F 380 ). The change in fluorescence ratio is the difference between the F 340 /F 380 values 2 min before and 4 min after the change of the extracellular solution. | 4,550 | 2011-07-14T00:00:00.000 | [
"Biology"
] |
Homogeneity and the illocutionary force of rejection *
Homogeneity inferences arise whenever an assertion implies a universal positive ( every/both ) and its denial implies a universal negative ( no/neither ). I present an account of homogeneity inferences based on two assumptions which together constrain the behavior of negation: rejection is non-classical, and vacuous models may be omitted (Neglect Zero). If both assumptions are enforced, the only definable negatives are universal ( no/neither ), predicting the homogeneity gap.
Particular negatives
In (1b), negation of the universal in (1a) implies the contradictory of an existential.The particular negative not all is not an available reading of (1b).
(1) a.He answered our questions.⇒ All questions were answered.
b.He didn't answer our questions.
⇒ No question was answered.
Similarly, negation of conjunction (2b) implies negation of the conjuncts, rather than the particular negative (not both).
(2) a.The White House saw Delta and Omicron coming.⇒ Both Delta and Omicron were expected.
b.The White House didn't see Delta and Omicron coming. 1 ⇒ Neither Delta nor Omicron was expected.
In homogeneity inferences, particular negative readings (not all/not both) seem to disappear.I will describe a semantic framework in which two independently plausible assumptions are jointly responsible for the gap: (i) Rejection is failure of assertion.
(ii) Vacuous models may be disregarded in formula verification (Neglect Zero).
These assumptions may be understood as parameters that determine the logic of negation.In classical logic, (i) and (ii) are false: rejection is assertion of falsity, not merely failure to assert, and formulas can always be vacuously satisfied.However, if (i) rejection is non-assertion and (ii) formulas are not vacuously satisfied, particular negative operators are not definable.Flexibility in the interpretation of negation, which is indispensable to understand its use in natural language, may be achieved by constraining the illocutionary strength of rejection with (i) and (ii).
(3) a.The objections were numerous.b.The ladies form a nice team.
(4) a. # Every lady forms a nice team.b. # No lady forms a nice team.
The collective predicates that fail to exhibit homogeneity are not just those that measure a plurality: they are the "purely collective" predicates (in the sense of Dowty 1987) characterized by the lack of an all-paraphrase (Champollion 2020).The correct generalization is, therefore, that homogeneity is a conditional: a sentence ϕ supports homogeneity inferences if, and only if, an utterance of ϕ implies a universal positive (all/both) only if an utterance of ¬ϕ implies a universal negative (no/neither).
In addition, if ϕ supports homogeneity, assertion and denial of ϕ tend to be unacceptable in mixed contexts in which the particular negative reading is true.
Context.Some boys are performing Hamlet and some are not.
According to Križ 2019, (5a) On my proposal, homogeneity effects are explained by the logic of assertion and rejection, which affects the interpretation of negation.One immediate advantage of this proposal is its consistency with widely-accepted semantic accounts of plurals, collective (but not "purely collective") and distributive predicates, bare plurals, and conjunctions: all of these expressions give rise to homogeneity inferences and all standard accounts of their semantics predict a universal reading in the positive.Below, I will compare my proposal with some alternative accounts of homogeneity, focusing in particular on Križ 2016, Križ & Spector 2021, and Bar-Lev 2021.
Assertion and rejection
The framework presented here follows Sbardolini 2023.The language L consists in countably many constants C, variables V , and n-ary predicates A, combined in the usual fashion.
⟩ are a non-empty set of possible worlds W M , a domain of individuals D M , and an interpretation function ⋅ g M,w .I will assume for convenience that all worlds share the same domain.
An atomic formula A n t 1 ...t n is true at a world w relative to (a model M and) a variable assignment g if and only if the interpretations of t 1 ,...,t n belong to the interpretation of A n at w (relative to M); otherwise it is false.
Homogeneity inferences are reasonable inferences perceived to obtain in natural language which deviate quite significantly from classical logic.To account for this discrepancy, I will look at the conditions for assertion rather than truth, assuming that "assertion aims at more than truth, and inference at more than preserving truth" (Stalnaker 1975: 270).
The semantics is bilateral, since it is specified by assertion-and rejectionconditions, and state-based, since formulas are asserted or rejected relative to information states, which are sets of possible worlds.Other applications of bilateral state-based models include Sbardolini 2023, Aloni 2022, and Cresswell 2004.
A state asserts (⊧) an atomic formula with respect to (a model M and) a variable assignment g if and only if the formula is true under g at every world in the state (in M).A state rejects ( ) an atomic formula if and only if the state is empty or it fails to assert.I will use p as a metavariable for atomic formulas.
Definition 1. Bilateral conditions for atoms in L .
On this definition, refusal is less demanding than endorsement: all worlds in s must agree that p is true for s to assert it, whereas a single dissenting voice is enough for rejection.Since on this definition rejection is the polar (or contrary) opposite of assertion, I will refer to it as polar rejection (Incurvati & Sbardolini 2022).Polar rejection is non-classical, since assertion and polar rejection are still compatible: a state that rejects p might have a substate that asserts it.For example, suppose that p is true at w 1 and false at w 2 .Then p is rejected in state {w 1 ,w 2 }, but it is asserted in state {w 1 }.Classical logic requires mutually exclusive assertion and rejection (Cresswell 2004;Sbardolini 2023).
The empty state represents absurdity, and management of absurdity is the second point of departure with classical logic.By Definition 1, if s = ∅ then both s,g x ⊧ p and s,g x p. From a classical perspective, absurdity is always a permissible ground for conversation: with no information, anything goes (ex absurdum quodlibet).
However, we are interested in reasonable pragmatic inferences, and it may not be very reasonable for a speaker to stand on the flimsy ground of "anything goes".
In the next two sections I will introduce a semantics for conjunction and (pluralgenerated) universal quantification, and a proposal about absurdity management inspired by recent work on Neglect Zero (Aloni 2022).I close this section with the notion of entailment.A sentence ϕ follows from Γ if and only if ϕ is asserted relative to all models, states, and assignments, on which all sentences in Γ are asserted.
I indicate entailment by '⊧', abusing notation.There is no ambiguity, since entailment is a relation between sentences, and assertion a relation between a sentence, a model, a state, and an assignment.
Connectives and quantifiers
Negation switches assertion and rejection.Conjunction has familiar assertionconditions, and rejected conjunction "splits" the state: a state rejects ϕ ∧ ψ if and only if it can be split into two substates that reject ϕ and ψ respectively (Cresswell 2004;Yang & Väänänen 2017;Hawke & Steinert-Threlkeld 2021;Aloni 2022;Sbardolini 2023).2Definition 3. Bilateral conditions for the connectives in L .
For illustration, consider Figure 1.Let D = {a,b}.The four worlds w ∅ ,w a ,w b ,w ab represent all possible extensions of A, indicated by the subscripts in the obvious way.
Both states s = {w a ,w b } and s ′ = {w a } reject Aa∧Ab.Since s = {w a }∪{w b } and each of the two substates of s rejects a conjunct, s,g Aa ∧ Ab.Moreover, s ′ ,g Aa ∧ Ab, since s ′ = s ′ ∪ ∅ and s ′ ,g Ab and anything, including Aa, is rejected by the empty state.
Let us now consider the quantifiers.For any variable assignment g, a variable assignment that is an alternative of g x (differing from g x nowhere except possibly on x) will be indicated by 'g ′ x '.The universal quantifier introduced by definite plurals is defined as follows: asserted ∀ is familiar, and rejected ∀ is a generalization of split conjunction.
Definition 4. Bilateral conditions for the universal quantifier in L .
The logic determined by these models is not classical logic, as noted above.Nevertheless, classical logic is described by the same assertion-and rejection-conditions for complex formulas, provided the notion of rejection on atomic formulas is given by the classical condition (as in Aloni 2022 and Cresswell 2004; for more details on the propositional fragment, see Sbardolini 2023).
Neglect Zero
The empty state ∅ allows to trivially assert and reject any formula.It is a staple of classical logic that one can always reason vacuously by relying on "empty" information.Thus if someone knows that Chomsky wrote Syntactic Structures and Harris didn't, they may assert (9) making no mistake in classical reasoning.
Vacuous speech arises in classical logic from more than one source.It is well known that classical logic licenses universal generalizations if the quantifier has an empty domain (Geurts 2008).By the definition above, s,g x ⊧ ∀xϕ if nothing is ϕ in s, since there are no assignments of variables to elements of the domain.Following Aloni 2022, Neglect Zero is the hypothesis that speakers are biased against vacuous models.Plausibly, speakers disregard mathematically possible scenarios that are not cognitively salient.For recent work on reasoning and cognitive biases which provides some indirect evidence for the Neglect Zero hypothesis, see Bott, Schlotterbeck & Klein 2019, Knowlton, Pietroski, Williams, Halberda & Lidz 2020and Knowlton, Pietroski, Halberda & Lidz 2022.In order to implement Neglect Zero, I will introduce the star ⋆.The star is a speech act operator: it modifies the illocutionary force of a speech act by making its performance non-vacuous.The star chases empty state and empty domain out of the assertion-and rejection-conditions of a formula. 3efinition 5.The star.
The star allows us to distinguish between possibly vacuous and obligatorily nonvacuous speech.In classical logic, speech is always possibly vacuous.In the current framework, under the star, vacuous models are ruled out.For illustration, consider Figure 1: both s,g x Aa ∧ Ab and s ′ ,g x Aa ∧ Ab, but s,g x [Aa ∧ Ab] ⋆ and s ′ ,g x / [Aa ∧ Ab] ⋆ , since the empty state is necessary to reject As ∧ Ab in s ′ .
Results
Negation of the universal quantifier and of conjunction, under Neglect Zero, express the semantic values of no and neither, respectively.
For illustration, assume that s,g x ⊧ [¬∀xA] ⋆ .Then s,g x ∀xA ⋆ , hence there is S ∶ s = ∪S and for all t ∈ S there is g ′ x such that t,g ′ x Ax ⋆ and for all g ′ x there is a t ∈ S such that t,g ′ x Ax ⋆ .From the first conjunct, it follows that S is split into non-empty substates and that there is an x in the domain in each substate for which Ax does not hold.From the second conjunct, it follows that for every value of x there is one of these non-empty substates of S in which Ax rejected.Since each substate of S is included in s, any world that makes Ax false belongs to s.Thus s,g x Aa ⋆ whatever a is.Hence s,g x ⊧ [¬Aa] ⋆ .
For the second conjunct in Observation 1, assume that s,g x ⊧ [¬Ax] ⋆ with g x = a.It does not follow that s,g x ⊧ [¬∀xA] ⋆ .For a countermodel, suppose that under an alternative assignment g ′ x such that g ′ x = b we have s,g ′ x ⊧ Ax.Then it is not the case that s is the union of a set of states S such that, for every alternative of g, there is some non-empty t ∈ S that rejects Ax, since for g ′ x we have t,g ′ x / Ax.In this way we can account for the homogeneity inference of definite plurals (by the first conjunct of Observation 1: see (1a/1b) above) without trivializing their semantics (by the second conjunct of Observation 1; cf.Bar-Lev 2021: 1047).
Neglect Zero matters for the derivation above: ¬∀xA / ⊧ ¬Aa, since some variable assignments can be vacuously satisfied in asserting the premise but not the conclusion.Under the star, such countermodels are out.Moreover, since a is arbitrary in the derivation of the first conjunction of Observation 1, the same derivation shows that [¬∀xA] ⋆ ⊧ [∀x¬A] ⋆ : the universal quantification contributed by the definite plural is not "seen" by negation, under Neglect Zero (of course, ¬∀xA / ⊧ ∀x¬A).The case of conjunction is similar.
For illustration, assume that s,g x ⊧ [¬(p ∧ q)] ⋆ .Then there are t,t ′ such that s = t ∪ t ′ and t,g x p ⋆ and t ′ ,g x q ⋆ .Hence there are w ∈ t ∶ V g (w, p) = 0 and w ′ ∈ t ′ ∶ V g (w ′ ,q) = 0. Since w and w ′ belong to s, we have s,g x p ⋆ and s,g x q ⋆ , hence both s,g x ⊧ [¬p] ⋆ and s,g x ⊧ [¬q] ⋆ .For the second conjunct, consider a state s = {w} such that V g (w, p) = 0 and V g (w,q) = 1.Then s,g x ⊧ [¬p] ⋆ , but s,g x / ⊧ [¬(p ∧ q)] ⋆ since s has no non-empty substate that rejects q.This accounts for the homogeneity inference with conjunction (by the first conjunct of Observation 2: see (2a/2b) above) without trivializing its semantics (by the second conjunct of Observation 2).
As for definite plurals, the reasoning above shows that [¬(ϕ ∧ ψ)] ⋆ ⊧ [¬ϕ ∧ ¬ψ] ⋆ : on the models presented here, Neglect Zero allows us to simulate in the semantics the effects of a negation that does not have fixed scope with respect to conjunction.We can do so without substantial hypotheses about the syntax.The rationale behind this approach is that natural language negation is not merely the contradiction operator of classical logic: the thesis "that all forms of negation are reducible to a suitably placed it is not the case that" is false (Prior 1967: 459).
The Rejection account of homogeneity
Bar-Lev 2021 distinguishes three approaches to homogeneity: the Trivalent account (Schwarzschild 1996;Križ 2016), the Ambiguity account (Krifka 1996;Malamud 2012;Križ & Spector 2021), and the Exhaustification account (Magri 2014;Bar-Lev 2021).I recommend a fourth approach-the Rejection account.In my discussion of existing literature, I will focus on a selection of authors who provide what seems to me to be a state of the art version of their respective proposals.The first desideratum is to account for the following inference (see also (1a/1b)).
(10) a.He saw the girls.
⇒ He saw every girl.
b.He didn't see the girls.⇒ He saw no girl.
I assume that the girls receives an interpretation that supports the inference to the universal positive in (10a).It is widely accepted that the semantics of definite plurals supports such an inference, and there are various models of it (Sharvy 1980;Link 1983;Farkas & de Swart 2010;Schwarz 2013;Šimík & Demian 2020)).On my proposal, we need not decide between these models, since homogeneity is due to how the illocutionary force of a speech act affects negation, not to the semantics of plurals (nor to the semantics of any other expressions that display homogeneity effects).The inference in (10b) follows from Observation 1 under the Neglect Zero hypothesis.
Other accounts of homogeneity do not take it to be an effect of rejection.On Križ's Trivalent account, homogeneity is a property of some lexical predicates.According to Križ, a homogeneous predicate ϕ is defined only if everything in the contextually salient domain is ϕ or nothing is.Thus, if ϕ( the girls ) is defined and true, ϕx is true for every girl x in the domain; if it is defined and false, ϕx is true for no girl.On Križ and Spector's Ambiguity account, homogeneity is a property of plurals, which are semantically underdetermined between ∀and ∃-readings.By the strong meaning hypothesis (Dalrympe, Kanazawa, Mchombo & Peters 1994), assertion of ϕ receives the ∀-reading, and its negation the ¬∃-reading.Finally, according to Bar-Lev 2021, homogeneity is an implicature.Bar-Lev assumes that ϕ( the girls ) is interpreted existentially.However, the (10a) inference follows from a process of exhaustification, which does not unfold under negation.All three accounts appear to offer a satisfactory model of homogeneity inferences, at least with regards to examples (1a/1b) and (10a/10b).
There is a worry for accounts of homogeneity that rely on a tight connection with plurals: some languages do not have English-style plurals, such as Japanese, and yet homogeneity inferences are observed with singular generics and demonstratives: If homogeneity is an effect of the semantic underspecification of plural morphology, as Križ & Spector 2021 claim, it is unclear how to account for Japanese-like languages, in which homogeneity arises without plural morphology.The present account runs into no troubles of this kind since I take rejection to be the culprit for homogeneity inferences, and rejection, as expressed by negation, is always on the crime scene.
(2) a.The White House saw Delta and Omicron coming.
⇒ Both Delta and Omicron were expected.
b.The White House didn't see Delta and Omicron coming.⇒ Neither Delta nor Omicron was expected.
Data about conjunction show that lexical properties of predicates are not necessary for homogeneity, and so the Trivalent approach fails to predict homogeneity with conjunctions-as acknowledged by Križ 2016: 522.Plural semantics is not necessary either, hence Križ and Spector's Ambiguity approach is no improvement, unless we assume that conjunctions are semantically underdetermined even if the conjuncts are not.
Bar-Lev's approach to homogeneity with plurals does not extend to conjunctions either.Perhaps definite plurals are interpreted existentially and strengthened into universals by exhaustification, but it seems unlikely that ϕ ∧ ψ should have the semantics of a disjunction, exhaustified into a conjunction.A previous exhaustificationist proposal for both plurals and conjunctions, by Magri 2014, is criticized and rejected by Bar-Lev 2021: 1055-1057.Clearly, however, the exhaustification mechanism delivers the wrong results: assuming the account of the relationship between ∧ and ∨ outlined in Bar-Lev & Fox 2017, the set of innocently excludable alternatives to ¬(ϕ ∧ ψ) is {¬(ϕ ∨ ψ)}, and the set of innocently includable ones is {¬(ϕ ∧ψ)}.Thus, exhaustification asserts (ϕ ∧¬ψ)∨(¬ϕ ∧ψ), which is incorrect. 5herefore, no alternative approach to homogeneity explains homogeneity with conjunctions, and no explanation extending these approaches seems forthcoming.In contrast, homogeneity inferences with conjunctions are predicted if rejection is non-vacuous, as shown by Observation 2.
A third desideratum concerns mixed contexts, in which neither assertion nor denial of ϕ is acceptable if ϕ supports homogeneity inferences.
Context.Some of the boys are performing Hamlet and some are not.
b. ?? The boys aren't performing Hamlet.
Suppose that a,b and c are the boys, and that only a is performing Hamlet in w a .Thus, {w a } is a state that captures the information of the mixed context of (5a) and (5b): some boy is performing Hamlet and some is not.If s = {w a }, the following holds (with quantification restricted to {a,b,c}).
Therefore, in a mixed context, neither (5a) nor ( 5b) is non-vacuously asserted.The case of conjunction is similar.
Context.Dean saw Robin but not Rachel.
b. ?? Dean didn't see Robin and Rachel.
In an information state that captures the information of the mixed context of (6a) and (6b), neither sentence is non-vacuously asserted.Suppose that p is true and q is false at w p .If s = {w p }, the following holds.
The predictions of other accounts of homogeneity concerning mixed contexts are not always straightforward, due to different approaches to non-maximal readings of definite plurals.Following Križ 2016, some authors have argued that definite plurals systematically give rise to non-maximal generalizations, and that homogeneity and non-maximality are "two sides of the same coin" (Križ & Spector 2021: 1132).
with plurals while maintaining that ϕ ∧ ψ has its classical meaning, by making some additional assumptions about which alternatives are computed in this setting-making sure that the additional assumptions are not ad hoc.
Although definite plurals may have non-maximal readings, homogeneity and nonmaximality pattern differently and should not be equated.
Non-maximality
The purported non-maximality of (5a) and ( 5b) is directly in tension with a previous datapoint, namely that (5a) implies that all boys are performing Hamlet and that (5b) implies that no boys are performing Hamlet.By non-maximality, (5a) and ( 5b) imply that almost all boys are performing, and that almost none are performing, respectively.If so, at least one of ( 5a) or (5b) should be assertable in a mixed context.But this is not so, at least not without some pragmatic arm-twisting.This observation is important: homogeneity and non-maximality are distinct phenomena, though sometimes overlapping.The kind of pragmatic considerations that license non-maximal interpretations are orthogonal to the acceptability of homogeneity inferences.
First of all, definite plurals and non-maximal generalizations are not equivalent (Lasersohn 1999: 525).
A: She read the required papers.
A: She read almost all the required papers.B1: No, she didn't read On Denoting.B1: * No, she didn't read On Denoting.B2: Yes, except for On Denoting.
B1 cannot disagree with A's almost all generalization on the right, since they are not disagreeing, but can disagree with A's definite plural on the left.Similarly, B2 cannot partially agree with A's almost all generalization, since they are fully agreeing, but can partially agree with A's definite plural.Secondly, as Križ 2016 recognized, non-maximal readings of definite plurals have the treacherous quality of disappearing even in contexts in which they are true.If we are going for a stroll after sunset while walking next to a very loud house party, (13a) is not acceptable, even if all townspeople are asleep in other neighborhoods.In the same context, the use of (13b) would raise no eyebrows.
(from Lasersohn 1999: 522) b.All townspeople are asleep, except those who live on this block.
There may be some overlap but no strong correlation between authentic non-maximal generalizations and the use of definite plurals.On the basis of these and additional considerations, Bar-Lev 2021 argues that non-maximal readings of definite plurals are significantly more context-sensitive than homogeneity inferences.Thirdly, conjunctions are extremely problematic if non-maximality and homogeneity are unified, as acknowledged by Križ 2016: 522, and Bar-Lev 2021: 1081, fn. 52.Since conjunctions support homogeneity inferences, equating homogeneity and non-maximality implies that the truth of a conjunction should allow for exceptions.Then, ϕ ∧ ψ may be true while ϕ is not true.This prediction is disastrous and should be avoided at all costs.
Therefore, homogeneity does not imply non-maximality.In addition, nonmaximality can be explained by independently available resources, which are also independently necessary to account for pragmatic imprecision.
For Križ, (5a) and ( 5b) are truth-valueless in their mixed context, since they have universal truth-conditions, but they may be accepted if the QUD allow for "true enough" non-maximal answers.Križ and Spector's appeal to the strong meaning hypothesis would make both (5a) and (5b) unacceptable in the mixed context, but not if homogeneity and non-maximality coincide.On the Ambiguity account they coincide, hence the prediction is that (5a) and (5b) are both acceptable, which is wrong.For Bar-Lev, non-maximality is a side-effect of exhaustification, and since negative plurals are not exhaustified, (5a) may be acceptable, but (5b) is not.
Experimental evidence shows that, in mixed contexts, positive plural definites are somewhat acceptable, that their negative counterparts tend to be judged unacceptable, and that a suitable QUD can improve the status of both (Tieu, Križ & Chemla 2019;Augurzky, Bonnet, Breheny, Cremers, Ebert, Mayr, Romoli, Steibach & Sudo 2023).The symmetricalists are correct in expecting non-maximal readings with both positives and negatives, but the asymmetricalist prediction that negatives resist non-maximality is also correct.
The basic prediction of the present account sides with Križ in the symmetricalist camp (Observation 3).Following Križ's proposal, QUD manipulations can redeem (5a) and (5b) in the mixed context, at least to some extent.Thus, while (5a) and (5b) are both unacceptable in their mixed context, both have weaker consequences: roughly, Some boys are performing and Some boys are not performing, respectively (with ∃ defined as ¬∀¬).
[∀xϕ] ⋆ ⊧ ∃xϕ [¬∀xϕ] ⋆ ⊧ ∃x¬ϕ Both weakenings are assertable in the mixed context of (5a) and (5b), in which some boys are performing and some are not.These weakenings, I suggest, approximate the non-maximal readings of (5a) and (5b) respectively, and can be retrieved with a suitable QUD.Following Augurzky et al. 2023, an Existential QUD (Is any boy performing?) facilitates a non-maximal interpretation of (5a), and a Universal QUD (Is every boy performing?) facilitates a non-maximal interpretation of (5b).Speakers may be driven by the appropriate QUD to accept (5a) by assenting to its true consequence ∃x ∶ performing-Hamlet , and to accept (5a) by assenting to its true consequence ∃x ∶ ¬ performing-Hamlet .Hence, QUD manipulations can improve the status of definite plurals in mixed contexts, whether positive or negative.However, a complication arises in the negative case.An existential assertion, under a Universal QUD, invites a quantity implicature to the denial of the universal.The same implicature is not supported under an Existential QUD.
A: Who ate all the cookies?A: Who ate some cookies?B: I ate some.
B: I did.⇒ I didn't eat all the cookies./ ⇒ I didn't eat all the cookies.
Therefore, an utterance of ¬∀xϕ, such as The boys aren't performing (5b), implies both ∀x¬ϕ (No boy is performing) under Neglect Zero, and a weakening ∃x¬ϕ (Some boys are not performing) that is assertable in the mixed context, and that is in principle retrievable under a Universal QUD.However the same QUD also invites a scalar inference from the latter implication (∃x¬ϕ) to ∃xϕ (Some boys are performing, or Not all boys are not performing).This conclusion is inconsistent with the universal reading of (5b) given by Neglect Zero (∀x¬ϕ).Hence, non-maximal readings of negative definite plurals short-circuit if a scalar implicature is derived, as the diagram below illustrates.
Therefore, it is hard for speakers to isolate a felicitous non-maximal reading for (5b) while avoiding contradiction.The reason is general.Typically, nobody is compatible with its non-maximal counterpart somebody-not, unless the context supports an inference from the latter to somebody, because this contradicts nobody.Hence, negative definite plurals resist non-maximal readings.Since non-maximal readings of positive definite plurals are licensed by an Existential QUD in mixed contexts, no contradiction arises. 6ummarizing, non-maximality judgments do not apply to all sentences that support homogeneity.Moreover, non-maximal generalizations are not sensitive to context in the same way as sentences that support homogeneity, and are not used in the same way.Although Križ and others have argued for a tight connection between non-maximality and homogeneity, Bar-Lev is more cautious: non-maximality is subject to different constraints and originates from different sources.I agree with this assessment.Non-maximality is pragmatic slack, not the counterpart to homogeneity.QUD manipulations in mixed contexts can explain the empirical findings on the non-maximality of definite plurals, consistently with the present account.
Focus and overt universal generalizations
There remain two desiderata: to explain why focus and explicit generalization by insertion of all and both can block homogeneity inferences.I will suggest that the same constraint on Neglect Zero explain both cases.Sharp data about focus can be obtained if we assume contrastive focus on and in (7a), as observed by Szabolcsi & Haddican 2004, and on the boys in (7b), repeated below.The relevant readings are also possible with narrow focus on a subsentential constituent that contains the logical element, and or the -s in the examples.There are other possible focus placements but not relevant to the present discussion.The focus data can be explained by extending my account of homogeneity inferences with some account of the well-known semantic effects of focus (Rooth 1992;Beaver & Clark 2008;Roberts 2012).There is more than one proposal in this area, but including some theory of focus is independently necessary.There are also many finer points about focus that I will not discuss.
Focus signals that an exception to Neglect Zero is to be made for the focused element.After all, if the element is focused speakers should pay attention, and shouldn't let biases determine interpretation.Consider (7a).Standard theories of focus interpretation have the consequence that (7a) presupposes that Dean saw someone, or someone among Robin and Rachel, depending on the domain of alternatives.Such consequences are incompatible with the non-vacuous assertion of (7a), since if s,g x ⊧ [¬(ϕ ∧ ψ)] ⋆ then s,g x ⊧ ¬ϕ and s,g x ⊧ ¬ψ.That is, if (7a) is non-vacuously asserted then Dean saw neither Robin nor Rachel, or, assuming that the domain is limited to the set of alternatives, Dean didn't see anyone.Thus, focus on a subsentential constituent that contains and in (7a) is incompatible with the non-vacuous performance of the speech act.Therefore, vacuous models cannot be neglected.If vacuous models are not neglected, namely if s,g x ⊧ ¬(ϕ ∧ ψ), assertion of (7a) is compatible with the continuation He only saw Robin, for ¬(ϕ ∧ ψ) / ⊧ ¬ϕ.
Likewise for (7b).Focus on a subsentential constituent which includes the -s may carry a consequence, by standard theories of focus interpretation, that is incompatible with non-vacuous assertion of (7b).Suppose contrastive focus on the boys.Depending on the domain of alternatives, (7b) may presuppose that a subset of boys are performing Hamlet, but not all of them.7However, the presupposition that a subset of boys are performing Hamlet is incompatible with the non-vacuous assertion of (7b), since s,g x ⊧ [¬∀x ∶ performing-Hamlet ] ⋆ implies s,g x ⊧ ¬ performing-Hamlet x for all boys x.
Thus focus signals an exception to the bias against vacuous speech.In addition, the exception is local: it is only the focused constituent that gets a free pass, so to speak.After all, focus is not optional, but a part of grammar, and if its effect was to block Neglect Zero everywhere then Neglect Zero should never have any visible consequences.Example (14) shows that the exception to the star is on the focused constituent and not on the entire speech act, since homogeneity inferences are still possible outside the focused element.( 14) Lea [and] F Bianca didn't talk to the professors.Only Lea did.
⇒ Bianca didn't speak to any professor.
In order to account for the effects of focus, I propose the following rule: if a complex sentence with focus on a constituent ψ is non-vacuously asserted or rejected, the focused constituent filters through the star.
Definition 6. Focus exception to the star. [ This rule predicts that the conjunction in ( 14) does not have homogeneity effects, but the definite plural does. 8Alternative accounts of homogeneity inferences do not address their focus-sensitivity, and it is an open question whether they can be extended to account for the data about focus.The final desideratum is to account for homogeneity cancellation with universal expressions such as all and both.For reasons of space I will only sketch how a proper account might go, and I hope to follow up in future work.
(8) a. Bianca likes the students ≈ Bianca likes all the students b.Bianca doesn't like the students / ≈ Bianca doesn't like all the students A strategy that I think is promising is to reduce the contrast in (8a/8b) to the effects of focus.English expressions such as all and both are known to be focus-sensitive (Rooth 1985(Rooth , 1992;;von Fintel 1994;Saebø 1997;Roberts 1995Roberts , 2012;;Beaver & Clark 2008): they quantify over contextually restricted domains of alternatives contributed by focus.If so, the rule of focus exception applies.Then (8a) is an equivalence with or without the star: in the former case, focus lifts the effects of the star, but not those of other pragmatic operators (such as Aloni's +) that rule out empty domains.In contrast, the equivalence in (8b) fails if speech is not vacuous, since the existence of students liked by Bianca is ruled out by the negated definite plural but not by the not all the students construction.Additional pragmatic effects cannot restore the (8b) equivalence without deriving the homogeneity inference.9On this approach, the effects of the rule of focus exception are limited to the focused constituent.This prediction is borne out with both and all: the exception to the star introduced by focus-sensitive elements is local, as (15) shows in a case analogous to ( 14).
(15) Not all the students answered the questions.
⇒ Some student answered no question.
Further evidence may come from languages in which the contrast in (8a/8b) is not replicated.In Japanese, some combinations of negation with a universal quantifier behave as in English, but in other cases homogeneity readings are possible if not preferred.(Case ( 16 In (16), interpretation is ambiguous despite the overt zenbu (all).Moreover, the phrase donohonmo (every book) yields a universal positive in (17a) and a universal negative in (17b).A hypothesis consistent with the current account is that, while English all conventionally associates with focus, having lexicalized the rule of focus exception, focus association for some Japanese universal quantifiers is contextual, and the rule may or may not apply.
On competing accounts, the equivalence in (8a) may be derived semantically (Križ 2016) or by disambiguation (Križ & Spector 2021).In addition, according to both the Trivalent and the Ambiguity account, one function of English all is to eliminate homogeneity, understood as a property of predicates.This approach is similar to the one I sketched, and predicts the non-equivalence in (8b).A further stipulation that some universal determiners, for example in Japanese, lack the homogenitycanceling function, would be consistent with both accounts.On Bar-Lev's account, the equivalence in (8a) is derived by exhaustification, but since the latter is blocked by negation, (8b) is predicted.
Summarizing, the Rejection account of homogeneity predicts homogeneity inferences with definite plurals and conjunctions, explains the unassertability facts in mixed contexts, the focus data, and (with more work to be done) the cancellation effects of focus-sensitive expressions like both and all.Alternative accounts, in particular the Trivalent, Ambiguity, and Exhaustification accounts cover some of these data, but none covers them all.
Conclusion
I presented an account of homogeneity inferences according to which rejection is responsible: homogeneity is predicted if rejection modifies the interpretation of negation.Speech acts are characterized by two assumptions: polar rejection as non-assertion (as opposed to classical logic, in which rejection is the complement of assertion), and a Neglect Zero option (as opposed to classical logic, in which there is no such option).Neglect Zero is a cognitive hypothesis about language use: speakers are biased against mathematically possible but vacuous scenarios, which can consequently be ignored in formula verification in contexts in which we can assume that interlocutors are not particularly vigilant.
Polar rejection and Neglect Zero are two separate components, though the account depends on both.They are motivated by different considerations: the force of a speech act (Incurvati & Schlöder 2017;Incurvati & Sbardolini 2022), and the cognitive effort required by reasoning about vacuous models (Bott et al. 2019;Knowlton et al. 2020Knowlton et al. , 2022)).Methodologically, it is useful to keep them separate: in Aloni's account of free choice, the free choice inference is derived as an effect of Neglect Zero, but negation may remain classical.An account of homogeneity which follows Aloni's approach more closely, in particular by keeping negation classical, is desirable, and it is left for future work.
(7) a. Dean didn't see Robin [and] F Rachel. b. [The boys] F aren't performing Hamlet.
-na-katta.eat-can-NEG-PAST Both 'I could not eat all of the pie' and 'I could eat none of the pie' For some speakers, plural readings of the morphologically singular demonstrative sono in (12a/12b) are not available, and a plural demonstrative sorerano is preferred.For others, sono has both singular and plural readings.Thanks to T. Nakamura.The same point can be made in Latin: medieval logicians took Homo est rationale (morphologically singular: 'Man is rational') to imply Socrates est rationale, and Homo non est equus ('Man is not horse') to imply Socrates non est equus, in what was then not called homogeneity but dictum de omni et nullo. | 8,344 | 2024-02-08T00:00:00.000 | [
"Philosophy",
"Linguistics"
] |
CAPACITOR VOLTAGE BALANCING IN SINGLE PHASE SEVEN-LEVEL PWM INVERTER
Multilevel inverter has emerged recently as a very important altrernative in the area of high voltage and high power applications. A multilevel inverter can synthesize stepped output voltages similar to sinisoidal wave. The main limitations of conventional topologies are high THD, large number of components, complex PWM control and voltage balancing problems. So to overcome these limitations, a single-phase seven-level PWM inverter with less number of carrier signals and components is introduced. It consist of a single dc voltage source with a series of capacitors, diodes, switches and an H-bridge cell. Simulation of proposed single-phase seven-level PWM inverter is done in MATLAB simulink software and voltage balancing issue in series connected capacitors is eliminated using modified PWM scheme.
Introduction
The concept of multilevel inverter was introduced in 1975.The term multilevel began with three level inverter.A multilevel inverter is a power electronic system that can synthesize stepped output voltages similar to sinusoidal wave.Using multilevel technique, the amplitude of the voltage is increased, stress in the switching devices is reduced and overall harmonics profile is improved.As the number of levels increases, the obtained output waveform approaches the sinusoidal wave with less distortion, less switching frequency, higher efficiency etc. Plenty of multilevel inverter topologies have been investigated, but only several of them are practical for industrial applications.Among existing multilevel inverters, diodeclamped and cascaded H-bridge (CHB) multilevel inverters are most widely used.It exhibits several attractive features such as simple circuit layout, less component counts, modular in structure and avoid unbalance capacitor voltage problem.However as the number of output level increases, the circuit becomes bulky due to the increase in the number of power device [1][2][3].
When dc voltages are scaled in power of three, it can maximize the number of output voltage levels.However, it increases independent dc voltage sources to generate higher output voltage levels.To solve this problem, a multilevel inverter employing a cascaded transformer is used.However, the cascaded transformer makes the system bulky because it operates in a low frequency [4].To eliminate this drawback transformer less circuit topologies were modified from the CHB multilevel inverter.Multilevel inverters have found potential application in high power systems due to there over Midhun G, Aleena T Mathew modulation ability without the need of any transformer.Despite its complexities, multilevel inverter is preferred due to its superior harmonics profile and its ability to produce a high voltage without any transformer [5].
The demand for renewable energy has increased significantly over the years because of shortage of fossil fuels and greenhouse effect.Among various types of renewable energy sources, solar energy and wind energy have become very popular and demanding due to advancement in power electronics techniques.Using multilevel inverters renewable energy sources can be easily interfaced to the grid.Improving the output waveform of the inverter reduces its respective harmonic content [6][7][8].
When the output voltage levels increases, the number of power semiconductor switches, sources and the number of the gate driver circuit required increases which would make the overall system more expensive and complex.So to overcome these limitations, a single phase seven-level PWM inverter is introduced in the proposed work.And also a new concept is put forward to reduce voltage unbalancing in series connected capacitors [10][11].
Single Phase Seven-level PWM Inverter
Most of the conventional multilevel topologies uses series connected capacitors and independent DC sources.Series connected capacitors makes voltage unbalancing problems and it will affect the performance of multilevel inverter.The proposed multilevel inverter is a useful way to minimize the number of independent DC voltage sources and also it is an effective configuration of a multilevel inverter that can increase the number of output voltage levels with a reduced number of switches.Fig. 1 shows the block diagram of the proposed seven-level PWM inverter.It consists of a single dc voltage source, level and polarity generation part and load.The level generation part is helps to generate the required levels.
The other part is called polarity generation part and is responsible for generating the polarity of the output voltage.
Capacitors Voltage Unbalance
The seven-level PWM inverter consists of three capacitors, i.e., C , C and C respectively.These This is the main reason for the voltage unbalancing in the series-connected capacitors of the proposed circuit topology.Hence, each capacitor voltage should be regulated to feed the appropriate amount of average current by satisfying the below condition
I = I = I C1(avg) C2(avg) C3(avg)
The capacitor voltage unbalancing occurs depending on just the switching angles of a , a and a regardless of the
Modified Switching Scheme
To solve the capacitor voltage unbalancing, a modified switching pattern is adopted for the proposed seven-level PWM inverter.The main idea of the proposed control strategy is to regulate the charging and discharging current rate of capacitor?C .It ensures the voltage The charging and discharging time of capacitor C 2 regulates voltage balancing of other two capacitors.This idea is adopted in the modified switching scheme.The simulink model of a single phase seven level inverter with modified switching scheme for RL-load is shown in The balanced output voltage of seven-level PWM inverter with modified switching scheme is shown in Fig. 10. with load (R=100ohm, L=25mH).Waveform of balanced capacitor voltage is shown in Fig. 11.Voltages of all three capacitor are balanced at 50V.It is clear from the simulation result the voltage unbalancing in series connected capacitors is rectified.So that the proposed PWM scheme will be an effective remedy for voltage balancing issues in seven-level PWM inverter.
Conclusion
A single phase seven level PWM inverter is presented.Simulations are done in MATLAB and concluded that the proposed multilevel inverter that can effectively increase the number of output voltage levels with simple PWM control and less number of components.Another major problem in multilevel inverters are the voltage unbalancing problem, so that a modified switching scheme is applied in the suggested topology for the balancing of capacitor voltage.This switching method ensures improved performance in the proposed sevenlevel PWM inverter.
5 6 7 Fig. 2 :
Fig. 2 : Circuit Diagram of Seven-level PWM Inverter Switching scheme for controlling the seven-level inverter is shown in Fig.3.Phase Disposition (PD-PWM) is adopted to control the inverter.The V , V and V are car1 car2 car3 the three carrier waves and V is the reference wave used ref for modulation.The reference and carrier waves have the same frequency but different offset voltages.By comparing the reference and each carrier wave, it produces the command signals, i.e., C , C and C a b c
1 2 3
capacitors have the major role in generating the exact output levels.If there is any voltage unbalance in series connected capacitor, that causes variation in output levels.Therefore, the voltage balancing of seriesconnected capacitors is very important factor for the working of the inverter.From Fig.4 I , Iand I are currentC1(avg) C2(avg) C3(avg)through the capacitors C , C and C respectively.
1 2 3 Fig . 4 :
Fig .4: Equivalent Circuit with average currents In other words, the difference between the charging and discharging of the series connected capacitors is determined by the switching angles.It means that the different periods for each voltage level are the cause of the capacitor voltage unbalancing problem.
2 2 C 1 and 2 3
regulation of C and the voltage balance of the upper and 2 lower capacitors.Because capacitor C locates between and C and the charging and discharging current of C 1 3 C should flow through C .Thus, the voltage 3 regulation of C is directly related to the voltage 2 regulation across C and C .In order to regulate the 1 charging and discharging current rate of C , it is possible 2 by controlling the amplitude of the second carrier (V ). car2
Fig. 5
Fig.5 shows the modified control method for regulating the C voltage.It controls the amplitude of the carrier2
Fig. 9 .
150V is applied as the input DC-voltage.The triggering pulses are generated by using the Phase Disposition pulse width modulation (PD-PWM) technique.The modified switching arrangement is done by taking voltage across the capacitor C from the output 2 and it is given as input through a PI controller.This feedback of voltage helps to vary the amplitude of second carrier in between other two carriers.Then the second carrier will control the charging and discharging of C and 2 eliminate the voltage unbalancing problem.Then the three carrier signals are given by three repeating sequence block and these are compared with a reference sine wave.The three command signals is then given to the switching subsystem and corresponding switching signals are produced.Then, given to each switches and Output is viewed from the scope block.
Table 1
Output Voltage Levels With Switching States | 2,010.4 | 2017-04-15T00:00:00.000 | [
"Engineering"
] |
Defining specificity and on-target activity of BH3-mimetics using engineered B-ALL cell lines
One of the hallmarks of cancer is a resistance to the induction of programmed cell death that is mediated by selection of cells with elevated expression of anti-apoptotic members of the BCL-2 family. To counter this resistance, new therapeutic agents known as BH3-mimetic small molecules are in development with the goal of antagonizing the function of anti-apoptotic molecules and promoting the induction of apoptosis. To facilitate the testing and modeling of BH3-mimetic agents, we have developed a powerful system for evaluation and screening of agents both in culture and in immune competent animal models by engineering mouse leukemic cells and re-programming them to be dependent on exogenously expressed human anti-apoptotic BCL-2 family members. Here we demonstrate that this panel of cell lines can determine the specificity of BH3-mimetics to individual anti-apoptotic BCL-2 family members (BCL-2, BCL-XL, BCL-W, BFL-1, and MCL-1), demonstrate whether cell death is due to the induction of apoptosis (BAX and BAK-dependent), and faithfully assess the efficacy of BH3-mimetic small molecules in pre-clinical mouse models. These cells represent a robust and valuable pre-clinical screening tool for validating the efficacy, selectivity, and on-target action of BH3-mimetic agents.
IntroductIon
One of the hallmarks of cancer is the ability of cancer cells to overcome the induction of apoptosis that should be triggered when they violate normal cellular checkpoints. To do so, cancer cells commonly select for the elevated expression of anti-apoptotic proteins such as BCL-2, BCL-X L , BCL-W, BFL-1, or MCL-1 to antagonize the induction of cell death [1]. These anti-apoptotic BCL-2 molecules possess a hydrophobic binding pocket that is capable of binding the BH3-domain of pro-apoptotic BCL-2 family members [2]. It is this protein-protein interaction that allows BH3-only molecules (e.g. BIM, PUMA, NOXA, BID, BAD, etc.) to inhibit anti-apoptotic proteins and promote the death of cells by activating the pro-apoptotic effector molecules, BAX and BAK [3]. To counter the apoptotic resistance of cancer cells, researchers in academia and in the pharmaceutical industry have focused on the development of small molecular inhibitors of anti-apoptotic proteins, known as BH3-mimetic molecules [1]. By mimicking the activity of BH3-only molecules, small molecule BH3-mimetics can act to pharmacologically promote the release of proapoptotic BCL-2 family members from the anti-apoptotic proteins, thus pushing cancer cells to undergo apoptosis.
A number of strategies are used to test and evaluate BH3-mimetic drugs. In many cases, the screening for BH3-mimetic agents utilizes the displacement of recombinant anti-apoptotic proteins as assessed by fluorescent polarization or surface plasmon resonance [4,5]. While these techniques are effective for high-throughput screening and evaluation of candidate small molecules, they are performed in vitro and do not assess biological processes including membrane permeability, specificity of interaction, and off-target effects that require cell based evaluation. As a secondary screen, it is common to test the efficacy of BH3-mimetics in a panel of cell lines. To this aim, researchers have used a variety of techniques including gene silencing by shRNA or BH3-profiling to identify cancer cell lines that are dependent on individual anti-apoptotic BCL-2 family members [6][7][8][9]. Therefore, the efficacy of a given BH3-mimetic in one of these cell lines is often evidence of the specificity of the BH3-mimetic. Unfortunately, often these cell lines represent a spectrum of different malignancies or sub-types making it challenging to compare the responses of one cell line with one another. Furthermore, these cells typically originate from human cancers requiring that in vivo pre-clinical testing be done in xenografts of immune compromised recipients. BH3 mimetics that are working "on pathway" should be dependent upon the expression of the multi-domain effectors BAX and BAK. However, human cancer cell lines are rarely deficient in both the pro-apoptotic effectors BAX and BAK; therefore, demonstration of on-target, pro-apoptotic activity of BH3-mimetics is challenging.
To aid in the development and testing of BH3-mimetic agents, we developed a panel of leukemia cell lines arising from a common parental population that have been engineered to be dependent on human anti-apoptotic BCL-2 family members. These mouse leukemia cells are suitable for cell-based screening as well as for testing in immune competent mouse models to allow the screening for toxic effects of the BH3-mimetics. By expressing human anti-apoptotic molecules, the transplanted leukemic cells can respond to treatment with small molecules designed for inhibition of human protein targets. Lastly, to demonstrate that the BH3-mimetics are acting in an "on-target" mechanism, we have generated cell lines that are deficient in their ability to undergo apoptosis by genetically ablating the multi-domain apoptotic effectors, Bax and Bak. Thus, this panel of re-programmed B-ALL cells represents an important tool to assess the specificity and potency of BH3-mimetic small molecules both in culture and in vivo.
results engineering bcr-Abl + b-All cells to express human anti-apoptotics
We have previously demonstrated that the anti-apoptotic activity of endogenous Mcl-1 is essential to maintain the survival of murine BCR-ABL-expressing B-lineage acute lymphoblastic leukemia (B-ALL) cell lines despite the concomitant expression of other anti-apoptotic molecules [10]. However, the ectopic expression of other anti-apoptotic BCL-2 family members can override the requirement for endogenous MCL-1 in these leukemic cells [10]. We sought to use this model to develop a panel of engineered, "re-programmed" B-ALL cell lines in which the endogenous Mcl-1 was replaced by human versions of anti-apoptotic genes. To do so, Mcl-1 f/f Arf-deficient pre-B cells expressing the p185 isoform of BCR-ABL (hereafter referred to as p185 + B-ALL) were stably transduced with cDNAs encoding human BCL-2, BCL-X L , BCL-W, MCL-1, or BFL-1 (also known as BCL2A1). Following drug selection, these cells were further transduced with Cre-IRES-GFP to delete the endogenous Mcl-1 ( Figure 1A). The expression of human anti-apoptotic BCL-2 family members, but not an empty vector, was capable of supporting the outgrowth of p185 + B-ALL cells that had efficiently deleted endogenous Mcl-1 from the cultures ( Figure 1B). Single-cell clones were sorted based on GFP expression and tested by immunoblot to detect the loss of endogenous MCL-1 and exogenous BCL-2 family member expression ( Figure 1C). These single cell clones were similar in their growth kinetics ( Figure 1D).
Cells lacking both pro-apoptotic effector molecules BAX and BAK (referred to as DKO cells) are resistant to the induction of apoptosis [3,11]. Thus, we sought to generate p185 + B-ALL cell lines defective in the core apoptotic pathway to use as controls to define whether tested BH3-mimetics are inducing leukemic death by triggering apoptosis. To do so, Mcl-1 conditional Arf-deficient mice were bred to mice bearing conditional alleles of Bax (Bax f/f ) on a Bak-deficient background. Bone marrow (BM) from these mice was harvested and transduced with the p185-IRES-Cre oncofusion virus to generate p185 + B-ALL cells in which Mcl-1-deletion is rescued by loss of both BAX and BAK (hereafter referred to as DKO p185 + B-ALL cells). Indeed, when p185 + B-ALL cells were compared with DKO p185 + B-ALL cells, the DKO p185 + B-ALL cells were markedly resistant to cell death induced by treatment with the pan-kinase inhibitor staurosporine ( Figure 1E). Therefore, the DKO p185 + B-ALL cells are inherently resistant to the induction of apoptosis.
testing the anti-apoptotic dependence of the engineered b-All cell lines
To confirm the anti-apoptotic dependence of our engineered p185 + B-ALL cell lines, we used BH3-profiling. This technique takes advantage of the selective interactions between BH3-only proteins and individual anti-apoptotic BCL-2 family members and uses mitochondrial membrane depolarization as a readout [12]. Mildly permeablized cells are treated with peptides derived from BH3-only family members to determine their anti-apoptotic dependence as measure by depolarization of their mitochondrial membrane potential induced by mitochondrial outer membrane permeabilization (MOMP). The response to treatment with different peptides allows the assessment of anti-apoptotic dependence; BAD BH3-peptides are selective for BCL-2, BCL-X L , and BCL-W; NOXA BH3-peptides are selective for MCL-1 and BFL-1; HRK BH3-peptides are selective for BCL-X L ; PUMA and BIM BH3-peptides work on any anti-apoptotic molecule [12,13]. To assess the dependence of our re-programmed p185 + B-ALL cell lines, cells were digitonin-permeablized and treated with the panel of BH3-peptides and mitochondrial membrane potential measured by staining cells with the membrane potential dye JC-1, which fluoresces red in the matrix of healthy mitochondria and green in depolarized cells. As expected, both BIM and PUMA peptides depolarized all of the leukemic cells tested except for those lacking BAX and BAK, further illustrating that the DKO p185 + B-ALL cells are defective in the core apoptotic pathway ( Figure 2F). In contrast, incubation of the p185 + B-ALL cells with the BAD peptide only induced the depolarization of cells in which exogenous human BCL-2, BCL-X L , and BCL-W replaced endogenous MCL-1 ( Figure 2B, 2C, 2E). In contrast, NOXA peptide depolarized cells expressing exogenous MCL-1 and BFL-1, but not other anti-apoptotic molecules (Figure 2A and 2D). Lastly, treatment with the HRK peptide only depolarized the cells expressing exogenous human BCL-X L ( Figure 2C). As expected, DKO p185 + B-ALL leukemic cells were resistant to depolarization mediated by all BH3-only peptides, consistent with the requirement for multi-domain effector pro-apoptotic molecules for the induction of MOMP ( Figure 2F). Therefore, BH3-profiling confirmed that re-programmed leukemic cells are dependent on the exogenously expressed human anti-apoptotic BCL-2 proteins.
testing bH3-mimetic agents on engineered b-All cell lines
To demonstrate the utility of using our re-programmed p185 + B-ALL cell lines for testing potential BH3-mimetics, we cultured this panel of cell lines with various doses of BH3-mimetic small molecules. The panel of re-programmed p185 + B-ALL cells (expressing exogenous BCL-2, BCL-X L , BCL-W, BFL-1, or MCL-1) or DKO leukemic cells lacking the intrinsic apoptotic pathway were cultured with titrated doses of BH3-mimetic agents and then analyzed for induction of apoptosis 24 hours later by staining with Annexin-V and propidium iodide (PI).
We investigated the response of the panel of p185 + B-ALL cell lines to several of the most advanced BH3-mimetic agents (ABT-263 and ABT-199) which are already being tested in clinical trials. ABT-263 (navitoclax) is a BH3-mimetic that is specific for BCL-2, BCL-X L , and BCL-W, but does not inhibit MCL-1 or BFL-1 [14]. ABT-263 has shown some promise in clinical trials, but is associated with the induction of thrombocytopenia due to the requirement for BCL-X L in maintaining mature platelet survival [15][16][17]. ABT-199 (venetoclax) is a potent, specific BCL-2 inhibitor that does not inhibit other anti-apoptotic molecules and avoids the thrombocytopenia associated with inhibition of BCL-X L [18]. Venetoclax has exhibited dramatic responses in several tumor types including chronic lymphocytic leukemia (CLL) treatment and is in advanced clinical trials [19][20][21]. Treatment of the panel of p185 + B-ALL cells with navitoclax induced the cell death only of leukemic cells re-programmed to be dependent on BCL-2 (IC 50 = 94 nM), BCL-X L (IC 50 = 146 nM), and BCL-W (IC 50 = 162 nM) ( Figure 3A). In contrast, re-programmed p185 + B-ALL cells expressing MCL-1 or BFL-1 were extremely resistant to navitoclax, similar to the resistance of cells lacking the pro-apoptotic effectors BAX and BAK ( Figure 3A). When the panel was treated with venetoclax, only p185 + B-ALL cells re-programmed with human BCL-2 (IC 50 = 12 nM) responded by inducing apoptosis, while cells expressing other anti-apoptotic molecules were resistant to ABT-199-mediated killing (IC 50 > 5 µM) ( Figure 3B). Neither navitoclax nor venetoclax induced death in DKO p185 + B-ALL cells, except at high concentrations (IC 50 > 20 µM), indicating that the main mechanism of action of these agents at effective concentrations in p185 + B-ALL cells is induction of intrinsic apoptosis ( Figure 3A and 3B).
Despite the thrombocytopenia associated with BCL-X L inhibition, there is desire to generate specific BCL-X L inhibitors to aid treatment of BCL-X L -dependent malignancies. One such molecule, A-1155463 is a BH3-mimetic reported to specifically inhibit the activity of BCL-X L [22][23]. When the re-programmed leukemic cells were treated with, A-1155463, the BCL-X L expressing cells were very sensitive (IC 50 = 97 nM) and BCL-W expressing cells were also killed at higher concentrations (IC 50 = 950 nM) ( Figure 3C). A-1155463 does not induce appreciable cell death in p185 + B-ALL cells re-programmed to be dependent on BFL-1, MCL-1, or BCL-2. Furthermore, A-1155463 appears to induce death by triggering intrinsic apoptosis as we were unable to detect death induced in DKO p185 + B-ALL cells ( Figure 3C).
Elevated MCL-1 expression has been demonstrated to be an important mediator of resistance to responses to navitoclax and venetoclax [24][25][26][27]. Therefore, there is intense interest in the development of MCL-1-selective inhibiting BH3-mimetics. We evaluated three MCL-1 inhibitors that have been recently reported in the literature (UM-36, EU-5346, and A-1210477). A UM-36 is a BH3-mimetic small molecule that was reported to kill cell lines only when those cells express MCL-1 [28,29]. Another MCL-1 selective BH3-mimetic, EU-5346, from Eutropics Pharmaceuticals has been reported to induce specific killing of MCL-1-dependent cell lines [30]. A-1210477 is a tool MCL-1 inhibitor developed by AbbVie that has also been reported to induce death selectively in MCL-1-dependent cell lines [31][32][33]. When UM-36 was applied to the panel of re-programmed leukemia cells it induced apoptosis in p185 + B-ALL cells re-programmed to express human MCL-1 (IC 50 = 2.5 µM) and, to a lesser extent, in cells expressing BFL-1 (IC 50 = 3.4 µM) ( Figure 3D). In contrast, the p185 + B-ALL cells expressing other anti-apoptotic BCL-2 family members were as resistant as DKO p185 + B-ALL cells (IC 50 > 6.8 µM). These data indicate that while UM-36 may have some specificity, the potency of the molecule is very meager across all cell types. When EU-5346 was tested against the panel of re-programmed p185 + B-ALL cell lines, it was most effective at inducing killing of the BFL-1 expressing cell lines (IC 50 = 334 nM) and MCL-1 expressing cells (IC 50 = 403 nM) ( Figure 3E). In contrast, EU-5346 was not potent against cells expressing other anti-apoptotic molecules or in cells lacking BAX and BAK (IC 50 > 23 µM). These data indicate that EU-5346 exhibits some specificity to induce the death of p185 + B-ALL cells expressing BFL-1 or MCL-1. Despite the reports of efficacy of A-1210477 as a single agent in other cell types, it did not induce any selective cell death in any of our re-programmed p185 + B-ALL cells with death of BCL-2, BFL-1, and MCL-1 expressing cells only occurring at high concentrations (IC 50 > 2 µM) ( Figure 3F). At marginally higher concentrations (IC 50 = 5.3 µM) A-1210477 also induced the death of DKO cells suggesting that these concentrations it induces cell death in a BAX and BAKindependent manner.
evaluating the in vivo response of reprogrammed leukemic cell to bH3-mimetic drugs
One of the strengths of the p185 + B-ALL model system is the ability to transplant these leukemic cells into immune competent C57BL/6 recipient mice and give rise to a rapidly fatal leukemia [34][35]. Therefore, we sought to test whether the panel of re-programmed p185 + B-ALL cells could respond appropriately to BH3-mimetic treatment in immune competent recipients as a proof of principle. To this aim, we intravenously injected C57BL/6 mice with 1 × 10 5 re-programmed p185 + B-ALL cells engineered to express green fluorescent protein (GFP + ) and monitored the mice for leukemia progression. Irrespective of the expression of antiapoptotic BCL-2 family members, the re-programmed p185 + B-ALL cells in which endogenous MCL-1 was replaced by human BCL-2, BCL-X L , BCL-W, MCL-1, or BFL-1 all succumbed to a fatal leukemia with a similar kinetic ( Figure 4A). Furthermore, analyses of the peripheral blood, bone marrow, and spleens of the recipient mice all revealed similar percentages of leukemia as detected by flow cytometry for GFP expression ( Figure 4B). Therefore, the re-programmed panel of leukemic cells exhibit similar abilities to give rise to a fatal leukemia.
To demonstrate the effectiveness of using our re-programmed leukemic cell lines to validate the efficacy of BH3-mimetic agents in vivo, we transplanted 1 × 10 5 p185 + B-ALL cells re-programmed to express either human BCL-2 or human MCL-1 into C57BL/6 recipients. The leukemic cells express GFP and luciferase to facilitate their detection in the peripheral blood of recipient mice. On day 7 after transplant, recipient mice were treated either with ABT-199 (100 mg/kg) or vehicle control for 5 days at which point the treatment ceased and mice were continually monitored for leukemia progression as previously described [19]. Within 13 days, the recipient mice treated with vehicle control rapidly succumbed to leukemia irrespective of whether they were transplanted with p185 + B-ALL cells re-programmed with human BCL-2 or human MCL-1 ( Figure 4C). In contrast, 5 days of treatment with venetoclax significantly extended the survival of recipient mice transplanted with re-programmed human BCL-2 expressing leukemic cells, but did not prolong the survival of MCL-1 expressing leukemic cells ( Figure 4C). Peripheral blood analyses on day 13 demonstrate that only mice transplanted with human BCL-2 re-programmed leukemic cells responded to venetoclax treatment by decreasing the leukemic burden ( Figure 4D). These data indicate that our engineered cell lines are capable of reflecting the in vitro sensitivity even when transplanted in vivo to C57BL/6 recipients.
Despite the survival delay, even mice bearing re-programmed BCL-2-dependent p185 + B-ALL cells that were treated with venetoclax for a 5 day window eventually developed a fatal leukemia. To address whether these cells had developed resistance to venetoclax in vivo or whether the cells survived the venetoclax treatment but remained sensitive, we harvested the leukemic cells from both venetoclax and vehicle treated mice at the time of sacrifice. The ex vivo leukemic cells were cultured in the absence of growth factors or supporting stroma. To test whether these cells retained sensitivity to venetoclax, the leukemic cells isolated from recipients (both vehicle and ventoclax-treated) were treated in culture with venetoclax and compared them to the parental human BCL-2 p185 + B-ALL re-programmed cells. No difference in the sensitivity of the human BCL-2 re-programmed leukemic cells to venetoclax was detected when we compared the parental human BCL-2 p185 + B-ALL cells to those that were isolated from the venetoclax-treated recipients ( Figure 4E). These data indicate that the cells that survived the 5 days of in vivo treatment with venetoclax did not select for intrinsic cellular resistance (i.e. venetoclax insensitive), but maintained their dependence on the exogenous human BCL-2. It is possible that 5 days of treatment was insufficient to kill the leukemic cells in vivo, either due to insufficient drug exposure or the leukemia homing to niches that provided extrinsic survival signals such as cytokines [34]. Therefore when the treatment was ended, the leukemic cells that failed to die in response to venetoclax treatment emerged. These data would suggest that longer treatment with venetoclax, even as a single agent might be even more effective at delaying leukemia progression of the BCL-2-dependent leukemia.
dIscussIon
Here we report the development of a panel of engineered mouse p185 + B-ALL cells that have been re-programmed to be dependent on individual antiapoptotic BCL-2 family members. These leukemic cells, which originate from a common precursor, are completely dependent on the exogenously expressed human anti-apoptotic proteins as assessed by BH3-profiling. The re-programmed leukemic cells faithfully recapitulate the response to the most advanced BH3-mimetic small molecules that are being used in the clinic. For example, only BCL-2, BCL-X L , or BCL-W re-programmed cells were killed by navitoclax, while venetoclax was remarkably potent in killing only BCL-2 re-programmed leukemic cells.
Our re-programmed B-ALL cells confirmed that A-1155463, a BCL-X L inhibitor from AbbVie, also induces specific apoptosis of BCL-X L -expressing cells and to a lesser extent has potency in our BCL-Wre-programmed B-ALL cells. These data would predict that A-1155463 should be effective in treating BCL-X L -dependent leukemia. Indeed, A-1155463 has shown some promise in xenograft models, but it is hampered by its poor solubility and dose limiting toxicity of the vehicle [22]. We anticipate that further development will improve pharmacokinetics of this class of inhibitor, permitting dosages higher than 5 milligrams per kilogram in mouse models and oral delivery.
Our testing of MCL-1 inhibitors has unfortunately not revealed any of the tested BH3-mimetics to exhibit highly potent cell death selectively in MCL-1 -dependent cells. UM-36 appears to have modest selectivity for MCL-1, with similar response in BFL-1 -dependent leukemia, which correlates with the in vitro binding affinity of this class of MCL-1 inhibitor showing less selective inhibition of BFL-1 [29]. However, UM-36 also induces apoptosis in leukemic cells lacking BAX and BAK expression at higher concentrations, reflecting a narrow window of efficacy. Our testing of EU-5346 indicates that this inhibitor has modest potency, needing greater than 334 nM concentrations of the compound to elicit a response in cultured cells. Furthermore, re-programmed p185 + B-ALL cells expressing BFL-1 appear to be the most sensitive to EU-5346, with MCL-1 expressing cells responding at higher concentrations. Our data confirm that EU-5346 does not induce any cell death in BCL-X L -dependent cell lines, consistent with the fact that it was identified using a positive screen for MCL-1-specific inhibition and a counter screen against BCL-X L inhibition [30]. At this time, it is not possible to treat mice with EU-5346 as it has high serum binding capacity (evident even in vitro assays that require 1% serum) and is poorly soluble; however, we look forward to testing improved versions of this potentially promising small molecule.
It was reported that A-1210477 is a specific inhibitor of MCL-1 and induces cell death in MCL-1-dependent human multiple myeloma cancer cells [32,33]. However, we were unable to detect any specific induction of cell death in our re-programmed p185 + mouse B-ALL cell panel when treated with A-1210477. Several possibilities for the discrepancy exist. First, in the re-programmed p185 + B-ALL cells there may still be endogenous buffering capacity of endogenous anti-apoptotic BCL-2 family members. Therefore, the activity of A-1210477 may be insufficient to overcome this capacity due to its high in vitro specificity for MCL-1 [31,33]. This interpretation would fit with the observation that A-1210477 efficacy can be potentiated by combination with navitoclax [32]. Secondly, it is possible that A-1210477 works more efficiently in human cancer cells than it does in mice. While our re-programmed mouse B-ALL cells do express human MCL-1, all of the other molecules in the cells are murine including other anti-and pro-apoptotic proteins such as NOXA, which is quite different in mouse and human [36]. Therefore, A-1210477 and other BH3-mimetics may trigger different responses in human versus mouse cells representing a potential caveat of this system. Lastly, it is possible that different cell types www.impactjournals.com/oncotarget respond differently to A-1210477. Further work, including testing new "next-generation" MCL-1 inhibitors, should be able to clarify this question.
Interestingly, all three of the inhibitors designed to inhibit MCL-1 also appeared to have some degree of specificity for BFL-1-dependent cell lines. The reason for this is still unclear, but several possibilities exist. First, MCL-1 and BFL-1 have the most similar BH3-binding pockets of anti-apoptotic proteins; making is possible that inhibitors targeted against MCL-1 may have cross reactivity for BFL-1 [37]. Secondly, both BFL-1 and MCL-1 are short half-lived proteins; therefore it is possible that the BH3-mimetics may affect the protein stability similarly repressing MCL-1 and BFL-1 proteins [38][39][40]. Further studies will be necessary to identify why both MCL-1 and BFL-1 anti-apoptotic molecules appear to respond similarly to MCL-1 inhibiting BH3-mimetics and whether this will be a common feature of MCL-1 BH3-mimetics.
Successful screening of BH3-mimetic molecules depends upon the fidelity of the response of cell lines both in culture and in animal models. In culture, the re-programmed p185 + B-ALL cell lines faithfully recapitulate the specificity and potency of advanced Mouse condition was monitored daily and sacrificed when moribund. Asterisk (*) denotes p < 0.001 by Log Rank Test. (d) Flow cytometric analyses of peripheral blood from treated mice (as described in panel C) on day 13. Each bar represents the average and standard error of the mean of at least 5 mice per group. Peripheral blood was stained with CD19 and the GFP expression in the transplanted leukemic cells. (e) Human BCL-2 expressing p185 + B-ALL cells were isolated from moribund mice (as described in C) either treated in vivo with or with vehicle and expanded in vitro. As a comparison, the parental BCL-2 re-programmed p185 + B-ALL cells which were never injected into recipients were also treated. The cells were treated with ABT-199 in culture at indicated doses. At 24 hours, the cell viability was analyzed by staining the cells with Annexin-V and propidium iodide (PI) and quantifying the viable cells. Data displayed are the average of 3 independent experiments (n = 3) and error bars indicate the SEM.
BH3-mimetic small molecules including venetoclax and navitoclax. Therefore, we posit that our panel of re-programmed cells is ideal for the testing of next generation BH3-mimetics and is capable of determining potency, selectivity, and on-target induction of apoptosis. Furthermore, our panel of re-programmed cells can rapidly test the efficacy of BH3-mimetic molecules to induce apoptosis in vivo. The evaluation of leukemic response in vivo is important as endogenous growth factors are important mediators of resistance to response to therapy. An important strength of our system is that the cells can be frozen, thawed and injected into recipient mice without the need for lethal irradiation. This allows the cells to be banked and expanded for a cohort of mice which facilitates replicates and reproducibility. Another benefit of this system is that the recipient mice still have an endogenous immune system and thus any BH3-mimetic mediated effects on normal T and B lymphocytes can be evaluated. The re-programmed leukemic cells are marked with luciferase as well as GFP and therefore recipients can be monitored for survival by assessing endogenous luciferase luminescence using Xenogen imagery or by assessing peripheral blood for GFP expression. All of the re-programming has been done with human cDNAs encoding anti-apoptotic BCL-2 family members, allowing testing of inhibition on human and not just mouse anti-apoptotic molecules. This system allows evaluation of on-target activity and can demonstrate whether the cell death induced by BH3-mimetic small molecules is mediated by the induction of intrinsic apoptosis as we can test leukemic cells that are BAX and BAK-deficient. While this panel of re-programmed mouse B-ALL cells is clearly not a substitute for testing in human cancer cells which express different amounts of anti-apoptotic molecules, the panel has significant strengths that make it an excellent way to screen, validate, and test new BH3-mimetic inhibitors.
ecotropic retroviral production and cell transduction
Retroviruses were produced by transient transfection as previously described [44].
treatment of leukemia in recipient mice
Leukemic cells (1 × 10 5 cells per recipient) were injected into sub-lethally irradiated (5 Gy) C57BL/6 recipients (Jackson Laboratory, ME) by tail-vein intravenous route. Peripheral blood was monitored for leukemia and recipients were observed for morbidity. Seven days after the transfer of leukemic cells, mice were treated with venetoclax (ABT-199) delivered by oral gavage. Venetoclax was formulated for oral delivery (gavage) in a mixture of 60% Phosal 50 PG, 30% PEG 400, and 10% EtOH and dosed at 100 mg/kg/day as previously described [19]. Treatment was given daily for 5 days (days 7-12) after which the mice were monitored daily for signs of leukemia progression.
BH3 profiling
Compounds are from Sigma Aldrich, MO unless otherwise indicated. BH3 Peptides (New England Peptide, MA) were diluted to 2X their final concentrations in MEB (150 mM mannitol 10 mM HEPES pH 7.5, 50 mM KCl, 20 µM EDTA, 20 µM EGTA, 5 mM potassium succinate, 0.1% protease-free BSA (Gemini Bio-Products, CA) containing 10 mM 2-mercaptoethanol, 4 µM JC-1 (Enzo Life Science, NY), 20 µg/mL oligomycin (Enzo Life Sciences, NY), and 50 µg/mL digitonin. Fluotrac 200 384 well plates (Greiner Bio One, NC) were loaded with 15 µL per well of peptide/profiling solution in batches and frozen at −80°C. Peptides were used at final concentration of 10 µM for all BH3 proteins, except for NOXA (peptide derived from A BH3 domain of human NOXA) which was used at 100 µM [13]. Prior to profiling, a plate was thawed at 28°C. Cells were spun down at 500 xg for 5 min and suspended in MEB at a density of 1.33 × 10 6 per mL. 15 µL of cell suspension was added to each well of the profiling plate, 20000 cells per well, and mitochondrial potential was monitored for three hours at five minute intervals on a Safire2 plate reader (Tecan, Switzerland) using Ex 545+/− 10 nm and Em 590+/− 10 nm to monitor only the potential sensitive, red fluorescent species of JC-1. Depolarization was determined by normalizing the area under each curve to the area of the fully depolarized 10 µM CCCP well or the fully charged inert control peptide PUMA calculated at Depolarization = 1-((Sample -CCCP)/(PUMA-CCCP)) [13]. | 6,731.2 | 2016-02-05T00:00:00.000 | [
"Biology",
"Medicine"
] |
Fuzzy Control Simultaneous Localization and Mapping Strategy Based on Iterative Closest Point and k-Dimensional Tree Algorithms
In this study, we apply laser and infrared sensors to a wheeled mobile robot (WMR) for simultaneous localization and mapping (SLAM). The robot utilizes a laser measurement sensor to detect obstacles and identify unknown environments. Fuzzy theory and the iterative closest point (ICP) algorithm are applied to control design. The proposed control scheme can control the WMR movement along walls and avoid obstacles. In addition, the k-dimensional (k-D) tree is used to reduce the computation time and achieve real-time positioning. By calculating the rotation and translation matrices among different sets of measured points, distance and angle information of the moving robot can be recorded. Furthermore, the worst point rejection method is applied to delete less corresponding points that can prevent the ICP process convergence to a local optimum.
Introduction
The wheeled mobile robot (WMR) is the most used carrier in mobile robot applications. It has some good properties such as high-speed mobility, easy control, and energy storage capacity. (1,2) Simultaneous self-positioning, environment map building, path planning, and obstacle avoidance are essential abilities for autonomous mobile robots. With the installation of various sensors or tools, mobile robots can be applied to multipurpose applications such as home services, medical care, entertainment, space exploration, military, and industrial automation. In this study, we focus on unknown environment exploration. Precise position estimation is one of the core issues in simultaneous localization and mapping (SLAM) research. In ref. 3, the sensor network provided an effective method for a mobile robot to adapt to changes and guided it across a geographical network area. To enhance the performance, a charge-coupled device camera and artificial landmarks were used for self-localization. (4) Hwang and Song (5) examined the monocular-vision-based SLAM of a mobile robot using an upward-looking camera. Gallegos and Rives (6) described a composite sensor approach that combined the information given by an omnidirectional camera and a laser range finder to efficiently solve the indoor SLAM problem. Most of the studies applied image processing to obtain feature points; the process was complex and time-consuming. Another drawback is that most visual sensors are sensitive to the light source, and the brightness will affect the result of image processing and its accuracy. The positioning systems currently known and widely used are laser scanning positioning systems, odometer calculation positioning systems, image video positioning systems, and ultrasonic sensing systems. In this study, the laser measurement sensor is used owing to its high accuracy, high receiving rate, and wide scanning range. Moreover, the laser is not affected by light and is very suitable for indoor usage. It has sufficient time for position calculation in real time using the iterative closest point (ICP) algorithm (7) and achieves positioning in an unknown environment. Fuzzy theory is applied to control the movement of the WMR.
System Setup
A WMR called Ihomer (2) is used in the entity test, as shown in Fig. 1(a). The control scheme mainly uses a laser measurement sensor SICK-LMS100, which is placed on top of the WMR, to detect the unknown environment around the WMR. Two wheels are located at the left and right sides under the body of the WMR and are driven by two 18 V DC motors. Two small casters are located at the rear and front under the body of the WMR. They support the balance and movement of the WMR. The encoders, which are located at the sides of the wheels, provide the measured value of the body movement. The receivers of the LMS100 measure the object distance and help collect information that is used for building the map and wall-following. Dynamic analysis of the moving distance and turning angle of the WMR can be found in ref. 4. The WMR is located on the Cartesian coordinate system (global coordinate system) with no lateral or sliding movement, as shown in Fig. 1
Wall-following
There are two common inputs of the proposed fuzzy controller for speed and angle control, which are the detected distances dr and r, where r is r = dfr cos(45°) − dr, as shown in Fig. 2.
The input variable for the distance dr is SR_r, and the fuzzy values are very near, near, medium, far, and very far. Fuzzy values of the input r are large negative, negative, medium, positive, and large positive. The output variable for turning angle is TA, and the fuzzy values are TR3, TR2, TR1, TZ, TL1, TL2, and TL3, which represent the angles turn right very large, turn right large, turn right, go forward, turn left, turn left large, and turn left very large, respectively. Fuzzy speed is selected on the basis of distance factor. Some examples of the control rules for turning angle are shown in Table 1.
Improved simultaneous localization and mapping
When accessing the door of an unexplored room, the control system starts to record the coordinates and angles, which are calculated using the ICP algorithm. The ICP uses two different curves from LMS100 as inputs, and the outputs are rotation and translation matrices. The curves are sets of 180 points from 0 to 180°. The characteristics can be used to find the modified rotation and translation matrix to revise the imprecise data VN TL3 TL1 TZ TZ TZ N TL2 TR1 TZ TZ TZ M TL2 TL1 TZ TZ TZ F TL2 TL1 TZ TR1 TR1 VF TL2 TL1 TZ TR2 TR3 from the robot encoder. There are three disadvantages of the ICP algorithm. The first one is that the computation time of the ICP algorithm is very long to be used in real time. To reduce the computation time in the process and achieve real-time positioning, the k-dimensional (k-D) tree (8) is applied to this study. The second disadvantage is the accumulated error. When the turning angle and environment changing rate are both small, a strategy of reducing the number of reads (9) is applied to obtain the rotation angle and displacement. The third problem is that the ICP algorithm usually converges to a local optimum. To avoid this situation, in this study, we apply strategies of increasing the initial angle and worst point rejection (10) to map building when the turning angle of the WMR and the environment changing rate are both large.
Iterative closest point algorithm
The ICP is often used to reconstruct 2D or 3D surfaces from different scans. It iteratively revises the translation and rotation, and minimizes the distance between the points of two different curves. In general, the ICP uses two different curves as inputs, and the outputs are rotation and translation matrices. The characteristics can be used to find the modified rotation and translation matrix to revise the incorrect data from the encoder of the robot. The ICP algorithm is described as follows. (7) Step 1: Define the data model of data shape (P) and model shape (X) as Here, n and k are the total numbers of data. The data measured by the LMS100 is a set of distance r and angle θ. Record a distance every 0.5° from −45 to 225°. At each iteration, 180 points are retrieved, from 0 to 180°. Then, use eq. (2) to translate polar coordinates to Cartesian coordinates.
After data processing, set a threshold value, which is the stopping condition of the ICP. If the mean square error is greater than the threshold value, then continue to repeat the process at each iteration. The threshold is the mean square error calculated using X and a new data shape (updated P). When the process achieves convergence and the mean square error is less than the threshold, stop the calculation process.
Step 2: After initial setting, find the correspondence between two sets of P and X. The corresponding relationship is the shortest distance between corresponding points in the ICP algorithm. Find the minimum distance from the point p i on X. The corresponding point a i is stored in A shape. The corresponding relationship is calculated as d min i = min d(p i , X) i=1,...,n .
Step 3: The geometric transformation matrix consists of two types of rotation and translation matrices. First, calculate the center of mass. p i and a i are points of P and A, respectively. N p and N a are numbers of P and A, respectively. By using the following equations, the rotation angle and displacement between the two data can be obtained as With the center of mass, calculate the cross covariance matrix between P and A.
Here, I 3 is the 3 × 3 identity matrix. The unit eigenvector q = [q 0 q 1 q 2 q 3 ] T corresponding to the maximum eigenvalue of the matrix Q(Σ pa ) is selected as the optimal rotation.
The optimal translation vector is given by Step 4: D is the data shape (P) and m is the number of iterations.
The changes in displacement and angle at each iteration can be obtained. Then, add the changes in displacement and angle individually. When the process achieves convergence and the mean square error is less than the threshold, the final displacement and angle are the displacement and angle between two different curves.
k-D tree
One of the most well-known data structures suitable for the ICP algorithm is the k-D tree. (8) The k-D tree can reduce the computation time and find the significant corresponding point. It is a space-partitioning data structure for organizing points in a k-D space. The k-D tree is a binary tree in which every node is a k-D point. Every nonleaf node can be considered as implicitly generating a splitting hyperplane that divides the space into two parts, known as half-spaces. Points to the left of this hyperplane are represented by the left subtree of that node, and points to the right of the hyperplane are represented by the right subtree. The hyperplane direction is chosen in the following manner: every node in the tree is associated with one of the k dimensions, with the hyperplane perpendicular to the axis of that dimension. Two experiments are carried out to compare the computation time. The results are shown in Table 2. The computation time obtained by using the k-D tree with ICP is shorter than that without the k-D tree. Its computation time is less than the SLAM's sampling time of 0.5 s; thus, realtime positioning can be achieved.
Reducing the number of reading cycles
Reducing the number of reading cycles (9) means a smaller number of alignments and less accumulated error. Consecutive data is not used since 1 s of computation time cannot tell the difference between the original ICP and the less-reading-cycle ICP. Here, a 20-s test is performed. Let the WMR continuously move straight forward for 20 s. The moving distance of the WMR measured is 197.82 cm, and that calculated using the lessreading-cycle ICP is 196.12 cm, as shown in Fig. 3, where the red dotted line is the track of the WMR, the blue dotted lines are the calculated results, and the solid black lines are the actual walls.
Worst point rejection
When the WMR turns at a large rotation angle, delete the points that do not correspond to the model shape. (10) Points that do not correspond make the ICP process converge to a local optimum. Thus, the predicted angle is used. The predicted angle is in accordance with the turning angle, and then carry out some fine tuning to fit the actual condition. The deleted points are according to the predicted angle and one point at each 0.5°. For example, if there are 20 points at 10°, we delete some points at the tail of the data shape and the head of the model shape. Figure 4 shows the comparison of the original ICP and the ICP with the worst point rejection. In the test, the WMR, i.e., the red dot on the map, turns left at 90°.
Experimental Results
The improved SLAM strategy was tested in different environments. One of the experimental results is shown in Fig. 5. The left part of the figure is the real situation of the WMR and the right part is the map of the scanned environmental data and the path calculated using the ICP algorithm, where the red lines are the WMR's moving path, and the yellow points are environmental data. Without the weighting process, the map can be obtained as the dashed line in Fig. 6(a). Compared with the real contour of the unknown environment, the average error is 3.8 cm. Furthermore, with the weighting process that gives more weight to the old data and the weights are descending with the new data, the result is shown in Fig. 6(b). The average error decreases to 1.6 cm. In this experiment, the WMR took 2 min and 6 s to complete the exploration using the improved SLAM strategy.
Conclusions
In this study, a control scheme based on an improved SLAM strategy and fuzzy logic theory is proposed to control a mobile robot for building an unknown environment map. In this research, we apply a laser measurement sensor to mark obstacles and positions. According to the laser measurement sensor's location and the detected distance between the sensor and the object, map building can be completed after the environmental exploration is finished. The task of building an unknown environment map can be accomplished without using visual images. In previous studies, the SLAM based on visual sensors is sensitive to the light source that affects the accuracy of the image process. In this study, the laser sensor is not affected by light; even in a dark room, it still works properly. Real-time PC-based control of the WMR on wall-following and map building is performed successfully. Moreover, in this study, a modified ICP algorithm is presented. It uses the k-D tree to reduce the computation time, less-reading-cycle ICP to reduce the number of alignments and the accumulated error, and the worst point rejection method to delete less corresponding points and prevent the ICP process convergence to a local optimum. Experiments show that the average error is less than 2 cm, which is better than the results of most of the previous studies. | 3,311 | 2015-01-01T00:00:00.000 | [
"Engineering",
"Computer Science"
] |
Homogeneous Black Strings in Einstein-Gauss-Bonnet with Horndeski hair and beyond
In this paper we construct new exact solutions in Einstein-Gauss-Bonnet and Lovelock gravity, describing asymptotically flat black strings. The solutions exist also under the inclusion of a cosmological term in the action, and are supported by scalar fields with finite energy density, which are linear along the extended direction and have kinetic terms constructed out from Lovelock tensors. The divergenceless nature of the Lovelock tensors in the kinetic terms ensures that the whole theory is second order. For spherically, hyperbolic and planar symmetric spacetimes on the string, we obtain an effective Wheeler's polynomial which determines the lapse function up to an algebraic equation. For the sake of concreteness, we explicitly show the existence of a family of asymptotically flat black strings in six dimensions, as well as asymptotically AdS$_{5}\times R$ black string solutions and compute the temperature, mass density and entropy density. We compute the latter by Wald's formula and show that it receives a contribution from the non-minimal kinetic coupling of the matter part, shifting the one-quarter factor coming from the Einstein term, on top of the usual non areal contribution arising from the quadratic Gauss-Bonnet term. Finally, for a special value of the couplings of the theory in six dimensions, we construct strings that contain asymptotically AdS wormholes as well as rotating solutions on the transverse section. By including more scalars the strings can be extended to $p$-branes, in arbitrary dimensions.
I. INTRODUCTION
Higher dimensional General Relativity (GR) possesses a broader spectrum of black hole solutions as compared with its four dimensional formulation [1,2]. Indeed, four dimensional GR is constrained by uniqueness theorems [3][4][5] that ensure that any black hole solution of the theory is contained in the Kerr family [6,7]. Moreover, topological restrictions allow only for horizons with spherical topology [8]. The spectrum of solutions is limited not only quantitatively but also qualitatively, setting the final state of black hole collapse to be described only by a small set of parameters [9]. On the other hand it is well-known that gravity in higher dimensions admits spacetimes with horizons that can have more general topologies than that of the (d − 2)-sphere [1,2], being the existence of black strings, a black hole solution with horizon structure S (d−3) × R, the simplest counterexample [3][4][5] as it coexists with the Schwarzschild-Tangherlini black hole [10]. Black strings also paved the road for the construction of more sophisticated asymptotically flat solutions with non-spherical topology such as black rings [11] and diverse black object solutions [2], demonstrating how topological restrictions [8] are weakened in higher dimensions. It was shown that black strings are affected by Gregory-Laflamme (GL) instability [12,13], a long-wavelength perturbative instability triggered by a mode that travels along the extended direction of the horizon and, moreover in dimension five the numerical simulations indicate that the instability ends in the formation of naked singularities [14,15], representing an explicit failure of the cosmic censorship in higher dimensions [16] 1 .
Black strings in GR in vacuum are easy to construct. In fact they are obtained by a cylindrical oxidation of the Schwarzschild black hole in d dimensions by the inclusion of p extra flat coordinates. This can be realized by seeing that the equations of motion along the extended directions are compatible with the field equations on the p-brane, due to the fact that the involved curvature quantities vanish on these coordinates.
Notwithstanding it is not hard to find simple scenarios in which the construction of analytic black strings fails. Indeed, the mere inclusion of a cosmological constant spoils the existence of cylindrically extended black strings, since the compatibility of the equations of motion on the flat coordinates with the trace of the field equations along the brane forces Λ to vanish. This implies that there is no simple oxidation of the Schwarzschild (A)dS black hole 2 .
In [19] two of the authors have shown that GR with a negative cosmological constant does admit exact, homogeneous black string solutions if each extended flat coordinate is dressed with a massless, minimally coupled scalar field that depends exclusively on that coordinate 3 .
To see this explicitly let us take the following black string ansatz in which a d-dimensional black hole is oxidated by including p flat directions where i, j = 1, 2, . . . , p and dΣ 2 d−2,K stands for a (d − 2)-dimensional Euclidean manifold of constant curvature K = 0, ±1. By virtue of the ansatz (1), the massless Klein-Gordon equations deliver scalar fields that depend linearly on the extended flat directions the λ (j) being integration constants. These scalars cure the incompatibility between the equations of motion on the brane and the extended directions leading to the metric where compatibility is ensured provided .
This solution represents the black string version of the Schwarzschild-AdS black hole and shows that the three-dimensional BTZ black hole can be also uplifted to a higher dimensional black string 4 .
A natural question arises: As higher dimensional objects, do homogeneous and cylindrically extended black strings and black p-branes exist in higher curvature extensions of GR?
In this paper we answer this question affirmatively for the Einstein-Gauss-Bonnet as well as for general Lovelock theories with arbitrary values of the coupling constants. To successfully 2 Numerical as well as perturbative solutions have been constructed in [20] in GR as well as in gauged supergravity in five dimensions. 3 Previously, AdS black strings in GR were constructed considering warped spacetimes [21] providing nonhomogenous configurations. 4 This can also be achieved in the Einstein-Skyrme system [27] and even more by using this approach, diverse BTZ black strings have been recently constructed in theories with non-trivial torsion [28]. apply the procedure before described, we shall observe that the extended directions must be dressed with scalar fields of the type (2) that have non-minimal kinetic couplings, such that the extra higher curvature terms involved in Lovelock theories do not break the compatibility of the field equations. Such couplings must fulfil the following requirements: They must enjoy shift symmetry, which allows the inclusion of non-minimal kinetic couplings. Secondly, their contribution to the equations of motion must be of the same type as that of the Lovelock terms under consideration. These types of non-minimal kinetic couplings arise naturally in Galileon/Horndeski theory namely, the most general scalar-tensor theory with second order field equations for both, the metric and the scalar field. Originally constructed in the early seventies, Horndeski theory [30] has re-emerged after the appearances of Galileon theories [31][32][33] mostly motivated by their several applications in cosmology [34][35][36]. The Horndeski Lagrangian, which has been constructed in four dimensions, has a non-minimal kinetic sector given by where G AB is the Einstein tensor. This term was extensively considered not only in cosmology [37][38][39][40][41] but also in the study of compact objects such as black holes and neutron stars [42][43][44][45][46][47][48][49][50]. We will see that the higher dimensional generalizations of this term are precisely the kind of couplings we need to consider in order to construct homogeneous black strings in Lovelock gravity. The shift invariant scalars will provide the dress we need in order to ensure compatibility of the equations of motion.
This paper is organized as follows: To fix ideas, Section II is destined to construct homogeneous black strings in Einstein-Gauss-Bonnet theory dressed by two scalar fields, a minimally coupled one accounting for the inclusion of the cosmological constant and a nonminimally coupled one accounting for the new R 2 curvature terms we are including. We present the equations in arbitrary dimension D = d + 1, nevertheless for the sake of con- in Section V we outline our conclusions and further developments that can follow this work.
II. HOMOGENEOUS BLACK STRINGS IN EINSTEIN-GAUSS-BONNET THE-ORY
Let's consider the Einstein-Gauss-Bonnet theory in arbitrary dimension coupled to two scalar fields as follows: where L GB := R 2 − 4R AB R AB + R ABCD R ABCD defines the Gauss-Bonnet term. Performing the variations respect to the metric and the scalar fields we obtain the following set of field where the Gauss-Bonnet tensor is given by and the energy-momentum tensors for the scalars read Note that the equations (9) are linear on the scalars.
On a metric of the form and scalars that depend only on the extended direction z, the equations for the scalars imply a linear dependence on z. The shift symmetry of the scalar field theories can be used to set to zero the additive integration constants that appears in both scalars. So we have with c 0 and c 1 , integration constants. Then, the trace of the field equations on the ddimensional manifold and the equation along the z direction respectively read whereR andL GB are the intrinsic Ricci scalar and Gauss-Bonnet combination of the ddimensional manifold with line element ds d . To avoid incompatibilities these two equations must be proportional term by term, i.e. E 1 = ξE 2 and therefore, when the higher curvature Gauss-Bonnet term is present, one obtains that the proportionality constant must be fixed as well as the integration constants of the scalars, leading to 5 Under these conditions, we will have a solution of the theory (6) in arbitrary dimension provided the d−dimensional metric ds 2 d fulfils the Einstein-Gauss-Bonnet field equations with the following rescaled couplings 5 Note that when α = 0, one obtains only two equations for the three constant ξ, c 0 and c 1 , leading to for an arbitrary ξ. Since we are interested in the inclusion of higher derivative terms, we do not elaborated further in the case α = 0.
Bonnet tensor for the d−dimensional metric ds 2 d on the constant z section of the black string 6 (10). SinceH µν vanishes identically in dimensions d ≤ 4, to have a non-vanishing contribution from the Gauss-Bonnet tensor, we need d ≥ 5 (in d = 4 the equation (16) is identically fulfilled for any metric and the system is degenerate at such point).
For simplicity, let's focus on the six dimensional case and consider the homogeneous black string metric where dΣ 3,K is the line element of an Euclidean, three-dimensional constant curvature manifold of curvature K, and assume that the scalars depend only on the z direction.
The explicit z-dependence of the scalars is fixed by the scalar equations to be linear, giving rise to and the metric function has to solve the following quadratic, polynomial equation where m is an integration constant and V Consequently, for the spherically symmetric case, the metric describes an asymptotically flat, homogeneous black string, with a regular horizon, in the six-dimensional Einstein-Gauss-Bonnet theory supported by a scalar field with an Einstein-kinetic term. These are the first known asymptotically flat, analytic and homogeneous black string solutions in general relativity with a Gauss-Bonnet term.
From the expression (18) we see that the bare cosmological constant must fulfil Λ 0 ≤ 0, therefore, for simplicity and without loosing generality, let us set For positive values of the Gauss-Bonnet coupling (α > 0) and spherically symmetric spacetimes on the brane (K = 1) only the branch with the negative sign in (21) might lead to an event horizon. In this case, the asymptotic behavior of the metric is which induces an upper bound on the Gauss-Bonnet coupling 0 < α < 9 16 , where we have defined 1 Then, the asymptotic behavior of the metric on the brane is that of the AdS 5 spacetime and the subleading term is controlled by the integration constant m, leading to a finite mass contribution (mass density if one considers the extended direction). Considering α positive and l 2 to be the curvature radius of the brane at infinity, leads to the restriction 9 2 < l 2 < 9. Wald's formula [51] can be used to obtain the following entropy per unit length of the string s = 4π 3 r 3 where r + is the horizon radius. Here we note that the Einstein contribution to the entropy receives a correction from the matter sector. Since in this case the Bekenstein-Hawking entropy should be A 4G = 8π 3 r 3 + L (with 16πG = 1). As expected on dimensional grounds, the term proportional to the Gauss-Bonnet coupling depends linearly on the horizon radius. As occurs for black holes, the entropy of the planar horizons do not receive corrections from the higher curvature terms.
The temperature is fixed in order to obtain a smooth Euclidean continuation on the horizon and is given by One can see that, identifying the integration constant m with the mass density, the thermodynamical quantities fulfil the first law dm = T ds .
Since the integration constants of the scalars are fixed in terms of the couplings, it is natural to expect that the first law does not receive contributions from the matter sector. A plot with different profiles for the function f (r) is presented in figure 1, for both the asymptotically flat (left panel) and asymptotically AdS solutions (right panel).
We have therefore shown that the inclusion of the non-minimal Einstein-kinetic coupling (5) allows to construct black strings in Einstein-Gauss-Bonnet theory, for arbitrary values of the coupling constants of the theory.
As mentioned above, the obstruction to the existence of cylindrically oxidated solutions comes from the incompatibility between the trace of the field equations on the brane and the equation along the extended direction. The scalar fields ψ and χ provide a natural manner to circumvent this incompatibility even in the asymptotically flat case. Below, we give a detailed explanation of the mechanism behind the existence of these solutions for general Lovelock theories, and show that the results can be extended beyond Einstein-Gauss-Bonnet by the inclusion of scalars with non-minimal kinetic coupling to Lovelock tensors, that naturally extend (5).
III. HOMOGENEOUS BLACK STRINGS IN GENERAL LOVELOCK THEORY
Let us supplement the Lovelock action by quadratic scalars in the following form where the Lovelock Lagrangians are given by and each of the matter fields φ (k) = {ψ, χ, ...} with k = 0, 1, ..., n , have different dynamics controlled by the Lagrangian which couples the k-th scalar directly to the k-th order Lovelock tensor E Varying (29) with respect metric g AB we obtain the field equations with the Lovelock tensor of order k defined as Furthermore, the energy-momentum tensor associated with the k-th scalar φ (k) is given by T (k) On the other hand, by varying the action with respect to field φ (k) , we obtain the field Below we will show that these equations admit homogeneous black strings by requiring the trace of the equations on the brane to be compatible with the equation along the extended direction.
We consider the ansatz where and the scalar fields depending only on the extended coordinate. The equations for the fields (35) imply that the scalars are linear in the extended direction, and the invariance under constant shifts of the matter actions can be used to write Here To explain the previously mentioned compatibility, we will be as explicit as possible in what follows. The field equations (32) read Then, introducing (36) and (38) into equation (39), we obtain the equations with free indices on the string E µν = 0 which imply and the equation along the z direction E zz reads −α Here we have introduced for simplicity both sets of shifted gravitational couplingsα k and α k , given respectively byα In general, the compatibility of the equationsg µν E µν = 0 and E zz = 0 will induce further restrictions on the metric function f (r) than those that come only from the equations on the brane E µν = 0. We can circumvent this clash by imposing the off-shell requirement g µν E µν ∼ E zz and introducing a proportionality constant ξ one obtainŝ and ξ (d − 2 (n + 1)) = 1 .
These equations allow to fix the proportionality constant ξ as well as the n integration constants c k for all the scalars in the following manner Then, the equations on the brane, reduce to an effective Wheeler-like polynomial that reads where m is an integration constant and V (K) d−2 stands for the volume of manifold with line element dΣ K,d−2 . This leads to a black string in a general Lovelock theory of gravity that can be asymptotically flat or asymptotically AdS depending of whether we include a cosmological term in the action. The temperature and the entropy of the corresponding black hole are respectively given by and and it can be checked that the first law dm = T ds is fulfilled, which lead to the interpretation of the integration constant m as the mass density.
The compatibility of the equationsg µν E µν = 0 and E zz = 0 is ensured for a general metric on the transverse section of the string, and the scalars allow to cylindrically extend any solution of Lovelock theory from dimension d to dimension d + 1. This will be exploited in the next section.
IV. EXTRA PHYSICALLY INTERESTING SOLUTIONS
As usual in Lovelock theories, from the polynomial equation (47) This theory admits a cylindrically extended wormhole solution with line element given by dressed by the scalars provided and The metric (52) It is interesting to notice that even though the latter solution has a simple warped structure in five dimensions, one can also embed in a similar manner, a rotating solution of the effective five dimensional Chern-Simons theory, into dimension six. Explicitly the following metric is a solution of the field equations: where ds L is the line element of AdS 5 with curvature radius L, in double oblate coordinates, i.e.
, and ρ 2 (r, µ) = r 2 + a 2 µ 2 + b 2 (1 − µ 2 ) . The scalar fields are given by (53) and the relations (54) and (55), hold. Note that l is a constant defined by the theory, while L is an integration constant as well as a and b. The latter are the so-called oblateness parameters. Since the vector field k defines a null and geodesic congruence of the background metric ds L , the metric (56) is a cylindrical oxidation of a Kerr-Schild metric in AdS 5 . The five dimensional metric in the section of the string defines the first known exact, analytic, rotating solution of Einstein-Gauss-Bonnet in five dimensions and it was originally found in [55]. It was also latter proven to be of the non-circular type in [56] 7 .
V. FINAL REMARKS
Until now in higher curvature gravity, exact and homogeneous black string solutions have been constructed only for special values of the coupling constants [22,23] also including pform fields [24], and the general problem of the construction of Lovelock branes was studied in [25], and for arbitrary values of the couplings only numerical or perturbative solutions were available (see e.g. [26]). In this paper we have constructed new, exact, homogeneous black strings in arbitrary Lovelock theories. The solutions are supported by scalar fields with non-minimal kinetic couplings constructed with Lovelock tensors, ensuring that the field equations are of second order. These scalars have been previously considered as part of the higher dimensional extension of Horndeski theories in [58,59]. Here, the scalars being dependent only on the coordinate along the extended direction, turn out to be linear, and the proportionality constant gets fixed by the requiring the compatibility of the whole system.
The transverse section of the string can be asymptotically flat or AdS. For concreteness we computed the thermodynamic quantities and showed that the entropy of the black string receives a contribution from the matter part. This is interesting because the pattern of transitions between black string and black hole can change due to the presence of the new Horndeski fields. The gravitational stability of the black string and p-branes in the presence of a single quadratic or cubic Lovelock term has been studied in [60]- [62], while the effect of quartic corrections coming from M-theory have been explored in [63]. It is interesting to mention that the Large D approach [64] allows to keep all the terms in the Einstein-Gauss-Bonnet Lagrangian [65].
For simplicity we focus on the case with a single extended direction, but this construction also works with p-branes. For example, in the Einstein-Gauss-Bonnet theory, with a cosmological constant, one would have to consider p minimally coupled scalars mimicking such of reference [19], as well as p scalars with Einstein-kinetic couplings which would also turn out to be linear and depending on a single extended direction. From this, the extension to arbitrary Lovelock theories, with flat p-branes is clear.
Interpreting our solutions as compactifications with non-trivial scalar fluxes along the extended direction, one obtains an effective Lovelock theory induced on the brane. We exploited this idea to construct cylindrically extended solution with wormholes on the transverse section, which are asymptotically AdS 5 ×R, in both directions. Within the same realm we also constructed a cylindrical oxidation of the rotating spacetime of Einstein-Gauss-Bonnet gravity, constructed from a Kerr-Schild ansatz in [55]. The wormhole solution can of course be extended to AdS 2n−1 × R provided one considers Lovelock theory with all the possible terms in dimension 2n. In such case, the wormhole on the string will be the one reported in [53]. | 5,006.4 | 2018-10-05T00:00:00.000 | [
"Mathematics"
] |
Parasitics Impact on the Performance of Rectifier Circuits in Sensing RF Energy Harvesting
This work presents some accurate guidelines for the design of rectifier circuits in radiofrequency (RF) energy harvesting. New light is shed on the design process, paying special attention to the nonlinearity of the circuits and the modeling of the parasitic elements. Two different configurations are tested: a Cockcroft–Walton multiplier and a half-wave rectifier. Several combinations of diodes, capacitors, inductors and loads were studied. Furthermore, the parasitics that are part of the circuits were modeled. Thus, the most harmful parasitics were identified and studied in depth in order to improve the conversion efficiency and enhance the performance of self-sustaining sensing systems. The experimental results show that the parasitics associated with the diode package and the via holes in the PCB (Printed Circuit Board) can leave the circuits inoperative. As an example, the rectifier efficiency is below 5% without considering the influence of the parasitics. On the other hand, it increases to over 30% in both circuits after considering them, twice the value of typical passive rectifiers.
Introduction
With the rapid development of wireless communications in the latest years, there has been an exponential increase in the number of radiofrequency (RF) transmitters operating in VHF and UHF bands. As a consequence, ambient RF power density has increased and RF energy harvesting has become an environment-friendly energy source for low-consumption electronic devices, such as sensors, regulators, oscillators and LCD screens [1,2]. Additionally, RF energy is present both indoors and outdoors, which is an advantage with respect to other harvestable sources. The most significant power contribution normally comes from mobile network (0.8, 0.9, 1.8, and 2.1 GHz) and WiFi frequency bands (2.4 and 5.2 GHz). Specifically, previous works have demonstrated that most part of the incoming RF power has its origin in mobile bands [3][4][5]. Concretely, Ref. [5] points out that more than an 80% of the power harvested is located in 0.8 and 0.9 GHz frequency bands.
Rural and remote areas are especially interested for looking at self-sustaining sensing systems due to the difficulty of access to them. Low-power sensors can benefit from the use of RF harvesting systems and be deployed in these challenging environments, forming wireless sensor networks (WSNs) [6] applied in, e.g., tracking and farming tasks [7,8] or monitoring fire risk areas [9]. As an example, Figure 1 shows a possible implementation of a low-power WSN formed by independent. Autonomous nodes. Each node is powered by a RF harvesting system, formed in four stages [10]: a RF harvester, a receiving antenna that collects energy from the bands of interest; a rectifier circuit that converts the signal acquired by the antenna into a DC supply source; a matching circuit, in charge of maximizing the power transfer from the antenna to the rectifier circuit; and a storage circuit, which stores the acquired power in order to feed a certain electronic device.
Nowadays, the bottleneck in energy harvesting is the design of the rectifier circuit. This is partially attributed to the losses present in the diodes. The low input power level provokes the diodes into dissipating an important part of the incoming power. Specifically, RF harvesting systems must operate with lower power densities [3][4][5] compared to other harvestable sources, such as the sun, wind or vibrations [11]. Moreover, the nonlinearity associated with the diodes represents an added difficulty [12]: the performance of the entire system is dependent, among other parameters, on the input power, which unfortunately hampers the design of the matching circuit. Because of these combined facts, the efficiency of different topologies of passive circuitries (not externally fed) is normally under 15% [10,[12][13][14]. On the other hand, there are some recent studies that have applied active circuits (externally fed) [14,15] in order to lower the threshold voltage of diodes/transistors. In these cases, the component losses are reduced and the efficiency enhanced, at the expense of using an external feed, which is prohibitive for self-sustaining devices [16,17].
The most commonly used topology for a passive rectifier circuit is the half-wave rectifier. It benefits from a simpler design and lower losses compared to full-wave schemes [18], since only one diode is required. On the other hand, the low-voltage input levels make multiplier circuits, such as the Cockcroft-Walton (CW) multiplier [14], an interesting option to consider. At least two diodes are needed in this configuration, so the losses are similar to those of a full-wave rectifier but higher compared to a half-wave rectifier. As opposed to the full-wave rectifier, the CW multiplier is capable of elevating the input voltage while rectifying. Ideally, the more stages are placed, the higher the output voltage is. However, the losses in the diodes typically prevent one from using more than one stage in the CW multiplier, since the efficiency rapidly decays.
In addition, there is a need for a circuit model that is capable of predicting how the parasitics affect the operation of the system. Regretfully, the vast majority of papers in the literature do not provide a clear insight on the matter. In this paper, we present a design methodology to maximize the power supplied to the sensor by taking into account the nonlinearity of the circuits and the effect of the parasitic elements. We study two different configurations: the half-wave rectifier and the CW multiplier. However, the steps followed in the document can be extrapolated, without loss of generality, to any other configuration. According to the estimations of the incoming power provided in [3][4][5], the circuits are designed to operate within 800-900 frequency bands, the center frequency Autonomous nodes. Each node is powered by a RF harvesting system, formed in four stages [10]: a RF harvester, a receiving antenna that collects energy from the bands of interest; a rectifier circuit that converts the signal acquired by the antenna into a DC supply source; a matching circuit, in charge of maximizing the power transfer from the antenna to the rectifier circuit; and a storage circuit, which stores the acquired power in order to feed a certain electronic device.
Nowadays, the bottleneck in energy harvesting is the design of the rectifier circuit. This is partially attributed to the losses present in the diodes. The low input power level provokes the diodes into dissipating an important part of the incoming power. Specifically, RF harvesting systems must operate with lower power densities [3][4][5] compared to other harvestable sources, such as the sun, wind or vibrations [11]. Moreover, the nonlinearity associated with the diodes represents an added difficulty [12]: the performance of the entire system is dependent, among other parameters, on the input power, which unfortunately hampers the design of the matching circuit. Because of these combined facts, the efficiency of different topologies of passive circuitries (not externally fed) is normally under 15% [10,[12][13][14]. On the other hand, there are some recent studies that have applied active circuits (externally fed) [14,15] in order to lower the threshold voltage of diodes/transistors. In these cases, the component losses are reduced and the efficiency enhanced, at the expense of using an external feed, which is prohibitive for self-sustaining devices [16,17].
The most commonly used topology for a passive rectifier circuit is the half-wave rectifier. It benefits from a simpler design and lower losses compared to full-wave schemes [18], since only one diode is required. On the other hand, the low-voltage input levels make multiplier circuits, such as the Cockcroft-Walton (CW) multiplier [14], an interesting option to consider. At least two diodes are needed in this configuration, so the losses are similar to those of a full-wave rectifier but higher compared to a half-wave rectifier. As opposed to the full-wave rectifier, the CW multiplier is capable of elevating the input voltage while rectifying. Ideally, the more stages are placed, the higher the output voltage is. However, the losses in the diodes typically prevent one from using more than one stage in the CW multiplier, since the efficiency rapidly decays.
In addition, there is a need for a circuit model that is capable of predicting how the parasitics affect the operation of the system. Regretfully, the vast majority of papers in the literature do not provide a clear insight on the matter. In this paper, we present a design methodology to maximize the power supplied to the sensor by taking into account the nonlinearity of the circuits and the effect of the parasitic elements. We study two different configurations: the half-wave rectifier and the CW multiplier. However, the steps followed in the document can be extrapolated, without loss of generality, to any other configuration. According to the estimations of the incoming power provided in [3][4][5], the circuits are designed to operate within 800-900 frequency bands, the center frequency being 870 MHz. Several combinations of components were tested in both circuits. Thus, the most harmful parasitics in the circuits were identified and modeled. The experimental results show that a proper modeling of the parasitic elements is fundamental in order to avoid a low conversion efficiency in the rectifiers.
The document is organized as follows. Section 2 presents the design methodology and the different steps involved in it. Section 3 gives useful insights on the choice of components. Section 4 describes the design of the matching circuit and the search for the optimal source impedance that maximizes the rectifier efficiency. Section 5 presents the model of the parasitics and their influence on the overall performance of the circuits. Finally, Section 6 presents the main conclusions.
Design Process
Due to the nonlinearity of rectifier circuits, their input impedance (and their response) is dependent on many parameters: the input power, the antenna impedance, the load impedance (the type of sensor we use), the operation frequency, etc. Furthermore, the rectifier cannot be directly attached to the antenna, since there exists an impedance mismatch between both, which translates into a low rectifier efficiency. Consequently, a matching circuit is commonly placed between the antenna and the rectifier to maximize the power transfer. However, the design of the matching circuit suffers from the same problems associated with the nonlinearity of the rectifier.
The design method that overcomes these difficulties and maximizes the rectifier efficiency is presented in Figure 2, as an iterative process. First, we must select the components that are part of the rectifier circuit, trying to reduce the losses in the diode and the output voltage ripple of the rectified DC signal. Then, we must design the matching circuit. The design of the matching circuit is based on the search, for a given load Z L , of the optimal source impedance Z s that maximizes the power transfer between the antenna and the rectifier. Thus, the components of the matching circuit are estimated in order to maximize the rectifier efficiency. However, the parasitics of the components and PCB (Printed Circuit Board) do influence the search of Z s . They should be taken into account in the circuits in order to avoid the frequency displacement they cause. Once they have been properly modeled, the circuit is measured in the laboratory. If the measurement does not correspond with the simulations, the optimal source impedance is recalculated, by taking now into account the effect of the parasitics that was measured, and the matching circuit is improved until acceptable results are achieved.
proper modeling of the parasitic elements is fundamental in order to avoid a low conversion efficiency in the rectifiers.
The document is organized as follows. Section 2 presents the design methodology and the different steps involved in it. Section 3 gives useful insights on the choice of components. Section 4 describes the design of the matching circuit and the search for the optimal source impedance that maximizes the rectifier efficiency. Section 5 presents the model of the parasitics and their influence on the overall performance of the circuits. Finally, Section 6 presents the main conclusions.
Design Process
Due to the nonlinearity of rectifier circuits, their input impedance (and their response) is dependent on many parameters: the input power, the antenna impedance, the load impedance (the type of sensor we use), the operation frequency, etc. Furthermore, the rectifier cannot be directly attached to the antenna, since there exists an impedance mismatch between both, which translates into a low rectifier efficiency. Consequently, a matching circuit is commonly placed between the antenna and the rectifier to maximize the power transfer. However, the design of the matching circuit suffers from the same problems associated with the nonlinearity of the rectifier.
The design method that overcomes these difficulties and maximizes the rectifier efficiency is presented in Figure 2, as an iterative process. First, we must select the components that are part of the rectifier circuit, trying to reduce the losses in the diode and the output voltage ripple of the rectified DC signal. Then, we must design the matching circuit. The design of the matching circuit is based on the search, for a given load , of the optimal source impedance that maximizes the power transfer between the antenna and the rectifier. Thus, the components of the matching circuit are estimated in order to maximize the rectifier efficiency. However, the parasitics of the components and PCB (Printed Circuit Board) do influence the search of . They should be taken into account in the circuits in order to avoid the frequency displacement they cause. Once they have been properly modeled, the circuit is measured in the laboratory. If the measurement does not correspond with the simulations, the optimal source impedance is recalculated, by taking now into account the effect of the parasitics that was measured, and the matching circuit is improved until acceptable results are achieved.
The approach proposed here is not limited to any particular power or frequency range. Furthermore, complementary tools can be utilized in any particular stage of the design method. As an example, the vector network analyzer (VNA) can be utilized for hand-tuning the matching circuit. Trimmable (variable) components can be added to the matching circuit, so the efficiency of the rectifiers can be optimized with the VNA. However, this approach should be seen as an ad hoc solution, specific and unique for each design. As a consequence, it could be difficult to extract conclusions about the deviations that the parasitics cause and to quantify their effect on the circuit, which is the main purpose of the method we propose. Gaining insight on the parasitics' impact could potentially ease the design of future efficient rectifiers. The approach proposed here is not limited to any particular power or frequency range. Furthermore, complementary tools can be utilized in any particular stage of the design method. As an example, the vector network analyzer (VNA) can be utilized for hand-tuning the matching circuit. Trimmable (variable) components can be added to the matching circuit, so the efficiency of the rectifiers can be optimized with the VNA. However, this approach should be seen as an ad hoc solution, specific and unique for each design. As a consequence, it could be difficult to extract conclusions about the deviations that the parasitics cause and to quantify their effect on the circuit, which is the main purpose of the method we propose. Gaining insight on the parasitics' impact could potentially ease the design of future efficient rectifiers.
Choice of Components
In this section, some advice is given in order to select the components that are part of the rectifier circuit. The diode is the critical element in the circuit design. It must switch quickly to ensure its operation in the GHz range, and it must consume very little power. Compared to p-n diodes, Schottky diodes (metal-semiconductor (M-S) junctions) benefit from a faster switching time and a lower forward voltage drop (0.2−0.3 V versus 0.6−0.7 V), which makes them perfect for use in RF energy harvesting. Two diodes frequently used in this context are the HSMS-2822, specifically designed for input power levels above −20 dBm at frequencies below 4 GHz; and the HSMS-2850 (single mode), optimized for use with small signals (P in < −20 dBm) at frequencies below 1.5 GHz. According to their datasheets [19], HSMS-2822 diodes can provide 0.1 mA with a maximum voltage drop of 0.22 V, while HSMS-2850 diodes can provide the same current with a maximum voltage drop of 0.15 V. Some studies point out that the power levels foreseen in RF energy harvesting are normally higher than −20 dBm [4,10,12,14]. Thus, we decided to use the HSMS 2822 diode.
The choice of the capacitor is a trade-off between the output ripple of the circuit, and the self-resonant frequency (SRF) of the capacitor itself. The higher the value of the capacitor, the lower the output ripple is, and normally, the lower its SRF. The SRF is directly related to the parasitics of a certain component and is calculated as The lower the SRF is, the higher the value of the parasitic element and the more harmful its effect on the circuit. With the use of Equation (1), we show an estimate in Section 5 for the parasitic elements associated with inductors and capacitors.
Circuit Design
In this section, we describe the development of the procedure to design the lossless matching circuit that maximizes the rectifier efficiency. The design is particularized for the two topologies of the rectifiers under study: the CW multiplier and the half-wave rectifier. The matching circuit is implemented with a L network in both circuits. However, the same procedure is still applicable for different topologies of rectifier and matching schemes.
The measurement setup and the fabricated circuits are visualized in Figures 3 and 4. The circuits were implemented in perforated boards: the components were placed in the top layer and the tracks in the bottom layer. Two different boards of similar characteristics were used in the design of the half-wave rectifiers and the Cockcroft-Walton multipliers. In Figure 4, label "Test" refers to the test CW multiplier and half-wave rectifier used to study the effect of the parasitic elements, and label "Final" refers to the redesigned final CW multiplier and half-wave rectifier.
Optimal Source Impedance
Usually, the input power of the circuit (the power acquired by the antenna) is a combination of carriers with different amplitudes and frequencies [4]. As illustrated in Figure 5, a smart approach can be applied in this scenario. The antenna impedance and the matching circuit were replaced together, by a source impedance Z s = R s + jX s . Afterwards, an L network was designed in order to transform the antenna impedance Z ant into the optimal source impedance Z s at the frequency of interest (870 MHz, in this case). To make a fair comparison between the performances of both circuits (CW and half-wave rectifiers), the input powers and the frequencies for both were kept the same (P in = 0 dBm, f = 870 MHz). However, the load was different, Z L = 2.34 kΩ in the CW and Z L = 8 kΩ in the half-wave rectifier. For the two given loads Z L , the optimal source impedance Z s was found via an optimization process in a harmonic balance simulation [20] performed in commercial software ADS. Since Z s is a complex value, the efficiency of the rectifier may be visualized in a 3D plot with respect to the resistance R s and the reactance X s . Thus, Figures 6 and 7 illustrate the search of the optimal Z s in. The CW and in the half-wave rectifiers, respectively, before and after considering the parasitics. Despite the optimal values being different ( = 42 + 120 Ω and = 10 + 50 Ω in the CW; = 30 + 280 Ω and = 10 + 130 Ω in the half-wave rectifier), both figures share some similarities. First, the reactance is positive in all the cases. This points out that the rectifiers show a mainly capacitive behavior (negative reactance), which should be neutralized with a positive reactance in the matching circuit to enhance a rectifier's efficiency. In addition, the optimal reactance decreases (but remains positive) after including the effect of the parasitics. This is due to the parasitic series-inductances associated with the via holes (see Section 5), which contribute with a positive reactance term and reduce the capacitive behavior of the rectifiers. Second, the shape of the 3D plot is completely different before and after considering the parasitic elements, which illustrates the importance of modeling them. Concretely, the curves show a steeper response after including the parasitics. This fact is directly related to the reduction of and indirectly indicates to us that the parasitic elements reduce the operation bandwidth of the circuit.
With the use of the formulas presented in [21], the optimal source impedance is transformed into the lumped elements that form the L matching network. The antenna impedance was assumed to be = 50 Ω here. With the components available in the laboratory (Table 1), we implemented the networks that can be seen in Figures 10a and 11a. The L network of the CW multiplier lacks a capacitor, as far as the optimal impedance = 42 + 120 Ω can be approximated by ≈ 50 + 120 Ω. Since the impedance of the antenna already covers 50 Ω, only a series inductance is needed (two in series, in our case, due to inventory shortage) to achieve 120 Ω at 870 MHz.
(a) (b) Figure 6. Efficiency with respect to the source impedance = + in the Cockcroft-Walton (CW) multiplier before (a) and after (b) considering the parasitics. similarities. First, the reactance is positive in all the cases. This points out that the rectifiers show a mainly capacitive behavior (negative reactance), which should be neutralized with a positive reactance in the matching circuit to enhance a rectifier's efficiency. In addition, the optimal reactance decreases (but remains positive) after including the effect of the parasitics. This is due to the parasitic series-inductances associated with the via holes (see Section 5), which contribute with a positive reactance term and reduce the capacitive behavior of the rectifiers. Second, the shape of the 3D plot is completely different before and after considering the parasitic elements, which illustrates the importance of modeling them. Concretely, the curves show a steeper response after including the parasitics. This fact is directly related to the reduction of and indirectly indicates to us that the parasitic elements reduce the operation bandwidth of the circuit.
With the use of the formulas presented in [21], the optimal source impedance is transformed into the lumped elements that form the L matching network. The antenna impedance was assumed to be = 50 Ω here. With the components available in the laboratory (Table 1), we implemented the networks that can be seen in Figures 10a and 11a. The L network of the CW multiplier lacks a capacitor, as far as the optimal impedance = 42 + 120 Ω can be approximated by ≈ 50 + 120 Ω. Since the impedance of the antenna already covers 50 Ω, only a series inductance is needed (two in series, in our case, due to inventory shortage) to achieve 120 Ω at 870 MHz.
(a) (b) Figure 6. Efficiency with respect to the source impedance = + in the Cockcroft-Walton (CW) multiplier before (a) and after (b) considering the parasitics.
Parasitic Elements
In this section, we describe the parasitics that are associated with the lumped elements and the PCB. Thus, a circuit model was derived to correct the frequency displacement they cause. Furthermore, the contribution of each parasitic was quantified and the most harmful parasitics were identified.
Circuit Model
From previous studies [14] and our observations, the necessity of a robust model for the complete circuit is clear. Firstly, the SRF of the inductors and capacitors was estimated in the laboratory by connecting the component in series in a 50 Ω line. As described in Figure 8, capacitors and inductors are modeled as series and a shunt LC tank, respectively, since the effect of the parasitic resistances can be neglected. Their parasitics are related with the self-resonant frequency (SRF), according to Equation (1). Furthermore, their SRF can be measured in the laboratory with the 50 Ωline shown in Figure 9a and with the use of a network analyzer. In the case of the inductor, its SRF was The CW and in the half-wave rectifiers, respectively, before and after considering the parasitics. Despite the optimal values being different (Z s = 42 + j120 Ω and Z s = 10 + j50 Ω in the CW; Z s = 30 + j280 Ω and Z s = 10 + j130 Ω in the half-wave rectifier), both figures share some similarities. First, the reactance X s is positive in all the cases. This points out that the rectifiers show a mainly capacitive behavior (negative reactance), which should be neutralized with a positive reactance in the matching circuit to enhance a rectifier's efficiency. In addition, the optimal reactance X s decreases (but remains positive) after including the effect of the parasitics. This is due to the parasitic series-inductances associated with the via holes (see Section 5), which contribute with a positive reactance term and reduce the capacitive behavior of the rectifiers. Second, the shape of the 3D plot is completely different before and after considering the parasitic elements, which illustrates the importance of modeling them. Concretely, the curves show a steeper response after including the parasitics. This fact is directly related to the reduction of R s and indirectly indicates to us that the parasitic elements reduce the operation bandwidth of the circuit.
With the use of the formulas presented in [21], the optimal source impedance Z s is transformed into the lumped elements that form the L matching network. The antenna impedance Z ant was assumed to be Z ant = 50 Ω here. With the components available in the laboratory (Table 1), we implemented the L networks that can be seen in Section 5.2. The L network of the CW multiplier lacks a capacitor, as far as the optimal impedance Z S = 42 + j120 Ω can be approximated by Z S ≈ 50 + j120 Ω. Since the impedance of the antenna already covers 50 Ω, only a series inductance is needed (two in series, in our case, due to inventory shortage) to achieve j120 Ω at 870 MHz.
Parasitic Elements
In this section, we describe the parasitics that are associated with the lumped elements and the PCB. Thus, a circuit model was derived to correct the frequency displacement they cause. Furthermore, the contribution of each parasitic was quantified and the most harmful parasitics were identified.
Circuit Model
From previous studies [14] and our observations, the necessity of a robust model for the complete circuit is clear. Firstly, the SRF of the inductors and capacitors was estimated in the laboratory by connecting the component in series in a 50 Ω line. As described in Figure 8, capacitors and inductors are modeled as series and a shunt LC tank, respectively, since the effect of the parasitic resistances R p can be neglected. Their parasitics are related with the self-resonant frequency (SRF), according to Equation (1). Furthermore, their SRF can be measured in the laboratory with the 50 Ωline shown in Figure 9a and with the use of a network analyzer. In the case of the inductor, its SRF was determined via the non-transmission peak in the |S 21 | parameter (red curve in Figure 9b). In the case of the capacitor, its SRF was determined via the non-reflection peak in the |S 11 | parameter (blue curve in Figure 9b). Subsequently, the parasitic element of the component was obtained by using Equation (1). To avoid considering unwanted terms in the calculus (parasitics associated with the cables in the measurement, to the microstrip line, etc.), the system should be calibrated beforehand. Table 1 shows the parasitic elements of the lumped elements used in the CW multiplier and the half-wave rectifier.
The diode is also the critical element from the point of view of the parasitics. Ohmic losses in the diode are modeled through the series resistance R sd = 7.8 Ω and the junction resistance R j . The series resistance has little effect on the circuits, so it was neglected in this work. However, the junction resistance is dependent on the current I flowing through the diode: the lower the current is, the higher R j . According to the datasheet of the diode, R j can be calculated as [19]: where I s is the saturation current, N is an ideality factor and T is the temperature. For the HSMS-2822 diode [19], I s = 48 nA, and N = 1.067. For the current levels foreseen in the work (0.1-1 mA), we may expect junction resistances within the interval R j = 26-260 Ω. The junction capacitance of a Schottky diode can be modeled by: where C j0 is the zero-bias junction capacitance and φ B is the built-in potential. For the HSMS-2822 diode [19], C j0 = 0.65 pF and φ B = 26.7 V. For the voltage values foreseen in the article (V < 2 V), we may expect junction capacitances within the interval C j = 0.65 − 0.68 pF. Additionally, the capacitive coupling between the metallic pins of the diode package can significantly affect the performance of the circuit. This term is modeled with a parallel parasitic capacitance C pd , whose value is slightly tuned in simulation to C pd = 0.75 pF to fit the measurements. nH = 5.08ℎ ln + 1 , where ℎ is the height of the PCB and the diameter of the hole, both in inches. Variations in the height of the PCB can modify the value of the parasitic inductance associated with the vias. On the other hand, variations in the diameter of the via have less influence on the parasitic inductance due to the logarithm involved in Equation (4). In the case of the Cockcroft-Walton multiplier, the height of the PCB is 1.61 mm, and the diameter is 1 mm, which leads to a theoretical parasitic inductance = 0.92 nH. In the case of the half-wave rectifier, both the height of the PCB (1.51 mm) and the diameter of the hole (0.90 mm) are smaller, which leads to a smaller inductance = 0.88 nH. In manufactured circuits, these values will be higher since the vias are not perfect cylinders. The effective height of the PCB is normally higher, and the welding process causes additional series inductances. Thus, the parasitic inductances associated with the via holes are slightly tuned in simulation, resulting in = 1.30 nH for the CW multiplier and = 1.20 nH for the half-wave rectifier. Figures 10 and 11 show the effect of the parasitic elements in the CW multiplier and the halfwave rectifier, respectively. The frequency displacement they cause (black dashed line versus black solid line) is noticeable in both circuits. However, note the good agreement between the complete simulation model (orange dashed line) and the measurement (black solid line). The contribution of each parasite to the total displacement has been quantified, and some conclusions were extracted. In both cases, the contribution of the parasitic inductance associated with the capacitors (green dashed line) was completely negligible. On the other hand, the parasitic shunt capacitance associated with the diode package (red dashed line) was the most harmful element, with a total contribution over of 64% to the total frequency displacement in both circuits. In that sense, recent works have shown the benefits of two-dimensional materials, e.g., MoS2 (molybdenum disulfide) [23][24], being applied to RF electronics. In particular, [24] presents a MoS2-based Schottky diode used as a rectifier in a RF energy harvesting system. To explain the different behavior of The parasitics associated with the lumped components have already been considered and modeled. The main contribution from the PCB comes from the via holes. The parasitic inductance associated with the via holes can be estimated as in [22]:
Discussion
where h is the height of the PCB and d the diameter of the hole, both in inches. Variations in the height of the PCB can modify the value of the parasitic inductance associated with the vias. On the other hand, variations in the diameter of the via have less influence on the parasitic inductance due to the logarithm involved in Equation (4). In the case of the Cockcroft-Walton multiplier, the height of the PCB is 1.61 mm, and the diameter is 1 mm, which leads to a theoretical parasitic inductance L vTheory = 0.92 nH.
In the case of the half-wave rectifier, both the height of the PCB (1.51 mm) and the diameter of the hole (0.90 mm) are smaller, which leads to a smaller inductance L vTheory = 0.88 nH. In manufactured circuits, these values will be higher since the vias are not perfect cylinders. The effective height of the PCB is normally higher, and the welding process causes additional series inductances. Thus, the parasitic inductances associated with the via holes are slightly tuned in simulation, resulting in L v = 1.30 nH for the CW multiplier and L v = 1.20 nH for the half-wave rectifier. Figures 10 and 11 show the effect of the parasitic elements in the CW multiplier and the half-wave rectifier, respectively. The frequency displacement they cause (black dashed line versus black solid line) is noticeable in both circuits. However, note the good agreement between the complete simulation model (orange dashed line) and the measurement (black solid line).
Discussion
Sensors 2019, 19 FOR PEER REVIEW 10 on the CW multiplier, and Figure 12b shows one on the half-wave rectifier. The minimum deviation observed in both figures between the nominal simulation and the measurement is within the variability range of the components. As observed, the frequency deviation caused by the variability of the components was much smaller than the one caused by the parasitics in Figures 10 and 11. It can be noticed in Figure 12 that the half-wave rectifier is more sensitive to deviation in the components than the CW multiplier. This is due to variations in the capacitor C ′ in the L network of the half-wave rectifier.
It is worth noticing that, in general terms, the most harmful parasitics are associated with lumped elements and not with the PCB. Even in the worst scenario, the CW multiplier, the effect of the vias was not so important and easily neutralized with the circuit model. A particularly important conclusion can be extracted: despite us using a perforated PCB (perfboard), considered a low-quality board in RF, its parasitics are not especially harmful at these frequencies. Therefore, if carefully chosen, low-quality RF PCBs can be utilized at frequencies below 1 GHz in order to ease the design and reduce costs of the rectifier stage in a harvesting system. The contribution of each parasite to the total displacement has been quantified, and some conclusions were extracted. In both cases, the contribution of the parasitic inductance associated with the capacitors (green dashed line) was completely negligible. On the other hand, the parasitic shunt capacitance C pd associated with the diode package (red dashed line) was the most harmful element, with a total contribution over of 64% to the total frequency displacement in both circuits. In that sense, recent works have shown the benefits of two-dimensional materials, e.g., MoS 2 (molybdenum disulfide) [23,24], being applied to RF electronics. In particular, [24] presents a MoS 2 -based Schottky diode used as a rectifier in a RF energy harvesting system. To explain the different behavior of traditional Schottky diodes though, the junction and parasitic capacitances of this MoS 2 -based diode are in the order of 20 fF, 35 times less than those shown in Figures 10 and 11. Since the parasitics of the diode are the most damaging, the performance of the rectifiers could be potentially improved with the development of MoS 2 diodes. Additionally, their cutoff frequency is also higher, which allows one to reduce losses at higher operating frequencies. As a comparison, the MoS 2 -based diode presented in [24] has a cutoff frequency of 10 GHz (zero external bias), while the HSMS 2822 diode utilized in this work only reaches up to 4 GHz.
The contribution of the parasitic capacitance associated with inductors in the L matching networks is represented in blue in Figures 10b and 11b. In the case of the CW multiplier (Figure 10b), the frequency displacement they cause (9.67%) is lower compared to other parasitic terms, since the SRFs of the 4.3 nH and 8.2 nH inductors (see Table 1) are large. In addition, the contribution to the frequency displacement of the parasitic inductance associated with via holes (yellow curve in Figure 10b) is higher in this case, 22.25%. On the other hand, Figure 11b shows that the contribution, in the half-wave rectifier, of the parasitic capacitance associated with the inductor in the L matching network (blue curve), is appreciable-26.57%. However, the contribution of the parasitic inductance associated with the via holes (yellow curve) is less, 9.05%.
As a comparison between both circuits, the inductor used in the L network of the half-wave rectifier possesses a lower SRF than the inductors of the CW multiplier (see Table 1). Thus, the parasitics of the latter are less harmful. Conversely, the contribution of the parasitic inductance associated with via holes is more prominent in the CW multiplier, despite its value being approximately a third of the inductance L L1 and a sixth of L L2 . However, since the parasitic capacitors C p1 and C p2 may be neglected in this circuit, there would be three parasitic inductances L v in series, and the sum of their values (3 × 1.3 nH) is of the order of L L1 = 4.3 nH. Figure 12 presents a Monte Carlo analysis on the effect of the variability of the components on the circuit efficiency. The analysis was applied to the CW multiplier and half-wave rectifier of Figures 10 and 11, respectively, after all the parasitics were included in the model. Capacitors (C, C , and C L ), inductors (L L1 , L L2 , and L L ) and loads (R L and R L ) were assumed to follow a Gaussian distribution of standard deviation ±5% from their nominal values. Figure 12a presents the Monte Carlo analysis on the CW multiplier, and Figure 12b shows one on the half-wave rectifier. The minimum deviation observed in both figures between the nominal simulation and the measurement is within the variability range of the components. As observed, the frequency deviation caused by the variability of the components was much smaller than the one caused by the parasitics in Figures 10 and 11. It can be noticed in Figure 12 that the half-wave rectifier is more sensitive to deviation in the components than the CW multiplier. This is due to variations in the capacitor C L in the L network of the half-wave rectifier.
Final Circuits
With the use of the circuit model that contemplates the effect of the parasitics, the CW multiplier and the half-wave rectifier were redesigned to center their operation frequency at 870 MHz. Figures 13 and 14 show the parasitic model of the final circuits. The frequency displacement caused by the parasitic elements is noticeable: more than 700 MHz from the ideal response. Again, the most It is worth noticing that, in general terms, the most harmful parasitics are associated with lumped elements and not with the PCB. Even in the worst scenario, the CW multiplier, the effect of the vias was not so important and easily neutralized with the circuit model. A particularly important conclusion can be extracted: despite us using a perforated PCB (perfboard), considered a low-quality board in RF, its parasitics are not especially harmful at these frequencies. Therefore, if carefully chosen, low-quality RF PCBs can be utilized at frequencies below 1 GHz in order to ease the design and reduce costs of the rectifier stage in a harvesting system.
Final Circuits
With the use of the circuit model that contemplates the effect of the parasitics, the CW multiplier and the half-wave rectifier were redesigned to center their operation frequency at 870 MHz. Figures 13 and 14 show the parasitic model of the final circuits. The frequency displacement caused by the parasitic elements is noticeable: more than 700 MHz from the ideal response. Again, the most damaging parasitic contribution comes from the shunt capacitance of the diode. The parasitic capacitance of the inductor had a bigger impact on the performance of the final circuits than for the test circuits since the operating frequency was higher (900 MHz versus 600 MHz).
A slight difference in amplitude existed between the simulated and measured efficiencies in Figures 13 and 14. In order to study the cause of this difference, a Monte Carlo analysis was performed on the variability of the components. Capacitors, inductors and the load were assumed to be random variables that follow a Gaussian distribution of standard deviation 5% from their nominal values. As seen in Figure 15, the measurement curve fits within the selected variability range in simulation. As a result, the difference in efficiency could be explained by the effect of the component variability. Figure 16 represents the efficiencies of both circuits (see their schematic) as a function of the input power. As it can be seen, the efficiency rapidly drops below 5% due to the frequency displacement the parasitics cause. After including them in our circuit model, the rectifier efficiency rose to over 30% in both circuits, which is approximately twice the values (15%-20%) typically shown in the literature [10,12,13]. The nonlinearity of both circuits is appreciated in Figure 16. In a linear scheme, the efficiency curve would be completely flat. However, the efficiency response is flatter for the half-wave rectifier compared to the CW. This implies that the Cockcroft-Walton multiplier has a higher nonlinear dependence with respect to the input power, compared to the half-wave rectifier. Additionally, there was a drop in the efficiency of both circuits above 13 dBm. The diodes are saturated by high input powers and the performance of the rectifiers degrade. The drop is more pronounced in the case of the half-wave rectifier (red curve) due to the non-linearity effect in the circuit.
Sensors 2019, 19 FOR PEER REVIEW 12 damaging parasitic contribution comes from the shunt capacitance of the diode. The parasitic capacitance of the inductor had a bigger impact on the performance of the final circuits than for the test circuits since the operating frequency was higher (900 MHz versus 600 MHz). A slight difference in amplitude existed between the simulated and measured efficiencies in Figures 13 and 14. In order to study the cause of this difference, a Monte Carlo analysis was performed on the variability of the components. Capacitors, inductors and the load were assumed to be random variables that follow a Gaussian distribution of standard deviation 5% from their nominal values. As seen in Figure 15, the measurement curve fits within the selected variability range in simulation. As a result, the difference in efficiency could be explained by the effect of the component variability. Figure 16 represents the efficiencies of both circuits (see their schematic) as a function of the input power. As it can be seen, the efficiency rapidly drops below 5% due to the frequency displacement the parasitics cause. After including them in our circuit model, the rectifier efficiency rose to over 30% in both circuits, which is approximately twice the values (15%-20%) typically shown in the literature [10,12,13]. The nonlinearity of both circuits is appreciated in Figure 16. In a linear scheme, the efficiency curve would be completely flat. However, the efficiency response is flatter for the half-wave rectifier compared to the CW. This implies that the Cockcroft-Walton multiplier has a higher nonlinear dependence with respect to the input power, compared to the half-wave rectifier. Additionally, there was a drop in the efficiency of both circuits above 13 dBm. The diodes are saturated by high input powers and the performance of the rectifiers degrade. The drop is more pronounced in the case of the half-wave rectifier (red curve) due to the non-linearity effect in the circuit.
Performance Comparison of Passive Rectifiers
Finally, Table 2 summarizes a performance comparison among previous rectifier designs published in the literature [25][26][27][28][29][30][31]. For a fair comparison, only passive rectifiers that operate with an input power close to 0 dBm (1 mW) were considered. Note that active rectifiers are able to reach
Performance Comparison of Passive Rectifiers
Finally, Table 2 summarizes a performance comparison among previous rectifier designs published in the literature [25][26][27][28][29][30][31]. For a fair comparison, only passive rectifiers that operate with an input power close to 0 dBm (1 mW) were considered. Note that active rectifiers are able to reach efficiency values of 75%-80%. However, they are not suitable for energy harvesting, and hence, were not considered in the study, since they need an external power supply. Most of the passive implementations presented make use of half-wave and Cockcroft-Walton schemes, as they usually offer the least losses by using the minimum number of diodes. To the best of our knowledge, the highest efficiency found in the literature (from a passive rectifier) was recently presented in [29], reaching a value of 60%. Conversely, the vast majority of works present low rectifier efficiencies, close to 20% or even much lower in some cases. As a consequence, the detailed study on the parasitic effects presented in this work could help to significantly improve the performance of future rectifier circuits and RF energy harvesting systems.
Conclusions
This work presents guidelines for the design of efficient rectifier circuits in RF energy harvesting. Some advice was given in order to face the problems associated with the nonlinearity and parasitic elements of the circuits. Without loss of generality, two different configurations were tested: a CW multiplier and a half-wave rectifier. For a given load Z L , it was shown that there is an optimal source impedance Z s that maximizes the rectifier efficiency, which was used to design an optimal matching circuit. Subsequently, the contribution of each parasitic element to the total frequency displacement was quantified and the most harmful parasitics were identified. In summary, the following conclusions have been extracted from the analyses:
1.
The most harmful parasitics come from the components and not from the PCB. Therefore, if carefully chosen, cheaper PCBs can be utilized in order to reduce costs. 2.
Although the diode was known to be the limiting component in terms of losses, this work has demonstrated that it also causes a large deviation with respect to the expected frequency response. Actually, it has the most harmful parasitic element, contributing two-thirds of the total frequency displacements in both Cockcroft-Walton and half-wave circuits. In that sense, future MoS 2 diodes could potentially help to improve the efficiency of rectifier circuits, since their parasitics are shown to be very low [24] compared to traditional Schottky diodes.
3.
The parasitic inductance associated with the capacitors is completely negligible. This fact allows one to use cheaper capacitors and reduce costs. It also allows one to use higher values of the capacitor in the rectifier stage, in order to reduce the DC output ripple when feeding the sensor. Note that the choice of this capacitor is a trade-off between the output ripple of the circuit, and its self-resonant frequency (SRF). The higher the value of the capacitor is, the lower the output ripple and the higher the parasitics. However, they do not affect the behavior of the circuit.
Finally, the circuit model of the parasitic elements was used to redesign both circuits, without considering the parasitics. The efficiency did not exceed the 5% in both circuits. After modeling them, the efficiency was shown to be over the 30%, twice the value compared to the passive rectifiers typically shown in the literature. | 11,151 | 2019-11-01T00:00:00.000 | [
"Engineering",
"Physics"
] |
Surveillance Robot with Face Recognition using Raspberry Pi
— International border security has become a very challenging task for any country. It is not always possible for border security forces to monitor long borders round the clock and in all seasons. Deployment of technology in the form a robot for intruder detection at the border and transmission of information to the control center is imperative in the geo-political situation of the world. Many of the high risk jobs in a hostile environment are best performed by a robot while it can be dangerous for soldiers. The proposed work aims to develop an automatic solution to detect the presence of an enemy or any hostile events such as fire/gas leakage in targeted places without loss of human life. It consists of a robotic vehicle for spying the pre-allocated area by continuously monitoring it. Whenever a sensor gets activated, the surveillance system checks for the presence of humans and then runs a face recognition algorithm. If the facial data of the person detected does not match with the pre-stored personal data of soldiers, the system recognizes him as an intruder and activates the laser gun to target him. In case of detection of unusual/dangerous events such as someone carrying a knife or a gun in high security zone, an alert message is sent to the operator. The system also provides the live streaming of surveillance data to the operator using Raspberry Pi and VNC Viewer.
INTRODUCTION
Security is the primary objective to protect nations from terrorist attacks, infiltration, smuggling etc. Hence international border areas require high level of security round the clock. Surveillance system requires security personnel for monitoring designated areas using surveillance cameras. The manual surveillance system suffers from the following challenges: 1. It is hard for humans to maintain focus on monitoring continuously.
2. Continuous monitoring of multiple screens showing video streams from surveillance cameras is challenging.
3. Security guard falling asleep due to exhaustion while on job results in serious security breach. 4. Providing 24/7 monitoring requires guards to work in shifts, resulting in high cost.
In order to address these issues, an automated surveillance system with a robot equipped with various sensors at its core is proposed in this work.
A mathematical model is proposed to explore the characteristics of a two-wheel self-balancing robot and control its behavior on a planar surface and on an inclined plane [1]. A Raspberry Pi based robotic system is proposed for surveillance to automatically detect intruders and inform the control room. While the system provides remote control of a robot, it fails to distinguish between a known person and an intruder [2]. A security system using Raspberry Pi and OpenCV image processing techniques is presented to detect the presence of human or smoke during night times and provide an Email alert. But it fails to distinguish between a known person and an intruder [3]. A robotic system is proposed using sensors for detection of harmful gases and fire in war fields for military applications. The system sends an alert message to user when any of the sensors become active but it is unsuccessful to decide the presence of human movement from surrounding objects [4]. A microcontroller based automatic gun targeting system is developed to target trespassers in high security zones. The system gets triggered upon activation of sensors, but it fails to recognize the identity of the person [5]. A surveillance system using Raspberry Pi as a controller and Python-OpenCV as a programming language is proposed to provide for real-time video footage, in black and white, using Internet/Wi-Fi as a medium of connectivity [6].
It is observed from the literature that surveillance systems are designed for detecting human/object movements, gas or flame in target areas. But they suffer from their inability to recognize between a known person and an unknown person. The proposed robotic system addresses this issue by recognizing the known person using image processing techniques. The system generates an alert message in case of dangerous events in areas under surveillance.
The remainder of the paper is organized as follows: While Section II presents the architecture of the surveillance robot system Section III describes its working. Section IV presents the algorithms for face recognition and unusual event detection. Section V describes the result and discussion and Section VI concludes with an outline of future work.
II. ARCHITECTURE OF SURVEILLANCE ROBOT
Surveillance robot is placed in a remote location to monitor the surrounding environment. It consists of Raspberry Pi, USB Camera, Sensors, Motor driver with two DC motors, and a driver relay with target system. The block diagram of surveillance robot is as shown in Fig.1. Robot is designed using Raspberry Pi as the controller and coded in OpenCV-Python programming language to implement various control functionalities of the robot. The DC motors are controlled by General Purpose Input Output (GPIO) control signals of Raspberry Pi with L293D motor driver module to drive DC motors using H-bridge. Signals from all sensor modules, relay and driver module are given to Raspberry Pi over GPIO pins. All hardware is powered by the supply board provided with the 12 V power supply except sensors requiring 5 V and regulated by LM317 voltage regulator. As the gas sensor requires more than 1.5 A current occasionally, it may affect the performance of the other modules. Hence, gas sensor is powered using LM317 and its DO pin is connected to Raspberry Pi. Fire detection works on sensing either smoke or heat or flame (light) or a combination of them. While IR sensors detect the obstacles in the surrounding area, ultrasonic sensor compute the distance between the sensor and the obstacle depending on the time interval between the emitted wave and the reflected wave. Further, a USB camera is interfaced with Raspberry Pi over USB port. In place of a laser gun that acts against the intruder, as proof of concept, an LED is connected to relay output. Robot system is controlled by Android application or from computer system to provide live streaming of surveillance video footage.
III. FLOW CHART OF SURVEILLANCE ROBOT
The working of surveillance robot is illustrated in the form of a flowchart shown in Fig.2. On power up, robot, sensors and camera get activated and the robot starts moving around in the region of surveillance with its camera traversing 54º. Robot starts moving forward with IR sensors keep checking for any object in the range of the sensor. If no obstacle is detected robot moves forward, otherwise the sensor output goes low and robot will stop to overcome the obstacle. Flame and gas sensors check for the presence of fire and gas. If sensor output is positive, a message is sent to the Android mobile operator in the control room to alert him. Further, the surveillance robot Fig.2: Flowchart of working of surveillance robot monitors the surrounding area continuously and checks for the presence of human beings. Once the face gets detected, the system takes the facial data and with the help of image processing techniques, the system determines if the detected face is that of known or unknown person by comparing with the pre stored personal data of soldiers in the database. Haar Cascade classifier and Local Binary Pattern Histogram (LBPH) algorithms are used for image processing to determine the presence and identity of the human [7,8]. The robot moves forward when the face of the detected person matches with the facial information stored in the database. Upon mismatch the intruder is detected, the surveillance robot stops and the relay activate the laser gun which fires at the intruder to deactivate him. However, in this work, this gun target control is replicated with an LED on/off control with the relay activating the LED implying triggering of the target controller. The LED turns on and the robot moves forward. This process continues in an infinite loop to provide for nonstop surveillance.
IV. ALGORITHMS FOR FACE RECOGNITION AND UNUSUAL EVENT DETECTION
Face detection is carried out by using classifiers that choose image as positive i.e. image with face, or negative i.e. image without face. Classifiers are trained from a large set of • Haar classifier has 'Integral Image' concept which provides features for fast computation by the detector.
• Algorithm is based on Adaboost, which choose a small number of important features from a huge set that provides efficient classifiers.
• Complex classifiers are combined to form 'cascade'. This rejects if any non-face region is present in the image while focuses on face region.
b) Face recognition algorithm Local binary patterns histogram (LBPH) comprising the generation of local binary patterns for each pixel is used for face recognition. The basic idea is to compare each pixel with neighborhood pixels in an image. First it considers one pixel as a center and compares it with the neighboring pixels. If the intensity value of considered pixel is equal to or greater than the neighboring pixel, then it writes the pixel with a 1. If not, a 0 is written. Then each binary pattern is converted into a corresponding decimal number and a histogram of all decimal values is drawn.
c) Algorithms involved in object classification
Deep neural network is classified as Base network and Detection network. The proposed system deploys MobileNet base network to generate high level features for classification / detection. Single Shot Detector (SSD) algorithm type detection network uses convolution layer upon base network for detection task.
V. RESULTS AND DISCUSSION.
A prototype of surveillance robot, shown in Fig.3, consisting of sensors and motor activators interfaced to the controller is developed and all functionalities are demonstrated. The face detection system using Haar-Classifier algorithm is implemented in Open CV Python programming and the working of the robot with face recognition is demonstrated.
a) Sensor Output
When robot is moving in forward condition, it keeps checking, in an infinite loop, for an obstacle in its path. Upon activation of left side IR sensor, the system displays of "left side object detected". When right side IR sensor gets activated, the system displays "right side object detected". Ultrasonic sensor measures the distance between the object and sensor to identify its location. After calculation, it displays the measured distance in the output window. A sample of sensor output generated is shown in Fig.4.
b) Detection of gas and fire
The system checks for the presence of fire and gas [9] in surrounding area. If gas/fire is detected, the system displays the message to the operator as "gas detected" or "fire detected", as shown in Fig.5.
c) Unusual event detection
In case of unusual event or dangerous situation such as someone carrying a gun or knife in high security zone, the system sends an alert message as "unusual activity detected". System loads the input image and displays one of top 5 predictions and is shown in Fig.6. The message transmitted to the operator is shown in Fig.7. A screw driver and a syringe are used as unusual objects for testing the system.
d) Known person recognition
The system continuously monitors the surrounding area and checks for the presence of facial data of human being. If the detected person is known, the system displays his name as shown in Fig.8.
e) Unknown person recognition
When the detected person is unknown i.e., facial data of the image does not match with the database, Robot system stops and the relay activates the laser gun to target him or LED turns on. Result of unknown person recognition is displayed on the system as shown in Fig. 9.
a) Conclusions
The proposed surveillance robot system with face recognition is continuously surveying the surrounding area. When the objects get detected, the robot overcomes them and moves forward. The robot is able to sense carbon monoxide and fire in the surrounding area. The system continuously monitors the given area and is able to recognize whether the detected person is known or unknown. If the detected person is unknown, then the system activates laser gun and shoots him down. The system is capable of providing live streaming of images and alert messages. Hence, it is suitable for surveillance application in war field or borders. The proposed work also detects unusual objects carried by the humans in high security zones.
b) Future Scope
The present work can be extended by adding unusual event detection in order to recognize the activities of unknown or known person. As algorithms used in image processing are illumination affected, advanced algorithm can be deployed to insulate the robot from light effects. | 2,917.6 | 2020-01-02T00:00:00.000 | [
"Computer Science"
] |
High‐frequency transcranial magnetic stimulation protects APP/PS1 mice against Alzheimer’s disease progress by reducing APOE and enhancing autophagy
Abstract Introduction The repetitive transcranial magnetic stimulation (rTMS) has clinically wide application prospect of psychiatry and neuroscience, for its painless, noninvasive, and high efficiency. So far, rTMS has been used in the treatment of Alzheimer's disease (AD) but the underlying mechanism is not clear. Methods and Results The APP/PS1 mice at 3‐month‐old were treated by 5 Hz high‐frequency (HF) rTMS for two weeks. After rTMS treatment, the AD‐like cognitive impairments of APP/PS1 mice were investigated subsequently, and molecular mechanisms underlying was further explored. The study showed that the 2‐week rTMS at 5Hz frequency improved cognitive impairments and AD‐like pathology (including a decrease in p‐Tau, APP, Aβ, and PP2A expression) of APP/PS1 mice. Although BDNF‐TrkB signaling was significantly enhanced, no differences of SYN, PSD95 and p‐AKT were observed in the brain of APP/PS1 mice. On the contrary, the LC3Ⅱ/LC3Ⅰ ratio was elevated with a significant reduction of ApoE and p62 in mice. Conclusions rTMS exerts a potentially protective role in the prevention and treatment of AD by reducing ApoE expression and promoting autophagic flux, which provides a new insight into the mechanism of rTMS.
| BACKG ROU N D
Alzheimer's disease (AD) is a progressive neurodegenerative disease that seriously endangers the health of middle-aged and elderly people. With the aging of the population, the number of people suffering from AD is increasing rapidly, which is estimated to increase three times by 2050, and brings heavy burden to families and societies (Frankel et al., 2019;O'Shaughnessy et al., 2020). The characteristic pathological signs of AD are senile plaques formed by β-amyloid (Aβ) deposition and neurofibrillary tangles formed by tau protein hyperphosphorylation, as well as neuron loss accompanied by glial cell proliferation. Cognitive disorders, personality and behavior disorders, insomnia, and autonomic nervous dysfunction are the mainly clinical symptoms of AD (Beauquis et al., 2014;Vergallo et al., 2018).
For now, all drugs for AD just ameliorate the clinical symptoms, but have no prevention in the pathological process of AD. Thus, it is urgent to develop a new effective treatment to regulate the pathogenesis of AD.
As a noninvasive intervention, rTMS has developed into a promising choice for therapy and rehabilitation of neuropsychiatric diseases (Brunelin et al., 2014;Etoh et al., 2019;Hirakawa et al., 2018;Sabbagh et al., 2019). Both low-frequency and high-frequency rTMS have been proved to improve the cognitive function and synaptic plasticity of AD model in mice (Cotelli et al., 2011). Besides, the ability of language expression and understanding of moderate AD patients were significantly ameliorated after treatment with HF rTMS on the left dorsolateral prefrontal cortex, suggesting rTMS can alleviate cognitive impairments induced by AD indeed. However, the mechanism of rTMS in the treatment of AD is still unclear.
β-amyloid (Aβ) begins to increase in the brain of APP/PS1 transgenic mouse (a classical AD mouse model) at about 3 months, and the plaque deposition can be detected around 6 months (Garcia-Alloza et al., 2006;Zheng et al., 2017). The APP/PS1 mice at 3-month-old were treated by 5 Hz HF rTMS for 14 days in our study. The AD-like cognitive impairments and AD-related neuropathological features of APP/PS1 mice were investigated subsequently after rTMS treatment, and molecular mechanisms underlying was further explored.
Our findings will provide new insights and research basis for the developing novel therapeutics for AD.
| Application of HF rTMS
The APP/PS1 transgenic mice were randomly divided into two groups: sham-rTMS APP/PS1 group (AD-sham group, n = 15) and real rTMS APP/PS1group (AD-rTMS group, n = 15). Mice in the AD-rTMS group were treated with one session of 5 Hz HF rTMS daily for 14 consecutive days. Mice were awake and fixed in a specially made plastic cylinder according to our previous report (Zhang, Lu, Wang, Yun, & Zhou, 2019).
The rTMS was delivered with a magnetic-electric stimulator (CCY-III, Wuhan Yiruide Medical Equipment Co., LTD.) with a round coil (6.5 cm diameter). The coil was held over the center of exposed head and parallel to the parietal bone of the mice. A total of 600 magnetic stimulation pulses consisting of 20 burst trains and 30 pulses each train at 5 Hz with 2-s intertrain intervals were applied daily. The stimulation intensity represented 120% of the average resting motor threshold.
The AD-sham group was delivered by the cage of the coil positioning (perpendicular to the head scalp) with the same protocol of rTMS.
| Novel objective recognition test
The novel object recognition (NOR) test was performed in a 50 × 50 × 50 cm white acrylic box. Each mouse was habituate in the box for two consecutive days without objects according to Shentu's study (Shentu et al., 2018). Next day the mice returned the arena from the same starting point, and two identical objects (old objects) were obtained for 5 min. The animal was later (after 2 or 24 hr, respectively) exposed to one of the old objects and a new object of a different shape and color. The video signal was transmitted to a computer in an adjacent room. After each trial, the objects and boxes were cleaned by 75% ethanol to eliminate odor cues. The recognition index was calculated as the time spent exploring the new object divided by the time exploring both objects.
| Morris water maze test
Morris water maze (MWM) was used to detect assess learning and memory of mice (Morris, 1984). A round pool (120 cm × 50 cm) was filled by water (25 ± 1°C) with a white titanium dioxide. Then, an escape platform (10 cm × 15 cm) was placed in the center of one quadrant of the arena, 1-1.5 cm below the water surface. The walls of the test room were pasted with black-and-white extramaze cues.
The trajectory of the mice was recorded by a video-tracking camera mounted to the ceiling centrally above the pool. Once the platform was found, mice were allowed to sit on the platform for 10 s before being dried with a towel and returned to a heated drying cage. If the mice were not able to find the platform within 1 min, it was gently placed on the platform 60 s. Probe tests were performed after acquisition. The swimming path and times to reach target quadrant were recorded by a digital device connected to a computer.
| Western blotting analysis
After behavior tests, total protein from the hippocampal tissues of the mice was collected for Western blotting. Hippocampal tissues were homogenized in radioimmuno-precipitation assay (RIPA) and phenylmethylsulfonylfluoride (PMSF) lysis buffer (Beyotime) and incubation at 4°C for 30 min. The lysate was then centrifuged at 12,000 g for 10 min at 4°C to collect the supernatant. Protein concentration was determined according to BCA protein assay kit instructions (Beyotime). Equal protein sample was mixed with 5× loading buffer (Beyotime) and boiled for 10 min at 99°C.
A total of 50-80 μg protein samples were separated with 10% SDS-PAGE and transferred onto a PVDF membrane (Millipore).The membranes were blocked with 5% nonfat milk for 1 hr at room temperature and then incubated with specific primary antibody diluted with TBST overnight at 4°C. The corresponding primary antibodies used were with TBST three times next day and incubated with secondary antibodies for 1 hr at room temperature. The protein was scanned with enhanced chemiluminescence kit (ECL, Thermo). Quantity-one software (BIO-RAD) was used to analysis the density of band.
Statistical significance was defined as p < .05.
| Restoration of rTMS on learning, memory, and cognitive function of APP/PS1 mice
After 14 days of consecutive intervention with HF rTMS (Figure 1), behavioral experiments (MWM and NOR) were used to evaluate the improvements of rTMS on learning, memory, and cognitive function of APP/PS1 mice. Compared with the AD-sham group, rTMS treatment had no effect on the swimming speed of APP/PS1 mice (Figure 2a), indicating that rTMS has no influences of motor function. However, the escape latency of the rTMS group was markedly shortened, and the time spent in the target quadrant was significantly increased (Figure 2b-d), which implied that rTMS recovered the spatial learning and memory defects of APP/PS1 mice. In addition, a significant elevation was observed after rTMS treatment and the NOR index (Figure 2e,f) compared with the sham animals. The above results revealed that HF rTMS alleviated the cognitive impairment of learning and memory in AD mice.
| Effect of rTMS on neuropathological features of AD in APP/PS1 mice
It is reported that rTMS is helpful to alleviate cognitive impairments.
| Effect of rTMS on BDNF/SYN/PSD95 in the hippocampus of AD mice
Synaptic plasticity-related proteins (PSD95 and SYN) play an important role in learning and memory function of hippocampus. In addition, BDNF is the most abundant neurotrophic factor in the body, which is the key factor in learning, memory, and cognitive function. To explore the mechanism of rTMS on AD, Western blots were used to detect the changes of these three proteins. The results showed that the expressions of PSD-95 and SYN remained F I G U R E 1 HF rTMS protocols delivered for 14 consecutive days. A total of 600 magnetic stimulation pulses consisting of 20 burst trains and 30 pulses each train at 5 Hz with 2-s intertrain intervals were applied in each day F I G U R E 2 High-Frequency rTMS ameliorates spatial memory and cognitive dysfunctions in APP/PS1 mice. Morris water maze (MWM) test was performed to assess learning and memory functions using this spatial reference memory task (a-d). blots (a, b). The quantification graph was shown and normalized by the AD-sham group (c-g). **p < .01,*p < .05 comparable between the two groups (Figure 4a,d,e), whereas the level of BDNF in the AD-rTMS group was substantially higher than the AD-sham group (Figure 4a,c). We therefore investigated the effects on BDNF-associated signaling downstream pathway: TrkB and AKT. Western blots showed that the level of p-TrkB was significantly increased in AD-rTMS mice compared with AD-sham animals, while the p-AKT level remained unchanged (Figure 4b,f-i).
These results imply that BDNF participated in the treatment of AD mice by rTMS, but there was possible other unknown molecular mechanisms involved.
| Improvement of rTMS on the APOE/PP2A signaling pathway and autophagy
ApoE is one of the greatest genetic risk factors for AD. ApoE and its receptor play an important role in the regulation of Aβ imbalance in the early stage of AD. To further study the mechanism underlying rTMS treatment of AD, the expression of ApoE was measured by Western blots. To our interest, the results showed that the expression of ApoE in the brain decreased dramatically after rTMS treatment (Figure 5a,c), and the expression of PP2A was reduced F I G U R E 4 Effects of HF rTMS on BDNF/SYN/PSD95 in the hippocampus. Hippocampal protein expression of BDNF/SYN/PSD95 was determined by Western blots (a). The expression of p-TrkB and p-AKT in the downstream pathway of BDNF was also shown by Western blots (b). The quantification graph was shown and normalized by the AD-sham group (c-i). ***p < .001, **p < .01, *p < .05 as well (Figure 5a,d).Then, the levels of autophagy marker proteins, p62 and lc3ii/lc3i, were detected. Meanwhile, the level of lc3ii/lc3i in the AD-rTMS group was significantly increased, accompanied by the decreased expression of p62 (Figure 5b,e,f). These data suggest that rTMS enhanced the hippocampal autophagy level in APP/PS1 mice by down-regulating ApoE in AD mice.
| D ISCUSS I ON
In this article, we systematically studied the neuroprotective effects of rTMS against AD by APP/PS1 mice. We found that HF rTMS significantly rescues the learning, memory, and cognitive impairment, and reduces the neuropathology associated with AD in APP/PS1 mice. Besides of BDNF-TrkB signaling, our results show the new insight into the APOE-PP2A and the autophagy system involved in the neuroprotection of rTMS on AD, which provides more experimental evidence for clinical applications of rTMS in the treatment of AD.
Although rTMS has been used to treat AD in clinic, specific treatment schemes are not unified, and the mechanism is unclear. Thus, the research on rTMS to treat AD needs further investigation (Alcalá-Lozano et al., 2018;Sabbagh et al., 2019;Turriziani et al., 2019).
Recent studies have focused on the cognitive impairment of rTMS in AD model mice or patients, and there are few reports on the characteristic pathological changes and the mechanism of AD lesions (Huang et al., 2017;Ma et al., 2017). This paper focused on the early intervention of rTMS on AD-related pathological indices, especially of Aβ deposition and phosphorylated Tau, to explore the molecular mechanism by which rTMS enhanced the cognitive function of AD mice.
The lysosomal degradation and clearance of Aβ mediated by ApoE signaling is one of the effective pathways to reduce Aβ accumulation in the brain (Bu, 2009;Langlois et al., 2019). An fMRI study of nondemented elderly found that rTMS intervention led to changes in the brain network connections with different ApoE subtypes of elderly carriers, and improved memory performance slightly as well, in which ε4 subtype was the most obvious effector (Peña-Gomez et al., 2012). Thus, is the therapeutic effect of rTMS on AD related to ApoE mediated Aβ degradation? Consistent with our results, the expression of ApoE in the brain of APP/PS1 mice was significantly down-regulated after rTMS intervention. More than that the autophagy level was also increased, and AD-related pathogenic marker proteins like Aβ, p-Tau, and their downstream molecules were correspondingly reduced.
F I G U R E 5
Regulation of rTMS on the APOE/PP2A signaling pathway and autophagy. The expression of ApoE and PP2A in the mouse brain was measured (a). The expression levels of autophagy marker proteins, p62 and lc3ii/lc3i, were also compared by Western blots (b). The quantification graph was shown and normalized by the AD-sham group (c-f). ***p < .001, **p < .01, *p < .05 In conclusion, HF rTMS intervention for two weeks can restore early AD-like dysfunctions in the brain of APP/PS1 mice by regulation of APOE and autophagy, which provides a new idea and experimental basis for the early prevention and treatment of AD.
ACK N OWLED G M ENTS
This study was supported by grants from National Natural Science
CO N FLI C T O F I NTE R E S T
The authors declare that there is no conflict of interest.
AUTH O R CO NTR I B UTI O N
Lin-Xiao Wang contributed to the conception of the study. Xia Chen performed the experiments and wrote the manuscript. Guo-Ying Dong helped perform the data analysis.
PE E R R E V I E W
The peer review history for this article is available at https://publo ns.com/publo n/10.1002/brb3.1740.
DATA AVA I L A B I L I T Y S TAT E M E N T
The data used to support the findings of this study are available from the corresponding author upon request. | 3,455.2 | 2020-06-26T00:00:00.000 | [
"Psychology",
"Biology"
] |
Label-free multiphoton microscopy as a tool to investigate alterations of cerebral aneurysms
Cerebral aneurysms are abnormal focal dilatations of arterial vessel walls with pathological vessel structure alterations. Sudden rupture can lead to a subarachnoid hemorrhage, which is associated with a high mortality. Therefore, the origin of cerebral aneurysms as well as the progression to the point of rupture needs to be further investigated. Label-free multimodal multiphoton microscopy (MPM) was performed on resected human aneurysm domes and integrated three modalities: coherent anti-Stokes Raman scattering, endogenous two-photon fluorescence and second harmonic generation. We showed that MPM is a completely label-free and real-time powerful tool to detect pathognomonic histopathological changes in aneurysms, e.g. thickening and thinning of vessel walls, intimal hyperplasia, intra-wall haemorrhage, calcification as well as atherosclerotic changes. In particular, the loss or fragmentation of elastin as well as fibromatous wall remodelling appeared very distinct. Remarkably, cholesterol and lipid deposits were clearly visible in the multiphoton images. MPM provides morphological and biochemical information that are crucial for understanding the mechanisms of aneurysm formation and progression.
www.nature.com/scientificreports/ Label-free multiphoton microscopy (MPM) including coherent anti-Stokes Raman scattering (CARS) microscopy in combination with endogenous two-photon fluorescence (TPEF) and second harmonic generation (SHG) could be helpful to fulfil this need. They visualize morphology and composition of different biological tissues and cells in a submicron resolution without photo-damage 9,10 . CARS imaging addresses molecular vibrations of CH 2 -groups in the tissue and, therefore, visualizes mainly the distribution of lipids 11,12 . This fact makes CARS microscopy a powerful tool for studying atherosclerosis 13 . TPEF microscopy exploits intrinsic cellular fluorescence originating from endogenous fluorophores like mitochondrial NADH and flavoproteins 14,15 . Moreover, two-photon excited autofluorescence of extracellular elastin is important for studying vessel wall remodelling 16,17 . SHG visualizes highly ordered tissue structures, which are non-centrosymmetric like type I collagen fibers 18,19 .
Raman spectroscopy is another analytical and non-destructive tool allowing the accurate identification of biochemical composition of different types of tissue 20,21 . This technique revealed that atherosclerotic plaques in peripheral arteries predominantly consist of cholesterol, cholesteryl ester, triacylglycerols, proteoglycans and crystalline calcium, typically in the form of calcium apatite [22][23][24] .
In this study, we applied label-free and non-destructive MPM to assess pathological changes in the morphochemistry of the vessel walls of human cerebral saccular aneurysm domes on the microstructural level. Moreover, Raman spectroscopy was used to obtain detailed biochemical information at selected positions of these alterations.
Results
Unaltered cerebral arteries. MPM was conducted to investigate transverse and longitudinal sections of a regular vessel wall of human cerebral arterial circle. Conventional histopathological stainings for hematoxylin & eosin (HE) and Elastica van Gieson (EvG) were used as reference (Fig. 1A). EvG can visualize elastin-bearing tissue structures in black-purple and collagen-bearing structures in red. A normal cerebral artery consists www.nature.com/scientificreports/ of three layers: tunica adventitia (1), tunica media (3) and tunica intima (5). TPEF (colored in green) visualized the external elastic lamina (EEL) (2) and the internal elastic lamina (IEL) (4) very clear. SHG (colored in blue) showed the collagenous connective tissue of the tunica adventitia, consisting mostly of collagen type I. CARS (colored in red) displayed the tunica media, which is characterized by a linearly organized smooth muscle cell (SMC) layer. TPEF and CARS mainly visualized the tunica intima with its subendothelial stratum and the single layer of endothelial cells. Noteworthy, all structures of the normal cerebral vessel wall were identified with labelfree MPM. Moreover, tissue structures appeared clearer with higher contrast compared to standard histological stainings. In particular, multiphoton images clearly revealed all elastic fibers, including the very thin and small ones within the tunica media (Fig. 1B). MPM imaging identified easily the abluminal-luminal orientation based on the strong SHG signal of the collagen-rich tunica adventitia, which was very helpful for the analysis. The tunica adventitia is always located at the top in the displayed images.
Aneurysms. Label-free MPM was applied to study five unruptured (diameter 9-16 mm) and five ruptured (diameter 5-20 mm) human cerebral saccular aneurysm domes (Table 1). All the pathological tissue changes visualized by MPM in this set of experiments are in accordance with previous studies made in rabbits 25 , pigs 13 and humans 26 . Therefore, we abstained from further special immunohistochemical stainings as reference. Instead, we used Raman spectroscopy to confirm the biochemical composition of different types of tissue visualized by MPM. Initially, pathological tissue alterations that were likewise visualized by HE staining and MPM were assessed (Fig. 2). Multiphoton images displayed areas with thickened and thinned aneurysm walls compared to normal cerebral vessel walls ( Fig. 2A). Pathological intima thickening (pathological intimal hyperplasia) was found in almost all resected human aneurysm domes in contrast to normal vessel walls ( Fig. 2A, Table 1). However, areas www.nature.com/scientificreports/ with disorganization as well as hypocellularized areas were better assessable in HE staining due to their distinctly stained nuclei (Fig. 2B, Table 1). Nevertheless, the multiphoton images showed a noticeable disorganization of the tissue structure in comparison to the normal vessel wall. Another histopathological alteration associated with vessel wall changes in aneurysms is calcification. In the multiphoton images, areas with high TPEF (green) signal matched regions of calcification that are visible in HE staining (Fig. 2C, Table 1). Raman spectroscopy was used to confirm the nature of the areas with high TPEF intensity. The spectra of those areas exhibited bands of calcium hydroxyapatite (690 cm -1 ) and calcium carbonate apatite (1073 cm −1 ) 27 consistent with the presence of calcification (Fig. 2D). As a next step, we found that some pathological tissue alterations related to aneurysm formation were visualized better by MPM than by conventional HE staining (Fig. 3).
Initially, the presence of the internal (IEL) and external elastic lamina (EEL) were assessed by MPM, HE as well as EvG (Fig. 3A,B). The elastic fibers were characterized by strong TPEF (green) signal and were better visible in the multiphoton images than in the EvG reference staining. In normal vessel walls, the sensitivity of EvG was sufficient to visualize the IEL and EEL. In addition, the IEL was visible in HE images as well. However, in aneurysm walls, the conventional stainings faced their limitations. The elastic laminas were not detectable by conventional histological stainings. In multiphoton images of aneurysms, the IEL as well as the EEL was fragmented or not visible (Table 1). Conspicuously, the EEL in aneurysms was no longer visible in its original compact and lined form (Fig. 3B). Furthermore, MPM was able to show the fibromatous remodelling in aneurysm walls by visualization of collagen accumulation by SHG (blue) (Fig. 3C, Table 1). Raman measurements validated the fibromatous changes by detecting the main bands associated with collagen at 817, 855 and 933 cm −1 27 (Fig. 3D).
Atherosclerotic changes are associated with lipid and cholesterol deposits and their accumulation. MPM was able to visualize intra-and extracellular lipid deposits in atherosclerotic changes of aneurysm vessel walls (Fig. 3E,H). Small amounts of lipids were detected by the high intensity of the CARS (red) signal indicating the presence of C-H bond of lipids (Fig. 3E). Lipid-laden foam cells typically found in atherosclerotic changes were evident in HE images (Fig. 3H, black arrows). In the MPM images, clearly demarcated small lipid spots, which occurred in larger accumulations, might represent foam cells (Fig. 3H, white arrow). The large areas with intense CARS signal might represent extracellular accumulated lipids (Fig. 3H, gray arrow). In addition, deposits of cholesterol in aneurysm walls were clearly visible in MPM (Fig. 3F). Cholesterol crystals are characterized by intense CARS (red) and SHG (blue) signal, therefore, they appear as magenta structures in the MPM images 28 . HE staining did not show crystalline structured clefts of cholesterol (Fig. 3F). The decellularized wall structure (Fig. 3G). Notably, Raman spectroscopy of the cholesterol 1 image also showed bands representing carotenoids at 1158 and 1521 cm −1 27 . Furthermore, MPM and HE staining are able to visualize coagulated blood originating from a rupture and intra-wall haemorrhage in an aneurysm wall (Fig. 3I). Coagulated blood is characterized by its unique structure of fibrin from plasmatic blood clotting in HE images. In multiphoton images, the coagulated blood displayed diffuse TPEF signal. Additionally, MPM is able to directly visualize single red blood cells (RBCs) in the intra-wall haemorrhage that are recognized based on their typical morphology in the CARS image. Their round biconcave disc-shaped character with central pallor was visible at higher magnification (Fig. 3J). Raman spectra of those areas confirmed the presence of blood. Raman bands of hemoglobin at 752, 1563, 1575 and 1620 cm -1 27 were detected (Fig. 3K).
Subsequently, an overview was generated summarizing the results of the comparison of MPM with the common histopathological stainings for H&E and EvG according to important histopathological alterations associated with pathological changes within the vessel wall during the process of aneurysm formation (Table 1). Most alterations were visible in both types of aneurysms, unruptured and ruptured; differences emerged more in the frequency of the occurrence. The differences we saw (e.g. fragmented IEL, fibrotic alterations and calcification) arise most likely from the small number of aneurysm domes we studied. However, the loss of elastin and collagen fibers in ruptured aneurysms are in line with the loss of elasticity and repair mechanism of the vessel wall during disease progression.
Bifurcation. Furthermore, MPM was used to investigate cryosections of bifurcations from the human cerebral arterial circle. The special hemodynamic situation of high shear stress on the branching points of vessel trees (apex-region of e.g. bifurcations) makes them susceptible to wall remodelling and atherosclerotic changes (Fig. 4A). This in turn also fosters the development of saccular aneurysms. Both bifurcations examined here displayed alterations of the vessel wall, and in particular an evident thickening of the tunica intima marked by asterisk (Fig. 4B,C). Patient 1 exhibited an intact muscular layer of the tunica media, the IEL was fragmented as well as thickened in a few areas and lipid accumulation (white arrows) was found near the IEL (Fig. 4B). Patient 2 showed a fragmented and thinned tunica media (Fig. 4C). However, the IEL was still intact but not organized as lamellae anymore. The lipid deposits (white arrows) were located close to the IEL and collagen deposits were visible in the thickened intima (Fig. 4C). In addition, we investigated by MPM the cerebral vessel wall structure distant from the two studied bifurcations (Fig. 4D) in order to verify whether the vessel wall alterations found in bifurcations are bifurcation-specific or patient-specific (Fig. 4E,F). Both vessel walls distant of bifurcations showed rather normal vessel wall structure. This observations support the idea that the alterations found in the vessel walls of the bifurcations were bifurcation-specific. www.nature.com/scientificreports/
Discussion
In this study, we highlight the application of MPM as label-free and non-destructive tool to assess the pathological remodelling processes of cerebral aneurysm vessel walls, including atherosclerotic changes, on the microstructural level with high resolution. In particular, alterations in presence, orientation and localization of elastin were easily recognized based on TPEF signal. Moreover, collagen of the adventita and of fibrous regions was visualized by SHG. CARS showed lipid droplets and lipid-laden cells and, if colocalized with SHG, indicated the presence of cholesterol. In addition, the crystalline structure of calcifications was visualized by TPEF and erythrocytes were detected by CARS. Label-free MPM was already reported to represent a very beneficial, fast and real-time approach for the investigation of pathological vessel wall changes in peripheral arteries with the aim to study aging, fluid-solid interaction and cardiovascular diseases 13,25,26,29,30 .
MPM was used to investigate vessel wall stiffening of unruptured human cerebral aneurysm domes 30 and in the ApoE mouse model of aneurysm 29 . Here, the combination of TPEF and SHG was applied to analyze structural reorganization of the extracellular matrix (ECM) microstructure. In particular, collagen and elastin fiber orientation and the degree of fiber alignment were addressed, which play an important role during onset and progression of arterial pathologies such as vessel wall stiffening 29,30 . In line with these previous findings, our data confirmed that MPM allows the visualization of fibromatous wall remodelling in cerebral aneurysms. The specific Raman bands of collagen supported the MPM findings of collagen accumulation. The results obtained by MPM on presence, fragmentation or full loss of the elastic laminas in aneurysm walls were consistent with the results of conventional EvG staining as shown by other groups 31 . Notably, MPM (TPEF) is able to visualize elastic fibers in cryosections more clearly.
Furthermore, MPM already assessed atherosclerotic plaque burden in different animal models such as pigs 13 and myocardial infarction-prone rabbits (WHHLMI) 25 as well as in human aortas 26 . In accordance with these studies, we showed that MPM is able to detect lipid-laden foam cells and lipid droplets in human cerebral aneurysm domes. The lipid accumulations in cerebral aneurysms are more diffuse compared to the more compact atherosclerotic plaque in peripheral arteries 5,6,8 . Apart from the lipid accumulation, low-density lipoproteins such as cholesterol esters are key components of an atherosclerotic plaque in coronary artery samples 32,33 . Multiphoton images showed cholesterol crystals within the vessel wall but those were not detectable in HE image.
Noteworthy, Raman spectroscopy demonstrated presence of carotenoids in atherosclerotic-altered areas in the studied cerebral aneurysms, which are absent in regular healthy tissues 34 . Carotenoids have already been found ex vivo in necrotic core regions of coronary arteries sections 33 . Moreover, the presence of carotenoids was confirmed also in vivo during carotid endarterectomy and femoral artery bypass surgeries by catheter-based Raman spectroscopy 35 , and in patients suffering from abdominal aneurysms 36 . This provides further evidence for the advanced pathological alterations of the studied cerebral aneurysms.
Another histopathological alteration occurring in cerebral aneurysms is calcification. MPM detected calcifications in human aortas by an intense TPEF signal of the crystalline structure of calcium 26 . Our findings show that MPM visualizes calcification in cerebral aneurysms as well.
Aneurysms are also associated with bleedings. Recently, it was shown that MPM is able to visualize single mature erythrocytes based on TPEF signal 37 . Our results confirm that MPM allows displaying the typical morphology of erythrocytes. However, we visualized erythrocytes with CARS signal and not with TPEF. The reason might be related to different excitation and signal collection schemes.
In addition, we investigated cerebral arterial bifurcations without saccular aneurysm with MPM. In particular, shear stress and pressure of the blood flow stream against the walls of bifurcations mechanically contribute to alteration of their vessel walls during normal aging. This can also foster the development of saccular aneurysms in peripheral arteries as well as cerebral arteries [38][39][40][41] . Histomorphological alterations during normal aging in cerebral arteries are a thickened intima and fragmented/flattened IEL 42,43 as well as thickened tunica media with collagen deposits compared to young vessels with a thinner media 39 . In this study, one bifurcation showed in the MPM a normal tunica media without collagen deposits images only the thickened intima and the fragmented IEL were visible, which goes in line with the literature. The other bifurcation displayed an intact but flattened IEL in the MPM images, the tunica media was fragmented at the apex and the strong thickened intima showed collagen deposits. Sheffield and Weller reported this flattening of the IEL over a tunica media gap at the apex of patients above 60 years of age 42 . They also mentioned the fibrotic accumulations in the thickened intima of elderly people, which we also observed in the MPM images. Furthermore, they described lipid deposits in deeper layers of the thickened intima 42 . This confirms the hypothesis that lipid droplets accumulating in parts of the thickened intima in visible both bifurcations might be related to aging. In addition, we imaged vessels walls distant of the bifurcations that displayed a comparatively normal vessel wall structure. These findings support the conclusion that the alterations found in the bifurcation vessel walls were bifurcation-specific and not patient-specific.
Our findings provide a starting point for future MPM based investigations addressing the transition of normal vessel aging towards pathological events: This includes the onset of aneurysms formation, atherosclerotic changes and progression until rupture. Nowadays, in vivo MPM of vessel function and morphology has been investigated only in rodents 44 and miniaturized endoscopic systems have been employed for label-free colonoscopy of mice 45 as well as for redox imaging of kidney ischemia-reperfusion model 46 . Latter research group used already a compact and flexible fiber-optic probe of about 2 mm diameter. Furthermore, clinically approved systems for label-free multiphoton analysis of the human skin already exist 47 . Taking into account further technical development towards clinical application, it might be possible to investigate aneurysm walls with endomicroscopes and possibly to predict the area of rupture in the future. www.nature.com/scientificreports/ Benefits. An extended set of special immunohistochemical stainings might be likewise able to visualize the tissue alterations occurring in aneurysm formation and progression. However, MPM has crucial advantages in comparison to conventional histological stainings: it does not require any fixation process and it is characterized by high specificity and high sensitivity 48 . In contrast, the quality of all conventional stainings is influenced by chemical fixation (e.g. methanol, acetone, formalin), the embedding process and the related chemicals (especially paraffin embedding-dehydration), antigen retrieval procedure (e.g. microwave) as well as the age and quality (i.e. how often they were used) of the different staining reagents/antibodies 49 . These steps may change the native morphology e.g. of elastin and collagen. Hence, quantification of fiber fragmentation, fiber length, disorganization and total volumetric density is difficult with conventional stainings but possible with label-free MPM that can be applied on fresh, unprocessed tissue 48 . Moreover, the assessment of different criteria of wall alterations requires the analysis of multiple histological stainings of individual sections. For example, Oil Red O stain can be used for investigation of lipids and cholesterol esters; Masson-Trichrome stain or EvG stain can address collagen and elastin. In contrast, MPM is able to detect simultaneously extra-and intracellular lipids, like lipid-laden cells, low-density lipoproteins such as cholesterol and cholesterol esters as well as collagen and elastin 13,25,28 .
Limitations
Label-free MPM does not possess the ability of immunohistochemistry to address single epitopes with high specificity. At present, label-free MPM can visualize only a limited number of tissue components such as elastin, collagen and lipids. Furthermore, the required microscopy systems are rather expensive and commercial systems integrating CARS microscopy, for instance, are still of limited availability. Raman spectroscopy provides better chemical specificity for reference of MPM images, but, as it is a single-point measurement, it requires very long acquisition time for high-resolution spatial mapping. Other limitations of our study are the small specimen size as well as the aneurysm dome extraction. Only the aneurysm domes were removed after clipping, while the necks of the aneurysms remained and could not be addressed in this study. Furthermore, only one time point of aneurysm formation can be assessed for each patient. No progression studies are possible. Therefore, it is not possible to investigate the whole histopathogenesis of a cerebral aneurysm.
conclusion
In summary, we showed that label-free multiphoton microscopy is well suited to provide morphological and biochemical information that are crucial for understanding the pathological vessel wall changes of cerebral aneurysms on a macroscopic and microstructural level. Histopathological alterations of aneurysms and their atherosclerotic changes such as: wall thickening and thinning, intimal hyperplasia, fibromatous wall remodelling, loss or fragmentation of elastin fibers, intra-wall haemorrhage, calcification, cholesterol and lipid accumulation and deposits can be visualized. Hence, MPM is at least as informative as different conventional histological stainings. Mentionable, MPM is performed without any fixation, non-destructively, in real-time mode and simultaneously. MPM is able to image biological thick specimens ex vivo and in vivo. In the future, MPM might help to improve the understanding of the mechanisms of aneurysm formation and progression, which will support a better predictability of the area of rupture.
Material and methods
Samples. Cerebral human saccular aneurysm domes were obtained from surgery after clipping procedure (unruptured n = 5, ruptured n = 5). Written informed consent was obtained from all patients. The ethics committee at Dresden University Hospital of the TU Dresden (EK 890998) approved the study. Human samples of the cerebral arterial circle (Circulus arteriosus cerebri, circle of Willis) were extracted from clinical autopsy (anonymized patients). Samples from surgery were snap-frozen in liquid nitrogen and samples from autopsy were fixed in 4% formalin. Cryosections of 16 µm thickness were prepared either on SuperFrost Plus™ glass slides or on CaF 2 slides for Raman spectroscopy.
Label-free multiphoton imaging. The cryosections were rehydrated with PBS before imaging. The used multiphoton microscope system was described previously 10 . Briefly, the multiphoton microscope is formed by an upright microscope Axio Examiner Z.1 coupled to a laser scanning module LSM 7, a W Plan-Apochromat 20 × /1.0 objective and non-descanned detectors (all from Carl Zeiss Microscopy GmbH, Jena, Germany). Two erbium fiber lasers (Femto Fiber pro NIR and TNIR, Toptica Photonics AG, Gräfelfing, Germany) were used for excitation and have a pulse length of around 1 ps. The pump laser emitted at a wavelength of 781 nm and the Stokes laser for the CARS signal at 1005 nm. They were used to excite TPEF, SHG and CARS signal from the symmetric stretching vibration of methylene groups at 2850 cm -1 . All nonlinear signals were excited and acquired simultaneously using the proper optical filtering. The CARS signal was collected using a band pass filter centered on 640 nm with bandwidth of 14 nm. The TPEF signal was obtained in reflection in the spectral range of 500-550 nm. The SHG signal was acquired in transmission with a band pass filter centered at 390 nm and bandwidth of 18 nm. The signals were combined as 8 bit RGB images (red channel: CARS; green channel: TPEF; blue channel: SHG). The acquisition of large areas was performed with a tiling procedure. Z-stacks were used in order to compensate uneven surfaces of samples, followed by maximum intensity projections to obtain the final images.
Raman spectroscopy. The spectroscopy was performed with a RamanRxn spectrometer (Kaiser Optical Systems Inc., Ann Arbor, MI) coupled to a light microscope (DM2500 P, Leica Microsystems GmbH, Wetzlar, | 5,174.4 | 2020-07-23T00:00:00.000 | [
"Medicine",
"Physics"
] |
A Review of the Protective Effects of Nanoparticles in the Treatment of Nervous System Injuries
One of the most vital organs in the body is the nervous system. Damage to the nervous system may lead to a variety of issues and illnesses in people, and each year, both the affected person and society incur significant financial, human-life, and spiritual expenses as a result. Although the activity in the field of nerve repair and regeneration is growing rapidly, until now, nerve repair is not done completely. A chain of events, including inflammation, elevated oxidative stress, and the progression of damage, occur after the initial insult to the nervous system. Damage to mitochondria, proteins, and cell membrane structures, damage to adipose tissue, and eventually illnesses of the nervous system can all be a result of oxidative stress, which is brought on by an imbalance between the creation of free radicals and metabolic responses. As a result of inadequate antioxidant levels or excessive formation of free radicals, damage to nerve cells might worsen. Nerve cells require a lot of oxygen and antioxidants. To stop oxidative stress and its harmful consequences, antioxidants—either synthetic or natural—must be used. In this context, the treatment of illnesses of the neurological system may hold promise for nanoparticles with a long half-life. As a result, the biological use of nanoparticles has been stressed as a novel therapeutic strategy for the treatment of neurological disorders and lesions, which is still in its early phases. Therefore, the purpose of this review is to ascertain how protective nanoparticles are in the therapy of nervous system damage.
INTRODUCTION
Peripheral nerves are usually subject to physical damage.Usually, construction and transportation accidents, natural disasters, injuries caused by war, and other traumas such as diseases and complications caused by surgery cause peripheral nerve damage [1,2].Following peripheral damage, a series of pathophysiological events occur, which leads to valerian disintegration in the distal part and the loss of a small part of the proximal part of the axon.Together, macrophages, monocytes, and Schwann cells remove the myelin sheath and axon debris.Schwann cells multiply and form a bridge called the band of Bungner [3,4].These cells produce extracellular matrix molecules and neurotrophic factors to stimulate axon regeneration [5].Axon sprouts are formed by the nodes of Rannoia and the new myelin sheath is formed by Schwann cells.Axon sprouts grow until the axon can perform its functions again.Spontaneous repair of the peripheral nerve is almost always incomplete and the function of the nerve does not completely return to its original state [6,7].Strokes, head trauma, spinal cord injuries, and retinal degeneration are some examples of central nervous system injuries.These lesions in children are often traumatic or congenital defects, while in adults they are traumatic or degenerative.Following damage to the central nervous system, events such as the death of nerve cells, destruction of nerve fibers and glycolysis, and an excessive increase in the number of glial cells (such as astrocytes, oligodendrocytes, and microglia) occur.Neurons cannot divide, so if a neuron is destroyed, a new neuron will not replace it, as a result, the central nervous system, unlike the peripheral nervous system, does not have the inherent ability to repair itself [8][9][10].Regenerative medicine is a branch of modern medical science whose goal is to restore and restore damaged or lost tissue or organs, which, according to the type of treatment approach and method, includes cell therapy, treatment using the patient's cells, treatment using non-autologous donor cells, treatment with growth factors, use of recombinant proteins, use of small molecules, tissue engineering, and gene therapy [11][12][13].One of the more recent and useful fields that has caught the interest of academics and offered several chances for advancement in the medical sciences is nanotechnology.This technology is employed in the medical field as well as in the military, agriculture, diagnostic procedures, magnetic imaging, sensors, and fast material detection.These days, scientists employ this technology to identify and treat a wide range of illnesses, including cancer.Thus, by concentrating on molecular techniques, this discipline has gained recognition as a significant branch that has made remarkable developments in recent years [14].Materials that are utilized in surgery, dentistry, all types of experimental science studies, biomechanical biosystems, the battle against germs, etc. may be created using nanotechnology, which is based on the utilization of atoms and molecules.Scientists currently have little control over the scope of nanoparticle impacts, despite the fact that there have been several studies on the subject [15][16][17].Less intrusive techniques are more appropriate for the discussion of imaging methods, making nanoparticles the best possible candidates for the creation of such techniques.In nanotechnology, they utilize specially designed materials that can interact with biological systems at the molecular level and stimulate the nervous system while causing the fewest possible adverse effects.Contrary to conventional systems like pills and liquids, nanoparticles intelligently regulate and sustain the distribution of medications in various organs, resulting in more and better effects [18,19].Nanoparticles are used for imaging in neuroscience and also to investigate the fate of adult stem cells in nervous systems and in the treatment of many nervous system disorders [20,21].Today, much research is conducted on smart materials that can help in the regeneration and treatment of nerves through various methods such as antioxidant effects, stimulating the proliferation of nerve cells, modulating inflammatory factors, etc.Therefore, due to their chemical and morphological characteristics, some nanoparticles are promising therapeutic methods that can have neuroprotective and antioxidant properties depending on the dose and size [22].So, the purpose of this study is to look at how nanoparticles might help guard against nervous system damage.
Nanoparticles as new drug delivery systems in the nervous system
Protective barriers make it difficult for biologists to deliver drugs to the central nervous system.Drugs must be able to penetrate the blood-brain barrier and enter therapeutic concentrations in the brain after administration for them to be effective in the central nervous system [23]; otherwise, they won't be able to do their jobs [23].As a result, ineffectiveness in the treatment of illnesses of the central nervous system is frequently not a result of a medicine's insufficient potency but rather of an issue with the way the drug is delivered.Recently, interesting results have been observed in the field of nanotechnology, particularly when nanoparticles are used to transport drugs [24].Typically, for a pharmacological therapy to be successful, it has to have a long shelf life in the blood.It is now possible to functionalize the surface of nanoparticles with positively charged biomolecules to create an electrostatic interaction, which facilitates the passage of nanoparticles through the blood-brain barrier because endothelial cells have negative charges on their surface.Transferrin and lipoprotein receptors in the cell allow nanoparticles to absorb and cross the blood-brain barrier [25].Additionally, the prolonged circulation of modified nanoparticles in the blood makes it simpler for them to interact with and enter endothelial cells, which opens up the prospect of greater control over the actions of the cells.The use of nanoparticles in medicine is still plagued by issues including unknown tissue interactions and unpredictable outcomes, despite the current advancements in the field of nanoscience.In this context, high-penetrating-power cerium oxide nanoparticles can inhibit the development of scar tissue that hinders healing in spinal cord lesions [26].As opposed to anionic nanoparticles, cationic nanoparticles are more permeable to the central nervous system and can remain in circulation for extended periods of time without having hazardous consequences.For instance, cationic gold nanoparticles may enter cells without using energy and by avoiding processes like endocytosis, which might have an impact on cell function [27].Enzyme carriers for antioxidants can be made from nanomaterials.Antioxidant enzymes can lower reactive oxygen species (ROS), but because of their transient presence in the blood and subsequent decomposition, they have a hard time crossing the blood-brain barrier [28].Polymer nanoparticles are the most common type of medication delivery technology because they can cross cells' tight connections.Additionally, they have a high drug-loading capacity and boost the efficiency of medications taken in combination.In this aspect, nanocapsules are crucial to current drug delivery because they can preserve the medication and have a high drug-loading capacity, increasing the likelihood that the drug will reach the brain.Additionally, the reticuloendothelial system's macrophages are protected from drug detection by these nanoparticles [29].
Nanoparticles in the treatment of central nervous system diseases Ischemia
A stroke caused by a lack of blood supply to a part of the brain is a neurological disorder.One of the most typical stroke symptoms is the generation of free radicals [30].Some nanoparticles have the potential to inhibit reactive oxygen species in stroke.Nanoparticles of platinum and cerium oxide, due to their antioxidant properties, have been promising answers for improving and treating stroke.These nanoparticles mimic the activity of antioxidant enzymes and destroy free radicals [31].The use of these nanoparticles significantly reduces the volume of the damaged area.The use of gold nanoparticles in the treatment of stroke depends on the size of the nanoparticles.A study showed that gold nanoparticles with a size of 20 nm reduced the volume of the damaged area, while the same nanoparticles with a size of 5 nm can cause damage to nucleic acids by accumulating in the nucleus, so the antioxidant property depends on the size of the nanoparticles.Also, in another study, it was shown that cerium oxide nanoparticles reduced the death of rats by reducing the induction of nitric oxide synthesis in the hippocampus of rats [32].Research has shown that the use of nanoparticles causes the neutrophils that cause the immune response to be inhibited and prevent severe brain damage in brain models [33].Increased nestin protein is effective in post-injury repair mechanisms.Also, this protein is expressed in large amounts during the early stages of development of the central and peripheral nervous system [34].Researchers showed an increase in the number of cells expressing Nestin as a result of treatment with silver nanoparticles in mouse models of stroke, which indicated the effectiveness of these nanoparticles in neurogenesis [35].
Alzheimer
Alzheimer's disease (AD) or amnestic disease is a type of brain disorder with a gradual weakening in which the functions and mental abilities of the patient are degraded.In Alzheimer's disease, a recent event usually occurs first, and unfortunately, a cause or a suitable treatment is not available.Accumulated evidence supports the hypothesis that oxidative stress produced by different mechanisms may be among the main factors promoting neurodegeneration [36].The accumulation of amyloid plaques is one of the known causes of Alzheimer's disease, which is found in all parts of the brain of these patients, and in laboratory environments, beta-amyloid is used to induce Alzheimer's disease in mice.In their research, D'Angelo et al. found that treatment with cerium oxide nanoparticles protects brain neurons against oxidative stress induced by beta-amyloid.The obtained results emphasized the neurotrophic role of these nanoparticles as a factor that can modulate the important pathways of nerve cell survival.Also, Das et al. investigated the antioxidant and neuroprotective properties of cerium oxide nanoparticles in spinal cord injuries.In this research, it was observed that treatment with this nanoparticle causes the growth and survival of nerve cells in the spinal cord [37].Among the factors of accumulation of amyloid beta proteins, we can mention metal ions such as copper and iron, which increase with age in the brain.Nanoparticles can remove metals from the body or prevent their undesirable functions through their specific bonds.Nanogels have been considered due to their high stability, ability to respond to external stimuli, and high and accurate loading of active substances such as drugs.In Alzheimer's disease, nanogels are also used to prevent the accumulation of amyloid beta plaques [34].In research that investigated the effects of silver nanoparticles on Alzheimer's disease, the results showed that the surfaces of silver nanoparticles can act as a nano chaperone and inhibit the formation of amyloid fibers.As a result, the medicinal use of these nanoparticles can be useful for the treatment of Alzheimer's disease.Dowding J and his colleagues showed that cerium oxide nanoparticles can switch between their Ce3+ and Ce4+ states and in this way can destroy superoxide anions and hydrogen peroxide.Also, these nanoparticles accumulate in the outer membrane of the mitochondria and prevent the collapse of the mitochondrial structure due to the toxicity caused by beta-amyloid.Therefore, cerium oxide nanoparticles have antioxidant properties, and drug treatment by this nanoparticle can prevent the destruction and death of nerve cells in Alzheimer's disease [38].
Parkinson
Parkinson's disease (PD) mainly affects brain dopaminergic cells.Parkinson's disease is a multifactorial cascade of destructive factors that usually affects people over 65 years old.Loss of dopaminergic neurons leads to tremors, speech, and memory impairment.A subset of patients appears to follow an autosomal dominant inheritance pattern, although in most cases the inheritance pattern is not discernible [39].Researchers used a method based on nanoparticles to prevent neurodegeneration in animal models of Parkinson's disease to transfer plasmids containing desired genes to the brain.This approach discovered a gene therapy-based method for the treatment of Parkinson's disease that had the potential to repair defective genes [40].Iron oxide nanoparticles, by affecting the interaction of neurons and surrounding cells, play a significant role in increasing the regeneration capacity of neurons after spinal cord injury.The ability of magnetic iron oxide nanoparticles to track the migration of leukocytes and track cells inside the body can be useful in the study of central nervous system lesions such as Parkinson's, stroke, brain tumors, epilepsy, and Alzheimer's.Stressed or disabled neurons need more energy to survive and repair and improve their function.Improving the metabolic pathways and improving the level of adenosine triphosphate (ATP) (Adenosine triphosphate; and Nicotinamide adenine dinucleotide; NADH)) is one of the characteristics of nanoparticles in the brain [41].For example, introducing a suspension containing gold nanoparticles into the body of rats has been effective in improving the symptoms of Alzheimer's and Parkinson's disease [42].
Multiple sclerosis
Although the cause of multiple sclerosis (MS) is unknown, it seems to be caused by the interaction of genes and the environment, and diet, sunlight, infections, and genetics are important factors in MS patients.Despite promising advances in the understanding of modern diseases, precise details about the inflammatory processes are still not available [43].MS is an inflammatory disease that destroys the central nervous system, especially in adults, which causes numbness and vision loss.In early definitions, MS was described as a disease characterized by inflammation around blood vessels and damage to myelin.This disease has been identified in more than 2 million people worldwide, mainly based on medical history and clinical examination of the patient [44].Obstruction of blood flow in narrow vessels and increased production and accumulation of reactive oxygen species in MS lead to the activation of macrophages and apoptosis in oligodendrocytes [45].The use of nanoliposomes in modern drug delivery systems, along with their structural similarity to biological membranes, can show fewer side effects and better treatment processes in the target tissue with controlled release and accurate targeting.In research, the use of nanocarriers such as nanoliposomes has shown promising results in improving MS symptoms [46].For the purpose of describing autoimmune illness in humans and understanding MS, Eitan and his colleagues used mouse models to show the impact of cerium oxide nanoparticles.Clinical symptoms, damage to the white matter of the central nervous system, and inflammation of the central nervous system were all decreased by drug therapy using nanoparticles [47].
Nanoparticles in the treatment of peripheral nervous system diseases
Considering that different mechanisms are involved in the repair of peripheral nerves, as a result, various molecular signals can be effective in these processes.These signals can play a role in these complex processes separately or in cooperation with each other using specific methods such as a specific expression or deletion of genes in nerve tissue cells or using specific antibodies.Several factors can cause damage to peripheral nerves, in addition to causing changes in the axon of damaged neurons, damage to peripheral nerves can also cause dysfunction of the organs associated with them [48].As a consequence of the nanoparticles' tiny size, which increases their surface-to-volume ratio and allows them to absorb more free radicals, they may be an effective technique to deal with free radicals produced as a result of nerve injury.It should be emphasized that because such modeling in mice is reasonably affordable, peripheral nerve researchers frequently employ the sciatic nerve as a study tool for nerve healing using varied dosages [49].The effects of cerium oxide nanoparticles on enhancing motor function and tissue alterations after sciatic nerve damage in rats were studied by Soluki et al.When compared to the control group, the groups that received cerium oxide treatment recovered considerably faster and had improved motor function.Additionally, it was shown that cerium oxide nanoparticles decreased cell apoptosis and were successful in peripheral nerve healing in a study that examined the effects of oxidative stress on endothelial cells and nerve cells.Reducing oxidative damage also increases the lifespan of neuron cells, and because cerium oxide has antioxidant properties, cerium oxide nanoparticles can swiftly act and absorb reactive oxygen species during this process.Additionally, this chemical has been shown to have impacts on angiogenesis, nervous system modulation, anti-cancer applications, decreasing high blood pressure, antimicrobial properties, lowering cholesterol levels, and preventing damage to injured tissue [11].There is a lot of optimism for developing medical diagnostic and therapeutic facilities thanks to the characteristics of nanoparticles.Magnetic nanoparticles are a popular molecule for diagnostic and therapeutic applications because they may deliver medications to desired areas using a magnetic field [50].Scientists are trying to repair nerves by optimizing the properties of nanoparticles and stimulation parameters.Gold nanoparticles, as a substrate and matrix that is electrically conductive, are a promising material for the regeneration of peripheral nerves [42].In diseases of the nervous system, it is also possible to disperse drug particles in a very small size in an external liquid phase using nanosuspensions.Ease of manufacturing process, much lower toxicity, and increased efficiency are the advantages of nanosuspensions [18].Nanocarbon formulation can also be used for various applications such as cancer diagnosis, imaging drug delivery, and tissue engineering [51].
CONCLUSION
Following damage to the nervous system, the use of neuroprotective agents is a suitable strategy to control the damage and restore the system.Nowadays, the use of nanoparticles as a new factor has been widely considered.Some nanoparticles have neuroprotective properties due to their antioxidant properties and other chemical and morphological characteristics.In general, nanoparticles are promising therapeutic methods that are still in the early stages, but considering extensive studies in this field, this therapeutic approach is expected to be one of the useful therapeutic agents in the treatment of neurological lesions in the future. | 4,270 | 2023-01-01T00:00:00.000 | [
"Medicine",
"Environmental Science",
"Materials Science"
] |
Smooth and fast versus instantaneous quenches in quantum field theory
We examine in detail the relationship between smooth fast quantum quenches, characterized by a time scale $\delta t$, and {\em instantaneous quenches}, within the framework of exactly solvable mass quenches in free scalar field theory. Our earlier studies \cite{dgm1,dgm2} highlighted that the two protocols remain distinct in the limit $\delta t \rightarrow 0$ because of the relation of the quench rate to the UV cut-off, i.e., $1/\delta t\ll\Lambda$ always holds in the fast smooth quenches while $1/\delta t\sim\Lambda$ for instantaneous quenches. Here we study UV finite quantities like correlators at finite spatial distances and the excess energy produced above the final ground state energy. We show that at late times and large distances (compared to the quench time scale) the smooth quench correlator approaches that for the instantaneous quench. At early times, we find that for small spatial separation and small $\delta t$, the correlator scales universally with $\delta t$, exactly as in the scaling of renormalized one point functions found in earlier work. At larger separation, the dependence on $\delta t$ drops out. The excess energy density is finite (for finite $m\delta t$) and scales in a universal fashion for all $d$. However, the scaling behaviour produces a divergent result in the limit $m\delta t \rightarrow 0$ for $d\ge4$, just as in an instantaneous quench, where it is UV divergent for $d \geq 4$. We argue that similar results hold for arbitrary interacting theories: the excess energy density produced is expected to diverge for scaling dimensions $\Delta>d/2$.
Contents
1 Introduction Universal scaling behavior in systems undergoing a quantum (or thermal) quench which involves critical points have been a subject of great interest in recent years [3][4][5][6]. The classic example of such behavior is Kibble-Zurek scaling [4,5] which involves a quench which starts from a gapped phase at a rate which is slow compared to the scale set by the initial gap. At the other extreme, there are a different set of universal behaviors in two-dimensional field theories which are quenched instantaneously from a gapped phase to a critical point [7,8] and for instantaneous quenches which can be treated perturbatively [9]. The AdS/CFT correspondence has yielded important insight in this area, both for Kibble-Zurek scaling [10] and for novel non-equilibrium phases [11]. Perhaps more significantly, holographic studies have led to the discovery of new scaling behavior for smooth quenches which are fast compared to the physical mass scales, but slow compared to the UV scale [12,13]. In [1] and [2] we argued that this scaling law holds regardless of holography, and is valid for time dependent relevant deformations of generic conformal field theories (see also [14]). Consider an action where the conformal dimension of the operator O is ∆ and λ(t) interpolates between the constant values λ 1 and λ 2 (with an amplitude variation of δλ) over a time of order δt. Then in the fast quench limit Similarly, the peak of the renormalized expectation value of the quenched operator, measured at times earlier than or soon after the end of the quench, was also found to scale as O ∆ ren ∼ δλ δt 2∆−d , (1.4) This general result emerged out of detailed investigations of exactly solvable mass quenches in free bosonic and fermionic theories. One important outcome of our analysis was an understanding of the relationship between smooth fast quenches for small δt and the instantaneous quenches of e.g., [7,8]. The latter involve a quench rate which is fast compared to all scales, including the UV cutoff, while smooth quench rates are faster than any physical scales, but slower than the cutoff scale. On the other hand, local quantities like the energy density or O involve a sum over all momenta all the way to the cutoff -for such quantities one does not expect the smooth quench result to agree with those in the instantaneous quench. By the same token, one would expect that for correlators at finite separations larger than δt, there should be agreement. In [1,2] we also explored if the late time behavior of local quantities also agree, finding agreement at least in the d = 3 case.
In this paper we continue to explore the relationship between fast but smooth quenches and instantaneous quenches in further detail. Our analysis will focus on quenches in free scalar field theory with a time-dependent mass. However we argue that the lessons we draw there will be valid for quenches in interacting theories of the type described above.
The scaling laws in [1,2] were derived for renormalized composite operators, which are the appropriate quantities for quench rates much slower than the cutoff scale. In this work, we examine the late time behavior of such operators. In addition, we focus on quantities which are UV finite, e.g., two-point correlation functions at finite spatial separations and the excess energy over the ground state energy at late times.
In section 3, we consider late time correlators, t δt. We will show that for (suitably defined) large spatial separations, these correlators agree with the correlators for an instantaneous quench. For separations r which are very small, i.e., mr 1 there is once again agreement, reflecting the fact that the dominant singular behavior for small separation is independent of any time dependence of the mass. The corrections to this leading small distance behavior are in one-to-one correspondence with the counterterms necessary to renormalize the composite operator φ 2 . In particular, the subleading small distance divergences involve derivatives of the mass function for d ≥ 6. For intermediate separations, the two quench protocols lead to genuinely different results.
In section 4, we turn our attention to correlators at finite times t ∼ δt and show that for rδt 1 the correlator becomes independent of δt as expected. For m −1 > δt > r we find that the correlator exhibits a scaling behavior identical to that of the renormalized local operator φ 2 .
In section 5, we consider the renormalized local quantity φ 2 at late times. We show that this quantity agrees for both quench protocols only for d = 3. For d = 5 and finite δt, there is a slight difference between the smooth and the instantaneous answer in the limit of δt → 0, while for the instantaneous quench, φ 2 is UV divergent for d > 5.
In section 6, we consider the difference of the energy at late times and the ground state energy with the final value of the mass. This is one measure of the excess energy produced during the quench. We show that this quantity is explicitly UV finite. For d ≤ 3 this becomes independent of δt, in the mδt 1 limit. The next order correction, which scales as a power of δt, is identical to the behavior of the renormalized energy in [1,2]. For d ≥ 4, the energy diverges in the δt → 0 limit, in the same way as the renormalized energy considered in [1,2].
In section 7, we discuss the validity of our results for the excess energy produced for general interacting field theories.
In section 8, we conclude with a brief discussion of our results and also consider various possible measures of the energy produced by the quench and their relationship.
Bogoliubov coefficients for smooth and instantaneous quenches
Consider a scalar field in d space-time dimensions with a time dependent mass, This theory is exactly solvable for a variety of different mass profiles, as described in [1,2]. The quench protocol which we focus on here, involves the mass going from an initial value m to zero at late times over a time scale δt with the smooth profile m 2 (t) = m 2 1 − tanh(t/δt) 2 . (2.2) To solve the Klein-Gordon equation, we decompose the scalar field into momentum modes The exact solution of the field equation is given by [1,2,15] where 2 F 1 is the usual hypergeometric function and ω in = k 2 + m 2 , ω out = | k| , (2.6) ω ± = (ω out ± ω in )/2 .
The modes u k are the "in" modes: they behave as plane waves in the infinite past and the a k annihilate the in-vacuum, i.e., a k |in, 0 = 0. There is also another set of modes, the "out-modes", which become plane waves in the infinite future, v k = 1 √ 2ω out exp(i k · x − iω + t − iω − δt log(2 cosh t/δt)) × 2 F 1 1 + iω − δt, iω − δt; 1 + iω out δt; 1 − tanh(t/δt) 2 . (2.7) In terms of these, the field operator is The Bogoliubov transformation that relates these two sets of modes is given by [15] u The Heisenberg-picture state of the system is the "in" vacuum, a k |in, 0 = 0 . (2.11) We will be interested in analysing several quantities: (i) the two-point correlator of the field at a finite spatial separation (ii) the expectation value of the composite operator φ 2 and (iii) the net energy density produced. In fact, the rate of change of the energy density is related to φ 2 by the Ward identity The two point correlation function of the scalar field under the quench reads We will be interested in the relationship of the results of a smooth quench as in (2.2) to that of an instantaneous quench from a mass m to zero mass, (2.14) The "in" and "out" modes for such an instantaneous quench have a trivial plane wave profile for before and after the quench, respectively The Bogoliubov coefficients for the instantaneous quench are determined by demanding that the mode functions and their first derivatives are continuous at t = 0. This yields: The correlator for an instantaneous quench can be easily computed using (2.16) (or by directly matching the operator solutions across t = 0 as in [8]), The comparison of the instantaneous quench with the smooth fast quench is only meaningful at late times when the variation of the mass in the smooth quench is over, i.e., when t δt and t δt. For such times, the mode functions v k ( x, t) → v instant k which are exactly the mode functions for t > 0 in instantaneous quench.
In what follows, it is useful to look at the behavior of the Bogoliubov coefficients in various regimes. 1. First consider the limit ω in δt, ω out δt 1 .
It may be easily checked that in this limit, the smooth quench Bogoliubov coefficients (2.10) reduce to the instantaneous quench coefficients (2.16), regardless of the value of | k|/m. This means that the smooth quench approaches an instantaneous quench when δt is small compared to all other length scales in the problem. In particular, this means that the momentum space correlators at some momentum k will approach the instantaneous correlator only when mδt 1 as well as | k|δt 1. In [1] we discussed the implications of this for expectation values of local quantities like φ 2 (x, t) or the energy density. Generically, the small mδt 1 limit of these local quantities will not agree with the instantaneous quench result since these quantities involve an integration over momenta all way upto the cutoff, and the physical smooth quenches, in which we are interested, are fast compared to physical mass scales but slow compared to the cutoff scale. It can be the case, however, that the integrand is a rapidly decaying function. If so, even if we have to integrate to arbitrarily high momenta, the main contributions will come from low momenta and then there would be agreement between the two protocols. For example, as shown in [2], this is what happens in evaluating φ 2 in d = 3. In section 5, we will go back to this discussion and show that in higher dimensions this is not generally true.
Now consider the limit
Once again in this limit, the Bogololiubov coefficients (2.10) approach the instantaneous quench coefficients (2.16), for any finite value of | k|δt. In fact, in this limit the coefficients (2.10) behave as where ψ(x) denotes the digamma function, i.e., ψ(x) = ∂ x log Γ(x). For the instantaneous quench, instead, they behave as Thus to leading order in m 2 /k 2 , we have α k = 1, β k = 0 for both smooth and instantaneous quenches regardless of the value of kδt. This is a reflection of the fact that very high momentum modes are not excited by the quench, i.e., to leading order the quench is immaterial for these modes. The subleading terms in (2.20) are of course dependent on δt. In fact, for finite kδt, the subleading term in α k is O(m 2 /k 2 ). However, if in addition we have kδt 1, this O(m 2 /k 2 ) term is cancelled, as it should be.
In the next section we discuss the implications of these observations for real space correlation functions.
Late time spatial correlators
In this section, we examine equal time correlation functions at finite spatial separations and compare the result for smooth fast quenches and instantaneous quenches at late times. For simplicity, we only explicitly consider the correlators in odd spacetime dimensions in the following. We will consider this correlator in eq. (3.1) in three different situations: the first one is the equal time correlator for a smooth quench from a mass m to zero mass, as in eq. (2.2), where α k and β k are given by eq. (2.10). The second quantity is the equal time correlator for an instantaneous quench which can be read off from eq. (2.17), This correlator was studied in e.g., [8]. Finally, we consider the correlator for a constant mass m = 0, Constant mass correlators are evaluated in detail in Appendix A, including the case of m = 0 -see eq. (A.8). Performing the angular integrals above we find where σ c = 2 Before proceeding with the detailed calculations, let us present our intuitive expectations for the comparison, as well as the results found below. As in section 2, we are considering quenches which take the mass from some fixed initial value m to zero after the quench. There are several different dimensionful parameters at play in our correlators, i.e., t, δt, r = | r | and m, and so first, we wish to clearly specify how the corresponding scales are ordered in our considerations below. First, for the smooth quenches, we are considering the fast quench limit and hence we have mδt 1. We are also examining the correlators in late time limit and hence δt t. While these inequalities do not fix a relation between m and t, we will only present results for the case mt > 1. That is, the following discussion explicitly considers quenches where We have verified that the general behaviour is the same in regimes where mt 1, as long as the inequalities for the fast quench and late time limits are both satisfied. Given the ordering in eq. (3.8), we still have one remaining scale unspecified, namely the spatial separation r = | r |. In the following, we compare the correlator (3.1) for fast smooth quenches and that (3.3) for instantaneous quenches for r in different regimes. The natural intuition is that in the Fourier transform, only momenta satisfying k 1/r will contribute significantly to the correlator. Hence given that we are in the fast quench regime with mδt 1, if we further choose r δt, then both of the inequalities in eq. (2.18) should be satisfied for the momenta contributing to the correlators. Hence the analysis in the previous section would indicate that at late times, the integrand in eq. (2.13) for the smooth quenches effectively reduces to that in eq. (2.17) matching the correlator for an instantaneous quench. We will explicitly verify that this expectation is realized by numerically comparing the full expression (2.13) for smooth quenches with the instantaneous quench result (2.17) at late times.
Continuing with the above intuition, differences between the late-time correlators for the two different quench protocols are expected to arise in a regime where the spatial separation is comparable to the quench time, i.e., r δt. In view of eq. (3.8), this means that we would be examining the correlator at short distance scales. However, we also found that for very large k m the leading behavior of the Bogoliubov coefficients are in fact independent of the quench rate -see discussion following eq. (2.19). This immediately implies that the leading singularity at small r is independent of any quench protocol and therefore one gets the same singular behaviour as the constant mass correlators in this regime, namely, C(t, r ) ∝ 1/r d−2 -see Appendix A. Hence the leading behaviour in the correlators produced by the smooth and instantaneous quenches again agrees in this regime. As we will show below, the subleading singularities are in fact different in high dimensions.
The interesting regime where the difference between a smooth and instantaneous quench would show up is therefore the intermediate values of r. To study this difference it is convenient to eliminate the leading small-r contribution by calculating the difference between the two quench correlators, i.e., C smooth (t, r ) − C instant (t, r ), or alternatively by subtracting the fixed mass correlator from each of the quench correlators individually. As we describe in detail below, this difference of the late-time correlators indicates that the subleading behaviour, in fact, also agrees for d = 3 but a small finite difference arises for d = 5. For d = 7 and higher dimensions, the difference still diverges in the limit r → 0.
Numerical results for various dimensions
We now evaluate the k integrals in eqs. (3.5) -(3.7) numerically. However the integrands are typically oscillating rapidly with a growing envelope. Hence to evaluate the integral properly, we need to regulate the integral. We do so by introducing a convergence factor exp(−ak) with a > 0 and evaluating the integral in the limit a → 0, as discussed in Appendix A. Using this regulator, the integral in eq. (3.7) can be evaluated to yield C const ( r) ∝ 1/r d−2 , as in eq. (A.8). This is the standard massless propagator in d dimensions. For our numerical calculations, we typically use a = 10 −3 , which we can verify is small enough that the integrals accurately converge to their limiting values.
As noted in the above discussion, for large k m, C smooth (k) and C instant (k) are essentially identical to C const (k), implying that the leading divergence in all the corresponding correlators is 1/r d−2 for small r. Hence, the integrands are very close to each other for a large range of k, as illustrated in fig. 1. Therefore, in order to highlight the differences between the smooth and instantaneous quenches, we will subtract off eq. (3.7) to define for both cases (3.9) In terms of the integrands, subtracting C const (k) suppresses the growing oscillations at large k that, e.g., we see in fig. 1. In the full correlator, this subtraction removes the divergent behaviour at r → 0, which makes it easier to identify differences in the finite remainder. If this behaviour was not removed, for instance, both the instantaneous and the smooth quench would both grow as 1/r d−2 in exactly the same way as r → 0 and it would be extremely difficult to find any differences between the correlators for the two different quench protocols in this regime. 1 In comparing the subtracted integrands C below, we start by considering d = 5.
In fig. 1, as well as the good agreement between the quench correlators and the constant massless correlator at large k, we see that the two integrands, C smooth (k) and C instant (k), agree for throughout the momentum range shown there. Given our discussion at the opening of this section, we only expect differences to arise when k 1/δt. One way to illustrate these differences is to make δt larger, as illustrated in fig. 2. Panel (a) shows the subtracted integrands in the range 0 ≤ k ≤ 2 with the same parameters as used in fig. 1, i.e., mt = 10, mr = 10 and mδt = 1/20 for d = 5, and the two curves precisely overlap in this momentum range. The only change of parameters in panel (b) is that here mδt = 1/2 and we clearly see that small differences appear between the integrand for the smooth quench and that for the instantaneous quench. Note, however, that with mδt = 1/2, the smooth quench only barely satisfies eq. (2.18) and so while useful to illustrate possible differences, this example is not really in the fast quench regime. Focusing on the parameters mt = 10, mr = 10 and mδt = 1/20 (for d = 5), we see in fig. 3 that the subtracted integrands continue to agree for much larger values of k. However, with k/m ∼ 20, differences are clearly visible in panel (b). However, comparing the vertical scale in these two plots to that in panel (a) of fig. 1, we see that these large k contributions to the subtracted integrand are highly suppressed. 2 Hence the differences should not be expected to contribute to the full integral, i.e., they should not produce significant differences in the position-space correlators. It turns out that examining the subtracted integrands for d = 3 yields essentially the same results. On the other hand, the situation is also similar in d = 7 for long distances. As we decrease r, for d = 7, we see analogous effects to those in fig. 4, i.e., the two integrands become clearly different. However, as we will see, after integration, the behaviour of the correlator at small distances is very different depending on the dimension. Given that we understand the behaviour of the (subtracted) integrands, let us now compare the (position-space) correlators for instantaneous and smooth quenches at different values of r, as shown in fig. 5. In the figure, we have chosen mt = 10 and mδt = 1/20 while mr varies from 10 to 0.001. As we have expected, the figure shows that the difference between the correlators goes to zero, or at least is of order O(δt 2 ), at large mr. The results for d = 3 indicate that the difference remains vanishingly small for all values of r. In the case of d = 5, a small but finite difference appears to develop as r goes to zero. The differences in fig. 5 are most evident for d = 7. In this case, the relative difference is already of order one at mr = 0.1 and the trend in the figure is that it continues to grow at smaller r. Our expectation is that in fact, this difference will in fact diverge as r → 0. This conclusion comes from comparing to the late-time behaviour of expectation value φ 2 ren in the next section. In summary then, we have explicitly shown that at times long after the quench, the correlators generated by instantaneous and the smooth fast quenches are identical at large separations. As might be expected, differences only appear at separations of the order the quench time δt. Further these differences are small in lower dimensions, e.g., d = 3, 5, but can be quite dramatic in higher dimensions. Interestingly, for d = 3 and 5, the subtracted correlator of both the instantaneous and the smooth quench (with the mr = 0 piece subtracted out) agree to a rather high precision for any distance mr. As we increase mr both answers become even closer.
Small r behavior and counterterms for local operators
In [1,2], we studied the UV divergences appearing in φ 2 with a momentum cut-off in great detail. Intuitively, one can think that the correlator at small r provides a point-splitting regulator of the same quantity. Hence, the divergences in the correlator at small r should be related to the UV divergences of the local quantity φ 2 . In this subsection, we make this connection precise.
Let's start with the constant massless correlator, (3.7). For small r we can expand the Bessel function to get, Inserting this in eq. (3.7), we get an integral of k d−3 , exactly the same as the leading divergence in φ 2 . Let us first recall the set of counterterms that we found in [1,2] for φ 2 . There the leading divergences in momentum space were determined by performing an adiabatic expansion in time derivatives and then expanding our results for large momentum. We then found that this was the same as expanding the integrand of φ 2 . So, to be more specific, in the "in"-basis, the integrand took the form k d−2 ω −1 in | 2 F 1 | 2 and for large k we found [2] Above, we are giving all the terms needed to regulate the expectation value up to d = 9. Apart from the divergent terms in the constant mass expectation value (that will appear as zeroth order in the adiabatic expansion), they include terms with time derivatives of the mass profile which produce divergences in φ 2 for d ≥ 6. These (perhaps surprising) terms were carefully analysed in [2]. Now we can express the bare expectation value of the local operator in terms of an energy cut-off Λ, obtained by integrating the momentum integral up to a maximum value k max Λ. This yields Working in terms of the "in" modes, the smooth quench correlator can be expressed as where in the last line we have presented the integrand in a way which allows us to make use of the above expansion in eq. (3.13). So we have all the ingredients to take the limit from the spatial correlator to the expectation value. In particular, if we take the r → 0, then the Bessel function can be replaced for its zeroth order expansion shown in eq. (3.10). The powers of kr in eq. (3.10) will cancel those same powers appearing in eq. (3.13), while the numerical factors will turn the σ c into a σ s . 3 Then we can use eq. (3.11) to expand for large k and find that the correlator behaves exactly in the same way as φ 2 when r → 0. In fact, Of course for any finite (positive) r the correlator will be UV finite. So in principle we should be able to perform the integral over momenta to obtain a series expansion in inverse powers of r. We now show that this small-r expansion of the correlator is directly related to the large-k expansion for the expectation value. Let us take expression in eq. (3.13) and replace k d−2 ω −1 in | 2 F 1 | 2 with the expansion given in eq. (3.11). The integrand is composed of a series of terms which are constants (not functions of momentum) multiplying the Bessel function and some power of k. For fixed value of r, we can integrate that expression, using .
Now, as an example, consider the leading divergence, i.e., k d−3 , which gives (3.16) 3 We remind the reader that σ s is a numerical constant that depends on the space-time dimension d and was used in [1,2] to normalize the expectation value of φ 2 . Explicitly, σ s ≡ 2(2π) d−1 where Ω d−2 is the angular volume of a unit (d − 2)-dimensional sphere.
after using eq. (3.15) with α = (d − 3)/2 and some algebra. This shows that UV divergences of the local quantity φ 2 appear as inverse powers of r in the finite spatial separation correlator, i.e., r plays the role of a point-splitting regulator, replacing the momentum cut-off Λ in eq. (3.13). In the above example we showed that the leading divergence is proportional to r d−2 . We can proceed to do the integral for α = d−3 2 − 2. This would correspond to divergences proportional to k d−5 and will lead to a term in the spatial correlator which is inversely proportional to r d−4 . Note that in general, eq. (3.15) maps the integral over k α to the power 1/r α+1 . Also note that there is an important difference between the leading divergence and the rest of the divergent terms. All of the subleading divergences are proportional either to the instantaneous mass m(t) or to time derivatives of m(t), while the leading divergence is independent of m(t). This means that the leading term as r → 0 will be inversely proportional to r d−2 but then there will be subleading terms inversely proportional to r d−4 , r d−6 , etc., that will also contain factors of the mass and its derivatives. Explicitly we find In particular, note that to analyse the structure of the correlator in d = 7, we would have to take into account a term that is proportional to the second derivative of the mass, that will increase as 1/r when r → 0. This will be important to understand the behaviour of the correlator in section 4. Also note that this term is also subleading compared to the term proportional to m 2 /r 3 , that comes second in the expansion of eq. (3.18). Finally let us note that, even though the momentum cut-off expression in eq. (3.13) and the r expansion expression in eq. (3.18) are similar in form, there is no simple way to relate the energy scale Λ with the point-splitting regulator 1/r. Rather, equating these two equations we get, This simply points-out that these divergent terms are unphysical and that these two regularization schemes have slightly different counterterms.
Universal scaling in quenched spatial correlators
In [1,2] we found an interesting set of universal scaling relations for the expectation value of the quenched operator φ 2 and the energy density. For the quenches considered in this work, this scaling takes the form φ 2 ren ∼ m 2 δt 4−d . We also found analytic leading order expressions for this expectation value in the case of δt → 0. For odd spacetime dimensions, we found which reproduces the above scaling with the mass profile 2.2 we are considering. On the other hand, we have already shown how the spatial correlator approaches the expectation value of φ 2 as the separation distance goes to zero. Then an interesting question to ask is whether there are any signs of the universal scaling in the spatial correlator.
To investigate on this question here, we will concentrate on early times, since this is the regime where scaling of the local quantities hold. Now we need a suitable object to compute. We remind the reader that the scalings hold for renormalized expectation values. Given that the bare expectation values are UV divergent, we had to add suitable counterterms to eliminate those divergences. On the contrary the spatial correlator is finite for any finite separation r. However, as discussed in the previous section, the counterterms are in precise correspondence with the small r expansion of the correlator. In particular the leading UV divergence of φ 2 goes as Λ d−2 , which reflects the leading small r divergence of the correlator behaving as 1/r d−2 . So from this perspective, the scaling behaviour is only exhibited in a higher order term, which remains finite as r → 0. However, we may still see the scaling in the correlator by subtracting a suitable fixed mass correlator to remove the terms which diverge in the small r limit. It turns out that in order to eliminate these divergences (which are proportional to powers of m 2 ) the interesting object to compute is the difference of the spatial quenched correlator at time t with the correlator at a constant value of the mass equal to the instantaneous mass at that time t. The latter fixed mass correlator has been computed in Appendix A and one finds, In order to numerically integrate the correlator, we will go back to the "in" basissee eq. (3.13)-to obtain First consider the correlator at t = 0. In fig. 6, we computed C(t = 0, r) − C f ixed (r) for a wide range of values of r and δt for d = 5 and d = 7. We see a very interesting behaviour. Basically we can divide the correlator in three different regions: (i) r > δt, (ii) r < δt < m −1 and (iii) r < δt ∼ m −1 .
For δt < r we see that the correlator is essentially a constant independent of δt that depends on r. In fact it turns out that this constant value is exactly the same value of the instantaneous quench correlator evaluated at t = 0. Recall that the instantaneous quench correlator at t = 0 is exactly the same as the constant mass correlator with m 2 = m 2 in . This coincidence might lead the reader to think that this behaviour is something special for t = 0. However, in what follows, we will show that is the general behaviour of the correlator at any finite t/δt, as long as δt r 1/m. Let's start by fixing the dimensionless time τ = t/δt. Now we want to analyse the r and δt dependence of the following object: (4.4) Note that the first term inside the big brackets has m 2 in in the denominator while the fixed mass part carries an m 2 equal to that at the particular time we are considering.
The second important thing to notice is where is the time-dependence in the quenched correlator. The only place where τ appears explicitly is in the last argument of the hypergeometric function. Recall that Then, if we fix τ by inserting any finite number (or zero) in that last argument, we are left with an object that depends only on δt and r, and we can take the desired limit without any problem. So consider now δt r. We get that limit by considering the limit of the hypergeometric function with δt → 0. As the second argument is proportional to δt, to lowest order all the terms in the infinite sum will vanish but the first one, so we just get that when δt → 0, 2 F 1 = 1 + O(δt). Note that this argument is valid only in the case where we fix τ and effectively there is no δt dependence in the last argument. Then, after taking this first limit, we are left with (4.6) But this is nothing more than C f ixed (m 2 = m 2 in ) − C f ixed (m 2 = m 2 (τ ))! So, at any time we get that for δt r our object becomes the difference of two fixed mass correlators.
In particular, it becomes independent of δt and that explains the horizontal dashed lines of fig. 6. However we can even go further and consider the limit of r 1/m. As it is just the limit for fixed mass correlators we can extract it directly from eq. (A.7) in Appendix A. As we are subtracting two fixed mass correlators, the leading term in the expansion, i.e., the one proportional to r d−2 , will cancel and the leading contribution will come from the first subleading term: In our plots of fig. 6, we have m in = 1 and m(τ = 0) = 1/2, so the difference of correlators in the limit of δt r 1/m should go as (4σ c r d−4 ) −1 , which agrees with the values that the horizontal lines take in the plots. We can add that the agreement gets more exact as r takes smaller and smaller values.
Note, however, that eq. (4.6) is valid for any value of m, as long as r/δt 1, but eq. (4.7) also needs rm 1. If we concentrate in a regime where rm ∼ 1 (see bottom line in each plot of fig. 6), then we should expect eq.(4.6) to hold rather than eq.(4.7). In fact, for r = m = 1, the bottom dashed line in fig. 6 corresponds to approximately 0.10 and 0.20 for d = 5 and d = 7, respectively. This is in perfect agreement with eq. (4.6) and clearly differs from the 0.25 that eq. (4.7) is predicting.
To further support our claim we provide equivalent plots but at different times for d = 5. In fig. 7, we examine the results for τ = 1/2 and τ = 1/4. In these cases, the expectation is that the limiting value would be The second regime r < δt < 1/m leads to the most interesting behaviour. The correlator now exhibits exactly the same scaling as the φ 2 expectation value. The solid lines we see in the plots are exactly the lines that come from evaluating eq. (4.1) for d = 5 and d = 7 with the present mass quench profile -see eq. (2.2). This means that in this regime exactly the same universal scaling we've been discussing for φ 2 is reproduced in the spatial correlator.
Finally, at least for d = 5, we see that when δt ∼ 1/m this behaviour breaks down and our calculation goes away from the universal scaling line. It would be interesting to understand better this slow regime as it could be connected to other set of important universal scalings in quantum quenches: namely, the Kibble-Zurek scaling [4,5] and this would give a connection between the fast and the slow regime universality in quantum quenches. We hope to report on this in the near future.
Late time behaviour of φ 2
In [2], we found some interesting behaviour for the expectation value of φ 2 when we examined d = 4 at late times. Essentially, the expectation value for the smooth quench did not depend on the quench duration δt. This result led us to conjecture that this late time behaviour agrees with that in an instantaneous quench.
In this section, we return to this issue, first by reviewing the d = 3 result and then by considering late time behaviour for higher dimensions. We will show that the agreement between smooth and instantaneous quenches found in d = 3 does not generally occur in higher dimensions.
Review of d = 3
The starting point will be to consider the correlator in eq. (2.17) for instantaneous quench, and evaluate this expression at coincident points in space and time, i.e., x = x , t = t . Of course, this expectation value is divergent in the UV, so it must be regulated. In [2] we showed how to carry out the regularization in detail, but for now it will be enough to compute the difference between the quenched expectation value and that for a fixed mass m to produce a finite result. After subtracting, we get the finite difference Interestingly, this expression can be integrated analytically and the solution expressed in terms of generalized hypergeometric functions, (5. 2) The complete analysis of this solution can be found in [2], but let us just say here that the expectation value begins by growing linearly when mt 1 (but still t/δt 1) but then for very late times, i.e., mt 1, the expectation value keeps increasing but now only at a logarithmic rate, i.e., φ 2 ren ∼ log(mt). As we show in [2], the instantaneous quench and the smooth quench calculation coincide for d = 3, basically because the integrand for the smooth quench decays fast enough, in a way that the approximation of ωδt 1 continues to be valid. Recall from the discussion at the end of section 2, that it is possible to obtain the instantaneous quench expectation value starting from the smooth quench and taking both the late time limit, i.e., t/δt 1, and the low energy limit, i.e., ωδt 1, for every ω in the problem. However, we generally need to integrate momentum k up to infinity with fixed δt, so usually this approximation will break down for large enough k (remember that ω out = k in the quench to the critical point). In the special case of d = 3, though, the integrand decays in a way that only the low momentum modes contribute and then the approximation is reasonable. In the next subsection, we will show that this is a particular effect of the three-dimensional case and does not hold in higher dimensional spacetimes.
Higher dimensions
The main problem that arises in taking the late time limit in higher dimensions is that the expectation value for the instantaneous quench cannot be regulated by simply subtracting the fixed mass expectation value for d > 3. Moreover we will show that it cannot be regulated using the usual counterterms found in [1,2]. This fact will be taken as a hint to argue that in fact, the low energy approximation is not valid in evaluating the late time expectation value of φ 2 in higher dimensions. Then, in order to get the expectation value for the smooth quench, what one should really do is to fully evaluate eq. (2.13) in the limit where t/δt 1. Of course, without taking the extra low energy approximation, it will be impossible to recover the instantaneous quench answer, that it will turn out to be UV divergent for d ≥ 7 and then, infinitely different from the UV finite result for the smooth quench.
So, let us start by evaluating the bare expectation value for φ 2 in the case of an instantaneous quench. In this case we have, To explore the UV behaviour, we expand the expression above for large k and for up to d = 9, the results can be summarized as Of course, the terms appearing in the first line are those same divergent terms that we expect from the constant mass case, But in eq. (5.4), we also have divergent terms in the second line proportional to sin 2 (kt) that do not correspond to any physical counterterm contributions found in eq. (3.11). In fact, as we are interested in the long time behaviour of the expectation value and given that the mass profile (and its time derivatives) decay exponentially in time, the only remaining physical counterterm in this limit should be the mass independent term of eq. (3.11), i.e., k d−3 .
In evaluating φ 2 ren , we integrate over all momenta, but the integral is divergent (even after taking into account the physical counterterms). The reason for this behaviour is that in higher dimensions the approximations of eq. (2.18) are not longer valid. One way to realize this is to compare it with the expression before that approximation. Recall that this is given by eq. (2.13), which after some manipulation, in the late time limit becomes, where α k and β k are given by eq. (2.10). Now we wish to compare this integral with the result for an instantaneous quench (5.7) For this comparison, we start by examining the integrands Φ 2 (k). For d = 5, this is done in fig. 8, where we choose δt = 10 −3 and we evaluate the expression at t = 10. However, our results generalize to the full range of values where the approximation of late times is valid. What we see is interesting: if we focus on small momenta, as shown in fig. 8(a), both the approximate and the full integrands agree. They both show a highly oscillating behaviour, that seems to continue to larger momenta and which would make both integrals diverge if it did so. However, what we see in fig. 8(b) is that in fact this behaviour does not continue for very large k in the case of eq. (5.6). It can be seen that Φ 2 (k) decays to zero for large momentum in the case of the full integral, as required to produce a UV finite result. Instead, the approximate integrand continues to oscillate and so produces a UV divergent integral. In fig. (8), we see that the two integrands differ substantially for k 1000, i.e., for kδt 1. Of course, the approximation of ω out δt 1 is no longer valid in this regime and hence it is natural to expect that they should differ there. The approximations of eq. (2.18) are not valid to obtain the correct late time limit of φ 2 in higher dimensions and hence the expectation value does not match that after an instantaneous quench. To complete this analysis we show that the same happens for d = 7 in fig. 9, where the oscillatory behaviour is even increased by a power law divergence in the approximate integrand. To conclude this section, let us summarize our findings with regards to the late time limit after the quench. We have considered two different protocols to quench a scalar field: the instantaneous one, where we suddenly start evolving an eigenstate of the massive case with the massless Hamiltonian; and the smooth one, where we continuously evolve the mass of the scalar field from the massive case to the massless in a time scale of δt. Now one would think that these different protocols must give different answers in the early time evolution, 5 but that in the limit of δt going to zero and for late times, we should obtain similar results. In [2] we showed that effectively, if we take the limit of t/δt 1 and also ωδt 1 for every ω, we can reproduce the instantaneous quench result from that for the smooth quench and so in principle, we might expect the same late time behaviour in both cases. This allowed us to identify the interesting logarithmic growth behaviour of the scalar field for late times in d = 3. In a self consistent way, we showed that both of these approximations were reasonable in d = 3 and so, the late time behaviour for the smooth and the instantaneous quench agreed. However, we found that this agreement in d = 3 was fortuitous because when we tried to repeat the analysis in higher dimensions, we found that the approximations of eq. (2.18) are no longer valid. That is, higher momenta (and hence, higher frequencies) contribute significantly to the expectation value of φ 2 in higher dimensions and cannot be neglected. Hence for d ≥ 4, the instantaneous quench gives a result for φ 2 at late times which is infinitely different from the smooth quench result. In particular, the smooth quench gives a finite late time limit for φ 2 as δt → 0 [2], while the corresponding result appears to diverge in an instantaneous quench.
Regulated instantaneous quench
It is interesting to note that the integrand in eq. (5.7) for the instantaneous quench in higher dimensions does not decay to zero for large momentum. Instead, it seems to show a rapid oscillatory behaviour around zero, as shown in figs. (8) and (9). So one may think that even though the amplitude is diverging, the positive and negative part are cancelling in every period and so, in some sense, we may be able to recover a finite result from these integrals. In fact, we are inspired here by the way that the fixed mass correlators were regulated in Appendix A.
Hence let us go back to our instantaneous quench results. For d = 5, the behaviour of the expectation value of φ 2 for large k can be extracted from eq. (5.4). This gives, The first divergence, proportional to k d−3 is our usual counterterm that we will subtract. But note, then, that the term proportional to sin 2 can be re-written to yield and this is one of the integrals that we now know how to regulate (just put α = 0 and x = 2t in eq. (A.4). Of course, this is just showing the large k behaviour of the integral. In order to get the full answer we should include all momenta and this, unfortunately, can only be done numerically. But, in principle, since we know how the integral behaves for large k, we should be able to get a finite result for our integral as well by using this new regulator. The results are shown in fig. 10, where we evaluate numerically the instantaneous quench solution of eq. (5.7) for d = 5 and adding a regulator exp(−ak), We evaluate the expectation value at late times, mt = 10, and compare it with the smooth quench also at late times, where we are using δt = 1/20. We find that as we take a to zero, the regulated integral for the instantaneous quench approaches some finite value, showing that the integral converges. However, this value differs from that for the smooth quench in a relative amount by So even if we found a way to make sense of the divergent integral in d = 5, the result does not quite coincide with the smooth quench result, where no approximation is made (apart from the late time limit approximation).
Note that the relative difference in eq. (5.11) is of order mδt. To quantify this difference more precisely we compute the expectation value in the instantaneous quench case with a = 10 −3 and mt = 10. We then vary δt in the case of the smooth quench and compute the relative error between the two results. The outcome is shown in fig. 11. We see that for δt ∼ 1, the two protocols give very different answers. But this is expected because a large δt means going into the adiabatic regime and this need not to agree with the rapid quench even at late times. Instead, as we decrease δt, we see that the relative difference between the two approaches also diminishes and in fact, when δt is of order 10 −3 , the relative error is also of that order of magnitude.
Naively, one may think that it is possible to understand this behaviour by expanding the expectation value in powers of δt. To do that we start with the smooth quench integral in eq. (5.6). We then expand the Bogoliubov coefficients α k and β k for small δt and compute the integrand to lowest orders in δt. This results in Let us analyse this last expression. The first term is independent of δt and one can easily see that it exactly matches the expression for the instantaneous quench in eq. (5.7). Of course, this match was known implicitly, since expanding for δt 1 in the previous expression is actually expanding for ωδt 1 and the agreement found above is the claim that we could reproduce the instantaneous result by taking the small frequency limit of the smooth quench. The next term in the δt expansion appears at order δt 2 . So, again naively, one might expect that φ 2 smooth = φ 2 instant + γδt 2 + O(δt 3 ), for some number γ. However, if we look carefully at the integral that gives this correction at order δt 2 , we will see that it is in fact divergent for d ≥ 5. We can try to regulate it by adding a regulator as in Appendix A, but in fact we will see that apart from the oscillating term (which can be regulated) there is an extra constant term in the integrand, i.e., − 1 24σs π 2 δt 2 m 4 , that will make the integral divergent as we integrate over k from 0 to ∞. This is closely related to the fact that if we try to fit the relative error by some power law expression in the region of small δt -see red dashed line in fig. 11 -we find that the error does not scale as δt 2 but the exponent is rather close to 1.40. This is another sign that this naive expansion is somehow ill-defined for d = 5. Again, we should say that behind this expansion it is assumed not only that δt is small but that ωδt 1, for every ω in the problem, and we already showed that the assumption is not valid for d ≥ 5. The situation is even worse in higher dimensions, where the first term in the series, i.e., the order δt 0 term in eq. (5.12), fails to converge. As an example, we show what happens in d = 7. Even though in fig. 9 the integrand appears to oscillate around zero, this is not the case. For large k, we have, after subtracting the usual counterterms, So, even though the first two terms could be regulated using the above prescription, there is an extra constant term that cannot. Adding the regulator to the term proportional to m 4 /8, we will get a result which diverges as a → 0, 14) and so, the limit of a → 0 in this case will be nonsense. The same also happens in any higher number of dimensions. In fact, the only reason why this worked in d = 5 was because the divergent terms with the sin 2 term, exactly matched the terms without the sin 2 term, in a way that made the whole integrand to oscillate around zero. But this, as shown above, does not happen in general and so, the instantaneous quench approximation in higher dimensions gives a value for φ 2 which differs by an infinite amount from the smooth quench result, even in the late time limit. 6 The energy density at late times In [1,2], it was argued that the renormalized energy density for a quench satisfying eq. (1.2) obeys a scaling relation (1.3), This result is consistent with the scaling of the expectation value of the operator (1.4) since it satisfies the Ward identity In the corresponding scaling relation (1.4) for the quenched operator, O ∆ ren is measured earlier than or soon after the end of the quench. However, the energy scaling (6.1) will be valid for arbitrarily late times since the energy is injected into the system only during the quench. The equation (6.1) gives the δt dependence. The energy density itself will have additional finite pieces, which would be subdominant for ∆ > d/2, but in fact give the dominant contribution for ∆ < d/2. In this section, we will concentrate on the energy density for the free bosonic field with the mass profile (2.2) at asymptotically late times and calculate a UV finite quantity: the excess energy above the ground state energy of the system with the value of the coupling at asymptotically late times. We will perform the δt → 0 limit and compare the results with that of an instantaneous quench.
In terms of the "in" modes the energy density is given by Since we are interested in the behavior of this quantity at late times, it is convenient to express this in terms of the "out" modes. In terms of the Bogoliubov coefficients α k , β k defined in (2.9) and (2.10) this becomes In deriving this expression, we have used the fact that α k and β k depend only on | k|. At t = ∞, the second line of eq. (6.4) vanishes. Using the relation |α k | 2 − |β k | 2 = 1 and the asymptotic form of the out modes at t → ∞, i.e., one gets However, the ground state energy of the system with the final value of the mass is given by Therefore the excess energy over the final ground state is given by Using the explicit form of the Bogoliubov coefficients in eq. (2.10) and integrating over the angles, we arrive at the final expression .
For the mass profile (2.2), the integral in eq. (6.9) is finite for any finite δt. In fact, for small k, the integrand approaches (k d−2 ) tanh(πmδt) 2πδt , while for large k, it becomes (k d−3 )m 4 (δt) 2 e −2πkδt . Hence the integral above is convergent both in the IR and UV for any physical d ≥ 2.
To analyze the small λ = mδt limit of eq. (6.9), let us first scale out a power of δt to write ∆E = (δt) −d I 1 (λ) where . (6.10) Clearly I 1 (0) = 0. However the small λ dependence is different for different dimensions. It turns out that The above behavior was determined from a direct numerical evaluation of the integral in eq. (6.10) and fitting the results shown in fig. 12. This means that for d = 2, 3, the excess energy has a smooth finite small δt limit with ∆E ∼ m d . The leading answer is exactly the same as the energy excess for the instantaneous quench, which can be read off easily from the corresponding Bogoliubov coefficients (2.16) (for the mass profile (2.2)) This quantity ∆E instant is finite for d = 2, 3 and hence we have To estimate the corrections to this leading small λ behavior consider the difference of the excess energy to the excess energy due to an instantaneous quench, both for d = 2 and 3. This behaviour is shown in fig. 13, which is a log-log plot of the quantity I 2 (λ). Clearly, we have I 2 (λ) ∼ λ 2 for d = 2 and I 2 (λ) ∼ λ for d = 3, which leads to the scaling in eq. (6.15). On the other hand, for d = 4, 5, . . ., one recovers the desired scaling from the leading behaviour, i.e., with logarithmic corrections for even dimensions. Thus for these dimensions, the energy density diverges in the mδt → 0 limit. At the same time, the energy density for an instantaneous quench diverges in the UV for these dimensions. Let us emphasize this point once again: our results show that the energy density is UV finite after a smooth quench; however, in the limit mδt → 0, that energy density diverges, just as in the instantaneous quench, where the divergence is in the UV. These results also indicate that for d ≥ 4, the excess energy is in fact given by linear response. This is in accord with the computation of the renormalized expectation value of φ 2 and the renormalized energy density for d ≥ 4, as described in [1,2]. Indeed if we extract the leading piece in a small λ expansion by expanding the integrand in eq. (6.10) we get the expression This expansion makes sense when the above integral is convergent. However the integral is IR divergent for d = 2, 3, 4. The latter explains is why I 1 (λ) does not have an expansion in terms of λ 2 in these dimensions.
Excess Energy for General Theories
The discussion in section 6 suggests that the scaling of the excess energy should be a property of a general interacting field theory. In this section, we argue that this is indeed true. Consider an action where S CF T is a conformal field theory action. The function λ(t) is of the form Alternatively, we may write λ(t) = λ 0 + δλ F (t/δt) if we specify F (y ≤ 0) = 0 and F (y ≥ 1) = 1. We leave the details of the function F (y) during the transition (i.e., 0 ≤ y ≤ 1) unspecified other than that the maximum is finite with F max ≥ 1. Further, this profile may dip below zero by some finite amount and so we specify the minimum as F min ≤ 0. Implicitly, we are also assuming that the profile is smooth.
The system is prepared in the ground state of the initial action. Let us evaluate the total energy density E(t) at some time t > δt in a perturbation expansion in δλ. To quadratic order in δλ, this expression is given by where H 0 is the initial Hamiltonian, |0, λ 0 is the ground state of the initial Hamiltonian, and E 0 denotes the initial ground state energy density. Here we have used space translation invariance as well as the fact that one point functions in the initial ground state are constants in both space and time. On the other hand, the expectation value of the operator O is, to order δλ, given by 3) Using this, it is straightforward to verify that the Ward identity is satisfied. 6 We are interested in evaluating eq. (7.2) at late times. However since the coupling is a constant for t ≥ δt, the energy density at infinitely late times is exactly the same as the energy density at t = δt. The ground state energy density of the final Hamiltonian is given by the standard expression where E n denote the energy densities of the excited states |n, λ 0 of the initial Hamiltonian and V is the volume of the system. It is clear from eqs. (7.2) and (7.5) that the excess energy density ∆E = E(δt) − E f starts at O(δλ 2 ). Moreover we expect that the UV divergences in E(t) for t ≥ δt are cancelled by those in E f . This expectation comes from the following fact: as seen in the previous sections, and in [1,2], the UV divergent terms depend on both λ(t) and its time derivatives. However for t > δt, the coupling is constant and these time derivatives vanish. Therefore, the UV divergent terms should be those of the constant coupling interacting theory. While this is explicit in the free field theory considered in section 6, we do not have an explicit proof for general interacting theories but it stands as a reasonable expectation. If the resulting expression for ∆E is also IR finite, it is determined to this order entirely by dimensional analysis, ∆E ∼ δλ δt d−2∆ . (7.6) Further, as discussed in [1,2], the corrections to this result would be a power series in the dimensionless coupling g = δλ δt d−∆ , which is small in the fast quench limit.
This argument will fail if the integrals involved in ∆E are IR divergent. This can be seen to happen when 2∆ > d, as we have explicitly seen for the free field theory for d = 2 and 3.
Discussion
The aim of this paper is to establish a precise relation between the smooth fast quench and the instantaneous quench. These are the most common quench protocols discussed in high energy theory and condensed matter physics literature, respectively. Naive reasoning would say that if one considers the evolution at very late times (with respect to the quench rate δt), then both protocols should give the same result since δt would be negligible. However, our results in this paper suggest that they may or may not give the same answers depending on a variety of factors such as the spacetime dimension, the scaling dimension of the quenched operator and how much time after the quench is considered. In this paper, we computed spatial correlators, local expectation values and the energy density. In this section, we summarize our results, making precise statements on when the abrupt approximation makes sense. We also discuss different procedures to regulate the energy density. The bulk of our comments below relate to the explicit calculations performed in the free field theory. However, as we will discuss at the end of this section, we expect that these conclusions hold for generic interacting theories for smooth fast quenches as defined in eq. (1.2).
Spatial Correlators
The study of spatial two-point correlation functions is interesting because they are UVfinite quantities that introduce a new scale to the problem, i.e., the spatial separation r. The behaviour of this object is very different depending on the time at which we compute it. We summarize the results here for early times, i.e., t/δt ∼ O(1), and for very late times, i.e., t/δt 1 and mt 1.
• At early times, we can distinguish between three different regimes.
When mδt > 1, independently of r, we are in the slow quench regime, so we cannot compare with our previous results. However, there should be some signatures of universal behaviour corresponding to the Kibble-Zurek scaling when quenching through a critical point. We leave this appealing point for further research in the future [16].
The most interesting feature appears when r < δt < 1/m. This means that the quench is fast since mδt < 1 but the spatial separation defines the smallest scale. Then we found that the same universal scaling that was reported in [1,2] appears in the two-point spatial correlation function. This holds in any spacetime dimension and for arbitrary "early" times. We can think of this correlator as a version of φ 2 regulated with point splitting and so, r plays the role of a short distance cut-off -see below.
In general, we would continue to decrease δt towards the instantaneous limit in which δt → 0. However, in this correlator, we are limited by the distance separation r. In fact, the correlator saturates as δt gets of order r and then the result becomes independent of δt. In all this analysis we were able to take the UV cut-off to infinity but we expect a similar behaviour when working in theories with a finite cut-off, with r −1 playing that role here.
• At late times, the results depend on the spacetime dimensions and on the separation distance. For long distances, in any dimensions, the correlator for the instantaneous quench and the smooth quench coincide. As the separation becomes smaller, the behaviour is different depending on the spacetime dimensions: for d = 3, the smooth and the instantaneous correlator continue to coincide as r → 0; for d = 5, there appears a small finite difference that goes to zero as δt goes to zero; finally, for d = 7 the two correlators differ by an infinite amount as r → 0. We expect the latter behaviour extends in higher dimensions.
Expectation value of φ 2
We showed that the short distance expansion of the correlator is in one-to-one correspondence with the counterterms needed to regulate the bare expectation value of φ 2 . Then, it should not be a surprise that the behaviour of the φ 2 at late times is very similar to that of the spatial two-point correlator at late times but with small spatial separation. In fact, we showed that for d = 3, the smooth and the instantaneous quench give the same answer. When evaluated for d = 5, the smooth quench differs from the instantaneous quench but only in a finite amount that is of order δt. In higher dimensions, however, it is impossible to regulate the expectation value of φ 2 in the case of the instantaneous quench. The smooth quench, in contrast, has a smooth finite limit as δt → 0 and so, the two approaches yield infinitely different results.
Regulating the energy density
Both in the present and previous [1,2] works, we worked in a framework where UVdivergent quantities where regulated by adding suitable counterterms. Of course, we showed how to construct those counterterms and how they yield finite values for quantities such as the expectation value of φ 2 and the energy density. The way in which such a subtraction is done is much in the spirit of how regularization works in AdS/CFT through what is known as holographic renormalization [17][18][19]. There we add an extra counterterm (boundary) action to the usual gravitational action to get finite expectation values. This is how, for instance, expectation values for holographic quantum quenches are regulated in [12], which served as a motivation to our studies. Our approach is also reminiscent of the way field theories in curved spacetimes are regulated. However, a number of things about this procedure may appear strange to a typical field theorist. In particular, the fact that our counterterms first, depend on time and second, some terms depend on time derivatives of the quenched coupling. In this section, we would like to go back to this procedure and compare it with other candidates.
To summarize, we define a renormalized energy density by subtracting counterterm contributions from a bare energy density (and taking the cut-off to infinity). Basically, E ren ≡ E quench − E ct where E quench and E ct separately diverge as the cut-off goes to infinity but E ren is finite. We also showed in [2] that with this definition of renormalized energy density (and an equivalent for the scalar field), we satisfy the Ward identity in any spacetime dimension and for any quench protocol.
A second, perhaps more standard approach, would be to recognize the divergences as coming from the zero-point energy for the scalar field. Each momentum mode behaves as a single harmonic oscillator and then if we sum all the zero-point energies, i.e., 1 2 ω(k), we get a divergent quantity. This is what we call E f ixed , that is, the energy density for a scalar field of fixed mass at any instant of time. Again, one would naively say that we should get a UV finite value if we subtract E quench − E f ixed . One nice thing about this is that if we go to very early or very late times where the mass is constant, there is a ground state and it has precisely zero energy density and any other state has a positive energy density. Even if this procedure works for low dimensional spacetimes, we showed that is not enough in higher dimension. In fact, for d = 3 and 5, we have where Λ is some energy UV cut-off. So first thing to note is that for d < 7 (actually, for d < 6) both the counterterm energy density and the fixed energy density only differ by a finite amount, so if one is sufficient to regulate the theory then, so is the other. Moreover, as most of our study corresponds to the fast quench regime where mδt 1, this finite amount would be negligible compared to the scaling with δt and so, the conclusion will be unchanged using either approach. 7 Let us also note that the subtraction of E f ixed also satisfies the Ward identity. This is easy to see as the only time dependence is on the mass, so 3) but the term in parentheses in the final expression is just the bare expectation value of φ 2 with an instantaneous mass m(t) -compare to eq. (5.5)-, which gives exactly the Ward identity in eq. (2.12).
The situation is completely different in higher dimensions, though. The energy density of the quench has more divergences than those appearing in E f ixed . These are proportional to time derivatives of the quenched coupling. If we suppose that all the quench happens within a time of order δt of, say, t = 0, then these terms will not affect what happens at very early and very late times, so it is possible to compute E quench − E f ixed in those regimes. However, if we want to follow the evolution through the actual quench, E quench −E f ixed is just divergent and we do not have a finite observable in the middle of the process. This is the main reason why E ren is a better measure of what is going on during the quench, i.e., because it allows us to compute the energy density at any time in any spacetime dimensions.
All of these situations are depicted in fig. 14, where to show clearly what is going on we set as the zero of energy density with E ct in the first row and with E f ixed in the second. For d = 3 and 5, both approaches are valid and we see that the only difference is on some small quantity proportional to m. We showed both d = 3 and d = 5 because E f ixed and E ct differ in each case by a different amount. While in d = 3, the difference is negative, in d = 5, it is positive. In d = 7, however, we can follow E ren but not the other one. Then, it is clear now that the naive intuition is wrong or at least is not complete. In the first row we exemplify the counterterm subtraction that allows us to follow the evolution for any time, even during the quench itself, characterized by the time scale δt. Taking the counterterm energy density as the zero of energy density, at very early times, the starting energy density is negative for d = 4k + 3 and positive for d = 4k + 1, with k ≥ 0 integer. In the second row we take the fixed energy density as the zero of energy density. In this case, all the quench energies are greater than this ground zero energy density. The reason is that the fixed mass energy density is the energy density for the scalar with a fixed mass and no quench, so any energy inserted during the quench will give a positive additional contribution. Note that in low dimensional spacetimes, the fixed energy density differs from the counterterm energy density but always by a finite amount proportional to a power of the mass at that instant of time, while the quench energy density usually scales also with δt, so our universal scalings, i.e., δE ∼ δλ 2 δt d−2∆ , will appear in any case. The same will happen in greater dimensions at very early and very late times. However, for d ≥ 6 during the quench, it is not sufficient to subtract the fixed energy density, as there are extra UV divergences in the quenched energy density that are proportional to time derivatives of the mass. In this case, subtracting the fixed energy density is sufficient to compute the energy density at very early or very late times but not during the middle of the quench. This is depicted in the plot in the bottom-right corner for d = 7 but is a general feature of higher dimensional spacetimes. In the same way, in the upper-right plot we cannot sketch E f ixed − E ct during the quench as they differ by an infinite amount.
Time Energy density
The next step would be to think whether there is some other way to regulate the energy density in higher dimensions. A possible answer already appeared in [1,2] while not completely emphasized. We know that the counterterms come from an adiabatic expansion. At zeroth order, this adiabatic expansion gives just the fixed energy density that corresponds to doing the quench infinitely slowly so that, at each instant of time, the energy density is just the energy density needed for the scalar field to have that particular mass m(t). What we do to get the counterterms in just to expand the adiabatic expansion for large momentum and then extract the divergent pieces. As mentioned, at zeroth order, the fixed energy density differs from the counterterm energy density by a finite piece proportional to m d (t). But we also know that for higher dimensional spacetimes we need to go to higher orders in the adiabatic expansion to capture the divergences involving time derivatives of the mass. So an idea to generalize the fixed energy density subtraction to higher dimensions would be that, instead of subtracting just the counterterms, to subtract the full energy density in the adiabatic expansion to that order. This would correspond to the energy of a slow quench but going beyond the zeroth order.
To be more explicit, in the adiabatic expansion shown in [2] we defined incoming modes of the form Then we found that where ω 2 k = k 2 + m(t) 2 . So the zeroth order term in Ω k is the fixed mode energy density but this is then corrected with a second term that is second order in time derivatives of the mass and so forth.
For d = 7, we showed that it is enough to expand the energy density to that order. So instead of regulating the energy density with the counterterm energy density what we can do is to subtract, at any t/δt, the whole energy density coming from that second order expansion. This will include, of course, the necessary terms to cancel all the UV divergences but it will probably introduce some extra finite terms, in analogy to the extra finite piece that the fixed energy density has with respect to the counterterm energy density in lower dimensions. Let us add that this subtraction is also consistent with the Ward identity. 8 In all, we have two different consistent ways of regulating the energy density in our scalar field quenches. It would be interesting to consider whether there is some analogy of these two methods in holography. Our counterterm subtraction is clearly the counterpart of the holographic renormalization approach. But what would be the equivalent of subtracting the fixed mass energy density in an holographic setup? Well, it seems reminiscent of the old method of background subtraction in the early days of the AdS/CFT correspondence (see, for instance, [20]). Usually, divergences in holography appear as we take limits toward the boundary due to the divergent nature of pure anti-de Sitter spacetime as we take the radial coordinate towards the boundary. So, the first idea in holography, which was inherited from early semi-classical calculations in quantum gravity, to get a finite renormalized quantity for some excited state was to subtract that same quantity but in the vacuum state, i.e., in pure AdS. Then both quantities will be divergent but their subtraction would be finite and this is quite analogous to our fixed energy density subtraction. Later on, this procedure was replaced by the more rigorous method of holographic renormalization.
There is an interesting effect in the use of these two different approaches in d = 3. In this case, the scaling is special because instead of giving a diverging behaviour as δt → 0, it gives a vanishing one. We analysed this case in [2], concluding that actually the energy density produced was given by δ E ren = m 3 8π , where m is the initial mass. The interesting thing was that then, if we do the reverse quench where the initial mass is zero, it appears that the work done by the quench is zero! However, this was an artifact of using the counterterm energy density to regulate the expectation value. If we use the fixed energy density then we will find that the energy density starts from zero at early times and it goes to some finite value, giving some non-zero finite work in the process, as depicted in fig. 15.
Upon taking the time derivative of that expression, one should get two different terms. First, a term proportional to that perfectly vanishes since that is the equation which Ω k should satisfy in order for the modes to satisfy the equations of motion (see [2]). The second term, however, is not vanishing and gives exactly the Ward identity. Finally, we wish to consider one last method of obtaining a finite energy density. In section 6, we considered the difference between two physical energies, i.e., E quench − E ground . Note that E ground , the ground-state energy density, should be something that we can easily define at very late and very early times. In particular, this looks like E quench − E f ixed at these early and late times. However, E ground is a real physical energy density of a particular state and it can be defined in any renormalization scheme. So in this case, we do not need to make any reference to our choice of scheme because all of the divergences cancel in the difference of two physical energies. Of course, the drawback is that this can only be computed at very early or late times.
Even dimensions
Most of the explicit calculations presented in this paper refer to odd spacetime dimensions. However, most of the conclusions also hold for even dimensions. As pointed out in [1,2], the only differences between even and odd dimensions are that there are additional logarithmic UV divergences which must be regulated in even dimensions, and as a result, the renormalized expectation values have an extra logarithmic enhancement in the δt scaling. For example, in even dimensions, the expectation value for φ 2 in the fast smooth quench scales as φ 2 ren ∼ δt 4−d log µδt, (8.8) where µ is a new renormalization scale introduced by the logarithmic counterterms.
The appearance of logarithmic counterterms adds an additional technical difficulty to the calculations presented in this paper but we do not expect that they would change the main results. In particular, the renormalized expectation values of φ 2 have a smooth limit at late times as δt → 0 in higher even or odd dimensions, while the analogous quantity diverges after an instantaneous quench. With regards to the energy density, we presented results for lower even dimensions in section 6, where we showed that the excess energy has a smooth limit in d = 2 as δt → 0, which matches the instantaneous answer. In higher dimensions, the excess energy diverges as expected from the scaling of φ 2 ren and the Ward identity (2.12).
Lessons for interacting theories
We end this discussion with a comment on the lessons of our work for general interacting theories. In [1,2] we showed that the scaling form of renormalized quantities holds for general quantum field theories for fast quenches as defined in eq. (1.1). It is natural to expect that the scaling for correlation functions found for the free theory in section 4 would have an analogue in interacting theories as well. When the length scale in the correlator is small compared to the quench time, this correlator can be viewed as a point-split version of the operator which is used for the quench and in the fast quench limit, the arguments of [1,2] then show that this quantity would scale in the expected fashion.
In this paper, we found that the relationship between the fast limit of a smooth quench and an instantaneous quench is non trivial for free field theories in high dimensions. This again should generalize to interacting theories. What really led to the non trivial relation is the fact that in higher spacetime dimensions, the conformal dimension of the quenched operator becomes large. Indeed, the scaling of the renormalized quenched operator O for general interacting theory together with the Ward identity shows that the renormalized energy density at late times behaves as δt d−2∆ and therefore diverges as δt → 0 for any d whenever ∆ > d/2. This can be consistent with the results of an instantaneous quench only if the latter is UV divergent in this case. This fact should have non trivial consequences for the ability to express the state after a quench in terms of a boundary state as in [7] even in low spacetime dimensions when the conformal dimension of the quenched operator is large enough.
The other interesting limit to consider is mr → ∞. In this case, the Bessel function decays exponentially and we find (1 + O(1/(mr))) . (A.9) We might note that the power of r in the leading term in eqs. (A.6) and (A.9) happens to coincide for d = 3 but otherwise they differ.
To conclude this appendix, we emphasize the two main results: The first one is that naïvely the integrals above seem to be divergent, especially for high d. However, because the integrand is mainly oscillating around zero, they can be regulated as in eq. (A.4) to get a finite result. The second lesson is that in the static case this correlator diverges as 1/r d−2 , as shown in eqs. (A.6) and (A.7). We will take these facts into account when we analyse spatial correlators in the instantaneous and smooth quenches in section 3. | 19,740 | 2015-05-20T00:00:00.000 | [
"Physics"
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Information technologies as a means of patriotic education of junior pupils
The study examines the theoretical aspects of the patriotic education of primary schoolchildren in the context of the use of information technologies, defines the meaning and functions of information technologies in the educational process of school education. The patriotic upbringing of primary school students is more than relevant, since the preservation and revival of cultural heritage begins with a small homeland (family, courtyard, school, etc.) and is a key moment in the upbringing of the modern generation.In order to study the level of patriotic education of primary school students, we conducted a survey of schoolchildren, the results of which showed: most of them have a low level of patriotic education, which is due to the lack of due attention of the state as a whole and educational institutions in particular to the issue of patriotic education of schoolchildren.Thus, the problem of patriotic education of primary schoolchildren in the context of digitalization of education has acquired new relevance in connection with new views on the quality of upbringing and education of the younger generation.
Introduction
Since the inception of the educational system to this day, scientists have been looking for optimal organizational and pedagogical conditions for education that would correspond to the modern requirements of society.In connection with the implementation of the updated the Federal state educational standard of primary general education (approved by order of the Ministry of Education and Science of Russia dated October 6, 2009 No. [3], pay special attention to the formation and development of a personality with the qualities of a citizen -patriot of the Motherland, capable of successfully performing civil duties in peacetime and wartime.
Patriotism -it is the foundation of the basic elements of the national identity of the people, manifested in the feeling of love, pride and devotion to their homeland, its history, traditions, culture, in the understanding of their moral duty to it, in the readiness to protect its interests, as well as in the manifestation of tolerance towards others [4].
Scientists in the field of pedagogy and psychology [5,6,7,8,9,10], etc.)had proved that patriotic education must be started even in preschool, early school age, since it is during that period the child identifies himself as a part of the micro and macro society in which he was born and raised; learns to love and respect himself, his family, school, yard, city, etc., learns to respect nature and the results of human activity.
Love for the Motherland is the result of the knowledge gained about it. The sources of this knowledge could be: a school lesson, excursion, observation, reading of works of art, conversation with adults. Many scientists believe that the use of information technology as a means of patriotic education of children of primary school age creates the most optimal conditions for the accumulation of impressions, the formation of ideas, the education of patriotic feelings in children. [11] The regionalization of Russian education has become the starting point for the activation of innovative processes associated with the modernization of the content and technologies of education and upbringing, with the development and scientific substantiation of new means and methods of cultural identification of a child in the space of culture and society. One of the conditions for the patriotic education of juniorschoolchildren is the use of information technology in the work of an educational institution [12].
Despite the fact that the issues of using information technologies in the primary grades of general education schools are discussed in the theoretical provisions and studies of the methodological nature [13,14,15], these studies mainly considered the use of information technologies in methodological work with teachers and in the process of document management of an educational institution.
In addition, in publications devoted to educational work, there are very few of those that consider the influence of information technology on the organization of patriotic education of primary school students.
Insufficient development of the problem determined the research topic; information technology as a means of patriotic education of junior pupils.
Materials and Methods
On the basis of secondary school No. 8, the city of Astrakhan, the diagnostics of the level of knowledge and pupil's understanding about the cultural, historical and natural values of the Astrakhan region and the city of Astrakhan as well as clarifying their relationship to these values junior schoolchildren was carried out. The study has involved pupils of the 3rd grade "B" in the number of 34.
With the aim of determining the patriotic education level of junior schoolchildren, we have selected indicators proposed by D.Phil. in education science, professor I.F. Kharlamov, based on the psychological and pedagogical characteristics of a child of primary school age. These components are cognitive, behavioral and emotional.
The research methods used for the analysis: cluster analysis, content analysis, comparative analysis, interpretation.
Results and discussion
After analyzing the results of primary school pupilsdiagnostics we have identified three levels of a sense of patriotism in junior pupils: the high level is characterized by affection and respect for oneself and others; shows concern for other people; strives for patriotic activity; interested in the history of his native land; the middle level: only under the control of an adult the moral qualities of the child, a sense of affection and respect for their family, home, school; a desire to care for others could be seen; the low level: sometimes shows a sense of affection and respect for his family, home, school; there is no desire to take care of other people; there is no desire to participate in patriotic events.
The study showed that only 4 students (11%) have a high level of formation of patriotic feelings, 9 people (26%) have an average level and 21 people (63%) have a low level of formation of patriotic feelings (see Fig. 1). Low level patriotic education of junior school children is the result of insufficient attention on the part of the state to the problems of patriotic education of the younger generation, which in turn led to a weakening of the educational function of educational institutions.
The search for means of solving this issue led to the need to increase theeffectiveness of the educational process through the use of information technologies inthe patriotic education of primary schoolchildren.
To achieve the assigned tasks the project "About courage, heroism, glory" dedicated to the Defender of the Fatherland' Day has been realizedin the 3-rd grade B of secondary school No. 8, the city of Astrakhan.
The goal of the project is to foster a sense of patriotism in primary school'pupils through the integration of regional material, including the study of the history of their native land, virtual excursions, meetings with interesting people, visiting museums (museum of local lore, museum of military glory), memorial sites (Memorial complex "Eternal Flame", Astrakhan Kremlin, Monument to Peter the Great, etc.), located within the city and beyond, and information technology in the pedagogical process of the school (internet, computers, multimedia projector for presentations).
Information technology teaching is the set of methods and technical means of collecting, organizing, storing, processing, transmitting and presenting information that expands the knowledge of people and develops their ability to manage technical and social processes.The importance of information technology for pedagogy lies in the ability to develop the mental, creative abilities of primary school pupils, their ability to work independently with various sources of information in order to gain new knowledge.
The effectiveness of the patriotic education of junior schoolchildren depends on taking into account their age characteristics, which are expressed in concentration on the object for a short time, the frequent change of the type of activity. The main method of obtaining information remains play and visual material. Visibility and bright, positive emotions give junior pupils the opportunity to easily memorize and assimilate the material. Therefore, the use of the graphic, sound and interactive capabilities of the computer evokes in the child a number of positive emotions, aesthetic experiences, which in turn contribute to the formation of a spiritual and moral attitude towards patriotism, the acquisition of social and emotional experience.
After the formative experiment, we conducted a control experiment in order to determine the levelpatriotic education of junior schoolchildren... In the control experiment, we used the same techniques that were considered according to the same criteria as in the ascertaining experiment (see Fig. 2). We see that at the control stage of our study, 28% of students had a high level of patriotic education of junior pupils, 53% -with an average and 19% -with a low level of patriotic education.
Based on the results obtained, changes were noted according to the three studied criteria. The following Table 1 gives the summary of theresults. In the process of analyzing the indicators of the cognitive component at the ascertaining stage of the experiment, the manifestation of a sense of patriotism in juniorschoolchildren, it turned out that the students' desire to do something for themselves prevails, which indicates a low level of its formation (74% of schoolchildren). After the experiment, the level of knowledge increased in 63% of the students. After analyzing the results obtained at the control stage of the experiment, we came to the conclusion that the majority of students (56%) have a stable positive awareness of their behavior, which is characteristic of a high level of formation of the behavioral component of patriotism. For 32% of schoolchildren with an average level of indicators formation patriotic education able to adequately perceive external circumstances, correctly assess oneself and the situation, leads to the right decisions, judgments, actions. 12% of students are at a low level of formation of the behavioral component of patriotism. This group of children is characterized by an unstable, negative awareness of behavior.
Analyzing the results of the emotional component of the feeling of patriotism, we came to the conclusion that 47% of schoolchildren have superficial ideas about their homeland, devoid of an emotional component. Pupils who have an idea of the Motherland, who love their home, family, for whom a patriot is not just a word, but a person endowed with certain moral qualities, rights and responsibilities, make up 22% of pupils.
For visual presentation of the results two diagrams were drawn (see Fig. 3, 4).
Conclusion
The demands of society to the younger generation have become the starting point for the activation of innovative processes related to the modernization of content and education technologies, with the development and scientific justification of new means and ways of cultural identification of a child in the space of culture and society. One of the conditions for the patriotic education of younger students is the integration of regional material into the pedagogical process of the school, taking into account the age characteristics of the child.
The analysis of the experimental results, as well as the mathematical processing of these results, allowed us to quantitatively confirm the qualitative changes that have occurred in the patriotic education of primary schoolchildren due to the use of information technologies, namely: the level of knowledge of children about the cultural, historical and natural values of the Astrakhan region has increased; there are positive changes in the emotional attitude of children to the values of their native land; the majority of pupils have a stable positive awareness in their behavior, which is characteristic of a high level of patriotism formation.
At the same time, aspects of the problem under consideration were identified that require further research, in particular: the development of regional, socio-cultural and sociopedagogical models of patriotic education, creation of favorable material, technical and social conditions. | 2,690.8 | 2021-01-01T00:00:00.000 | [
"Education",
"Computer Science"
] |
Integration of custom DAQ Electronics in a SCADA Framework
LHCb is one of the 4 experiments at the LHC accelerator at CERN. During the upgrade phase of the experiment, several new electronic boards and Front End chips that perform the data acquisition for the experiment will be added by the different sub-detectors.
These new devices will be controlled and monitored via a system composed of GigaBit Transceiver (GBT) chips that manage the bi-directional slow control traffic to the Slow Control Adapter(s) (SCA) chips. The SCA chips provide multiple field buses to interface the new electronics devices (I2C, GPIO, etc). These devices will need to be integrated in the Experiment Control System (ECS) that drives LHCb.
A set of tools was developed that provide an easy integration of the control and monitoring of the devices in the ECS. A server (GbtServ) provides the low level communication layer with the devices via the several user buses in the GBT-SCA chip and exposes an interface for control to the experiment SCADA (WinCC OA), the fwGbt component provides the interface between the SCADA and the GbtServ and the fwHw component, a tool that allows the abstraction of the devices models into the ECS. Using the graphical User Interfaces or XML files describing the structure and registers of the devices it creates the necessary model of the hardware as a data structure in the SCADA. It allows then the control and monitoring of the defined registers using their name, without the need to know the details of the hardware behind. The fwHw tool also provides the facility of defining and applying recipes named sets of configurations which can be used to easily configure the hardware according to specific needs.
Introduction
The LHCb experiment is one of the detectors collecting data at the LHC accelerator at CERN. It is specialized in b-physics and is composed of several sub-detectors and subsystems. All of these subsystems have specialized custom electronic boards and devices to acquire the data from the events produced by the collisions of the LHC beams in the detector. During the upgrade phase, many of these components will be replaced, to be capable of handling the increased luminosity delivered by the accelerator. The control and monitoring of the new subdetectors electronics will be achieved with the usage of a radiation hard chipset -the GigaBit Transceiver (GBT) and the Slow Control Adapter (SCA) chips [1] -which provide the bidirectional optical links and various user-configurable interfaces in order to meet the requirements of the different front-end ASICs of the subdetectors. In order to easily and reliably control and configure these devices they need to be integrated in the SCADA System (WinCC OA) [2] so they can be driven by the Experiment Control System (ECS). Due to the custom nature of these devices, this requires the implementation of a framework that is capable of handling the communication with the front-end devices via all the available fieldbuses, providing a link to the ECS and abstracting the description of the hardware and model it into the data structures used by WinCC OA. Figure 1. Architecture of the control system for the front-end electronics boards Fig. 1 is a depiction of the typical architecture of the control system for the Front End electronics devices of the experiment. The Front End Boards (FEBs) include one or more SCA chips, which provide the communication interfaces to the devices of the board via the several available field-buses (I2C, SPI, etc.); the SCA chip(s) are connected via Elinks to a master GBT, which is connected through optical links to a board that contains an FPGA, connected to a remote PC. This PC is then connected to (or is itself) a control PC that is part of the distributed ECS. On the software side, the framework for the control system is composed of 3 main components:
Architecture
• A GBT Server (GbtServ) -runs on the host PC that holds the FPGA board • A GBT Client (fwGbt) -runs on the controls PC • A hardware abstraction tool (fwHw) -installed on the controls PC All the LHC experiments at CERN use as their SCADA system the software WinCC OA. In order to reduce duplication of development, the JCOP (Joint Controls Project) [3] was created in order to provide common controls solutions for the four experiments. JCOP provides a framework for the creation of JCOP components -WinCC OA packages containing all the required user panels, libraries, scripts and other software -that can be easily installed and distributed. The 2 latter components of the control system software for the FE electronic devices (fwGbt and fwHw) are developed as Framework components.
The GBT Server
The Gbt server (GbtServ) implements the lower level communication with the FPGA board devices and firmware, the master GBT, and the SCA chips. It also implements the connection to the Control System, acting as the bridge between the Control System and the hardware devices and firmware.
For the local FPGA board, the GbtServ can control and monitor devices using the I2C and SPI protocols, and can communicate with the FPGA firmware using the local bus (typically PCIe).
For the remote Front End devices, which are connected via the GBT-SCA chipset, the GbtServ provides control and monitoring through the multiple field-buses supported by the GBT-SCA (I 2 C, GPIO, SPI, ADC, DAC, JTAG).
This server is based on DIM (Distributed Information Management system) [4], which can easily be interfaced from WinCC OA.
DIM is a communication system for distributed / mixed environments and it provides a network transparent inter-process communication layer. It is based on the server/client paradigm and it uses the concept of publishing/subscribing services and commands.
The GbtServ provides the connection to the control system as it implements services and commands via DIM for all the available field-buses, both to the local FPGA board and remote GBT-SCA chips, which are then exposed to the GBT client (fwGbt) in the Control System.
The Control System abstraction tool (fwHw) can also send a description of the connected hardware and the GbtServ exposes DIM services and commands based on these descriptions.
The fwGbt component
The way the GBT interface is integrated into WinCC OA requires the installation of a specific framework component, a GBT client, which provides the basic communication between the SCADA and the GbtServ running on the interface PC.
The fwGbt is developed as a JCOP Component and connects to the GbtServ by subscribing to the DIM services and commands published by the server.
For each of the existing protocols it implements a minimum of 3 types of operationread, write, write-read -and enables the communication with the electronics at a low level. To each type of protocol correspond 2 DIM services (one for readings status and other for writings status) and a DIM command (for operations) subscription from the GbtServ. The fwGbt also allows for an easy debugging of all the communications by providing an easy to use User Interface for tests (Fig. 2). This UI allows access to all the implemented protocols and their different settings from a central place. It can be used to verify what the status of the connection with the GbtServ is and how the hardware reacts and replies to different commands.
This component provides the lower-level functions to access the different types of registers, which are used by the abstraction tool (fwHw).
The fwHw component
The framework Hardware tool (fwHw) [5] is developed as a JCOP component, allowing for easy installation by the subdetectors. The tool provides a user interface, which allows for the easy modelling and configuration of the existing hardware devices and can also serve as a debugging tool. However, its purpose is mostly setting up the system and the different subdetectors or subsystems should then implement their hierarchical control Finite State Machine (FSM) trees and their own user interfaces more suitably geared to the operation of their electronics.
Hardware abstraction
The fwHw tool models the hardware into WinCC OA datapoint structures. The WinCC OA data structure is a treelike structure, where a logical model is defined in Datapoint Types, which can be instantiated in datapoints that share this logical model. Similarly the fwHw tool produces the logical model of the electronic devices as Datapoint Types, but providing an interface more adapted to the modelling of electronic devices. In the fwHw tool, the data is hierarchical organized with the following types: • Registers -The registers are the representation of a register on a real hardware device. A register can be of any size and implement any type of protocol. The hardware tool allows the configuration of each register according to the settings necessary to access the hardware via the different protocols, the size of the register and the type of readout it will require. The registers can also represent a local variable, i.e. a logical data item of a given area (e.g. a string which holds a filename to configure a given area). These are the leaves or the lower level nodes of a hardware device model tree.
• Areas/Sub-Areas -Areas are logical groups of registers and/or other areas, which represent a logical division of a part of the hardware device (e.g. a chip or a group of chips). Defined areas can be declared as sub-areas of other areas and can be used multiple times. For example, in Fig. 3 we can see that both areas 2 and 3 have the same type and thus have the same structure. The defined areas can also be used by different Device Types, so if some devices share a common structure, there is no need to duplicate similar structures.
• Device Types -The topmost node of the description of the hardware is the Device Type.
The device type is the definition of a device (e.g. a board) with the areas and registers that compose it and the definition of the interface to the hardware they will have.
After the model of the hardware device is defined, we can create as many instances of that model as required and configure the particular settings for those devices. The created models hide the complexity of the communication with the hardware. Settings like the specific protocol, addresses, sub-addresses and all others necessary to access the hardware registers are
Hardware model creation
There are three ways to create the model of an electronics device using the fwHw tool: • via the User Interface Panels: The fwFw tool provides a user interface, which can be used to create the models of the electronics devices to be configured. It is intuitive and easy to use, however it can be cumbersome to create a device model with many registers/subareas, as the registers need to be created one by one and the sub-areas will also need to be included one by one into other areas. Another disadvantage is that it is not particularly easy to update a given model if the changes required are somewhat extensive.
• via scripts: The tool also provides the functionality of using a script to create the hardware models; this improves the creation of big hardware models as well as improves the update or modifications to those models. It can also be used to automate the creation of devices quite easily. It requires writing of scripts using the provided library functions, which requires a learning curve and the scripts may be quite long.
• via XML description files: There is also the possibility of creating the hardware models by describing them in XML files. These XML files will then be used to generate the scripts, which will create the hardware models in the fwHw tool. The usage of an XML hardware description file has the advantage of being easily readable, being validated against an XML schema file and being easily changed or updated. It is also foreseen in the future to have these XML files generated automatically from other descriptions (e.g. an FPGA firmware file).
The implementation of the configuration via XML description files allows also for the easy export of the currently defined models of hardware in a project to be adapted by different sub-detectors or sub-systems.
Hardware interface
The hardware devices for the upgraded experiment will be controlled via the GBT-SCA chipset. The connection between the electronic devices and the Control System is achieved, at a lower level by the GbtServ and the fwGbt tool. These provide the hardware interface to the fwHw tool.
After an electronic device is modelled in the fwHw tool, devices of this type can be instantiated. Specific settings need then to be set, in order to configure the GbtServer connection through which the device will be connected.
Once the devices are instantiated in the fwHw tool, it is needed to make available to the GbtServ the names of the declared registers of the model. The configuration is automatically passed to the GbtServ at startup, and the server is then aware of all the existing registers of the hardware as well as all the settings necessary to access them, their size and the desired readout mode.
The control PC is connected to the host PC where GbtServ is running via the network. The GbtServ is aware of the modelled devices, the necessary settings to access them, and the required readout modes (poll, update on change, etc).
Configuration DB and Recipes
One of the components provided by JCOP is the fwConfigurationDB [6]. This component provides a way to store and apply different sets of data to WinCC OA datapoints. It introduces the concept of recipes -named configurations for a given device or set of datapoints. These configurations can be both static configurations in order to setup equipment (e.g. configuring a spare device that is replacing one that failed) as well as dynamic configurations (e.g. configure the devices for different LHC modes of operation).
The fwHw Tool provides an interface for the configuration of recipes for the defined hardware models and this allows for the easy configuration of the devices according to specific needs. For instance it is possible to set specific values to the registers of the devices when the LHC provides physics conditions for data taking.
The created recipes can be both cached locally in the systems where they will be used and also stored on an Oracle database.
Integrated Solution
A final integrated solution will look like the schema in Fig. 4. Here we can see an example of a fully configured and integrated system, where all the components are running: • GbtServ is providing the lower level communication layer with the hardware; • fwGbt is configured and it's User Interface can be used as Test UI to debug the communication from the Control System to the hardware; • The model of the hardware devices has been abstracted with the fwHw tool, and the existing devices have been instantiated; • Custom User Interfaces for configuration and monitoring of the modeled devices have been easily developed and integrated in the global ECS Operation UI.
Conclusion
The developed framework provides a complete, easy and reliable solution to integrate custom electronics devices into the LHCb Experiment Control System. Even though the existing electronics devices in LHCb are of varied types, the developed tools provide a way to easily address all the devices and a way to easily abstract and create models of these devices, so they can be integrated and controlled from the global Experiment Control System. It is also easy to modify or extend the already existing models without major impact to the existing system. These tools are able to facilitate the integration of the subdetectors electronic devices as they provide a base for the subdetectors to integrate their devices into their ECS control trees and develop their specific user interfaces.
The usage of fwHw tool to abstract the hardware models also makes possible an easier control of the devices by providing a way to interface the registers of these devices using named registers. This hides the complexity of the communication from the user and enables the possibility of using the configuration DB and recipes to configure the electronics according to the specific needs of the experiment in different operation modes. It also provides a base for increasing the automation of the running of the experiment [7]. | 3,774.4 | 2020-01-01T00:00:00.000 | [
"Computer Science"
] |
Neutrino oscillations: ILL experiment revisited
The ILL experiment, one of the"reactor anomaly"experiments, is re-examined. ILL's baseline of 8.78 m is the shortest of the short baseline experiments, and it is the experiment that finds the largest fraction of the electron anti-neutrinos disappearing -- over 20%. Previous analyses, if they do not ignore the ILL experiment, use functional forms for chisquare which are either totally new and unjustified, are the magnitude chi-square (also termed a"rate analysis"), or utilize a spectral form for chi-square which double counts the systematic error. We do an analysis which utilizes the standard, conventional form for chi-square as well as a derived form for a spectral chi-square. Results for the ILL, Huber, and Daya Bay fluxes are given. We find that the implications of the ILL experiment in providing evidence for a sterile, fourth neutrino are significantly enhanced. Moreover, we find that the ILL experiment provides a set of choices for specific values of the mass squared difference. The value of the mass square difference for the deepest minimum and its statistical significance, using the flux independent spectral chi-square and the Huber or Daya Bay flux are 0.92 eV$^2$ and 2.9 $\sigma$; for the conventional chi-square and the Daya Bay flux are 0.95 eV$^2$ and 3.0 $\sigma$; and for the conventional chi-square and Huber flux are 0.90 eV$^2$ and 3.3 $\sigma$. These probabilities are significantly larger than the 1.8 $\sigma$ found for the ILL experiment using a rate analysis.
However, there are experiments that are not consistent with the three neutrino analyses.
These experiments require a mass-squared difference of order 1 eV 2 . These experiments are: • The LSND [4] and MiniBoone [5] experiments measure ν µ → ν e and ν µ → ν e oscillations. The LSND experiment indicates a sterile neutrino that oscillates via a mass eigenstate with a mass-squared difference that is greater than 0.1 eV 2 . MiniBoone has a longer baseline and compensating larger energy than LSND. These two experiments have recently been found [6] to be compatible.
• Experiments with radioactive sources at the Gallium solar neutrino facilities, Sage and Gallex [7], see fewer neutrinos than expected. This can be explained by the disappearance of electron neutrinos oscillating via a mass-eigenstate with mass-squared difference greater than 1 eV 2 . This is called the "gallium anomaly".
• A new calculation of the electron antineutrino flux [8] yielded a net increase of the predicted rate of antineutrinos emitted by the four dominant decays that drive a reactor. This implied [9] for a number of short-baseline reactor experiments from the 1980's and 1990's that the antineutrinos oscillated away via a mass-eigenstate with ∆m 2 > 1 eV 2 . This is called the "reactor anomaly".
This work focuses on one of the reactor anomaly experiments -the ILL experiment [16,17]. This experiment is distinctive in several ways. It has an 8.79 m baseline, the shortest baseline of any of the reactor anomaly experiments. The short baseline gives ILL sensitivity to the largest values for ∆m 2 . The original publication [16] of this experiment found the total number of measured antineutrinos to be 4.5 ± 11.5% less than predicted. However, the power of the reactor was found [17] to have been under-measured by 18%, implying that approximately 20% of the antineutrinos had disappeared. This is by far the largest fraction of electron antineutrinos disappearing in any short-baseline reactor experiment.
In the Mention analysis [9], the reactor anomaly data indicate that a fourth antineutrino exists at the 2.1 σ level, but the ILL experiment is omitted from this analysis. When they combine other data with the reactor anomaly data, they use a spectral chisquare function for the ILL experiment which we argue below is incorrect. In the Kopp-Dentler analysis [18][19][20], the magnitude chisquare is used for all but the Bugey experiment [21]. Use of the magnitude chisquare underestimates the impact of experiments which have spectral information, including ILL. They find that the reactor anomaly experiments indicate the existence of a fourth antineutrino at the 2.7 σ level. In the Collin analysis [22], only the Bugey [21] experiment from the reactor anomaly experiments is included. In the Gariazzo study [23] only the magnitude analysis for the ILL experiment is used. They find a 2.9 σ indication of a fourth antineutrino after including results from the NEOS experiment, and the near detector data from the Daya Bay [24], RENO [25], and Double CHOOZ [26] experiments were also included. They find that the existence of a fourth antineutrino is indicated at a 3.1 σ level when these additional data are included. There is agreement that evidence exists supporting the existence of a fourth neutrino, but a correct analysis of the ILL experiment beyond the use of the magnitude chisquare (a rate analysis) does not yet exist.
Here, we address two fundamental questions within the context of providing new results for the ILL experiment. The first, in Sections II and III, the importance of the choice of the chisquare function used in the analysis is examined. The second, in Section IV, the dependence of the results on the choice of the flux is presented. We find that including the spectral information gives results that favor a number of particular values of ∆m 2 . In Section V we demonstrate how this comes about. In Section VI, we review our conclusions and comment on possible future work.
II. CHISQUARE FUNCTIONS
Given that different authors utilize different functional forms for their chisquare function, we ask the question of how does the choice of the chisquare function impact the physical results implied by an analysis of the experiment? We give the formulae for each of the chisquare functions of interest. We postulate that one is not free to create any function one chooses. It is necessary to extract from the calculated chisquare the answer to various questions that involve probabilities. This usually is done by knowing that the likelihood function that results from the chisquare function is a probability distribution. To be correct, a mathematical proof of how to extract probabilities is required. Here, we maintain this constraint by limiting ourselves to the conventional chisquare and normal (Gaussian) statistics. This is the standard chisquare found in books on probability theory. The extraction of probabilities then follows a prescription which has been rigorously derived, using what is commonly called a "frequentist" approach or else a "Bayesian" [27,28] approach. One can divide this conventional chisquare into two parts. One part we call the spectral chisquare. This chisquare is independent of the magnitude of the antineutrino flux. This second form is the limit in which one simply counts the number of neutrinos without measuring their energy. This is also called a "rate" calculation. This is the limit of the conventional chisquare when there is only one energy bin. Since both of these chisquares derive from the conventional chisquare, extracting probabilities utilizing either the "frequentisit" or "Bayesian" approach is mathematically rigorous. In addition, we examine the results of using the sum of the magnitude and spectral chisquare. The sum of the two parts is not rigorously equivalent to the conventional chisquare.
We begin with the well-known and mathematically rigorous conventional χ 2 function as given by where N exp i is the experimentally measured number of neutrinos and σ i is its statistical error given in percent of N exp i , both for bin i centered at energy E i , with i max being the total number of spectral bins. We stress that this functional form of the chisquare follows in a mathematically rigorous way from the property that the data satisfies normal statistics.
By dividing the number of neutrinos by the run time, the number of neutrinos can be replaced by the rate of measuring the neutrinos in all formulae. Systematic errors are included through the use of a set of nuisance parameters {a} with j max the number of such parameters. These parameters are varied, subject to the constraint imposed byσ j in the is the theoretical model for the number of neutrinos in bin i. We use a two neutrino model, with our independent variables taken as sin 2 2θ and ∆m 2 . The two neutrino approximation results [22] from taking ∆m 2 21 = ∆m 2 32 = 0 in the full four neutrino mixing matrix.
The probability that an electron antineutrino leaving the reactor remains an electron antineutrino when it arrives at the detector is given by where L is the distance traveled by the antineutrino in m and E is its energy in MeV.
The mass-squared difference parameter is in units of eV 2 . In order to incorporate the finite energy resolution of the detector the oscillation probability must be convoluted with an with N E a normalization factor. The distance L must be averaged over the distance between points in the core and points in the detector. This can be done with a one dimensional integration by defining a weight function W L (L )/L 2 dL that extends from the smallest (largest) distance, L min (L max ) between a point in the core to a point in the detector. We divide L max − L min into bins. The 1/L 2 factor accounts for the inverse square drop in the flux with distance.
We generate randomly located pairs of points with constant density in the core and in the detector and calculate the distance between each pair of points, then put a point in the appropriate bin for that distance. The number of points in each bin then gives a weight function, W L (L )/L 2 dL , which we normalize. With this weight function, we then need only do a one dimensional integral over L weighted by W L (L )/L 2 . To include these two effects, we define this averaged P ee by where E th is the antineutrino threshold energy for the inverse beta decay reaction. The theoretically predicted number of neutrinos in bin i is then where N no i is the theoretical number of neutrinos that would have been measured in bin i in the absence of oscillations, and a is the one nuisance parameter we employ.
An alternative approach, as used in Ref. [17], arises from separating the χ 2 function into two pieces, a magnitude piece, χ 2 mag , and a spectral piece, χ 2 spec The magnitude part, χ 2 mag , describes experiments where the total number of antineutrinos is detected but their energies are not measured. This chisquare function, χ 2 mag , is given by where N exp tot is the total experimental number of antineutrinos detected, and N th tot is the total theoretically predicted number of antineutrinos. This is simply a one energy bin form of Eq. 1.
The spectral chisquare function, χ 2 spec , is constructed to be a chisquare that is independent of the magnitude of the flux. Physically this means you have no knowledge of the magnitude of the flux. This can be accomplished by lettingσ go to infinity in Eq. 1 yielding In Ref. [17] a different and unique form for the spectral chisquare was proposed. We disregard that definition. Our definition is manifestly and completely independent of the flux. In Mention, Ref. [9], another chisquare function that is independent of the magnitude of the flux is used, a flux we will call ∆χ 2 specM . There they take the limit ofσ going to infinity and then insert the systematic error by adding it in quadrature to the statistical error. This chisquare, χ 2 specM , is defined by Eq. 12 in Ref. [9] as In taking the limit ofσ going to infinity, the effect of the systematic error has been included; one could even say "we have over-included it". Putting the second term in the denominator of Eq. 8 is double counting the systematic error.
We have sufficient data to calculate each of these chisquares. In Table IV of Ref. [16] we are given the energy grid, E i ; the experimental rate of particles being detected in units of MeV −1 h −1 in each bin; and its error σ i . We use one nuisance parameter with errorσ for the error in the magnitude of the flux, number of protons, etc. We find for the error a value of 11% in [16], a value of 8.87% in [17] , and a value of 9.5% in [9] . We choose to be conservative and use the largest of these, 11%. Also from Ref. [16] we get the dimensions needed to construct W L (L ). The core has a radius 0.2 m and a height of 0.8 m. The detector is 1.2 m tall, 0.8 m wide, and (we estimate) 0.9 m deep, the first two taken from the diagram in Fig. 1, Ref. [16], while the depth is estimated to be 1.0 m, as it is not provided anywhere.
We find that the inclusion of the energy resolution integration is not needed as its impact is less than one percent. On the other hand the spatial integration over the size of the core and the size of the detector is approximately a 25% correction.
III. RESULTS -CHISQUARE DEPENDENCE χ 2 (sin 2 2θ, ∆m 2 ) does not return to zero as ∆m 2 tends to infinity. It approaches a ∆m 2 independent valley arising from the limit of ∆ 2 m large, The usual approach to extract probabilities from a chisquare function is to define a likelihood function, L(sin 2 2θ, ∆m 2 ) =: exp(−χ 2 (sin 2 2θ, ∆m 2 )/2, and realize that the likelihood function is proportional to a probability distribution. This cannot be done here since the probability distribution is not integrable. The solution to this situation can be found in Ref. [21]. The question one asks must be altered and the approach is termed the "raster" interpretation. In this approach, one asks the question "for a given ∆m 2 , what is the minimum (best fit) value of the chisquare and at what value of sin 2 2θ does it occur?" We define the answer to this question as ∆χ 2 min (sin 2 (2θ min ), ∆m 2 )) = χ 2 (sin 2 (2θ min , )∆m 2 ) − χ 2 (0, 0), where θ min is the minimum value for the chosen value of ∆m 2 . The no oscillation chisquare in the two neutrino analysis is the value of the chisquare function for three neutrinos. Thus ∆χ 2 min tells you how much better a fit the inclusion of a fourth neutrino yields. Note that the sign of ∆χ 2 min is the opposite of the sign often used. We use this sign as the best fit is then given by the smallest value of ∆χ 2 min . Also note that the chisquare is a one variable, sin 2 (2θ), chisquare, and hence for a frequentist analysis the improvement due to the fourth neutrino as measured in number of standard deviations is the square root of ∆χ 2 min . We first investigate the dependence of results on the choice of the chisquare function in Table I we quantify our results by giving the depth for each minima, χ 2 min and its location sin 2 2θ min and ∆m 2 min . For all curves in this section we use the Huber [29] flux. In Fig, 1 the solid (black) curve depicts ∆χ 2 min as a function ∆m 2 for the conventional chisquare, χ 2 conv , defined in Eq. 1. The first thing we note is that the curve is a set of individual minima. The origin of multiple minima will be investigated in Section V. This phenomenon is new to this work. Each value for the minima is exceptionally deep. The ILL experiment finds about 20% of the antineutrinos have oscillated away -much more than found in any other experiment. The next curve to examine is the dot-dash (red) curve which is generated by χ 2 mag , Eq. 6, the magnitude (or rate) chisquare. This is the most commonly used chisquare function for analyzing the reactor anomaly experiments. First, we see that without the spectral information, it has no sensitivity to a particular mass and is nearly a straight line. Secondly, it underestimates the significance of the experiment substantially; any analysis that uses the rate approach for an experiment that has spectral information will be significantly underestimating the impact of that experiment. Next we examine the results obtained from the spectral chisquare, Eq. 7, the dash (blue) curve. It too produces predictions of possible mass-squared differences, in fact, nearly identical values to those predicted by the conventional chisquare. The dot-dot-dash (indigo) curve is for the sum of the magnitude and spectral chisquares. It gives results that are reasonably close to the conventional chisquare. This supports our definition of the spectral chisquare. Finally the dot-dot-dash green curve is the result of the Mention spectral chisquare, Eq.8. These results are quite small. This is not surprising as the systematic errors are included twice.
The spectral chisquare, which is independent of the magnitude of the flux is of special interest. Note that because the Huber flux and the Daya Bay flux differ [37] only in magnitude, the spectral chisquare, χ 2 spec , the dash (blue) curve, gives identical results for these two fluxes. The revision of an increase by 18% of the flux appeared fourteen years after the original publication and is authored by a fraction of the original collaboration. It is also a much larger disappearance fraction than any other oscillation experiment. This makes us cautious of this change in the flux. We see that the spectral chisquare produces results with the location of the valleys, best fit values, very similar to what was found from the full conventional chisquare with the minima reduced, but much deeper than that found by Mention [9]. If the flux increase is less than the full 18% increase, the results will lie between the conventional chisquare solid (black) curve and the spectral chisquare dash (blue) curve.
IV. RESULTS -FLUX DEPENDENCE
The question of the flux, both its magnitude and its energy dependence, has received much attention [30][31][32][33][34][35][36][37][38] lately. The historical way of modeling the flux is to start with a measured beta decay spectrum and then theoretically predict a neutrino spectrum that is consistent with the measured beta spectrum. The most recent flux of this type is that given by Huber [29]. The alternative is to measure the flux directly, the most recent such flux is Bay experiment sees a lower flux rate for its particular mix of isotopes than is predicted by Huber. It cannot tell you directly how much of the decrease comes from which isotope.
Unfolding the decrease must be done theoretically. In Ref. [37], the conclusion reached by the Daya Bay experimentalists is that the Daya Bay flux is a reduction by 7.8% for the 235 U flux with the other isotopes unchanged as compared to the Huber flux. We here present results, Fig. 2 and Table II, for the ILL experiment utilizing the Huber flux, the Daya Bay flux, and the ILL flux. We include the historical LL flux purely out of curiosity concerning what would have been the results had there been an analysis performed looking for a fourth neutrino, rather than focusing on the 90% disallowed region, the general approach adopted at the time.
The Huber flux for 235 U is given in Appendix B of Ref. [29]. Rather than utilize the Table I. magnitude of the flux given there, we put an emphasis on staying as close to what the experimentalists did in their analysis as is possible. In the second ILL paper [17] and in the Mention paper [9] we are given the ratio of the total number of experimentally measured neutrinos to the no-oscillation expected number, 0.802. In [16] we find that the total number of electron antineutrinos measured is 4890. Thus the Mueller flux is to be normed to 6070 events. In [29] we find the 235 U Huber flux is 1.004 times the Mueller flux or is to be normed to 6100. From [37] the Daya Bay flux is 7.8% smaller than the Huber flux or is to be normed to 5620 counts. From [9] the ILL flux is 2.6% smaller than the Mueller flux or is to be normed to 5910 and approximately has the energy dependence of the Mueller flux, which is given in Ref. [8] ∆χ 2 min versus ∆m 2 is presented in Fig. 2 for the Huber flux, the Daya Bay flux, and the ILL flux and for the conventional chisquare, ∆χ 2 conv . In addition, in Table II the depth of each ∆χ 2 min and the location of the chisquare minima, sin 2 2θ min and ∆m 2 min , are given for the Daya Bay and ILL flux. The results for the Huber flux was given in Table I.. We see that the change in the flux does not cause much of a change in the location of the χ 2 min and does not cause a major change in the depth of the χ 2 min . This is because of the 20% disappearance of the antineutrinos. This is sufficiently large that the 7.8% reduction in the flux reduces the impact of the experiment, but not overwhelmingly. If we investigate an experiment where we have pure 235 U fuel, and the Huber flux gave a 6% or less disappearance, the reduced flux of the Daya Bay experiment would lead to a null result for the existence of a fourth neutrino.
We see that all three fluxes give substantial evidence for the existence of a fourth neutrino.
Indeed, the conventional chisquare implies the lowest two minima for the Daya Bay flux are quite deep, with ∆χ 2 min given by -10.5 and -11.7 (3.2 and 3.4 σ). We see similarly that the ILL flux gives -10.2 and -11.6 (3.2 and 3.4 σ) for the depth of the two deepest minima. Had the ILL experiment been modeled with a conventional chisquare, the reactor anomaly would have been discovered much earlier.
V. ORIGIN OF MULTIPLE MINIMA
Finding multiple minima brings up the question of whether the results are predicting more than one sterile antineutrino or are offering several possible values for the mass-square difference. The analysis was performed using an oscillation probability from a 3+1 model.
Logically the results could not be for multiple sterile antineutrinos. In Fig. 3, the solid (blue) curve is for the first minimum of the chisquare function found at sin 2 2θ = 0.26 and E ν = 6.0 MeV. The dash (red) curve is for the second minimum found at sin 2 2θ = 0.25 and E ν = 5.6 MeV, and the dot-dash (green) curve is for the third minimum found at sin 2 2θ = 0.22 and E ν = 5.3 MeV. All three curves have a minimum near 0.5 eV 2 . What is happening is that the solid (blue) curve fits with its first minimum near 0.5 eV 2 , the dash (red) curve fits with its second minimum near 0.5 eV 2 , and the third curve fits with its third minimum near 0.5 eV 2 . With less than perfect data, a fundamental and its harmonics can all produce reasonable fits. Thus the data is producing a series of possible mass-square differences. For data from a model calculation with small errors given in Ref. [39], it is shown how the data can distinguish between multiple possible single antineutrino solutions and a solution that actually represents the existence of multiple sterile antineutrinos. One can be cautious of the suggested 18% increase in the flux suggested in Ref. [17], but we believe that unless and until other data contradict this claim, the results of a full analysis of the reactor antineutrino data utilizing the standard chisquare should be the default.
VI. CONCLUSIONS
Of the nineteen reactor anomaly experiments, the ILL experiment has the shortest baseline, 8.78 m. In Ref. [17] a correction to the measured power of the reactor during the experiment was reported and an increase by 18% to the reactor flux was proposed. This means that approximately 20% of the electron antineutrinos emitted from the reactor had oscillated away. This large fraction of antineutrinos disappearing would intuitively imply the existence of a sterile fourth antineutrino at the mass-squared scale ∆m 2 ≥ 1 eV 2 and with a large probability for the existence of this sterile antineutrino. The analysis performed in Ref. [17], however, used an unusual and peculiar functional form for the chisquare function, which we ignore. The analysis done in Ref. [9], the work that originally proposed the existence of a reactor anomaly, used a spectral chisquare which we believe included the systematic errors twice. Other global analyses, Refs. [15,[18][19][20]22], either omitted the ILL experiment or used the magnitude chisquare, which we find underestimates the significance of an experiment that contains spectral information. We also demonstrate that the conventional chisquare, ∆χ 2 conv , can be quantitatively broken into a magnitude (or rate) part and a spectral part, with the spectral part, ∆χ 2 spec , given by the form that we propose in Eq. 7 We find that using the standard, rigorously justified by mathematicians for normal statistics, chisquare function, ∆χ 2 conv , Eq. 1, gives results that imply the existence of a fourth neutrino at a number of specific values for the possible mass-squared differences. The set of mass-squared differences preferred is given in Table I together with the statistical significance of each. We also examine the results implied by the spectral chisquare, ∆χ 2 spec , given in Eq. 7. The significance of an experiment is necessarily reduced by utilizing only the spectral form of the chisquare function, but there is the advantage of the results being independent of the magnitude of the flux. We find for the Huber flux that ∆χ 2 min for the two lowest mass-square differences are -12.1 and -13.0 (3.5 and 3.6 σ ) with mass-squared differences of 0.90 and 2.36 eV 2 . For the spectral chisquare, χ 2 spect the mass-squared difference values of the minima remain nearly the same as those found for the conventional chisquare, 0.95 and 2.36 eV 2 ,and have a depth of -8.22 and -9.45 (2.9 and 3.1 σ).. We note that the spectral chisquare puts a lower limit on the implications of an experiment that can result from not knowing the magnitude of the flux. The value for the magnitude chisquare, ∆χ 2 mag , for the Huber flux is found to be -4.0 (2.0σ) and independent of the value of ∆m 2 for ∆m 2 > 0.1 We find that the use of the magnitude chisquare (rate analysis) underestimates the significance of an experiment that has spectral information. Studies of the reactor anomaly experiments, with the exception of the Daya Bay experiment, utilize a rate analysis or ignore the ILL experiment. This has motivated us to redo all nineteen experiments in which we will include this new analysis of the ILL experiment and spectral information when available.
We also find that when spectral information is included, each experiment predicts individual values for ∆m 2 that are preferred. This alters how one can view the process of combining individual experiments. The question of coherence between the individual values preferred by one experiment and those values found by all the other experiments becomes very important.
The discussion of coherence between the ∆m 2 values found here for the ILL experiment and the values found by other experiments will be presented when the new results for the reactor anomaly are complete. In addition there are five newer reactor anomaly experiments that have been published or have preprints that have appeared in the archive. These also need to be combined and included in with the older experiments. These experiments are Nucifer [10], NEOS [11], Nuetrino-4 [12], DANSS [13], and PROSPECT [14]. As these experiments should be more reliable than the older experiments, the question of coherence becomes a more important consideration.
The question of the magnitude of the flux remains. With 20% of the antineutrinos disappearing, the ILL experiment finds that the 7.8% reduction for the Daya Bay flux does reduce the impact of the ILL experiment, but leaves the results with the deepest two values of ∆χ 2 min at the significant values of -10.5(3.2) and -11.7(3.4). The PROSPECT experiment will measure the 235 U flux to a much improved accuracy, both its measured energy dependence and its magnitude. For research reactors that use pure 235 U, the flux question will be resolved. For other experiments, this measurement will reduce the uncertainty. If the Daya Bay flux is confirmed, the question will be resolved. Otherwise, given the level of discussion, Refs. [30][31][32][33][34][35][36][37][38], we will follow the conclusion of Ref. [38], "The present analysis suggests that there is currently insufficient evidence to draw any conclusions on this issue." Further measurements would be necessary. | 6,813.8 | 2018-02-21T00:00:00.000 | [
"Physics"
] |
Structured approach for designing drug-loaded solid products by binder jetting 3D printing
Additive manufacturing allows for designing innovative properties to pharmaceutical products. Binder jetting (BJ) 3D printing is one of the key techniques within innovative manufacturing. In this study, a structured approach according to the Quality by Design (QbD) principles was implemented to explore the factors affecting fabrication of drug-loaded products produced by BJ 3D printing. The investigated factors included the weight ratio of binder in primary powder and the process parameters related to printing (layer thickness and number of layers). Critical quality attributes, namely disintegration time, tensile strength, friability, dimensions (diameter and height accuracies), residual water content, weight and drug loading were determined based on the quality target product profile of a tablet analogue. The experimental results with a 2-level full factorial design were modeled by multiple linear regression. It was found that binder content was an important factor determining the integrity of the printed products, and the formation of the microstructure of the product was affected by multiple material properties and process parameters. QbD is a systematic and effective approach providing mechanistic understanding of BJ 3D printing and allowing for an efficient design of products with the desired quality.
Introduction
Additive manufacturing (AM) is getting an increasing attention as an approach to develop and fabricate pharmaceutical products.AM refers to a construction of an object in a successive layer-upon-layer manner.It has several advantages compared with traditional manufacturing, such as the flexibility to rapid prototyping and small-scale manufacturing.Additional benefit is the ability to fabricate products with complex geometry and tailored microstructure.During the past decades, pharmaceutical products based on AM have demonstrated its possibility to fabricate drug delivery systems that cannot be achieved by conventional pharmaceutical manufacturing processes (Trenfield et al., 2018, Lepowsky and Tasoglu, 2018, Goole and Amighi, 2016, Prasad and Smyth, 2016).Binder jetting (BJ) 3D printing is a powder-based AM method.The primary powder, which refers to feeding powder mixture loaded in the BJ printer forming the powder bed, typically contains active pharmaceutical ingredient(s) (APIs) and various functional excipients such as inactive matrix material(s).The liquid binder, which is also called ink, is sprayed onto the powder bed in a designed pattern with a goal to bind powder material into a solid object.Another strategy is to add a solid binder in the primary powder, which will subsequently get partially dissolved by the sprayed ink used for binding.Several drug delivery systems have been successfully fabricated by BJ, with examples covering personalized medicine, multicompartmental/multi release drug delivery devices, high/low drug loaded pharmaceutical products, and orodispersible formulations (Sen et al., 2021, Rahman et al., 2020).
Structured and risk-based drug development work is a key to successful design of pharmaceutical products.Quality by Design (QbD) is a well-established approach that emphasizes the focus on quality of the product early in drug development process (Yu et al., 2014, Juran, 1992).It is especially important to implement QbD to the development of novel products, such as the AM-based innovative drug delivery Abbreviations: ACN, Acetonitrile; AM, Additive manufacturing; APIs, Active pharmaceutical ingredients; BJ, Binder jetting; CMAs, Critical material attributes; CPPs, Critical process parameters; CQAs, Critical quality attributes; DoE, Design of Experiments; HPLC, High-performance liquid chromatography; IBU, Ibuprofen; MLR, Multiple linear regression; Num, Layer number; PCM, Paracetamol; Ph.Eur., European Pharmacopoeia; PVP, Polyvinylpyrrolidone; QbD, Quality by Design; QTPP, Quality target product profile; SEM, Scanning electron microscopy; TGA, Thermogravimetric analysis; Thk, Layer thickness.
* Corresponding author at: Department of Pharmacy, Faculty of Health and Medical Sciences, University of Copenhagen, Universitetsparken 2, 2100 Copenhagen, Denmark.
Contents lists available at ScienceDirect systems.QbD is underlining the importance of product and process understanding.Key elements in this are to identify the statistically significant correlations and explain the observed phenomena at a mechanistic level, instead of merely listing the statistical parameters.It is a common misconception of QbD to consider this approach only as a statistical exercise without including the mechanistic explanation.BJ 3D printing is still a relatively new technique in the pharmaceutical context, and there is only limited number of published work focusing on key principles determining the formation of a drug-loaded solid product within this processing solution.
In this work, a structured approach according to the QbD principles was used to explore the BJ 3D printing.The targeted product was an analogue of a pharmaceutical tablet for oral delivery.The quality target product profile (QTPP) of the product was defined, followed by a qualitative risk assessment on BJ 3D printing process.Material selection and process parameters were investigated with Design of Experiments (DoE) to identify their criticality to examined critical quality attributes.A special focus was on linking the experimental findings to a mechanistic understanding of the general factors determining the quality of BJ 3D printed products.
The primary powder comprised one model drug, PVP, and lactose.All the compositions of primary powder were mixed in Turbula® shakermixer (Willy A. Bachofen AG, Muttenz, Switzerland) at 35 rpm for 5 minutes.Ink solution used for printing was either water based or waterethanol co-solvent based systems.All the ink solution contained 5% w/V of PVP to reach the viscosity for a stable spray (Fromm, 1984).
In the Screening study of this work, the composition of primary powder is indicated in the sample code in the following way API_-DrugLoad:PVP:Lactose_EthInk.For example, a code of PCM_3:1:6_0 refers to the primary powder comprised 30% w/w of PCM, 10% w/w of PVP, and 60% w/w of lactose, and the ink was based on water without ethanol.In the Optimization study, the layer thickness (Thk)*layer number (Num) is indicated, such as API_DrugLoad:PVP: Lactose_Thk*Num.
Design of Experiments
The factors including critical material attributes (CMAs) and critical process parameters (CPPs) for a printable product by BJ were analyzed in the risk assessment and visualized with an Ishikawa diagram.Selected factors were explored in the following DoE for their impacts on the critical quality attributes (CQAs) related to a QTPP of the current product of an oral tablet.The Screening study and the Optimization study were designed with MODDE 12.1 (Umetrics AB, Umeå, Sweden), with a goal to identify the link between CQAs and selected CMAs and CPPs.
The Screening study on two APIs, i.e., IBU and PCM, was designed by using the full factorial (2 levels) interaction model with triplicate at the center point, investigating three factors, namely, the drug content in primary powder, the binder content in primary powder, and the ethanol content in ink (Table 1).Hence, there were 22 runs in the Screening study, and all were executed in a random order generated by the software MODDE.
The Optimization study was subsequently designed according to results from the Screening study, where primary powder composition with high drug loading (Screening study, 30% w/w of PCM) and aqueous ink without ethanol were further studied.Three factors, namely, the binder content in primary powder and two process factors (layer thickness and layer number) were investigated by the same interaction model (Table 2).There were 11 runs in the Optimization study, and all were executed in a random order generated by MODDE.
Particle size
Particle size and size distribution of raw materials were measured with Malvern Mastersizer 2000 using a Scirocco dry sampling system (Malvern Panalytical Ltd., Malvern, UK).The vibration of feeding plate was 50% intensity, and the dispersive air pressure was at 3 bar.The obscuration was within 0.5 to 6%.Particle size at 10%, 50% and 90% fractiles was presented as D10/D50/D90 (μm).Span was calculated by Eq (1).
Binder jetting 3D printing
According to the DoE plan, different compositions of primary powder and ink solution were printed into designed shapes (simple cylinder of different heights, designed by TinkerCAD, Autodesk, Inc., San Rafael, CA, US) by Easy3DP-M300 printer (EasyMade, Wuhan, China).The controlling and pattern slicing software installed in the system is Easy3DColor by EasyMade.For the 22 runs in the Screening study, the printed products were designed as a cylinder of 12 mm in diameter and 2 mm in height with the layer thickness of 0.10 mm.For the 11 runs in the Optimization study, the diameter of products was still 12 mm, but the height varied as layer thickness and number of layers were two investigated factors.Other process parameters and the environmental condition were at a constant level for all the printing experiments, including the roller spreading speed of 10 m/minute and rotation rate of 10 pulse/ second, as well as room temperature at 25 • C and room humidity at 55 ± 3% of relative humidity.The ink was sprayed from 4 rows of 320 nozzles in Gen5 MH5420 piezoelectric printhead (Ricoh China Ltd., Shanghai, China) at a fixed volume of 3.2 to 3.4 µl per product per layer.The vacuum pressure of ink cartridge was ranging from -0.4 to -0.6 kPa.In both the Screening study and the Optimization study, successfully solidified products were dried for 12 hours at 50 • C and collected afterwards by removing the powder residue manually.
Thermogravimetric analysis
The residual water content of the printed products from the Optimization study was measured by thermogravimetric analysis (TGA) after they were dried and collected.Around 5 mg of sample was placed in a tared platinum pan and subsequently heated from 30 to 120 • C at a rate of 10 • C/minute with nitrogen purging in TGA 5500 from TA Instruments (New Castle, DE, US).The percentage of weight loss during the heating was recorded.The test was performed in triplicate for each composition.As a reference, raw powder of PCM, PVP, and lactose was measured by the same method.
Scanning electron microscopy
The printed products from the Optimization study were manually dissected vertically to the circular plane with a scalpel.Samples were coated with gold for 20 seconds by Cressington 108 Auto sputter coater from Ted Pella, Inc. (Redding, CA, US) under argon purging.The exposed face by dissection was observed by TM3030 scanning electron microscopy (SEM) from Hitachi (Tokyo, Japan).Images were taken with an accelerating voltage of 5 kV.
Disintegration
The disintegration time of printed products from the Optimization study was measured in PTZ 2E disintegration apparatus (Pharma Test, Hainburg, Germany) according to the basket-rack method from European Pharmacopoeia (Ph.Eur.) 2.9.1 (European Pharmacopoeia Commission, 2019).
Weight, size, and tensile strength
Six products from each successfully printed composition in both the Screening study and the Optimization study were weighted and dimensional measured in diameter and height by using a vernier caliper.The diameter and height accuracies were indicated by the ratio of measured size to the designed size expressed as percentages.Subsequently products were placed in Dr. Schleuniger Pharmatron tablet tester 8M (SOTAX AG, Aesch, Switzerland) for measuring the diametral crushing strength.In the Optimization study, tensile strength was used for further analysis, which was calculated based on sample diametral crushing strength, diameter, and height by Eq (2).
Friability
Friability of successfully printed products from the Optimization study was tested by a modified Ph.Eur.2.9.7 method (European Pharmacopoeia Commission, 2019) using a standard drum apparatus equipped with motor (Parvalex, Greve, Denmark).Since products from different compositions varied in weight, a sample of whole products corresponding to a modified weight range from 6.2 to 6.8 g, instead of 6.5 g, was collected and weighed.Products were placed in the drum for 100 times rotation in 4 minutes.After test, products were carefully dedusted and weighed again to calculate the percentage of weight loss.The test was performed in triplicate for each composition.
Dissolution and drug loading
The dissolution of printed products from the Optimization study was measured in a paddle apparatus (DT 700, ERWEKA GmbH, Langen, Germany) based on the method from Ph. Eur.2.9.3 (European Pharmacopoeia Commission, 2019).The weight of each printed product was firstly determined.Samples were placed at the bottom of vessel containing 500 ml water at 37 ± 0.5 • C with a paddle rotating at a speed of 50 rpm.2 ml supernatant was taken at predetermined time points (1, 5, 10, 30, and 60 minute) and stored for quantitative analysis.After sampling, fresh water of the same volume was added.Medium of all the samples at time point of 24 hour was collected for calculating drug loading, assuming all the loaded drug has been dissolved and released.The test was performed in triplicate for each composition.
Quantitative analysis
The selected API in the Optimization study, PCM, was quantified by a HPLC method using Agilent 1260 Infinity instrument (Agilent Technologies, Santa Clara, CA, US) installed with a reverse phase C18 column (Kinetex® 00D-4462-AN, Phenomenex, Inc., Torrance, CA, US).Dissolved samples were pretreated by filtering through a 0.45 µm nylon syringe filter (Frisenette Aps, Knebel, Denmark).The mobile phase was mixture of water-ACN (90:10, V/V) pumped at a constant flow rate of 0.15 ml/minute at 25 • C. To each HPLC run, 5 µl sample was injected.At the retention time of 4.2 minute, peak detected at 254 nm by 1290 Diode Array detector (Agilent Technologies, Santa Clara, CA, US) was identical to PCM, and its area under curve was recorded.The R 2 of calibration (n=3) on PCM at concentration from 0.005 to 0.360 mg/ml was 0.9991, and all the concentrations of determined samples were within this range.
Statistics
All the statistical analysis of the DoE results was performed in MODDE.Multiple linear regression (MLR) was used to fit data.Nonsignificant model terms were removed.Significance test was conduct by Student's t-test with a confidence interval of 95%.
Risk overview
The printed products were designed to be an analogue of oral tablet that meets basic requirements defined by Ph.Eur.The QTPP of a printed product together with the CQAs is summarized and justified in Table 3.In this work, the focus was on the CQAs related to disintegration, mechanical hardness, friability, uniformity of dimensions, residual solvent, Table 3 An overview of the quality target product profile (QTPP) and critical quality attributes (CQAs) of the printed product as an analogue of oral tablet.and drug loading.To obtain a solid product with targeted quality attributes, it is necessary to investigate the relevant factors in BJ process that determine the QTPP, and further, to identify the underlying mechanisms related to each CQA.Factors affecting the properties of a printable product by BJ are visualized and presented in an Ishikawa diagram (Fig. 1).A general BJ 3D printing process is powder-based (Mostafaei et al., 2021), hence the quality of a printable product is affected by the solid material composing the primary powder and the liquid material of ink.A key material affecting the powder binding is binder, which can be either a part of the solid material or dissolved in the liquid phase (Chang et al., 2020), and the binder selection is specifically mentioned in the Ishikawa diagram.The technical parameters and specifications of mechanical parts including the printer and the installed printhead are also important to process.Some printer-related parameters can be controlled in the printer by user to optimize the printing process.These usually include the printing pattern and array, layer thickness and number, roller spreading and rotation speed, as well as the printhead moving speed and direction (Lu and Reynolds, 2008).The environment influence during fabrication and the post-process procedure are another two factors determining the success of printing.
Based on this cause-and-effect diagram, a simple product was designed comprising a model drug, a binder of PVP, and a matrix of lactose.As mentioned earlier, two powder systems with either IBU or PCM were prepared.PVP was selected because it is a widely used hydrophilic binder in BJ 3D printing of pharmaceutical products (Chang et al., 2020, Sen et al., 2020, Wilts et al., 2019, Tian et al., 2019, Tian et al., 2018, Yu et al., 2009, Wang et al., 2006, Lee et al., 2003, Rowe et al., 2000).Modified spherical lactose was selected in this research work due to its reported good performance in BJ (Chang et al., 2020, Sen et al., 2020, Wilts et al., 2019, Tian et al., 2019, Yu et al., 2009, Rowe et al., 2000).It can assist the process of powder spreading and act as the filler in pharmaceutical products to achieve the targeted drug loading.In the Screening study, besides the type of API, weight ratio of solid materials and the type of ink were explored as factors, and in the Optimization study, the weight ratio of binder and product dimensions were studied, which are factors indicated in red font in Fig. 1.Other factors, namely, the printer and printhead, parameters for the printing process, environment, and post-process also determined the printability of BJ process in this study, which were set within an optimal range according to preliminary studies, hence they were not further explored.
Screening study
The Screening study was a starting point to evaluate the printing feasibility of the two model drugs together with PVP and lactose in the primary powder.IBU and PCM are two painkiller drugs with different physical properties, such as melting point (IBU 78 • C, PCM 169 • C), aqueous solubility (IBU 0.021 mg/ml, PCM 14 mg/ml, room temperature), and particulate properties, e.g., particle size and size distribution (Table S1).At this stage, the evaluation focused on the printing feasibility.Only two samples (PCM_3:1:6_0 and PCM_3:3:4_0) could be successfully printed and collected (Table S2).Three types of failure modes of printing were observed, namely, size expansion, groove, and fragile (Table S2), which are discussed below.
Ibuprofen products
None of the IBU samples was printable, because size expansion and groove with powder spreading occurred in the printed powder area.Size expansion was observed as the detaching of the wetted area from powder bed (Fig. 2A).When the volume of sprayed ink is not optimal considering the porosity and the solubility of primary powder, saturation occurs at the surface leading to an increase in the surface roughness degree (Mostafaei et al., 2021, Lu andReynolds, 2008).Consequently, the friction force from fresh powder during spreading increases, and the printed area is pushed forward with the fresh powder spreading, which causes groove along with powder spreading direction (Fig. 2B).Additionally, if the printing process is too fast to let the surface of wetted powder get dried, there is a tendency for the wetted powder to bind the fresh powder during powder spreading.This often happens in the beginning of the process (at the firstly printed several layers), because mass of the printed lamination is not large enough to resist the friction generated by powder spreading.Different from the case of size expansion where the printing can still proceed, the groove destroys previously printed area and impedes the printing process immediately.In SEM images of the two examples, IBU_3:3:4_0 (Fig. 2C) had less pores than IBU_3:1:6_0 (Fig. 2D).This is consistent with the fact that PVP acts as the binder in primary powder and contributes to the formation of solid bridges.It can also be observed from SEM images that the appearance of IBU crystals was not changed by the process, which indicates IBU particles barely participated in the formation of solid bridges during solidification.It can be concluded that printing of low soluble drug compound can be challenging, and particle engineering is necessary (Kozakiewicz et al., 2021).
Paracetamol products
With the same printing conditions, two PCM samples PCM_3:1:6_0 and PCM_3:3:4_0 were printable (Fig. 3A).When using 20% V/V ethanol co-solvent system, printing could be performed, but the obtained products were too fragile for further analysis (Fig. 3B).Although PVP is freely soluble in both water and ethanol, ethanol can reduce the solubility of lactose (Majd and Nickerson, 1976), which limits the formation of solid bridges during solidification.The SEM images show PCM_3:3:4_20% (Fig. 3F) was more porous with more undissolved particles than PCM_3:3:4_0 (Fig. 3E).
In the experiments with 10% and 20% w/w of PCM in the primary powder (Fig. 3C and Fig. 3D), both size expansion and groove were observed, while 30% w/w of PCM products did not have this problem, Y. Wang et al. which indicates the weight ratio of PCM in primary powder was a critical factor for printing.PVP and lactose used in this work are commercially modified products for general tableting purpose, and they are of similar particle size with a narrow size distribution (span < 2, Table S1).
The measured D50 of PVP and lactose was around 50 µm, which is in the optimal range of 30-50 µm for BJ processing reported by Antic et al. (Antic et al., 2021, Antic et al., 2018), and D90 of PVP and lactose was slightly higher than the layer thickness of 0.10 mm.However, this is consistent with the observation from Infanger et al. (Infanger et al., 2019) who stated particles that were 17 µm larger than the layer thickness could still be printed.The model drug PCM had a relatively broad size distribution (span > 7, Table S1).D10, D50, and D90 of PCM were all smaller than those of PVP and lactose.Several studies have identified that using primary powder with a bimodal size distribution is an effective way to increase the powder bed density (Mostafaei et al., 2021, Miyanaji et al., 2018, Bai et al., 2015, Zhou et al., 2014).Fine particles in primary powder fill voids between big coarse particles and provide more binding sites (German and Park, 2008), and consequently they improve physical integrity and strength of printed products (Mostafaei et al., 2021, Miyanaji et al., 2018, Bai et al., 2015, Tan et al., 2017, Bai et al., 2017, Spath et al., 2015, Lanzetta and Sachs, 2003).The primary powder containing 30% w/w PCM had two apparent peaks in particle size distribution (Fig. S1), which might explain why only 30% w/w of PCM samples were printable in this work.On the other hand, powder with bimodal size distribution may result in segregation (Infanger et al., 2019).This could cause the loss in drug loading of printed products, which is discussed in 3.3.2Critical factors affecting the properties of printed product.
In the representative SEM images, 10% and 20% w/w of PCM samples (Fig. 3G and Fig. 3H) contained more unbound lactose particles and void space than 30% w/w of PCM sample (Fig. 3E).In the 30% w/w of PCM sample, crystals of PCM were visible and distributed among dissolved PVP clots being a part of solid bridges.This visually supports the finding that the density of BJ product is improved by using powder with a bimodal size distribution.Nearly unimodal size distribution might be one more cause for failures in printing IBU products besides the influence from solubility, as particle size of IBU, comparing with PCM, is closer to particle size of PVP and lactose (Table S1).
The successfully printed products of PCM_3:1:6_0 and PCM_3:3:4_0 were collected and tested on crushing strength.There was no significant difference (P-value=0.0669) between the two samples, but they were generally too soft for further analysis.
Characteristics of optimized products
In the Optimization study, 30% w/w of PCM in primary powder and the ink system with 5% w/V PVP aqueous solution were used.To increase the hardness of printed products, the number of layers was increased and investigated between 30 and 40 layers, and the layer thickness was explored between 0.10 and 0.20 mm.In the Optimization study, all the 11 primary powders were successfully printed (Fig. 4) and
characterized (Table 4).
General appearance of all the 11 compositions of printed products was similar to the designed tablet shape, although size shrinkage and expansion could be observed.All the products were strong enough for collecting and further analysis.The disintegration time of 10% and 20% w/w of PVP samples was within 3 minutes, which would be ideal for an orodispersible product.Especially, the 10% w/w of PVP samples showed a fast disintegration within 10 seconds.For the 30% w/w of PVP samples, the disintegration time was within 30 minutes.However, the friability of all the printed samples was more than the 1% weight loss as required by Ph.Eur.The poor friability is a common problem in BJ 3D printing pharmaceutical products (Tian et al., 2019, Lee et al., 2003, Antic et al., 2021, Yu et al., 2009).Comparing with conventional compacted tablets, BJ-based processing does not allow for formation of interparticulate interactions via brittle and plastic deformation (Vromans et al., 1985), which contributes to a porous microstructure in products but compromises the product induration.The problem with friability can also be related to the large particle size of the primary powder (Infanger et al., 2019).The issue on product quality caused by the poor friability can be mitigated with in-cavity printing technology by which each BJ product is fabricated directly in an individual blister that is immediately packaged after printing (Beach-Herrera et al., 2019).There is an obvious need for novel formulation strategies to solve this challenge without all too complicated packaging solutions.
Dissolution behavior of all the samples was further studied.Since the disintegration time of 10% w/w of PVP samples was remarkably shorter than that of 20% and 30% w/w of PVP samples, the dissolution profiles were presented by the binder content (Fig. S2).All the samples released more than 90% of drug within 1 hour.PCM was released relatively slower from the 30% w/w of PVP samples than others, which is related to not only the slow disintegration but also the retarding effect from PVP. PVP is a well-known viscosity-increasing agent, and during dissolution it can form viscous barrier surrounding the sample in media that slows down the overall dissolution.It should be highlighted that since BJ requires much higher content of PVP in the product than the conventional compacted products that typically contain 0.5-5% w/w of PVP (Guy et al., 2009).The impact on dissolution related to the high amount of PVP in products should be taken into consideration when designing a BJ pharmaceutical product.This is underpinning the importance for identifying strategies for reducing the amount of binder (PVP) in the pharmaceutical product.
Critical factors affecting the properties of printed product
Results from Table 4 were analyzed with the MLR model, and the procedure is described in the Supplementary information.The coefficients of significant factors related to the responses for all the successful models are presented in Table S3.
It was observed that within the investigated design space, the disintegration time and tensile strength of products were logically positively correlated to the binder content, and the weight loss during friability test was negatively correlated to the binder content.This proved the binder (PVP) plays an essential role in product solidification and integrity, and the poor friability of samples can be improved by increasing the content of PVP in primary powder.The responses of tensile strength and friability were strongly related (|correlation val-ue|>0.8)to the response of disintegration time as indicated in Table S4.
The diameter accuracy was affected by the binder content, layer thickness, and the interaction of these two factors, while the height accuracy was only affected by the layer thickness.Based on the numeric results in Table 4, both shrinkage and expansion in size were observed on printed products at horizontal direction, but only expansion happened at vertical direction.In the model of diameter accuracy, the results indicate that samples with 10% w/w of PVP expanded slightly at the horizontal direction, and with the increase on layer thickness, this expansion was less dominant.However, for the samples with more PVP in the primary powder, shrinkage at the horizontal direction occurred.Shrinkage in size is an expected phenomenon in BJ, because the binder forms solid bridges linking particles after drying, which reduces the void space between particles leading to a decrease in porosity (Mostafaei et al., 2021).This is consistent with the observation in this study, i.e., a high binder content in primary powder leading to a large extent of shrinkage.Simultaneously, the size expansion can occur when too high volume of ink is used.In the model of height accuracy, the thinner layer was, the greater size expansion occurred at the vertical direction.This indicates that the volume of sprayed ink was too high for 0.10 mm layer thickness (low level) samples, and the extra ink penetrated the powder bed driven by gravity and diffusion, which finally resulted in the size expansion dramatically at vertical direction and slightlyat horizontal direct.In representative SEM images it can be observed that the 10% w/w of PVP sample (Fig. 5A), where crystals of undissolved PCM and coarse particles of lactose were visible, comprised more pores than the 30% w/w of PVP sample (Fig. 5B).The 30% w/w of PVP sample had a microstructure of agglomerated clots with some undissolved drug crystals.On the clots, there were near-spheric holes resulted from the hollow structure of primary PVP particles.SEM images show that the 30% w/w of PVP sample was more condensed than the 10% and 20% w/w of PVP samples (Fig. 5C).This confirms that the size shrinkage of printed products is due to a decrease in porosity of solid materials influenced by the binder content.The two phenomena (size expansion and shrinkage) impact the sample dimension accuracy and microstructure in the opposite directions, and their dominance is determined by the nature and the composition of primary powder and ink.Size expansion is not desired, since it can cause the failure of printing as discussed in 3.2.1 Ibuprofen products.The size shrinkage mainly happens during drying (50 • C for 12 hours in this study) when printing is done.As indicated by the TGA result (Table 4, Residual water content %), all the final samples had slightly higher residual water content than raw materials of PCM (0.0 ± 0.0) and lactose (0.8 ± 0.1%) but lower content than PVP (7.4 ± 0.9%) as starting materials.
Since these two factors (binder content and layer thickness) also interacted in the model of diameter accuracy, the phenomena of size shrinkage and expansion might be more complicated to explain.For example, the response of weight, which was affected by all the three factors, was also strongly correlated to the diameter accuracy (Table S4).This indicates a connection between printed product density and the size shrinkage, both being related to the binder content.Hence, it can be concluded that 100% size accuracy of printing can be difficult to achieve as the complex nature of particle-ink interactions that are affected by multiple factors, and their influence on the size of printed product can cause the failure of printing or compromise the uniformity.
Regarding the drug loading that was supposed to be 100% for a homogeneous and perfectly filling primary powder, all the samples were within 100 ± 5% except for the sample of PCM_3:3:4_0.20 mm*40.Coefficients of the three factors (binder content, layer thickness, and layer number) in the statistical model for the drug loading (Table S3) indicate that a high PVP content in matrix, as well as a thick layer and/or a large number of layers, can cause a decrease on the percentage of PCM loaded in the printed products.The response of drug loading was strongly correlated to the weight of printed product (Table S4) since the two responses were both affected by all the three factors.The deviation on drug loading can be resulted from the segregation of particles with a different size.Infanger et al. (Infanger et al., 2019) reported that the sample with the largest particle size difference in their study showed the largest decrease on drug loading by the segregation effect.When the roller spreads fresh layer on printed area, undissolved particles in previously wetted powder bed can stick to the fresh powder and result in inhomogeneity in primary powder (Mostafaei et al., 2021).As the layer thickness and number of layers were studied at different levels, the degree of segregation variated.This remains a topic for further studies.
Critical overview to the model
Overall, the BJ 3D printing process involves several steps: ink spreading, powder wetting, imbibition, and absorption, followed by dissolution on binder and other materials, which all contribute to the formation of solid bridges after evaporation of the ink (Goole and Amighi, 2016, Mostafaei et al., 2021, Lu et al., 2009).These steps are driven by physical forces including capillary action, diffusion, and gravity that are determined by various material attributes, including primary powder composition, bulk and particulate properties, ink properties, and weight ratio of powder to ink.Besides the evident impact of binder content on product integrity, three other phenomena were identified affecting the product CQAs, namely, dissolution of powder materials leading to formation of liquid bridges, too high volume of ink penetrating the powder layer, and the size shrinkage due to the formation of solid bridges (Fig. 6).Material selection, a robust control of weight ratio of powder to ink, and setting proper product dimensions are important for assuring the quality of the printed products.
Moreover, an important practical step in BJ 3D process is the removal of printed products from powder residue.In this study, this step was conducted manually, and it was observed that with some samples, the boundary between printed region and powder residue was uncertain.It was further observed that some powder clots were stuck on the surface of the printed products, which required a manual removal of these particles.These clots can be formed by too high volume of ink that is binding extra particles (Mostafaei et al., 2021).This manual work might compromise the uniformity, which is the reason why the standard deviations of weight of all the printed products were close to or higher than 5%.Such problem can reduce the robustness of BJ method in fabricating uniform products.This is underpinning the importance of selecting the right weight ratio of powder to ink that can be achieved by ink volume or layer thickness.This is not a challenge when BJ 3D printing metal and ceramic materials, where the ink volume is only determined by the binder saturation level calculated by material porosity (Mostafaei et al., 2021, Lu andReynolds, 2008).With pharmaceutical materials, the solubility and dissolution rate of materials should be always considered.
Conclusions
A structured approach according to QbD principles was implemented for BJ 3D printing of an analogue of pharmaceutical tablet for oral delivery.Based on the QTPP of the solid product and its qualitative risk assessment, CQAs including disintegration time, tensile strength, friability, diameter accuracy, height accuracy, residual water content, weight, and drug loading were identified as responses.Factors related to API and binder (i.e., the primary powder composition), the type of ink, and product dimensions were explored using factorial design.It was found that the PVP content in the primary powder was critical to the integrity related characteristics.During the solidification of particles in the primary powder, size expansion and shrinkage occurred simultaneously, which contributed to the final microstructure of the printed products.To control this, weight ratio of powder to ink and product dimensions were two CPPs.Primary powder with a broad particle size distribution is favorable as it can increase the powder bed density and Fig. 6.Schematic illustration of the physical phenomena occurring during binder jetting 3D printing process.The blue droplet is illustrating ink, the grey solid circle is polyvinylpyrrolidone particle, the yellow solid circle is lactose particle, the red dot is paracetamol, and the black square in dash line is referring to the designed printed area.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
Y. Wang et al. improve power printability, but it might also cause the powder segregation leading to inaccurate drug loading in printed products.Finally, it can be concluded that acceptable PCM products can be fabricated by the BJ 3D printing technique.This study demonstrates the benefits of using a structured approach for designing a BJ 3D printed pharmaceutical product.It is of key importance to connect the experimental observations to the mechanisms related to solidification affecting the quality of printed products.
Fig. 1 .
Fig. 1.Ishikawa diagram of factors in binder jetting 3D printing to the outcome of a printable product.The factors marked in red were explored in this study.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).
Table 1
Levels of composition factors in the Screening study of ibuprofen and paracetamol.
Table 2
Levels of composition and process factors in the Optimization study of paracetamol.
Table 4
Characterization results of printed paracetamol (PCM) products from the Optimization study.Sample code follows Drug DrugLoad:Polyvinylpyrrolidone:Lactose_-LayerThickness*LayerNumber.Values are presented by mean ± standard deviation, n=3 or 6 according to each method.
Y.Wang et al. | 8,281 | 2022-08-27T00:00:00.000 | [
"Materials Science"
] |
Measurement of partial (n, n’ γ ) reaction cross-sections on highly radioactive nuclei of interest for energy production.
. In the context of the development of Gen. IV nuclear reactors, the GIF (Generation IV. International Forum) has selected six innovative technologies. Among them, one can highlight the concept of breeding for 232 Th / 233 U and 238 U / 239 Pu fuel cycles. But those nuclei, crucial for such cycles, su ff er from a lack of precise knowledge (nuclear structure, reaction cross sections). In particular, it has been demonstrated that neutron inelastic scattering reaction cross sections are not known with su ffi cient precision for the isotopes 238 U and 239 Pu, and not known at all experimentally for 233 U. In order to perform simulations of innovative reactor cores for the development of those technologies, the knowledge of the reaction cross section has to be improved which implies that new measurements have to be done. The GRAPhEME (GeRmanium array for Actinides PrEcise MEasurements) experimental setup, developed by the IPHC laboratory from CNRS and installed at the EC-JRC-Geel GELINA facility is a powerful tool to answer this need [1, 2]. Combining the prompt γ -ray spectroscopy and the time-of-flight methods, it measures partial (n, xn γ ) reaction cross sections. This paper reports on the improvements made on the GRAPhEME setup and data analysis methodology to tackle the challenge of (n, xn γ ) cross section measurements on high activity actinides. Results obtained so far on 233 U are presented compared to TALYS calculations.
Introduction
In the context of the development of Generation IV nuclear reactors, innovative breeding 232 Th/ 233 U and 238 U/ 239 Pu fuel cycles are closely studied [3]. Having an accurate knowledge of neutron scattering on those nuclei is mandatory to meet industrial needs. In particular, the neutron inelastic scattering reaction plays a key role in the slowing down of neutrons in a nuclear reactor core. But fissile 233 U and 239 Pu nuclei suffer from a lack of precise experimental data, which explains notable discrepancies between evaluations shown for 233 U target in Figure 1. The increase of the cross section at low energy varies from evaluated data to another and the plateau (between 2 and 6 MeV) varies in terms of shape or amplitude. Moreover, in the case of the 233 U nucleus, there is no experimental data at all, neither for the total (n, n') reaction cross section, nor for partial (n, n'γ) reaction cross sections. This paper presents a methodology developed for (n, n'γ) reaction cross section determination for highly radioactive nuclei, * e-mail<EMAIL_ADDRESS>based on the GRAPhEME experimental setup installed at the EC-JRC-Geel GELINA facility. Section 2 presents the experimental setup. Section 3 gives main features of the undertaken data analysis methodology. First preliminary results of 233 U(n, n'γ) will be shown and discussed in section 4. They will be compared with theoretical predictions from the nuclear reaction code TALYS. Finally, section 5 summarizes this work and gives an outlook on the next experiment with GRAPhEME.
GRAPhEME at GELINA
To answer the need of precise experimental data, the DNR (Données Nucléaires pour les Réacteurs) team from IPHC developed the GRAPhEME experimental setup. It is installed at the GELINA (Geel Electron LINear Accelerator) facility, operated by the EC-JRC Geel [4]. It combines two experimental methods: the prompt γ-ray spectroscopy and the time-of-flight technique in order to produce experimental (n, xnγ) reaction cross section data [5].
GELINA
The GELINA facility is an electron linear accelerator producing 1 ns bunches of electrons of energies between 70 and 140 MeV at a repetition rate of 800 Hz [6]. They are sent on the primary target, a rotating disk of depleted Uranium. By the Bremsstrahlung effect, they emit photons that induced (γ, f) and (γ, n) reactions on nuclei of the primary target. The latter reactions produce neutrons with an energy between a few tens of keV up to 20 MeV, with a maximum neutron flux at 30 m from the primary target (where GRAPhEME is installed) of around 1.10 4 neutrons.keV −1 .cm −2 .s −1 for a incident neutron energy of E n ∈ [0.6, 1] MeV.
GRAPhEME
Since the genesis of the GRAPhEME project, experimental (n, xnγ) reaction cross sections for several nuclei have been obtained, namely 235, 238 U, 232 Th and nat,182,183,184,186 W nuclei [7]. The experimental campaign presented here is the very first experiment for which the studied nucleus is highly radioactive. To deal with the very high counting rate of this experiment, a segmented (in 36 pixels) HPGe (High Purity Germanium) detector has been added to GRAPhEME. Each pixel, due to their small area, lowers significantly the counting rate and thus, their energy resolution is very good: FWHM(E γ = 59,54 keV) = 0.724 keV and FWHM(E γ = 1014,6 keV) = 1.317 keV. These features allow a fine identification of γ transitions. Figure 2 shows a portion of radioactivity spectrum obtained from the segmented HPGe detector and a classical one. One can see the good improvement in terms of energy resolution for the segmented detector.
To measure the neutron flux, a Fission Chamber (FC) is used. It is made out of a highly enriched in ( 235 U > 99.5%) UF 4 deposit of an arial density of 323.757 (1740) µg.cm −2 . A Cu-Cd-Pb shielding protects the target from background contamination. Finally, 13 TNT2 cards (100 MHz sampling frequency) are used for data acquisition [8]. This experiment ran from 2014 to 2017, representing a total acquisition time of 4794 hours.
Incident neutrons produced by GELINA may interact with the 233 U target and induce nuclear reactions ((n, f), (n, γ) or (n, xn) for instance), leaving the residual nucleus in an excited state. GRAPhEME detects γ-rays that are emitted after such reactions. For each event (in the FC or HPGe detectors), the acquisition system reads and stores the detection time of γ-rays and their energy. The software ROOT [9] is used to read data and bi-dimensional timeenergy diagrams are constructed. With time and energy projections of those diagrams, one can extract quantities of interest from time spectra and energy spectra.
Angular differential cross section determination
For each detector, placed at a specific angle with respect to the neutron beam (110 • and 150 • ), a differential angular cross section can be derived as follows: where N233 U is the number of target nuclei, n DET γ (E n ) the area under the γ peak of interest, N n (E n ) the number of detected neutrons, τ DET PU the detector's pile-up rate, ε FC the fission chamber efficiency, ε DET the detector efficiency and α air a correction factor due to air absorption of neutrons.
N233 U is determined by studying radioactivity γ spectra. From γ transition of 229 Th and using the radioactive decay law, we can obtain the number of 233 U nuclei in the target. This gives N233 U = 1.327(60) × 10 21 nuclei.cm −2 , which corresponds to a mass of m233 U = 7.60(35) g. To extract the n DET γ (E n ), one constructs γ spectra from different energy windows in the neutron inelastic scattering energy range (i.e. E n ∈ [0.1; 10] MeV). The dedicated software gf3 [10], especially developed for γ spectroscopy with Ge detectors is then used to obtain the quantity of interest. In the framework of this data analysis, a specific care has been taken for the extraction of the γ transitions of interest. The radioactivity component has been subtracted from spectra and the meticulous work on peaks identification helped in the fitting procedure of remaining γ-rays of interest and from fission products.
Semi Monte Carlo method to determine integrated (n, n'γ) cross section
From the differential cross section dσ dΩ , the Gaussian quadrature method is used to determine the integrated (n, n'γ) cross section as a finite and weighted sum of differential cross sections as the following: where θ 1 = 150 • , θ 2 = 110 • , ω 1 = 0.69571 and ω 2 = 1.30429. Up to now, the cross section and its uncertainty were computed with a deterministic approach. However, this method implies strong assumptions. In particular, it does not take into account correlations and covariances between parameters. To meet all these issues, we developed a semi Monte-Carlo (sMC) tool, implemented for the first time in the data analysis methodology with GRAPhEME data. It was developed in python3 along with G. Henning and its principle is the following. One realises N random draws of each parameter x of the cross section from a Gaussian distribution. For each set of parameters, a cross section is calculated and stored in a histogram. At the end of the N calculations, the obtained distribution is fitted with a Gaussian function. Its central value is thus the value of the cross section and its standard deviation the associated uncertainty. To test the validity of this method, a comparison between deterministic and semi Monte-Carlo calculations has been made. Looking at results variation between the two methods, one can see that there is a good agreement in term of cross section (less than 0.2% variation). However, some discrepancies arise in term of uncertainties. Variations on the cross section uncertainty ∆σ goes from 0.11% up to 27%. Especially, strong uncertainties variation are observed at low neutron energy. This can be explained by the low statistics of γ transitions near the threshold energy which implies a high dispersion of data in the sMC calculation that increase the width of the distribution [11].
With the data analysis that was described before, for the first time, 233 U(n, n'γ) reaction cross sections data were obtained for 12 γ transitions. Table 1 sums up structure data from the ENSDF data base [12] for 233 U γ transitions for which a cross section has been computed.
Results and Discussions
As mentioned previously, since there is no experimental data available for this nucleus, we will only compare our results with theoretical predictions obtained with the nuclear reaction code TALYS-1.95 [13]. As a first and preliminary approach, TALYS-1.95 have been run with parameters adjustment based on best inputs from TALYS data, optical model parameters from [14], level density parameters and level scheme (taking into account the first 30 levels) from the TENDL data base [16] and the preequilibrium prescription [15]. With this input, the total cross section (n, tot) is rather well reproduced but it is not the case for fission (n, f) and radiative captive (n, γ) ones which will have impact on the inelastic (n, n') and (n, n'γ) cross sections as shown on Figure 3. Since preliminary results are presented here, Figure 3 does not show all transitions but only some of interest for the discussion. For the transition ( 7 2 + ) → 9 2 + (Figure 3a), One can observe an increase of the cross section at high neutron energy, which is characteristic of polluted transitions. Identification work highlighted γ transitions coming from fission products that could explain this increase of the cross section. Table 1. Sum up of analysed 233 U γ transitions for which a (n, n'γ) reaction cross section has been extracted. For each transition, the energy of the transition and initial and final state spin/parity and energy are given. Beside, various discrepancies arise between experimental data and theoretical predictions in terms of (n, n'γ) reaction cross section amplitude and shape. Let us consider three cases of particular interest. For the transition ( 5 2 − ) → 5 2 + (Figure 3b), with γ-ray energy E γ = 298 keV, one sees a good agreement between theoretical predictions and experimental data. Aside from the rapid increase of the cross section after the threshold energy which is more pronounced in the experimental case, both shape and amplitude of the cross section are well reproduced. In the case of transition 7 2 − → 7 2 + (Figure 3c), with energy E γ = 280 keV, one notices that predictions reproduce the (n, n'γ) reaction cross section shape well, but not its amplitude which could be explained by a wrong branching ratio used in the nuclear structure file. The latter case i.e. transition 11 2 − → 9 2 + (Figure 3d), with a γ-ray energy E γ = 305 keV, shows discrepancies in terms of both shape and amplitude of the cross section.
We can conclude that TALYS calculations are not able to reproduce experimental cross sections. This is why a better and meticulous optimization of parameters is needed to improve theoretical predictions. A first step of this optimization will be to improve the modelling of radiative capture and fission cross sections by tuning the level density parameters. A second action tool is the adjustment of deformation parameters for which fission cross section is sensitive. Once fission and radiative capture well described by TALYS, discussions about the description of (n, n'γ) cross sections will be more relevant. This work will be, as this measurement was, a challenge because this nucleus is not well known, in particular in terms of nuclear structure and only a few experimental data are available to constrain the models.
Conclusion and Outlooks
The prompt γ-ray spectroscopy, combined with a timeof-flight installation is a very good method for studying (n, n'γ) cross section. Even though it was a very challenging experimental work 233 U(n, n'γ) reaction cross section data were measured for the very first time. In total, 12 γ transitions have been studied. A deeper investigation of the theoretical description with TALYS is planned. To complete this study, a comparison with another nuclear reaction code, namely EMPIRE [17] is foreseen. In particular, R. Capote [18] worked on the modelling of the fission reaction cross section for 233 U. It will be now interesting to compare both calculations.
With this work on 233 U, we have demonstrated that (n, n'γ) cross section measurements of highly radioactive nuclei is possible with GRAPhEME. The next challenge is now the measurement of the 239 Pu(n, n'γ) cross section [7]. | 3,290 | 2023-01-01T00:00:00.000 | [
"Physics",
"Engineering"
] |
Analysis of heat shock protein 70 gene polymorphisms Mexican patients with idiopathic pulmonary fibrosis
Background Idiopathic pulmonary fibrosis (IPF) is a fatal lung disease of unknown etiology. Genetic variation within different major histocompatibility complex (MHC) loci contributes to the susceptibility to IPF. The effect of 70 kDa heat shock proteins (HSP70) gene polymorphisms in the susceptibility to IPF is unknown. The aim of this study was to explore the association between HSP70 polymorphisms and IPF susceptibility in the Mexican population. Methods Four HSP70 single nucleotide polymorphisms (SNPs) were evaluated using real time PCR assays in 168 IPF patients and 205 controls: +2763 C>T of HSPA1L (rs2075800), +2437 of HSP HSPA1L A>G (rs2227956), +190 of HSPA1A G>C (rs1043618) and +1267 of HSPA1B G>A (rs1061581). Results The analysis of the recessive model revealed a significant decrease in the frequency of the genotype HSPA1B AA (rs1061581) in IPF patients (OR = 0.27, 95 % CI = 0.13–0.57, Pc = 0.0003) when compared to controls. Using a multivariate logistic regression analysis in a codominant model the HSPA1B (rs1061581) GA and AA genotypes were associated with a lower risk of IPF compared with GG (OR = 0.22, 95 % CI = 0.07–0.65; p = 0.006 and OR = 0.17, 95 % CI = 0.07–0.41; p = <0.001). Similarly, HSPA1L (rs2227956) AG genotype (OR = 0.34, 95 % CI = 0.12–0.99; p = 0.04) and the dominant model AG + GG genotypes were also associated with a lower risk of IPF (OR = 0.24, 95 % CI = 0.08–0.67; p = 0.007). In contrast, the HSPA1L (rs2075800) TT genotype was associated with susceptibility to IPF (OR = 2.52, 95 % CI = 1.32–4.81; p = 0.005). Conclusion Our findings indicate that HSPA1B (rs1061581), HSPA1L (rs2227956) and HSPA1 (rs1043618) polymorphisms are associated with a decreased risk of IPF. Electronic supplementary material The online version of this article (doi:10.1186/s12890-015-0127-7) contains supplementary material, which is available to authorized users.
Background
Idiopathic pulmonary fibrosis (IPF) is a progressive and usually lethal disease of unknown etiology characterized by alveolar epithelial cell activation, fibroblast/myofibroblasts proliferation and activation and exaggerated accumulation of extracellular matrix (ECM) in lung parenchyma [1]. A wide variety of genetic risk factors likely involved in susceptibility to develop IPF have been described including common variants in MUC5B [2], TERT, a component of telomerase [2,3], Tollinteracting protein (TOLLIP) [4], surfactant protein A and B [5] and polymorphisms within the major histocompatibility complex (MHC) [6]. In this context, we have reported that MHC class I chain-related gene A (MICA) polymorphisms might also contribute to IPF susceptibility in Mexicans [7]. These findings and the multifactorial nature of IPF suggest that there may be other unidentified genetic factors within the MHC region involved in IPF susceptibility. HSP70 genes are coded within MHC class III region and their products are involved in the binding and stabilization of nascent peptides for their correct folding to achieve appropriate conformations and in the removal of misfolded and denaturized proteins [8][9][10]. Emerging evidence indicates that endoplasmic reticulum (ER) stress and activation of the unfolded protein response (UPR) may play a role in the pathogenesis of IPF [11]. Variations in the sequence of HSP70 genes appear to affect the expression or function of HSP70 proteins resulting in altered stress tolerance mechanisms and contributing to the susceptibility to different pathological conditions [12]. HSP70 gene variations are also associated with alterations in oxidative stress [13][14][15][16][17][18][19][20][21][22]. There are three major genes of the family of human HSP70 within the MHC class III region; these genes are HSP70-1 (HSPA1A, OMIM: 140550), HSP70-2 (HSPA1B; OMIM: 603012) and HSP70-HOM (HSP70A1L; OMIM: 140559) [23]. The products of the first two genes encode a similar heat-inducible Hsp70 protein that differ only in two amino acids; whereas HSP70-HOM encodes a non-heat-inducible protein that shares high homology with the protein products of HSP70-1 and HSP70-2 [8][9][10]24]. Some report functional consequences of the HSP70 SNPs, for example in the +190 C allele of HSPA1A, located in the 5′ UTR region, provokes a reduction in the promoter activity and HSP70 protein expression than +190 G allele [25]. The polymorphisms HSPA1B-179 C>T and HSPA1B 1267 A>G have been also associated with differential production of HSPA1A and HSPA1B mRNA [26]. Also, the HSP70-HOM +2437 A>G (Met493Thr) polymorphism in the peptide-binding domain appears to affect the substrate specificity and chaperone activity of this protein [12,27].
The aim of the present study was to examine the possible association of HSP70 gene polymorphisms with the susceptibility to IPF in the Mexican population.
Patients
One hundred sixty eight Mexican patients with diagnosis of IPF were included in this study (103 males, 65 females, 64.5 ± 11.0 years old). Patients were recruited from the Interstitial Lung Diseases Clinic of the Instituto Nacional de Enfermedades Respiratorias "Ismael Cosio Villegas". Diagnosis of IPF was made with the currently accepted international criteria [28].
Patients with known causes of interstitial lung disease (i.e., collagen vascular disease, drug toxicity, environmental exposure) were excluded.
As controls, we included 205 unrelated healthy volunteers (36 males, 169 females), with an average age of 47 ± 5.4 years. Control subjects included non-smokers and smokers with normal lung function.
Patients and controls were individuals with the same ethnic origin and with at least two generations born in Mexico.
Written informed consent letter was obtained from all patients and controls. The protocol was reviewed and approved by the Scientific and Ethics Institutional Review Board of the Instituto Nacional de Enfermedades Respiratorias "Ismael Cosio Villegas".
DNA isolation
Venous blood samples were collected in 5-ml EDTA coated tubes from IPF patients and controls and DNA was isolated using a BDtract genomic DNA isolation kit (Maxim Biotech, San Francisco CA).
TaqMan 5' genotyping allelic discrimination assay
Variations of HSPA1L +2763 C>T (rs2075800), +2437 of HSPA1L A>G (rs2227956), + 190 of HSPA1A G>C (rs1043618) and +1267 of HSPA1BG>A (rs1061581) were genotyped by predesigned 5' nuclease SNP genotyping assays in accordance with the manufacturer protocol (Applied Biosystems Foster City, CA). The selection of these SNPs was based on the availability of previous studies regarding gene and allele frequencies in different ethnic groups. The reagents included primers and allelespecific probes 5'-labeled with VIC or FAM fluorochromes to detect the alleles of HSPA1. Each reaction contained 10 ng of genomic DNA, TaqMan Universal PCR Master Mix (PE Applied Biosystems), 900 nM primers, and 50 nM probes in 25 μl. The analyses were performed using an ABI Prism Step One Real time PCR System (Applied Biosystems Foster City, CA). Thermal cycling conditions were 2 min at 50°C, 10 min at 95°C and 40 cycles each of 95°C for 15 s and 50°C for 1 min.
Statistical analysis
Hardy-Weinberg equilibrium (HWE) was tested for all genotypic combinations of each variant using the Haploview software (Version 4.2) [29]. The allelic and genotypic frequencies were determined by direct counting in patients and controls. Differences in allele, genotype and haplotype frequencies were evaluated by the Pearson Chi-square test that combined the 2 × 2 contingency tables in IPF patients and control group using the EPIINFO statistical program (Version 6.04b). Corrected P (Pc) values, odds ratio (OR) with 95 % confidence interval (CI) were also estimated using EPIINFO. Statistical significance of associations with minor allele positivity (dominant model) or minor allele homozygosis (recessive model) was assessed by OR and their 95 % CI were obtained. In these models, the wild-type homozygous group was the reference group for comparisons [21].
For genotypes the value "p" of hypothesis testing between 4 polymorphisms under the 3 different models of inheritance and the presence or absence of FPI was adjusted. The test used was the Bonferroni correction and the calculation was carried out as follows: the level alpha/number of comparisons, the number of comparisons was determined by the number of SNPs (four) multiplied by the number of models of inheritance (three) between the alpha value that was 0.05 and the result was 0.004. This indicates that the values of p <0.004 can be considered statistically significant. For the alleles, the number of comparisons was determined by the number of alleles (four), between the alpha value (0.05); the result was 0.0125 and this indicates that any values of p <0.0125 can be considered statistically significant. We decided to use genotypes as the primary comparison due to the interest of establishing the possible association from models of Mendelian inheritance: dominance, co-dominant and recessive; furthermore, this approach gives more comprehensive information these polymorphisms' role in this disease. The hypothesis was built under the dominant pattern of inheritance; the calculation power for this study was 0.885, this was calculated in the Power and Sample Size software [30]. To adjust the estimates and determine if these protection associations are independent, we performed a multivariate logistic regression analysis for four SNPs of HSP70 and their association with the IPF for three models of genetic inheritance.
Results
The allele and frequencies of HSP70 gene SNPs are shown in Table 1. A decreased frequency of the G allele of the SNP rs2227956 of HSPA1L gene was observed in IPF patients when compared to controls (OR = 0.27, 95 % CI = 0.10-0.75, Pc = 0.01). The genotype frequencies and the ORs for the codominant, dominant and recessive models are also shown in Table 1. A significant decrease in the frequency of the heterozygous AG genotype of the SNP rs2227956 of HSPA1L gene (OR = 0.26, 95 % CI = 0.09-0.72, Pc = 0.01,) and in the frequency of the homozygous AA genotype of the SNP rs1061581 of the HSPA1B gene was also found in the IPF group (OR = 0.30, 95 % CI = 0.13-0.57, Pc = 0.001) when compared to the control group. These associations were observed in co-dominant and dominant models for genotype AG of HSPA1L (rs2227956) and co-dominant and recessive model for genotype AA of HSPA1B (rs1061581) ( Table 1). To adjust the estimates and determine if these genetic associations with IPF are independent, we performed a multivariate logistic regression analysis of the four SNPs of HSP70 and their association with the disease for three models of genetic inheritance ( Table 2). The pattern observed in codominant HSPA1B (rs1061581) GA genotype was associated with a lower risk, compared with GG (OR = 0. 22 Finally, we also performed a haplotype analysis (Table 3) and we found 10 haplotypes [HSPA1A-HSPA1B-HSPA1L] in both studied groups. No significant differences in the distribution of haplotypes between IPF patients and healthy controls were detected. To calculate linkage disequilibrium in the control group the Haploview 4.2 program was used [29]. In Fig. 1, we show the plot of the linkage disequilibrium HSPA1B (rs1061581) with HSP1AL (rs2075800) and HSPA1B (rs1061581) with HSPA1A (rs1043618).
Discussion
Hsp70s, together with their Hsp40 co-chaperones, are the most prominent chaperone families that participate in chaperone-assisted proteosomal degradation of misfolded proteins [31]. Previously published functional studies have highlighted the importance of HSP70 to attenuate the abnormal lung remodelling after injury in experimental models [32,33]. Accordingly, it has been shown that upregulation of HSP70 significantly decreases the inflammatory and fibrotic response in bleomycininduced pulmonary damage, blocking the production of TGF-β1 [33]. Likewise, there is evidence indicating that gefitinib-induced exacerbation of bleomycin-induced lung fibrosis is mediated by suppression of pulmonary expression of HSP70 [34]. However, studies in human IPF are scarce. Intriguingly, it was found that a subgroup of IPF patients has significantly greater extent of anti-HSP70 humoral and cellular autoreactivities compared with healthy controls. Moreover, abnormal anti-HSP70 humoral autoimmunity was associated to poor outcome. Whether the development of this autoreactivity is related to some HSP70 polymorphisms is unknown [35]. Interestingly, the autoimmune-associated HLA-B8-DR3 haplotypes seems to include the HSPA1B 1267A/G polymorphism [36]. Likewise, it has been reported in the Chinese population that the A allele is more predominant in patients with enterocutaneous fistulas than in healthy controls [37]. In this study, we determined variants of HSP70 genes in IPF patients and healthy controls from Mexican ancestry. The most striking findings confirmed by a multivariate analysis were that the GA and AA genotypes of the HSPA1B (rs1061581) polymorphism were associated with a lower risk of IPF. Also, AG genotype and the AG + GG genotypes (in a dominant model) of the SNP HSPA1L (rs2227956) were also associated with a lower risk to develop IPF. On the other hand, the HSPA1L (rs2075800) TT genotype was significantly associated with susceptibility to IPF. The polymorphism rs2227956 is located in the coding region of the HSPA1L gene and leads to an amino acid change at position 493 from a non-polar hydrophobic Met to a polar neutral Thr. Amino acid 493 is present in the 18 kDa peptide-binding domain on the beta sheet that forms the floor of the peptide binding groove [38]. The HSPA1L polymorphic G allele translates to a Met residue, an hydrophilic amino acid that may affect the interaction of the HSP70 with hydrophobic proteins and consequently impairs its ability to assemble and transport proteins within cells [38,39]. Intriguingly, a recent meta-analysis study indicated that individuals with HSPA1B AG/GG genotype, which seem to protect from IPF, have an increased risk of cancer [40]. Previous studies have highlighted the functional consequences of different HSP-70 gene polymorphisms. The polymorphisms [25,26]. Also an important functional effect at protein level of the polymorphism HSP70-HOM +2437 A>G (Met493Thr), affecting the substrate specificity and chaperone activity of HSP-70 HOM, has been described [12,27]. The possible mechanisms of HSP70 gene-disease associations in IPF are unclear. In this context, strong evidence has revealed the accumulation of unfolded and misfolded proteins with severe endoplasmic reticulum (ER) stress in alveolar epithelial cells lining areas of fibrosis [41]. It is possible that the functional effect of the HSPA1B 1267 A>G polymorphism in the differential expression of HSPA1B mRNA [26] might influence the protein expression of pro-fibrotic proteins associated to the pathogenesis of IPF. Moreover, it has been shown that the same cells also display activation of pro-apoptotic pathways [42]. In addition, ER stress may contribute to the pathogenesis of IPF through the induction of epithelial to mesenchymal transition, which may play a role in the expansion of the fibroblast population. Consequently, a transient increase in the expression of heat shock proteins is critical to prevent alveolar epithelial cell death and the shift of epithelial cells to a mesenchymal phenotype. In this perspective, an age-dependent decrease in the ability of different cell types to synthesize HSP70 has been observed, and moreover, some gene variants seem to contribute to this decrease [43]. In our study, the combination of the two genotypes associated with protection was only found in healthy controls and not in IPF patients (p = 0.005). In comparison with former data of associated functional polymorphisms [12,18,26,27,44], it seems that there is no direct relationship among them and those reported herein, since these previous studies show that HSP70 protects from fibrosis development. Strikingly, our results point out that genotypes involved in the decreased induction of these proteins might provide protection against IPF. Moreover, the association between these polymorphisms and IPF protection may be due to LD with other adjacent genes. In this regard, an LD has been reported between the TNF locus and HSPA1B [45].
To determine whether the associations described in the three models of inheritance are independent of LD between the SNPs analyzed, a multivariate analysis was performed. As a result we confirmed that these associations are independent of LD. The differences in the association with IPF between the three models of inheritance may indicate that the segregation of one or two genotypes of protection or risk act independently, either as protective or risk IPF factors, respectively. The present study has some limitations and replications in other populations are needed to verify these findings, since polymorphisms suggesting fibrosis protection are relatively rare. Notwithstanding, we were able to confirm HSP70 polymorphisms association with the protection to IPF with a statistical power greater that 80 %, even with the stringently defined number of IPF cases studied. Another limitation was the imbalanced distribution of males and females among IPF and control group. In this regard, a possible bias of the genetic association analysis may be due to the gender disparities. However, in previous genetic-association studies of MHC genes, no marked differences in the MHC genes frequencies have been detected between males and females from Mexican ancestry [6]. Furthermore, it is well know that IPF is more frequent in Mexican males and due to the age of onset of the disease, it is more frequent to have healthy females than males.
Finally, we compared the frequencies of HSP70 SNPs genotypes between Mexicans and other ethnic groups (Additional file 1: Table S1). In this analysis we found that the homozygous TT genotype of the polymorphism rs2075800 of the HSPA1L gene is the most common genotype, whereas CC genotype is the least frequent genotype in Italian Caucasians [46] and Croatian [47] subjects. We also observed that in Asian populations including Chinese [48] and Taiwanese [49] as well as in Mexicans, the CC genotype is frequent and the genotype TT is uncommon. The genotypic frequencies HSPA1L with rs2227956 are similar in all population groups. Likewise, for the HSPA1A rs1043618 gene, the GG genotype is more frequent in Chinese, Taiwanese, Polish [50,51] and Mexicans; in contrast, the most common in Italians is heterozygous CG, and the least frequent in all populations, is the homozygous CC.
Conclusions
In summary, the present study suggests that genetic variation in the HSPA1L and HSPA1B genes may influence the susceptibility of developing IPF in our population. Additional investigations with other populations are needed to confirm the significance of our findings and the functionality properties of these polymorphisms.
Additional file
Additional file 1: Table S1. | 4,092.2 | 2015-10-24T00:00:00.000 | [
"Biology",
"Medicine"
] |
The Application of Watershed Delineation Technique and Water Harvesting Analysis to Select and Design Small Dams: A Case Study in Qara-Hanjeer Subbasin, Kirkuk-NE Iraq
Received: 12 October 2021 The rainwater harvesting technique is one of the solutions to overcome the effect of water shortage crises in arid and semi-arid regions. In this study, the feasibility of using small dams in water harvesting has been examined at QaraHanjeer sub-basin that lies east of Kirkuk, N-Iraq with a surface area of 503.88 Km. Watershed boundary for entire basin has been delineated comparatively by mask method, using hydrology toolset in ArcGIS (10) software. Direct surface runoff is calculated using Soil Conservation Service Curve Number method based on data from Kirkuk meteorological station for the period (1995-2020), information obtained from land use map, and soil type, the basin is divided into six zones with different CN values, Moreover, for average annual rainfall (334.33 mm/year), water surplus was 190.2 mm and surface runoff was 25.77 mm representing 7.708 % of the total rainfall. The runoff depth was 167.03 mm/year and the total annual harvested runoff is 12.99x106 m Several temporary and semi-permanent check dams could be built across the valleys, with height (< 3m.). These dams are of low cost, reduce the loss of runoff water, improve agriculture, tourism and add impetus to the ecosystem programs in Qara-Hanjeer city. Accepted: 17 November 2021 Published: 28 February 2022
Introduction
Most Iraqi basins, in recent decades, is suffering from water shortage due to irregularity of rainfall as a result of global climate change, increasing groundwater use, land use abuse, and lack of a proper policy of management of water. Accordingly, there is a vast need for studies and researches that works on the effectual use of all water resources capability in the region to minimize the bad consequences of water shortage in drought seasons. In the study area, the climate is semi-arid to humid, following the general climate trend of Mediterranean regions (Soran and Refan, 2019). As rainfall is the essential source of water in the area a large amount of surface water runoff will be vanished due to either the evaporation processes or that the excess water will flow into the valleys and pour into the Tigris River without bringing any benefit to inhabitants and ecosystems. So, the basin was tested for the feasibility of Rainwater Harvesting (RWH) using small local dams. Their locations were suggested, depending on the drainage system and the geometry of the valley (Al-Ansari et al., 2013). The first use of such a technique was originated in Iraq over 5000 years ago by the Assyrian, Sumerian, and Babylonians in agriculture (Hardan, 1975). The RWH system deals with all the procedures which achieve the rainfallrunoff relation to retain water in the soil or underground for later beneficial use (Abdelaziz et al. 2017). However, GIS techniques were recently applied as a new approach to select dam sites (Kumar et al. 2008), where the ArcGIS hydrology tool is used to delineate watersheds directly from DEMs (Woodrow et al. 2016), and these DEMs based on the SRTM digital elevation model, which derives the area concerned to the current study by Mask Technique (Merwade, 2011). Application of the above techniques and the geological information of the studied basin provides valuable datasets to examine the kind of dam suitable for the particular site. In this paper, check dams (temporal or semi-permanent types) have been suggested to be built on some wades in a short time by natural available local materials, so they are of low cost and resists for several years. The policy to build such a dam is feasible, and great benefits are attached to the local society.
Study Area
The study area is located between coordinates 35º27' to 35º43'N and 44º22' to 44º50' E (UTM) coordinates (475300-505500 East) and (3915000-3936000 North) which lies in Zone 38N with an area of 504Km 2 (Fig.1). Situated thirty-five kilometers to the Northeast of Kirkuk city (265 kilometers north of the capital Baghdad); with a population of 51000 inhabitants live in about 49 villages. Located within the semi-arid zone of Iraq and according to Kirkuk meteorological station, it is characterized by a mean maximum temperature of 43.9 0 C during July and a mean minimum temperature of 4.9 0 C during January, where the annual rainfall is approximately 334mm.yr −1 (IMOS, 2021). The study area is a part of the Butmah-Chamchamal sub-zone of the Foothill Zone, related to the unstable shelf units (Buday and Jassim, 1987). The main observed structure in the area is Qara-hanjeer syncline (asymmetrical, double plunging, long and broad syncline extends for 65 Km in NW-SE direction), bounded by Chamchamal anticline, and by Kirkuk anticline to the northeast and southwest respectively (Jassim and Goff, 2006). The geology of the study area was studied by several authors (Buday and Jassim, 1987;Stevanovic and Markovic, 2003). Generally, all the rock units in the study area belong to the Tertiary age. The main exposed formations in the area are Fat'ha, Injana, Mukdadiya, Bai Hassan formations, and Quaternary deposits (Fig.2). Fatha formation (middle Miocene); is characterized by the prevalent evaporitic (sulphatic and halogeneous) facies.
Fig.2. Geological map of the study area
The rocks composing the formation are Anhydrite, Gypsum, and salt, interbedded with limestone, marl, and relatively fine-grained clastic. The basal unit of the Injana formation (Late Miocene) comprises thin red and green mudstone with thin-bedded gypsum and purple sandstone horizon. The calcareous sandstones contain Miliolides oscillation ripple marks overlain by fining upward cycles, of sandstone, siltstone, and mudstone. While Al-Mukdadya (Pliocene) and Bai-Hassan (Pleistocene-Pliocene) formations, as well as Holocene-Pleistocene Quaternary deposits, are constituted by alteration of recent alluvial deposits, conglomerate, gravel, and sandstones. Hydrologically, the aquifer within the area is unconfined, composed of alluvial with sequences of sand, clay, and silt layers of various thicknesses. The movement of groundwater is in the direction of the topographic slope of the basin (from the north and northeast toward the southwest). The depth to the groundwater table varies from 45-90m to ground level. The chemical analysis of water indicates that the water quality is dominated by Ca-HCO3 geochemical facies (Al-Saud, 2008). It plays a great role in the irrigation and drinking water supply of the inhabitants of this area.
Watershed delineation
A Watershed is a natural hydrologic unit enclosed by a drainage divide lying upslope from a specified spillway outlet, or "Pour point." (Zhang et al. 2011), it is topographically separated from adjacent watersheds by ridges in the landscape. Therefore, an understanding of the geospatial dataset (geology, topography, geomorphology, soil, and land cover) determines the quality of ground and surface water, as well as the magnitude and timing of streamflow and groundwater outflow of the area. The watershed area of the Qara Hanjeer basin is about 503.8km 2 , considered as a small watershed, and has been delineated using ArcGIS (10) software based on an SRTM digital elevation model of (30 x30 m EDM), and have been downloaded from the United States Geological Survey Earth Explorer (USGSEE). To Extract hydrologic information from a digital elevation model (DEM) in ArcGIS using Hydrology Toolset; Arc Catalogue10, and Spatial Analyst Tools which enclosed with Arc Map (10), has been used to extract the area concerned to the current study by Mask Technique (Merwade, 2011).
The first step is to prepare a DEM to represent the topography (terrain) of the area (Fig.3), which should have no depressions or sinks. Therefore, all sinks in the elevation grid are removed from the DEM layer using the Fill Sink function of the Hydrology toolbox (Figs.4 and 5). The flow direction raster is created from the DEM, Fig. 6 shows the direction of water flow of overland runoff. Then, to create a stream network, the flow accumulation tool is, used to compute the number of high flow cells flowing to a location. Flow accumulation defines a drainage Network, from where the stream grid is, calculated to extract Stream orders (Fig.7). Finally, delineate watersheds by converting the watershed layer from a raster to polygons before assigning their attributes (Figs.8 and 9). The point source of inlet and outlet of the flowing watershed was additionally chosen (Fig. 10).
Rainwater harvesting
RWH is the collection and storage of runoff to mitigate the effect of temporal shortages of rain in areas of arid and semi-arid regions for purposes such as cultivation, livestock, and domestic water supply (Fentaw et al., 2002)). It depends on the quantity of water stored from an area under a given climate condition (rainfall intensity, evaporation, runoff, infiltration capacity) and the nature of the covered topsoil within the whole basin (Fink, 1984). The Macro RWH technique is the most suitable technique to be tested in this region where all the requirements and variables (semi-arid, rainfall, and runoff) that needed to apply such technique were available (Gupta et al. 1997). The foregoing Watershed modeling system was used to estimate the harvested runoff volume at the studied area, based on The NRCS Runoff Curve Number (CN) method. The details are described in NEH-4 (SCS, 2004). The curve numbers (CN) values are calculated from runoff volume using rainfall data (Fig.11) for the studied period (1995-2020), soil type and land use map (Hawkins, 2004). Runoff for each month and for each geological formation zone (Fig.2) is calculated according to the following equations (USDA, 2004(USDA, , 1986: (1) Where: Q = runoff in (mm) of depth P = total precipitation (mm) (average monthly records used). S = potential maximum retention which is assumed to be 0.2S. CN is curve number, it has a range of 0 to 100 , and S is related to CN by (2) Based on the land morphological features and the lithology of expected rock units (Fig.2), soil cover and land use /land cover (Fig.12).
The study area could be divided into 6 zones (Table 1), so it has more than one CN value, where the total CN value was calculated using the following equation: Where: A1, A2... An is the areas of various zones. CN1, CN2 ...CNn is the curve members. The water balance condition of the study area is conducted by using the mean monthly water balance method, depending upon the meteorological data from Kirkuk meteorological station for the period (1995-2020), used to determine the climatological characteristics of the study area and its effect on the water balance condition. The monthly average rainfall (P) and potential evapotranspiration (PE) values calculated by Thornthwait method (Thornthwaite, 1948) used for calculating of monthly averages of Actual water loses (AE), and water surplus (WS) values as shown in Table 2.
Dam site selection
The selection of harvested dam locations is to be carefully considered (Stephens, 2010). Therefore, the position of the dams was selected depending on the drainage area and valley characteristics and built on bedrock or highly compacted soil in selected parts of the valleys, especially in the transitional zone between the hills and plains. Check dams at the studied basin are suggested to be constructed although they aren't, proposed for perennial streams, they can serve for few years. Temporary check dams are usually built at first-order stream, using local natural materials of stone, lumber (timber or wood), and sandbag (Piyapit & Cheng, 2011) (Fig.13-a), so as to reduce stream water flow and create water pools behind them to store water for several days or months. Position on streams of (order three), was proposed to be suitable places to construct semi-permanent check dams (Fig.13-b). The stream branching drainage patterns are parallel to a semi-dendritic.
Results and Discussion
In light of the foregoing, Fig.3 shows that the elevation of the North and East parts is high (> 800m.a.s.l.) and decreasing towards the Southwest part (300-250 m.a.s.l.), so the topographical gradient is also decreasing in the same direction. Fig.6 declares that the flow direction coincides with the topographical slope trend. The stream network shows two large streams in the study area, the first one, figured at the upper part of the area along the main highway between Kirkuk city and Qara-Hangeer, has a length of 43.744km with a stream slope of about (11.9 m/km). The second is located at the southeastern part of the area and has a length of 31.688 km with a gradient of 18.3 m/ km (Fig.7). Both streams are assigned to order four. Watersheds are delineated automatically to 24 catchment watersheds, and the area of each watershed was estimated (Fig.9). The Pour points of the inlet and outlet of the flowing watershed were selected (Fig. 10).
Applying the equation based on the annual rainfall average, which is equal to 334.33 mm, the amount of runoff is calculated by compensating the CN total value and the annual rainfall average in the equation 2. The result shows that the CN value of the basin is high; indicating the potentiality of a high rate of surface runoff (Manhi and Alkubaisi, 2021). The total value of water surplus is 190.2 mm forming 26.88% of the total annual rainfall, such value can be used to determine the recharge volume for groundwater after subtracting about 100mm from the total water surplus (Thornthwaite and Mather,1957), and surface runoff values.
The surface runoff (SR) was calculated of this basin using an equation based on experimental work by Sogreah (1983) Hence, the total runoff depth from the annual rainfall is equal to 167.03 mm/year. So the annual volume of water that can be harvested from the studied area is about 12.99 x10 6 m 3 for the studied period . Several temporary check dams, could be built on the first-order streams where the gradient is about 11-18m/Km. Table4: list some of the suggested suitable places for the building of temporary dams with a height of (1-1.5) meters on the cross-section of the valley while construction of one or two semi-permanent check dams was suggested to be built, at the head of second or third-order stream, with a maximum width, of such dams of about 3-5 meters.
Conclusions
The study area is a part of a semi-arid region, suffering as the majority of Iraqi water basins from water shortage problems, especially in drought seasons. In this study, hybrid techniques use the combination of Remote sensing data and ArcGIS hydrological tools to delineate a watershed so as to select the promising areas of surface water harvesting in Qara-Hanjeer sub-basin (East Kirkuk), using monthly rainfall data and land use map. Results based on The NRCS Runoff Curve Number (CN) method reveal that 49.96 % of the total annual rainfall goes as Surface Runoff, contributing about 84.13x10 6 m 3 of water to be harvested, but unfortunately, they are lost and unused. So, to manage that quantity of water, local check dams (temporary or semi-permanent) were suggested to be built across the valleys. The location was selected upon drainage system map and field survey. These dams are of low cost, reduces the loss of runoff water, improve agriculture via tourism and add impetus to the ecosystem programs in the city of Qara-Hanjeer. | 3,480.4 | 2022-02-28T00:00:00.000 | [
"Environmental Science",
"Engineering"
] |
iSEE: Interactive SummarizedExperiment Explorer
Data exploration is critical to the comprehension of large biological data sets generated by high-throughput assays such as sequencing. However, most existing tools for interactive visualisation are limited to specific assays or analyses. Here, we present the iSEE (Interactive SummarizedExperiment Explorer) software package, which provides a general visual interface for exploring data in a SummarizedExperiment object. iSEE is directly compatible with many existing R/Bioconductor packages for analysing high-throughput biological data, and provides useful features such as simultaneous examination of (meta)data and analysis results, dynamic linking between plots and code tracking for reproducibility. We demonstrate the utility and flexibility of iSEE by applying it to explore a range of real transcriptomics and proteomics data sets.
Introduction
Interactive data exploration is critical to the analysis and comprehension of data generated by high-throughput biological assays, such as those commonly used in genomics. Exploration drives the formation of novel data-driven hypotheses prior to a more rigorous statistical analysis, and enables diagnosis of potential problems such as batch effects and low-quality samples. To this end, visualisation of the data using an intuitive and interactive interface is crucial for enabling researchers to examine the data from different perspectives across samples (e.g., experimental replicates, patients, single cells) and features (e.g., genes, transcripts, proteins, genomic regions).
Most existing tools for interactive visualisation of biological data are designed for specific assays and analyses, e.g., pRoloc for proteomics (Gatto et al., 2014), shinyMethyl for methylation (Fortin et al., 2014), HTSvis for high-throughput screens (Scheeder et al., 2017). Opportunities for customisation are generally limited, making it difficult to re-use the same visualisation software for new technologies or experimental designs where different aspects of the data are of interest. Moreover, standalone tools such as the Loupe Cell Browser from 10x Genomics (Zheng et al., 2017) do not easily integrate into established analysis pipelines such as those based on the R statistical programming language (R Development Core Team, 2008). This complicates any coordinated use of these tools with a reproducible, transparent, and statistically rigorous analysis.
Here, we present the iSEE software package for interactive data exploration. iSEE is implemented in R using the Shiny framework (Chang et al., 2017) and exploits data structures from the open-source Bioconductor project (Gentleman et al., 2004), specifically the SummarizedExperiment class. iSEE allows users to simultaneously visualise multiple aspects of a given data set, including experimental data, metadata and analysis results. Dynamic linking and point selection facilitate the flexible exploration of interactions between different data aspects. Additional functionalities include code tracking, intelligent downsampling of large data sets, custom colour scale specification and tour construction. We demonstrate the capabilities of iSEE by applying it to a diverse range of real data sets.
Operation
The iSEE software package requires R version 3.5.0 or higher, along with packages from Bioconductor version 3.7 or higher. The interface is initialised with a single call to the iSEE() function, accepting a SummarizedExperiment object (Huber et al., 2015) as input. Any analysis workflow that generates a SummarizedExperiment object is supported.
Motivation for using the SummarizedExperiment class
Each instance of the SummarizedExperiment class stores one or more matrices of experimental observations as "assays", where rows and columns represent genomic features and biological samples, respectively. For instance, individual assays may represent gene expression matrices, either in the form of raw counts or normalised values. In addition, per-feature or persample variables are stored in the "rowData" and "colData" slots, respectively; these may include experimental metadata as well as analysis results.
The flexibility of the SummarizedExperiment class is the driving factor behind its broad deployment throughout the Bioconductor ecosystem. SummarizedExperiment objects are currently used in analysis pipelines for RNA sequencing (Love et al., 2014), methylation (Aryee et al., 2014 and Hi-C data (Lun et al., 2016), amongst others. Package developers can also easily use the base SummarizedExperiment class to derive new bespoke classes for particular applications, such as the Single-CellExperiment class for single-cell 'omics data. By accepting SummarizedExperiment objects as input, iSEE immediately offers interactive visualisation for a variety of data modalities. This complements the state-of-the-art analysis workflows and methodologies already available in R/Bioconductor packages.
Interface implementation
Using a multi-panel layout All data aspects stored in a SummarizedExperiment can be simultaneously examined in the multi-panel layout of the iSEE interface ( Figure 1A). The interface layout is built using the shinydashboard package (Chang & Borges Ribeiro, 2018), with colour-coded panels to visualise each data aspect. Individual panel types include: • Column data plots, for visualising sample metadata stored in the colData slot of the SummarizedExperiment object.
• Feature assay plots, for visualising experimental observations for a particular feature (e.g. gene) across samples from any assay in the SummarizedExperiment object.
• Row statistics tables, to present the contents of the rowData slot of the SummarizedExperiment object.
• Row data plots, for visualising feature metadata stored in the rowData slot of the SummarizedExperiment object.
• Heatmaps, to visualise assay data for multiple features where samples are ordered by one or more colData fields.
• Reduced dimension plots, which display any two dimensions from pre-computed dimensionality reduction results (e.g., from PCA or t-SNE). These results are taken from the reducedDim slot if this is available in the object supplied to iSEE.
Each sample is represented as a point in column data, feature assay and reduced dimension plots. Similarly, each feature is represented by a point in row data plots. For these panel types, a scatter plot is automatically produced if the selected variables on the x-and y-axes are both continuous. If exactly one variable is categorical, points are grouped by the categorical levels and a (vertical or horizontal) violin plot is produced with points scattered within each violin. If both variables are categorical, a "rectangle plot" is produced where each combination of categorical levels is represented by a rectangle with area proportional to the frequency of that combination. Points are scattered randomly within each rectangle. For ease of interpretation, the rectangle plot collapses to a mirrored bar plot when one of the categorical variables only has one level.
Custom panel colouring
Sample-based points can be coloured according to the values of any sample-level metadata field in the colData slot or by the assay values of a selected feature. Similarly, feature-based points can be coloured according to any feature-level metadata field in the rowData slot. Heatmaps are coloured according to the expression values of the selected features in the chosen assay, with additional colour annotation for each of the colData fields used to order the samples. In all cases, the variable to use for colouring can be dynamically selected for each plot. This enables users to easily examine relationships between different variables in a single plot.
By default, colour maps for categorical and continuous variables are taken from the ggplot2 (Wickham, 2009) and viridis packages (Garnier, 2018), respectively. However, iSEE also implements the ExperimentColorMap class, which allows users to specify arbitrary colour maps for particular variables. Each colour map is a function that returns a vector of distinct colours of a specified length, and will be called whenever the associated variable is used for point colouring in a particular panel. The returned colours will be mapped to factor levels for categorical variables, or used in colour interpolation for continuous variables. For categorical variables, the function may also return a constant vector of named colours corresponding to the levels of a known factor. Colour maps can be specified for individual variables; for all assays, all column data variables, or all row data variables (with different functions for continuous or categorical variables); or for all categorical or continuous variables. This provides a convenient yet flexible mechanism for customisation of colouring schemes within the interface.
Dynamic linking between panels
A key feature of iSEE is the ability to dynamically transmit information between panels ( Figure 1B). Users can define and reorganise arbitrary links between "transmitting" and "receiving" panels, whereby selections in transmitting panels control the inclusion and appearance of the corresponding data points in receiving panels. This feature facilitates exploration of the relationships between different aspects of the data. For example, users can easily determine co-expression patterns of genes in a particular region of a reduced dimensionality embedding -this is achieved by selecting points in a reduced dimension plot (using the standard rectangular brush or a lasso selection) and transmitting that selection to any number of feature assay plots.
This linking paradigm extends to multiple panels, whereby a panel can transmit to multiple receivers, and a receiving panel can transmit its own selection to another plot. Chains of linked plots allow users to mimic the arbitrarily complex gating strategies often found in analyses of flow cytometry data Figure 1. iSEE uses a customisable multi-panel layout (A) that simultaneously displays one or more panels of various types, where each panel type visualises a different aspect of the data. New panels of any type can be added (i), and all panels can be removed, reordered or resized (ii). Panel types are available to visualise sample-based reduced dimensionality embeddings (iii), sample-level metadata (iv), and experimental observations across samples for each feature (v). Other panel types include row statistics tables (vi), to facilitate searching across features and their metadata; heatmaps (vii), to visualise experimental observations for multiple features; and feature-level metadata plots. Panels of each type are colour-coded for ease of interpretation. (B) Information can be transmitted between panels according to a user-specified scheme. Here, the selection of feature X in the row statistics table determines the y-axis of the feature assay plot, and colours the samples in the reduced dimension plot by the expression of X. Selection of points in the reduced dimension plot (dotted blue line) also determines the samples that are shown in the column data (i.e., sample metadata) plot; further selection of points in the column data plot determines the samples that are shown in the heatmap. (Finak et al., 2014). With iSEE, this concept is extended to any assay data, feature-level or sample-level metadata present in a SummarizedExperiment object, providing a powerful framework for interrogating multiple interactions between data aspects. Row statistics tables can also transmit to various plot types, by selecting a table row to control the colouring of sample-based points; or by defining a s ubset of features to visualise in a heatmap. Furthermore, row data plots can transmit to row statistics tables, whereby selection of points in the former will subset the latter.
Code tracking and reproducibility iSEE automatically memorises the exact R code that was used to generate every plot, extending previous work by Marini & Binder (2016). This code is fully accessible to users at any time during the run-time of the interface. By integrating the code reported by iSEE into their own scripts, users can easily reproduce the results of any exploratory analysis. Similarly, the code required to reproduce the current state of the interface can also be reported. This can be used in startup scripts to launch an iSEE instance in any preferred layout, including the panel organisation, variable selection, colouring schemes, links between panels and even individual brushes and lasso selections.
Additional functionalities
Row statistics tables can be augmented with dynamic annotation based on the selected row, linking to online resources such as Ensembl (Zerbino et al., 2018) or Entrez (Coordinators, 2017). For large data sets, points can be downsampled in a densitydependent manner to accelerate rendering of the plots, improving the responsiveness of the interface without compromising the fidelity of the visualisation. Users can also include a bespoke step-by-step "tour" of their data set via the rintrojs package (Ganz, 2016), guiding the audience through an examination of the salient features in the data.
Use cases
Plate-based single-cell RNA sequencing To demonstrate iSEE's functionality, we used it to explore a plate-based single-cell RNA sequencing (scRNA-seq) data set involving 379 cells from the mouse visual cortex (Tasic et al., 2016). This demonstration guides the user through the main features of the iSEE interface including the multi-panel layout, colouring and dynamic linking.
An interactive tour of this use case can be viewed here.
Droplet-based single-cell RNA sequencing
We applied iSEE to a larger scRNA-seq data set involving 4,000 peripheral blood mononuclear cells (PBMCs), generated by 10x Genomics (Zheng et al., 2017). This demonstration explores the differences between different methods for distinguishing cells from empty droplets in droplet-based scRNA-seq protocols (Lun et al., 2018).
An interactive tour of this use case can be viewed here.
Bulk RNA sequencing from TCGA We applied iSEE to bulk RNA sequencing data from The Cancer Genome Atlas (TCGA) project, using a subset of expression profiles involving 7,706 tumor samples (Rahman et al. , 2015 ).
This demonstration examines the elevation of HER2 expression in a subset of breast cancer samples.
An interactive tour of this use case can be viewed here.
Mass cytometry
Finally, we explored a mass cytometry study involving more than 170,000 PBMCs from multiple donors before and after stimulation with BCR/FcR-XL (Bodenmiller et al., 2012). We used iSEE to visualise and refine a gating analysis to obtain B cells, and to investigate differences in expression of the functional marker pS6 after stimulation.
An interactive tour of this use case can be viewed here.
Conclusion
iSEE provides a general interactive interface for visual exploration of high-throughput biological data sets. Any study that can be represented in a SummarizedExperiment object can be used as input, allowing iSEE to accommodate a diverse range of 'omics data sets. The interface is flexible and can be dynamically customised by the user; supports exploration of interactions between data aspects through colouring and linking between panels; and provides transparency and reproducibility during the interactive analysis, through code tracking and state reporting. The most obvious use of iSEE is that of data exploration for hypothesis generation during the course of a research project. However, we also anticipate that public instances of iSEE will accompany publications to enable authors to showcase important aspects of their data through guided tours.
Software availability
The The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. 1.
2.
3. The authors implement an interactive tool, called iSEE, to perform exploratory analyses for high-throughput experiments. The tool inputs a Bioconductor core structure, the SummarizedExperiment object (coerced into a SingleCellExperiment object) and builds an interactive interphase for data exploration. iSEE provides several tools for data exploration by plotting features of an assay along with sample metadata, feature metadata, and reduced representations of the assays. Furthermore, iSEE enables users to interact with the plots and to dynamically link panels with different representations of the data. The analyses performed using iSEE are reproducible, since the code that was run through the graphic interphase can be downloaded.
Open Peer Review
Overall, the manuscript presents a very good idea and the code implementation is of great quality. iSEE will be very useful for people without programming background to perform basic analyses. I believe that the success of this tool will depend on whether the authors continue to develop it based on feature requests from users. I don't have major concerns. However, I do have some recommendations to increase the interest of potential users.
Enable users to select more than one group of samples from the dimensionality reduction plots. Furthermore, it would be very useful to enable users to fill new columns of colData based on the interactive grouping of samples.
Enable users to retrieve an R data object if the initial input was modified during the analysis.
In the context of single-cell or large-scale analyses, it would be helpful to implement tools for differential abundance analyses and gene set enrichment analyses. For instance, one could think of an implementation where users manually define groups of cells from tSNE/PCA plots, retrieve the genes that are differentially expressed between these groups, and extract the pathways that are enriched among the differentially expressed genes.
When grouping samples manually on the tSNE/PCA plots, the violin plots of individual features (for example, genes) could be stratified based on these selections (e.g. plot one violin per group of selected points in the "Feature assay plot" panel). In the current implementation, it is only possible to colors the points within the violin plot, which makes difficult to compare distributions between groups of samples.
Is the rationale for developing the new software tool clearly explained?
Is the description of the software tool technically sound? Yes
Are sufficient details of the code, methods and analysis (if applicable) provided to allow replication of the software development and its use by others? Yes
Is sufficient information provided to allow interpretation of the expected output datasets and any results generated using the tool? Yes
Are the conclusions about the tool and its performance adequately supported by the findings presented in the article? Yes No competing interests were disclosed.
Competing Interests:
I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. Authors show an interactive visualization tool for a very common data type used for many of the packages in Bioconductors (SummarizedExperiment). It has enough flexibility to explore all kind of information the object can contain, an interactive tool based on Rshiny, is customizable so it can be adapted to each user.
I only have minor some comments: Tutorial 2: step 10 gets the text box in the upper left of the windows, but I think it should be at other position since it says to change the y-axis of the plot. I think this happens when the user doesn't follow the instruction to click on to some button that should expand the menu with more options.
It would be nice the tour re-start from the position it was left, with an option to start over. It happened many times that I click accidentally outside the box and I had to start over.
In the cases the object doesn't have reducedDim for more than the 2 dimensions shown in the plot. I tried to use 3, and it gave an error. Maybe a more informative error would help the user to understand that there is no that information.
I am not totally sure how to use the rintrojs package to generate a tool. It would be nice a reference I am not totally sure how to use the rintrojs package to generate a tool. It would be nice a reference to some documentation on how to do it or clarification if I am not understanding this correctly.
For the features mentioned like code tracking and additional functionality, it would be nice to have a link to the vignette in the paper so the user can jump into how to get it done.
I think it would be nice to make available a docker image with all the requirements to run iSEE installed. It would promote the use of the tool a lot among bioinformaticians working with non-computational researchers.
It is nice to change the color for all the variables. I would add an example on how to change the palette for all categorical since the code would be slightly different than the one for continuous variables. It would make the user quickly using that option and avoid silly errors.
I don't know if this is possible as it is right now, but it could be an option to load a RDA/RDS file containing the SE object instead of creating an app only for that data? That would open the door to deploy the tool independent of the data. For instance, I can see a scenario where iSEE is installed in a docker container, where the user just starts the image and when opening the browser at localhost:8787, there is an option to load a file with the object.
Is the description of the software tool technically sound? Yes
Are sufficient details of the code, methods and analysis (if applicable) provided to allow replication of the software development and its use by others? Yes
Is sufficient information provided to allow interpretation of the expected output datasets and any results generated using the tool? Yes
Are the conclusions about the tool and its performance adequately supported by the findings presented in the article? Yes The iSEE package was developed to allow people to easily perform exploratory data analysis with data that are stored in a Bioconductor SummarizedExperiment object. A SummarizedExperiment container allows researchers to store one or more matrices of data, where the columns represent samples, and the rows represent either genomic positions or genomic features (genes, exons, transcription start sites, etc). In addition to the matrices of data, the SummarizedExperiment also contains two additional objects that describe the samples (the colData) and the rows (the rowData or rowRanges).
iSEE allows users to interactively plot the underlying data from a SummarizedExperiment, and also choose subsets of the data based on either interactive selection of data in a plot, or by selecting samples or genomic regions based on the colData or rowData. The chosen subsets can then be linked to other plots in the Shiny Dashboard. This simplifies what could be a complex process, allowing both experienced R users a quick way to check over their data, and allowing less experienced R users the ability to do things that they otherwise might not have been able to do.
All the underlying code generated while making interactive changes is saved and can be printed out later, in order to make the exploratory data analysis reproducible. This is an excellent feature, particularly for those who want to share observations with colleagues that may not be local.
The only negative for this package is that, being based on the Shiny framework, to allow a colleague to explore the data requires that the colleague either have R, iSEE, and all its dependencies installed, or that you have a server running all necessary packages that you can point the colleague to. This limits sharing with people who are not R savvy, but is a function of how Shiny works, rather than the iSEE package. This is a high quality package, and given the generalizability of the SummarizedExperiment package, is applicable to a whole range of different data types. Given the ease of use, self documenting features, and applicability to multiple data types, this package will likely become very popular for exploratory data analysis.
Is the description of the software tool technically sound? Yes
Are sufficient details of the code, methods and analysis (if applicable) provided to allow replication of the software development and its use by others? Yes
Is sufficient information provided to allow interpretation of the expected output datasets and any results generated using the tool? Yes
Are the conclusions about the tool and its performance adequately supported by the findings | 5,292 | 2018-06-14T00:00:00.000 | [
"Biology",
"Computer Science"
] |
System Construction of Athlete Health Information Protection Based on Machine Learning Algorithm
. The exercise volume and exercise level can be quantitatively assessed by measuring and collecting athletes ’ health and exercise data. The protection of athletes ’ health information has lately become an important research topic due to a rise in sports activities. However, due to the nature of the data and the limits of protection models, protecting athlete health data is a complex undertaking. Machine learning and blockchain have caused worldwide technological innovation, and it is bound to bring deep modi fi cations to the sports industry. The main purpose of blockchain is security, decentralization, traceability, and credibility of the athlete ’ s health data protection and gathering system. To progress and increase the sports industry and methodically assess the physical fi tness of sportspersons ’ health information, this study concentrates on the Machine Learning and Blockchain-based Athlete Health Information Protection System (MLB-AHIPS) proposed in the sports industry. The ML technique is utilized to clean and handle the information to comprehend the recognition and secure managing of the sportsperson ’ s fi tness information. The system uses attribute-based access control, which permits dynamic and fi ne-grained access to athlete health data, and then stores the health data in the blockchain, which can be secured and tamper-proof by expressing the respective smart contracts. The simulation outcomes illustrate that the suggested MLB-AHIPS attains a high accuracy ratio of 97.8%, security ratio of 98.3%, an e ffi ciency ratio of 97.1%, scalability ratio of 98.9%, and data access rate of 97.2% compared to other existing approach.
Introduction
The intelligent sports health management system quantifies, gathers, and preserves diverse health data from various perspectives [1] and does a comprehensive dialectical analysis so that individuals may completely comprehend their health state [2]. As a complete and systematic approach to health management, smart sports health management [3] has attracted the public's curiosity. Smart sports health management attempts to syndicate conventional medicine's fundamental diagnostic tools [4] with new information technology to evaluate health status using a summary and classification of previous health management research [5]. A large amount of technologically-based biomechanical and physiological data [6] is combined with mathematical algorithms to define sports monitoring [7]. On the other side, algorithms based on mechanical assumptions about how athletes work cannot collect, measure, and effectively support athletes' health and performance [8].
Machine learning (ML) is a part of Artificial Intelligence (AI) that permits a machine to think like a human and make decisions without involving humans [9]. It is the method of making robots learn without being overtly programmed [10]. The basic purpose of ML is to develop computer software that can access and learn from athletic data [11,12]. Combined with the Internet of Things, machine learning may uncover hidden patterns in massive amounts of athlete health data, enabling improved prediction and recommendation systems [13]. In healthcare, IoT and machine learning have been utilized to enable automated technologies to compile medical records [14], diagnose illnesses, and most significantly, monitor patients in real-time [15]. Different machine learning algorithms perform differently on different datasets. The utility and effectiveness of a machine learning solution, in general, are determined by the kind and characteristics of health data and the efficiency of the learning algorithms [16].
Due to increased sports activities, the protection of athletes' health information has recently become an important research topic. However, it is challenging to protect athlete health data because of the nature of the data and the limitations of protection models. Machine learning is the way to go when large athlete health data collection is necessary for analysis or pattern identification [17]. Athlete information such as health, performance, fitness, training, evaluation, and winning strategies has been protected. Blockchain technology guarantees the transparency, openness, and unforgeability of information in the sports industry. Distributed transactions and data management are features of the blockchain. Both referees and competition organizers are entitled to upload sportspersons' performances. Blockchain technology can streamline data management and ease the pressure of information uploading and correcting for data center supervisors [18]. A tamper-proof record of sensitive activities may be created securely and quickly using blockchain technology. Teams may create new revenue sources and methods to interact with their supporters using blockchain in sports. The employment of private and public keys in blockchain transactions gives users full control over their data, enabling them to own it. It is illegal for third-party intermediaries to abuse or access data. Personal data saved on the blockchain can be accessed only by those who have the right to do so.
The contributions of the proposed method are as follows: (i) Constructing the machine learning and Blockchainbased Athlete Health Information Protection System (MLB-AHIPS) in the sports industry (ii) Focusing on data sharing and athlete data privacy protection of smart healthcare, this study explores in-depth traditional encryption approaches, proxy re-encryption, attributed-based encryption, etc (iii) The numerical outcomes have been executed, and the recommended model improves the accuracy, security, scalability, efficiency, and data access rate compared with other existing methods The rest of the study is structured as follows: sections 1 and 2 deliberate the introduction and related analysis of athlete data protection systems. In section 3, the MLB-AHIPS have been suggested. In Section 4, the results and discussion have been performed. In Section 5, the conclusion and future scope have been deliberated.
Related Work
Xin et al. [18] suggested a Mobile Edge Computing Technology (MECT). This study is aimed at using mobile edge computing to collect real-time data from physical fitness tests, analyze it, and then transmit the results using machine learning technology. One of the key issues in physical education at the country's top schools and institutions is developing sports management systems that concentrate on data collecting, organization, analysis, timeliness, and direction. As a result, a data-driven health management system and physical fitness have emerged, making the value of guiding and instruction increasingly difficult to accomplish.
Rahaman et al. [19] proposed an IoT-based Smart Health Monitoring System (SHMS) to emphasize common design and implementation trends for intelligent IoT-based smart health monitoring data. The findings of the testing demonstrate that it can reduce data security concerns. The model is intended to utilize a Raspberry Pi as a Microcontroller Unit (MCU) and the Lo-Ra module for data spread and recognition of headaches, hearing problems, and rapid pulse rate, and utilizing an RFID tag for security and ZigBee for data transfer.
Ahmid et al. [20] proposed an intelligent and secure Internet of Things method for healthcare systems to monitor patient heart rate, detect a critical condition before it occurs, and make quick and appropriate judgments in an emergency. Depending on the results of the experiments, the suggested system is suitable, dependable, and provides data security at a cheap cost.
Yang and Chen [21] introduced a Web Database-based Sports Health Data Management System (WD-SHDMS). This study is aimed at creating a workable athletic health plan based on technical analysis and assessment to improve students' physical quality while minimizing effort. The experimental findings in the research involved scientific analysis and evaluation of data to improve athletes' health data while reducing workload.
Cheng [22] presented a sports data gathering system based on the Internet of Things (IoT). This study showed a sports data gathering system based on the IoT that was expressly developed and developed for the healthcare industry, specifically in sports. Measures of professional medical equipment are compared to acquiring equipment in a practical situation. These findings backed the data gathering equipment's accuracy and proved that the proposed system meets its design criteria.
Feng and Chang [23] introduced the IoT system for spatial structure health monitoring with spatial structure health monitoring data characteristics. The numerical outcomes reveal that when great temperatures exist, the overall stress of the rods decreases to some extent. The basic design of an IoT system for monitoring the health of a building's spatial structure was presented in this paper. An algorithm for data handling at the application layer was constructed using cloud computing, and cloud information for spatial structure observing was achieved.
Sun [24] proposed an adaptive federated learning technique and a personalized federated learning algorithm based 2 BioMed Research International on DL to investigate the elements impacting pupil sports performance and make recommendations for development. It was resolved that the model provided in this study can precisely forecast the pupil's athletic performance with the average accurateness ratio.
Abhishek et al. [25] proposed a Modified Blowfish Algorithm to keep patient data safe and secure while stored on various platforms. The method encrypts files 72 percent of the time and decrypts them 48 percent. Hospitals around the country have medical records that may be used for comparison by professionals. It is still possible for hackers to obtain access to critical information, putting security, and privacy at risk.
Zhao et al. [26] proposed a Posture Recognition Algorithm (PRA). This study uses the IoT and big data technology to improve the physical exercise restoration system's data processing and combines it with big data processing technology to investigate the factors impacting exercise recovery and increase its effectiveness. The findings demonstrate that the strategy developed in this work positively affects physical practice recovery.
Meng et al.
[28] suggested a Sports Health Management Model based on Deep Learning (SHMM-DL). This article aimed to develop an SHMM-DL that will teach students how to actively participate in physical activity, consequently improving their physical fitness. It creates a plan for sports health management and likens and examines data. The experimental results include the development of a positive attitude toward health and increased health awareness, reversing the general deterioration in athletes' physical fitness data.
When a massive amount of athlete health data must be examined, the protection of the athlete health data becomes a concern. As a result, machine learning is the best approach to follow. Machine Learning and Blockchain-based Athlete Health Information Protection System (MLB-AHIPS) has been constructed to use artificial intelligence to predict athletes' health information accurately and protect using Homomorphic encryption. The Machine Learning and Blockchain-based Athlete Health Information Protection System (MLB-AHIPS) results will help enhance the shield-ing methodology, athlete health information protection accuracy, and the variables that impact security.
Machine Learning and Blockchain-Based
Athlete Health Information Protection System (MLB-AHIPS) AI and machine learning in sports applications allow sports companies to leverage their data to better every aspect of their operations. A sports team may benefit from predictive analytics in every aspect of its operation, from player recruitment, and performance to ticket sales and marketing. In sports, Artificial Intelligence (AI) is being utilized to help athletes improve their performance and health. Sports people may avert major injury using wearables that monitor strain and tear levels. Machine learning can be applied to security in the sports industry, such as malware analysis, prediction, and clustering security events. It can identify previously unknown attacks with no recognized signature. Personal and sensitive data, such as phone numbers, IDs, and medical records, are often included in the athlete data used for machine learning training. This article aims to address the privacy problem in machine learning and how it may be attacked and then highlights the privacy protection techniques and characteristics in machine learning utilizing blockchain technology. Individual athletes and the team benefit from modern coaching's utilization of big data. Using data science, coaches of professional sports teams, in particular, can construct hyper-personalized player matches and other plans for every match the team participates in. This study introduces blockchain technology into athletic data protection, management, and storage to decrease maintenance costs and guarantee data security. This study proposes that the MLB-AHIPS system has been constructed for sports health data protection in the sports industry. Figure 1 shows the proposed MLB-AHIPS system. The decentralized ledger stores all information acquired by the athletes' wearable sensors. These records are kept for the benefit of medical professionals, who may use them to see how the athlete's condition has changed over time. As a 3 BioMed Research International result, the original data set is preserved, yet the raw data is transformed into numerical features extracted that may be processed. The machine learning model observes the attack detection in the data transmission network. Compared to applying machine learning directly to raw data, this method provides better results, athletes with a high risk of injury may be identified using the current ML model. A great deal of personal information is exchanged between many athletes in our use case. These medical records must be kept secret and only accessible by a few people inside our system to ensure athletes' integrity because of attacks. Blockchainbased machine learning for electronic health records is at the heart of our architecture's design. This paper incorporates an improved smart contract-based inference engine that leverages real-time fitness equipment and user profiles to infer new information in the proposed intelligent fitness blockchain platform. The security of the proposed athlete fitness system is examined in light of potential threats. The encryption utilized by the safe fitness system is based on an elliptic curve that is difficult for an attacker to calculate. To generate a private key by solving the elliptic curve technique, an intruder would need a lot of computing power. Blockchain can monitor, plan, analyze, and execute athlete health data. For each session agreement, each node takes the information of the private key. Finally, smart contracts store the athlete's health and fitness records effectively. A smart contract is a program recorded on a blockchain that executes when a set of criteria is satisfied. When a contract is automated, both parties may be sure of what will happen without the need for an intermediary or a waste of time and resources. Figure 2 shows the athlete's health information function. Athletic health data protection collects and analyses athletes' vital statistics, such as their physical fitness levels and other relevant data. They use this information to provide person-alized sports health fitness services, access, collect feedback from athletes, transfer information, protect the information, and then do the same information analysis as before. To conduct experimental research, people may use these criteria to watch athletes' health and closely change their exercise levels. Figure 3 shows the Machine learning and threats to athlete health data. Athlete raw data has been collected, and features are extracted. Furthermore, a feature vector is formulated for cleaning data. ML models have been utilized for predicting attacks such as re-construction attacks and model inversion attacks. The testing and training results are obtained. Secure channels may transfer private information between data owners and computation parties if they are not connected. To be sure, it would be stored in its unmodified state on the compute server(s), and it is not a guarantee. This is the most severe vulnerability since sensitive data is vulnerable to insider and outsider assaults. Personal data might be recorded as raw information or features derived from the raw information and stored in a database. Storing information in a raw state puts it at greater risk since it is ready for processing in any manner. Even when just the features (extracted from the raw information) are sent and kept to the computing party servers, reconstruction attacks pose a hazard. Data records and class labels produce the attack model with the target model to produce an athlete's data record in a training set.
The adversary's purpose is to use their feature vector knowledge to reassemble the secret raw data. Reconstruction attack needs white-box access to the machine learning model, i.e., knowledge of the feature vectors inside the model. Such attacks are conceivable when the feature vectors used in the machine learning training phase are not detached after generating the intended ML model. K-Nearest Neighbor (KNN) and Support Vector Machine BioMed Research International (SVM) approaches store feature vectors in models. It is possible to successfully reconstruct an image of a fingerprint (raw data) using a minutiae template (features), and it is possible to successfully reconstruct a touch event (raw information) using gesture characteristics like direction and velocity on mobile devices. SVM and KNN are excellent examples of the trade-offs that may be made when using machine learning (ML). However, SVM can only recognize a small subset of patterns since it is less computationally intensive than KNN. It is possible to identify complicated patterns with the help of KNN, and its output is more difficult to decipher than with other methods. As a consequence of not securing private information in its feature form in both circumstances, authentication systems were put at risk, putting its users' privacy at risk (since attackers may acquire access to the users' devices). A machine learning system may be misled into thinking; the raw information belongs to a certain information owner, while another re-construction attack may disclose sensitive information, like the location or age of the data user. In contrast to model inversion attacks, membership inference attacks infer whether a sample was included in the training set based on model outcomes.
3.1. Preposition 1 (machine learning for athlete data gathering). Most data can be categorized into four basic types from a machine learning perspective: categorical data, numerical data, text, and time-series data. Machine learning is a collection of technologies that excel at extracting insights and patterns from large data sets. Recall and precision rates are utilized as assessment indicators to reproduce the accuracy of the sport's health information protection system. The recall of a machine learning model depends on positive samples and is unaffected by negative samples. Positive sam-ples are as follows: all positive samples, whether rightly or mistakenly labeled, should be considered when calculating Precision's value. The recall is concerned with categorizing all positive samples accurately. This model will get the information for the input data in this model. Accuracy defines the fraction of samples that be possessed by the type D j amongst every sample that the model judges to be D j ; the recall ratio denotes the deliberation of the data and the fraction of samples judged to be right. In the binary classification issue, supposing that the positive sample sets output by the model is B, and the real positive sample dataset is A, the formulation for recall and precision are As shown in equation ((1a) and (1b)), where the positive sample sets output by the model is B, and the real positive sample dataset is A for precision and recall. The accuracy ratio signifies the fraction of data samples that are properly categorized. Supposing that the overall number of samples in the data field is m, for samples j, the forecasted type labels are actual category labels; the accuracy ratio can be described as As shown in equation (2) The data backhaul is primarily examined in the transmission model and data processing. The connection from the user to the computing server-side utilizes the millimeter-wave frequency band. A backhaul is a telecommunication phrase that refers to sending a signal from one location to another, most often a central location. Lines capable of transferring large amounts of data at high speeds are often known as backhauls. A backhaul is a telecommunication phrase that refers to sending a signal from one location to another, most often a central location. Lines capable of transferring large amounts of data at high speeds are often known as backhauls. Millimeter waves range from 30 to 300 gigahertz and have a wavelength range of 1 to 10 mm, making them an ideal carrier for transmitting data. They are known for their beam forming technique, low interference, high-frequency band, stable and reliable transmission, and the ability to penetrate solids like smoke, sand, dust, etc. As outside weather significantly impacts millimeter-wave communication, this study will not be addressing the fading issue specifically. There is no direct line of sight between the signal receiver and the signal transmitter when traveling through intermediate obstructions.
DB expresses the path loss at a given location in this way: Path loss = P Transmission − P Receiver + H Transmission + H Receiver : As inferred from the equation (3), P Transmission signifies the overall transmit power, P Receiver symbolizes the overall received power, H Transmission denotes the transmit antenna, and H Receiver indicates receiver antenna gain. Propagation loss is used to describe the loss due to radio waves traveling across space at a constant speed. The transmitter and receiver characteristics do not affect the free space path loss (dB); hence, the transmission method has nothing to do with it.
K loss H ð Þ = 32:5 + 20 log 10 f ð Þ + 10β log 10 g ð Þ + B × g: ð4Þ As discussed in equation (4), where f ðMHzÞ denotes carrier frequencies, and d signifies the path loss index, its value relies on the atmosphere in the transmission path. g symbolizes the transmission space among nodes, where the units are km; B indicates the attenuation coefficients of the environment. This study makes the transmission node on the backhaul connection aid every viewpoint in the simulation.
In the feature-to-result mapping, a layer of sigmoid function mapping is auxiliary to limit the forecasted values to [0, 1], which can output the likelihoods of diverse types. The likelihood q ðx = 1jy, θÞ specifies that the likelihood of x is 1 when the typical parameter y is provided and ðxÞ = q ðx = 1jy, θÞ, and logistic regression models are determined.
As shown in equation (5), where θ = fθ 1 , θ 2 , ⋯θ q g denotes coefficient values respective to every feature, θ values. It can be determined by resolving the maximum probability estimation functions. Supposing that every sample in the dataset is independent of the others, the probability functions are As discussed in equation (6), where JðθÞ denotes BioMed Research International probability functions, g θ indicates transmission distance, y represents number of samples. A case with a high probability value is selected as the final category for categorizing feature occurrences in real-world applications.
As defined in equation (7), where x denotes feature occurrences. A solitary data stream is primarily examined here. Supposing that the data gathering end user's demand is C, it primarily relied on the application and the user utilized. To reproduce the demand, it is presumed that the sensitivity and ambiguity of demand are contrariwise proportionate. This article uses the subsequent formulation to define the association between them As shown in equation (8), where end user's demand is C.
Preposition 2 (blockchain technology for data security).
Public and private keys or an encryption method and an encryption key are used to encrypt athlete health data written on the blockchain. As a result, anybody who does not have the secret key cannot decipher what is written on the blockchain's public ledger. Figure 4 shows the blockchain technology. The sender's private key signs each transaction. The security of the transaction is assured based on the signature. Thus, any alteration of these transactions throughout transmission can be evaded. Blocks are a blockchain records that consists of confirmed transactions. Therefore, every exposed transaction can be auxiliary to a block. Eventually, for a fresh block com-prising transactions to be auxiliary to the blockchain, it should be validated by a designated person termed a minor. This validation process is termed manage. Every block in the blockchain is connected to the prior blocks. This connection is prepared by implanting the hash particular to the prior blocks. Data integrity is ensured by using hash functions, which are often paired with digital signatures. A 1-bit change in a message will result in a different hash when using a suitable hash function (on average, half of the bits change). A message is first hashed, and then the hash is signed using digital signatures. Stage 1. Healthcare centers A and B request cloud service providers to produce their private and public keys. After the provider distinctly produces a pair of private keys and public keys for Healthcare centers A and B, cloud service providers will return to Healthcare centers A and B. Stage 2. Arbitrarily select two moderately large and independent prime numbers u, v, to create As inferred from the equation (9), where u, v is prime numbers.
Stage 3. Compute As shown in equation (10), where n is the data to be encrypted.
Stage 4. Select random integers h to create h ∈ Z * m . Stage 5. Utilize expression (10) below and compute the existence of modularized multiplicative inverse to identify As shown in equation (11), where function K is described as the following expression: Stage 6. The public key is ðm, hÞ, and the private key is ðλ, μ:Þ Stage 7. Produce encrypted files.
Healthcare center A first utilizes Rivest-Shamir-Adleman (RSA) encryption to compute and encrypt information to produce the encrypted file C1. Then, Healthcare center A encrypts in line with the second layer, encrypts the keys of RSA with its public key, and produces the encrypted file C2. In conclusion, Healthcare center A uploads two encrypted files: C1 and C2, into servers.
Stage 8. Make n the data is encrypted and n ∈ Z m Stage 9. Randomly choose r and make r ∈ Z * m Stage 10. Compute ciphertext Stage 11. Create the key of proxy re-encryption. Healthcare center A requests the public key of Healthcare center A from cloud service providers. The provider can return these public keys to Healthcare center A. Healthcare center A uses the public key of Healthcare center B and its private key to produce the re-encryption key, and then Healthcare center A uploads the afresh produced reencryption key into the server.
Stage 12. Compute public keys and private keys (RpK, RsK) Stage 13. The Paillier algorithm produces the reencrypted ciphertexts, and public key (Rpk) are sent to the cloud computing services.
For the provided public key (Rpk) and the subsequentlayer ciphertexts, this model can utilize the re-encryption keys and produce the initial-layer ciphertext of public key (Rpk). The server utilizes re-encryption keys and ciphertexts uploaded by Healthcare center A deportment proxy reencryption calculating and makes novel ciphertexts. Stage 14. Healthcare center B requests information and decrypts ⟶ Decðc, wlÞ Healthcare center B requested the cloud servers to decrypt the information and the respective ciphertexts. The cloud server sends the re-encrypted text to Healthcare center B. Healthcare center B decrypts ciphertexts, acquires keys, The extent of the capability of this system against malicious attacks, initially, create the client set to establish encryption tasks σ T . For the jth responder in σ T , its encrypted information is n-dimensional vectors, signified by w j . So, w j = fw j,i , i = 1, ⋯ng. After receiving the encrypted information, cloud nodes EN T can request σ T the trustworthiness of each client in the response side to cen-tral verification center. The dependability extent w j is weighed through the variance among w j and the final result w T . Here, this study has described the extent of the variance among w j and w T as the square of Euclidean distance among w j and w T , which can be computed via the subsequent expression as As shown in equation (16), the lesser values of d j , the greater the trustworthiness of w j . The degree of variance is the degree of dissimilarity among the parameter values, and it is utilized to measure the safety hazard. Figure 5 shows the athlete's health data and smart contract configuration. Wearable devices should be available to every athlete, allowing them to keep checks on various health-related data points that help determine their current condition (like calories, heart rate, steps, distance, and temperature). The data on this device is synchronized with the mobile app via Bluetooth. The mobile application reads the wearable device's health data and stores it in the athlete's smart contract. Depending on the patient's setup, the data upload to the blockchain may be done on-demand or as a task that runs each day for 2 epochs. A wearable device keeps tabs on each patient in our design. Athletes' smart contracts need devices like this to collect data. A single smart contract is used for each athlete.
The transaction proposal (transaction request) is submitted to the network's validating peers (miners) to accept the transaction and add value to the smart contract based on the wearable device's data. A legitimate or invalid transaction is based on a consensus protocol determined by verifying peers. Valid transactions are added to the new block by the other peers who sign them. The modern health data input is recorded in the smart contract, and the transaction's success is reported to the mobile application after the transaction is confirmed. The suggested MLB-AHIPS system using blockchain technology achieves a high accuracy ratio, security ratio, data access rate, efficiency ratio, and scalability ratio compared with other existing methods.
Results and Discussion
This study suggested the MLB-AHIPS system using blockchain technology for athlete health data protection. 100 athletes were selected to analyze the accuracy ratio, security ratio, data access rate, efficiency ratio, and scalability ratio. This study utilized the https://libguides.und.edu/ kinesiology/data-sets [27] for athlete health data protection. The Equity requires coeducational postsecondary Institutions with Athletics Disclosure Act (EADA) to submit annual sports data via a web-based data gathered for all institutions that receive Title IV funding (i.e., federal learner aid program) and have an intercollege sports program to this database. Visitors to the website may examine or download information about specific institutions and aggregate (i) Accuracy ratio Machine learning and blockchain-based solutions for the security of sports and athlete health data are examined in this article. Data backhaul and accuracy indexes show how a blockchain's capabilities might be used for data gathering systems. This article analyzes the medical data collecting system's demand, accuracy and recall rates, and data access rate. This research indicated that collecting sports medical data is advantageous to the training of sportspersons and the growth of the sports sector to satisfy the rising demands of sportsperson health. This paper assumes the accuracy indices as shown in equations (1a) and (1b), (2)) and the formulation of information return and conducts accuracy demand study and recall analysis of the athlete medical data gathering system. The Accuracy Rate measures the proportion of correctly predicted values in a dataset. In this research, the number of right predictions is divided by how many samples were used to make those predictions. Figure 6 demonstrates the accuracy ratio.
(ii) Security ratio As a prerequisite for objective and precise athlete performance assessment, ensuring the authenticity and reliability of every piece of included sportsperson training or test information is becoming a critical and demanding problem requiring extensive research. In this article, blockchain technology has been used to ensure the dependability and validity of sportsperson information that is likely integrated, shared, and sent across several parties. A new approach for reliably predicting athlete performance is based on timeaware training or test information created in the past and secured by machine learning and blockchain technology. The security ratio has been predicted based on equation (10). Figure 7 denotes the security ratio.
(iii) Efficiency ratio Cryptographic protocols could perform machine learning testing/training on encrypted information for sports health information protection when a specific machine learning application needs data from multiple input parties. To improve efficiency, several of these solutions require data owners to submit their encrypted information to the computing servers, which reduces the difficulty of secure twoor three-party calculations. Along with being more efficient, these methods do not need the input parties to stay online in sports. The efficiency of data is one of the most enticing benefits of blockchain technology, which creates a transaction log that is both auditable and valid. Anyone may join the network and see all its data, which is the whole point of blockchain as a transparency mechanism. From equation (12), the efficiency ratio has been calculated. The proposed MLB-AHIPS achieves a high-efficiency ratio. Figure 8 illustrates the efficiency ratio.
(iv) Scalability ratio The scalability of blockchain networks is the ability of sports platforms to support an increasing load of transactions of athlete health data and increase the number of nodes in the network. Limitations, transaction fees, block size, and reaction time impact the blockchain's scalability. Massivescale internet-scale analysis of large volumes of athlete health data is made possible using a flexible, frequently nonparametric, scalable statistics systems, machine learning, and data mining approaches. Scaling in the setting of blockchains denotes increasing the system's throughput, as measured by transactions per second. Layer 1 solutions enhance the blockchain network's core features and traits, like increasing the block size limit or decreasing the block verification time. Equation (14) shows the scalability ratio effectively. Figure 9 shows the scalability ratio.
(v) Data access ratio Access to the blocks is granted to all resources linked to the blockchain. Consensus algorithms, like Proof of Stake (PoS), Proof of Work (PoW), and so on, are used to verify the blocks. Only one authentication is required to access the services offered. Randomly chosen miners validate transactions in the Proof of Stake (POS) system. Blockchain transactions and new blocks are added to the network through a process known as Proof of Work (POW). The sports sector hopes to enhance data security and openness by creating this app. The strategy is doable due to the system implementing an access process to determine authentication. The use of machine learning and blockchain technology ensures that account information can only be accessed by those to whom the data owners have granted permission. Since the very beginning, blockchain has been nothing more than a public ledger used to record and preserve information about transactions. To utilize blockchain, users must have access to their private keys. Users do not require usernames and passwords to keep their sensitive information online. In addition, blockchain technology has long been regarded as an excellent method of storing sensitive information. Equation (15) signifies the data access ratio. Figure 10 signifies the data access ratio.
The suggested MLB-AHIPS system achieves high accuracy, security, scalability, efficiency, and data access rate
Conclusion
This study discussed the MLB-AHIPS system for secure data transmission in the sports industry using blockchain technology and understanding systems constructing the benefits and risks of using ML-based analysis of encrypted athlete medical data. Large-scale data training is an essential part of machine learning advancement. Cryptographic technologies create a 10 BioMed Research International new decentralized distributed database known as the blockchain. According to this research, blockchain-based machine learning may be used to secure athletes' medical data privacy and security by combining two encryption methods: proxy re-encryption and attribute-based encryption. This research introduces a new and highly customizable privacypreserving sports data fusion system. Privacy in synthetic databases may be protected using this strategy. A differential privacy system that is both flexible and adaptable is used to keep the data safe. Furthermore, this study investigates how to employ blockchain and machine learning technology in smart health scenarios. The numerical outcomes signify that the proposed MLB-AHIPS attains a high accuracy ratio of 97.8%, security ratio of 98.3%, an efficiency ratio of 97.1%, scalability ratio of 98.9%, and data access rate of 97.2% compared to other existing methods. Overall, this paper is fairly widespread; because of its limited space, the study on following-up must deliberate on achieving an effective assessment of sport-data protection with improved neural touch in time sequence data function testing.
Data Availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Conflicts of Interest
There are no potential conflicts of interest in our paper and all authors have seen the manuscript and approved to submit to your journal. We confirm that the content of the manuscript has not been published or submitted for publication elsewhere. | 8,310.4 | 2022-09-28T00:00:00.000 | [
"Computer Science",
"Medicine"
] |
A Blockchain-Supported Framework for Charging Management of Electric Vehicles
: Profound changes driven by decarbonization, decentralization, and digitalization are disrupting the energy industry, bringing new challenges to its key stakeholders. In the attempt to address the climate change issue, increasing penetration of renewables and mobility electrification augment the complexity of the electric grid, thus calling for new management approaches to govern energy exchanges while ensuring reliable and secure operations. The emerging blockchain technology is regarded as one of the most promising solutions to respond to the matter in a decentralized, efficient, fast, and secure way. In this work, we propose an Ethereum-based charging management framework for electric vehicles (EVs), tightly interlinked with physical and software infrastructure and implemented in a real-world demonstration site. With a specifically designed solidity-based smart contract governing the charging process, the proposed framework enables secure and reliable accounting of energy exchanges in a network of trustless peers, thus facilitating the EVs’ deployment and encouraging the adoption of blockchain technology for everyday tasks such as EV charging through private and semi-private charging infrastructure. The results of a multi-actor implementation case study in Switzerland demonstrate the feasibility of the proposed blockchain framework and highlight its potential to reduce costs in a typical EV charging business model. Moreover, the study shows that the suggested framework can speed up the charging and billing processes for EV users, simplify the access to energy markets for charging station owners, and facilitate the interaction between the two through specifically designed mobile and web applications. The implementation presented in this paper can be used as a guideline for future blockchain applications for EV charging and other smart grid projects.
Background and Motivation
Profound changes are disrupting the energy industry, bringing new challenges for utilities, system operators, users, and governments around the world. The three Ds, namely decarbonization, decentralization, and digitalization, are the main drivers of a disruptive transformation in the energy sector [1]. International and national policies facilitate decarbonization by imposing ambitious targets on emissions reduction to address climate change. Moreover, the widespread adoption of renewables and improvements in energy efficiency related to power generation, transport, and usage contribute to shifting away from fossil fuels. The transportation sector accounts for 27% of global greenhouse gas emissions in the EU, 72% of which are devoted to road transport [2]. Therefore, a shift toward electric mobility is regarded as an effective way to reduce local pollution and alleviate the current energy crisis.
Blockchain
This section presents the basics of blockchain technology and provides a brief overview of smart contracts. Blockchain is a decentralized digitally distributed ledger that stores transactions of a trustless network of peers in a secure manner. Participants in the blockchain are represented as nodes that cooperate to maintain the data stored on the blockchain. The transactions are packaged in blocks of a certain size that are chained in a chronological order using advanced cryptography, thus making the blockchain grow as time progresses. The representation of a blockchain is depicted in Figure 1. A combination of hashing and encryption is used for securing the various elements of the blockchain. The hash function transforms each input data point into a unique value of a fixed length so that no one can derive the original content from the hash value. Therefore, the additional security level is added, and the size of the incoming data is reduced. The transactions packaged into the block are hashed pairwise using the Merkle tree until a single hash value remains that forms the block's Merkle root hash. The hash of the block itself is generated by hashing together the timestamp, hash of a previous block, Merkle root, and other important information. Therefore, blocks in a blockchain are interlinked as every block points to the previous block's hash value except the genesis block. Such a link structure makes blockchain immutable, as changing a single data point would entail recalculation of the hash value of the respective block. As a result, all subsequent blocks will become invalid, and the modification will be rejected.
Hash
Blockchain uses asymmetric cryptography to encrypt and decrypt data based on public-private key pairs, as seen in Figure 2. The public and private keys are cryptographically linked so that the public key can be derived from the private key using a hash function, while the opposite is impossible. The transaction begins with sender and recipient exchanging their public keys, which are essentially their addresses within a blockchain network. Afterward, the sender signs the transaction digitally using a combination of their private key and the transaction's hash value and encrypts the message with the recipient's public key. The latter verifies the sender's identity using a previously received public key and decrypts the message using their own private key.
Depending on the permission model, blockchain technology can be classified into three main types: public, consortium, and private blockchain [6]. A public or permissionless blockchain is an open network accessible to any party, where any node can view, read, and write data on the blockchain. Being essentially decentralized, public blockchain does not have any association with third parties that act as governing authorities. A consortium or permissioned blockchain is a semi-private network, where a group of organizations controls the ability of a node to join, read, or write to the blockchain. In particular cases, nodes external to the consortium can access the content without modification rights to achieve greater transparency. A private blockchain is a restricted type of a permissioned blockchain, where a single organization has full control over the network. Therefore, it offers only partial decentralization as a single entity determines participating nodes and governs the consensus process in the network of trusted parties.
Sender Recipient
Private key Public key Private key Public key Digital signature Message encryption A blockchain node is a critical element of the infrastructure classified as either a normal or a mining node. Although all nodes are responsible for safeguarding the integrity and reliability of the blockchain, their roles vary. Normal nodes can be further classified into full and light nodes. Full nodes are data-heavy as each of them stores a copy of an entire blockchain, including transactions, timestamps, and all created blocks. Their main role is to verify, authenticate, and store the blocks in the network. Light nodes do not hold copies of the blockchain as they store only headers of each block, thus depending on full nodes to access complete validated information. Mining nodes are responsible for generating new blocks, broadcasting them to other nodes in the network, and adding them to the blockchain on top of pre-existing nodes once the validation from full nodes is received. As the blockchain technology is decentralized, a consensus mechanism is required to achieve agreement between nodes in the current state of the network. The consensus protocol's main requirements are being fault-tolerant, energy-efficient, secure, synchronized, low latency, deterministic, resilient to faulty nodes and message delays, and resistant to sophisticated hardware [7]. The most popular consensus mechanisms for blockchain are proof-of-work (PoW), proof-of-stake (PoS), proof-of-authority (PoA), practical byzantine fault tolerance (PBFT), proof-of-capacity, proof-of-burn (PoB), and proof-of-luck. In PoW, miners compete in solving complex mathematical puzzles to claim the right to add the block to the blockchain and obtain rewards. Although this process is computationally heavy and energy-intensive, it gives robustness to PoW against malicious attacks as it is almost impossible to acquire 51% of computing power to gain control of the network. The PoS and PoB are examples of more environmentally friendly consensus mechanisms that do not require energy-hungry calculations. The prior algorithm favors miners with larger amounts of cryptocurrency at stake, while the latter demands miners to invest coins to an unspendable address.
The advent of the Bitcoin blockchain [10] in 2009 has transformed the concept of digital payments by removing the middle-man and introducing cryptocurrency. Since then, the scope of blockchain expanded far beyond financial applications when the Ethereumdecentralized platform [11] established smart contracts previously proposed in [12]. The user-created smart contract is essentially an executable piece of code that resides on the blockchain and runs automatically when predefined initial conditions are met. To make the smart contract functional, one has to define the parties that enter into the agreement, the agreement's subject, and specific terms of the contract. The latter include requirements expected from all participants, mathematical rules that define the contract's enforcement, and rewards and penalties associated with the smart contract's successful run. To execute the smart contract, the operations comprising it are performed by miners within the Ethereum Virtual Machine. Each operation, such as addition or subtraction, is associated with a specific gas cost that measures the computational effort required to carry it. Thus, the total amount of gas needed by the contract depends largely on its size and complexity. The resulting transaction fee can be calculated by multiplying the gas by its unit price, which is determined based on the supply and demand of computing power.
The main advantages of smart contracts are their speed, accuracy, and trust, as all nodes in the blockchain witness the execution of a smart contract, savings due to third-party elimination, and security due to the cryptographic basics of blockchain. The disadvantages are uncertain legal status and high implementation costs, as an experienced programmer with expertise in the field is required to establish the agreement's rules correctly. Moreover, the deployment of a smart contract on the blockchain is irreversible, meaning that it cannot be altered once created. Although immutability is the main asset of smart contracts, encoded errors and loopholes can threaten security and lead to hacker attacking, which happened with Decentralized Autonomous Organization (DAO) [13], resulting in a radical change of Ethereum's blockchain protocol, referred to as a hard fork.
Literature Review
The use of blockchain in smart energy systems has been a topic of growing research interest over the past few years. The unique features of blockchain, together with specific challenges of the energy sector, motivate researchers to explore new implementation scenarios, define various objectives, and examine diverse energy systems. Previous works, particularly in the EV management application, can be grouped into three categories according to the type of blockchain deployed: public, consortium, and private blockchain.
The first group of studies uses public blockchain, mainly Ethereum, as a transaction mediator in various energy management tasks within smart-energy communities. Researchers in [14] developed an autonomous charging station selection process using the smart contract capability of the Ethereum network. The design aims to reduce EV charging costs while considering the planned routes, traffic conditions, user preferences, and additional incentives from the energy provider. Similarly, the authors in [15] deployed a charging station scheduling algorithm based on the Bitcoin lightning network to minimize various user-incurred costs, waiting time, and distance traveled to the charging point. The work in [16] resolved the optimal charging station selection problem using the cost-distance trade-off. Although the solution was not implemented practically, both Bitcoin and Ethereum blockchain networks were discussed as a reasonable choice for a small number of EVs. A real-time cryptocurrency-based incentive approach was proposed in [17] to maximize the usage of renewables in the energy system consisting of EV, charging station, PV generation, and battery ESS. Researchers in [18] suggested coupling the Ethereum blockchain with an EV valley-filling charging strategy to reduce overhead on the electric grid. Another example of Ethereum usage was demonstrated in [19], where the energy flows of a microgrid consisting of EVs with their charging stations, residential homes, and renewable generation were managed to minimize the impact of injecting or consuming an excessive amount of power into or from the grid. The authors of [20] developed an Ethereum-based EV charging coordination scheme by substituting the standard PoW consensus mechanism with the PoA.
The second group of work deploys consortium blockchain. Researchers in [21] applied an iterative double-auction mechanism to resolve the optimal energy allocation problem. Their system included plug-in hybrid EVs, charging stations, local energy aggregators, and smart meters. The solution aimed to maximize social welfare using consortium blockchain with the PoW consensus mechanism. The authors in [22] focused on satisfying the needs of EVs while maximizing the operator's utility in the smart community with PV generation and ESS. The formulated energy blockchain system deployed a reputation-based delegated byzantine fault tolerance algorithm to reach consensus among the participating nodes. Yet another consensus scheme, proof-of-reputation, was implemented in [23] to maintain regional energy balance and maximize EV user's utility and satisfaction whilst deploying wireless EV charging technology. The capabilities of EV charging were extended toward V2G and vehicle-to-vehicle concepts in the work of [24], where the optimal charging scheduling was considered to maximize EV satisfaction while minimizing the charging costs. Researchers in [25] gathered EV manufacturers, EV service providers, EVs, charging station operators, and software providers in a consortium blockchain enabled through Hyperledger Fabric with an improved PBFT consensus mechanism. Their work aimed to minimize overall load variance under the distribution network by shifting peak loads while respecting power flow constraints and EV charging demands. The authors of [26] included the government as a participant of the consortium blockchain to achieve fair and reasonable EV allocation to charging stations. The proposed EV management scheme addressed the profit allocation problem among various energy companies that provide EV charging services. An incentive economic-based mechanism enabled through EV coins was suggested in [27] with a particular focus on PV generation. The authors developed a prioritization ranking algorithm to guide the EV charging patterns toward maximizing renewables' utilization. Researchers in [28] considered the internet of EVs and local energy aggregators for the sake of facilitating demand-response measures through consortium blockchain with a standard PoW consensus mechanism.
The third group consists of a few studies that implemented private blockchain for energy exchange purposes. The authors in [29] deployed a private Ethereum blockchain with PoA consensus mechanism among the network of four entities: EV, energy provider, smart meter, and utility company. The blockchain in their system manages the market auction mechanism and the billing procedure to maximize social welfare. Researchers in [30] deployed a practical BFT consensus mechanism in a private blockchain to minimize operation, transportation, and transaction costs in a peer-to-peer trading network of loads and EVs designated as prosumers.
Contribution
As was demonstrated in the literature review, very few studies go beyond theoretical framing of blockchain for EV management towards practical implementations in the real world. Therefore, motivated by the developments mentioned earlier, in this paper, we aim to illustrate a concrete test case implementation of a blockchain-based EV charging framework, tightly interlinked with physical infrastructure in a trustless environment. Our particular contributions include the following points: • We provide an extensive comparison between some of the most popular blockchain platforms, such as AragonOS, Energy Web Chain, Hyperledger Fabric, and Ethereum, across a set of comprehensive criteria, such as deployment, maintainability, and scalability, crucial for the proof of concept. • We develop the first Ethereum-based architecture of the EV charging management framework, tightly interlinked with real-world infrastructure. Using a Solidity programming language, we design a particular smart contract that guides the EV charging process while ensuring the correct accounting for participating entities. • We build a web interface and a mobile application based on the client's journey to provide a user-friendly experience of EV charging encompassing the capabilities of the Ethereum blockchain. The two created instruments serve as the media for EV and charging station owners to monitor the charging process while being securely credited for respective energy flows.
• We demonstrate the application of the proposed blockchain-enabled EV charging framework on a real-world case study and document the whole EV charging process. Moreover, we assess our Ethereum-based framework's performance by evaluating some of the most common metrics in the field, such as transaction latency and fees.
The remainder of this paper is structured as follows. Section 2 presents the research approach, particularly elaborating on the choice of blockchain, system architecture, and smart contract design. Section 3 discusses the system's implementation details and introduces the web interface and mobile application. Section 4 presents the real-world case study used to validate the approach and summarizes the main results. Section 5 concludes the paper.
Choice of Blockchain Technology
Despite being a powerful and flexible technology, blockchain is not a uniform solution to any problem. Therefore, one has to choose the most suitable blockchain for the problem at hand and customize it if necessary. According to [31], the following blockchain features have to be considered when choosing a reasonable blockchain implementation: consensus mechanism, speed, permission model, and resilience. The latter signifies the capability of a blockchain-based system to resist to attacks and malicious behaviors. In the current work, we aim to develop a blockchain-enabled energy exchanges framework applicable to real-world scenarios. Therefore, we add the following criteria to the choice of appropriate blockchain implementation: • Deployment follows the blockchain life-cycle from the development, including listing the requirements and actual programming, to the final release of the system into production. • Maintainability refers to the degree of difficulty and effectiveness with which the intended maintainers can modify the blockchain system through updates. The modifications can contain corrections and error handling, system improvements, and adaptation. • Scalability signifies the capability of blockchain to handle the growing amount of participants and transactions. In particular, it is expressed in how fast the blockchain can reach the consensus among nodes and add a new transaction into a block, and how many transactions per second it can process.
In this work, we analyzed and compared four popular development frameworks for decentralized applications (DApps) that support blockchain implementation of smart contracts: AragonOS [32], Hyperledger Fabric [33], Energy Web Chain (EWC) [34], and Ethereum basic smart contract [11]. Table 1 summarizes the main features used for qualitative comparison among considered frameworks, where the speed is measured in transactions per second (TPS). One has to note that despite planning to switch to Aragon Chain with the PoS consensus mechanism in the upcoming future [35], the AragonOS currently deploys DApps on Ethereum's main network. Therefore, we directly compare the permissioned Hyperledger Fabric with permissionless Ethereum and EWC. As can be seen in Table 1, Hyperledger Fabric and Ethereum use different types of consensus algorithms, which are Apache Kafka and PoW, respectively. The lotterybased Ethereum consensus mechanism scales well to a large number of nodes but results in a longer time to finality than Hyperledger Fabric. Finality signifies the state of the blockchain under which the transaction cannot be canceled, reversed, or changed by any of the network's participants under any circumstances. If two winning miners simultaneously propose a new valid block, the blockchain will experience a temporary fork, and the acceptance of the blockchain state by all nodes will be delayed. The voting-based algorithm of Hyperledger Fabric, instead, provides low-latency finality but scales less efficiently as the time to reach consensus increases with the expansion of the network. Moreover, the algorithm's crash-fault-tolerant nature prevents the blockchain from achieving agreement in the presence of faulty or malicious nodes [36]. The PoA reputation-based consensus mechanism of EWC is a hybrid approach that resides in between the lottery-based and voting-based consensus mechanisms. The PoA relies on a set of trusted miners, called authorities, to take on the leader's responsibility for a new block creation in a rotation manner. Despite being faster and more energy-efficient, the PoA consensus mechanism does not claim a full decentralization while questioning immutability. As authorities' identities are visible to everyone in the network, such things as censorship, blacklisting, and third-party manipulation can be potentially achieved, thus compromising the safety of the blockchain. In energy-specific Ethereum-based EWC, the largest global energy companies host the validation nodes, thus executing the power to approve the new blocks in a highly regulated energy market. The speed of considered blockchain frameworks varies significantly, as Ethereum currently processes only 15 TPS, while Hyperledger processes 3000 TPS. However, researchers in [37] recently demonstrated an upscale of Hyperledger Fabric to 20K TPS, and Ethereum 2.0 is expected to yield 100K TPS in the upcoming future with the switch to PoS consensus mechanism. The EWC is currently capable of processing around 76 TPS [38]. However, the Energy Web Foundation organization that launched the EWC repeatedly claims that the TPS metric is not suitable to assess the scalability of the blockchain correctly.
To discuss the resilience of considered blockchain frameworks, one has to identify potential cyber threats. The attacks on the blockchain can be grouped into five main categories: blockchain network attacks, user wallet attacks, smart contract attacks, transaction verification mechanism attacks, and mining pool attacks [39]. The permissioned nature of Hyperledger Fabric adds a layer of security by authorizing access to only a predefined pool of participants. Moreover, the business purpose design of Hyperledger Fabric requires the system to quickly recover from attacks without compromising sensitive client data. Researchers in [40] have concluded that blockchains using different programming languages and architectures have different vulnerabilities and are thus susceptible to different types of attacks. The smart contracts of Ethereum written in Solidity language are considered to be more vulnerable than the chaincodes of Hyperledger Fabric programmed in Go. The EWC enterprise-grade blockchain exhibits good resilience, specifically due to the known list of validators that contribute to the overall integrity and security of the network. However, the underlying PoA consensus mechanism is widely criticized for being susceptible to distributed denial-of-service attacks in the case of insufficiently large pool of validators. Table 2 summarizes our assessment of blockchain systems' deployment, maintainability, and scalability on a scale from 1 to 5, where 5 signifies easiness and 1 means difficulty. Notably, the criteria considered do not have the same weight, with deployment and scalability being the most and the least important, respectively, for our concept of real-world implementation. We consider the deployment of the basic smart contract in Ethereum to be more straightforward than the deployment in Hyperledger Fabric and AragonOS, despite the latter two providing smart contract templates for cloning. Indeed, it consists of two steps successive to writing the contract code itself: compiling the smart contract into bytecode and deploying it by sending an Ethereum transaction without specifying any recipients. All these actions can be performed through Remix IDE. In Hyperledger Fabric, the multilayered access control framework complicates the process as one has to first install the smart contract on peers and then instantiate it on the channel. However, a single chaincode can define several smart contracts at once, which simplifies the development. The AragonOS has a multi-step deployment procedure with the installation of Node.js runtime environment, Web3 provider to interact with Ethereum, MetaMask to sign transactions, and Aragon command line interface to install the new app. The Ethereum-based EWC offers a comprehensive toolkit with open-source templates of energy-specific digital applications to speed up the development of customized DApps. In addition, the general procedure for deploying a smart contract is similar to the one of Ethereum, where installing the mandatory packages and related development environments is required. However, a preliminary step of setting up the Energy Web Decentralized Operating System is necessary. Moreover, a recent analysis of the EWC network has shown that over 80% of the smart contracts were deployed from only three participating entities [41], thus indicating either the lack of interest from the general public, the novelty of EWC, or the difficulty to deploy the smart contracts in the energy field.
The AragonOS shows the highest maintainability thanks to easily updating the smart contract to a newer version. Such a feature is available in AragonOS due to the specific design solution: the smart contract's logic is decoupled from its location using proxies. Therefore, developers can fix bugs and push enhancements without changing the address of the smart contract. Similarly, in Hyperledger Fabric, the contracts can be upgraded; however, one has to install the contract with the same name and a different version on all peers before upgrading the smart contract. If the order is reversed, certain peers will lose their ability to participate in the network by endorsing transactions. The smart contracts on Ethereum have the lowest maintainability as they are immutable by default. However, certain approaches to enable upgradability exist. To release the smart contract update, one can deploy a proxy contract that delegates the execution of methods and functions to implement smart contract. Such a methodology allows switching the logic contract easily, as users interact only with a proxy contract. However, one has to think of such a maintenance option, while the smart contract is still in the design stage and is not deployed on the blockchain. The life-cycle of smart contracts on EWC network is supposedly guided by the OpenZeppelin secure smart contract library that gives a possibility to securely destroy and pause the smart contract. However, we did not find any comprehensive description of its functionality on the EWC blockchain.
The scalability criterion was previously discussed with the qualitative comparison of blockchain frameworks. The Hyperledger Fabric currently scales better than AragonOS, EWC, and Ethereum due to its permissioned nature and absence of the PoW consensus mechanism. However, upcoming releases of Ethereum 2.0 that will potentially include sharing to increase the amount of TPS, and Aragon Chain aims to resolve the scalability issue. For EWC blockchain, the great scalability promises are held due to its PoA consensus mechanism. On a side note, the scalability of AragonOS is seen as less of a challenge due to focusing mainly on governance and not on transactions. In particular, large decentralized organizations can define a quorum to simplify the consensus process, thus eliminating the need to achieve 51% majority of the whole network.
To summarize, the four considered blockchain frameworks for smart contract development vary in their purpose, features, and challenges they are facing. As EWC and Ethereum both acquired the same amount of points in our subjective evaluation scheme, we had to make a choice between the two. Despite the prior being suitable for energy-related applications specifically, its consideration of not being fully decentralized has contributed to our decision. Thus, with the focus on fast deployment and high accessibility of the blockchain network for testing purposes in real-world scenarios, we concluded that the choice of the basic Ethereum smart contract is the most appropriate. Figure 3 presents the system's architecture that includes the main hardware assets and respective interaction flows between them. It should be noted that the demonstrated system architecture is scalable and can accommodate several hotels, electric vehicles, and charging stations, despite the fact that they are drawn in single quantities. The information flows are shown using the dashed line, while the power flows are depicted with the solid line. The following elements compose the architecture of the blockchain system:
Blockchain System Architecture
• The PV installation in our system belongs to the hotel and is usually located on the rooftop of the building. The renewable power from PV is used to satisfy the load demand of the hotel. The excess of the PV production is supplied to the charging station when needed or is fed back to the utility grid by the hotel. • The utility grid provides power to the hotel and the charging station whenever there is demand. • The hotel is the main physical entity in the system architecture. The hotel is characterized by its load demand, which can be satisfied either by the rooftop PV or by the utility grid. The hotel sends the smart meter power measurements and the information about PV production to Time Series Database (TSDB). The hotel owner or the hotel manager interacts with the Server to issue charging requests to the charging station in manual mode. • The charging station itself is not endowed with the layer of intelligence. Therefore all interactions with the charging station are conducted through the UniPi controller. The charging station is either AC or DC and can be operated in both manual and automatic modes. In manual mode, the maximum charging current is set by the hotel owner, while in automatic mode, the current is regulated according to the optimized EV charging strategy. The charging process is supported by both the utility grid and the PV installation. Once the charging is complete, the charging station returns to UniPi the charging status and the amount of energy consumed in kWh.
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The UniPi is a programmable logic controller mounted inside the charging station. The UniPi enables the automatic control of the charging process through the commands received from the Server. The internal API allows the UniPi to send requests to the charging station using Modbus in write and read modes. Particularly, the UniPi can set the charging station's status, the energy consumption required, and the maximum amount of amps the charger can deliver to the EV. Once the charging is complete, the UniPi returns the overall amount of energy consumed during the charging process in kWh to the Server. • The EV on the scheme represents both the vehicle itself and the EV driver, who interacts with the UniPi of the charging station using a mobile application. When the EV arrives at the charging station, the driver optionally sends out the information about the EV's current state of charge and the amount of time the EV can spend at the charging station until the next departure. This information is used to optimize the charging process and deliver the highest PV self-consumption possible while satisfying the EV's charging needs and maximizing the state of charge at departure. Further information about the optimization procedure can be found in [42]. If no supplementary information is provided by the driver at arrival, the charging process proceeds without the optimization feature.
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The TSDB stores all data collected from the hotel. Besides the load consumption and PV production, the information might contain hot water usage and other measurements related to the hotel's equipment, such as heat pumps, boilers, energy storage, etc. TSDB feeds the data to the Server for visualization purposes in the front-end and for determining the optimal EV charging strategy.
• The Meta Database contains the hotel-related data used for creating the front-end of the visualization dashboard. The information includes the hotel's profile, the list and the characteristics of the installed equipment, etc. When the system scales up to include multiple hotels, Meta Database becomes particularly useful for differentiating the static hotel-related data from dynamic time-series data stored in TSDB.
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The Server links the elements of the system architecture and enables communication from within. Moreover, it provides the visual dashboard to the hotel owner, where the latter can view the information in the interactive mode and issue the requests to the charging station. The data displayed include the hotel's measurements and the information related to the concluded charging processes such as charging start and finish times, duration, cost, and energy content. In particular, the hotel owner can browse through the charging history of either the charging station or the EV that belongs to the hotel.
The following section describes how the blockchain facilitates the energy exchanges within the system using Ethereum smart contracts.
Smart Contract
The Ethereum smart contract is written in Solidity programming language and is used to settle energy exchanges between charging stations and EVs in the form of blockchain transactions. The following entities with their particular attributes are considered participants of the smart contract: • Hotels are the central parties in the smart contract defined by their Ethereum addresses. Each hotel possesses at least one charging station and eventually one EV, uniquely differentiated by their idChargingStation and idVehicle identifiers.
The charging stations and EVs do not have their own Ethereum addresses, as in the charging process they act on behalf of the hotel they belong to. Therefore, a charging transaction is conducted between two hotels, where one behaves as the energy provider and the other as the energy consumer. If the EV is charged at the hotel it belongs to, this hotel takes on a double role resulting in a transaction with itself. Each hotel stores the history of its charging transactions in the chargingTransactions list.
The hotels' respective energy balances are kept in the hotelBalances list, which can be queried by the hotel's address. To participate in the charging process by issuing a charging transaction, the hotel's registration is required and is verified using the onlyRegisteredHotels modifier. • The owner of the smart contract is the sender of the transaction that deploys this smart contract on the blockchain. The owner is characterized by an Ethereum address and is endowed with two exclusive capabilities enabled by the onlyowner modifier: registering new hotels and resetting energy balances. The prior allows the owner to add a new hotel to the registeredHotels list, thus enabling its participation in energy exchanges between EVs and charging stations. The latter gives the contract owner a possibility to reset the energy balance of a specific hotel to zero if needed. Moreover, the owner has the right to disable a hotel by modifying its status in the registeredHotels list.
The ChargingTransaction object of the smart contract is defined as a custom structure containing the state variables presented in Table 3: Where addressHotelSupplier is the address of the hotel owning the charging station, addressHotelConsumer is the address of the hotel owning the EV, startDate and endDate are the Unix times of the beginning and the end of the charging process, respectively, and energyConsumption is the amount of energy transmitted in the process.
At the beginning of the smart contract, we define the following public and private mapping functions, where the prior type enables an automated getter-creation in the Solidity language: • mapping (address => bool) public registeredHotels allows for a quick verification of the hotel's registration. The addChargingTransaction function is the core of the smart contract. The function uses the onlyRegisteredHotels modifier, thus allowing only the charging stations from registered hotels to initiate charging transactions. The input to the function contains the following variables inherited from the ChargingTransaction object: It is important to notice that the supplier's hotel address is absent from the function input as it is automatically defined by the msg.sender property of the charging station issuing the transaction. The _minusEnergyConsumption variable, which differs from the _energyConsumption only by its negative sign, is introduced to avoid the additional cost on blockchain related to the subtraction of the _energyConsumption value.
The function's body contains the following expressions: The detailed smart contract class diagram is presented in Figure 4.
Pilot Site
The case study is based on the Digitalization project [43] conducted within the research framework of the SCCER FURIES [44]. The project, established as part of the activities related to the Swiss National Action Plan on Digitalization [45], integrates a network of EVs and charging stations available to guests staying in the hotels of the Val d'Hérens alpine region in Switzerland. Each of the eight partner hotels owns one charging station and at least one EV, allowing guests to explore the region with maximum independence and minimum harm to the environment. The EVs are rented to the hotels' guests daily free of charge, based on the principle "pay what you want". Figure 5 describes the steps of the EV charging process flow. The main entities implicated in the process are the hotel owners and managers, EV charging stations, and hotel guests. The prior participate in the process using the web interface detailed in Section 3.4, while the latter issue charging-related commands through the mobile application described in Section 3.5. To enable the EV's participation in the blockchain-supported charging process, the hotel owner must register the EV in the web interface. Once the EV can be found in the hotel's digital vehicle inventory, this step becomes unnecessary. The registration procedure generates a unique vehicle identifier idVehicle together with the username-password pair. The latter is shared with hotel guests to enable access to the mobile application used for managing the EV charging process. Besides the standard way to log in, the EV user can utilize the generated QR code, thus avoiding memorizing complex login details. It is expected that the password and QR code will be automatically regenerated.
Transaction and
Once the guest has rented the EV and has connected to the mobile app, the charging process unfolds as follows. First, the EV driver chooses an unoccupied charging station on the map. Second, the user optionally shares the EV's state of charge and the available time to spend at the charging station. If transmitted by the EV driver, these details allow the charging station to optimize the charging process according to the algorithm described in [42]. Third, the EV user starts the charging process by clicking the dedicated button on the mobile application. Otherwise, the charging process can be initiated by the hotel's manager from the web interface. From that moment on, the charging station manages the EV charging process flow.
During the EV charging, the charging station collects the data required to populate the ChargingTransaction object and execute the addChargingTransaction function. The charging station retrieves such data from the web interface using the application programming interface (API). The EV charging ends with either the user terminating the process through the mobile application or the charging station when the maximum state of charge is reached. Once the charging is complete, the charging station initiates the blockchain transaction by sending the data to the smart contract. The hotel owner can access the history of charging transactions and their details by interacting with the blockchain.
Technical Details
The technical specifications of the platform that implements the blockchain system architecture presented in Section 2.2 are depicted in Figure 6. The back-end of the web interface residing on the Ubuntu server is built using PHP, a general-purpose scripting language. At the same time, the front-end is realized using HTML5, CSS3, Angular, and AngularJS. The HTML5 and CSS3 are used to visualize the web interface and define the graphical content style. The Angular and AngularJS aid the visualization by interacting with the back-end through an API to retrieve the data to be displayed and pass them to the HTML5. InfluxDB and MySQL support the two major databases deployed. The prior serves the TSDB that stores the measurements collected from the hotels. The latter provides the hotel-related data such as hotel profiles and characteristics in the Meta Database.
Web Interface
The web interface is designed to ease the hotel owners' interaction with the blockchain system architecture and simplify EV management. Once the hotel is connected to the green mobility program and the necessary hardware such as UniPi is installed, the hotel owner can create the hotel's account on the web platform. The main dashboard contains various instruments for managing the hotel's participation in the program. Specifically, the three major tabs, namely energy flow, charging station management, and clients, are designed to give the hotel owner an interactive and visual experience of EV management. Figure 7 depicts the energy flow tab, where the hotel owner can monitor the status of its major energy-producing and -consuming assets in real time. In particular, the tab shows the quantities of PV and grid power consumed by the hotel, the amount of PV fed back to the grid, and the power consumed by the charging station to refill the EV battery. The clients' tab depicted in Figure 9 is the hotel's point of interaction with the vehicle inventory and the blockchain system. The history of charging transactions is displayed on the tab's left-hand side, where the date, identifiers of the EV and the charging station, energy, and charging duration can be seen. The hotel's energy balance is placed underneath the charging transactions and can be used for the hotel's reporting at desired time periods. The tab's right-hand side provides the hotel owner an overview of the EV inventory with the possibility to register additional vehicles.
Mobile Application
The mobile application is the means for the EV user to interact with charging stations participating in the green mobility program. The application, developed in NativeScript, is available for both mobile operating systems Android and iOS. The following figures demonstrate the mobile application's design and functionalities. Figure 10 depicts the login page, where the EV user is asked to either input the username-password pair or scan the QR code. Both are transmitted to the user by the hotel owner or manager at the beginning of EV rental. Figure 11 shows the EV user's profile, where the username is displayed. In the future releases of the application, other information about EV, such as model, battery capacity, charger type, etc. will appear on the account screen. Figure 12 presents the map screen that depicts the charging stations in the area and their status, thus helping the EV driver choose where to charge. If the charging station is not occupied, the icon's color on the map appears green and red otherwise. Clicking on the icon opens the details about the charging station, as shown in Figure 13. In particular, the user can see the name of the charging station, its address, the hotel it belongs to, the types of charging plugs at its disposal, and the charging station's availability. Optionally, to optimize the charging process concerning the hotel's demand and PV production, the EV driver can input the EV's state of charge and the time planned to spend at the charging station. Otherwise, the required charging time is calculated based on the charging power of EV. The charging process is activated using the button.
Results
To validate the proposed blockchain system architecture and demonstrate its application to the use case of EV charging, we recreate the process flow depicted in Figure 5 in a real-world case study. The two hotels, Hotel du Pigne and Hotel Aiguille de la Tza, both located in Val d'Hérens region in Switzerland, act as the demonstration participants. The former owns the EV, while the latter provides the charging station. Thus, the test aims to show how the EV-charging procedure unfolds in the blockchain-enabled EV management framework. The experiment is conducted using the UniPi Axon S105 programmable logic computer installed inside the charging station, with the following characteristics: 1.2GHz quad-core ARM CPU, 1GB RAM, 8GB eMMC onboard memory, and 1Gbit Ethernet connection. Figure 14 depicts the charging infrastructure used for testing. To enable the vehicle's participation in the blockchain-supported charging, the hotel must register the EV in the inventory using the web interface. Thus, the Hotel du Pigne that already owns a Tesla Model X, uses the 'clients tab' in their web interface's account to add a new EV. The respective dialog window shown in Figure 15 prompts the hotel manager to input the necessary information for describing the new EV.
The hotel manager makes the following entries to add the Hyundai Kona [46] to the vehicles' inventory and confirms their choices with the blue "create" button: A corresponding confirmation message depicted in Figure 16 pops up on the web interface screen to validate the new addition to the EVs' inventory. The updated list of EVs owned by the Hotel du Pigne is shown in Figure 17. Once the new EV is registered, a QR code with its username and password is generated and can be shared with the hotel's guests willing to rent the vehicle. Knowing these details allows the guests to access the mobile application and utilize it for charging management. To conduct the charging process, the user logs in to the mobile application using the provided credentials and choose the charging station of the Hotel Aiguille de la Tza as our destination. At the arrival, the EV is charged to 50%, which we optionally report in the respective field of the screen in Figure 13. Omitting the time-to-departure input, the user initiates the EV charging process by clicking on the green "start charging" button.
To form the ChargingTransaction object, at the beginning of the charging process, the charging station retrieves the following information: Once the charging is complete, the additional details about the charging process are included: After all the necessary information is collected, the charging station calls the addChargingTransaction function implemented in the smart contract. Once such blockchain transaction is validated, its record can be observed on the Etherscan [47], as shown in Figure 18. One has to note that the resulting transaction constitutes the call to the smart contract and is conducted between the hotel possessing the charging station and the smart contract itself. Thus, the hotel owning the EV does not appear as the beneficiary of the transaction due to its public address being included as the input to the addChargingTransaction function. Since the transaction is sent automatically by the charging station, the private key of the consumer's Ethereum account is stored locally on the charging station's computer. To ensure the security and protect the system from malicious attacks, the private key can be encrypted to avoid being revealed to unauthorized users. The address of the deployed smart contract is referenced as follows: • _contractAddress 0x69B320F9284183C0E97f21a7956e6D718a62939e Once the transaction is validated, the charging record and the updated energy balance appear on each hotel's web interface. Therefore, as shown in Figure 19, the Hotel Aiguille de la Tza sees the last charging transaction with Hyundai Kona in green, as it was the hotel providing the energy. The same transaction appears in red in Figure 20 for Hotel du Pigne, as it was the hotel that owned the EV that consumed the energy. Although the sign varies, the total resulting energy balance of 0.15 kWh is the same for both hotels, as they were the only ones included in the testing procedure. Thus, such an energy balance signifies the correctness of the accounting and the execution of blockchain transactions.
Discussion
To assess the performance of the proposed blockchain-supported EV-charging framework, we discuss the following metrics widely applied in the blockchain the literature:
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Transaction latency, or average transaction time, is the time elapsed between the transaction's generation and its final appearance in the block on the blockchain. Despite being widely used, this metric varies strongly depending on the following parameters: the number of simultaneous transactions on the network, the average gas price of every pending transaction, and the gas price the user is willing to pay. If the network is overloaded, users will have to set a higher gas price for their transaction to be processed and written on the blockchain by miners. • Transaction fee is a cryptocurrency fee collected from users to process the transaction on the blockchain network. The fee differs depending on the complexity of the transaction, the gas price set by the user, and the price of Ethereum at the date of the transaction. This metric is related to the average transaction time since a higher transaction fee results in a shorter transaction time.
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The contract deployment fee is the price of the smart contract's initial deployment on the main Ethereum blockchain. This must be done once for every update of the smart contract's code. The fee works the same way as the regular transaction fee, and the price depends on the same parameters. • The number of nodes is a good measure to understand the size of the blockchain network. However, it is more suitable for private blockchains. As the current work was conducted using the Ethereum public network, the total number of nodes, which currently equals 12473 on Ethereum [48], is not a metric of interest. • Transaction throughput is the number of transactions per second that the network can process. Thus, it gives a good idea of how scalable the system could be in the future. However, such a metric is not applicable to evaluate our methodology's performance as we utilize the Ethereum public blockchain and are thus limited by the main network's capabilities without having the means to influence it.
To gather the data for analyzing the aforementioned metrics, we performed manual tests on the blockchain. At the time of this work, the price of a single transaction of our smart contract on the main network would be over USD 80. Therefore, for financial reasons, we only conducted our tests on the Ropsten test network.
First, we had to choose the appropriate gas price to be set for our transaction, thus indicating how fast we want our transaction to be mined. The online service [49] provides the statistics of recommended gas prices based on supply and demand for the computational power of the network needed to process smart contracts and other transactions, as seen in Figure 21. At the time of the experiment, the recommended gas price for a standard transaction was 155 Gwei, equal to 0.000000155 ETH. Once the gas price was defined, we had to set the gas limit to ensure that our transaction could be executed. If the computational power that is needed to execute the transaction exceeds the predefined gas limit, the transaction will be aborted as it runs out of gas. Therefore, gas limits are largely overestimated in practice to ensure the transaction's safe validation, especially as the unused gas is reimbursed. Figure 22 refers to the estimation provided by the same online service [49], which results in predicted transaction cost and mean confirmation time. In comparison to the blockchain-based energy trading platform presented in [29] and also running on public Ethereum network, our charging transaction consumes twice as muc gas. However, such discrepancy in the gas utilization can be explained by additional calculations that have to be performed prior to adding the charging transaction to the list. Moreover, the ChargingTransaction object contains a higher number of fields than the similar agreement report object in [29]. Table 4 summarizes the results of our experiment, particularly reporting the transaction times. The start and end of the transaction are specified as a Unix timestamp. Considering we have applied a constant gas price, the difference in transaction times can be explained by the number of simultaneous transactions in the network. Due to each Ethereum block having a maximum size of 1.5 million gas, the number of standard transactions that can fit inside is around 70. Therefore, if our transaction is processed close to the end of the block's formation, the transaction time can be fast. Otherwise, the transaction has to wait for the block's completion to be recorded on the blockchain. The authors in [15] achieved a similar transaction latency of 16 (s); however, a different blockchain network was used during the experiment. Therefore, it might be subjected to different market dynamics governing the supply and demand for computing power. Nevertheless, all transactions on the Ropsten test network are worthless and do not reflect the price we would have paid on the main Ethereum network. Thus, the following discussion of the proposed framework's viability does not directly consider the calculated transaction fee. Moreover, the debate about the chosen blockchain's energy intensity is deliberately left out of focus as the technology, being continuously under development, is improving. As of August 2021, Ethereum successfully went through the "London Upgrade", heading to the switch from PoW to PoS consensus mechanism scheduled for late 2021. This major change is expected to reduce costs of transactions and energy consumption, thus making blockchain applications financially and energetically viable.
The typical EV charging business model usually involves three parties, who collectively determine the price of EV charging, with their respective roles, responsibilities, and cost structures defined as follows [50]: • Charging station owner, who owns the charging station and respective location. The type of ownership can be semi-public, public, and private. • Charging station operator (CSO), who is responsible for the management, maintenance, and operation of the charging station. • Electric-mobility service provider (EMSP), who offers EV charging services to endcustomers.
According to [51], the cost structures of CSO and EMSP are defined in Equations (1) and (2), respectively, where C i is the infrastructure cost related to annual amortization of charging station investment and operation and maintenance, C e is the electricity bill, C c is the communication cost, C mp is the access to marketplace cost, C o is the staff and overhead cost, and C cm is the customer management cost: One has to note that Equation (2) reflects only the EMSP's fixed costs, while the variable costs are assumed to be passed through directly to EV users [51]. Moreover, the terms in Equations (1) and (2) are used to indicate the nature of compounded costs without implying any similarity in orders of magnitude. To generate revenues and effectively compensate for their expenditures, the CSO determines the minimum average charging price, which can be both energy-based (CHF/kWh) and time-based (CHF/min), and EMSP defines the minimum value of a subscription fee, which allows the EV driver to access the EMSP's charging network [51]. Importantly, if the EV charging process is conducted outside the EMSP's network, roaming fees must be paid. At the end of the charging event, the EV driver pays EMSP, who shares its revenue with CSO, who in turn compensates the charging station owner.
As one can notice, utilization of the conventional EV charging business model leads to the accumulation of various non-charging related costs, such as C mp , C o , C c , C cm , and roaming fees. Implementing the proposed blockchain-supported EV charging management framework can potentially reduce these costs by automating the charging records procedure, impacting the role of EMSPs and influencing the rules to access the EV charging market.
To test this hypothesis, we consider the example of EVPass, one of the largest public EMSPs in the highly fragmented Swiss market [52]. The driving-related statistics required to assess the conventional business model are summarized in Table 5 along with technical details of three popular EV models: Citroen C-Zero (CCZ), Hyundai Kona (HK), and Tesla Model X Long Range (TMX). In this study, we assume that one charging event performs complete battery charging from 20% to 100%, although in practice, EV drivers prefer to top up their batteries before the minimum state of charge is reached. The number of annual recharges N i and annual energy consumption E i are calculated according to Equations (3) and (4), where i is the EV model:
Variable Notation Value Unit
Minimum EV state of charge SOC min 20 % HK battery size [46] B HK 64 kWh HK real driving range [46] D HK 395 km CCZ battery size [53] B CCZ 16 kWh CCZ real driving range [53] D CCZ 85 km TMX battery size [53] B TMX 100 kWh TMX real driving range [53] D TMX 440 km Average daily distance driven in Switzerland by car [54] D The EVPass EMSP offers three different subscription services along with a pay-as-yougo (PAYG) option. The Night, Day, and Anytime subscription packages amount to 550 CHF, 990 CHF, and 1320 CHF annually, while the first PAYG option charges a 1.5 CHF flat-rate for each charging event along with 0.5 CHF/kWh, and the second PAYG option charges 59 CHF annually along with 0.45 CHF/KWh [55]. Single-charging-event-related cost for EV driver per EV model under different payment options is calculated using the number of annual recharges and annual energy consumption determined in Table 5 and is presented in Table 6. According to the research conducted in [56], the division of revenues in the EV charging market can be approximated as follows: charging station owner 17.6%, CSO 21.2%, EMSP 7.3%, and electricity provider 53.9%. Therefore, assuming that the blockchainsupported charging system can potentially impact the role of EMSPs and reduce some of the expenses mentioned earlier, 7.3% of the charging-event costs calculated in Table 6 could serve as the reference to set cost-efficiency objectives for blockchain in EV charging. As shown in Table 6, the potential impact of implementing blockchain in the EV charging process on cost reduction varies depending on the EV model and becomes more pronounced the lower the amount of annual recharges is. In particular, in the case of CCZ, the blockchain-incurred costs would have to demonstrate higher cost-competitiveness than for HK and TMX to effectively offset the EMSP's expenditures.
Besides financial and security advantages, implementing the proposed blockchainsupported EV charging framework would result in an additional set of benefits facilitating EVs' adoption. First, simplified access to the market would give private and semi-private charging station owners the possibility to offer their charging assets to a wider public, thus increasing the size and efficiency of the EV charging network. Additionally, blockchain records' immutability would serve as a guarantee for private and semi-private owners in a trustless and often insecure environment. Second, blockchain implementation would improve the EV driver's experience by eliminating the need to manage several charg-ing subscriptions, choosing only permitted charging stations, and paying roaming fees when charging outside the chosen network. However, one must keep in mind that using blockchain in EV charging processes is currently not fully compatible with the European Union's General Data Protection Regulation (GDPR) enforced in 2018. First, distributed data storage and processing complicate the attribution of responsibility to a single person as requested by GDPR. Second, blockchain's fundamental immutability principle contradicts the GDPR's obligation to make data editable and erasable. Therefore, despite our beliefs in data encryption solving the GDPR compliance problem, there is still a long way to go to achieve full legal compatibility.
To conclude, we note that the suggested application of blockchain technology can be adapted and extended to other use cases beyond EV charging management. For instance, the Blockchain Grid project [57] leverages blockchain in the smart grid setting to enable electricity sharing among peers by means of a decentralized platform. The authors of [58] propose a blockchain-based incentive mechanism to increase collective PV selfconsumption and reduce peak demand, while the startup Sunchain [59] already provides such capabilities to their communities through an automated sharing platform compliant with the current regulatory framework [60].
Conclusions
In this work, we have proposed a blockchain-supported EV charging management framework that aids the participating parties in monitoring and controlling the charging process while ensuring the correct accounting of the energy flows in a trustless ecosystem. We have compared several popular blockchain implementations, such as AragonOS, Hyperledger Fabric, Energy Web Chain, and Ethereum, across comprehensive criteria and have chosen Ethereum as the framework's basis. Moreover, we have designed an EV charging-specific smart contract that governs respective energy exchanges and records the charging transactions on the blockchain. To simplify the interaction of participating entities with the suggested framework, we have designed and developed a web interface and a mobile application. Finally, we have demonstrated our framework's real-world application on the demonstration case study in Switzerland, where the charging procedure was performed between an EV and a charging station, both belonging to the hotels in the area. The conducted test has shown the viability of the proposed solution while assessing the framework's performance according to common blockchain metrics. The discussion focused on the current EV charging business model, highlighting potential cost-reduction benefits related to blockchain implementation alongside other advantages facilitating the adoption of EVs, such as access-to-market simplification for private and semi-private charging station owners. Overall, this research has helped to define the opportunities and barriers that blockchain offers in a trustless environment where energy sharing and the amount of EVs are increasing and can serve as the guideline for future blockchain implementations in the context of EV charging and smart grids.
Future work to improve the EV charging management framework and enhance the application of blockchain solutions in energy should focus on addressing the blockchain's limitations, such as high transaction costs when the network is busy, immutable transactions in case of an error, and high energy consumption implied by the consensus mechanism [61].
Specifically, further research should be conducted in four main directions: • The system's security should be tested by conducting simulated experiences of potential cyber threats. Specifically, the reliability of storing the consumer's private key on the charging station's computer should be assessed, and various encryption methods should be tested. • The suggested framework's scalability limits should be analyzed through a set of extensive experiments involving multiple EVs and charging stations, where the charging processes are handled simultaneously. Thus, the respective blockchain performancerelated metrics should be reassessed for several scaled scenarios.
•
The energy consumption information included in the blockchain transaction should be enhanced by indicating the energy content of the EV charging conducted. Particularly, the indication of respective energy shares supplied by PV and grid should be given to trace the effective usage of renewable energy. • The current and future legal status of blockchain should be investigated in more detail to assess the policy implications beyond the already existing data protection and privacy regulations (GDPR) in the EU.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Acknowledgments:
The authors would like to thank Georges Darbellay (Head of Strategy and Innovation at OIKEN), without whom this work would not have been possible. The infrastructure and the collection of data realized by OIKEN made this proof of concept possible.
Conflicts of Interest:
The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript: Vehicle-to-grid | 14,201.6 | 2021-11-01T00:00:00.000 | [
"Engineering",
"Environmental Science",
"Computer Science"
] |
Exosome derived from CD137-modified endothelial cells regulates the Th17 responses in atherosclerosis.
Abstract The role of exosomes derived from endothelial cells (ECs) in the progression of atherosclerosis (AS) and inflammation remains largely unexplored. We aimed to investigate whether exosome derived from CD137‐modified ECs (CD137‐Exo) played a major role in AS and to elucidate the potential mechanism underlying the inflammatory effect. Exosomes derived from mouse brain microvascular ECs treated with agonist anti‐CD137 antibody were used to explore the effect of CD137 signalling in AS and inflammation in vitro and vivo. CD137‐Exo efficiently induced the progression of AS in ApoE−/− mice. CD137‐Exo increased the proportion of Th17 cells both in vitro and vivo. The IL‐6 contained in CD137‐Exo which is regulated by Akt and NF‐КB pathway was verified to activate Th17 cell differentiation. IL‐17 increased apoptosis, inhibited cell viability and improved lactate dehydrogenase (LDH) release in ECs subjected to inflammation induced by lipopolysaccharide (LPS). The expression of soluble intercellular adhesion molecule1 (sICAM‐1), monocyte chemoattractant protein‐1 (MCP‐1) and E‐selectin in the supernatants of ECs after IL‐17 treatment was dramatically increased. CD137‐Exo promoted the progression of AS and Th17 cell differentiation via NF‐КB pathway mediated IL‐6 expression. This finding provided a potential method to prevent local and peripheral inflammation in AS.
In our previous studies, CD137-CD137L signalling has been shown to be involved in AS. 6 We have also demonstrated that increased CD137 level may contribute to the instability of atherosclerotic lesion. Endothelial cells (ECs) located in the intima layer are in direct contact with the lumen. 7 ECs can be activated by various factors, among which a number of pro-inflammatory cytokines are produced by immunocytes in blood, including interleukin (IL)-6, IL-12 and tumour necrosis factor (TNF). 8,9 Helped with the ECs-derived exosomes, peripheral inflammation and vascular inflammation are triggered, and then, the dysfunction of ECs is amplified, promoting atherosclerotic process to the next step. Therefore, we hypothesized that the changes of the blood vessels triggered a local endothelial inflammation via activating of CD137 signalling and inducing the EC dysfunction. Exosomes derived from ECs mediate cell-to-cell communication, and crosstalk between organs further promotes peripheral inflammatory responses, which induces Th17 cell differentiation to promote progression of the atherosclerotic plaque.
In the present study, we hypothesized that the CD137-CD137L signalling induced the formation of atherosclerotic plaque via regulating the Th17 cell responses through modulating EC-derived exosomes. The results showed that CD137-CD137L signalling regulated EC-derived exosomes to induce Th17 cell differentiation through IL-6 and promoted AS progression in ApoE −/− mouse. Therefore, our findings implied that EC-derived exosomes could be used as a new cell therapy of AS.
| Animals
ApoE −/− mice aged eight weeks were used in this study. The protocol was approved by the Animal Care and Use Committee of the Twenty micro grams exosomes were induced with or without co-cultured with siRNA IL-6 were injected weekly to 8-week-old male mice for 12 weeks. The mice of control group were injected with PBS. Mice were divided into five groups: (a) control; (b) con-EXO; (c) CD137-EXO; (d) siR IL-6; and (e) siR-NC. The mice at the age of 20 weeks were killed and removed the aortas, spleen from connective tissue.
| EC culture
To determine whether CD137-CD137 signalling regulated ECderived exosomes to induce Th17 cells responses through IL-6, we activated the CD137 signalling with agonist anti-CD137 antibody (10 μg/mL, Sangon Biotech) in the absence or presence of IL-6 siRNA to induce exosomes. EC-derived exosomes were divided into four groups as follows: (a) con-Exo: ECs were cultured in the absence of agonist anti-CD137 antibody; (b) CD137-Exo: ECs were cultured in the presence of agonist anti-CD137 antibody; (c) si IL-6: ECs were cultured in the presence of agonist anti-CD137 antibody and IL-6 siRNA; and (d) si-NC: ECs were cultured in the presence of agonist anti-CD137 antibody and siRNA NC.
| Isolation, analysis and labelling of exosomes
Serum-free conditioned medium was collected after treatment of ECs. Exosomes were also isolated with the ExoQuick Plasma prep and the Exosomes Precipitation Kit according to the manufacturer's instructions (System Biosciences). [11][12][13] The size distribution and ultrastructure of exosomes were analysed by NanoSight and transmission electron microscopy, respectively. Protein markers, including CD81, CD9 and calnexin, were determined by Western blotting analysis.
For uptake studies, purified exosomes were labelled with a PKH-26 (Life Technologies) kit.
| Flow cytometric analysis
The cell suspensions from spleen were stained with anti-CD4 mAbs
| Quantitative real-time PCR (qRT-PCR)
Total RNA was isolated and reverse-transcribed using the ReverTra
| Small-interfering (si) RNA experiment in CD4 + T cells
IL-6 siRNA was obtained from Guangzhou RiboBio. There sequences were as follows: CCAAGACCATCCAAATTCAT. siRNA was prepared according to the transfection protocol for cell culture.
| Statistical analysis
All values are presented as the mean ± SD. Results were analysed by an unpaired, two-tailed Student's t test (two groups) or ANOVA F I G U R E 1 Successful isolation of exosomes from ECs culture medium and the uptake assay of exosomes in vitro and vivo. A, The ultrastructure of exosomes by transmission electron microscopy. Bar: 200 nm. B, Expression of exosomes markers, CD81, CD9 and calnexin. C, The size distribution profile of exosomes by NanoSight. D, The uptake of PKH26-labelled ECs-derived exosomes (red) by splenic CD4 + T cells in vitro. Nuclei were stained with DAPI (blue). Bar: 10 μm. E, The uptake of exosomes by spleen (Bar: 10 μm) and aorta (Bar: 30 μm) in vivo. Nuclei were stained with DAPI (blue). The aortas were stained with CD31 (green) and DAPI (blue) (three or more groups) as appropriate. All the analyses were performed using SPSS software (11.5). P < .05 was considered to indicate statistical significance.
| Successful isolation of exosomes from culture medium of ECs
The ultrastructure of exosomes was analysed by using transmission electron microscopy and NanoSight ( Figure 1A,B). The results showed a cup-shaped morphology of 30-150 nm in size, reaching a peak size of 110 nm ( Figure 1C). The expressions of exosomal markers, CD81 and CD9, as well as the negative marker for exosomes, Calnexin were confirmed by Western blotting analysis ( Figure 1D).
To examine whether CD4 + T cells could uptake exosomes, we labelled exosomes with a red fluorescent marker, PKH26, and incubated the exosomes with CD4 + T cells. The results showed that CD4 + T cells could uptake exosomes within 6 hours, and more exosomes were further up-taken within 24 hours. Next, we intravenously injected PKH26-labelled exosomes into ApoE −/− mice and found that exosomes could be up-taken by spleen and aorta ECs ( Figure 1E).
| CD137 signalling regulates Th17 cells through modulating IL-6 of EC-derived exosomes in vitro
Because chronic inflammation plays an important role in AS, 14,15 we selected four pro-inflammatory cytokines (IL-6, IL-12, IL-23 and IL-1β) in our investigation, which are involved in AS. Using qRT-PCR and ELISA, we observed that the expression of IL-6 in exosomes was significantly increased after activation of CD137 signalling (Figure 2A,B).
Studies have shown that IL-6 signalling in CD4 + T cells facilitates Th17 cell development. 16 To determine whether CD137 regulated EC-derived exosomes to promote Th17 cell differentiation through IL-6 signalling, we depleted IL-6 in EC-derived exosomes ( Figure 2C).
We observed that the proportion of Th17 cells was increased compared with the control and con-Exo groups upon CD137-Exo treatment. In contrast, the siRNA IL6-EXO treatment significantly decreased the proportion of the Th17 cells ( Figure 2D).
| CD137 signalling regulates Th17 cells through modulating IL-6 of EC-derived exosomes in vivo
After weekly injection of exosomes for a period of 12 weeks ( Figure 3A), we demonstrated that the CD137-EXO group had a larger plaque size compared with the control and the con-Exo groups, while the si IL-6 group showed a smaller plaque size compared with the control and the si-NC groups ( Figure 3B).
| CD137 signalling promotes the plaque inflammation by enhancing of Th17 cell responses
From the above-mentioned data, we hypothesized that the CD137-
| Akt and NF-КB mediate IL6 induction by CD137
First, we activated the CD137 signalling with agonist anti-CD137 antibody. We found that the expressions of pAkt (Ser473) and NF-КB p65 were significantly increased after the exposure to agonist anti-CD137 antibody. Figure 5C shows that the expression of pAkt (Ser473) was gradually increased in a time-dependent manner, and it reached the peak at 3 hours after exposure to agonist anti-CD137 antibody.
We inhibited the Akt activity by the specific inhibitor, AktI. We found that the CD137L-induced expression of Akt at serine 473 could be significantly attenuated by AktI. Furthermore, CD137L-induced upregulation of IL-6 could be blocked by AktI ( Figure 5A). Similarly, we inhibited the NF-КB activity by the specific inhibitor, PDTC. We found that CD137-induced NF-КB p65 translocation into the nucleus could be significantly attenuated by AktI ( Figure 2D). In addition, CD137induced up-regulation of IL-6 could be blocked by PDTC ( Figure 5B).
| IL-17 stimulates EC dysfunction upon lipopolysaccharide (LPS) exposure
We next assessed whether the increased proportion of Th17 cells, which mainly secrete IL-17, also played a crucial role in EC dysfunction in an inflammatory environment. Since it is difficult to achieve the co-culture of Th17 cells and ECs, we explored the effect of IL-17 on EC functions, such as cell proliferation, viability and apoptosis. We found that the expressions of sICAM-1, MCP-1 and E-selectin were dramatically increased in the supernatants of ECs after IL-17 treatment ( Figure 6F). These data suggested that IL-17 could activate ECs and contribute to endothelial dysfunction.
| D ISCUSS I ON
In this study, we achieved three major findings. First, exosome de- has been reported that IL-6 plays a crucial role in the Th17 cell differentiation in AS. 17,18 Our recent study has shown that CD137-CD137L signalling stimulates inflammatory responses in AS development with pro-inflammatory cytokines, such as IL-6. 4 However, the molecular mechanism underlying the induction of CD137-producing Th17 cells remains largely unexplored.
IL-6 has been observed to induce the improvement of Th17 cells and considered as a biomarker in the development and progression of inflammation during AS. 19,20 Therefore, blockade of IL-6 attenuates the inflammatory responses in AS. IL-6 contains several elements for binding of transcriptional factors, including AP-1, NF-КB and Camo-responsive elements, and NF-КB plays a crucial role in the induction of IL6 transcription. 21 In this study, we observed that the expression of IL-6 in exosomes was significantly increased after activation of CD137 signalling. We further investigated the molecular mechanism of CD137-producing IL-6 in ECs. Increasing evidence has linked CD137 and NF-КB signalling in chronic inflammatory diseases, 4 and then the CD4 + T cells were exposed to EC-derived exosomes. We found that the proportion of Th17 cells was markedly decreased, and the size of atherosclerotic plaque became smaller, suggesting that blockade of IL-6 exerted a protective effect in AS.
The present study has three limitations. First, considering that the specific inhibitor of Akt or NF-КB might induce other changes in exosomes, we only specifically blocked IL-6, and it is necessary to elucidate complete identification of CD137-CD137L signalling pathway in further studies. Second, because it is currently impossible to achieve the co-culture of Th17 cells and ECs, and Th17 cells mainly secrete IL-17, we explored the effect of IL-17 on the function of ECs, which only partially explained the effect of Th17 F I G U R E 5 CD137 signalling regulated IL-6 expression in ECs through Akt and NF-КB pathway. A, CD137-provoked up-regulation of IL-6 is blocked by Akt inhibitor (*P < .05, n = 5). B, CD137-provoked up-regulation of IL-6 is blocked by NF-КB inhibitor (*P < .05, n = 5). C, CD137 increased expression of Akt at serine 473 after 30 min of incubation, whereas attenuated by Akt inhibitor (*P < .05, n = 3). D, CD137-induced expression of nuclear NF-КB p65 is attenuated by Akt inhibitor (*P < .05, n = 3)
CO N FLI C T O F I NTE R E S T
The authors declare that they have no conflict of interest.
AUTH O R CO NTR I B UTI O N
Hong Zhou and Liangjie Xu conceived the concept of the study.
DATA AVA I L A B I L I T Y S TAT E M E N T
All data included in this study are available upon request by contact with the corresponding author.
Jinchuan Yan
https://orcid.org/0000-0001-6050-8007 F I G U R E 7 Schematic view of CD137 signalling pathway of amplifying Th17 generation in the progression of atherosclerosis. CD137-CD137L interaction activates a downstream signalling pathway, resulting in the production of pro-inflammatory cytokine, IL-6. CD137 signalling for IL-6 is regulated by Akt and NF-КB. Th17 cell differentiation that induced by IL-6 reaches a common downstream signalling pathway leading to atherosclerosis | 2,955.4 | 2020-03-09T00:00:00.000 | [
"Medicine",
"Biology"
] |
Optimization of CO2 Adsorption on Solid-Supported Amines and Thermal Regeneration Mode Comparison
For improving the CO2 adsorption capacity of solid-supported amines, five commercial porous supports have been selected and impregnated with tetraethylenepentamine (TEPA), and their CO2 adsorption performances have been evaluated using a fixed-bed reactor coupled with mass spectrometry. For solid-supported amines, CO2 adsorption capacities coincide with the texture characterization of the adsorbent supports (mesoporous alumina, montmorillonite, silica gel, porous resin, MCM-41 molecular sieve), and the optimum TEPA loading amount is mainly affected by the pore volume. The mesoporous supports were found to be more conducive to uniform loading of organic amine, with more than 370 mg/g CO2 adsorbed per unit TEPA. Other components in flue gas, especially H2O, favor CO2 adsorption on solid-supported amines. SO2 inhibited the CO2 adsorption, which was mainly attributable to the strong and irreversible binding of SO2 on some amine sites. NO had little effect on CO2 adsorption. Thermal stabilities of solid-supported amines have been tested based on thermogravimetry curves, and the main weight loss peak for TEPA appears at 513 K for solid-supported amines. Linear and step regeneration modes have been compared, revealing that the temperature for step regeneration is 37 K lower than that for the linear regeneration mode. Moreover, the desorption peak area for the step regeneration mode is 20% higher than that for the linear regeneration mode, indicating that the step regeneration mode can be used in practical applications, to reduce energy consumption during regeneration.
INTRODUCTION
CO 2 is the main component of greenhouse gases; the exacerbation of the greenhouse effect causes increased atmospheric temperature and species' extinction. 1 CO 2 capture and storage technologies is the main method to reduce CO 2 emissions, though the relatively high capture cost remains the bottleneck of this process. 2−4 Applied decarbonization technology is mainly based on ethanolamine solution adsorption, such as the traditional monoethanolamine (MEA) method. The average CO 2 adsorption efficiency by MEA can reach 325.6 mg/g. 5 However, the MEA regeneration process is quite energyintensive, associated with large wastage of fresh MEA solution and high cost of CO 2 separation, which in combination with the corrosive and toxic nature of MEA, limit its systematic use. 6,7 Because of the high affinity between amine and CO 2 , amine functional groups supported on solid porous substrates have become the focus for CO 2 removal by solid adsorbents. 8−10 Amine solid adsorbents are composed of porous support and organic amine. The supports are generally mesoporous with a large pore volume, for example, zeolites, carbon, metal− organic frameworks (MOFs), and silica, 11−14 which exhibit adequate affinity for CO 2 under flue gas conditions, even at a low CO 2 concentration and in the presence of moisture. 15 The most widely used organic amines are tetraethylenepentamine (TEPA) and polyethylenimine (PEI). 16 Solid-supported amines have a high CO 2 adsorption capacity and a high CO 2 selectivity and can overcome the limits and drawbacks of currently used technologies (e.g., corrosion, energy-efficient regeneration, oxidation, or degradation of liquid amines). 17 For realizing industrial applications, the current research studies on solid-supported amines for CO 2 adsorption are mainly focused on two points: to improve the CO 2 adsorption capacity and to improve the thermal stability and reduce the regeneration energy consumption of the adsorbents.
Mesoporous supports are the dominant factor for improving CO 2 adsorption in terms of both CO 2 adsorption capacity and the organic amine loading amount. 11−15 Chen et al. 18 synthesized a hierarchical porous carbon as the amine support, which displays CO 2 adsorption capacity up to 178.2 mg/g at 273 K. McDonald et al. 19 found that diamine-appended MOFs display a CO 2 adsorption capacity of 149.6 mg/g at 283 K. Pires et al. 20 prepared amine-modified clays by the insertion of amino acids in raw clay, the CO 2 adsorption capacity of which reached only 35.2 mg/g at 298 K and 800 kPa. The proper choice of commercial mesoporous supports is crucial for obtaining the ideal CO 2 capture effect. As the mesoporous supports account for over 90% of the preparation cost for absolute adsorbents, 3 commercially available cost-effective porous materials are appropriate for use as the supports for amine adsorbents.
Mesoporous silica is commonly used as adsorbent support at present. Zhang et al. 21 obtained CO 2 adsorption capacity of 220 mg/g by impregnating TEPA on SBA-15. The TEPA loading amount is ∼60 wt %; however, the heterogeneous loading of organic amines on porous support may lead to a channel block, and the effective amount of organic amine needed for CO 2 adsorption has not been considered and calculated. For industrial applications of amine adsorbents, the economic and effective amine loading amount is equally important.
Thermal and chemical stabilities are also crucial factors for solid-supported amines during the regeneration process. 22 The stability of solid-supported amines determines the lifetime and replacement frequency of the adsorbent and greatly affects the cost. Drage et al. 23 studied the stability of silica-immobilized PEI in air, nitrogen, and CO 2 , and reported a good cyclic regeneration capacity of 88 mg/g by temperature-swing adsorption; however, there was a loss in the cyclic capacity and the lifetime of the adsorbent because of the secondary reaction between amine and CO 2 , forming an irreversible urea linkage at temperatures above 408 K. Sayari 24 reported that water vapor vastly improved the cyclic stability of amineimpregnated adsorbents at a regeneration temperature of 378 K. Therefore, determining the thermal stability and the suitable regeneration temperature of amine adsorbents before applications is worthwhile.
To improve the CO 2 adsorption capacity of solid-supported amines, five commercial porous supports, mesoporous alumina (MA), montmorillonite (MMT), silica gel (SG), porous resin (PR), and MCM-41 molecular sieve (MCM-41), were selected herein. The impregnation method was applied and the optimum CO 2 adsorption capacity was investigated. To improve the thermal stability of the solid-supported amine and to reduce the adsorbent consumption because of thermal regeneration, two different regeneration methods, linear and step thermal regenerations, were compared. Considering that 71% of the CO 2 emissions arise from coal-fired flue gas in China, 25,26 the effects of SO 2 , NO, and H 2 O in flue gas on CO 2 adsorption were also studied.
RESULTS AND DISCUSSION
2.1. Adsorbent Characterization. The texture properties of the supports are given in Table 1. The five supports are mesoporous materials with an average pore width (D 0 ) ranging from 3.38 to 11.652 nm. Among the five supports, MCM-41 has the largest specific surface area (S BET ) of 1173.6 m 2 /g and pore volume (V T ) of 1.024 mL/g, MMT has the smallest S BET of 94.1 m 2 /g, V T of 0.125 mL/g, and D 0 of 3.38 nm, and PR has the largest D 0 of 11.652 nm. where w is the TEPA loading ratio (%), m TEPA is the mass of TEPA (g), and m 0 is mass of solid-supported amine (the sum of the masses of TEPA and support) (g). CO 2 adsorption characteristics of different solid-supported amines are summarized in Figure 1. For each solid-supported amine, with increasing TEPA loading amount, CO 2 could hardly be detected at the early stage of adsorption; after a period, CO 2 penetrates the adsorbent bed and the slope of the adsorption curve increases sharply, until the adsorbent bed reaches saturation.
According to a previous research, 27 CO 2 first reacts with TEPA on the support surface layer. After the surface TEPA is completely consumed, the CO 2 starts to react with the TEPA molecules in the inner or finer pores. The CO 2 diffusion rate limited the entire process and with increasing CO 2 concentration, the slope of the CO 2 adsorption increases a Specific surface area (S BET ) was calculated from the N 2 adsorption isotherms using the BET equation. b The pore volume (V T ), average pore width (D 0 ), and pore size distributions were also calculated by the BJH method. sharply at first. With increasing difficulty of the reaction between CO 2 and TEPA, the concentration of CO 2 in the atmosphere gradually increases, the slope of the curve gradually decreases, and eventually penetrates. Solid-supported amines prepared using each support have an optimal TEPA loading ratio. For the MA-solid-supported amine, the CO 2 adsorption capacity is largest on MA-26.5%, reaching 99.6 mg/g. For the SG-solid-supported amine, CO 2 adsorption capacity reaches 161 mg/g on SG-38.7%. For the PR-solid-supported amine, CO 2 adsorption capacity reaches 155.8 mg/g on PR-41.9%. For the MCM-41-solid-supported amine, CO 2 adsorption capacity reaches 199.4 mg/g on MCM-41-55.7%. For the MMT-solid-supported amine, CO 2 adsorption capacity reaches 39.0 mg/g on MMT-23.4%. CO 2 adsorption capacities of MA-26.5%, SG-38.7%, PR-41.9%, MCM-41-55.7%, and MMT-23.4% were 11.2, 50.3, 25.1, 33.8, and 21.6 times greater than those on blank supports, respectively. Compared with ionic liquid sorbents, there are mainly physisorption and chemisorption with CO 2 ; CO 2 and ionic liquids undergo physical dissolution or chemical reaction; the absorption capacity can reach 0.28−3.04 mol/kg; solidsupported amines have a better CO 2 capture effect. 28 Below the optimal loading amount, more TEPA favors CO 2 adsorption, whereas above the optimal loading amount, TEPA blocks the pores inside the support, hampering CO 2 adsorption.
For different adsorbents, the trend of CO 2 adsorption curves is consistent for different loading amounts. With increasing loading amount, the penetration time of the CO 2 adsorption curve increases and the slope decreases. After reaching the optimal loading amount, the penetration time decreases and the slope increases. Figure 2 shows the CO 2 adsorption capacities of different solid-supported amines with increasing TEPA loading ratios. CO 2 adsorption capacities of all the five solid-supported amines studied increased with increasing TEPA loading ratios until the optimum TEPA loadings are reached, after which the adsorption capacities started to decrease.
Among the five supports, the highest CO 2 adsorption capacities at 343 K and 101 kPa are in the following order: MCM-solid-supported amine > SG-solid-supported amine > PR-solid-supported amine > MA-solid-supported amine > MMT-solid-supported amine. For the SG-solid-supported amine, the maximum CO 2 adsorption capacity is 160.9 mg/ g; the value of the adsorption capacity is similar to that of Linneen's investigation (silica aerogel-solid-supported amine with TEPA). 29 This shows that the structure of the support and the type of amines are the key to determine the adsorption capacity. In accordance with the pore volumes (Table 1), for mesoporous or macroporous supports, the optimum TEPA loading amount is mainly affected by the pore volume and the CO 2 adsorption capacity is determined by the optimum TEPA loading amount. It is because TEPA molecules rely on the van der Waals force to load on the surface of the support. The pore volume and pore structure of the supports are the decisive factors for the loading of TEPA. When the TEPA loading exceeds the maximum loading, excess TEPA deposits were blocked on the surface of the support, causing a decrease in CO 2 adsorption efficiency.
2.2.2. Utilization Efficiency of TEPA under the Optimum Loading Ratio. According to the reaction of 2RNH 2 + CO 2 → R 2 NH 2 + + R 2 NCOO − (in the absence of water), the theoretical CO 2 adsorption capacity of a solid-supported amine can be calculated as follows ν T CO 2 theoretical adsorption capacity on solid-supported amine, mg/g. M TEPA the molecular weight of TEPA, 189.3 mol/g. M CO 2 the molecular weight of CO 2 , 44 mol/g. Figure 3 shows the comparison between the theoretical and experimental CO 2 adsorption capacities for the optimal TEPA loading ratios. The result shows that the experimental adsorption capacities of all the solid-supported amines are smaller than the corresponding theoretical adsorption capacities. The difference between the experimental and theoretical adsorption capacities is the largest for MMT-23.4%; the theoretical and experimental CO 2 adsorption capacities were 139.1 and 31.5 mg/g, respectively, the difference exceeding 100 mg/g; the differences for MA-26.5% and SG-38.7% were relatively small (∼60 mg/g).
TEPA utilization efficiency, which refers to the amount of adsorbed CO 2 per unit organic amine, can be calculated as follows QCO 2 adsorption capacity per unit TEPA, mg/g. νCO 2 adsorption capacity, mg/g. wthe TEPA loading ratio, %. Figure 4 shows the TEPA utilization efficiency on the five adsorbents for the optimal loading ratios. CO 2 adsorption capacities per unit TEPA for MA, SG, PR, and MCM are close, exceeding 370 mg/g, whereas for MMT, the TEPA utilization efficiency reaching only 131 mg/g, which is 35% of that obtained for SG-38.7%. Thus, it can found that the main Figure 4 shows that SG-38.7% has the highest CO 2 adsorption capacity per unit TEPA; therefore, SG-38.7% was adopted to investigate the atmospheric effect. The atmosphere tags and descriptions are given in Table 2. Figure 5 shows the CO 2 adsorption capacities under different atmospheres on SG-38.7%. The CO 2 adsorption capacity under different atmospheres was quite different; for C + H, the CO 2 adsorption capacity was 197.9 mg/g, it was 18.7% higher than that of C. Moisture in flue gas favors CO 2 adsorption on solid-supported amines, according to the reaction of 2RNH 2 + CO 2 ↔ (NH 3 + )(NHCOO − ) (R 1 ) 30 But in the presence of SO 2 , the CO 2 adsorption capacity was reduced by 25.0% (C + S), in the presence of NO (C + N), the CO 2 adsorption capacity was almost unchanged from C. The results showed that SO 2 inhibited the CO 2 adsorption, and NO had little effect on CO 2 adsorption. It can be attributed to the strong binding of SO 2 on some amine sites, and NO had little interaction with TEPA. 31 2.3. Thermal and Regeneration Properties of Solid-Supported Amines. 2.3.1. Thermal Stability of Solid-Supported Amines. The solid-supported amines used in this study were prepared by the physical impregnation method, in which the organic amine molecules distributed on the support surface are mainly subjected to two forces: attraction between TEPA molecules and support and the interaction between the organic amine molecules. These two forces mainly include van der Waals forces and hydrogen bonds, which are overcome by the solid-supported amines on heating. 32 Figure 6 shows the derivative thermogravimetry (DTG) curves for TEPA and the five solid-supported amines with the optimal TEPA loading amount. For pure TEPA, only one major weight loss peak appeared at 523 K. For the solidsupported amines, the DTG curves of the solid amine absorbents at 318 K might be due to vapor volatilization from the supports. The major weight loss peak for TEPA appears at 513 K. The difference between the two peak positions is only 10 K, indicating that the affinity between the TEPA molecules and the support is smaller than the interaction between the organic amine molecules. The weight loss can be mainly attributed to volatilization of TEPA; 33 when the temperature was higher than 623 K, TEPA was degraded, and the degradation products may include diethylenetriamine and triethylenetetramine (see the Supporting Information for additional details).
Linear and
Step Regeneration of Solid-Supported Amines. The thermal stability results of the solid-supported amines show that TEPA would volatilize when heated. It begins to volatilize at temperatures higher than 373 K, and the volatilization rate of TEPA maximizes at 513 K. Therefore, the regeneration temperature of the solid-supported amines should not exceed 373 K.
Thermal regeneration technology is commonly used for the regeneration of solid-supported amines, the linear heating mode being the most frequently used. In this mode, a constant heating rate is used to obtain a relatively higher regeneration temperature, which cannot distinguish the desorption process and the products; therefore, the step regeneration mode has also been used. These two regeneration modes have been compared and the results are shown in Figure 7.
ACS Omega
http://pubs.acs.org/journal/acsodf Article For linear regeneration, CO 2 mainly desorbed at 329 K, and was completely desorbed at ∼410 K. For step regeneration, CO 2 desorption occurred in five steps, at temperatures of 293, 313, 333, 353, and 373 K, the majority of CO 2 being desorbed at 293 and 313 K. After the first four regeneration steps, hardly any CO 2 was desorbed at 373 K, showing that the temperature for step regeneration can be set below 373 K, which is 37 K lower than that of the linear regeneration mode. The regeneration temperature range can achieve a good regeneration effect. 29 Compared with ionic liquid sorbents, the absorb system recovers essentially 100% of its CO 2 capacity at as low as 343 K; the regeneration temperature is lower than that of a solid-supported amine, but the temperature rise of the liquid needs to consume a lot of energy. 28 The regeneration effect can be compared by using the area integrals of the CO 2 desorption peaks. The desorption peak area for the linear regeneration mode (S 1 ) is 432, and that for step regeneration mode (S 2 ) is 518, S 2 being 20% higher than that of S 1 , indicating that the regeneration effect in the step regeneration desorption mode is more complete than in the linear desorption mode.
Although the step regeneration mode has a lower regeneration temperature and imparts a more complete regeneration effect, the regeneration time is more than that for the linear regeneration mode. Energy consumption and the number of operation cycles should also be considered for the selection of industrial applications; to this end, more comprehensive research is still needed for ideal operation.
CONCLUSIONS
For solid-supported amines, CO 2 adsorption capacities follow the order of MCM-41-solid-supported amine > SG-solidsupported amine > PR-solid-supported amine > MA-solidsupported amine > MMT-solid-supported amine, which is coincident with the texture characterization results of the supports. For mesoporous and macroporous supports, the optimum TEPA loading amount is mainly affected by the pore volume, and the CO 2 adsorption capacity is in turn determined by the optimum TEPA loading amount. CO 2 adsorption capacities per unit TEPA for MA, SG, PR, and MCM are close, exceeding 370 mg/g, showing that the effect of the same type of supports on TEPA utilization is insignificant, whereas the macroporous support of MMT limits TEPA utilization efficiency, reaching only 131 mg/g, 35% of that obtained for SG-38.7%. Thus, mesoporous supports are more conducive to uniform loading of organic amines, affording a higher TEPA utilization efficiency.
Study of the atmosphere effect on CO 2 adsorption properties revealed that moisture and acidic gases in flue gas favors CO 2 adsorption on solid-supported amines. The actual flue gas has no negative effect on CO 2 adsorption by solidsupported amines, instead is suitable for this system.
For solid amine adsorbents, the major weightlessness peak for TEPA appeared at 513 K, indicating that the affinity between TEPA molecules and the support is relatively smaller than the interaction between the organic amine molecules. The weight loss of solid-supported amines can be attributed to volatilization of TEPA.
In the linear regeneration mode, CO 2 desorption was mainly concentrated at 329 K, and it is completely desorbed at about 423 K. The temperature for the step regeneration mode can be set below 373 K, which is 37 K lower than that for the linear regeneration mode.
The desorption peak area for the step regeneration mode is 20% larger than that for the linear regeneration mode, indicating that the regeneration effect for the step regeneration desorption mode is more complete than that for the linear desorption mode.
The supports were impregnated with TEPA (189.3 g/mol, Xilong Chemical Ltd., PR) as follows. TEPA (1−15 mL) was dissolved in 40 mL of methanol under stirring for about 15 min, followed by adding the supports (10 g) to the TEPA/ methanol solution. The slurry was continuously stirred for 2 h and then dried at 373 K for 24 h. The prepared adsorbent was named as X-Y (X: support, Y: loading ratio). The solidsupported amines were then tableted, milled, and sieved to a 20−40 mesh. The samples were stored in a desiccator before use.
4.2. Solid-Supported Amine Characterization. The nitrogen adsorption and desorption isotherms were obtained at 77 K on an Autosorb iQ (Quantachrome, USA). The adsorbent (100 mg) was placed in the sample cell and was degassed at 323 K for 8 h. The adsorption points' relative pressure range from 10 −7 to 1(p/p 0 ). The specific surface area (S BET ) was calculated from the N 2 adsorption isotherms using the Brunauer−Emmett−Teller (BET) equation. The pore Thermal stabilities of the adsorbents were studied using a thermogravimetric (TG) analyzer (VersaTherm HM, Thermo, USA). Approximately 50 mg of a solid-supported amine was placed in a quartz crucible, and heated to 373 K for 30 min with 300 mL/min N 2 flow to remove moisture. Then, the samples were cooled to room temperature (∼293 K), and heated to 1273 K at 10 K/min with N 2 flow, and the weight change of the sample with increasing temperature was recorded simultaneously. The TG analysis curves and DTG curves were obtained. The DTG is the first derivative of the TG analysis curve versus temperature.
4.3. CO 2 Adsorption Tests. CO 2 adsorption capacity of a solid-supported amine was investigated using a fixed-bed reactor. The quartz tube reactor had an external diameter of 20 and a height of 500 mm, with a sieve plate placed in the middle. Figure 8 is the experimental setup for CO 2 adsorption and desorption. The experimental gas was produced by the cylinder standard gas, and the volume flow corresponding to the concentration of different reaction gases could be calculated. The volume flow of the gas was controlled by a mass flow controller, which can accurately control the volume of experimental component gases.
The gas flow was 100 mL/min. The amount of solidsupported amine was 1.0 g. The simulated flue gas comprising 5 vol % CO 2 , 5 vol % O 2 , and a balance of N 2 (99.99%), 1000 ppm SO 2 , 1000 ppm NO, and 5 vol % H 2 O was used for investigating the effect of other pollutants. The gas adsorption temperature was set as 343 K. After thorough mixing in the mixing vessel, the gas was fed into the reactor, and the effluent gas was continuously detected using a quadrupole mass spectrometer (GAM200, IPI). CO 2 was identified by the major mass ion of 44.
The CO 2 adsorption capacity was calculated from the area integral of the breakthrough curve, given by the following equation where ν is the adsorption capacity (mg/g), M is the mole fraction of the adsorbate, F 0 is the volumetric feed flow rate (mL/min), m 0 is the adsorbent mass (g), 22.4 is the molar volume of the adsorbate (L/mol), C 0 is the adsorbate feed concentration (ppm), C t is the adsorbate concentration (ppm) at time t, and dt is a minimal amount of time variation.
Solid-Supported Amine Regeneration Test.
The regeneration experiments were all conducted using the fixedbed reactor mentioned in Section 2.3. The adsorptionsaturated adsorbent (300 mg) was placed in the middle of the reactor, and 100 mL/min N 2 was flowed through, with the effluent gas continuously detected by the mass spectrometer.
The linear regeneration temperature was 293−423 K with the heating rate set at 2 K/min, and the temperature was maintained at 423 K for 60 min. For step thermal regeneration, the initial and terminal regeneration temperatures were 293 and 423 K. The regeneration process was divided into six steps, at 293, 313, 333, 353, 373, and 393 K. Each temperature step was maintained for 60 min, and the heating rate of each gradient was 5 K/min. | 5,517.4 | 2020-04-20T00:00:00.000 | [
"Chemistry"
] |
Natural Killer KIR3DS1 Is Closely Associated with HCV Viral Clearance and Sustained Virological Response in HIV/HCV Patients
Aim To evaluate the influence of the presence of the killer cell immunoglobulin-like receptor (KIR) 3DS1 on HCV treatment response in HIV/HCV genotype 1 co-infected patients Methods HIV/HCV co-infected patients were included. KIR3DS1, their specific HLA-B ligands and IL28B gene were genotyped. Reductions of plasma HCV RNA levels between baseline and week 1, week 2 and week 4 were analyzed for IL28B genotype and KIR3DS1 (HLA Bw4 or Bw6). Rapid and sustained virological response (RVR and SVR) rates were also analyzed. Results Sixty HIV/HCV genotype 1 co-infected patients were included. Patients with KIR3DS1 and Bw4 had higher rates of HCV viral decline than those who were not carriers of KIR3DS1 (week1: p = 0.01; week2: p = 0.038; week 4: p = 0.03). Patients carrying KIR3DS1/Bw4 had higher rates of RVR and SVR than those who did not carry KIR3DS1 (RVR: 46.15% versus 17.02%, p = 0.012; SVR: 63.6% versus 13 26.5%, p = 0.031). With respect to patients carrying the IL28B-CC genotype, those with KIR3DS1/Bw4 had greater rates of HCV viral clearance (week1: p<0.001; week2: p = 0.01; week 4: p = 0.02), RVR (p = 0.015) and SVR (p = 0.029) than those not carrying KIR3DS1. Conclusion Our results show that the KIR3DS1 genotype has a positive effect on HCV viral clearance during the first weeks of Peg-IFN/RBV treatment in HCV/HCV co-infected patients bearing genotype 1, and higher RVR and SVR rates.
Introduction
In recent years, the IL28B rs12979860 polymorphism has been identified as the best baseline predictor of sustained virological response (SVR) in both HCV monoinfected and HIV co-infected patients bearing genotype 1 [1,2]. The mechanism of action of the IL28B gene remains unknown. We do know however that its beneficial impact on HCV viral clearance is due to a greater and more rapid HCV viral decline in the first weeks following start of treatment with pegylated-interferon (Peg-IFN) plus ribavirin (Peg-IFN/RBV) [3,4]. It has been hypothesized that this beneficial impact is due to the fact that patients with the IL28B-CC genotype are more susceptible to exogenous IFN administration than those with the IL28B non-CC genotype [5]. However, the association between interferon-stimulated gene (ISG) expression and the IL28B genotype is a controversial point [6]. This suggests that there may be other factors that modify the effect of the IL28B genotype on HCV treatment response [7,8].
The IL28B-CC genotype has been associated with higher rates of spontaneous resolution of acute HCV infections, and so with lower proportions of chronically infected patients [9]. This point suggests that the IL28B mechanism of action could be related, at least in part, to some immunological component. More specifically, it has been suggested that there could be a close relation between IL28B and the expression of certain receptors present in Natural Killer (NK) cells [6]. NK cells are the most prevalent lymphocyte in the liver and they play an important role in innate immune response [10]. It has been reported that a decrease of intrahepatic and peripheral blood NK cells in the progression of HCV infection [11] leads to deficiencies in activation which would favor disease chronicity. HCV treatment, however, seems to lead to a massive activation of the innate immunity response [12,13] due to the fact that IFN-a is a potent activator of NK cells [14]. Natural killer cell immunoglobulin-like receptors (KIRs) are receptors on the NK cell surface associated either with activating (with short [S] cytoplasmic tails) or inhibiting (with long [L] cytoplasmic tails) NK cell action [15]. The presence of several KIRs has been associated with the outcome of HCV virus treatment (2DL2, 2DL3, 2DS1 2DS2 and 3DL1) [16,17]. The expression of S-KIR on the NK cell surface promotes cytolysis and IFN-gamma production against target cells expressing the specific major histocompatibility complex class I ligand [15,18,19]. So, NK cell function is tuned by the interaction of NK cell receptors, such as KIR, with their ligands, so that, in order to evaluate the possible influence of KIRs on treatment response, it is necessary to determine the presence of its specific ligand.
KIR3DS1, responsible for activating NK cells, has been described as having a protective role against the development of hepatocellular carcinoma in HCV infected patients [19]. However, its impact on HCV treatment outcome has not been described.
The aim of our study therefore was to evaluate the influence of KIR3DS1 variants on HCV viral decline in HIV/HCV genotype 1 co-infected patients in the first weeks after the start of Peg-IFN/ RBV treatment.
Ethical aspects
The study was designed and performed according to the Helsinki Declaration and approved by the ethical committee of the Reina Sofía University Hospital, Cordoba, Spain. All patients provided written informed consent before participating in this study.
Patients
Caucasian HIV-infected patients with chronic hepatitis C bearing genotype 1, naïve to HCV treatment and receiving a Peg-IFN/RBV combination therapy, were included in this prospective study. The criteria used to determine hepatitis C therapy followed international guidelines [20]. Host, clinical and virologic characteristics were collected. Fibrosis stage was determined by biopsy or liver transient elastography (FibroScanH, Echosen, Paris). Significant fibrosis was defined as a METAVIR fibrosis score of F3-F4 in liver biopsy or a liver stiffness value of $11 kPa.
Treatment regimens
All individuals were treated with Peg-IFN a2a, at doses of 180 mg, combined with a weight-adjusted dose of oral ribavirin (1000 mg/day for ,75 kg, 1200 mg/day for $75 kg), in accordance with international guidelines [20], and completed at least 4 weeks of treatment.
Virologic evaluation and definition of treatment response
Plasma HCV RNA loads were measured at baseline and at weeks 1, 2 and 4, using a quantitative PCR assay (Cobas TaqMan, Roche Diagnostic Systems Inc., Pleasanton, CA, USA), with a detection limit of 15 IU/mL. SVR was defined as an undetectable serum HCV RNA level at 24 weeks after completion of HCV therapy. Undetectable plasma HCV RNA at week 4 was considered a rapid virological response (RVR).
Single Nucleotide Polymorphism (SNP) genotyping
DNA was extracted using the automated MagNA Pure DNA extraction method (Roche Diagnostics Corporation. Indianapolis, IN 46250, USA). SNP rs129679860, located 3 kilobases upstream of the IL28B, and in strong linkage disequilibrium with a nonsynonymous coding variant in the IL28B gene (213A.G, K70R; rs81031142), was genotyped. Genotyping was carried out using a custom TAQMAN assay (Applied Biosystems, Foster City, California, USA) on DNA isolated from whole blood samples, using a Stratagene MX3005 thermocycler with MXpro software (Stratagene, La Jolla, California, USA), according to manufacturer' instructions. The researchers responsible for genotyping were blinded to other patient data. The IL28B genotype was defined as CC or non-CC (TT/CT).
KIR genotyping
KIR genotyping was performed using sequence-specific primers able to detect the presence of 16 different KIR genes previously used by Gomez-Lozano et al [21]. This method provided a high degree of resolution, since each primer pair identifies two linked, cis-located polymorphic sites (Invitrogen Corporation).
Human leukocyte antigen (HLA)-B genotyping
HLA-B genotyping was performed with the INNO-LIPA HLA-B Multiplex kit (Innogenetics N.V.), using HLA-B multiplex primers for nucleic acid amplification of the second to the fourth exon of the HLA-B locus, and HLA-Bw4 primers for exon 2 of the HLA-Bw4 alleles. This is based on the PCR-SSO reverse method. Next, HLA-B alleles and Bw4 or Bw6 specificities were determined with LIRASTM software for INNO-LIPA HLA. Patients carrying KIR3DS1 were defined on the basis of specific ligands Bw4/Bw4 or Bw4/Bw6 (KIR3DS1/Bw4) or Bw6/Bw6 (KIR3DS1/Bw6) [22].
Statistical Analysis
Continuous variables were expressed as mean6standard deviation or median and quartiles (Q1-Q3) and were analyzed using the Student's t test, the Mann-Whitney U-test or the Kruskal-Wallis test. Categorical variables were expressed as number of cases (percentage). Frequencies were compared using the x 2 test or Fisher's exact test. Significance was set at a p value of less than 0.05. Reductions in plasma HCV RNA were analyzed for IL28B and KIR3DS1 between baseline and weeks 1, 2 and 4. RVR and SVR rates were analyzed in terms of KIR3DS1 and IL28B genotypes. For the purpose of this analysis, SVR was assessed in an on-treatment approach, excluding those who voluntarily dropped out or discontinued therapy due to an adverse event. A linear regression model of HCV viral decline between baseline and weeks 1, 2 and 4 was performed. The analysis was performed using the SPSS statistical software package, version 18.0 (IBM Corporation, Somers, NY, USA).
Baseline patient characteristics
Sixty HIV/HCV genotype 1 co-infected patients were included in this prospective study. Baseline characteristics are shown in Table 1
When HCV viral clearance of patients carrying KIR3DS1/Bw4 was compared, those with the IL28B-CC genotype had higher rates of viral decline than those with the non-CC genotype (week 1: p,0.001; week 2: p = 0.03; week 4: p = 0.037). On the other hand, when we compared patients who did not carry KIR3DS1/ Bw4, we did not find any differences of HCV viral clearance in the first weeks of treatment on the basis of IL28B genotype (week 1: p = 0.827; week 2: p = 0.725; week 4: p = 0.429).
The linear regression models showed that having KIR3DS1/ Bw4, the IL28B-CC genotype and a low baseline HCV viral load were independent predictors of HCV viral decline between baseline and weeks 1, 2 and 4 ( (Table 4).
Discussion
Our results show that the KIR3DS1 genotype had a positive effect on HCV viral clearance during the first weeks of Peg-IFN/ RBV treatment in HCV/HCV co-infected patients bearing genotype 1, leading to higher rates of RVR and SVR. Our results also suggest that the beneficial impact of IL28B-CC on HCV treatment response may be enhanced by the presence of KIR3DS1.
NK cells play an important role in the outcome of several inflammatory diseases and contribute to the spontaneous resolution of infection [10]. The mechanism involves the activation of NK cells via endogenous IFN-c production. Since HCV viral treatment is based on administering IFN-a, a dose of IFN-a activates NK cell cytotoxicity and improves HCV clearance [12,13]. The presence of a specific KIR on the surface of the NK cell or its specific ligand on the hepatocyte surface could therefore increase or reduce the elimination of infected HCV cells and, in consequence, modify HCV viral decline. In this respect, the presence of some inhibitor KIRs (2DL1, 2DL3 and 3DL1) on the NK cell surface has been associated with weak HCV viral decline [16,17,[23][24][25]. The ligand for KIR3DS1 has not been clearly identified, since no experimental evidence has been reported [19,22]; even though Martin et al found an association between HLA-Bw4 and KIR3DS1 [26], there is still no consensus about the matter. Nonetheless, since KIR3DS1 and KIR3DL1 share a high degree of amino acid similarity in their extracellular domains, they might be expected to share a similar set of ligands [27]. In our study, we tested KIR3DS1, which participates in activating NK cells, and found that those patients who carried it showed greater HCV viral decline, leading to higher viral response rates, than those who did not.
In our study, the positive effect of the IL28B-CC genotype on HCV viral clearance during the first weeks of treatment was closely associated with KIR3DS1/Bw4. In this respect, patients carrying the IL28B-CC genotype had high HCV viral clearances only in the presence of KIR3DS1. In contrast, we found that, among those carrying the IL28B non-CC genotype, it made no difference whether they carried KIR3DS1 or not, in terms of influence on viral clearance. This is an important point because it tends to suggest that the positive effect of the IL28B-CC genotype on HCV treatment response could be conditioned by innate immunological status. This finding coincides with a recent report by Naggie et al, who reported that patients carrying the IL28B-CC genotype have a superior innate immune response to IFN-therapy than IL28B non-CC genotype patients [6]. These findings would be consistent with the accepted IL28B mechanism (endogenous-IFN activity), in the sense that, in chronic HCV infection, NK cells exhibit a polarized NK cell phenotype with decreased IFN-c production [12]. This also supports the finding that patients carrying the IL28B-CC genotype have lower endogenous IFN activity than those with the non-CC genotype. Thus, a higher, but inadequate, endogenous IFN activity would lead to suboptimal stimulation of NK cells and a refractory effect when exogenous IFN was added [12]. This activity might condition the response to IFN-based therapy, depending on the host's baseline characteristics. So, determining the IL28B genotype alone would have limited power, since it could be conditioned by NK activation, regulated, at least in part, by KIR3DS1. KIR3DS1, on the other hand, has been associated with slowing disease progression in HIV infection [28][29][30][31]. For this reason, we cannot rule out the possibility that patients with KIR3DS1 may have both an innate and adaptive immune system that is less negatively impacted by HIV infection, and so have a stronger immune response to HCV treatment than patients who are not carriers of KIR3DS1. However, the observed effect of KIR3DS1 on HCV treatment response could be due to the relative absence of KIR3DL1, rather than the presence of KIR3DS1. KIR3DL1 play an inhibitory role on NK cell activity. The functional union of KIR3DL1 with HLA-Bw4 triggers a ''do not eat'' reaction in NK cells with respect to the target cell [32]. One study showed that highly expressed KIR3DL1 alleles were beneficial in HIV disease and suggested that indirect effects on HIV could be the cause [33]. Consequently, if this effect is independent of HIV co-infection, the absence of KIR3DL1 alleles may release inhibition, resulting in more efficient lysis of infected hepatocytes in a KIR3DS1independent manner.
The standard of care HCV treatment is due to change for HIV/ HCV genotype 1 patients in the coming years [34]. The incorporation of the new protease inhibitors (PIs) to Peg-IFN/ RBV will improve the rate of treatment response in this group of patients, as they did with HCV monoinfected patients [35,36]. However, in the particular case of HIV protease inhibitors, interactions with antiretroviral treatment will have to be added to the drawbacks of the new PIs, along with a higher rate of adverse events and the cost of HIV/HCV co-infected patients [37]. This will be a key aspect of HCV treatment for HIV co-infected patients, since some will need to switch antiretroviral treatment, which has various clinical limitations. This is why identifying HIV/HCV co-infected patients who will respond to Peg-IFN/ RBV therapy is a key feature of HIV clinical practice. Our results show that the major impact of NK cells, principally KIR3DS1, is on HCV viral decline during the first week of treatment. These findings could be used to optimize the choice of the most appropriate therapy for HIV/HCV co-infected patients bearing genotype 1 and to enhance the value of IL28B determination. Our findings could enable clinicians to detect patients with higher or lower probabilities of responding to Peg-IFN/RBV therapy.
However, our study has several limitations. Firstly, this study is a preliminary investigation since it included a small number of patients and did not have the statistical power to detect differences of KIR3DS1 among patients carrying the IL28B non-CC genotype. A larger cohort of HIV/HCV genotype 1 co-infected patients is required to analyze this. Secondly, our study determined only KIR3DS1 and rs12979860 when considering the respective impacts of NK cell KIR and IL28B. Studies analyzing the synergistic effect of other known KIRs (3DL3, 2DS2, 2DL2, 2DL3, 2DL5, 2DS3, 2DS1, 3DL2, 2DP1, 2DL1, 3DP1, 2DL4, 3DL1, 2DS5 and 2DS4) and IL28B (rs8099917) are needed. Thirdly, Bw4 alleles (Bw4*80I and *80T) were not considered in our study, which may be a limitation since these variations could play a role in conditioning the affinity of KIR3DS1 for Bw4. A fourth limitation is that this study included only HIV/HCV co-infected patients, which represents a unique population. In fact, HIV/HCV co-infected subjects attain SVR less frequently than HCV monoinfected individuals and their HCV viral decline is slower [38]. Hence, further studies of the predictive yield of KIR3DS1 variants are needed, which include HCV monoinfected patients. Finally, in our study, every patient carrying the IL28B-CC genotype with KIR3DS1 had HLA-Bw4, whereas no patient carrying the IL28B-CC genotype with KIR3DS1 had HLA-Bw6. It is not known whether there is a possible association between these factors. It is likely, however, that our observation was due to the small number of patients. A larger cohort would clarify these findings.
In conclusion, our study shows that KIR3DS1 has a positive impact on HCV viral clearance in Peg-IFN/RBV treatment in HIV/HCV co-infected patients bearing genotype 1, and this may be associated with the IL28B mechanism of action in HCV treatment response. | 3,872.4 | 2013-04-16T00:00:00.000 | [
"Biology",
"Medicine"
] |
A simulation framework for simultaneous design and control of passivity based walkers
In this paper, we propose a simulation framework which simultaneously computes both the design and the control of bipedal walkers. The problem of computing a design and a control is formulated as a single large-scale parametric optimal control problem on hybrid dynamics with path constraints (e.g. non sliding and non slipping contact constraints). Our framework relies on state-of-the-art numerical optimal control techniques and efficient computation of the multi-body rigid dynamics. It allows to compute both the parametrized model and the control of passive walkers on different scenarios, in only few seconds on a standard computer. The framework is illustrated by several examples which highlight the interest of the approach.
I. INTRODUCTION
Passive walkers are bipedal robots essentially powered by gravity.They exploit their natural dynamics to move forward, but in the meanwhile they are unable to exhibit quasi-static behaviors.Such mechanical systems show an excellent cost of transport (CoT).They are effective platforms, both for biomechanicians to better understand the essence of bipedal walk, and for robot designers to build efficient humanoid robots.
The purpose of this paper is to propose a generic dynamic simulation framework for optimizing both the design and the controller of such robots with respect to a given cost function.An overview of the framework is given in Fig. 1. [1], many passive walkers have been designed and crafted.A great introduction to this field is given in Collins et al. [2].A complete methodology to build incrementally complex passive walkers is described by Wisse et al. [3].It starts from a simple compass-like model and goes to Denise, a 3D dynamic walking robot with a bisecting mechanism for the torso, two arms rigidly coupled to the hip angle, knees that are unlocked during the swing phase, and ankles engineered to steer in the direction that prevents falling.Such incremental approach reveals the critical issues in the design of walker with an anthropomorphic shape.The first issue is the transition from the simplest compass model evolving in the sagittal plane to 3D system [4], [5], [6].A second issue is the extension of the compass model to articulated legs [1], [4], [6], [7], [8].The addition of ankles is addressed in [6], [9], arms in [4], [6] and even neck and head in [10], [11].The mass distribution<EMAIL_ADDRESS>for a given kinematic structure is also an important question which is addressed in [12], [13].
By opposition to non-passive preview control approaches (e.g.Kajita [18], capture-point [19]) that require footstep planning, the control of passive walkers aims at maintaining at the best the natural steady gait that originates from the mechanical design.Passive walkers do not compute their footsteps in advance.Mechanical design and control are deeply connected and the challenge is to consider both simultaneously.The natural dynamics of passive walkers is periodic.The mechanical design tends to create limit cycles at the origin of the steady gait.The role of the controller is to maintain the system around this limit cycle in spite of environment perturbation.
In model-based optimization, the problem of finding a good controller is expressed as a constrained numerical optimization problem that benefits from solid theoretical analysis of stability [20].This general numerical framework has been applied to passive bipedal walkers for the optimization of mass distribution [12].It has been also instantiated to the study of passive quadrupeds [21] and then to passive walkers for the creation and analysis of efficient gaits [13].In this last paper, the authors propose a dynamic simulation package whose scope is illustrated by various examples including passive walkers and running robots.Our paper falls in the same framework.
B. Problem statement
In this paper, we want to simultaneously solve the two following objectives: 1) for a given kinematic chain architecture, we want to optimize the parameters of a robot (e.g.mass distribution, body segments lengths, slope of the ground, mean forward velocity, etc.), 2) for a given robot, we want to find the best controller with respect to a cost function (e.g. the cost of transport, the minimal time, etc.).In short, for a given kinematic structure, we propose a generic approach to design all robot parameters together with the controller that optimizes a given cost function.
C. Contribution
The first originality of this approach is its ability to deal with complex architectures like human-like walkers, both in 2D and 3D.We do not restrict the motion to only lie in the sagittal plane.Moreover and contrary to similar works on this topic, our framework automatically computes the full dynamics.Therefore, there is no need of writing down the complex dynamic equations of polyarticulated systems.Hence, many passive walkers can be efficiently designed, optimized and compared.
Secondly, control can be chosen to be active or passive.We also handle periodic as well as non-periodic gaits.
Finally, we can optimize various parameters of a given walker (slope, lengths, masses, speeds, etc.) with respect to a given cost function.Fig. 1 illustrates the global architecture of our framework.
D. Outline of the paper
In Sec.II, we first introduce the dynamic contact simulator at the root of the framework.We highlight how the various problem parameters are distributed either in the mechanical model or in the controller.In Sec.III, we set up the generic optimal control formulation which allows the computation of both design and control parameters.Finally, the setup is introduced in Sec.IV and experimental results are presented in Sec.V.
II. DYNAMIC CONTACT SIMULATION
Passive walkers are intrinsically hybrid systems.They are submitted to a continuous dynamics when the stance leg is in contact with the ground, and they are also subject to impacts when the swing foot hits the ground.In addition to this hybrid dynamics, some contact constraints must be satisfied to ensure the feasibility of the entire motion.
In the following of this section, we expose the notations, the parametric model of the walkers and the contact formulation used inside the framework.
A. Notations
In this paper, we assimilate a passive walker to a free-floating base system.We denote by q ∈ SE(3) × R n its configuration vector, with SE(3) the special Euclidian group of dimension 3 encoding the placement of the robot base and n the number of degrees of freedom (DoF).The tangent velocity and acceleration of the configuration vector are denoted by q and q respectively and live in R 6+n .Finally, the torque applied at each joint is denoted by τ ∈ R n .
B. The parametric model
A passive walker is primarily a kinematic tree, i.e. a tree of joints where each joint has its own topology (e.g.revolute, free-flyer, spherical, etc.) and a particular placement regarding to its parent joint.The joints are the nodes of the tree.In addition, each joint supports a body, which is defined by its mass, its center of mass (CoM) and its inertia matrix.All the bodies together define the mass distribution of the model.The tree structure with the mass distribution correspond to the structural parameters of the system.The model of the passive walker is then parametrized by those two sets of parameters: model(tree, mass_distribution)
C. The parametric controller
A gait is characterized by its controller which is represented by a set of real parameters.For instance, a controller may be a set of splines which encode the torque trajectories or just the PID gains (stiffness and damping of the spring attached to the joint) in the case of pure passive controller.
D. Continuous contact dynamics
For the continuous dynamics, we make the hypothesis of punctual rigid contact with Coulomb friction cone.The dynamic equation of the polyarticulated system with constraints can be stated as: J c (q)q + Jc (q, q) q = 0 where M (q) is the joint space inertia matrix, b(q, q) corresponds to the Coriolis, centrifugal and gravitational effects, S is a selection matrix encoding the underactutation, J c (q) is the contact Jacobian with f c the contact forces and .denotes the transpose operator.
A necessary and sufficient condition for non-sliding and non-slipping of the contact is described by the constraint that f c must remain inside the Coulomb friction cone K c .This cone reflects the fact that the normal component of the contact force is positive (the ground cannot pull), the norm of its tangential components and the normal torque are limited by the normal component.
We make the choice to solve (1)-( 2) together, and to add the conic constraint inside the optimal control problem to enforce the Coulomb contact model [22].This implies that we have to impose contact phases where (1)-( 2) are enforced.Other approaches have tried to get rid of this extra hypothesis [23], [22] leading to difficult and still incompletely solved problems for trajectory optimisation [24], [25].In the context of this paper, selecting in advance the contact phases is not a limitation.
The joint acceleration and contact force vectors are then given by: with Λ c def = J c M −1 J c the so-called operational-space inertia matrix and I n the identity matrix of dimension n.The dependences on q and q have been omitted for simplicity of notation.
E. Impact dynamics
Passive walkers are also subject to impacts.Here, we make the assumption of instantaneous inelastic impacts with a restitution coefficient sets to zero, i.e. the post-impact velocity of the contact point is null.The impact dynamics then leads to a discontinuity in the joint velocity space, which is described by the two following equations: with q− , q+ the pre-impact and post-impact generalized velocities and λ c is the impulse resulting from the impact [22].Other impact model (e.g.elastic) could also be introduced without loss of generality.This impact model is frequently used in the litterature [26], even though it is contested for its physical consistency [27].
F. Efficient rigid-body dynamic computation
The optimal control solver must evaluate thousands of times the multi-body dynamics either inside the numerical integration procedure or for the evaluation of the dynamic sensitivities regarding to the model and control parameters.For that purpose, we used Pinocchio [28], a whole new, open-source and efficient C++ library to model and compute the forward and the inverse dynamics of polyarticulated systems in contact.Pinocchio is written on top of the efficient Eigen C++ library [29] for Linear Algebra.It is based on Featherstone's algorithms [30] but they have been implemented in a way to take profit of branch prediction and cache mechanisms of modern processors [31].
CONTROL
Optimal control is a powerful and generic mathematical tool which allows the exhibition of a particular solution among an infinite number of candidates.While geometric results only exist for a very limited class of systems, the past few years have seen the emergence of efficient and reliable numerical optimal control frameworks working on high dimensional and complex systems [32], [33].
In our framework, the simultaneous search of model and control parameters is set up as an optimal control problem with a prescribed cost function.This cost function reflects the objective of the gait and can be any real value function.Some examples of cost functions in the context of passive walkers are the cost of transport or even the minimal time.In addition, we add the possibility to set the duration of the motion as a free parameter of the problem.Other free variables, like the gait stride length for example or the slope of the ground, can be stacked to the list of parameters.
A. Notations
We denote by x def = (q, q) the state of the systems, u is the control vector and p is the vector of parameters, composed of both the model parameters and the aforementioned free variables.State and control trajectories are denoted by x and u respectively.The cost function and dynamics of the system are then written as (t, x, u, p) and dx dt = f (t, x, u, p) respectively.Here, we use a slight abuse of notations to denote with the same notation both the continuous and the impact dynamics.Finally, g(t, x, u, p) corresponds to the inequality constraints that must be satisfied along the path (equality constraint can be also considered without loss of generality).As mentioned in Sec.II-D, the function g is first and foremost composed of the Coulomb conic constraints.
B. The Optimal Control Problem formulation
The hybrid dynamics of passive walkers can be seen as a multi-phase system, each stage corresponding either to the single, double support or impact phases.Thereafter, the integer s refers to the index of the s th stage.
The generic optimal control problem for simultaneously computing model and control parameters with multi-phase dynamics can be written as: where π in (7d) is a function which acts both on the state and control trajectories to enforce periodicity constraints.∆t s is the duration of the phase s, and T = ∆t s is the total duration of the motion.In case of impacts, the phase duration is reduced to 0.
C. Solving the Optimal Control Problem
Two major directions exist to solve the infinite dimensional problem (7).The first direction belongs to the so-called indirect methods.It consists in exploiting the necessary conditions for optimality, namely the Pontryagin's maximum principle [34], which transforms the problem (7) into a boundary value problem working on ordinary differential equations.However, such methods are currently unable to track path constraints.
The second direction corresponds to direct methods.Direct methods first discretize the original problem into a finite dimensional nonlinear programming problem (NLP), which is then solved with standard NLP strategies.Among NLP strategies, three of them are now popular: (i) single shooting, (ii) collocation and (iii) multiple shooting.In what follows, we briefly survey these three methods.For further details, we refer the reader to the general overview on numerical optimal control methods written by Diehl et al. [35].
1) Single shooting: discretizes the control and constraints according to a temporal grid.The state trajectory is recovered by integration of the discrete control trajectory along this grid.As single shooting method reduces the NLP to the search of a control trajectory, the optimization problem is of low dimension.However, the solver is hard to initialize if only an initial guess on the state trajectory is available or it may not converge at all in the context of unstable systems.
2) Collocation: disctrizes both the control and the state trajectories according to a temporal grid.In addition to the classic discritized constraints, the state trajectory is enforce to match the dynamics equation (7b) at each grid node.The problem can then be easily initialized from a given state trajectory and collocation handles well unstable dynamics.However, a very fine grid is required to make the state trajectory closer to the true dynamics of the system.
3) Multiple shooting: takes profit of both previous methods.It works on a coarser time grid, which are called multiple shooting intervals.On each interval, the control is discretized as well as the initial state value.The final state value on the interval is then obtained by integration of the system dynamics (7b).In this way, each interval is set independent from its neighbours.And the dependencies between successive intervals is shifted as equality constraints of the NLP.The NLP remains a low dimensional problem and can be easily warm-started with an initial guess on the state trajectory.Furthermore, multiple shooting is really suited for multi-phase dynamics, as each phase is set independent to the others.
Multiple shooting has been successfully applied for the modelling of human running [26].Following several advantages listed in Sec.III-C3, we chose this strategy to solve the problem (7).
D. Efficient optimal control solver
Our framework relies on the 20 years old optimization package MUSCOD-II [32], a multiple shooting solver for highly nonlinear systems submitted to path equality and inequality constraints, developed inside the Optimization and Simulation group at the University of Heidelberg.MUSCOD-II handles multi-phase systems with discontinue dynamics and periodic constraints with efficiency.While MUSCOD-II is a closed-source framework, one can depend on ACADO [33] which implements similar features.
IV. EXPERIMENTAL SETUP
The generality of our simulation framework is illustrated by various examples depicted in Tab.I.Those examples include different kinematic structures and different control schemes.Doing so, we may compare different polyarticulated topologies and, for a same topology, different control schemes, including either active or passive actuators.
Once a topology is chosen, we show that it is possible to replace the active actuation by a passive spring damper system.The motions of the first five robots are constrained to lie in the sagittal plane.Such restriction is removed for the robot with arms which is in 3D.
A. Inputs and Outputs
Fig. 1 shows the general inputs and outputs of our framework.In the experiments of Tab.I, the inputs of the system are the kinematic structure of the robot with the anthropometric parameters of the body segments (see Sec. IV-E), and the cost function, constraints and actuation type (see resp.Sections IV-B to IV-D).
In those experiments, we choose to set at a fixed value both the step duration (0.8 s) and the slope (0.05 rad) for each scenario, and let the solver optimize the step length.We limit the step length to the bounds [0.4; 1.] m.
The outputs of the system are the optimal cost of transport, together with the associated step length of the gait and the state and control trajectories of the joints during one step.
We also collect the number of iterations needed by the solver to converge and the total computation time for each experiment.
B. Cost function
We use the same cost function in each scenario.This cost function corresponds to the classic cost of transport (CoT).The CoT is a non-dimensional quantity which reflects the energy efficiency of a locomotion pattern.By definition, the CoT is the ratio between the energy consumed by the system (E) and its weight (mg) multiplied by the traveled distance (d): with g the gravity field value and m the mass of the system.The energy (E) consumed by the system is the sum of the potential energy mgh (with h the variation in altitude of the center of mass) with the integral of the power input In this last formula, δ is the Dirac impulsion corresponding to the impact instant, • is the dot product operator and x M def = √ x M x.Finally, on a slope with angle α, the CoT is given by: This cost function is only used as an example for the different case studies in Sec.V; in real life examples, the choice of a better suited cost function is still an open problem.Moreover, the CoT we give are not meant to be compared with examples outside of this paper.
C. Constraints
To reduce the dimension of the NLP, we compute a solution only for a half-step due to the periodicity and the symmetry between right and left segments.We then constrain the swing leg to be in contact with the ground only at the beginning and the end of the simulation.Then, the cyclicality Cases studies are based on six walkers models to measure the impact of the knees, torso, neck, arms and actuation type.For each example, the considered output are the cost of transport and the step length.The two last lines give the performance of the algorithm.In all examples the duration of a step is fixed (0.8s) as well as the slope of the ground (0.05rad).
and the symmetry of the motion is enforced by periodic constraints on both the initial and final configuration, velocity and torque of each joint trajectory.
D. Actuation
In a first stage, we propose an active actuation.The torque trajectory of each joint is modelized by piecewise cubic polynomials.An hardware implementation would then need an external source of power for the system, as a battery or an air canister, and an intelligent controller to deliver the desired torque.
In a second stage, we compare this active actuation with a passive one, which is simply a proportional derivative (PD) controller.In this case, we apply the torque τ j to the joint j: τ j = −K pj (q j − q 0j ) − K dj qj (10) where q j is the position of the joint and qj its velocity.K pj is the spring constant, q 0j the free length of the spring, and K dj the damping coefficient.Those three parameters are optimized by the solver.From those spring-damper parameters, one may craft a purely passive walker.In this case, the single source of power is the gravity field.Of course, another constraint for the numerical solver is to use the same spring and damper for each symmetrical joint.
E. Body parameters
All the robots have an anthropometric mass distribution, i.e. segment length, mass, center of mass position and inertia tensor are scaled according to a reference height and a reference mass.Those inertial parameters follow the anthropometric table proposed in [36].
Our minimal model is composed of a pelvis, two thighs and two legs.Ankles (and knees on the model M B ) are actuated.On top of that, in the models M C , M D and M E , we add a torso and a head.This head is only actuated in the model M D .At last, we add two arms and forearms in the model M E with actuated shoulders.All actuated joints are revolute along parallel axes.
V. EXPERIMENTAL RESULTS
In the following, all the experiments are composed of 9 nodes for the single support phase and 1 single node for the impact phase.
A. Influence of the knees
The influence of the knees is highlighted by comparing models M A and M B in Tab.I.
The experimental results show that adding knees to a compass walker roughly divides by two the CoT while increases the optimal step length.The computational cost of adding knees is negligible.
B. Influence of the torso
Here, we study the impact of adding a fixed torso-head segment attached to the pelvis.This situation corresponds to the models M A and M C of Tab.I respectively, with a non-passive actuation.
Then, adding a fixed torso on top of the pelvis leads to a 40 percent decrease of the CoT and also reduces the optimal step length down to 40 cm, which is the lower bound we allowed.In the meanwhile, the computation times remain the same.
C. Influence of the neck
We consider the influence of actuating the neck by comparing the models M C and M D while keeping the actuation type.
The experiments on those models show that the increase of the CoT is lower than one percent even if we add an actuator.However, the solver needs more time to converge.
D. Comparison of actuation type
This experiment considers the model M C only and study the differences between active and passive controllers.
If we confront the results of the third and fourth columns of Tab.I, it appears that the cost is higher for the passive walker with respect to the choosen cost function, while the computational time is lower in the passive case.This can be explained by the dimensionality of the problems: in the first case, the dimensionality of the joint actuation is defined by four polynomial parameters times the number of shooting nodes while it is defined by three scalar parameters corresponding to the spring-damper model in the other case.
E. Beyond the 2D sagittal plane
Our simulation framework is general and it allows to address 3D model.In order to let the robot keep its balance, we add two actuated arms on the model M E .
In comparison to the 2D model without arms M C , the CoT is a bit higher, but remains lower than the first compass walker M A .We also notice that both the computation time and the number of iterations are higher, but the solver still converges in a similar time.
VI. DISCUSSIONS AND FUTURE WORKS
While our framework shares some common features with the Matlab package developed by Remy et al. [13], its differs on various aspects.The first difference lies at the optimal control method level.In [13], the authors use either collocation or shooting methods.Still, as mentioned in [35] and recalls in Sec.III-C, the multiple shooting approach is the most suited in the context of multi-phase dynamical systems submitted to impacts and constraints.In addition, the choice of the C++ programming language to write both our dynamic simulation and optimal control problem is fundamental for efficient and fast computation.
Currently, we do not check the stability of the resulting motions, but only its balance at a dynamic level.As future extension, we plan to implement an approach similar to [37] to converge on optimal and stable open-loop motions.
An other extension of this framework can be achieved at the level of contact modelling.Currently, punctual contacts are the standard for passive walkers.They are easy to simulate and to mechanically integrate as feet for passive walkers.However, rolling contacts may lead to more efficient gaits, as suggested by Kuo et al. [38].We recently proposed in [39] an analytical formulation of the rolling contact which is compatible with our dynamic formulation presented in Sec.II-D.The addition of this contact model inside our framework can largely improve the quality of the generated motions and enable us to deal with more complex scenarios.
Our framework is not restricted to passive walkers.On a wider scale, it can evaluate some paradigms in the design and the control of new humanoid robots [40], [41] and exoskeletons [42].In the near future, we will exploit this framework to evaluate and design a bipedal robot inspired from passive walkers.
Fig. 1 :
Fig.1: Overview of the simulation framework.The simulator is described in Sec.II, and the solver is detailed in Sec.III. | 5,888.4 | 2016-12-13T00:00:00.000 | [
"Computer Science"
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The first genetic map for yellow lupin enables genetic dissection of adaptation traits in an orphan grain legume crop
Background Yellow lupin (Lupinus luteus L.) is a promising grain legume for productive and sustainable crop rotations. It has the advantages of high tolerance to soil acidity and excellent seed quality, but its current yield potential is poor, especially in low rainfall environments. Key adaptation traits such as phenology and enhanced stress tolerance are often complex and controlled by several genes. Genomic-enabled technologies may help to improve our basic understanding of these traits and to provide selective markers in breeding. However, in yellow lupin there are very limited genomic resources to support research and no published information is available on the genetic control of adaptation traits. Results We aimed to address these deficiencies by developing the first linkage map for yellow lupin and conducting quantitative trait locus (QTL) analysis of yield under well-watered (WW) and water-deficit (WT) conditions. Two next-generation sequencing marker approaches - genotyping-by-sequencing (GBS) and Diversity Array Technology (DArT) sequencing - were employed to genotype a recombinant inbred line (RIL) population developed from a bi-parental cross between wild and domesticated parents. A total of 2,458 filtered single nucleotide polymorphism (SNP) and presence / absence variation (PAV) markers were used to develop a genetic map comprising 40 linkage groups, the first reported for this species. A number of significant QTLs controlling total biomass and 100-seed weight under two water (WW and WD) regimes were found on linkage groups YL-03, YL-09 and YL-26 that together explained 9 and 28% of total phenotypic variability. QTLs associated with length of the reproductive phase and time to flower were found on YL-01, YL-21, YL-35 and YL-40 that together explained a total of 12 and 44% of total phenotypic variation. Conclusion These genomic resources and the QTL information offer significant potential for use in marker-assisted selection in yellow lupin. Electronic supplementary material The online version of this article (10.1186/s12863-019-0767-3) contains supplementary material, which is available to authorized users.
Background
Being sessile organisms, plants must adapt to the environments in which they find themselves. This is achieved primarily by genetic adaptation. Key adaptation traits such as abiotic stress tolerance, are typically complex and controlled by several genes. Quantitative trait locus (QTL) analysis is a powerful tool to investigate the genetic control of complex traits and can be used to identify linked molecular markers for use in markerassisted selection (MAS) [1][2][3]. QTLs are identified by integrating phenotypic measurements with genome-wide marker information either in purpose-made experimental populations (conventional linkage QTL analysis) or in a diverse panel of unrelated lines (association QTL analysis) [4]. A pre-requisite of QTL analysis is the availability of a genetic map or genome sequence in which regions of the genome controlling quantitative traits can be delineated.
Yellow lupin (Lupinus luteus L., 2n = 52) is an annual grain legume which offers advantages over its sister domesticates: narrow-leafed lupin (L. angustifolius L.) and white lupin (L. albus L.). Yellow lupin is adapted to acid soils [17], is more water-logging tolerant [18] and has enhanced resistance against cucumber mosaic virus [19]. It has the highest protein content (average of 45%) of domesticated lupins and an oil content of 6% making it a candidate for human food and aquaculture feed, as well as animal feed [20][21][22].
Despite this promise, yellow lupin has not been generally embraced by farmers because of its low productivity compared to narrow-leafed lupin. Consequently, more focus has been given to the narrow-leafed lupin on research [22]. Apart from some studies on yellow lupin domestication traits and disease tolerance potential [23][24][25], we lack information on yellow lupin adaptation, its physiology in diverse environments and the genetics controlling these adaptation traits. This lack of knowledge prompted the current study.
A serious impediment to making progress in yellow lupin adaptation and breeding is the limited knowledge available on genomic resources with mere two RNAseq datasets [26,27]. No linkage map or reference genome has been reported. In contrast, these resources are available to its close relatives narrow-leafed lupin and white lupin, which have allowed investigation of genomic regions controlling yield, nutritional, domestication and physiological traits on these species [27][28][29][30][31][32][33][34][35][36][37][38]. Identification of genomic regions controlling desirable traits (high yielding, low alkaloid, indehiscence and adaptation to diverse environments) would help researchers efficiently select for those traits through MAS in order to adjust these adaptive traits for the development of more sustainable and resilient yellow lupin production [39][40][41][42].
With the rapid advances in next generation sequencing (NGS) technologies, the cost of genomic analysis has fallen significantly. Entire mapping populations can be genotyped resulting in the generation of millions of genomic data points and thousands of markers [11,43,44]. These approaches could be used to improve our understanding of the yellow lupin genome and to enable QTL analysis of adaptation and phenology traits. In this study, we report the first yellow lupin linkage map and use it to conduct a QTL analysis of plant productivity and phenology under well-watered (WW) and waterdeficit (WD) conditions.
Marker discovery
Using the GBS approach, a total of 13,462 SNP markers were discovered. Preliminary mapping using relaxed filtering (< 25% missing values and < 25% heterozygosity) led to illegitimate fusion of linkage groups (data not presented). Therefore, increased stringency was applied After filtering markers based on quality parameters (< 6.4% heterozygous values and < 10% missing values), which left 948 high quality SNP markers (prefixed 'SCAFFOLD'). We considered these insufficient to develop a new and comprehensive linkage map. Additional markers were developed using the DArT-seq approach. Two categories of DArT-seq markers were discovered: 5, 590 SNP and 8,854 PAV (presence/absence variation) markers. After quality filtering these markers based on the above threshold, a total of 1,049 SNP (prefixed 'DArT-SNP') and 957 PAV (prefixed 'DArT-PAV') markers were retained, giving a total of 2,945 markers in 97 RILs for linkage map development.
Linkage map development
Linkage mapping was performed with the aid of Multi-Point 3.3 using 2,945 markers. Linkage groups containing 5 or more markers were considered as the framework genetic map. The framework genetic map consisted of 40 linkage groups representing yellow lupin's 26 chromosomes. These linkage groups contained a total of 919 framework markers along with 1,262 redundant markers (exactly similar to framework markers but with more missing values). A total of 277 (majority of them were DArT markers), potentially problematic markers, were moved to the MultiPoint section termed the 'Heap' , either due to moderately high segregation distortion (Chi-square 0.0001 < P < 0.001) or due to disturbances in the monotonic increase in recombination frequencies along linkage groups, which is normally caused by genotyping errors [45]. These markers were subsequently attached to most likely interval in the established framework map, thus comprising of 2,458 markers in total. A total of 487 out of 2,945 markers mapped to small linkage groups of less than five framework markers or remained unlinked singletons and were excluded from the final map.
The length of linkage groups ranged from 3.8 to 167.9 cM with an average of 56.5 cM, while the average interval size among loci on each linkage group ranged from 0.76 cM to 5.18 cM with an average size of 2.29 cM (Table 1, Fig. 1). The maximum interval size was 12.8 cM. The length of the entire linkage map was 2, 261.3 cM.
ANOVA and QTL analysis of adaptation and phenology traits
The ANOVA revealed that moisture treatment, genotypic and interaction effects were significant (P < 0.001) for total seed yield, total biomass, 100-seed weight, time to flower and length of reproductive phase ( Table 2). Among the main effects, water regime differences were far more influential than genotypic effects for all traits except time to flower ( Table 2). Small but significant interaction effects were observed for all traits, especially for total seed, where the interaction effect was statistically different (larger) than the genotypic effect (F value of 1.50 vs 1.55) ( Table 2). The wild parent P28213 out yielded the domesticated parent Wodjil in both Total seed yield and Total biomass. The total seed-yield of P28213 was 204 g/m 2 and 139 g/m 2 under well-watered and water-deficit treatments respectively, while Wodjil exhibited the total seed yield of 134.5 g/ m 2 and 85 g/m 2 under well-watered and water-deficit treatments respectively. Similarly, the total biomass of P28213 was 713 g/m 2 and 629 g/m 2 under well-watered and waterdeficit treatments respectively, while Wodjil exhibited the total biomass of 477 g/m 2 and 365 g/m 2 under well-watered and water-deficit treatments respectively ( Table 3). The 100-seed weight among both the wild and domesticated parents was not significantly different, As the parent P28213 showed the 100-seed weight of 10.6 g and 9.4 g under well-watered and water-deficit treatments respectively, while the 100-seed weight of Wodjil was 9.2 g and 10 g under well-watered and water-deficit treatments respectively (Tables 2 and 3). Average total seed yield of RIL population was 221 g/m 2 under well-watered (WW) conditions whereas under water-deficit (WD), the yield was 114 g/m 2 . Most of this difference is attributable to difference in lateral stem productivity. The difference in main stem yield between moisture treatments was comparatively low with 132 g/m 2 in WW and 99 g/m 2 in WD treatment. By contrast, major differences were seen for lateral stem yield with a mean of 87 g/m 2 recorded in WW and only 12 g/m 2 in the WD treatment. The variances for total biomass among treatments were also found significant according to ANOVA and they measured 705 g/m 2 and 480 g/m 2 in WW and WD treatments respectively ( Table 3).
As with the yield traits, water regime also showed a significant effect on the duration of reproductive growth although the moisture stress treatment was applied only after flowering. The differences for time to flower between treatments were non-significant as expected. Within moisture treatments genotypes differed significantly (P < 0.001) in time to flower, however difference among genotypes in maturity days were non-significant. Overall, the flowering duration and reproductive phase were reduced (P < 0.001) under WD treatment. This phenology difference resulted in reduction of time to maturity under WD environment. The time to flower from transplanting ranged between 70 and 87 days in both moisture treatments with the parent Wodjil flowering after 70 days and P28213 flowering 14 days later (Tables 2 and 3).
The regions of the yellow lupin genome contributing to these heritable traits were identified through QTL analysis. The small but significant interaction effect of water regime on total seed yield that was observed by ANOVA was supported by QTL analysis, which exclusively found only interaction QTLs (i.e. no main effect QTLs) for total seed yield (Tables 2 and 4). In contrast, the genotype main effect was relatively strong for total aerial biomass, 100-seed weight and phenology. In other words, the same QTLs contributed to the genotype main effect and were identified in both water regimes for these traits. Two significant QTLs (−log (10) > 3.82) on linkage groups YL-06 and YL-26 were found to be associated with total biomass. But the biomass QTL on YL-06 showed significant QTL x e interaction meaning that it was only detected in one environment. The QTL associated with biomass on linkage group YL-26 explained 9% of total phenotypic variation (Table 4).
Two main effect QTLs (−log (10) > 3.82) were found to be associated with 100-seed weight under both WD and WW environments. The two QTLs were located on linkage groups YL-03 and YL-09, which together explained 28.4% of total phenotypic variation in the population (Table 4).
Four significant (−log (10) > 3.82) loci were found to be associated with time to flower. These QTLs were found on linkage groups YL-01, YL-21, YL-35 and YL-40, which together explained 43% of total phenotypic variation in the population (Table 4).
Discussion
Here we present the first reported linkage map of yellow lupin using GBS and DArT-seq methods to genotype a new wild x domestic F 8 RIL population. The linkage map composed of 2,458 markers in 40 linkage groups. Furthermore, QTL analysis revealed significant loci controlling yield-related and phenology traits: total biomass, 100-seed weight, time to flower and length of reproductive phase.
Linkage map development
We genotyped the RIL population along with parents using a genotyping-by-sequencing approach described by Poland et al., [46]. As a result, only 948 good quality SNPs markers (with < 10% missing values and low segregation distortion) out of a total of 13,462 originally discovered SNPs were selected for mapping. A large number of missing values are a common feature of GBS which could cause ambiguity in the true location of markers. While imputation methods appear to be efficient in using data matrices with a high proportion of missing values [47], linkage mapping is very sensitive to the systematic errors given the varying accuracy of imputation reads [48]. In a recent study, only 6% of sequence reads were found to be useful for genotype calls after filtering for genotype quality and missing data [49]. Therefore, we took a conservative approach of removing markers with excessive missing values. The combination of restriction enzymes that produces highly polymorphic fragments is also critical for an efficient GBS protocol, and each organism may differ in the optimum set of restriction enzymes [50,51]. Possibly a higher proportion of robust, polymorphic markers may have been achieved with a different combination of restriction enzymes (here, PstI and TaqαI were used). This highlights the advisability of carrying out preliminary testing of different restriction enzyme combinations prior to embarking on large-scale genotyping of populations. Given that, the second NGS approach -DArT-seq yielded a much higher number of robust, polymorphic markers using a different restriction enzyme pair than in our GBS approach: PstI and MseI. In total 5,590 SNP and 8,854 PAV markers were discovered and out of that a total of 1,049 SNPs and 957 PAV markers were retained for linkage mapping after filtering for missing values and genotype quality. The length of the entire linkage map was 2,261.3 cM, comparing well with the well-established maps of white lupin and narrow-leafed lupin genomes, where markers were distributed over 25 chromosomes and covered the 1,916 cM of the white lupin genome [28]. While narrow-leafed lupin map was comprised of 20 linkage groups covering a total of 2, 361.8 cM of its genome [52].
The combination of GBS and DArT-seq methods greatly improved the number of markers with acceptable quality. A substantial number (2,945 out of original 27,906) of high-quality markers with low segregation distortion and very few missing values were achieved to develop the linkage map. The resultant SNP and PAV markers from both techniques integrated well. This huge reduction in the number of markers was in large part related to high (See figure on previous page.) Fig. 1 A genetic map of yellow lupin based on 912 framework markers in 40 linkage groups (YL01-YL40). Each vertical bar represents a linkage group with marker names on right side of the bar while the position in Kosambi centiMorgan are on the left side of the bar. The markers prefixed 'SCAFFOLD' represents SNP markers from genotyping-by-sequencing while markers prefixed 'DArT-SNP' are SNP markers from DArT-seq and 'DArT-PAV' are presence/absence variant markers from DArT-seq. Full marker data including redundant and attached markers are provided in Additional file 2: Table S1 Table 2 Split-plot ANOVA for 1) yield traits; total seed yield (g/m 2 ), total biomass (g/m 2 ) and 100-seed weight (g) and 2) Phenology traits; time to flower (days) and length of reproductive phase (days) in the yellow lupin RIL population under two moisture treatments i.e. well-watered and water-deficit. Moisture treatments were main blocks while genotypes were sub-plots in this experiment. Where d.f. is degree of freedom and MS is means sum of squares segregation distortion from the expected 1:1 ratio. We removed markers deviating (P < 0.0001) from an expected 1: 1 ratio of an F 8 RIL population to avoid segregation distortion that may have illegitimately joined linkage groups containing similarly skewed markers, with subsequent effects on QTL analysis [53,54]. At the same time, we were careful not to apply an excessive filtering that would remove genuinely skewed regions of the genome, such as those containing domestication traits (for example, the low-alkaloid iucundus genes in narrow-leafed lupin [52,55]. The markers associated with low alkaloid in yellow lupin was also highly segregated but was captured the current levels of stringency (data not presented; manuscript in preparation). The wide crosses with wild material often used for RIL population development for linkage mapping due to the typically high level of marker polymorphism [56], However, reduced recombination in such crosses can also cause high segregation distortion [57].
Given that, we conclude that this phenomenon may have occurred in our experimental RIL population as it was developed by employing a wide cross. The use of cluster analysis was novel in terms of identifying segregation distortion in this population so that the subsequent analysis could be conducted on an unbiased subset.
In total, we identified 40 linkage groups to represent the 26 chromosome pairs of yellow lupin. This excess number of linkage groups highlights that this remains a first draft linkage map. Development of further genomic resources and suitable mapping populations of yellow lupin would facilitate the refinement of this map and the production of more complete map with the 26 linkage groups expected for this species.
QTL mapping
The new genetic linkage map was used as the basis for the first QTL analysis of yellow lupin, which identified Table 3 Means of total seed yield (g/m 2 ), main stem seed yield (g/m 2 ), lateral stem seed yield (g/m 2 ), total biomass (g/m 2 ), 100seed weight (g) and time to maturity (d) in yellow lupin under well-watered and water-deficit treatments and their Least Significant Difference (LSD)
RILs
Wodjil P28213 Treatments Well-watered Water-deficit Well-watered Water-deficit Well-watered Water-deficit Overall mean LSD genomic regions controlling total biomass, 100-seed weight and phenology under different moisture conditions. The effect of QTLs associated with biomass and 100-seed weight was 14 and 23% respectively, while the effect of QTLs associated with time to flower and length of reproductive phase was 71 and 55% respectively (Table 4). This compares favourably to similar studies conducted in other legumes where QTLs associated with adaptation traits captured 5-69% of phenotypic variation [4,7,8,10,12]. It was notable that the main effect QTLs associated with important yield traits such as total biomass, 100-seed weight, time to flower and length of reproductive phase were not significantly affected by the water treatments applied in this study. This is positive news for lupin breeders as it suggests that superior alleles can be selected in a range of water regimes. However, total seed yield, which is one of the most important traits could only be detected under WW conditions, suggesting that it may prove difficult to identify QTLs for improved yield under WD conditions. However, the small plot size in our studies enforced by limited space under a rainout shelter inflated the residual error that reduced both heritability and our capacity to detect significant QTLs. The yield QTLs were not associated with phenology, so it should be possible to introduce these higher yield alleles without compromising early phenology, a drought avoidance trait which is essential for reliable yields in Australian growing regions that experience severe terminal drought. These results highlight that the yellow lupin breeding effort is still in its infancy, and greatly improved yields could be achieved if given the opportunity to conduct further rounds of crossing and selection. Currently there is no active yellow lupin breeding in Australia. If breeding programs were to be established, NGS-derived SNP markers developed here can readily be converted to single locus assays for use in marker-assisted selection to aid any renewed breeding effort [58,59].
From an ecophysiological perspective, the lack of interaction between moisture regime and QTLs for yield traits (total biomass and seed weight) and phenology was unexpected, given that water deficit is likely to select for drought escape, whereas longer season, higher-rainfall environments may favour delayed phenology to maximize biomass [60]. This may be because maturity differences between WW and WD environments were relatively small i.e. 10 days probably because of forced maturity at the end of the season? (Table 3). We expect that if the same experiment was conducted in a longer season environment with greater contrast between WW and WD treatments, we would have detected a stronger role of phenology on productivity.
The QTLs associated with time to flower explained a modest amount of 44% of total phenotypic variation in a trait with 71% heritability. On the other hand, QTLs controlling very low heritable yield traits only explained 9-28% of total phenotypic variation. The results suggest the presence of valuable diversity in the experimental germplasm that could be utilised for crop improvement.
Recombinant-inbred line (RIL) population development
An experimental recombinant-inbred line (RIL) population was developed from a wide bi-parental cross between a wild yellow lupin accession P28213 and an Australian cultivar Wodjil (a selection from Polish cultivar Teo) at the Department of Primary Industries and Rural development (South Perth, Western Australia). The parents were selected on the basis of contrast in adaptation traits such as phenology, below/above biomass, and response to terminal water stress and domestication traits [60]. Wodjil was bred for short season environments and exhibits ruderal traits such as early phenology, low above/below ground biomass and low yield potential and exhibits a drought escape strategy. The wild parent P28213 originates from a high-moisture environment (average seasonal rainfall 1163 mm) in the Azores (38.70 N, − 27.22 W) and exhibits competitive traits such as delayed phenology, high above/below biomass and high yield potential, but is prone to early water stress onset. Parents also differ in key domestication traits such as vernalisation response, growth habit, seed dehiscence, alkaloid content, seed permeability, and both flower and seed coat colour. The experimental RIL population was developed from a single F 1 plant. One F 1 individual was grown in a screen house and 300 F 2 seeds were harvested. All F 2 seeds were scarified by hand (due to hard seed coat segregating in the population) and sown in a screen house to obtain F 3 seeds. Single seeds were taken from individual F 3 plants and progressed to the F 8 generation by single seed descent [61] to produce a total of 202 recombinant inbred lines. This RIL population of 202 lines was multiplied prior to phenotyping in a screen house and a total of 156 RILs were randomly selected for phenotyping and genotyping.
Genotyping of RIL population
Genotyping of the RIL population was conducted using two NGS approaches: Genotyping-by-sequencing and DArT-seq methods.
Genotyping-by-sequencing (GBS)
DNA extraction from 156 RILs and parents was performed using Qiagen DNeasy Plant 96 kit and Quant-iT™ PicoGreen (Life Technologies, Carlsbad, California) for DNA quantification. DNA for each genotype was normalised to the concentration of 40 ng/ul. Libraries were prepared for GBS using the protocol of Poland et al. [46]. Briefly, PstI-HF and TaqαI restriction enzymes were used to digest DNA samples. A total of 96 barcoded adapters [46] for downstream identification were ligated to the 5′ end of digested DNA fragments, while a Y-shaped adapter was ligated to the 3′ end. PCR was used to amplify the resultant fragments along with the addition of Illumina adapters. The PCR-product was cleaned by using a Promega SV Wizard Gel Clean-Up System (Promega Corporation, Madison, Wisconsin). Samples were sent for Illumina HiSeq analysis by Beijing Genome Institute (BGI) at University of Davis, California for 150 bp paired-end sequencing.
GBS reads were trimmed based on quality parameters using Sickle [62] and were subsequently demultiplexed using a custom Perl script. Every pair of reads was isolated based on its exact match with one of the barcodes, which were then trimmed. The GSNAP program [63] was employed to map the reads to an unpublished SOAPdenovo genome assembly of L. luteus line '9242X4' , which had been produced using short-read denovo assembler developed by Luo et al., [64] (Joshua Udall, unpublished data). SAMtools [65] was used to produce BAM alignment files.
BamBam tools [66] were employed to process BAM files including single nucleotide polymorphism (SNP) calling, imputation and characterization. SNP markers were accepted if they had a minimum of 3 read coverage, had < 30% missing genotypes and minor allele frequency of ≥0.1. Imputation of missing genotypes was carried out by K-Nearest neighbour with k = 10. Further quality control was performed during linkage mapping. The number of markers (948 SNPs) obtained from this approach were not considered enough to create linkage map, hence, another genotyping method-DArT-seq was employed to obtain additional good quality markers.
DArT-Seq
DNA isolation was performed on 156 RILs and parents using the CTAB method [67]. Qubit fluorimetry (Invitrogen, Carlsbad, CA, USA) was used for DNA quantification and results were confirmed by tallying with the corresponding band brightness on gel electrophoresis wells. DNA was normalised at the concentration of 50 ng/ul. Samples were sent for library preparation (using restriction enzymes PstI and MseI) and sequencing to Diversity Arrays Technology Pty Ltd. (Canberra, Australia).
Trimming of DArT-seq reads involved removal of the reverse adapter only and was not based on Illumina quality parameters but rather by alignment of multiple sequences and the consensus was taken across the population. The minimum average read depth of 2 for the reference allele and 1.5 for the alternative allele was used. For PAV (presence /absence variant) markers the minimum average allele read depth was 5.
Linkage map development
After SNP calling from both GBS and DArT-seq pipelines, output loci were subjected to additional filtering. Those loci which showed significant (P < 0.0001) segregation distortion from the Mendelian expectation of 1:1 parental alleles were excluded from the analysis. Marker x RIL combinations with > 10% missing values were removed, thus leaving a total of 140 RILs out of 156 RILs for linkage map development. Initial mapping with 140 RILs in MultiPoint 3.3 software [68] failed to produce satisfactory linkage groups, which led us to investigate the structure of the RIL population. The NTSYS program [69] was employed to generate distance matrixes among RILs, which were then visualised by cluster analysis (Additional file 1: Figure S1) in Primer6 software [70]. Rather than the random genetic relationships expected within a RIL population that had been developed by single seed descent, there was distinct clustering of 43 RILs with the domesticated parent 'Wodjil' , possibly indicative of unintended cross-pollination with domesticated-types of yellow lupin during single seed descent or seed admixture. Therefore, these 43 RILs were excluded from further linkage mapping to minimize bias. Thus, 97 F 8 RILs were used for the final linkage map development in MultiPoint3.3. All loci with Chi 2 P < 0.0001 and missing values > 10 were removed at the beginning of linkage analysis. Moderately distorted loci (P < 0.001) were moved to the 'Heap' within the MultiPoint linkage analysis but were not used to calculate linkage groups since segregation distortion may have led to illegitimate joining of separate linkage groups. Instead, such markers were allocated approximate genetic positions as 'attached' markers at the end of the analysis. Initial clustering was started at recombination fraction (rf ) of 0.05. Marker ordering in each linkage group was performed in Multipoint and jack-knife re-sampling enhanced the robustness of marker order by keeping only markers with jack-knife value of > 90%. Those markers were designated as 'framework' markers. Other markers which mapped to the same location as framework markers were termed 'redundant markers' and they were assigned the same genomic location on the map as the framework markers. The same procedures were followed at each clustering cycle gradually increasing from recombination frequencies from 0.05 to 0.24. Manual inspection of clusters at each step helped to distinguish valid cluster mergers (two progenitor clusters most closely linked through their terminal loci) from invalid clusters (two progenitor clusters most closely linked through non-terminal markers). Joining of valid clusters was accepted, while invalid joining of clusters was rejected. Typically, the markers causing spurious linkage between clusters had higher segregation distortion values and/or missing values.
Upon the completion of the framework map, interval size values were transformed to account for multiple generations involved in F 8 RIL population development and expressed in Kosambi centiMorgans (cM). Linkage groups were drawn using MapChart 2.3 [71].
Phenotyping of RIL population Experimental procedures and design
This experiment was conducted in a split-plot design in 2013 in a rain-out shelter at CSIRO Floreat (31°56′53.5″ S 115°47′52.4″E), WA, Australia [72]. Where water regimes were placed as main plots and genotypes as sub-plots. A total of 156 recombinant inbred lines with sufficient number of seeds along with both parents Wodjil and P28213 were studied for their response to limited moisture and WW conditions. Experimental seed was scarified to remove the effect of variation in hardseededness in the population. Imbibed seeds were vernalized by growing in Jiffy pots (Garden City Plastics Pty Ltd) at 8°C for 3 weeks from 16th May, 2013 to avoid the confounding effect of variation in vernalization response in the experiment. All plant material was transplanted into the field on 10th June, 2013. Rhizobium inoculation was undertaken at transplantation into the field to promote nodulation. Manual weeding was done as needed.
Genotypes were grown under two water regimes applied to contiguous regions of a single field: a) WW: this treatment was kept watered from sowing till ripening and b) WD: terminal drought administered using an automatic rainout shelter after the onset of pod set. There were four replications of genotypes, with the two parents (Wodjil and P28213) replicated 8 times within each treatment. DiGGer package of R software was employed for spatially optimized randomisation [73]. A rainout shelter of dimension 11 × 14.5 m was used for the WD treatment with a frame area 0.5 m wide retained empty to reduce border effects. An immediately adjacent field area of similar dimensions was used for WW treatment. Sub-plot size was 0.25 × 0.5 m. Each plot was planted with five seeds 10 cm apart within a row and the row-to-row distance was 25 cm.
Moisture treatment
The WD treatment was applied at the post-anthesis stage when the first pod had developed on the main stem, while the plots of late flowering lines under the rainout shelter were individually irrigated until first podding. All the plant material grown under WW treatment was maintained with irrigation (rain or reticulation if required) in the open field.
From the time of the application of the WD treatment, soil moisture was measured 0, 15, 30 and 45 days poststress imposition at three depths (0-20, 20-40 and 40-60 cm). The maximum, minimum and average temperature data and rainfall were obtained from Bureau of Meteorology, Australia website www.bom.gov.au for metrological station Shenton Park, WA 31.94°S, 115.79°E (approximately 2.9 km from the experimental site).
Trait measurements
Measurements were made for total seed yield, seed yield from main and lateral stems (in g/m 2 ), total biomass (dry weight of aerial plant mass in g/m 2 ), 100-seed weight (g), time to flower (days) and length of reproductive phase (days). The time to flower was measured from the day of transplanting until 50% of plants in a plot flowered while the length of reproductive phase was calculated by subtracting the time to flower from time to maturity.
Analyses of phenotypic data and quantitative-trait loci (QTLs) for adaptation traits ANOVA was used to analyze quantitative traits in a split-plot model with water regime in main plots and genotype as sub-plots in GenStat version 17 (VSN International, UK). Residual plots were generated to visualize ANOVA assumptions and identify outliers. Heritability (H 2 ) for traits studied separately in both treatments was calculated by the following formula: H2 ¼ σ 2 g ms g ð Þ− ms e ð Þ r , σ 2 p σ 2 g þ σ 2 e: À Á where r is the number of replications, (σ) is variance components, ms is mean square values of genotype (g), phenotype (p) and error (e) [74]. Heritability of those traits which were compared among both treatments was calculated by the following formula [75]: H2 ¼ σ 2 g ms g ð Þ− ms e ð Þ rÃt , σ 2 p σ 2 g þ σ 2 e À Á GenStat version 17 was used for QTL analysis. Three data files were used for QTL analysis e.g. phenotypic data from the field, genotypic data for framework markers, and positions of framework markers on the linkage map. QTL analysis involved four steps: (i) identification of the most appropriate model; (ii) simple interval mapping (SIM) in which main effect QTLs are calculated against the default threshold -log10(P) = 3.82 and QTL x E interaction; (iii) composite interval mapping (CIM) using SIM-derived QTLs as co-factors; and, (iv) A final scan, all candidate QTLs are compared, and the effect of each QTL is calculated.
All 140 RILs, for which both phenotyping and genotyping data were available, were used for QTL analysis. The QTL analysis was performed for yield traits (total seed yield, total biomass and 100-seed weight) and phenology traits (time to flower and length of reproductive phase). It should be noted that the linkage map was developed based on the 97 unskewed RILs as outlined previously. Comparative QTL analysis of 97 RILs and full set of 140 RILs (not presented) showed no notable differences in the resultant candidate loci thus justifying the use of all 140 RILs for QTL analysis.
Conclusion
This study reports the first linkage map for yellow lupin, based on NGS-based genotyping methods for this species. It is also the first example of QTL analysis conducted in yellow lupin that identified QTLs for yield and phenology traits. It provides a starting point for engaging in the development of productive yellow lupin cultivars adapted to low rainfall regions of Australia and beyond.
Additional files
Additional file 1: Figure S1. The diagram presenting the clustering of RILs based on their genetic distances compared to population parents. The RILs are clustering on x-axis while y-axis shows the distance measured in NTSYS software. (DOCX 140 kb) Additional file 2: Table S1. Summary table of all the markers used to develop a yellow lupin map. The table comprised of marker name (SNP markers from DArT-seq appears as DArT_SNP, SNP from GBS approach appears as Scaffold and PAV markers appears as DArT-PAV), type (Framework = main skeleton markers, Redundant = exact duplicates of Framework markers and Attached = the markers which were initially not used for mapping because of high segregation distortion or missing values but later connected to closest possible location on map) and the chisquare values (expressed both in chi2 and chip values) which show the deviation from expected 1:1 ratios. (XLSX 1258 kb) | 8,110.2 | 2019-08-14T00:00:00.000 | [
"Biology",
"Agricultural And Food Sciences"
] |
Freundlich Isotherm: An Adsorption Model Complete Framework
: The absolute majority of modern studies dealing with the interpretation of experimental data on the basis of the Freundlich isotherm ignore the fact that the data obtained for regions of low and moderate adsorbate concentration/pressure can be analytically continued within the Freundlich adsorption model to the adsorptive saturation area with coverages tending to 100%. Needless to say, this would give valuable extended information about the corresponding adsorption process. This message proposes a framework to comprehensively analyse experimental data first recognised as complying with the Freundlich adsorption model. An algorithm-driven method is presented which enables one to translate the data obtained in the area of small and moderate the coverages of the area of adsorptive saturation regime. As examples, three sets of experimental data for adsorption of mercury (II) on N-rich porous organic polymers and of protein on carrier nano-Mg(OH) 2 have been processed and presented according to the framework developed.
Introduction
Long ago the Freundlich isotherm found itself among the isotherms through which one typically checks experimental data obtained. The purpose of this action consists most often of the determination of fitting parameters in order to choose on the R 2 approximation basis which model out of the de facto standard set (Langmuir-, Temkin-, and maybe, Dubinin-Radushkevich) of models provides the best fit. Should it be the Freundlich model, one could dwell on the degree of energetic inhomogeneity of the surface (the magnitude of parameter α in Equation (1)): where x and θ are in bulk concentrations (for solutions with a constant ionic power. As c, pressure in the gas phase or ionic activity in the solution can be considered) of a surfaceactive substance being adsorbed and related surface coverage, respectively. The power of x is often considered as α = 1/n, where n > 0 is an integer or real number, and the coverage is expressed through adsorption q and limiting adsorption q ∞ as θ = q/q ∞ . More advanced analysis of fitting results gives rise to a conclusion on which type of the surface (in)homogeneity takes place for a pair "adsorbate/adsorbent" considered, that is, evenly inhomogeneous (Temkin adsorption model, or AM), exponentially inhomogeneous (Freundlich) or homogeneous (Langmuir) (for a more complete set, one could consider a linear inhomogeneity as well [1], but its representation through the proper equation is much more complicated than those for the other three. The Dubinin-Radushkevich AM is to be mentioned again as well but this is more applicable for adsorption on materials with pronounced porous properties). A huge variety of realizations of the Freundlich AM, among whose are the works having studied the adsorption of organic and inorganic substances on substrates of different nature in the framework of chemical, physical, biophysical processes including nano-particles as just examples [2][3][4][5][6][7][8][9][10], seems to represent a substantial reason for revisiting the basics of the Freundlich AM. While the monograph by McBain first convincingly elucidated the meaning of Equation (1) for interpretation of experimental data [11], the proper theoretical model was developed by Zeldowitch (1934) [12,13], and later reproduced as one of parametrical limits while expanding the general solution for energetically heterogeneous surfaces, expressed through a hypergeometric function into an infinite series [14,15]. The limiting adsorption is bounded through the surface available and an effective number of layers (should it be multi-layer). As it follows from the functional form itself of Equation (1), it does not describe a saturation regime, so that deviations from Equation (1) appear at bigger x. It has become typical for the research community, that data obtained and to be analysed in the framework of Freundlich AM, are to be typically checked for their relevance to Equation (1) with a successive determination of constants K and a as fitting parameters. Nevertheless, Zeldowitch's theory of the Freundlich AM goes beyond the small and moderate coverages and mathematically describes the saturation regime too. This circumstance seems to be most typically either ignored or forgotten by the research community although studies with the employment of the Freundlich isotherm for pairs "adsorbate/adsorbent" appear to be published in hundreds (if not more) of articles annually.
On the basis of Zeldowitch's theory, it appears possible to link the area of small coverages and that at saturation. Furthermore, the theory is applicable to both monoor multi-layer adsorption. In the last case, one has to distinguish between successive adsorption of layers "one after one" like a staircase and simultaneous adsorption when successive layers are being filled without completely filling the foregoing ones. For the former, the theory is to be applied to each "stair" separately.
The goal of this message is to revisit Zeldowitch's theory, to propose a mathematical methodology for bridging a chasm between the small (moderate) adsorption regime satisfactorily described by Equation (1) on the one hand and the limiting adsorption on another hand and, thus, cover the whole range of surface coverages within the Freundlich AM. This is to be formulated in the form of an algorithm for the proper analysis of adsorption in those systems where the Freundlich AM is considered the true one. What we need for that is just the experimental data obtained and published by the research community before for small and possibly moderate coverages only.
A Brief Excursus to Zeldowitsch's Theory
Zeldowitch considered the problem of finding such a distribution a(b) of surface adsorption centres on their adsorption heat that local application of the Langmuir AM would lead to an overall functional form (1) for the whole surface. For any particular surface patch with particular adsorption heat b, the Langmuir adsorption is to take place. The patches are arbitrary laterally distributed, a is proportional to the number of patches whereas b depends on their properties [12,13,16]. Mathematically, this meant solving the following integral equation where the upper limit b 0 was introduced artificially to enforce the integral convergence. Since Equation (2) is intractable with respect to a(b), the problem was simplified through the following replacement: instead of the Langmuir isotherm ax x+b as the integrand in Equation (2), the following local adsorption function was employed: With such a kernel function in Equation (2), the distribution function a(b) = Ab α−1 was shown to meet Equation (2), should the isotherm have the form as in Equation (1). The following relationships appear to be an integral part of Zeldowitch's theory: at small x whereas for big x b 0 one has Thus, should constant b 0 be approximately determined on the basis of experimental data according to Equation (3) as the saturation regime (4) at big x appears to be identified as well. Noticeable is that, according to Zeldowitch's theory, it has the Langmuir-type functional form but with different adsorption equilibrium constants.
The Consistent Algorithm of Analysis of Experimental Data
According to the above said, dependencies like Equation (1) appear to be determined and carefully studied on the basis of small and/or moderate concentrations, which include determination of constants K and α (blue curves in Figure 1). The saturation regimes (4) (shown grey in Figure 1) turn out to be, as a rule, omitted both in experimental studies and discussions of obtained results. Nevertheless, there are a lot of evident reasons why such regimes, as well as intermediate regions (orange in Figure 1), can represent considerable interest for the research community and do.
Therefore, in step 1, upon the determination of the fitting parameters K and α, one is expected to determine the saturation regime. It has the Langmuir-like form f 3 (x) = x x+b where b ≡ b 0 / 1 + 1 α (we now redefine constant b as different from that in Equation (2)). Thus, the use of Equations (4) and (5) enables one to perform this without an introduction of a rigorous boundary between the saturation regime (grey curves) and the intermediate coverage area (orange). Such a boundary (a point between solid and dashed grey curves in Figure 1) will be imposed later.
Step 2 is related to the determination of the intermediate area with its boundaries. Technically, the most obvious way to model the intermediate region of concentrations would be to perform some interpolation. One would need to identify boundaries x m and x s of the intermediate area and to perform linkage on the class of continuously differentiable functions. Whereas boundary x m is naturally given as the experimental data point (x m , f 1m ) for the biggest concentration (it depends on an experimentalist's judgement whether the power law area has not yet been left there), point x s is to be determined on the basis of some consideration, at which x the saturation regime begins. This would be a relative judgement. To avoid this, one can properly determine x s within the method itself linking the intermediate and saturation regime areas. We employ in the intermediate area a quadratic form f 2 (x) to be continuously linked with the adsorption function f 1 (x) in the area of small and moderate coverages on the left and with adsorption function f 3 (x) in the saturation regime area on the right. Out of parabolic, hyperbolic, and elliptic forms we chose parabola whose upper branch in a Cartesian coordinate system with apostrophe has the canonical form f 2 2 = 2px . Accompanying the linking point arbitrary for a while with sub/superscript "0", we use the expression for a tangent line to our parabola at this point: . In order to continuously differentiably adjust the parabola to f 1 (x) and f 3 (x) at x m and x s , respectively, we apply a translational transformation x = x + c, f 2 = f 2 + d, where c and d are constants to be determined later, to Equation (6): where f . At x 0 = x m , the tangent line (7) is expected to coincide with f 1 (x)'s tangent line. As the latter has the form the continuously differentiable linkage conditions at x 0 = x m instantly follow: At x 0 = x s , adsorption function f 3 (x) produces its tangent line with the equation from where and according to Equation (7) the continuously differentiable linkage conditions where f 3s ≡ f 3 (x s ). Thus, 4 parameters (c, d, p, and x s ) appear to be determined through four equations at the linkage points at x m and x s , that is, the right linkage point itself has turned out to be determined within this procedure. The solution of set of Equation (8) can be represented in the analytical form of relations between parameters c, d, and p.
which has a well localised sought root in the area x x m and is to be easily solved numerically. As it follows from the parabola canonical form above with the translational transformation applied, the equation for the parabola bridging the chasm in the intermediate area x ∈ (x m , x s ) has the form: presented in Figure 1 in orange. Therefore, in step 1, upon the determination of the fitting parameters K and , one is expected to determine the saturation regime. It has the Langmuir-like form ( ) = where ≡ / 1 + (we now redefine constant b as different from that in Equation (2)).
Thus, the use of Equations (4) and (5) enables one to perform this without an introduction of a rigorous boundary between the saturation regime (grey curves) and the intermediate As in step 3, one has to check if the bridging between the low and high concentration regions has been performed correctly. The first and obvious condition is to be checked is certainly Further obligatory conditions are otherwise, geometrically obviously, the bridging would not be possible. If conditions (11) are not met, either the approximation of the experimental data with Equation (1) went beyond the region in which the power law is indeed valid, or the Freundlich AM is not the true one for the system considered.
Results and Discussion
The parameters finally determined for the systems considered in Figure 1 are presented in Table S1.
The calculations performed demonstrate the most important practical result indicating how close to (or far from) the saturation regime the rightmost experimentally determined point is situated. Alongside this de facto extension of the source works, values b = b 0 / 1 + 1 α in Equation (4) appear to be determined and to characterise both saturation rate and surface adsorption properties at big coverages. How properly the chasm in the intermediate area has been bridged, is to be judged on the basis of experimental data to be obtained for the corresponding region. Even in the framework of the proposed approach, one could choose between at least three global linkage options, that is, parabolic, hyperbolic, and elliptical ones with a lot of opportunities (for example, to add the rotational transformation) for local tuning.
The concentration ranges studied experimentally in the works considered above appeared to be easily analytically continued (in the intermediate area approximately) from 0.09 mg/L (protein on nano-Mg(OH) 2 ) and~300 mg/L (mercury (II) on N-rich porous organic polymers) up to "reasonable infinity".
Conclusions
In view of umpteen works having employed the Freundlich isotherm for interpretation of experimental data, Zeldowitch's theory of the corresponding AM has been revisited to demonstrate an analytical continuation from typically scant data sets for small and moderate coverages to the area of saturation regime. This enables one to judge the saturation rate and to bridge a chasm between low (moderate) and high pressure (activity or concentration) areas. Experimental data for adsorption of mercury (II) on N-rich porous organic polymers and of protein on nano-Mg(OH) 2 published by independent researchers have been processed to demonstrate how the analytical continuation method of the Freundlich isotherm developed in this article works.
J. Zeldowitch underlined in his historical work that his goal had been to contribute to the correct interpretation of the community's experimental data rather than to develop a quantitative theory of adsorption on heterogeneous surfaces [12,13]. Like that, we are to emphasize our goal to be to suggest a framework useful for analysis of the community's experimental data first recognised as complying with the Freundlich isotherm but indeed as those to be essentially more comprehensively interpreted within this framework of Freundlich-Zeldowitch AM.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/app11178078/s1, Table S1: Parameters of the systems with adsorbate and adsorbent (the isotherms are presented in the article's Figure 1). | 3,379.6 | 2021-08-31T00:00:00.000 | [
"Chemistry",
"Materials Science"
] |
Quantum hypothesis testing in many-body systems
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as"is the system in state A or state B?". In quantum mechanics, the latter type of measurements can be studied and optimized using the framework of quantum hypothesis testing. In many cases one can explicitly find the optimal measurement in the limit where one has simultaneous access to a large number $n$ of identical copies of the system, and estimate the expected error as $n$ becomes large. Interestingly, error estimates turn out to involve various quantum information theoretic quantities such as relative entropy, thereby giving these quantities operational meaning. In this paper we consider the application of quantum hypothesis testing to quantum many-body systems and quantum field theory. We review some of the necessary background material, and study in some detail the situation where the two states one wants to distinguish are parametrically close. The relevant error estimates involve quantities such as the variance of relative entropy, for which we prove a new inequality. We explore the optimal measurement strategy for spin chains and two-dimensional conformal field theory, focusing on the task of distinguishing reduced density matrices of subsystems. The optimal strategy turns out to be somewhat cumbersome to implement in practice, and we discuss a possible alternative strategy and the corresponding errors.
Introduction
The purpose of this work is to i) introduce and review quantum hypothesis testing for readers with a background in quantum field theory and many-body theory, ii) develop some new results in a perturbative setup, and then iii) apply the tools to distinguish in particular two reduced density matrices in a subsystem of a quantum many-body system.
We begin with some background motivation. An elementary quantum task is to distinguish between two quantum states. Recently there has been much effort to study this question in quantum field theory and many-body theory, and to develop methods to compute various quantum information theoretic distinguishing measures analytically. A particularly interesting case is a large or infinite system in two different global states viewed from a small subsystem. The problem is then to distinguish the two reduced density matrices (RDMs) resulting from a partial trace over the complement of the subsystem. For this problem, critical systems modeled by conformal field theories have offered a fruitful arena for analytic progress. Additional motivation for studying conformal field theories comes from the connections between quantum information and gravity. In this context, a famous issue is the state of Hawking radiation escaping from an evaporating black hole: how can one detect in subsystems the subtle quantum correlations between radiated quanta at different times, to distinguish a conjectured pure state of radiation from something resembling thermal radiation?
In quantum field theory and many-body theory, there has been much progress in studying wellknown distinguishing measures both analytically and numerically. For example, in the context of conformal field theory and critical lattice models, there are studies of fidelity F (ρ, σ) [1,2], relative entropy S(ρ σ) [2][3][4][5][6][7], generalized divergences [8][9][10][11][12][13] and trace distance D(ρ, σ) = 1 2 ρ−σ [14,15]. In this work, our focus is instead to distinguish two states by measurements. We begin with three remarks: i) a rigorous framework for the task is quantum hypothesis testing, ii) many results obtained for relative entropy and generalized divergences can be embedded in this framework, giving them an operational interpretation, and iii) hypothesis testing also suggests an optimal measurement protocol to minimize the error in distinguishing two states. We are thus lead to study how quantum hypothesis testing can be implemented in many-body theory and quantum field theory.
Quantum hypothesis testing builds on the classical theory of hypothesis testing, which is a cornerstone of statistical analysis and the scientific method. Borrowing terminology from the classical theory, one may want to test whether the system is in a state ρ called the null hypothesis, thought of as the "background", or in another quantum state σ called the alternative hypothesis, which is the "signal" that one desires to detect. The framework of quantum hypothesis testing then provides rigorous estimates for the probabilities of the errors of mistaking the two states in an asymptotic limit of many measurements 1 . Here, it is important that by "many measurements" we mean simultaneous measurements on many copies of the system, as opposed to performing a sequence of individual measurements on independent single copies of the system. The error probability estimates involve various quantum information theoretic quantities, which depend on the details of the quantum hypothesis testing protocol. For example, for the case of so-called asymmetric testing, the error estimate involves the relative entropy as well as the relative entropy variance between the two states; both measures can be obtained from generalized divergences.
Quantum hypothesis testing has numerous applications in quantum information science, such as quantum illumination [18][19][20], entanglement-assisted communication [21], and the analysis of environment-parametrized quantum channels [22,23], to name a few. In particular, there are rigorous studies of particular quantum hypothesis testing protocols to distinguish states in spin chains, see e.g. [17,24,25].
Here, we are interested in connecting various mathematical results about hypothesis testing to implementations and applications of hypothesis testing in models at criticality with an emphasis on distinguishing reduced density matrices of subsystems associated to different global states. For example subsystems of free fermion chains have been extensively studied in the context of entanglement, because subsystem reduced density matrices are determined analytically by two-point functions [26][27][28][29]. The analytic tractability allows one to study for example entanglement spectra [30,31] and entanglement entropies of subsystems [32] (see also [33,34] for reviews). Distance measures such as relative entropy and Rényi divergences have also been explored [35,36].
We now summarize the main results of this work, which is divided in two parts. In the first part of this paper, we consider quantum hypothesis testing for general systems and develop a perturbative approach to hypothesis testing. Many applications often involve a setup where the two global states are parametrically close, as functions of one parameter (such as the ambient temperature). In that case it is natural to use a perturbative expansion to approximate two neighboring states. After giving a general review of quantum hypothesis testing in section 2, we study error probability estimates combined with a perturbative approach in section 3. The relevant error estimates involve the perturbative expansions of relative entropy and relative entropy variance, with leading terms appearing at second order. To examine the behavior of the error estimate, we study the relative size of these leading terms. In doing so, we find a universal result, a lower bound for the ratio of the two terms, applicable for any system in the perturbative setting. The result also allows us to develop a new joint perturbative bound on the two types of errors.
In section 4, we discuss and compare different types of measurements. We argue that independent (i.e. factorized) measurements perform poorly in general. We review the optimal measurement described in [37], which saturates the theoretical error bound. This measurement turns out to be rather difficult to describe explicitly. As an alternative, we consider a simpler but suboptimal measurement, the likelihood ratio (or Neyman-Pearson) test, which is easier to describe and performs rather well.
In the second part of this work, we implement these measurement protocols in quantum systems of increasing complexity: a single qubit, Gaussian fermion chains and finally two-dimensional conformal field theories.
We consider the qubit in section 5 and we construct the optimal measurement. Surprisingly, an explicit description is difficult as it leads to a challenging combinatorial problem, involving Krawtchouk polynomials and related to the Terwilliger algebra of the Hamming cube. This motivates the simpler likelihood ratio test, which can be described explicitly, and implemented with a quantum circuit given in Figure 5. Using numerical methods, we study the optimal measurement and compare it to the likelihood ratio test.
In section 6, we move on to spinless fermion chains with quadratic Hamiltonians. Motivated by hypothesis testing, we derive formulas for the relative entropy and the relative entropy variance in subsystems of free fermions (with only hopping interactions) at different temperatures. Then we present a prescription to compute overlaps between eigenstates of two different modular Hamiltonians of the same subsystem. The main technical tool is a generalization of Wick's theorem to correlators that involve Bogoliubov transformations [38,39]. The resulting overlaps allow the construction of the optimal measurement that distinguishes two thermal states by a local measurement. We find that in the simplest single fermion subsystem, the likelihood ratio test is optimal for distinguishing any two reduced density matrices, whereas for a two-fermion subsystem, it is not sufficient in general. In the XY model at finite temperature, for a two-fermion subsystem, the likelihood ratio test is again optimal.
We finally consider two-dimensional CFTs in section 7. We focus on states for which the modular Hamiltonian can be written as an integral of the stress tensor [40]. We construct optimal measurement protocols for subregions, using techniques of boundary CFT [41] to compute the necessary ingredients. This general framework can be applied to distinguish two thermal states from a subregion, and we study explicitly the case of the free fermion. We explain how to implement the optimal measurement, which is difficult to describe explicitly, and the simpler likelihood ratio test. We also consider the detection of a primary excitation on top of the vacuum, for which the likelihood ratio test can be implemented with a relatively simple procedure: by measuring one-point functions of the lightest operator interacting with the primary excitation.
We conclude with a discussion and some open questions, and summarize various useful properties and technical results in the appendices.
After the completion of this paper, related work studying various properties and applications of relative entropy variance (there called "variance of relative surprisal") from an information theoretic point of view appeared in [42].
Review of quantum hypothesis testing
In this section, we give a brief review of quantum hypothesis testing, to provide background for readers unfamiliar with this theory. In (binary) hypothesis testing, we have to choose between two hypotheses, the null hypothesis H 0 and the alternative hypothesis H 1 .
In the classical theory, the two hypotheses are associated with two probability distributions p(X), q(X) over the space Ω, and the problem is to discriminate between the two by a test T : Ω → I. If I = [0, 1], the test is randomized, if I = {0, 1}, the test is deterministic. The probability of detection for the hypothesis H 1 is then the expectation value E q [T ] = x∈Ω Q(x)T (x). If the test is deterministic, it is often expressed as an indicator function T = 1 H = 1 {x ∈ H} over an acceptance subset H ⊂ Ω.
In the quantum theory, H 0 and H 1 are two quantum states ρ and σ, and the test becomes an operator T = E 1 . More precisely the decision is made by measuring observables E 0 = A and E 1 = 1 − A which form a positive operator-valued measure (POVM), i.e. 0 ≤ E i ≤ 1 and i=0,1 E i = 1. In making a measurement, the probabilities of identifying the two states correctly are Tr(ρE 0 ) and Tr(σE 1 ), the latter being the probability of detection of the hypothesis H 1 . There are two ways to make errors, which are called of type I or type II. Type I error (false positive) corresponds to identifying H 1 while in fact H 0 is true. Type II error (false negative, missed detection) corresponds of choosing H 0 while H 1 is true. The probabilities of the two errors are given by α = Tr ρ(1 − A) (type I) , (2.1) β = Tr σA (type II) .
The objective of hypothesis testing is to find the best measurement which jointly minimizes the two errors. In this work we focus on the independent and identically distributed (i.i.d.) setting, and consider a joint measurement A (n) on n identical copies of the system, to discriminate between the states ρ ⊗n and σ ⊗n . The error probabilities then become n-dependent, α n and β n , given by α n = Tr ρ ⊗n (1 − A (n) ) (type I) , (2.2) β n = Tr σ ⊗n A (n) (type II) .
Quantum hypothesis testing addresses the question of the optimality of a measurement A (n) . The notion of optimality depends on the error optimization strategy. Symmetric testing optimizes the sum of the two errors, while asymmetric testing optimizes the type II error under the condition that the type I error remains bounded. 2 We review these two cases below.
Symmetric testing
In symmetric hypothesis testing, we treat the two types of errors equally and define the symmetric error 3 P n = 1 2 (α n + β n ) . (2. 3) The optimal measurement is obtained by minimizing P n over all possible measurements A (n) , where A (n) is a Hermitian operator satisfying 0 ≤ A (n) ≤ 1. We can define the minimum error as Tr ρ ⊗n (1 − A (n) ) + σ ⊗n A (n) . (2.4) The asymptotic behavior of this quantity is given by the quantum Chernoff bound [43], which says that where the quantum Chernoff distance is defined as We can see that − log Q s (ρ, σ) are proportional to the relative Rényi entropies defined by Petz [44]. As a result, symmetric hypothesis testing gives an operational meaning to these quantities. More precisely, their maximum for 0 ≤ s ≤ 1 gives the asymptotic exponent of the symmetric error It is also interesting that Q(ρ, σ) is related to other information quantities [43]. We have where T = 1 2 ρ − σ 1 is the trace norm distance and Q ≤ Q s=1/2 = Tr ρ 1/2 σ 1/2 ≤ F (ρ, σ) , (2.9) where F (ρ, σ) = ρ 1/2 σ 1/2 1 is the Uhlmann fidelity. If one of the states is pure, we have Q = Tr ρ σ. Q also satisfies the data-processing inequality (B.17).
Asymmetric testing
In this work, we will be interested in the asymmetric treatment of the two types of errors, which is the setting which gives an operational meaning to the relative entropy. In asymmetric testing, we require that the type I error is bounded, α n ≤ ε, and examine the asymptotic behavior of the type II error β n 4 . More precisely, we estimate the asymptotic behavior of the quantity where the infimum is taken over Hermitian operators A (n) satisfying 0 ≤ A (n) ≤ 1.
The asymptotic behavior of this quantity is given by the quantum Stein's lemma [45,46] which is the statement for any 0 < ε < 1. The relative entropy S(ρ σ) is defined as The quantum Stein's lemma shows that the type II error decays exponentially at large n with exponent given by the relative entropy, The asymptotic formula (2.11) was improved in [37,47] to subleading order. 5 The refined quantum Stein's lemma says that and involves the relative entropy variance 6 defined as 15) and the inverse Φ −1 of the cumulative distribution function of the normal distribution, In analogy with the quantum Chernoff distance, one can also define [48] the quantum hypothesis testing relative entropy for 0 < ε < 1. This quantity is another generalized divergence, satisfying the data-processing inequality [47]. In the rest of this work we will be focusing on asymmetric testing and the refinement of the quantum Stein's lemma (2.14).
The refined quantum Stein's lemma should be understood as a refined estimate of the asymptotic error of an optimal measurement. Following [37], it is useful to define the quantity This is the best type I error if we require that the type II error exponentially decays with leading exponent E 1 and subleading exponent E 2 . It is similar to β * n (ε) in that it measures the interdependence between the type II and type I errors. It is shown in [37] that an equivalent way to formulate the refined quantum Stein's lemma is to say that We see that the relative entropy S(ρ σ) acts as a threshold value for the leading exponent E 1 . Above the threshold, the type I error becomes uncontrolled and goes to one, while below the threshold, it can be made to vanish. The refined asymptotics become relevant when we are exactly on the threshold. On the threshold, we define and we have which varies smoothly from 0 to 1 when E 2 ranges from −∞ to +∞.
Single qubit example
We now consider a toy version of our problem: what would be the optimal measurement for a single qubit? This example gives a nice illustration of quantum hypothesis testing. Here, we only take a single copy of the system: we describe the "one-shot" measurement. As we will see, it can be formulated as a constrained optimization problem which has a simple geometrical interpretation.
We have a qubit in the two possible states ρ and σ and we would like to find the best Hermitian operator A with 0 ≤ A ≤ 1 to distinguish between these two states. In symmetric testing, we are minimizing the error 1 2 (α + β). In the asymmetric case, we are minimizing the type II error β under the condition that the type I error α is less than a given ε.
This can be formulated geometrically using a parametrization in terms of Pauli matrices. Defining the four-vector of 2 × 2 matrices σ = (σ 1 , σ 2 , σ 3 , 1), we write 22) in terms of two four-vectors a, b. From Tr ρ = Tr σ = 1, we have that a 4 = b 4 = 1. We parametrize the Hermitian operator A using a four-vector c as Figure 1: Geometrical problem for the one-shot optimal measurement of a qubit. We optimize over a vector c in R 4 and plot here the coordinates (c 1 , c 2 , c 4 ) (suppressing c 3 ). The condition 0 ≤ A ≤ 1 restricts c to lie in the gray diamond. Left: Symmetric testing. This corresponds to minimizing the product ( b− a)· c. The optimal vector c is the point on the black circle that is most opposite to b − a. Right: Asymmetric testing. This corresponds to minimizing β = b · c under the condition α = 1 − a · c ≤ ε, which restricts c to be above the green plane. The intersection of this plane and the boundary of the diamond and is the black circle, on which the optimal c must lie. In both cases, we show the optimal solution in red. The values chosen for these plots are a = (−0.3, 0.3, 0, 1), b = (0.5, 0, 0, 1) and ε = 0.1.
The type I and type II errors take the form The condition 0 ≤ A ≤ 1 gives 0 ≤ c 4 ≤ 1 and This defines a diamond in R 4 depicted in gray in Figure 1. Then, we have two different optimization problems corresponding to symmetric or asymmetric testing.
Symmetric testing. This is depicted in the left of Figure 1. Here, we have to find the vector c that minimizes ( b − a) · c under the condition that c lies inside the gray diamond. We can see that the optimal c lies on the circle corresponding to c 4 = 1 2 and c 2 1 + c 2 2 + c 2 3 = 1 2 (depicted in black). We can write down the solution explicitly as which is shown in red.
Asymmetric testing. This is depicted in the right of Figure 1. In this case, we have to find the vector c that minimizes β = b · c under two conditions: the requirement 0 ≤ A ≤ 1 forces c to lie inside the gray diamond and the constraint α ≤ ε implies that c must lie above the green plane. The optimal c is inside the intersection region where these two inequalities are saturated (shown in black) and is shown in red. It is also possible to write down explicit expressions for the optimal vector c by solving the quadratic equations that define it.
Perturbative hypothesis testing
In this section, we study quantum hypothesis testing in a pertubative regime. We consider the case where the alternative hypothesis and the null hypothesis states belong to a one-parameter family, and are perturbatively close. This setting is natural in many applications. We will derive a new joint bound on the type I and type II errors, and a universal lower bound on the ratio of the relative entropy variance to the relative entropy, for systems with a finite dimensional Hilbert space.
We are interested in a one-parameter family of states, with the two states related by the series expansion 7 where λ is a small parameter. This setting is natural in many applications of hypothesis testing. For example, consider the analysis of environment-parametrized quantum channels [20], where a system is interacting with an environment whose state is dependent on a parameter with unknown value.
As concrete examples, [20] studied thermal and amplifier channels, where the environment is a thermal state parametrized by the temperature. The problem then is to distinguish two channels with two nearby temperatures, differing by a small parameter λ.
Another motivation is to consider CFT reduced density matrices in subsystems in the limit where the subsystem size is perturbatively small. An example could be the eigenstate thermalization hypothesis, in which expectation values of reduced density matrices of high energy eigenstates appear close to thermal, and it is of interest to study how the system responds to changes in the ratio of the subsystem size to the global system size. Another setting is to study global thermal states reduced to a subsystem, and consider the dimensionless ratio of the subsystem size to the thermal wavelength as a parameter to vary. We study optimal measurements for such subsystems in section 7.
A perturbative bound on errors
The quantum Stein's lemma was derived by first proving a bound [45] and then showing that it can be achieved [46]. For the first part, the following bound was used: which holds for a general measurement A (n) and any n. This can be seen as a bound on how good a measurement can be. It characterizes the trade-off between the two types of errors: α n and β n cannot be made arbitrarily small at the same time.
The bound (3.2) can be seen as a "first order in n" bound that holds for a general measurement. We will now derive a "second order in n" bound that holds for a restricted set of measurements that are optimal at first order in n. This consists of all the measurements with errors satisfying the two conditions for some fixed choice of ε and E 2 . The refinement of the Stein's lemma implies that with saturation for the optimal measurement. In the notation of section 2.2, we have α n ≥ α * n (E 2 ) and β n ≥ β * n (ε), which implies that We can then use the asymptotic estimate to obtain the bound This is a bound on the measurements satisfying (3.3) and can be interpreted as a second order in n refinement of (3.2). It also characterizes the trade-off between the two types of errors, implying that we cannot make both α n and β n too small. Note that this also gives a bound on the LHS of (3.2) since we have (1 − α n )(− log β n ) ≤ log α n log β n . It becomes stronger than (3.2) for We now consider measurements satisfying (3.3) in the perturbative regime (3.1), taking ε and E 2 to be independent of λ, and we consider the perturbative version of the upper bound (3.7). As will be shown in the next subsection, the leading terms of both the relative entropy and the relative entropy variance are quadratic in λ: In the perturbative limit, we see that at leading order where we have restricted to E 2 < 0 for α * n (E 2 ) to be close to zero rather than close to one. Note that α * n (E 2 ) is non-perturbative in λ, which is a consequence of the fact that the variance becomes small in the perturbative λ → 0 limit. Because the estimate for α n is obtained using the central limit theorem, it has an error of order n −1/2 . As a result, we can trust the above result only in the regime where n is non-perturbatively large: where c is some positive constant. We can now consider the perturbative λ → 0 limit of (3.6) and we find Interestingly, this gives a finite answer in the λ → 0 limit. This implies the bound which holds on all measurements satisfying the conditions (3.3).
In the next subsection, we will obtain a general lower bound V (2) (ρ σ) ≥ 2S (2) (ρ σ) which is saturated when ρ and σ commute at first order in λ. This implies that the above bound becomes log α n log β n ≤ nE 2 It is interesting to note that this bound is universal in the sense that it is independent on the state. It is saturated for the optimal measurement if and only if ρ and σ commute at first order in λ.
Lower bound for the ratio
We will now prove a lower bound on the ratio V (ρ σ)/S(ρ σ) in the perturbative regime (3.1).
The relative entropy has the perturbative expansion with no linear term, because S(ρ σ) ≥ 0 with saturation at λ = 0. The perturbative relative entropy S (2) (ρ σ) is given by [49] 8 where L is the logarithmic derivative (3.16) Relative entropy variance has a similar expansion and the linear term vanishes again, since V (ρ σ) ≥ 0 with saturation at λ = 0. Then, where the perturbative variance is given by 9 Since perturbative relative entropy and variance have the same behaviours for small λ, their ratio is finite in the limit λ → 0: Our main result is the following universal lower bound for this ratio: Theorem 1. Let ρ(λ) be a one-parameter family of density matrices over a finite dimensional Hilbert space. Given the expansion ρ = σ + λρ (1) + λ 2 2 ρ (2) + O(λ 3 ), the ratio obeys the lower bound with an equality if and only if σ, ρ (1) = 0.
To prove the theorem, we need an expression for L in the eigenbasis of σ. Let the eigenvalues of σ be λ i . Then a generic function f (σ + X) has the following expansion in the eigenbasis of σ: Applying this to to log σ + λρ (1) , we can identify ij is also diagonal with eigenvalues λ (1) i , then L is diagonal with eigenvalues λ (1) i /λ i : where we used A(1) = 1. With these ingredients, we can prove theorem 1. We prove that Tr (σL 2 ) ≥ Tr (ρ (1) L) with an equality if and only if σ, ρ (1) = 0. Applying this inequality to V (2) (ρ σ) = 2 Tr(σL 2 ) then proves the lower bound. We emphasize that the proof is inherently finite dimensional and does not directly apply to infinite dimensional Hilbert spaces.
Proof. Assume σ, ρ (1) = 0. In the eigenbasis of σ, we can write where on the second line, we used (3.22). Using and relabeling the dummy indices i ↔ j, the second term can be written as is symmetric in i, j. Thus the second term in (3.26) can be written as We get Tr We also used A(1) = 1 in the diagonal term. As illustrated in Figure 2, it can be shown that Because of this and ρ (1) ij L ji > 0, when λ i < λ j , we get where the final equality follows by using the symmetricity of ρ (1) ij L ji . We finally get An interesting question is whether there exists special classes of density matrices for which there is also a constant upper bound for the ratio (3.19). Such an upper bound would imply an upper bound for the perturbative variance by perturbative relative entropy. To gain more intuition, it is useful to study the lower bound (3.20) in explicit examples. At least in the simple examples studied next, no upper bound appears. 10
Single qubit
We consider a single qubit example for which the Hilbert space is two dimensional. A general initial density matrix σ has two eigenvalues which we parametrize as 1 2 + a and 1 2 − a with − 1 2 < a < 1 2 . Working in the eigenbasis of σ, we consider the following one-parameter family of states ρ(λ) = σ + λρ (1) : where a, λ ∈ R. The eigenvalues of ρ(λ) are and the positivity of p − requires that Hence we expect saturation of the lower bound when a = 0. Relative entropy and its variance can be explicitly computed for the states (3.36), but the expressions are quite complicated. For a = 0 they are so that the lower bound is saturated as expected in this case. For a = 0 we can expand the non-perturbative expressions of S, V or use the perturbative formulas (3.15) and (3.18) directly.
The results agree and are given by We find that the ratio obeys the lower bound with an equality if and only if a = 0 as required by Theorem 1. The ratio is depicted in Figure 3.
Maximally mixed initial state
In the above single qubit example, the lower bound is saturated when σ is proportional to the identity matrix, or in other words, when σ is maximally mixed. This should hold more generally for arbitrary perturbations ρ (1) in Hilbert spaces of dimension N ≥ 2, because the identity matrix commutes with all matrices. So let 1 N be the N -dimensional identity matrix and let σ = (1/N )1 N ≡ σ max be maximally mixed. To check saturation of the lower bound (3.20) we can use the fact that relative entropy and relative entropy variance generally reduce to von Neumann entropy S(ρ) and capacity 12 C(ρ) when σ = σ max : where ρ is arbitrary. Computing the expansions of von Neumann entropy and capacity explicitly using ρ = σ max + λρ (1) + O(λ 2 ), we find Combining with (3.48), we get as expected. 11 The proportionality constant is fixed by normalization to be the same. 12 By capacity we mean the quantity C(ρ) = Tr [ρ(log ρ) 2 ] − S(ρ) 2 , which for a reduced density matrix is known as the capacity of entanglement (other names include for example variance of surprisal and varentropy), see Appendix B.1. For a thermal state ρ β , it becomes the heat capacity C(β). 13 This is of course in agreement with the general definitions for V (2) (ρ σmax) and S (2) (ρ σmax).
Two thermal states
Let us consider two thermal states ρ 2 and ρ 1 of the form When the Hamiltonian H is quadratic in creation/annihilation operators, the states are Gaussian, so the result should reduce to the previously studied case in [20]. With a straightforward calculation, we obtain where all the terms involving logarithms of traces have cancelled. From this equation we recognize the heat capacity C(β 2 ) of a thermal state and we end up with a simple result (3.54) In the limit β 1 → 0, ρ 1 becomes a maximally mixed state, and the relative entropy variance reduces to the heat capacity, On the other hand, in the limit β 2 → ∞, ρ 2 reduces to the ground state, and the relative entropy variance vanishes (along with C(β 2 ) → 0). 14 Clearly, [ρ 1 , ρ 2 ] = 0 for all temperatures β 1 and β 2 so that the lower bound (3.20) should be saturated for temperature perturbations β 2 = β 1 + λβ (1) + O(λ 2 ). We can check this explicitly. Relative entropy is given by which expanded to second order in λ gives where C(β 1 ) is the heat capacity of the initial thermal state ρ 1 . Because (β 2 − β 1 ) 2 is second order in λ, we can just replace C(β 2 ) by its initial value C(β 1 ) to obtain variance of relative entropy (3.54) at order O(λ 2 ). We get which saturates the bound (3.20). Interestingly, non-perturbative relative entropy variance between two thermal states turns out to be proportional to the capacity of entanglement (3.54). This might have implications for thermodynamics of AdS black holes in the AdS/CFT correspondence where the holographic dual of the capacity of entanglement is known [50,51]. However, the holographic dual of relative entropy variance is not yet known, but further results in this direction will be reported in upcoming work [52].
Relation to parameter estimation
The framework of perturbative asymmetric hypothesis testing is related to parameter estimation and quantum Fisher information [53]. Quantum parameter estimation is the problem of determining the value of a parameter λ appearing in a density matrix ρ(λ) by performing n independent measurements of an observable E(x). For each measurement, the probability of the outcome x is Denoting the outcomes of n measurements by x i , which are random variables, an estimator is a function λ est = λ est (x 1 , . . . , x n ) used to estimate λ from the data {x i }. Suppose that the estimator is unbiased so that the quantum Cramér-Rao bound then states that is the quantum Fisher information [54]. Here, the symmetric logarithmic derivative operator L λ is defined implicitly via dρ dλ We focus on states ρ(λ) = σ + λρ (1) with λ 1 that are perturbatively close to ρ(0) = σ. Setting λ = 0 in the above equations gives The bound (3.64) gives the best accuracy for estimating the small parameter λ. Quantum Fisher information (3.65) is closely related to perturbative relative entropy 15 which has a similar expression (3.15). In the eigenbasis of σ with eigenvalues λ i , the symmetric logarithmic derivative has the expression and can be compared with the expression (3.22) for the logarithmic derivative L . When [σ, ρ (1) ] = 0, the two expressions are equal: are the eigenvalues of ρ (1) in the eigenbasis of σ. In general, we can prove the following inequality whose proof is similar to the proof of Theorem 1.
Proof. Assuming [σ, ρ (1) ] = 0, we have and relabeling the dummy indices i ↔ j in the second term, we get where we used L ii = L ii in the last term. Applying the inequality which is displayed in Figure 4, we obtain where the inequality is strict. Assuming [σ, ρ (1) ] = 0, the cross-terms vanish in (3.68) and We can also combine (3.67) with the lower bound (3.20) to give with equality if and only if [σ, ρ (1) ] = 0. This shows that both S (2) and V (2) /2 give quantum Cramér-Rao bounds, although the quantum Fisher information F provides the tightest bound. The inequality (3.67) provides a heuristic connection between perturbative hypothesis testing and parameter estimation. Suppose that the estimator is asymptotically normal, that is the probability distribution for the value of the estimator 16 is effectively described by a Gaussian distribution for large n. Then the Cramér-Rao bound (3.64) implies that the optimal probability distribution for the estimate is This distribution (3.74) is similar to the optimal type II error probability in asymmetric hypothesis testing (2.13) between two perturbatively close states σ and ρ(λ) = σ + λρ (1) : where λ is fixed here. The inequality (3.67) then implies that This can be interpreted heuristically as follows: the binary problem of distinguishing ρ(λ) from σ is easier than estimating the exact value of λ.
Generalities on measurements
In this section, we compare different measurement protocols in a setting where we have a large number n of copies of a physical system. We begin by discussing independent measurements on the n copies, and explain why they fail to be optimal. We then turn to optimal measurements for distinguishing between two states ρ and σ in the context of asymmetric hypothesis testing. Following section 2.2, we call a measurement optimal if it saturates the refined quantum Stein's lemma in the asymptotic limit n → +∞. We would like to understand this optimal measurement in order to apply it in many-body systems in the remainder of this paper. We also consider the likelihood ratio test, which is optimal among the classical measurements. Simple examples where these measurements can be described and tested are then discussed. In Appendix A, we describe and discuss similar measurements for symmetric hypothesis testing. We recall that we take n copies of the system so that we have to distinguish between the states ρ ⊗n and σ ⊗n in the asymptotic limit n → +∞. More precisely, we look for a Hermitian operator A (n) with 0 ≤ A (n) ≤ 1 which minimizes the type II error β n = Tr σ ⊗n A (n) while ensuring that the type I error α n = Tr ρ ⊗n (1 − A (n) ) remains bounded.
Independent measurements
The likelihood ratio test and the optimal measurement, which are described below, use in a crucial way correlations between the n copies. In this section, we demonstrate that independent measurements perform badly. A trivial but notable exception is the case where ρ is a pure state, for which the optimal measurement is simply the projector onto this pure state on each copy. This example is discussed in section 4.4.1.
Let's consider an independent measurement, by which we mean a factorized measurement of the form and denote a which satisfy 0 < a i < 1 and 0 < b i < 1. The type I and type II errors are then given by We see that the type I error α n becomes dangerously uncontrolled in the asymptotic limit. To obtain a bounded type I error, we have to make the a (n) i tend to 1 as n → ∞. This implies that the operators A (n) i should become close to the identity. This will make the b (n) i also close to one and spoil the type II error β n .
To illustrate this argument, consider the following example. Let's pick where B is some bounded positive Hermitian operator. This ensures that the type I error remains smaller than 1, since we have However, we see that the type II error is Thus we see that β n goes to a finite limit as n → ∞, instead of decaying exponentially to zero, as in an optimal measurement. Hence, we expect that in general independent measurements should be far from optimal.
We can reformulate the independent measurement optimization as follows. Denote We then have to impose i v ). This leads us to consider the function If the function f (x) is convex, the optimal choice is to choose one of the v (n) i to be equal to − log(1 − ε) while taking the others to be equal to zero. In other words, multiple measurements yield in this case no improvement over a single measurement.
If, on the other hand, f (x) is concave, then the optimal choice is to choose all v (n) i equal to each other, and the resulting error is whose detailed form for large n depends on the small ε behavior of β * 1 (ε). Of course, if f (x) is neither concave or convex, a more detailed analysis is required.
Optimal measurement
Let's now describe an optimal measurement which was used in [37] to prove the quantum Stein's lemma. Although we will often refer to it as the optimal measurement, it is important to note that it is not unique. 17 We define the modular Hamiltonians K and K by We consider n copies of the system with the states σ ⊗n and ρ ⊗n labeled by i = 1, . . . , n. We denote by {|E } and {| E } the set of normalized eigenstates of σ ⊗n and ρ ⊗n . They are of the form and are labeled by their eigenvalues of K and K respectively. We can define the average modular operators We will use the notation |E| and | E| to denote the eigenvalues of the states |E and | E for the average modular operators. In other words, To describe the optimal measurement, we decompose the state | E in the {|E } basis We then restrict the sum only to the states |E satisfying the acceptance condition |E| − | E| ≥ E for some fixed E that we will call the acceptance threshold. This defines the states We define the acceptance subspace The optimal measurement is then the projection onto this subspace: Unfortunately, explicit constructions of the acceptance subspace and the projection are non-trivial even in simple applications, as we will see.
To obtain the optimal type II error β n for a bounded type I error α n ≤ ε, the optimal acceptance threshold is As explained in section 2.2, this measurement leads to a bounded type I error α n ≤ ε and a type II error exponent The proof of optimality of this measurement is given in [37].
Likelihood ratio test
The optimal measurement described above is in general rather complicated to implement. In this section, we review a simpler measurement, which is efficient and becomes optimal in the classical case, when ρ and σ commute [25]. When ρ and σ are viewed as classical probability distributions, this measurement is the likelihood ratio (Neyman-Pearson) test which is known to be optimal in classical hypothesis testing.
In this setup, we consider two probability distributions P and Q on the same probability space Ω, and we would like to distinguish them by making a test modeled as a function A : Ω → [0, 1]. Let's consider n copies of the system. The task is then to distinguish between the probability distributions P (n) and Q (n) on Ω n defined as with a function A (n) : Ω n → [0, 1]. The optimal type II error is defined as where E P denotes the expected value in the probability distribution P. We are interested in the asymptotic limit n → +∞. We have the estimate (4.21) The first order in n result was originally obtained by Chernoff and Stein and the second order correction by Strassen [56] (see [57] for a review). In the above expression, the relative entropy and its variance are defined as the first and second cumulant, in the probability distribution P , of the log-likelihood ratio log P (x) The measurement that achieves optimality (in this classical setting) is the likelihood ratio test. It is a deterministic test, choosing the function A (n) to be an indicator function which takes the value 1 on an acceptance subspace, the subset of x ∈ Ω n satisfying the acceptance To apply this measurement to quantum systems, we need to express it in quantum mechanical language using the setup described in the previous section. We take the probability space Ω = {|E } to be a basis of eigenstates of K (n) = − 1 n log σ ⊗n . The probability distributions are the ensemble probabilities given by and we have 1 n log Q (n) (E) = |E| from the definition (4.12). The acceptance condition is which can also be written more transparently as We note that this measurement only involves the diagonal part of ρ (defined with respect to the basis defined by σ), which we denote We can then define the "classical" acceptance subspace To implement the likelihood ratio test, we then replace the indicator function of the acceptance subspace by an operator, the projector onto H C : When ρ and σ commute, it can be seen that H C = H Q so this is actually the optimal measurement described in the previous subsection. From the relation with classical quantities S(P Q) = S(ρ D σ) and V (P Q) = V (ρ D σ), we see that the optimal choice of threshold is and leads to a bounded type I error α n ≤ ε and a type II error exponent In general, this measurement is less efficient than the optimal measurement because the monotonicity of relative entropy implies that since the map ρ → ρ D is (completely) positive and trace preserving [58]. Nonetheless, this measurement achieves an exponentially decreasing type II error for bounded type I error. The likelihood ratio test with n LRT copies of the system achieves the same accuracy to leading order as the optimal measurement with n opt copies with In the simple example of a qubit, the likelihood ratio test can be implemented using a quantum circuit, displayed in Figure 5, and a comparison between the likelihood ratio test and the optimal measurement is shown in Figure 6.
Examples
In this section, we describe the optimal measurement in some simple cases.
Pure versus mixed
We consider the simplest possible example. We take ρ to be a pure state and σ to be a general mixed state In this case, an optimal measurement is just the projector A = |ψ ψ|. On n copies of the system, we take the factorized measurement A (n) = A ⊗n . The type I error α n = 0 and the type II error is given by which indeed saturates the quantum Stein's lemma. The second order asymptotics in n do not play a role because according to the proposition explained in section B.2.
Global thermal states
We consider two thermal states with different temperatures and we would like to distinguish between them. The modular Hamiltonians are where the free energy is defined as The relative entropy and variance are We are in a situation where ρ and σ commute so the likelihood ratio test is actually the optimal measurement. It can be described as follows. We consider n copies of the system and we define the average Let {|E } be a basis of eigenstates of σ ⊗n . These are formed from eigenstates of H. Notice that we are using the actual energies to label the states as opposed to using the eigenvalues of the modular Hamiltonian. In particular, we denote by |E| the average energy of the corresponding state The measurement is simply the projection onto the states in this basis with the acceptance condition This translates into the condition We have to distinguish two cases depending on the sign of β 1 − β 2 . The acceptance condition is where the threshold energy is The measurement is then a projection on the states satisfying the condition It is interesting to note that the optimal measurement actually doesn't depend on the value of β 1 , but only on whether it is bigger or smaller than β 2 .
Measurements of a qubit
In this section, we consider a simple system to illustrate the measurements that we have been discussing. The system is just a single qubit in two possible states ρ or σ. We are interested in the optimal measurement on n copies of the system in the asymptotic limit where n is large.
Likelihood ratio test
The best classical measurement is the likelihood ratio test and was discussed in section 4.3. In this section, we will write it explicitly for the case of a qubit. We will also give a quantum circuit that realizes it.
Setup
Let {|0 , |1 } denote the basis which diagonalizes σ, with 0 ≤ p ≤ 1. The likelihood ratio test only involves the diagonal part ρ D of ρ, which we can write as A basis of the Hilbert space for the n copies is given by the states labeled by the bit strings a 1 a 2 . . . a n . The acceptance condition for the likelihood ratio test takes the form Denoting by n(E) the number of 1s in E (the Hamming weight of the bit string), this is where we use the ceiling function · so that n * is an integer. The optimal value for E is given in (4.31) in terms of the relative entropy and its variance and leads to the acceptance threshold The acceptance subspace is 8) and the measurement is the projection onto H C . We can also identify H C with a subset of {0, 1} n , the complement of the Hamming sphere of radius n * − 1 centered at the zero string.
Quantum circuit for the likelihood ratio test
We now describe a quantum circuit that implements the likelihood ratio test. In the language of quantum computing, our problem can be posed as follows. We are given a blackbox gate V acting on a pair of qubits producing a state we wish to identify. More explicitly, acting with V on |00 and tracing over the second qubit gives a density matrix ρ V for the first qubit, and we assume that there can be only two possibilities: where ρ and σ are known a priori but we do not know the outcome. Our goal is to determine which alternative is true by making a measurement on n of these pairs of qubits, and operating only on the first qubit of each pair. The likelihood ratio test is the best classical measurement and becomes the optimal measurement when ρ and σ commute. From the previous analysis, the measurement is a projection P H C onto the acceptance subspace (5.8). Hence, we would like to compute If this quantity is close to one, we declare that ρ V = ρ while if it closer to zero, we declare that ρ V = σ. Because the state V |00 is a purification of ρ V , we can rewrite (5.10) as the overlap where P H C only acts on the first qubit on each pair. This quantity can be computed using the quantum circuit depicted in Figure 5. We start with n pairs of qubits in the state |0 together with a register of n auxiliary qubits in the state |ψ . We first act with V on each pair. We then use a controlled-I gate where I is a "increment" gate which counts the number of 1s in the register while preserving the superposition.
The register is designed to incorporate the threshold condition associated with the projection P H C by measuring the overlap of some of its qubits with some fixed state. For example, we can Circuit that prepares the state Ψ Swap test to compute the overlap take a register of n + 1 qubits and count the number of 1s as follows. We initialize the register in the state |ψ = |1 ⊗ |0 ⊗n and define I to be the cyclic permutation i → i + 1 on the n + 1 qubits. If the number of 1s is k, all the qubits in the register are in the state |0 except for a |1 in the (k + 1)-th position. Then, we can see that by measuring the overlap of the first n * qubits of the register with |0 ⊗n * , we exactly implement the projection P H C . 18 Indeed, all the states with n(E) ≤ n * − 1 are projected out. Measuring at the same time the overlap of the n pairs of qubits with |00 ⊗n precisely gives (5.11). The remaining qubits of the register should remain unmeasured. This overlap operation should be implemented using a swap test between the 2n + n * qubits consisting of our n qubit pairs and the n * first qubit of the register, with 2n + n * auxiliary qubits in the state |0 . This allows us to measure the overlap (5.11) to arbitrary precision using iterations of the circuit. We note that the register can be optimized by using only log n qubits and storing the number of 1s in binary instead of unary.
Optimal measurement
We now investigate the optimal measurement for a qubit. When ρ and σ commute, the optimal measurement reduces to the likelihood ratio test, which was described in the previous section.
Here, we would like to study the optimal measurement more generally, in a setup when ρ and σ do not commute. We consider a very simple non-commuting example, taking Moreover, we assume that the change of basis is just a rotation matrix In a basis where |0 = 1 0 and |1 = 0 1 , we have and we have e −E 0 + e −E 1 = 1 so it is useful to define p such that and we have p ≤ 1 2 . The relative entropy is The basis states of σ and ρ are defined as bit strings |E = |a 1 a 2 . . . a n , a i ∈ {0, 1} , (5.18) We define n(E) to be the number of 1s and n( E) to be the number of 1s. The acceptance condition with threshold E takes the simple form This allows us to define the states that span the acceptance subspace. For every E, we define The optimal measurement is then the projector to the acceptance subspace H Q = span Formally, we first define the operator so that the acceptance subspace H Q is the image of Q. The optimal measurement is the projector onto it, given by where G ≡ Q † Q is the Gram matrix of the vectors (5.20): the 2 n × 2 n matrix of the overlaps ξ( E 1 )|ξ( E 2 ) . The above expression is well-defined because the restriction of G to the image of Q † is invertible, and P H Q can be extended by zero on the vectors that are annihilated by Q † . Note that the above expression makes it clear that P 2 H Q = P H Q . We see that explicit construction of the projector involves finding the inverse of the Gram matrix G, which is a challenging computational problem.
Complexity of measurements. It is intuitively clear that the optimal measurement is more complicated than the likelihood ratio test, since the former involves a more complicated construction of the acceptance space and the projector. It would be interesting to formalize this intuition by defining various notions of complexity of a measurement. The definitions of complexity could be based on different resources, and could also depend on the algorithm carrying out the measurement or computing the projector. A simple algorithm independent characteristic resource is the size of the acceptance subspace, or more precisely, its dimension. If one of the states to be compared is pure, the optimal measurement involves the projection to the state. In this simplest case, the acceptance space is smallest with just one state, while its complement is maximal. Hence, for comparing the complexity different measurements, it is helpful to define the minimum dimension of the acceptance space and its complement, This defines a complexity measure which depends on the predetermined maximum size ε of the type I error, the number n of identical copies, and the two states ρ, σ through the acceptance threshold n * . Once these are given, we can compare the minimum acceptance dimension dim H < acc of the optimal measurement and the likelihood ratio test. The latter depends on the volume of the Hamming sphere and its complement, so we have an analytical formula dim H < acc,C = min For the optimal measurement, finding an analytical formula or at least an estimate for the minimum acceptance dimension dim H < acc,Q is a mathematical challenge. We study it numerically for n up to 14, by performing the Gram-Schmidt orthogonalization of the vectors |ξ( E) that span the acceptance space and then counting the number of orthonormal basis vectors. The (very limited) investigation suggests that dim H < acc,Q grows exponentially with n with a faster rate than dim H < acc,C . 19 This indicates that already at the level of the acceptance spaces the optimal measurement is "more complex" than the likelihood ratio test. There are additional levels of complexity involved in computing the Gram matrix and finding its inverse, it would be interesting Figure 6: Optimal quantum measurement (blue) vs. optimal classical measurement (yellow). We see (left plot) that the optimal measurement gives a type II error β that is one order of magnitude smaller for n ∼ 14. We also see (right plot) that the minimum acceptance dimension is much larger for the optimal quantum measurement than for the optimal classical measurement. The curves with the logarithmic y-axis indicate exponential growth in n with a faster rate for the optimal measurement. These plots are done with the parameters θ = π 3 , p = 0.015, ε = 0.2 using a Mathematica notebook that we have made publicly available [61].
to develop rigorous complexity measures taking into account everything involved in constructing the projection.
Numerical results. The numerical implementation of the optimal measurement and the likelihood ratio test are done in a Mathematica notebook that we have made publicly available [61]. We analyze the numerical implementation of the measurements only up to n = 14, but this already proves sufficient to see some interesting features. For the threshold value E, we use the optimal value (4.17). Including the second order term (in n) is necessary because n is not very large (the second order term brings the ε-dependence). Choosing parameter values such that the finite n effects are not too strong, we see that the optimal measurement is better by an order of magnitude. This is depicted in Figure 6. This demonstrates that quantum hypothesis testing is much more efficient than classical hypothesis testing. The tradeoff is that quantum hypothesis testing is more complex. The growth of the minimum acceptance dimension with n is exponential for both measurements, but the growth rate appears to be faster for the optimal quantum measurement. It would be interesting to carry out a more extensive numerical investigation and see how generic this feature is.
Some mathematical observations. We finish this section by providing some partial results to the more challenging problem of constructing the optimal measurement in the general case. The partial results illustrate interesting connections to combinatorics and coding theory, which should inspire further study. For the rest of this discussion, we will restrict to the case θ = π 4 where many simplifications occur. In this case, the rotation matrix (5.14) is just the Hadamard matrix and we have | 0 = |− and | 1 = |+ . In this case, we have a rather explicit description of the states |ξ( E) : where n 01 (E, E) is the number of pairs (a i ,ã i ) which are equal to (0, 1) using (5.18). We now need to do the Gram-Schmidt procedure for these vectors to obtain a basis of H Q . This requires to compute the Gram matrix G of overlaps ξ( E 1 )|ξ( E 2 ) . The overlaps can be expressed as partial sums of products of binomial coefficients. Using a generalization of Vandermonde's identity, we can re-express the overlap as follows. Define the polynomial where n( E 1 + E 2 ) is the number of 1s in the the boolean sum (i.e. the sum in the ring Z 2 ) of E 1 and E 2 . The overlap is then obtained as a partial sum of the coefficients P n,k where n * ( E 1 , E 2 ) = max(n * ( E 1 ), n * ( E 2 )). We refer to Appendix C for details on the derivation of this formula. There, it is also shown that P n,k are related to binary Krawtchouk polynomials K k (x; n), and the overlaps of the Gram matrix take the explicit form It is also interesting that this problem seems related to coding theory and combinatorics. In Appendix C, we show that the Gram matrix is an element of the Terwilliger algebra [62] of the Hamming cube H = {0, 1} n (see [63,64]). This is done by identifying the labels ξ( E) as subsets of H, given by the supports of the bit strings E. In this way we obtain the explicit expansion in the basis {M t ij } of the Terwilliger algebra. Identifying the expansion coefficients x t ij then allows at least a block diagonalization of G, exploiting the results of [63], which may turn out to be a useful step towards finding G −1 , and for the construction of the projector P H Q .
Measurements in fermion chains
In this section, we study subsystem measurements in spinless fermion chains. Our goal is to construct measurements that are optimal in distinguishing between two different states, while acting only on a small subsystem. We will take these two states to be two thermal states with different temperatures. We will mostly focus on simpler hopping models, but some of our results also apply to fermion chains with Hamiltonians being arbitrary bilinears of creation and annihilation operators. This setup is the discrete analog of the chiral fermion CFT that will be studied in section 7.2.2. For small subsystem sizes, we will be able to give a more explicit description of the optimal measurement.
Spinless fermion chains
We consider spinless fermions on a chain of length L → +∞ with periodic boundary conditions. 20 The total Hamiltonian of the chain is and the fermion operators obey the anticommutation relations Here is real symmetric andB is real antisymmetric to ensure Hermiticity. In addition, they are taken to be positive semi-definite so that the total energy is non-negative. The hats are used to denote L × L matrices supported on the whole chain, to be distinguished with matrices restricted to a subsystem that we study below.
As an example, the anisotropic XY model can be mapped to a Hamiltonian of the form (6.1) via a Jordan-Wigner transformation [65]. We will consider the simpler isotropic XY model in section 6.3.3 below.
Diagonalization of fermion Hamiltonians
The Hamiltonian (6.1) can be diagonalized by the Bogoliubov transformation where the vectorsv k ,û k are solutions of the equations where the constant sets the zero point energy. 21 The operators η k , η † k generate a Fock space of positive energy excitations. 20 In what follows, there is a possibility of an order of limits issue with the thermodynamic L → ∞ and the perturbative λ → 0 limits. To circumvent the issue, we simply take L to be larger than any scale in the problem and take the perturbative limit λ → 0 while keeping L fixed. We thank the referee for pointing out this subtlety. 21 The constant is explicitly 1 For fermion chains withB = 0, the diagonalization procedure can be made more explicit. One first solves the eigenvalue problemÂv k = Λ kvk which allows to writê A =v Dv (6.8) whereD is a diagonal matrix with entries Λ k . Then, performing the Bogoliubov transformation the Hamiltonian becomes where Λ k can be negative. The form (6.7) with absolute values is obtained by performing an additional particle-hole transformation on a k , a † k (which is automatically included in (6.4)). For our purposes, the form (6.10) is sufficient and the Bogoliubov transformation (6.9) is a special case of (6.4) withû =v.
Reduced density matrix of a subsystem
We consider a subsystem V = {1, . . . , } containing fermions, and place the chain (6.1) in a global thermal state 22σ = e −βH Tr e −βH . (6.11) The reduced density matrix (RDM) on V is obtained by tracing over its complement V c and takes the form where the modular Hamiltonian 23 K takes the same form as total Hamiltonian of the chain: The matrices A, B are different from the matricesÂ,B. Indeed, the modular Hamiltonian K, which depends on the global state, is not equal to the Hamiltonian H| V of the subsystem. The matrices A, B in the modular Hamiltonian can be obtained from the following equations [28,66] Tr which follow from the fact that expectation values of operators supported in the subsystem can be computed using either the global state or the reduced state. The two-point functions are sufficient, because higher-order correlators reduce to two-point functions by Gaudin's theorem (an extension of Wick's theorem). Since both σ andσ are exponentials of one-body operators, these traces can be computed explicitly (see Appendix D) to write the equations in terms of the parameters appearing in K and H. For simplicity, we will restrict to free fermion chains withB = 0, so that the Hamiltonian is Due to the absence of the pair creation/annihilation terms, the anomalous two-point function Tr (σψ † i ψ † j ) = 0 vanishes. This is reflected in the modular Hamiltonian which has B = 0 [28]: The partition function Z can now be easily obtained in terms of A as where the determinant is taken over the matrix indices. Let C denote the thermal two-point function restricted to the subsystem from which we also obtain an expression for Z in terms of C: . (6.20) Hence for free fermions, the reduced density matrix of a subsystem in a thermal state is simply given by the thermal two-point function C.
Relative entropy and its variance for free fermions
We introduce a second global thermal stateρ with temperatureβ. This induces a different reduced density matrix ρ on the subsystem: Let us now compute the relative entropy and the relative entropy variance for the two reduced density matrices. Relative entropy is given by where we have and we used The partition functions are given by (6.20): As a result, we obtain for the relative entropy 26) and the relative entropy variance is given by which doesn't depend on the partition functions. The first term can be written as Because ρ is an exponential of one-body operators, we can use Gaudin's theorem to compute the four-point function [67] (see also Appendix D). The result is and we get The first term equals ∆K 2 ρ which cancels in (6.27) and leaves us with As far as the authors are aware, the expressions (6.26) and (6.33) for relative entropy and its variance have not appeared in the literature before. However, sandwiched Rényi relative entropy between RDMs of a free fermion chain was computed in [35] (see also [36]) and one can check that the relative entropy (6.26) matches with the first derivative of their expression. Unfortunately, we did not manage to compute the second derivative to see whether the result matches with the variance. As an independent consistency check of (6.33), we will see below that it obeys the lower bound (3.20).
The expressions for S(ρ σ) and V (ρ σ) can be written explicitly in terms of eigenvalues and eigenvectors of A, A. We have so that where v k · v l = i v ki v li is the overlap between the eigenvectors. There is also a similar expression for the variance. A further simplification occurs if A and A commute so that their eigenvectors are the same: In this case, one obtains simple expressions The vanishing of the commutator of A, A is equivalent to commutativity of the RDMs [ρ, σ] = 0. This can be seen by performing Bogoliubov transformations on K and K respectively. In a similar way the full Hamiltonian was diagonalized using (6.9), the modular Hamiltonians become If (6.36) holds one finds from (6.38) that c k = c k and c † k = c † k so that [K, K] = 0. In addition, one can check that for a perturbative entanglement spectrum of the form E k = E k + λE (1) k , the expressions (6.37) saturate the lower bound (3.20), as expected for commuting RDMs.
Optimal measurement
In this section, we describe the implementation of the optimal measurement for spinless fermion chains. This involves computing overlaps between eigenstates of two modular Hamiltonians, which can be done using the generalized dick's theorem [38,39]. For free fermions, this gives a prescription on how the overlaps v i · v j between eigenvectors translate into overlaps between eigenstates E I | E J . For completeness, we will consider general modular Hamiltonians of the form (6.13) with nontrivial A and B. We will restrict to modular Hamiltonians of free fermions with B = 0 in the end.
Eigenstates of modular Hamiltonians and their overlaps
To unify the computations, we introduce some convenient notation. Let be -dimensional vectors. We define similarly the -dimensional vectors c, c † and c, c † , and combine them further into 2 -dimensional vectors as Following the analysis for the Hamiltonian of the chain, modular Hamiltonians K, K of the form (6.13) are diagonalized by transformations where The transformation matrices are obtained by solving equation (6.6) for A and B (and similarly for v, u): The matrices v, u, v, u are real and orthogonal so that W, W real and orthogonal as well. 24 They are thus Bogoliubov transformations, because the real Bogoliubov group is the orthogonal group (see Appendix D.1). As a result, the modular Hamiltonians become The exact values of E vac , E vac are not important for the upcoming analysis. From these expressions it follows that eigenstates are generated by acting on two quasi-particle vacua |E vac , | E vac with creation operators. The vacua are defined via 47) and the eigenstates are where we used -bit binary strings to keep track of the occupation numbers of the modes k. The corresponding eigenvalues are We want to compute overlaps between these eigenstates Standard Wick's theorem does not directly apply to correlators of this type because c † i is not the Hermitian conjugate of c i . The trick is to realize that the operators α and α are related via a Bogoliubov transformation T (orthogonal matrix): which is explicitly We introduce the operator T that implements the Bogoliubov transformation T in the Hilbert space [38,39]: and we have that T is unitary since T is real. The expression for T in terms of α is not relevant in what follows. However, if T can be written as an exponential T = e −ΩS , where Ω is the matrix (D.3) and S is antisymmetric, then T is an exponential of one-body operators [38,39]. It follows that | E vac = T |E vac so that all the eigenstates of the modular Hamiltonians are related according to The overlaps (6.50) are therefore and unitarity of T ensures that these overlaps determine a unitary basis rotation in the Hilbert space. All the operators in (6.55) are expressed in terms of the annihilation and creation operators c, c † which allows the use of Wick's theorem. In Appendix D, we show that the overlaps involving two operators are where T 11 = T 22 , T 12 = T 21 are the two × blocks of (6.52) and the overlap between the vacua is The overlaps (6.55) involving more operators can be computed using generalized Wick's theorem [39] and it is non-zero only when n + m = 2t is even. In that case: appearing on the right hand side are the three two-point overlaps (6.56) and we refer to Appendix D for more details. In other words, all the overlaps (6.55) can be expressed in terms of the two-point overlaps (6.56) using the generalized Wick's theorem. The computation of the contractions (6.56) requires the knowledge of v, u and v, u that determine the block matrices T ij according to (6.52). These can be computed from (6.45) knowing A, B and A, B which are obtained from two-point functions in the global state according to (6.14). Although these equations are in general difficult to solve, they become simpler for free fermions, because B vanishes and A is directly given in terms of C according to (6.19). We will demonstrate this below for the XY model.
The power of this approach is that it gives a way to compute the overlaps without the need of the explicit form of the ground states |E vac , | E vac . It can therefore be applied to modular Hamiltonians of the general form (6.13). However, there is one situation where the above computation of the overlaps fails: when det T 11 = 0 so that T 11 is not invertible. This happens when the two quasi-particle vacua are orthogonal.
Overlaps of eigenstates for free fermions
The above algorithm to compute overlaps simplifies for free fermions since B = B = 0 which implies that we can use the Bogoliubov transformations (6.43) with u = v and u = v. Hence all the overlaps are determined by the eigenvectors v, v of the two-point functions C, C.
With B = B = 0, the modular Hamiltonians are As shown before, they take the diagonal form (6.39) after the transformation (6.38): From these we get which is block diagonal. The overlap between the quasi-particle vacua is then where we used the fact that the determinant of vv ∈ SO(2 ) is unity. In this case, the quasiparticle vacua coincide with the true vacuum |E vac = | E vac = |0 (annihilated by ψ i ).
Noting that (T 11 ) −1 = v v , the only non-zero contractions are Because of this, the higher order overlaps (6.55) are non-zero if and only if n = m. The generalized Wick's theorem (6.58) for t = n gives The result (6.65) could have been obtained directly from the correlator (6.50) without reference to the generalized Wick's theorem. For example, inverting (6.38) yields with a similar strategy for the higher order correlators. It is for modular Hamiltonians with B = 0 when the generalized Wick's theorem becomes very useful.
Examples
We now give explicit examples for the general procedure described above.
A single fermion subsystem
The simplest possible subsystem contains only a single fermion. For a generic quadratic modular Hamiltonian (6.13) with = 1, the matrix B does not contribute as it is antisymmetric. Hence modular Hamiltonians of a single fermion at site k = 1 take the form The two-dimensional Hilbert space of the fermion is spanned by the vacuum state |0 and the state |1 ≡ ψ † 1 |0 , (6.68) with a fermion occupying site k = 1. In the above formalism, they are eigenstates of the modular Hamiltonians since we have T = 1 2×2 . The fermion Hilbert space spanned by |0 , |1 is equivalent to the single qubit Hilbert space studied in section 5. The two RDMs of the fermion take the form We see that the RDMs always commute. As a result, the optimal measurement is given by the likelihood ratio test described in section 4.3. The acceptance subspace for the RDMs (6.69) was determined in section 5. Relative entropy and its variance are given by (6.37) and the acceptance condition becomes where n(E) is the number of fermions in the n copies of the subsystem. The optimal measurement is then a projection onto states that contain n * or more fermions.
Two fermion subsystem
The situation is more interesting for subsystems containing more fermions. We consider here a subsystem of two fermions in a free fermion chain, taking the two fermions to be on sites i = 1, 2.
The matrices A, A have two eigenvalues E 1,2 , E 1,2 and eigenvectors which we parametrize as v = cos ϕ − sin ϕ sin ϕ cos ϕ , v = cos ϕ − sin ϕ sin ϕ cos ϕ . (6.72) Using the binary string notation for the eigenstates, we have There is a total of sixteen overlaps. From (6.65), the non-zero overlaps are and Thus the unitary rotation is given by 78) and it acts non-trivially only on the subspace spanned by |E 1 , |E 2 . The basis rotation (6.78) is effectively the same as the one studied in section 5 where the optimal measurement on a single qubit is constructed. The eigenstates |E 1 and |E 2 , with a single fermion on either site 1 or 2, correspond to the rotation between two states of a qubit. In addition, we also have an unrotated qubit. As discussed in section 5.2, the explicit description of the optimal measurement for the one-qubit case is challenging due to the difficult inversion of the Gram matrix. We will thus describe the suboptimal but simpler likelihood ratio test.
Assuming for simplicity that the two eigenvalues of K are equal E 1 = E 2 ≡ E vac + ∆, E 12 = E vac + 2∆ with ∆ > 0, and likewise for the tilded values, we have where E 0 ≡ E vac + log Z and a similar definition of E 0 . The eigenstates of ρ ⊗n , σ ⊗n are |E ≡ |a 1 a 2 · · · a 2n−1 a 2n , (6.80) | E ≡ | a 1 a 2 · · · a 2n−1 a 2n , labelled by 2n-bit strings. The average modular energies are where n(E), n( E) count the number of 1s in the binary strings. The acceptance condition |E| − | E| ≥ E becomes The likelihood ratio test is then the projector Note that E 0 − E 0 cancels in (6.82) with the same term coming from relative entropy once the threshold E = S(ρ D σ) + . . . is substituted. It's also possible to obtain an explicit expression for S(ρ D σ) using the overlaps (6.76).
The acceptance space is given by (the complement of) the Hamming sphere of radius n * centered at zero in the Hamming cube {0, 1} 2n . While the likelihood ratio test is in general a suboptimal measurement, it becomes optimal when the reduced density matrices commute. The next example gives a situation where this happens.
Example: XY model at finite temperature
The isotropic XY spin chain has the Hamiltonian [65] where σ x,y i is the Pauli matrix at site i and the boundary conditions are periodic. In the thermodynamic limit, this Hamiltonian can be mapped to a periodic free fermion chain [65] 26 Hence the Hamiltonian is of the form (6.1) withB ij = 0 and the eigenvectorsv k and eigenvalues Λ k can be found in [65]. Due to translation invariance, the thermal two-point function is a function of i − j only, and in the thermodynamic limit L → ∞, it takes the form ] e β cos q + 1 . which corresponds to ϕ = π/4 in equation (6.72). We see that v is independent of the temperature β and of the distance r. This is true in any translation invariant fermion chain for which the thermal two-point function is of the form (6.88). Now when considering thermal states of two different temperatures, leading to two modular Hamiltonians K and K, the unitary rotation (6.78) between their eigenstates is trivial: U IJ = δ IJ . Hence the RDMs of the two fermions commute and the optimal measurement is the likelihood ratio test. If the fermion chain is not translation invariant this is no longer true, because then the modular Hamiltonians K, K do not generally commute. It is interesting that translation invariance implies commutativity of two-fermion density matrices in global thermal states.
Measurements in conformal field theory
We now turn to the implementation of quantum hypothesis testing in quantum field theory. We will discuss in detail how the measurements described in section 4 are realized as operators acting on states. For simplicity, we restrict to two-dimensional conformal field theory because the infinitedimensional group of conformal transformations in two dimensions allows for a certain flexibility. For an introduction to the subject, we refer to [68].
The physical system we consider will live on a line or on a circle. We will be particularly interested in distinguishing two different states from an interval subregion. Our main technical result is the construction of the optimal measurements for special types of states, studied by Cardy and Tonni [40]. As an illustration, we study the free chiral fermion CFT, which could be viewed as a continuous limit of the discrete fermion chain studied in section 6.
While we obtain some basic technical results in implementing measurements in conformal field theories, we are merely scratching the surface of a vast number of possibilities in the choices of theories and states. As our free fermion case will show, there are interesting analytical challenges when trying to simplify the implementation of efficient measurements.
Subregion measurements
We now describe the situation where we want to distinguish between two states in a CFT 2 while only having access to a subregion. After tracing out over the rest of the system, the two states are given by two density matrices σ and ρ supported in that subregion.
The measurements described in section 4 are given in terms of the modular Hamiltonians. In general, the modular Hamiltonian of a reduced density matrix would be a complicated non-local operator and be difficult to study. For a special class of states in a CFT 2 , the modular Hamiltonian is local: it can be written as a suitable integral of the stress tensor. We will restrict to these types of states in the following two sections, drawing on the results of [40]. We will first describe the optimal measurement in the generic situation, and then explore in some more detail the task of distinguishing between two thermal states at different temperatures in the next section. We will explain how to implement the likelihood ratio test to distinguish between the vacuum and a primary excitation.
Setup
Let's now describe the setup. The CFT 2 is defined on a line or on a circle and the subregion we consider is an interval I = [− 2 , 2 ]. We consider the Euclidean spacetime described by a coordinate z. We cut out little disks of size around the endpoints of I to regulate the entanglement entropy. The boundary conditions are given by two boundary states |a and |b and they contribute a finite amount to the entanglement entropy via Affleck-Ludwig boundary entropies [40].
We consider two reduced density matrices σ and ρ defined on the interval I. The corresponding modular Hamiltonians K = − log σ and K = − log ρ are assumed to be local. As a result, each of them can be viewed as generating a flow along a vector field, as represented on the left of Figure 7. To define the optimal measurement, we are interested in the eigenstates of both K and K, and their overlaps. To obtain a useful description of these states, we will use the flexibility of two-dimensional CFTs to conformally transform the setup to a simpler geometry for each state, as represented on the right of Figure 7. In this simpler geometry, the modular Hamiltonian becomes a dilatation operator, whose eigenstates are easily described.
We first use the conformal map which takes the spacetime to an annulus of width W . 27 More precisely, the interval is mapped to w ∈ [− W 2 , W 2 ], and the imaginary part of w is periodic with period 2π. The modular Hamiltonian in these new variables becomes simple: it just generates translations in the imaginary w direction.
To describe the eigenstates of the modular Hamiltonian, it is useful to consider the universal cover by allowing the imaginary part of w to be unconstrained. The geometry becomes an infinite strip. We can then map it to the upper half plane with The interval becomes a half unit circle C + , ranging from u = 1 to u = −1. As explained in [41], the choice of boundary conditions is such that one can extend this to the other half plane and perform radial quantization on the full plane. The modular Hamiltonian K is simply related to the generator L 0 of dilatations in this geometry: where c is the central charge and the additive constant ensures that Tr e −K = 1 [40]. We refer to [69] for a more detailed discussion of this setup. The upshot of all these manipulations is that we can now relate the spectrum of the modular Hamiltonian to the spectrum of L 0 in the presence of two boundary conditions |a and |b . For example, we can choose |a = |b = |0 where the Cardy state |0 projects onto the vacuum sector of the theory [41], so that the only states in the entanglement spectrum are the vacuum and its descendants.
Iũ L 0 ρ σ Figure 7: The modular Hamiltonians K = − log σ and K = − log ρ are conformally mapped to dilatation operators in the upper half plane. The entanglement spectrum is then obtained using radial quantization. The inverse maps give expressions for K and K in the original spacetime, giving a way to compute the overlaps of their eigenstates, as required to implement the optimal measurement. The modular flows are depicted in blue for K and in orange for K. 29 In the u-plane, we obtain from radial quantization the Virasoro generators where C is the unit circle. This is then translated to an integral over the original interval I: The entanglement spectrum of a state σ can then be generated by acting with these operators on the vacuum. We can use the same procedure for another state ρ using a different map w =f (z) giving an annulus of width W . The spectrum of ρ is then generated by another Virasoro algebra Similarly, the modular Hamiltonian K = − log ρ is them given by Since both Virasoro algebras are written on the interval, we can compare them. Their commutators can be computed using the general commutation relation of two stress tensors in a CFT 2 : We can restrict to the vacuum sector by choosing the boundary condition |a = |b = |0 . Then, the eigenstates of K are given by the eigenstates of L 0 which takes the form Similarly the eigenstates of K at the eigenstates of L 0 and take the form The general commutation relation (7.8) can be used to compute the commutators [L n , L m ], even though this is difficult in practice. This then gives a way to compute the overlaps ∆| ∆ , as required to describe the optimal measurement.
Optimal measurement
The optimal measurement can then be implemented in this language, following section 4.2. Let's now consider n copies of the system. The eigenstates of σ ⊗n and ρ ⊗n are respectively denoted |∆ = |∆ 1 ⊗ |∆ 2 ⊗ · · · ⊗ |∆ n , | ∆ = | ∆ 1 ⊗ | ∆ 2 ⊗ · · · ⊗ | ∆ n . (7.11) Using the formula (7.3), we see that the average modular energies for K and K are respectively where the average conformal dimension is denoted The optimal measurement is then described by first decomposing | ∆ in the {|∆ } basis where we have ∆| ∆ = n i=1 ∆ i | ∆ i . We then restrict the sum over ∆ to those satisfying the acceptance condition K (n) − K (n) ≥ E which is here: This allows us to define the states The optimal measurement is the projector onto the subspace with the choice of acceptance threshold being
Likelihood ratio test
We will see that the optimal measurement is difficult to describe explicitly. A simpler measurement, which is suboptimal but still performs well, is the likelihood ratio test discussed in section 4.3. The measurement projects on part of the spectrum of σ ⊗n . More precisely, it is a projection on the acceptance subspace 19) and the best value of E is given in (4.31). We can rewrite the acceptance condition as where we define the averages To obtain a more explicit description, we should compute ∆| L 0 |∆ , which can be written As a result, a fairly explicit description of this measurement can be given with only the knowledge of the overlaps ∆| ∆ .
Thermal states
As a concrete example of the procedure described above, we can consider the problem of distinguishing two thermal states of different temperatures, having only access to a subregion. We take the subregion to be an interval I = [− 2 , 2 ] in the infinite line. Following [70], the reduced density matrix obtained from a thermal state is associated to the conformal mapping f β (z) = log e 2πz/β − e −π /β e π /β − e 2πz/β (7.23) which allows to obtain the corresponding modular Hamiltonian, as described in section 7.1.1. We consider two reduced density matrices σ and ρ in the interval I obtain from global thermal states of inverse temperature β 1 and β 2 . The corresponding modular Hamiltonians are explicitly where T 00 is the energy density of the CFT and c(β 1,2 ) are normalization constants.
Entropy and variance
In a thermal state at temperature β, the one-point function of the energy density is T 00 = πc 6β 2 . We can determine the constant c(β) in (7.24), because we know that the entanglement entropy is where is the UV cut-off and g a , g b are the Affleck-Ludwig boundary entropies originating from boundary conditions at the entangling points [40]. This allows us to compute the relative entropy The variance can be computed directly from the formulas (7.24) and the two-point function (7.28) At leading order in the small interval limit /β 1 → 0, we have We note that we have the ratio satisfying the lower bound (3.20). 30 It turns out that this ratio is an interesting quantity to study for more general states, and further results on this ratio will be presented elsewhere.
Free fermion
The description of the optimal measurement in section 7.1 is valid for a general CFT 2 . We can try to be a bit more explicit by considering the example of the free fermion in two dimensions. This theory can be seen as a continuum analog of the fermion chain considered in the previous section. The free boson is very similar and presented in Appendix E.
We consider a free fermion ψ on a circle with antiperiodic boundary conditions (Neveu-Schwarz sector). It has a mode decomposition As above, we can compute the Fourier mode where we are using the notation The anticommutation relation of the field is This implies that for the Fourier modes, we have from which one can show that {ψ n , ψ m } = δ m+n . For the state ρ, we have similarly We would like to compute overlaps between the eigenstates of ρ and that of σ. This information is contained in the commutator Although explicit, this integral is hard to compute analytically.
The Hilbert space is a Fock space generated by acting on the vacuum with creation operators. A basis adapted to σ is given by where s = (s k ) k with s k ∈ Z + 1 2 and s k > 0, which we take to be in an increasing sequence. The conformal dimension (eigenvalue of L 0 ) of such a state is Similarly, we can consider a basis adapted to ρ given by the states wheres = (s k ) k being an increasing sequence.
To describe the optimal measurement, we would like to compute the overlap ∆ s | ∆s . We see that the overlap is non-zero if and only if |s| = |s| where | · | denotes the cardinality of the set s. Moreover, we see that the overlap is simply given by the corresponding minor of the matrix A which defines a matrix M . The eigenvalue E of K is related to that of L 0 via the relation (7.3).
We now consider n copies of the system to implement the optimal measurement. Following section 7.1.2, we have the acceptance condition (7.15). This allows us to define the states |ξ( ∆) using the overlaps computed above. The optimal measurement is then the projector onto the subspace (7.17) spanned by these states. It is difficult to obtain a more explicit description of this optimal measurement. The first obstacle is the computation of the integral (7.38) which is needed to obtain the states |ξ( ∆) more explicitly. Furthermore, even if we managed to have a simple expression for these states, describing the subspace (7.17) will be even harder, involving their orthonormalization using for example the Gram-Schmidt process. This procedure was discussed in section 5.2 in the much simpler case of a qubit, where it already leads to a challenging combinatorial problem.
It is then of interest to find suboptimal but simpler measurements which still perform well. A good candidate is the likelihood ratio test discussed in section 4.3 in a general context. Following section 7.1.3, implementing this measurement in CFT only requires the computation of the onepoint function ∆ s | L 0 |∆ s . For the free fermion, it can be written as This only requires the computation of A nm and its minors, which is much more tractable, as compared to what is required to describe explicitly the optimal measurement.
Primary excitation
We now consider a setup consisting of a primary excitation that we wish to distinguish from the vacuum. We are interested in the case where we have only access to a subregion of the system. We will take the example of an interval in the circle. Let σ and ρ be the states on this interval corresponding respectively to the vacuum and to the excitation. 31 Considering n copies of this setup, we would like to distinguish between the two states σ ⊗n and ρ ⊗n .
The optimal measurement is more difficult to describe because in this case, we do not have an analytic expression for the modular Hamiltonian of the excitation. Nonetheless, we will be able to implement the likelihood ratio test, as discussed in section 7.1.3.
Consider a two-dimensional CFT on a circle with circumference L at zero temperature. The Euclidean space is then an infinite cylinder of circumference L with a complex coordinate w = φ + iτ where φ ∼ φ + L is the spatial coordinate and τ ∈ R is the Euclidean time coordinate. We will study the interval I = [0, ] with 0 < < L on the τ = 0 circle. We map the cylinder to the complex plane using the map w −→ z = e 2πiw/L , (7.45) so that the Cauchy slice τ = 0 is mapped to the |z| = 1 circle. The interval I is mapped to the circular arc between z = 1 and z = e 2πiλ with λ = /L. Using a primary operator Φ, we create an excited state |Φ = Φ(0)|0 in radial quantization by performing the path integral over the unit disk with Φ(0) inserted at the origin. The corresponding bra state is then defined as Φ|= 0|Φ (0) We further perform the conformal transformation which maps the Cauchy slice |z| = 1 to the real axis with the interval I mapped to the negative real axis. 32 We define two reduced density matrices on I by tracing over its complement: The vacuum modular Hamiltonian is defined as K ≡ − log σ. In our conventions, K/(2π) generates counter-clockwise rotations in the ζ-plane. The excited state ρ is computed by a path integral over the ζ-plane with a cut along the negative real axis and with operator insertions Φ(e −πiλ ) and Φ † (e πiλ ). We rotate the boundary conditions above and below the cut to the positive real axis using σ 1/2 which gives the Rindler representation of the density matrix: Here the vacuum 2-point function · = Tr (σ ·) in the denominator ensures that Tr ρ = 1. 33 See [71] for an analogous representation of ρ in higher dimensions. As in [71], we expand ρ in the short interval limit λ → 0 using the OPE 34 32 See [2] for more details on this setup. 33 The expression (7.48) is Hermitian since the adjoint maps the operator insertions Φ † and Φ into each other. 34 Note that e πiλ − e −πiλ h O e −πiλ − e πiλ h O = (2πλ) ∆ for small λ.
where ∆ is the scaling dimension of the lightest primary O of the theory that couples to Φ (in the sense that the OPE coefficient C O ΦΦ † is non-zero), which we assume to be spinless and real for simplicity. Since two-point functions of real primaries are normalized to the Kronecker delta, we can lower the index in the OPE coefficient C O ΦΦ † = C OΦΦ † . Based on the OPE, we take the expansion parameter to be (πλ) ∆ so that We can now start constructing the acceptance subspace. Given an eigenbasis |E of σ ⊗n in H ⊗n A , the optimal classical measurement is determined by an acceptance condition of the form We first consider the case n = 1 of a single copy, for which we have |E = |E . From we obtain E + log E|ρ|E = (πλ) ∆ e E E|ρ (1) |E + . . . , (7.54) Next, using the above Rindler quantization, we see that where the states |E now live on the positive real axis in the complex ζ-plane. Rotating the expectation value E|O(1)|E to the negative real axis and mapping back to the w-cylinder, we get where O(E) ≡ E|O( /2)|E is the one-point function in the eigenstate |E of the operator O inserted at the midpoint of the interval I. Hence to determine the acceptance subspace, one has to compute these one-point functions first. This can be seen as a precomputation that can be done once and for all for each O that one wishes to use.
Let us now return to the case of n copies using the same notation as in section 4.2. We denote and eigenstate of σ ⊗n and we use |E| = 1 n n i=1 E i . The acceptance condition is and we have where we denote the average of the precomputed values O(E i ) . (7.60) In the short interval limit, relative entropy has the expansion 35 Although it might be subtle to properly define ρ D in a continuum CFT, we expect that S(ρ D σ) has a similar expansion since positivity and monotonicity implies that 0 ≤ S(ρ D σ) ≤ S(ρ σ).
Hence, in the short interval limit, the acceptance condition becomes This is a condition on the one-point functions of the lightest primary O which couples to Φ, inserted at the interval midpoint. The measurement that implements the likelihood ratio test is then the projection on the eigenstates of σ ⊗n satisfying this condition:
Discussion
In this paper we have reviewed some aspects of quantum hypothesis testing and studied a few applications in quantum many-body systems and two-dimensional conformal field theories. We have mostly focused on asymmetric testing, with a few comments about the symmetric counterpart.
We believe that we have only scratched the surface of this subject and would like to conclude by mentioning some possible avenues for future investigation. We have seen that the error estimates of different types of hypothesis testing involve different interesting quantum information theoretic quantities. One is therefore led to wonder which notions of distance on the space of states can arise in error estimates of different types of quantum hypothesis testing, and whether there is a more direct connection between properties of the distance measure and features of the type of test.
We have also observed that the (non-unique) optimal measurement which saturates the error bound in the large n limit tends to be rather difficult to implement in practice. For the case of asymmetric testing, the measurement we studied requires knowledge of the spectra of eigenstates of the modular Hamiltonians associated to subsystems, which is in general difficult if not impossible to obtain. An important question is therefore whether there are simpler testing protocols that one can develop which still do reasonably well in the large n limit. In this paper we have considered the likelihood ratio test as a possible alternative, but it would be interesting to explore this question in more detail. From a practical point of view, one ultimately would like to find the simplest possible protocol whose asymptotic error does not deviate too much from the optimal one.
An important assumption of quantum hypothesis testing is the ability to perform simultaneous (collective) measurements on n copies of the system, for arbitrarily large n. Clearly, this assumption is not realistic, and the finite n or finite blocklength case has been considered in [16,17]. One could imagine applying finite n measurements in cases where one has an evenly spaced collection of subsystems in a translation invariant state, where the distance between the subsystems is large enough for the subsystems to be approximately uncorrelated. But the situation that is most realistic is arguably to make a repeated series of single-shot measurements, i.e. one prepares the systems in a particular state, makes a measurement, and then repeats this procedure n times. It is not necessarily true that the best strategy in this case is to repeat the optimal n = 1 measurement n times, it is conceivable that a series of different measurement protocol yields a better outcome. Such adaptive measurement strategies in symmetric testing are known to attain the optimal error probability of collective strategies [73] and we leave the asymmetric case to future work. There are various closely related questions which deserve further study, such as distinguishing more than two states through POVM's [74], and contrasting these results with continuous parameter measurements and ideas from quantum metrology.
One important motivation for this work came from quantum gravity and holography. For example, in [75] a relationship was found between distinguishability measures and bulk reconstruction in entanglement wedges. One could imagine that the quantum hypothesis testing protocol whose errors are bounded by these measures plays an operational role in the actual reconstruction process and it would be interesting to explore this in more detail. Many other questions in quantum gravity center around the issue of whether or not different states can be distinguished by low energy observers, and if so, whether the necessary measurements are very complex or not. Translated into the language of quantum hypothesis testing, one would like to bound the error associated to restricted measurements (e.g. the measurements can only be made by low energy observers). In particular, can one bound the errors in hypothesis testing as a function of the maximal complexity of the measurements? This question involves the need to first develop rigorous definitions of complexity of a measurement. We briefly touched upon this in section 5.2 by considering the minimum dimension of the acceptance space as one resource associated with a measurement. More sophisticated definitions would take into account additional steps involved in the construction of the POVM, and the time and space associated with the algorithms or circuits executing the measurement. We hope to return to some of these questions in future work.
for asymmetric testing. In this appendix, we will discuss the optimal measurement for symmetric testing, where we try to distinguish between ρ ⊗n and σ ⊗n by minimizing the combined error where β n = Tr(σ ⊗n A) and α n = 1 − Tr(ρ ⊗n A). In section 2.1, we considered the case κ = 1 2 but the same result holds for any κ with 0 < κ < 1. Asymptotically, the optimal error is given in terms of the Chernoff distance The optimal measurement was obtained in [43] and is the projection on the positive part of This involves diagonalizing the operator L and projecting onto the subspace corresponding to positive eigenvalues. In general, it is difficult to describe explicitly this measurement. We consider simplified cases below.
A.1 Classical testing
We use the same notation as in section 4. We take {|E } to be the eigenstates of σ and for n copies of the system, the eigenstates of σ ⊗n can be written As in section 4.3, we can define the best classical measurement by the acceptance condition where we recall that |E| ≡ 1 n n i=1 E i . The measurement is the projector onto the subspace spanned by the states |E satisfying this condition. This is also a likelihood-ratio test but with a different threshold value.
When ρ and σ commute, the acceptance condition (A.5) is precisely the positivity of the operator L so this is actually the optimal measurement. When ρ and σ don't commute, we can define the diagonal part of ρ ρ D ≡ E E|ρ|E |E E| , (A.6) and the above measurement optimally distinguishes between ρ D and σ but doesn't make use of the off-diagonal components of ρ. This gives an error and the data-processing inequality for the Chernoff distance implies that so this measurement is suboptimal as expected. In conclusion, as in asymmetric hypothesis testing, the likelihood-ratio test (with a different threshold value) provides a simple measurement for symmetric testing which is the optimal classical measurement.
A.2 Perturbative testing
We now consider the perturbative setting where we have where ρ is in the i-th position and there are n tensor factors. Perturbatively, we have We see that perturbative testing is non-trivial only for κ = 1 2 . For κ > 1 2 , L is positive so that the measurement is the identity while for κ < 1 2 , L is negative so the measurement is zero. Focusing on the case κ = 1 2 , the measurement is a projection on the positive part of In the case where ρ (1) and σ commute, this reduces to the classical measurement described in the previous section.
B General properties of the relative entropy variance
The relative entropy variance is a less familiar concept than the relative entropy, and we survey here some of its properties. Introducing the modular Hamiltonians of ρ and σ, we consider the so-called relative modular Hamiltonian Then, the relative entropy and the relative entropy variance are its first and second cumulants, i.e. the expectation value and the variance, in the state ρ:
B.1 Relations to other quantities
We give here the relations between the relative entropy variance V (ρ σ) and other information quantities.
Rényi relative entropies. In the literature there are different generalizations of the relative entropy. Petz's defines [44] Rényi relative entropies as with D 1 (ρ σ) = S(ρ σ). On the other hand, the sandwiched Rényi entropy or the quantum Rényi divergence is defined in [76,77] as The relative entropy variance can be obtained from both versions of Rényi relative entropy [21,78], It is shown in [21] that the sandwiched Rényi entropy is the minimal quantity that satisfies the axioms expected from a relative Rényi entropy. In particular, we always have Refined Rényi relative entropies. In [11], a refined version of the Rényi relative entropies was defined as where D α (ρ σ) is the sandwiched Rényi entropy. In AdS/CFT, this quantity was shown to have a holographic dual when σ is the vacuum state reduced to a spherical subregion. It is analogous to the refined Rényi entropies defined in [79]. The relative entropy variance is obtained as (B.10) Higher cumulants. It's also possible to give an interpretation to the higher α derivatives of the Petz relative Rényi entropy D α (ρ σ) at α = 1. This is better done in the algebraic formulation given in section B.4. They correspond to cumulants of the operator − log ∆ Ψ|Φ , which are not equivalent to cumulants of ∆K. 36 Their first and second cumulants are the same and give the relative entropy and its variance, but the higher cumulants differ. Following [21], the higher α derivatives of D α (ρ σ) can also be interpreted as classical cumulants of the log-likelihood of the Nussbaum-Szkola probability distributions associated to ρ and σ. Note that the higher α derivatives of D α (ρ σ) differ from that of D α (ρ σ) because they are different functions of α.
Capacity of entanglement. For density matrices in a finite dimensional Hilbert space with dim H = N , it is simple to derive a relationship between the Rényi entropy and its relative generalization. Let σ max be the density matrix with uniform spectrum, i.e. proportional to the unit matrix, Then the Rényi relative entropy between an arbitrary state ρ and σ max reduces to is the Rényi entropy. The relative entropy, respectively, reduces to the von Neumann entropy by S(ρ σ max ) = log N − S(ρ) (B.14) and, the relative entropy variance reduces to the variance of the entropy, also known as the capacity of entanglement (see [50] and references therein), The capacity of entanglement vanishes for a pure state ρ ψ = |ψ ψ| and for the maximally mixed state σ max . It follows that the relative entropy variance vanishes between a pure state and a maximally mixed state We next give necessary and sufficient for the vanishing of the relative entropy variance.
B.2 Vanishing of the variance
The relative entropy variance V (ρ σ) is nonnegative. In this section, we consider the conditions for it to vanish, for finite-dimensional Hilbert space. When ρ is full-rank, the variance vanishes if and only if ρ = σ. More generally, the variance vanishes if and only if ρ and σ are proportional on the complement of ker ρ, where ker ρ is the subspace on which ρ vanishes. This is explained in [37] and follows from the saturation case of the Cauchy-Schwarz inequality. This implies that the relative entropy variance V (ρ σ) vanishes when ρ = |ψ ψ| is a pure state and σ has no matrix element between |ψ and any other state. For example, the relative entropy variance vanishes between the vacuum (the ground state) and any thermal state.
B.3 Violation of data processing inequality
The hypothesis testing relative entropy and the relative entropy are generalized divergences D(ρ σ), satisfying the data processing inequality where N is a quantum channel. The refinement of quantum Stein's lemma (2.14) gives an asymptotic expansion for the hypothesis testing relative entropy (2.17), involving the relative entropy and the relative entropy variance, so it is interesting to note that the latter alone does not satisfy the data processing inequality. Given a quantum channel N , there is no general inequality between V (ρ σ) and V (N (ρ) N (σ)). This can be seen in a simple two-qubit system with pure density matrices As a quantum channel, consider the partial trace over the second qubit. It produces the reduced density matrices We obtain for the relative entropy 37 in agreement with monotonicity that says that S(ρ A σ A ) ≤ S(ρ σ). For the relative entropy variance, we obtain This shows that the variance is not monotonous since we have
B.4 Algebraic formulation
We can also define the relative entropy variance for infinite-dimensional Hilbert space, in the context of algebraic quantum field theory (we refer to [80] for a review). This allows a rigorous definition of this quantity in the case of conformal field theory. Araki defined the relative entropy between two states Ψ and Φ S Ψ|Φ = − Ψ| log ∆ Ψ|Φ |Ψ , (B.23) in terms of the relative modular operator ∆ Ψ|Φ defined with respect to a subsystem for which Ψ is cyclic and separating. In the finite-dimensional case, ρ and σ are the reduced states of Ψ and Φ in that subsystem. We recover the usual definition of relative entropy, as can be seen from the formula Ψ|∆ 1−α Ψ|Φ |Ψ = Tr ρ α σ 1−α .
(B.24)
This also allows us to write the Petz relative Rényi entropy as which realizes it as a well-defined UV finite quantity in quantum field theory. In particular, taking two derivatives gives us an algebraic definition of the relative entropy variance which shows that the relative entropy variance is well-defined in quantum field theory. This formulation also gives an interpretation for the higher α derivatives of the Petz relative Rényi entropy at α = 1. The Petz relative Rényi entropy is the cumulant generating function of the operator Note that this operator is not equivalent to the operator ∆K defined in (B.2). In particular, the Petz relative Rényi entropy does not generate the cumulants of ∆K. It is however true that the first and second cumulants of K Ψ|Φ and ∆K agree ; they give the relative entropy and its variance. An algebraic version of the sandwiched relative Rényi entropy has been investigated in [81].
C Optimal measurement of a qubit
We discuss here the optimal measurement in the case of a qubit and give the derivations of the formulas of section 5.2. We focus on the case θ = π 4 which appears to be the simplest case when ρ and σ don't commute and we want to describe the optimal measurement. It is useful to write As a result, the optimal threshold value for ε = 1 2 gives We recall that |E and | E are binary strings where we used the fact that | 0 = |− and | 1 = |+ for θ = π 4 . It is useful to introduce the notation n ss (E, E), with s ∈ {0, 1} ands ∈ {−, +}, counting the number of pairs (a i ,ã i ) which are equal to (s,s). We then have Let's now compute the overlap of two states |ξ( E 1 ) and |ξ( E 2 ) . We can write where we introduced the notation We also denote ns 1s2 for the number of overlapping pairs (s 1 ,s 2 ) in ( E 1 , E 2 ) and n ss 1s2 for the number of overlapping pairs (s,s 1 ,s 2 ) in (E, E 1 , E 2 ). We have the relations n 0s 1s2 + n 1s 1s2 = ns 1s2 , (C.7) and we have n(E) = n − (n 0−− + n 0−+ + n 0+− + n 0++ ) . (C.8) Hence, the acceptance condition is We can rewrite the sum over E as a sum over the four integers n 0±± with the combinatorial factor counting the number of basis state |E for a given choice of n 0±± . We then have It is convenient to define P n,k = 1 2 n n 0−− ,n 0−+ ,n 0+− ,n 0++ n 0−− +n 0−+ +n 0+− +n 0++ =k It can be noted that P n,k are coefficients of the polynomial This follows from expanding each factor using the binomial theorem. Note that we can write where E 1 + E 2 denotes the boolean sum. This follows from the fact that n( E 1 + E 2 ) = n ++ + n −− . This second expression gives an alternative representation of the coefficients P n,k as Let us introduce binary Krawtchouk polynomials K k (X; n) which can be defined via the generating relation These are discrete orthogonal polynomials related to the binomial distribution which have many applications [82,83]. From the definition for P n,k in (C.15), we see that As a result, we can express the overlap as This relation might be useful since many combinatorial identities involving Krawtchouk polynomials are known [84,85].
Relation to the Terwilliger algebra. The Hamming cube H n = {0, 1} n is the set of binary strings of length n with Hamming distance as the metric. The Terwilliger algebra of the Hamming cube [62,64] is an algebraic structure which is useful in combinatorics and coding theory (see [63] and references therein). We proceed as in [63], and identify the binary strings a 1 a 2 · · · a n with their support, the subset X of labels i for which the bit a i in the string takes value 1. There are 2 n possible such subsets, in other words every X is an element of the power set P (H n ) of the Hamming cube. We then define a P (H n ) × P (H n ) matrix M t ij whose coefficients are where we are using |X| to denote the number of elements in X (the number of 1s, the Hamming weight of the binary string). The Terwilliger algebra is defined as the set of matrices of the form n i,j,t=0 x t ij M t ij , x t ij ∈ C , (C. 21) which is closed under matrix multiplication. To the state |ξ( E) , we can associate the element X ∈ P (H n ) by writing E as a binary string and identifying it with its support X. Then we have |X| = n( E). The Gram matrix of the set of vectors {|ξ( E) } can be represented by an P (H n ) × P (H n ) matrix G such that where X 1 and X 2 are the elements of P (H n ) associated to E 1 and E 2 . Let's denote We have n * ( E 1 , E 2 ) = max(i, j), n( E 1 + E 2 ) = i + j − 2t .
(C. 24) so that the Gram matrix element is G X 1 X 2 = 1 2 n n k=n−max(i,j) (−1) k K k (i + j − 2t; n) . From this observation, we could attempt to use the techniques of [63] to diagonalize the matrix G, and construct the optimal measurement.
D Overlaps in fermion chains
The purpose of this Appendix is to review the tools used in the computation of overlaps in section 6.2.1. We review Bogoliubov transformations, generalized Wick's theorem and the computation of correlators that contain insertions of Bogoliubov transformations. Then we show how the results lead to the overlaps presented in the main text.
D.2 Generalized Wick's theorem as a limit of generalized Gaudin's theorem
Let σ be a density operator that satisfies for some matrix M . Operators of the exponential type (such as reduced density matrices of subregions of spinless fermion chains) σ = 1 Z exp 1 2 α Sα , Z = Tr σ, (D. 10) belong to this family with M given by [38,39] M = e −ΩS A (D. 11) where S A is the antisymmetric part of S. However, not all σ that satisfy (D.9) can be written as exponentials (D.10). Let T be the operator that implements a real Bogoliubov transformation T on the Hilbert space: T αT −1 = T α (D.12) Since T is real, this equation implies that T −1 = T † is unitary. In addition, we do not assume that T can be written as an exponential of one-body operators. The generalized Gaudin's theorem states that [39] α µ 1 · · · α µn T α ν 1 · · · α νn σ T σ = pairings (−1) P pairs (contraction of a pair). (D. 13) There are three different types of contractions that can appear on the right hand side: and they are categorized based on the location of the pairs. Equation (D.13) generalizes Gaudin's theorem [67] by including insertions of T i in the expectation value. 38 Generalized Wick's theorem is analogous to equation (D.13), but with the expectation values in the quasi-particle vacuum state |E vac which is a pure state. It is obtained as a limit of (D.20) by sending σ to |E vac E vac |. For this, we take σ to be of the exponential type (D.10) with (this would correspond to a free fermion Hamiltonian) The generalized Wick's theorem is then E vac |α µ 1 · · · α µn T α ν 1 · · · α νn |E vac E vac |T |E vac = pairings (−1) P pairs (contraction of a pair) (D. 20) and the three types of contractions appearing on the right hand side are the lim {s i }→∞ G (1,2,3) µν . We will next compute the contractions.
D.3 Computation of contractions
We start with the simple 2-point function α µ α ν σ = Tr (σα µ α ν ) in a mixed state σ that obeys the relation (D.9). Using the canonical anticommutation relations and (D.9), we can write α µ α ν σ = Ω µν Tr σ − α ν α µ σ = Ω µν Tr σ − where we used cyclicity of the trace. Using we get (D.30) The quasi-particle vacuum expectation values are obtained by focusing on exponential σ with M = e −ΩS and taking the limit {s i } → ∞: We focus our attention to the following 2-point functions that appear in the computation of the overlaps: The other limits were not given in [39], but we can compute them using the identity The normalization factor is computed in [38,39]: with the normalization given in (D.39). This leads to the formula (6.58) presented in the main text.
E Optimal measurement for the free boson
In this appendix, we consider the free boson CFT and attempt to describe the optimal subsystem measurement that distinguishes between two thermal states, using the setup of section 7.2.
Let φ(z) be a free boson and define j(z) = ∂φ(z). We have the modes α n = 1 2πi 0 du u n j(u) = 1 2πi C + du u n j(u) − 1 2πi C + dūū n j(ū) . Using the above formula, we can check that [α n , α m ] = nδ m+n as expected. We now consider the state ρ with α n = 1 2πi I du i n e inπ f (z)/ W j(z) + h.c. .
(E.4)
To obtain the overlaps between the eigenstates of ρ and that of σ, we need to compute the commutator [α n , α −m ]. After some manipulations, we find [α n , α m ] = i n+m n 2W I dz f (z)e iπ(nf (z)/W +m f (z)/ W ) + h.c. ≡ A nm , (E.5) which appear difficult to compute explicitly. A basis of normalized eigenstates for K is labeled by k = (k 1 , k 2 , . . . ) with where the normalization is N k = i≥1 i k i k i ! and we have Similarly, for K, we have k = (k 1 ,k 2 , . . . ) and The overlap ∆ k | ∆ k is non-zero only if N = i k i = ik i . Is is given as where M k k is the N × N matrix constructed by starting with the matrix A ij and replacing each entry (i, j) by a k i ×k j block where all the elements are equal to A ij . Here, perm denotes the permanent which is similar to the determinant, but with only plus signs in the sum over permutations.
We will now attempt to describe the optimal measurement for the free boson, where we have two global thermal states as described in section 7.2. To compute the overlaps, it is convenient to change variable to w = f (z) so that where F (w) = f (f −1 (w)). Unfortunately, this quantity is hard to compute analytically. It can be probed in the small L expansion. At first order, we get As a result, we see that |∆ k and | ∆ k can have a non-zero overlap at first order only if they differ in less than one place. We can write k = k 0 + δ a , k = k 0 + δ b , a + b odd, a = b (E. 12) where δ i means a one in position i. We compute . (E. 13) We have N k N k = N 2 k 0 ak a bk b so we get for a + b odd . (E.14) Following section 7.1.2, we can also define perturbatively the states |ξ( ∆ k ) which span the acceptance subspace H Q . Although it's possible to write explicit perturbative expressions, this is not enough. Indeed, to understand this subspace and define the measurement, we would need them to do a Gram-Schmidt procedure to orthonormalize these vectors. To do this, we will have to go beyond the perturbation theory in L and we don't expect to be able to obtain analytical results using this approach. In conclusion, the optimal measurement seems to be difficult to describe explicitly, even in simple examples. An alternative is to use the likelihood ratio test following section 7.1.3, which will be more tractable to implement here, because it requires only the knowledge of the overlaps. | 29,601.6 | 2020-07-22T00:00:00.000 | [
"Physics"
] |
Analysing Tumour Growth Delay Data from Animal Irradiation Experiments with Deviations from the Prescribed Dose
The development of new radiotherapy technologies is a long-term process, which requires proof of the general concept. However, clinical requirements with respect to beam quality and controlled dose delivery may not yet be fulfilled. Exemplarily, the necessary radiobiological experiments with laser-accelerated electrons are challenged by fluctuating beam intensities. Based on tumour-growth data and dose values obtained in an in vivo trial comparing the biological efficacy of laser-driven and conventional clinical Linac electrons, different statistical approaches for analysis were compared. In addition to the classical averaging per dose point, which excludes animals with high dose deviations, multivariable linear regression, Cox regression and a Monte-Carlo-based approach were tested as alternatives that include all animals in statistical analysis. The four methods were compared based on experimental and simulated data. All applied statistical approaches revealed a comparable radiobiological efficacy of laser-driven and conventional Linac electrons, confirming the experimental conclusion. In the simulation study, significant differences in dose response were detected by all methods except for the conventional method, which showed the lowest power. Thereby, the alternative statistical approaches may allow for reducing the total number of required animals in future pre-clinical trials.
Introduction
The development of new radiotherapy (RT) beam delivery techniques, e.g., laser driven particle acceleration [1], micro beam RT [2] or ultra-high dose rate irradiation (FLASH) [3], is a long-term process, where the general concept should be proven early on, even though clinical requirements, such as a stable dose delivery, are not yet fulfilled. In particular, with regard to the later application in RT, the respective concepts should be tested in a translational manner [4] to validate their ability of tumour killing and the effects on the surrounding normal tissue. Starting with physical optimization and in vitro experiments, a successful concept will be validated by in vivo trials before considering it for clinical application. Regarding the requirements of stability and reproducibility of beam parameters,
Results
The results of the different statistical methods for analysing experimental and simulated tumour-growth data are summarized in Tables 1 and 2, respectively. For the experimental data, no significant differences between the beam qualities were observed by any of the statistical methods (Table 1), as reported previously [12]. The tumour-growth time to reach the sevenfold volume (t V7 ) in the 3 Gy group was somewhat longer after irradiation with laser-driven electrons (mean 16.46 days) than after irradiation with the Linac (mean 13.88 days). However, this difference was not statistically significant, as estimated by the conventional method (p = 0.14) and by the Monte-Carlo-based method (p = 0.18). Figure 1a shows the experimental data and the corresponding linear regression lines, which are close to each other. In addition to the experimental data, a simulated dataset was generated, in which the laser-driven irradiation led to a dose-response slope that was 50% larger than that of the Linac (Figure 1b). Results of the statistical tests are presented in Table 2. The difference in the slope of the dose response between the groups was not detected using the conventional method (p = 0.15). All other statistical methods, however, were able to identify this difference. The Monte-Carlo-based method identified a difference in the slope between 0 Gy and 3 Gy (p = 0.012). In linear regression, the differing dose response was reflected by the significant interaction term b DoseGroup (p = 0.006) and by the overall R 2 test (p = 0.001). Similar results were obtained using Cox regression, where the differing dose-response relationship was reflected by the interaction term β DoseGroup that was significantly different from zero (p = 0.049) and by the overall likelihood-ratio test (p = 0.010).
The presented simulation was repeated 10000 times with different randomly chosen dose and t V7 values. Overall, the power to detect the existing difference between the groups was only 42% for the conventional method, while the Monte-Carlo-based method reached a higher power of 75%, linear regression achieved a power of 93% and Cox regression of 87%, Table 2. Experimental (a) and simulated (b) tumour growth data, i.e., time to achieve sevenfold relative volume increase (tV7), and the corresponding linear regressions for treatment with laserdriven (black squares) and Linac electrons (blue triangles). For the experimental data, the dose region useable for conventional analysis is marked in grey. Therefore, black squares outside the grey area mark mice, which were not included in the conventional analysis.
Discussion
The starting point for the statistical analyses performed in this manuscript was the substantial exclusion rate of animals from the analysis of a treatment comparison study [12] due to deviations from the prescribed dose. Following the translational chain from bench to bedside, the radiobiological effectivity of laser-driven electrons and conventional Linac electrons was compared to reveal potential pitfalls of the new acceleration regime. Although the campaign itself was performed successfully, 43% of all animals treated with laser-driven electrons had to be excluded from analysis due to deviations of more than 10% from the prescribed radiation dose. This lowers the statistical power to reveal a significant difference between the beam qualities.
Conventionally, growth data from xenograft subcutaneous tumours were obtained for dedicated, pre-defined treatment groups [13][14][15][16][17] with a sufficient number of animals. Since the allocation in different groups took place before treatment, deviations from the treatment schedule and censoring of animals during follow-up must be taken into account. The latter is considered both in planning of an animal trial and in analysis using approaches that allow for handling censored tumour growth data [13,18,19]. At conventional accelerators, like X-ray tubes or clinical Linacs, deviations from the scheduled treatment regime are very rare. Hence, there was no standard approach available that can handle data with substantial dose deviations as occur, e.g., at the experimental laser-driven accelerator considered here. In a similar experiment with pulsed proton Figure 1. Experimental (a) and simulated (b) tumour growth data, i.e., time to achieve sevenfold relative volume increase (t V7 ), and the corresponding linear regressions for treatment with laser-driven (black squares) and Linac electrons (blue triangles). For the experimental data, the dose region useable for conventional analysis is marked in grey. Therefore, black squares outside the grey area mark mice, which were not included in the conventional analysis.
Discussion
The starting point for the statistical analyses performed in this manuscript was the substantial exclusion rate of animals from the analysis of a treatment comparison study [12] due to deviations from the prescribed dose. Following the translational chain from bench to bedside, the radiobiological effectivity of laser-driven electrons and conventional Linac electrons was compared to reveal potential pitfalls of the new acceleration regime. Although the campaign itself was performed successfully, 43% of all animals treated with laser-driven electrons had to be excluded from analysis due to deviations of more than 10% from the prescribed radiation dose. This lowers the statistical power to reveal a significant difference between the beam qualities.
Conventionally, growth data from xenograft subcutaneous tumours were obtained for dedicated, pre-defined treatment groups [13][14][15][16][17] with a sufficient number of animals. Since the allocation in different groups took place before treatment, deviations from the treatment schedule and censoring of animals during follow-up must be taken into account. The latter is considered both in planning of an animal trial and in analysis using approaches that allow for handling censored tumour growth data [13,18,19]. At conventional accelerators, like X-ray tubes or clinical Linacs, deviations from the scheduled treatment regime are very rare. Hence, there was no standard approach available that can handle data with substantial dose deviations as occur, e.g., at the experimental laser-driven accelerator considered here. In a similar experiment with pulsed proton beams, Zlobinskaya et al. [20] circumvented the grouping problem by analysing the growth time for each of the treated animals individually.
To improve the analysis of animal trials at experimental radiation sources, in this manuscript, different statistical approaches were compared based on the data published by Oppelt et al. [12]. We considered the conventional method, including only animals with an applied dose close to the prescribed dose and as alternatives a Monte-Carlo-based method, linear regression and Cox regression, which allow for including animals with applied doses that strongly deviate from the prescribed dose. As for the previous publication of Oppelt et al. [12] no significant differences between Linac and laser-accelerated electron treatment were obtained for the time to sevenfold tumour growth (t V7 ) regardless the method applied. Also for other endpoints, i.e., t V3 , t V5 and t V10 , a dose response similar to Figure 1a with no significant difference between the radiation sources was observed and the variability between individual mice was similar to t V7 . The large variability of the tumour growth data (Figure 1a) complicates the comparison of the two treatment regimens and the detection of significant differences between the radiation modalities. With respect to this large variability, one may question the previously applied threshold of the conventional method excluding animals with more than 10% deviation from the prescribed dose. Increasing this threshold would improve the power of the conventional method, while the precise assignment of mice to particular dose groups would be lost.
Compared to patient treatment with large inter-patient variability, in preclinical experiments aiming on the comparison of treatment regimes, one tries to minimize the variability as much as possible. For the experiment described in Oppelt et al. [12], a previously established protocol was applied, which used mice of a strain with defined immune status, age and radiation doses, showing measurable differences between dose groups. However, despite standardized handling procedures, subtle changes, i.e., in the number of tumour cells inoculated in the mice [12], in the position of inoculation, in the stress status of the individual mouse etc., might result in variations in the tumour radiation response, as visible in Figure 1a. This biological variability is hard to predict and must be taken into account by a sufficient number of animals per group and improved tumour models [16].
In order to reveal advantages of the applied statistical methods, a dataset was simulated in which laser-driven electrons deliberately led to a steeper dose-response curve than Linac electrons. Overall, the conventional method, excluding animals with doses too far from the prescribed dose, was able to detect the differing dose response only with a probability of 42%, while the other methods showed a power of more than 75%. The highest power was reached by linear regression, which is due to the assumed linear dose-response relationship in the simulation. It is expected that for a non-linear dose response, the power of linear regression would decrease, while the power of the nonparametric Monte-Carlo-based method would remain stable.
The considered statistical methods have different advantages and disadvantages: The conventional method applies t-tests for every dose level. In addition to the reduced power due to large drop-out, repeated testing generates a multiple testing problem and applying corresponding corrections would further reduce the power. However, the conventional method does not use a specific assumption on the dose-response relationship, as is required for the regression approaches. The developed Monte-Carlo-based method is similar to the conventional method. It includes all data, does not assume a dose-response relationship and analyses the change in response in neighbouring dose groups. However, in contrast to the other methods, it is not available in standard statistical software and first has to be implemented. While linear regression assumes a linear dose response, Cox regression models the hazard function of tumour recurrence that is related to the tumour control probability using a linear dose dependency. It is also able to handle animals that do not reach the considered endpoint as censored observations, thereby further increasing the sample size. More advanced models like linear mixed models or time-dependent Cox regression also with non-linear terms may be considered as further alternatives [21].
Experimental Data
In the experiment described by Oppelt et al. [12], tumour-bearing mice were irradiated with a prescribed dose of 0, 3 or 6 Gy. After electron treatment, either with laser-driven or conventional Linac electrons, the tumour growth was followed up to a predefined final size. The tumour growth time was determined by the time needed to develop a tumour size, which is a multiple of the size at irradiation. In this manuscript, the time for observing a sevenfold volume, t V7 , was considered and analysed by different statistical approaches.
Animal numbers are summarised in Table 3. There were 47 mice irradiated at the laser accelerator and 27 mice irradiated at the Linac with a prescribed dose of 3 Gy or 6 Gy. Additionally, 41 mice at the laser accelerator and 20 mice at the Linac were used as controls (0 Gy), which were not irradiated but handled in the same way. In Oppelt et al. [12], 20 of the 47 mice irradiated at the laser accelerator were excluded (43%). The detailed experimental data, comprising treatment doses and the corresponding tumour growth data for the two radiation qualities are tabularized in the Supplement (Tables S1 and S2). Table 3. Overview of the animals allocated and finally analysed for the electron irradiation experiments described in Oppelt et al. [12] and in this manuscript.
Simulated Data
In the experimental data, no difference between laser-driven and conventional Linac electrons was observed. Thus, to reveal advantages of the applied statistical methods, we simulated dose-response data in which we deliberately included a different dose-response relationship for both groups. For simulating the laser-irradiated mice, 40 data points were generated in three steps. First, a dose D was chosen as uniformly distributed in the interval [1,8] Gy. The tumour growth time was then estimated by a normal distribution with mean µ and standard deviation σ according to and The given parameters of Equations (1) and (2) were chosen such that the simulated data distribution resembled the experimental data. For 20 control animals, the dose 0 Gy was used.
The process of generating the simulated data for the mice irradiated by the Linac was similar. It differed in the distribution of dose D, using the fixed dose values of 0 Gy, 3 Gy and 6 Gy, including 20 data points for every dose group. Furthermore, the slope of the dose response was reduced, i.e., Equation (1) was replaced by: Results of the statistical methods are presented for one particular example in Table 2. Furthermore, the outlined procedure was repeated 10000 times using different random realizations. For every statistical method, the power to detect the difference in the dose-response relationship was calculated as the ratio of the number of significant results divided by 10000. Methods with a high power should be preferred.
Methods for Analysing Tumour Growth Data
The statistical tests described in the following were performed using SPSS Statistics version 25 (IBM Corporation, Armonk, NY, USA), while Monte-Carlo sampling was performed in Python (Python Software Foundation, Python Language Reference, version 3.6). In this manuscript, p-values smaller than 0.05 were considered as statistically significant.
Conventional Analysis
For calculation of the mean tumour growth time per dose group, animals with applied doses not too far from the prescribed dose were included, leading to the 0 Gy, 3 Gy and 6 Gy dose groups. Tumours with more than 10% deviation in the absolute dose were excluded from analysis, i.e., the dose had to be within the intervals of [2.7; 3.3] Gy or [5.4; 6.6] Gy, respectively. After that selection, the mean t V7 of the selected N mice and its standard deviation were calculated for every dose group. The data of the two beam qualities were then compared by a two-sided t-test with Welch correction.
Monte-Carlo-Based Method
In contrast to the conventional analysis, the Monte-Carlo-based method includes all irradiated animals, but it does not require the explicit specification of a regression function as the following alternatives methods. The Monte-Carlo-based method is visualized in Figure 2. Data points (D i , t V7,i ) for each beam quality were divided into three groups according to the applied dose, named "0 Gy", "3 Gy" and "6 Gy". In general, every combination of two data points belonging to two different dose groups defines a linear function with a slope parameter A and a constant n. We randomly selected as many pairs as there were data points in the dose group with the smallest sample size and calculated A and n for every pair. Subsequently we calculated the difference of the mean slopes, ∆A = A Linac − A Laser , and constants, ∆n = n Linac − n Laser , between the beam qualities. This bootstrap procedure was repeated 10000 times for pairs based on data points from the 0 Gy and 3 Gy groups and for pairs based on data from the 3 Gy and 6 Gy groups. A significant difference in slope or constant between the beam qualities was observed if the central 95% range of the corresponding distributions did not include the value 0. To increase robustness, pairs with too small dose differences were excluded using a minimally allowed difference of 0.5 Gy.
Cancers 2019, 11, x FOR PEER REVIEW 8 of 11 The statistical tests described in the following were performed using SPSS Statistics version 25 (IBM Corporation, Armonk, NY, USA), while Monte-Carlo sampling was performed in Python (Python Software Foundation, Python Language Reference, version 3.6). In this manuscript, p-values smaller than 0.05 were considered as statistically significant.
Conventional Analysis
For calculation of the mean tumour growth time per dose group, animals with applied doses not too far from the prescribed dose were included, leading to the 0 Gy, 3 Gy and 6 Gy dose groups. Tumours with more than 10% deviation in the absolute dose were excluded from analysis, i.e., the dose had to be within the intervals of [2.7; 3.3] Gy or [5.4; 6.6] Gy, respectively. After that selection, the mean tV7 of the selected N mice and its standard deviation were calculated for every dose group. The data of the two beam qualities were then compared by a two-sided t-test with Welch correction.
Monte-Carlo-Based Method
In contrast to the conventional analysis, the Monte-Carlo-based method includes all irradiated animals, but it does not require the explicit specification of a regression function as the following alternatives methods. The Monte-Carlo-based method is visualized in Figure 2. Data points (Di, tV7,i) for each beam quality were divided into three groups according to the applied dose, named "0 Gy", "3 Gy" and "6 Gy". In general, every combination of two data points belonging to two different dose groups defines a linear function with a slope parameter A and a constant n. We randomly selected as many pairs as there were data points in the dose group with the smallest sample size and calculated A and n for every pair. Subsequently we calculated the difference of the mean slopes, ΔA = A̅ Linac − A̅ Laser, and constants, Δn = n̅ Linac -n̅ Laser, between the beam qualities. This bootstrap procedure was repeated 10000 times for pairs based on data points from the 0 Gy and 3 Gy groups and for pairs based on data from the 3 Gy and 6 Gy groups. A significant difference in slope or constant between the beam qualities was observed if the central 95% range of the corresponding distributions did not include the value 0. To increase robustness, pairs with too small dose differences were excluded using a minimally allowed difference of 0.5 Gy. The grouping of the experimental data from the Linac as well as of the simulated Linac data, was based on the prescribed dose, which was close to the applied dose (0 Gy, 3 Gy or 6 Gy). For the experimental laser-driven electron data, the dose was prescribed accordingly (0 Gy, 3 Gy and 6 Gy), but may differ from the applied dose, which is used for the calculation. Here the groups were defined by the intervals of [1.0; 4.5) Gy and [4.5; 8.0] Gy containing 26 and 21 data points, respectively. This definition was also used for the simulated laser-driven irradiations.
Linear Regression
This method is based on the assumption of a linear dependency of the tumour-growth time on the applied dose, which was observed, e.g., in an independent experiment with the same tumour model [16] using irradiation with 200 kV X-rays. The high-energy electrons may exhibit the same dose-effect relationship, because it is also a beam quality with low linear energy transfer. The grouping of the experimental data from the Linac as well as of the simulated Linac data, was based on the prescribed dose, which was close to the applied dose (0 Gy, 3 Gy or 6 Gy). For the experimental laser-driven electron data, the dose was prescribed accordingly (0 Gy, 3 Gy and 6 Gy), but may differ from the applied dose, which is used for the calculation. Here the groups were defined by the intervals of [1.0; 4.5) Gy and [4.5; 8.0] Gy containing 26 and 21 data points, respectively. This definition was also used for the simulated laser-driven irradiations.
Linear Regression
This method is based on the assumption of a linear dependency of the tumour-growth time on the applied dose, which was observed, e.g., in an independent experiment with the same tumour model [16] using irradiation with 200 kV X-rays. The high-energy electrons may exhibit the same dose-effect relationship, because it is also a beam quality with low linear energy transfer.
Linear regression was performed using where t V7 (D) are the t V7 derived for individual tumours treated with a certain dose D, and the parameters b 0 and b Dose were fit to the data. The fit was performed for both beam qualities individually, including all irradiated animals, as shown in Figure 1. The quality of the fit can be measured by the coefficient of determination R 2 .
To compare the slopes and intercepts of the regression lines between the radiation qualities, the following multivariable model was applied, where the group variable G represents the radiation quality and b are the fit coefficients. Here, we set G = 0 for tumours treated with laser-accelerated electrons and G = 1 for those treated with electrons delivered by a clinical Linac. The comparison of the two beam qualities was evaluated by the p-values corresponding to b Group and b DoseGroup . If b Group significantly differs from 0, a global shift between the growth times of both radiation qualities is observed, while a parameter b DoseGroup significantly different from 0 describes differing slopes of the dose-effect curves. As an alternative, the change in R 2 between a model with b Group = b DoseGroup = 0 and a model including all fit parameters can be tested for a significant difference from 0 using an F-test.
Cox Regression
Cox regression can handle censored data, i.e., include mice that did not reach the endpoint of achieving a sevenfold volume increase. First, the hazard function given by: was fitted for the two beam qualities individually. It consists of a time-dependent baseline hazard h 0 (t) that is not estimated, and a time-independent factor containing the regression coefficient β Dose. In a second step, multivariable Cox regression was performed by: where G is the same group parameter as used for the multivariable linear regression. A global difference between the groups is obtained if β Group significantly differs from zero, while a significant parameter β DoseGroup describes a dose-group interaction. As an alternative, a likelihood-ratio test can be performed using the difference in twice the negative log-likelihood between the model with β Group = β DoseGroup = 0 and the model including all fit parameters.
Conclusions
In this work, we applied different statistical approaches to identify differences between the time to sevenfold tumour volume increase after treatment of mice with laser-driven and conventional Linac electrons. Except for the conventional approach, these methods allow for including animals with applied doses considerably differing from the prescribed dose. Overall, a Monte-Carlo-based method, linear regression and Cox regression were more sensitive than the previously used conventional method and may be applied in future studies.
Funding: This research was funded by German Government, grant numbers 03ZIK445, 03Z1N511 and 03Z1O511. | 5,608.4 | 2019-08-31T00:00:00.000 | [
"Physics",
"Medicine"
] |
An AI-powered navigation framework to achieve an automated acquisition of cardiac ultrasound images
Echocardiography is an effective tool for diagnosing cardiovascular disease. However, numerous challenges affect its accessibility, including skill requirements, workforce shortage, and sonographer strain. We introduce a navigation framework for the automated acquisition of echocardiography images, consisting of 3 modules: perception, intelligence, and control. The perception module contains an ultrasound probe, a probe actuator, and a locator camera. Information from this module is sent to the intelligence module, which grades the quality of an ultrasound image for different echocardiography views. The window search algorithm in the control module governs the decision-making process in probe movement, finding the best location based on known probe traversal positions and image quality. We conducted a series of simulations using the HeartWorks simulator to assess the proposed framework. This study achieved an accuracy of 99% for the image quality model, 96% for the probe locator model, and 99% for the view classification model, trained on an 80/20 training and testing split. We found that the best search area corresponds with general guidelines: at the anatomical left of the sternum between the 2nd and 5th intercostal space. Additionally, the likelihood of successful acquisition is also driven by how long it stores past coordinates and how much it corrects itself. Results suggest that achieving an automated echocardiography system is feasible using the proposed framework. The long-term vision is of a widely accessible and accurate heart imaging capability within hospitals and community-based settings that enables timely diagnosis of early-stage heart disease.
potentially leave the profession.Therefore, an advanced echocardiography system that can capture data either automatically or be assisted mechanically is highly demanded.
Currently, teleoperated 2D ultrasound systems are commercially available and have been tested for real-world medical uses 4,5 .Such systems, while not strictly requiring an operator in-situ, still require remote guidance from trained sonographers.This has led to the development of automated 2D ultrasound systems, which allow for the acquisition of ultrasound images without or with limited operator intervention.Such systems have been developed for imaging the cervix 6 , foetus 7 , carotid artery 8 , and breast 9 .Note that automated systems differ from assisted systems that guide the user to position the probe correctly, for which a comprehensive review of such systems for cardiac imaging was done in 10 .Except for proof-of-concept studies as in 11 where a bladder ultrasound was used to image the heart in the case of porcine cardiac arrest, no automated systems have been developed for use in human cardiac image acquisition.This is partly due to echocardiography requiring a specific set of probe handling and positioning techniques that differ in practice and convention from other non-invasive ultrasound acquisitions 9 .Other challenges for automated echocardiography include the use of phased-array transducers in echocardiography and the difficulty of obtaining good images of the heart due to its fast movement compared to other internal organs.The introduction of an automated echocardiography acquisition system would pave the way for fully end-to-end acquisition and analysis systems when used in conjunction with so-called assisted echocardiography methods which detect anomalies and assist diagnosis such as in 12,13 .
With regards to the way the automated methods adjust transducer position, the existing automated 2D ultrasound systems can be categorised into three groups: landmark-based, greedy, and feedback-based.Landmarkbased systems use visual input of the body's surface (typically easily distinguishable surface landmarks such as the nipple) to approximate the location to obtain ultrasound images, such as the system in 14 .Greedy systems such as 6,7 involve acquiring images of a set of regions to generate an overall view of the local anatomy for postprocessing.Feedback-based systems employ sensory and/or visual feedback and a set number of rules that govern decision-making in transducer movement 8,15 .Feedback-based systems are theoretically transferable for other types of ultrasound imaging as long as the associated rules are adapted to the specific application.
The rules associated with echocardiography aim to produce an image of a specific cardiac view (e.g., the parasternal and apical views at their intercostal spaces) suitable for diagnosis.The views are typically further classified according to their associated tomographic planes.Several studies have developed systems that classify the view type and image quality, but Pop 16 stated that standard image classification models like InceptionV3 and VGG16 give a promising baseline accuracy in recognising echocardiography images of various views.
Overall, while automated systems have been developed for medical ultrasound imaging, they have not been developed for cardiac imaging, which has different challenges.Existing automated ultrasound imaging systems use different scanning protocols, such as landmark-based, greedy, and feedback-based approaches, but none are designed explicitly for echocardiography.Feedback-based systems can be adapted for other types of ultrasound imaging by modifying the associated rules.In the case of echocardiography, the goal is to produce images of specific cardiac views that have sufficient quality for diagnosis.The novelty of this work is the introduction of a navigation framework for echocardiography, powered by artificial intelligence, that allows automatically capturing required high-quality images without requiring assistance from radiographers.This research is to pave the way for potential future implementation using a robotic arm.from the body camera, while the image quality model employs an InceptionV3 architecture trained to distinguish between 'good' and 'bad' ultrasound images from manually labelled data.
Methods
A main contribution of this research lies in the control module, the key element of which is a novel echowindow search algorithm.This algorithm takes inspiration from the rule-based feedback scanning protocol developed in 8 .It takes echocardiography images and their location descriptors as inputs and outputs the optimal location of the probe in the next step of scanning based on the inputs, with respect to the idealised constraints of the ultrasound positioning system.
Finally, the perception module acts as an interface to the real-world environment, containing a body-facing camera to obtain an image of the current scanning regime, the ultrasound probe as a real-time feed for cardiac imaging, and the robotic arm which manipulates the ultrasound probe's location.It should be noted that this study provides a conceptual framework for a system that involves a positional controller ideally in the form of a robotic arm.However, for this study, movement is simulated using software, traversing over a set of images with positions that correspond to a physical acquisition on a HeartWorks cardiac ultrasound simulator.
The echo images used in this study were sourced from simulations, publicly available datasets, and those acquired by a cardiologist on a staff member within the cardiology department of Milton Keynes University Hospital who volunteered himself for echocardiography scanning for this study, along with a healthy member from the research team.No patient data was used.The project was approved by Cranfield University Research Ethics System (CURES) with reference number 18154.All confidential information was handled in agreement with the Declaration of Helsinki.All communications were made through National Health Service secure email accounts.
Implementation.System setup.This study developed a simulation system to analyse the feasibility of the proposed automated echocardiography acquisition framework.Figure 2a shows that the HeartWorks ultrasound simulator, manufactured by MedaPhor Ltd UK 17 , was used to simulate the data capture process of echocardiography.A Garmin VIRB X action camera was placed at a vertical distance of 76 cm to the surface of the patient's torso, parallel to the patient's groin area, facing down, as shown in Fig. 2b.The camera, shown in Fig. 2c, aims to locate the transducer automatically.A typical view of the camera is shown in Fig. 2d.
The location of each captured cardiac ultrasound image is obtained by applying the probe locator model on the videos from the body camera while synchronised to the TTE video.Once done, each image was stored in a file directory according to location (in x-y coordinates) and given a unique image ID.The scanning process is simulated by fetching an image according to the location of its corresponding point.Tests were carried out by varying the step size interval, the search region, and the length of the rolling window.These tests were conducted to obtain a few parameters to evaluate the performance, including success rate, traversal length, simulation time taken and quality of the last image.
Image quality assessment model.This model aims to assign a quality metric of a given image obtained in real time through the ultrasound feed.This quality measure is then fed to the control module as input for the window search algorithm.The image quality model employs a convolutional neural network (CNN) to distinguish between 'good' (positive) and 'bad' (negative) TTE images from a novel echocardiography image quality dataset.
To train the model, an image quality dataset containing 5166 images (2852 'bad' images, 2314 'good' images) was used.The first part of the image quality dataset comprises 1137 anonymised images (22% of the whole dataset) collected from Milton Keynes University Hospital using a medical cardiac ultrasound system (Philips Epique CVX). Figure 3a shows an example image with four chambers.The second part of this dataset comprises 3679 synthetic images (71% of the total dataset) sourced from the HeartWorks ultrasound simulator, an example of which is shown in Fig. 3b.The third part of this dataset comprises 346 anonymized ultrasound images (7% of the total dataset) collected by a portable GE Vscan Extend ultrasound device for a healthy participant.Figure 3c shows an example of this in the A2Ch view.The Philips and GE Vscan devices are shown in Fig. 3d.Labelling for this dataset was done manually with reference to views already manually labelled by healthcare professionals.
The CNN architecture implemented in this classification model is the InceptionV3 architecture.This architecture was selected following recommendations presented in 16 , using the InceptionV3 model, which comprises 13 layers and takes an input size of 299 × 299 × 3. Implementation of this model within the proposed system was achieved using the TensorFlow machine learning package, which comes with the InceptionV3 model prepackaged in its keras.applicationssub-module. 1 provides the configurations used to train the model.An additional final gate comprising two sigmoid layers was added to the InceptionV3 architecture in 18 to serve as an output layer, which also serves as a probabilistic representation of the classification process.On inference, the model will output the probability that an image is either a 'good' or 'bad' quality image.If an image is determined as 'bad' , the model outputs the image quality by multiplying the probability by − 1.The model outputs the image quality by multiplying the probability by 1 if an image is identified as 'good' quality.The closer the quality score is to 1, the better the model predicts the image to be a 'good' quality image, and inversely the closer it is to − 1, the lesser the quality of the image.This convention was used to store both label and probability data as a single value.This value is then sent to the window search algorithm within the control module.
Echo-window classification model.This classification system differentiates images from two TTE echo windows: the apical 4-chamber (A4Ch) and 2-chamber (A2Ch) views, the principle of which can be extended to other types of echo windows.The CNN used in this model is almost identical to the image quality assessment model but with a different dataset.This dataset comprises 12,980 images from the HMC-QU public echocardiographic videos dataset 19 .Videos are categorised into A4Ch and A2Ch views, which were cut into frames with 6,500 A2Ch images and 6480 A4Ch images.All images in this dataset have a size of 299 × 299 pixels.Sample images are shown in Fig. 4.These views were selected because it is possible to derive a measure of heart function using only these two windows 20 .Furthermore, both views are acquired from the same position; rotating the transducer on the position of the apical 4-chamber view anticlockwise gives the apical 2-chamber view.Note that this research focused on the simplification of the echocardiography image search problem into a 2-dimensional domain, which does not include transducer rotational angle.Once the pre-processing step was complete, the window classification model was trained for 150 epochs using an 80/20 training/validation split of the HMC-QU dataset.The training configurations for this model are given in Table 2.The main difference between this classification model and the image quality assessment model is the output scheme.The output of this scheme is a probability score that indicates how likely a TTE image is to be from an A4Ch view or an A2Ch view.
Probe locator model.The dataset for this model comprises 149 images of a simulated TTE examination on the HeartWorks simulation suite.Images were manually labelled using bounding boxes, indicating the 'probe' and 'probe-tip' using the web-based image labelling software Make Sense 21 .An example is shown in Fig. 2d.All images within this dataset are 1080 × 1080 pixels, each with a .txtfile describing the bounding boxes shown in Early stopping condition Yes, on no improvement in validation loss during 3 consecutive epochs the image in the YOLO format: the object class, coordinates, height, and width of the bounding box.The images have been resized into that required in YOLO format and are not in their original aspect ratio.The model used in this application belongs to the YOLOv5 object detection architecture.This method divides the entire image into a grid system-each cell within the grid is responsible for detecting objects within itself 22 .The specific model architecture used in this implementation is YOLOv5s, which was selected because it offers a good balance between inference time and accuracy.The probe locator model was trained for 200 epochs on an 80/20 training/validation split of the manually labelled probe location dataset.The training parameters used for this implementation are described in Table 3.
It should be noted that this probe localisation system is currently in place for simulation purposes only.Once further developments permit the use of the robotic arm for physical testing, the inverse kinematics functions on the robot will be used in conjunction with this vision-based mechanism to obtain the probe location.
Echo-window search algorithm.The heart of this proposed system is the window search algorithm, which governs the decision-making process of the robot's movement.This algorithm finds the best echocardiography window location based on the known traversal positions and corresponding image quality.The proposed algorithm, inspired by the rule-based feedback scanning protocol in 8 , takes echocardiography images and their location descriptors as the input and outputs the optimal scan sequence constrained to the possible movements of the robotic actuator.In the case of a robotic arm, the constraints would differ based on the robot configuration and the degrees of freedom available on the selected system and its working envelope.However, this study has idealised the movements to a two-dimensional space to demonstrate the feasibility of the window search algorithm.The flowchart of this algorithm is shown in Fig. 5.Other parameters were set to default as in 22 Firstly, the search region is manually calibrated by the operator, which is done by selecting 4 points on the first image obtained through the body camera feed.By connecting the four points, a polygon can be formed, which denotes the available search area for the window search algorithm, i.e., the window search algorithm's traversal is restricted to only within the boundaries of the 4 points.
Next, a start location is selected-while this start point could theoretically be selected randomly, the ideal start point should follow the general guidelines in performing a TTE examination.This start point is set in the same manner as the search region calibration process using the available user interface.Once this is set, the algorithm commences its iterative search process.
At the beginning of each iteration, the search algorithm checks the image quality at the start point using the image quality assessment system.If the quality meets a preset threshold, the search process will stop.In most cases, the quality of the image at the first step would not meet the threshold.If this is the case, the search algorithm directs the arm to scan the start point's neighbouring positions, i.e., to the north, south, east, and west directions, where north refers to the direction pointing above the transverse plane of the patient and west refers to the direction pointing towards the patient's anatomical right on the frontal plane.This study refers to a group of these neighbouring positions as the step group.While it is possible to consider a larger step group, this study restricts this to four directions, as mentioned above.As a step in each direction also translates to a change in the pixel coordinates, one can relate the images obtained in each direction with a unique pixel coordinate set.Note that the step size may increase or decrease according to reasons further explained.
Next, the image quality assessment model assesses the quality of all 4 images obtained at each neighbouring position.The algorithm would then store the position corresponding with the best-quality image.This position is chosen as the next starting position in the next iteration.This step also predicts the echo window type to determine whether the image given is of an A4Ch or A2Ch view.
The algorithm employs a set of checks that decide to increase or decrease the step size to improve convergence speed and ensure the search process covers a wider area.This step involves storing the best position and quality score in a so-called rolling window.The length of this window can be varied, as further explained in the simulation testing process.
After the selection of the best position, the algorithm checks whether the position's coordinates are within the rolling window (indicating the arm has traversed this position before) and whether the mean quality score of images within the rolling window has decreased with the addition of the new position (indicating the decisionmaking process has resulted in obtaining a worse position).If any of the checks are true, it increases the step size in the next iteration, thus avoiding this position in further iterations.If the checks are both false, the step size decreases thus focusing on the area currently traversed.Note that the step size is initialised as 1; however, the amount it decreases or increases is a user-set variable, denoted by the step size interval.The introduction of these checks was necessary for a few reasons: the first check ensures the system is not 'stuck' at a given search area, and the second check ensures that the search algorithm does not waste its time in areas where only suboptimal TTE images can be obtained.
The next iteration carries over some information obtained in this iteration of the search process, including the step size, rolling window, next start position, and its corresponding quality measure.If the measure meets a set threshold, the traversal ends as mentioned above, but if it does not, the iterative search process continues with new start positions.
Results and discussion
Intelligence module.This section presents the results to indicate the performance of the AI models that make up the intelligence module.Figure 6 Table 4 shows the confusion matrix for the validation set.The number of False Negative is slightly higher than that of False Positive, but the overall accuracy is more than 99%.The results from the image classification model are satisfactory for making judgments about image quality.In an ideal scenario, multiple runs with different training parameter configurations should be carried out to find the optimal results.There is potentially some room for optimisation to reduce the risk of over-fitting, however, this study did not focus on fine-tuning the classification process, so additional work is required to achieve the best performance.
Figure 7 shows the precision-recall curve of the probe locator model, and Table 5 shows its corresponding confusion matrix for the validation set.Table 5 and Fig. 7 show that the model can detect probes with high accuracy of 96% but requires optimisation in detecting probe tips.While these training results indicate that there may be room for improvement, it was found that it offered a good balance between accuracy and inference time, which is important when considering the multi-model inference events occurring in each iteration of the proposed system.The outcome of the training and validation process of the window classification model can be visualised in Fig. 8 and Table 6.The loss and accuracy curves in Fig. 8 show a similar phenomenon as in Fig. 6, showing a continually decreasing loss and increasing accuracy in window classification.Additionally, the model shows a good final accuracy of over 99% in recognising both apical views, as shown in Table 6.While further improvements can be achieved by tuning the hyperparameters, it is noted that the research scope of this work lies mainly in the proof-of-concept of the search process.www.nature.com/scientificreports/Control module.Search region.This experiment tests the efficiency of data acquisition by varying the search region size (and thus restricting the starting points) according to the parts of the torso.This is done to showcase the performance of the proposed search algorithm and to understand its behaviour during different calibration scenarios.Images of the different search regions are given in Fig. 9.Other parameters were set as: step size interval: 2; rolling window length: 10; maximum allowed steps: 100; the number of random starting points: 1000.Table 7 gives the results outlining the success rate, the mean quality of the last image, the mean traversal time, and the mean length for each variation of the search region.
The simplest observation to be obtained in Table 7 is that it is impossible to obtain a good echo window by defining a search region in the lower left torso of the patient.This observation is supported by the fact that running 1000 simulations with various start points on the lower left torso area does not yield any successful searches.It is possible to obtain successful window locations using the search algorithm by restricting the search region to either the whole torso, upper left torso, or whole left torso.It is shown that the optimal search region lies in the middle of the left torso.This observation is consistent with the mean quality of the last image, suggesting that setting the search region to the middle-left torso area can yield a higher image quality at the end of the traversal.
Furthermore, the average traversal length and time of the middle-left torso shows that setting the system to search in this region can find the optimal echo window quicker.As Koratala et al. 23 stated, the location of the apical window is approximately around the 4th or 5th intercostal space, in line with the midclavicular line.Visually this is located slightly towards the anatomical left, below a male patient's left nipple, or laterally beneath a female patient's left breast.Considering the anatomy of our 'patient' in this case, one can estimate this area to be just around the middle of the torso, towards the patient's anatomical left.The results in Table 7 show that setting this area as the search domain allows the system to have a higher success rate.As such, the results can be considered reliable, concurring with guidelines for manual acquisition as previously mentioned in 1,2 .
Rolling window length and step size interval.In Fig. 10, the dots represent the observation's value for the entire population of search simulations, which are coupled with a second-order polynomial trendline to ease visualisation and help understand the impact of step size and rolling window length on said observed parameters.Figure 10a shows that a higher step size interval would support a higher likelihood of simulation success.This is further shown in Fig. 10b, indicating that traversals that have a higher step size on average end up in a position better suited to obtain a higher quality image.Furthermore, Fig. 10c shows that traversal length is shortened with an increase in step size, which is expected as the system is designed to terminate the traversal if the search succeeds.This observation indicates that the more the search algorithm corrects itself after being penalised for going over a low-quality area, the higher its likelihood of obtaining a good final image.However, the current iteration of this research does not consider simulating how the movement of the arm may affect the traversal time or whether fast repeated movements could be deemed erratic.As the step size interval represents how much the transducer moves during a single adjustment, one could claim that a high step size interval would promote excessive probe movement.Figure 10d illustrates the relationship between the rolling window length and the success rate of simulations: it is observed that the longer the rolling window, the higher the chance of success.This hypothesis is further supported by Fig. 10e, showing how the quality of images improve as the rolling window length increases.Furthermore, Fig. 10f shows that traversals tend to be shorter when the system records a larger number of past coordinates.These observations are consistent with the design of the rolling window system whose role is to prevent the search from landing on positions it has seen before and move towards better positions to maximize the resulting image quality, and thus reduce the length of time it takes to obtain a good image.The length of the rolling window governs how long it remembers these positions, which can all be deemed sub-optimal as end coordinates are not recorded in the rolling window (i.e., all past steps can be considered mistakes).In essence, it can be considered a short-term memory array that forces the search algorithm to learn from its mistakes-the longer the array, the more it can remember.
Start point.This section investigates how the start point impacts whether the proposed search algorithm can successfully find a good-quality echocardiography image.Figure 11 shows the impact of the start position across the four different searching domains (The lower left torso is ignored as it ends with no success).Points in each image represent the start position, whereas colour represents whether the traversal ended up successful (black indicates failure, white indicates success).While most simulations were unsuccessful, starting points around the left mid-torso area tend to result in a successful traversal.This area is larger than the footprint of a real cardiac ultrasound transducer, which is designed to fit in a tiny area like the intercostal space.This observation www.nature.com/scientificreports/ is consistent with existing practical guidelines for where the ultrasound probe should be placed during a real cardiac ultrasound acquisition as in 2 and 1 .
Window type recognition.The system's capability to obtain the apical echo window type was investigated.Figure 12 shows the endpoints for various search domains, with the colour representing whether the traversal was completed with an apical image (black indicates false, white indicates true).It can be observed that while there still exists several failed traversals, the search algorithm outputted A4Ch and A2Ch views in the middle portion of the left torso, occupying a region much smaller than the initial start points.Also, the main distribution of white points does not have a noticeable variation in position on the surface of the patient's body, the cluster of which forms a slanted thin line on the anatomical left of the torso, akin to the intercostal space, where the desired A4Ch imaging window would be in a real cardiac ultrasound acquisition.
Conclusion
This research introduced a framework for automated ultrasound image acquisition of the heart.The proposed framework is a feedback-based approach that uses AI algorithms to determine the best location for acquiring images based on feedback from live images.It consists of an intelligence, control and perception module.The main contributions of this paper lie in three AI models in the intelligence module and a window search algorithm in the control module.The framework was implemented and tested using simulations and different data sources.The results suggest the proposed framework can achieve high efficiency and automation if a robot arm is employed.The system could potentially address challenges such as the skill requirements and workforce shortage for echocardiography.It will also reduce the risks of viral transmission and improve the care throughput.
This paper introduces the proof-of-concept of such a solution, where the AI models based on the simulator cannot be used on real-world echocardiography systems directly.For the models to be applied to real-world echocardiography systems, they must be trained on a larger database with considerable subjects and types of echocardiography systems.Other limitations include using a limited simulation environment and the need for consideration of probe depth, imaging settings, and skin contact.It also relies on the calibration of the search region, which requires some training for operators.Future research could address these limitations by constructing a physical platform and performing automated scans on an ultrasound training simulation platform, integrating a force sensor to maintain skin contact, and facilitating an interface to adjust imaging settings.Furthermore, using a robot arm should provide precise step size control and achieve good linearity with the motion.
Figure 1 .
Figure 1.Flowchart of the proposed framework.
Figure 3 .
Figure 3. Example 'good' images to construct the dataset for image quality evaluation from (a) Medical standard device-Philips Epique CVX; (b) Heartworks simulator; (c) portable device-GE Vscan Extend; (d) devices.
Figure 5 .
Figure 5.The flowchart of the echo-window search algorithm.
shows the training and validation loss of the image quality assessment model.The training and validation loss curves both decrease throughout the training process, which indicates a good fit.Also, the accuracy curve increases for both training and validation sets and converges after a certain epoch.Note that the model was set up to stop training prior to a divergence in validation loss to avoid over-fitting.
Figure 6 .
Figure 6.Training and validation (a) loss and (b) accuracy for the image quality assessment model.
Figure 7 .
Figure 7.The precision-recall curve of the probe locator model.
Figure 8 .
Figure 8. Training and validation (a) loss and (b) accuracy of the window classification model.
Figure 9 .
Figure 9. Search regions used in the simulation process: (a) Whole torso.(b) Left side of torso.(c) Left upper torso.(d) Left lower torso.(e) Left middle torso.
Figure 10 .
Figure10.The impact of step size interval and rolling window length on success rate, traversal length and mean last quality, where the scatters denote the measurement and the dash lines plot the fittings.
Figure 11 .
Figure 11.Initial start points for various search domains for (a) whole torso, (b) left side, (c) left upper, (d) left middle.Black points represent failed traversals; white represents otherwise.
Figure 12 .
Figure 12.End points for search domain traversals for (a) whole torso, (b) left side, (c) left upper, (d) left middle.White points indicate positions for A2Ch and A4Ch imaging, black points otherwise.
Table 1 .
Image quality assessment model training parameters.
Table 2 .
Window classification model training parameters.
Table 3 .
Probe locator model training parameters.
Table 4 .
Confusion matrix of the image quality assessment model on the validation set.
Table 5 .
Confusion matrix of the probe locator model.
Table 6 .
Confusion matrix of the window classification model on the validation set.
Table 7 .
Results of the search domain experiment. | 7,085.4 | 2023-09-11T00:00:00.000 | [
"Computer Science",
"Engineering",
"Medicine"
] |
Effect of Pre-Existing Symmetrical Cracks on Propagation Behaviors of a Blast-Induced Crack
Defects such as voids, pores, and joints will transform into big scale cracks in the rock of tunnel surrounding under dynamic load like blasting and earthquake. In this paper, three kinds of symmetrical cracks were chosen as an example, and experiments and numerical simulations were conducted to study the effect of symmetric cracks on a blast-induced crack. +e relationship of main crack propagation characteristic and distribution of symmetrical cracks was investigated. Some circular specimens using two kinds of material, PMMA and sandstone, including a center hole charged with a detonator and pre-existing cracks were used in the experiments. +e test system consisted of an oscilloscope and an ultradynamic strain amplifier and crack propagation gauges (CPGs) were employed in monitoring propagation velocity. AUTODYN code was applied in numerical simulation to investigate the propagation behavior of main crack between symmetrical cracks. Linear equation of state and a modifiedmajor principal stress failure criterion was utilized to describe the status of rock material. Based on experimental and numerical results, it can be concluded that (1) the pre-existing symmetrical cracks have arrest effect on main crack propagation, (2) compressive stress in y-direction plays very important roles in crack arrest, and (3) the spacing of parallel cracks has a great influence on crack propagation length and velocity.
Introduction
Fragmentation by drilling and blasting is widely employed in mining, quarrying, and civil construction excavations because of its effectiveness and economic efficiency. However, the blasting shock wave by explosive will cause damage of rock mass that is unnecessary, which may lead to many accidents. erefore, the dynamic response of rock under blasting load has attracted many scholars' attention [1][2][3][4][5][6][7][8][9][10].
e process of rock fracture and fragmentation by explosive under is very complicated, which is relevant to the characteristics of rock mass, explosive material, and charge method. erefore, many numerical methods have been presented. Zhu et al. [11] established a surface blasting model using finite difference method in AUTODYN code and investigated the effect of different defects including voids, pores, and open joints on dynamic strength of rock and two kinds of boundary were considered in his study. Zhang et al. [12] studied the crack propagation mechanism under blasting load using numerical simulations, and his result agreed that there is a different stress state resulting in crack propagation in time sequence. Yilmaz and Unlu [13] investigated the behavior of rock under different blasting loads using a three-dimensional finite difference model and concluded that the most efficient explosive is the one with low-frequency content but with a sufficient high borehole pressure. Wang et al. [14] used a coupled method combining UDEC and LS-DYNA to study the effect of blasting wave on the faulted rock masses, and the result showed that the existence of faults influences the pattern of rock damage.
Zhong et al. [15] applied RFPA dynamic in investigating the function of loading rate, distance from the borehole to the free boundary, and size of hole between two charge holes on propagating crack. Yi et al. [16] analyzed numerically the effect of situ stress on rock fracturing under explosive load and concluded that the crack propagation is governed by explosive stress wave but influenced by the high situ stress in far field. Fakhimi and Lanari [17] simulated rock fragmentation under blasting load using the DEM-SPH method and indicated that the last stage of rock is owing to the infiltrating of explosive gas.
Experimental study is very important in studying rock dynamic response under blasting. erefore, Hu et al. [18] investigated the propagation rule of a crack under blast loading and the results indicated that the side close to borehole will propagate toward it, but the other one will expand away from it. Liu et al. [19] tested the dynamic fracture toughness of brittle material under explosive load using PMMA plates and the crack propagation gauge and concluded that dynamic propagation toughness is greater than initiation toughness. Yu et al. [20] studied the effect of blasting on the mechanical behavior of sandstone and agreed that the mechanical parameters of sandstone will change after blasting. He and Yang [21] explored the effect of two holes on propagating crack and analyzed the crack arrest mechanism of empty holes. Yang and Ding [22] used digital image correlation method to study granite dynamic response under blasting load with different lateral pressure coefficient K and the results indicated that the radius of the crush zone decreases with the increment of lateral pressure coefficient. Yang et al. [23] investigated the dynamic behavior of jointed rock under blasting in high-stress condition by caustics method and agreed that, in the crack initiation stage, the high stress influences a little, and in the propagation stage, it can change the crack propagation speed, and by the same method, Wang et al. [24] explored the interaction of a running crack and blasting wave and concluded that a blasting wave can influence dynamic stress intensity factor at the tip of a propagating crack.
As is known well, there are many voids, pores, and joints in rock masses of tunnel surrounding, which can transform into big scale open precracks in the later period of construction owing to repeated blasting. ese big cracks certainly will have an effect on the propagation of blastinginduced cracks and there will be different functions for precracks with different orientations. In this paper, three kinds of symmetric precracks were chosen to study its effect on a propagating main crack.
In this study, some big scale circular plates using two materials, PMMA and sandstone, with a center charge holes, three radial main cracks, and three pairs of symmetric secondary cracks were applied in the experiments and an electrical detonator was used to generate blasting load. Crack propagation gauges (CPGs) were employed in measuring the main crack propagation speed. e explicit dynamic software AUTODYN [24] was applied in the numerical study, which is a highly nonlinear dynamic software and can solve the dynamic problems of solid, liquid, gas, and its coupling; similarly, AUTODYN code has good adaptability in simulating the process of rock fracturing [25][26][27]. According to experimental and numerical study, the behavior of a propagating crack between secondary cracks could be obtained.
Experimental Study
Rock contains a plenty of joints and cracks; when a moving crack encounters these cracks, they will affect the moving crack dynamic propagation behavior. In this study, a pair of symmetric cracks about the horizontal axis as shown in Figure 1 was considered and the effect of these two cracks on a moving crack was investigated.
Specimen and Its Dimension.
ree types of large circular specimens with a centralized charge hole as shown in Figure 2 were applied in this study. ree radial main cracks were designed in each specimen, and the angle between them was 120°. ere is no effect between the three main cracks, and such design can save materials.
Two materials, sandstone and polymathic methacrylate (PMMA), were selected to make the specimens. Sandstone material was obtained from Zigong area in China where the sandstone has the property of homogeneity and high density. An experimental study by Rossmanith [28] showed that PMMA has a similar fracture characteristic with homogeneous rock under dynamic loads. PMMA has the property of transparency so that crack propagation patterns after blasting can be observed easily. erefore, PMMA was also selected to make the specimens in the blasting tests.
For all the specimens, the distance b between the main crack tip and the center point A of the line connecting the two crack center was 30 mm; the diameter of the charge hole was 8 mm; the outer diameter, the inner diameter, and the length of the electric detonator were 7 mm, 6 mm, and 50 mm, respectively.
In order to make sure that main crack can propagate successfully and the distance a from the center of the borehole to the main crack tip was 20 mm for sandstone and 30 mm for PMMA. e length of main cracks and the pair of cracks were, respectively, 70 mm and 40 mm for sandstone and 30 mm and 40 mm for PMMA.
Two groups of PMMA specimens were tested. In the first group, the pair of cracks was parallel, and the crack spacing was designed as 20 mm, 35 mm, 50 mm, 65 mm, 80 mm, and 95 mm, respectively, to make sure that the existence of parallel cracks has an obvious influence on main crack propagation. In the second group, the distance between the pair crack centers was kept as a constant 40 mm, and the angle θ was designed as 20°, 50°, 80°, −20°, −50°, and −80°, as shown in Figures 2(b) and 2(c).
For sandstone specimens, the pair of cracks was parallel to the main crack, and the spacing of the pair of cracks S was only one variable. e spacing was designed as 20 mm, 30 mm, 40 mm, 50 mm, 60 mm, 70 mm, 80 mm, and 90 mm, 2 Shock and Vibration respectively. In addition, the tests by using the sandstone specimens without the pair of cracks were also conducted for comparison. e density of sandstone and PMMA was 2370 kg/m 3 and 1180 kg/m 3 , respectively, and their elastic wave velocity is obtained by the SonicViewer-SX system as shown in Figure 3, and according to the speed of P-wave and S-wave, the dynamic parameters such as elastic modulus and Poisson ratio can be calculated by the following equation: where c p and c s are the speed of P-wave and S-wave, and E, v, and ρ are the elastic modulus, the Poisson ratio, and the density, respectively. e measured dynamic material parameters have been listed in Table 1.
Because the length of the base charge of the detonator is larger than the thickness of both the sandstone and the PMMA specimens, a circular rubber ring was employed to fix the detonator in the blasting experiments so that the loads produced by explosive could fully apply to the face of the boreholes as Figure 4 shows. e base charge of the detonator is hexogen (C 3 H 6 N 6 O 6 ), and the length and density are 16 mm and 1.8 g/cm 3 , respectively; no coupling and no stemming were applied, and the location of the detonators is shown in Figure 4.
When stress waves encounter a free boundary, reflection will happen. e reflected tensile wave will affect the dynamic stress intensity factor (DSIF) at crack tip, and accordingly, the propagation behavior of the crack will vary [29]. erefore, the size of the specimen should be large enough to weaken the effect of the reflected tensile wave from the boundary, and the corresponding test results could be, therefore, similar to the reality of blasts in infinite rock mass. In this study, the diameter of the circular specimens for the sandstone and PMMA was 600 mm and 500 mm, respectively. e thickness was 15 mm for sandstone specimens and 10 mm for PMMA specimens, shown in Figure 4.
Measuring Systems.
Measuring systems, as shown in Figure 5, consists of an ultradynamic strain amplifier, a bridge box, a constant voltage source, an oscilloscope, a strain gauge stuck near borehole, a crack propagation gauge (CPG) circuit, and a computer. e ultradynamic strain amplifier is used to amplify the dynamic voltage signal and convey the signal to the oscilloscope. e constant voltage
Moving crack
Moving crack Moving crack Figure 1: ree cases of a moving crack approaching a pair of symmetric precracks. source offers a voltage of 16 V for the crack propagation gauge (CPG) circuit, and the CPG was connected with two resistors of 50 Ω. e CPG consists of 21 fine wires, and it is 40 mm in length, and 10 mm in width as shown in Figure 5. In the tests, the CPG was stuck along the main crack propagation path to measure crack propagation speed. e oscilloscope and the computer were applied in storing the experimental data, and the acquisition time of the oscilloscope was set as 1.2 ms which was enough to record the complete data.
Main crack
When the detonator is fired, the detonation pressure exerted on the borehole wall sets off a shock wave in the adjacent rock mass, but it soon decays to a high-amplitude stress wave propagating at the longitudinal wave speed in the rock mass. When the stress wave encounters the main crack tip, dynamic stress intensity factor (DSIF) at crack tip will be developed. And if it exceeds dynamic fracture toughness of materials, which is called as threshold value to predict crack status, the crack initiation and propagation will happen which will result in the fine wires of the CPG breaking one by one. e corresponding voltage signal recorded by the oscilloscope will jump step by step due to the changing of the CPGs' resistance. By calculating the derivatives of the CPGs' voltage signal with respect to time, the breaking times of the wires T(n) can be obtained. e spacing between two wires was 2 mm, so the average crack propagation speed can be calculated by 2 mm/(T(n + 1)−T(n)).
Crack Propagation Patterns under Parallel Symmetrical
Cracks. Blasting results when the pair of symmetrical cracks is parallel are shown in Figure 6 for sandstone specimens and Figure 7 for PMMA specimens. For sandstone, every main crack has propagated successfully and travelled through zones between the parallel cracks. When the spacing was less than 50 mm, main cracks propagated until it connected one of the parallel cracks. When the spacing is longer than 50 mm, main cracks just propagated forward. (a) Shock and Vibration 5 Crack propagation patterns for PMMA specimens are shown in Figure 7, and it can be found that all main cracks branch in the propagation process in the first and one of the branches keeps propagating in the later, and this is because the fracture toughness of PMMA is lower that rocks and crack branch will take place easier when stress at crack tip is strong enough.
To comparing results for different models, crack propagation length for sandstone and PMMA specimens was measured and the function of crack propagation length and the spacing of parallel cracks is shown in Figure 8. It can be observed that the main crack will propagate for a longer distance with the spacing of parallel cracks, and according to Figures 6 and 7, when there are no parallel cracks, crack propagation length is the longest among all the models. erefore, the existence of parallel cracks can arrest main crack propagating, which is related to the spacing of parallel cracks.
Crack Propagation Velocity in Sandstone Specimens.
To study main crack propagation in details, crack propagation gauges (CPG) were applied in measuring the main crack propagation speed in sandstone specimens for S � 40 mm, 60 mm, 80 mm, and no existing parallel cracks, and voltage signals of CPGs and its derivatives are shown in Figure 9.
Blast Results under Oblique Symmetrical Cracks in PMMA
Specimens. For investigating main crack propagation between oblique symmetrical cracks, just PMMA specimens were designed because it is earlier to make by the laser technique. Crack propagation patterns of these models are shown in Figure 11.
When parallel cracks exist, main crack arrest occurs at different times and different locations for different secondary spacings, and arrest location is near 11th fine wire for S � 40 mm, near 16th wire for S � 60 mm, and near 18th wire for S � 80 mm, respectively. eir arrest times are 127.80 μs, 152.40 μs, and 179.36 μs, respectively. From Figures 9(a), 9(b), and 9(c), after the crack arrest, main cracks keep propagating for a while. From Table 1, the P-wave speed of sandstone is 2430 m/s. e shortest distance that explosive stress wave travels from borehole to the free boundary and back to the running crack tip is about 460 mm. us, it will spend at least 189.30 μs so that the reflected wave from a free boundary can affect main crack propagation. Because all arrest times for three models are less than 189.30 μs, crack arrest is unrelated to the reflected wave, but which leads to main crack propagation again. When there are no parallel cracks, the time of 21th wire fracturing is 146.48 μs, so the CPG voltage signal is not influenced by the reflected wave.
Main crack propagating speeds can be obtained based on CPGs voltage signals, as shown in Figure 10, and it is the function of crack propagation speed versus crack extending distance. When parallel cracks exist, main crack propagation speeds have a tendency of decreasing gradually until it arrests and it will continue to propagate for a while when reflected waves reach, but later crack propagation speeds are much lower than previous propagation speeds. ere is a different trend of the change of crack speed when the spacing changes. For S � 40 mm, the velocity of the main crack seriously decreases with crack propagating, and for S � 60 mm, crack propagation speed varies fluctuantly at first and then decreases gradually, and for S � 80 mm, crack speed diminishes fluctuantly during the whole process. erefore, main crack arrest takes place earlier with the decrease of the spacing of parallel cracks. When there are no parallel cracks, crack speed varies fluctuantly, but has no tendency to decline.
When θ is negative, crack branching can be observed for all models, and the longest propagation lengths are 26.5 mm, 29.5 mm, and 23.5 mm, respectively, for θ � −20°, −50°, and −80°. When θ is positive, the longest propagation distances are 29 mm, 22.5 mm, and 18.5 mm, respectively, for θ � 20°, 50°, and 80°. So, the included angles of symmetrical cracks have an effect on main crack propagation and the function mechanisms are more complex compared to that under parallel cracks.
Numerical Study
Owing to the complexity of oblique symmetrical cracks, we will focus on exploring the function mechanism of parallel cracks on main crack propagation behaviors. In this section, numerical models are established based on the explicit dynamic software AUTODYN according to experimental specimens and stress distribution versus time in the specimen can be obtained.
Numerical Model.
In the numerical simulation, the numerical model included two parts: sandstone and explosive, in which quadrilateral element and Lagrange calculation method were applied. According to the specimen dimension shown in Figure 2(a), some numerical models of Shock and Vibration sandstone were established in AUTODYN code, as shown in Figure 12, and it is 1 mm in width for every crack. e dynamic mechanic parameter of sandstone has been shown in Table 1, and linear equation of state (EOS) was used to describe the state of sandstone under explosive stress wave, and it can be written as follows: where P is pressure, k is the bulk modulus, and ρ/ρ 0 is the ratio of the present density and the initial present. Because sandstone belongs to brittle material, linear elastic strength model was employed to express the relation of its strain and stress. And a modified principle stress failure criterion [30] was applied in predicting whether an element fails, which can be written as follows: where σ 1 is the maximum principal stress, σ 3 is the minimum principal stress, τ max is the maximum shear stress, σ T (_ ε) is the dynamic tensile strength, and τ C (_ ε) is the dynamic shear strength. e failure criterion means that when the maximum principal stress exceeds the dynamic tensile strength, or the maximum shear stress exceeds the dynamic shear strength, the element of sandstone will fail, which is not able to sustain any tensile or shear loading, but still be able to sustain compressive loading. For explosive material, hexogen in the detonator is used in AUTODYN code, and its density, C-J pressure, velocity of detonation, and detonation energy per unit volume are 1.891 g/cm3, 42 GPa, 9110 m/s, and 1.05 × 107 kJ/m3, respectively. Johns Wilkins Lee (JWL) is applied in describing Shock and Vibration 7 the state of explosive and it can be described by the following equation: where P is the pressure, V is the specific volume, E is the total initial energy, and A, B, R 1 , R 2 , and ω are constants. For hexogen explosive, and R 2 � 1.0, ω � 0.3. e erosion criterion was applied in the explosive material to avoid grid distortion, which says that when the geometric strain of explosive element exceeds 1.8, the element will vanish.
Numerical
Results. e dimensions of models in numerical simulations are the same as that in experiments, and there are 9 models in all, and numerical results are shown in Figure 13. Shear failure and tensile failure occurred in Shock and Vibration simulations, and the first is near borehole, and the second occurred in further location and propagation paths of main cracks. According to the simulation results, the propagation length of main cracks increases with the spacing of parallel cracks and it is less than that without parallel cracks. When S < 40 mm, main crack propagates toward the free surface of parallel cracks in the later period, which agrees with experiment results.
According to the distribution of pressure during the whole process, as shown in Figure 14, when explosive stress wave encounters free boundary, it will reflect and change to tensile wave, which can enhance the stress at crack tip. In the case of small space of parallel cracks, main crack arrest occurs earlier according to experiment results, and reflected wave will make crack propagate again, but this moment crack tip is different from that in initial circumstance, so crack propagation route will be easier to deviate.
Stress Distribution between Parallel Cracks.
To explore the mechanism of main crack arrest between parallel cracks, a target point was set in the location of 30 mm ahead of main Shock and Vibration crack tip to record the compressive stress in y-direction for models when S � 40 mm and no existing parallel cracks, as shown in Figure 15, and tensile stress is positive and compressive stress is negative. Comparing two kinds of models, there is much larger tensile stress from 42.5 μs to 52.5 μs and much larger compressive stress from 52.5 μs to 62.5 μs than that without parallel cracks, which says that bigger tensile stress and compressive stress occur in crack propagation path when parallel secondary cracks exist. Stress contour of model with S � 40 mm is shown in Figure 16, and there is strong compressive stress between parallel cracks at first, but which is not able to influence main crack propagation. When main crack propagates to the zone between parallel cracks, a strong compressive stress occurs, which can result in crack arrest.
Effect of the Spacing of Parallel Crack.
In order to investigate the difference among models with different spacings, nine target points were set along crack propagation path to record the maximum compressive stress in y-direction, as shown in Figure 17.
It can be found that there is obvious compressive stress between parallel cracks for all the models. However, some differences exist for different models according to these curves. For models of S � 20 mm, 30 mm, 40 mm, 50 mm, and 60 mm, the maximum compressive stress in y-direction firstly increases and then decreases with distance from initial main crack tip. However, it rises steadily, and the location corresponding to peak value is further from the initial main crack tip. When S is less than 35 mm, the maximum compressive stresses at target points increase with the spacing of parallel cracks, which leads to different arrest effects on main crack. When the spacing is small enough, the compressive stress between parallel cracks is very large, and the arrest function, therefore, is very large.
Discussion
Based on the foregoing analysis, main crack will arrest between parallel cracks and it is related to the spacing of them. e smaller the spacing, the more obvious the arrest effect on main crack propagation. In reality, the arrest effect is caused by the reflected compressive wave of the rarefaction wave.
For parallel cracks as shown in Figure 18(a), on the one hand, with the spacing increasing, the reflected angle will be increasing and it will can enhance the magnitude of stress component in y-direction, which suggests that stress component in y-direction is increasing with the reflected angle; however when the spacing is small, the compressive stress in y-direction is still big according to Figure 17, which is because that wave's travelling route is short and stress waves 15 keep strong enough. When the spacing of parallel cracks is increasing, the compressive stresses in y-direction decrease obviously firstly and then keep almost invariable according to Figure 17. For oblique symmetrical cracks, there still exists arrest effect on main crack propagation according to the results in experiments. When the included angle is toward inside as shown in Figure 18(b), the mechanism of crack arrest is similar to that of parallel cracks and it is also owing to the reflected compressive wave of rarefaction waves. When the included angle is toward outside as shown in Figure 18(c), the mechanism changes because the reflected wave is away from propagation path of main cracks, which is not able to have an effect on main crack propagation. In this situation, explosive waves are reflected on the face of symmetrical cracks so that blast energy which drives crack propagating decreases, and the strength of diffraction wave between secondary cracks will decline sharply; therefore, crack propagation length is smaller than that in the model without symmetrical crack.
Conclusions
is paper explored the effect of two symmetric cracks on the propagating crack using PMMA specimens and sandstone specimens, and crack propagation gauges were used to measure the main crack propagation speed in the sandstone blasting experiments. e explicit dynamic software AUTODYN was employed in doing explicit dynamic analysis for models and acquiring stress distribution between parallel cracks. Combining experimental and numerical results, the following conclusions can be obtained: (1) e pre-existing symmetrical cracks have arrest effect on main crack propagation under blast loads and it weakens with the spacing between them (2) Compressive stress in y-direction plays very important roles in crack arrest and it is caused by the reflected waves of rarefaction wave (3) As parallel cracks spacing increases, the terminal propagation length of main crack is increasing and crack propagation velocity declines slower
Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
e authors declare that they have no conflicts of interest. | 6,213.2 | 2020-08-07T00:00:00.000 | [
"Materials Science"
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Characterizing W2,p Submanifolds by p -Integrability of Global Curvatures
We give sufficient and necessary geometric conditions, guaranteeing that an immersed compact closed manifold \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^m \subset \mathbb{R}^n}$$\end{document} of class C1 and of arbitrary dimension and codimension (or, more generally, an Ahlfors-regular compact set Σ satisfying a mild general condition relating the size of holes in Σ to the flatness of Σ measured in terms of beta numbers) is in fact an embedded manifold of class \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C^{1,\tau} \cap W^{2,p}}$$\end{document}, where p > m and τ = 1 − m/p. The results are based on a careful analysis of Morrey estimates for integral curvature–like energies, with integrands expressed geometrically, in terms of functions that are designed to measure either (a) the shape of simplices with vertices on Σ or (b) the size of spheres tangent to Σ at one point and passing through another point of Σ. Appropriately defined maximal functions of such integrands turn out to be of class Lp(Σ) for p > m if and only if the local graph representations of Σ have second order derivatives in Lp and Σ is embedded. There are two ingredients behind this result. One of them is an equivalent definition of Sobolev spaces, widely used nowadays in analysis on metric spaces. The second one is a careful analysis of local Reifenberg flatness (and of the decay of functions measuring that flatness) for sets with finite curvature energies. In addition, for the geometric curvature energy involving tangent spheres we provide a nontrivial lower bound that is attained if and only if the admissible set Σ is a round sphere.
Introduction
In this paper we address the following question: under what circumstances is a compact, m-dimensional set Σ in R n , satisfying some mild additional assumptions, an m-dimensional embedded manifold of class W 2,p ? For p > m = dim Σ we formulate two necessary and sufficient criteria for a positive answer. Each of them says that Σ is an embedded manifold of class W 2,p if and only if a certain geometrically defined integrand is of class L p with respect to the m-dimensional Hausdorff measure on Σ. Σ itself is required in Definition 1.1. Both these properties follow from the finiteness of geometric curvature energies we consider here. It is relatively easy to see that F (m) contains immersed C 1 submanifolds of R n (cf. [Kol11, Example 1.57] for a short proof), or embedded Lipschitz submanifolds without boundary. It also contains other sets such as the following stack of spheres Σ = ∞ i=0 Σ i ∪{0}, where the 2-spheres Σ i = S 2 (c i , r i ) ⊂ R 3 with radii r i = 2 −i−2 > 0 are centered at the points c i = (p i + p i+1 )/2 for p i = (2 −i , 0, 0) ∈ R 3 , i = 0, 1, 2, . . . . Note that the spheres Σ i and Σ i+1 touch each other at p i+1 , and the whole stack Σ is an admissible set in the class F (2); see Figure 1.
A slightly different class A (δ) of admissible sets was used by the second and third author in [SM11b]. Roughly speaking, the elements of A (δ) are Ahlfors regular unions of countably many continuous images of closed manifolds, and have to satisfy two more conditions: a certain degree of flatness and a related linking condition; all this holds up to a set of H m -measure zero. The class A (δ) contains, for example, finite unions of C 1 embedded manifolds that intersect each other along sets of H m -measure zero (such as the stack of spheres in Figure 1), and bi-Lipschitz images of such unions, but also certain sets with cusp singularities. For example, an arc with two tangent segments, A = x ∈ R 2 : x 1 , x 2 ≥ 0 and x 2 1 + x 2 2 = 1 or max i=1,2 is in A (δ) for each δ > 0. However, A is not in F (1) as the β A (·, r) goes to zero as r → 0 at the cusp points while θ A (x, r) remains constant there. On the other hand, the union of a segment and countably many circles that are contained in planes perpendicular to that segment, where γ j = 2 −j (1, cos ϕ, sin ϕ) : ϕ ∈ [0, 2π] For triangles with angles bounded away from 0 and π, both quantities are in fact comparable. Therefore, in this case our global curvature function K G does not exceed a constant multiple of the global curvature as defined by Gonzalez and Maddocks [GM99], and widely used afterwards; see e.g. [GMSM02,CKS02,SMM03,SM03, SM04,SM07, GM11,GM11], and for global curvature on surfaces [SM05,SM06]. Also for m = 2, integrated powers of a function quite similar to K(x 0 , x 1 , x 2 ) in (1.4) were used in [SM11a] to prove geometric variants of Morrey-Sobolev imbedding theorems for compact two-dimensional sets in R 3 in an admissibility class slightly more general than the class A (δ) defined in [SM11b].
To define the second integrand, we first introduce the tangent-point radius, which for the purposes of this paper is a function Of course, the definition of K tp : Σ → [0, +∞] depends on the choice of H. However, we shall often omit the particular map H from the notation, assuming tacitly that a choice of 'tangent' planes Σ x → H(x) ∈ G(n, m) has been fixed.
A quick comment on the equivalence of (1) and (3) should be made right away: it is a relatively simple exercise to see that for a C 1 embedded manifold Σ the L p norm of K tp (·, H(·)) can be finite for at most one continuous map H : Σ → G(n, m)-the one sending every x ∈ Σ to T x Σ ∈ G(n, m).
Let us also mention a toy case of the equivalence of conditions (1) and (2) in the above theorem. For rectifiable curves γ in R n the equivalence of the arc-length parametrization Γ of γ being injective and in W 2,p , and the global curvature of γ being in L p has been proved by the second and third author in [SM07]. To be more precise, let S L := R/LZ, L > 0, be the circle with perimeter L, and denote by Γ : S L → R n the arclength parametrization of a closed rectifiable curve γ : S 1 → R n of length L. Then the global radius of curvature function ρ G [γ] : S L → R, ; see, e.g., [GMSM02], is defined as where, again, R(·, ·, ·) denotes the circumradius of a triangle, and the global curvature κ G [γ](s) of γ is given by . (1.7) In [SM07] we prove for p > 1 that Γ ∈ W 2,p (S L , R n ) and Γ is injective (so that γ is simple) if and only if κ G [γ] ∈ L p . Examples show that this fails for p = 1 = dim γ: There are embedded curves of class W 2,1 whose global curvature κ G is not in L 1 . The first part of the proof (3) ⇒ (1) for m = 1, namely the optimal C 1,τ -regularity of curves with finite energy, is modelled on the argument that was used in [SM12] for a different geometric curvature energy, namely for˜γ ×γ 1/R q tp . We conjecture that the implications (1) ⇒ (2), (3) of Theorem 1.4 fail for p = m > 1.
Remark. If (2) or (3) holds, then according to Theorem 1.4 Σ is embedded and locally, for some R > 0, Σ ∩ B n (x, R) is congruent to a graph of a W 2,p function f : R m → R n−m . Since p > m, we also know from a result of Calderón and Zygmund (see e.g. [EG92, Theorem 1, p. 235]) that Df : R m → L(R m , R n−m ) is differentiable a.e. in the classic sense.
Remark. One can complement Theorem 1.4 by the contribution of Blatt and the first author [BK12] in the following way. Suppose that 2 ≤ k ≤ m + 2 and in Definition 1.2 one takes the supremum only with respect to (m+2)−k points of Σ, defining the respective curvature K G,k as a function of k-tuples (x 0 , x 1 , . . . , x k−1 ) ∈ Σ k . Suppose that p > m(k − 1) and Σ is a C 1 embedded manifold. Then, K G,k is of class 1). If k = m + 2 and p > m(m + 2), then the assumption that Σ be a C 1 manifold is not necessary; one can just assume Σ ∈ F (m). See [BK12] for details. We believe that the characterization of [BK12] does hold for all 2 ≤ k ≤ m + 2 without the assumption that Σ is of class C 1 . (The regularity theory of [Kol11] has been generalized to all curvatures K G,k ).
Blatt's preprint [Bla11] contains a similar characterization in terms of fractional Sobolev spaces of those C 1 manifolds Σ for which the tangent-point energỹ Remark. Allard, in his classic paper [Al72], develops a regularity theory for mdimensional varifolds whose first variation (i.e., the distributional counterpart of mean curvature) is in L p for some p > m. His Theorem 8.1 ascertains that, under mild extra assumptions on the density function of such a varifold V , an open and dense subset of the support of V is locally a graph of class C 1,1−m/p . For p > m Sobolev-Morrey imbedding yields W 2,p ⊂ C 1,1−m/p and one might naïvely wonder if a stronger theorem does hold, implying Allard's (qualitative) conclusion just by Sobolev-Morrey. Indeed, Duggan [Dug86] proved later an optimal result in this direction. For integral varifolds, W 2,p -regularity can be obtained directly via elliptic regularity theory, see Menne [Men11, Lemmata 3.6 and 3.21].
In Allard's case the 'lack of holes' is built into his assumption on the first variation δV of V . Our setting is not so close to PDE theory: both 'curvatures' are defined in purely geometric terms and in a nonlocal way. Here, the 'lack of holes' follows, roughly speaking, from a delicate interplay between the inequality θ(x, r) β(x, r) built into the definition of F (m) and the decay of β(x, r) which follows from the finiteness of energy. A more detailed account on our strategy of proof here, is presented in the next subsection.
At this stage we do not know for our curvature energies what the situation is like in the scale invariant case p = m. For two-dimensional integer multiplicity varifolds, however (or in the simpler situation of W 2,2 -graphs over planar domains) Toro [Tor94] was able to prove the existence of bi-Lipschitz parametrizations. For m-dimensional sets Toro [Tor95,Eq.(1)] established a sufficient condition for the existence of bi-Lipschitz parametrizations in terms of θ. Her condition is satisfied, e.g., by S. Semmes' chord-arc surfaces with small constant, and by graphs of functions that are sufficiently well approximated by affine functions; see [Tor95,Section 5] for the details.
Remark. Following the reasoning in [SM07, Lemma 7] one can easily provide nontrivial lower bounds for the global tangent-point curvature for hypersurfaces (n = m + 1), and also for curves m = 1 < n; see Theorem 1.5 below. Indeed, setting such that Σ ∩ B n (a, R) = ∅, then we could find a strictly smaller sphere tangent to Σ in x and containing yet another point y ∈ Σ contradicting the definition of R. Hence we have shown that the union of such open balls which by definition of R can be rewritten as with equality if and only if Σ equals a round sphere. Hence, we obtain the following simple result.
Similarly, for m = 1 one concludes that any of those great circles on any of the balls B n (a, R) generating M in (1.8) that are also geodesics on M uniquely minimize E among all closed simple C 1 -curves Σ ≡ γ ⊂ R n \ M , which provides the lower bound (1.10) This is exactly what we found for curves in [SM07, Lemma 7 (3.1)], and is also consistent with (1.9) if n = 2 = m + 1.
Essential ideas and an outline of the proof.
we realized how slicing can be used to obtain optimal Hölder continuity of arc-length parametrizations. 2 (The scale invariant exponent p = 3 is critical here: polygons have infinite M p -energy precisely for p ≥ 3; see Scholtes [Sch11] for a proof). One crucial difference between curves γ and m-dimensional sets Σ in R n for m ≥ 2 lies in the distribution of mass in balls on various scales: If γ is a rectifiable curve and r < 1 2 diam γ, then obviously H 1 (γ ∩ B n (x, r)) ≥ r for each x ∈ γ. For m > 1 the measure H m (Σ ∩ B n (x, r)) might be much smaller than r m due to complicated geometry of Σ at intermediate length scales. In [SM11a] we have devised a method, allowing us to obtain estimates of H m (Σ ∩ B n (x, r)) for m = 2, n = 3 and all radii r < R 0 , with R 0 depending only on the energy level of Σ in terms of its integral Menger curvature. This method has been later reworked and extended in the GAFA CHARACTERIZING W 2,P SUBMANIFOLDS 945 subsequent papers [SM11b,Kol11], to yield the so-called uniform Ahlfors regularity, i.e., estimates of the form for other curvature energies and arbitrary 0 < m < n (to cope with the case of higher codimension, we used a linking invariant to guarantee that Σ has large projections onto some m-dimensional planes). Combining such estimates for H m (Σ ∩ B n (x, r)) with an extension of ideas from [SSM10] we obtained in [SM11a,SM11b,Kol11] a series of results, establishing C 1,α regularity for surfaces, or more generally, for a priori non-smooth m-dimensional sets for which certain geometric curvature energies are finite. Finally, we also realized that the well-known pointwise characterization of W 1,p -spaces of Haj lasz [Haj96] is the missing link, allowing us to combine the ideas from [Kol11,SM11b] in the present paper in order to provide with Theorem 1.4 a farreaching, general extension of [SM07, Theorems 1 & 2] from curves to m-dimensional manifolds in R n . Let us now discuss the plan of proof of Theorem 1.4 and outline the structure of the whole paper.
The easier part is to check that if Σ is an embedded compact W 2,p manifold without boundary, then conditions (2) and (3) hold. We work in small balls B(x, R) centered on Σ, with R > 0 chosen so that Σ ∩ B(x, R) is a (very flat) graph of a W 2,p function f : B m (x, 2R) → R n−m . Using Morrey's inequality twice, we first show that β Σ (a, r) g(a)r, a ∈ B(x, R) ∩ Σ, 0 < r < R, for a function g ∈ L p that is comparable to some maximal function of |D 2 f |. Next, working with this estimate of beta numbers on all scales r = R/2 k , k = 0, 1, 2, . . ., we show that in each coordinate patch each of the global curvatures K G and K tp can be controlled by two terms, where C(R) is a harmless term depending only on the size of the patches. (It is clear from the definitions that for embedded manifolds one can estimate both K G and K tp taking into account only the local bending of Σ and working in coordinate patches of fixed size; the effects of self-intersections are not an issue). This yields L p -integrability of K G and K tp . We refer to Sect. 4 for the details.
The reverse implications require more work. The proofs that (3) or (2) implies (1) have, roughly speaking, four separate stages. First, we use energy estimates to show that if K G L p or K tp L p are less than E 1/p for some finite constant E, then Here κ denotes a number in (0, 1 − m/p), depending only on m, p with different explicit values for K G or K tp , and A Σ is the constant from Definition 1.1 measuring Ahlfors regularity of Σ. By the very definition of m-fine sets, such an estimate implies that the bilateral beta numbers of Σ tend to zero with a speed controlled by r κ . In particular, Σ is Reifenberg flat with vanishing constant, and an application of [DKT01, Proposition 9.1] shows that Σ is an embedded manifold of class C 1,κ . See Section 3.1 for more details. Next, we prove the uniform Ahlfors regularity of Σ, i.e. we show that for all radii r ∈ (0, R 0 ), where R 0 depends only on the energy bound E and the parameters n, m, p, but not at all on Σ itself. Here, we rely on methods from our previous papers [Kol11,SM11a,SM11b]. Roughly speaking, we combine topological arguments based on the linking invariant with energy estimates to show that for each (There is a certain freedom in this phase of the proof; it would be possible to prove uniform Ahlfors regularity first, and estimate the decay of β Σ (x, r) afterwards. This approach has been used in [SM11a,SM11b].) After the second step we know that in coordinate patches of diameter comparable to R 0 the manifold Σ coincides with a graph of a function f ∈ C 1,κ (B m , R n−m ). The third stage is to bootstrap the Hölder exponent κ to the optimal τ = 1 − m/p > κ for both global curvatures K G and K tp . This is achieved by an iterative argument which uses slicing: if the integral of the global curvature to the power p over a ball is not too large, then this global curvature itself cannot be too large on a substantial set of good points in that ball. Geometric arguments based on the definition of the global curvature functions K G and K tp show that |Df (x) − Df (y)| |x − y| τ on the set of good points. It turns out that there are plenty of good points at all scales, and in the limit we obtain a similar Hölder estimate on the whole domain of f . See Section 3.3.
The fourth and last step is to combine the C 1,τ -estimates with a pointwise characterization of first order Sobolev spaces obtained by Haj lasz [Haj96]. The idea is very simple. Namely, the bootstrap reasoning in the third stage of the proof (Section 3.3) yields the following, e.g., for the global Menger curvature K G : On a scale R 1 ≈ R 0 , the intersection Σ∩B n (a, R 1 ) coincides with a flat graph of a function f : for τ = 1 − m/p. Such an inequality is true for every p > m so we can easily fix a number p ∈ (m, p) and show that where M (·) p is the Hardy-Littlewood maximal function of the global curvature.
Since p/p > 1, an application of the Hardy-Littlewood maximal theorem yields M p ∈ L p/p , or, equivalently, M ∈ L p . Thus, by the well known result of Haj lasz (see Section 2.3), (1.11) implies that Df ∈ W 1,p . In fact, the L p norm of D 2 f is controlled by a constant times the L p -norm of the global Menger curvature K G . An analogous argument works for the global tangent-point curvature function K tp . This concludes the whole proof; see Section 3.4. For each of the global curvatures, there are some technical variations in that scheme; here and there we need to adjust an argument to one of them. However, the overall plan is the same in both cases.
The paper is organized as follows. In Section 2, we gather some preliminaries from linear algebra and some elementary facts about simplices, introduce some specific notation, and list some auxiliary results with references to existing literature. Section 3 forms the bulk of the paper. Here, following the sketch given above, we prove that L p bounds for (either of) the global curvatures imply that Σ is an embedded manifold with local graph representations of class W 2,p . Finally, in Section 4 we prove the reverse implications, concluding the whole proof of Theorem 1.4.
The Grassmannian.
In this paragraph we gather a few elementary facts about the angular metric < )(·, ·) on the Grassmannian G(n, m) of m-dimensional linear subspaces 3 of R n .
Here is a summary: for two m-dimensional linear subspaces This will become especially useful in Section 3.3. For U ∈ G(n, m) we write π U to denote the orthogonal projection of R n onto U and we set Q U = Id R n − π U = π U ⊥ , where Id R n : R n → R n denotes the identity mapping.
3 Formally, G(n, m) is defined as the homogeneous space where O(n) is the orthogonal group; see e.g. Hatcher's book [Hat02, Section 4.2, Examples 4.53, 4.54 and 4.55] for the reference. Thus G(n, m) could be treated as a topological space with the standard quotient topology. Instead, we work with the angular metric < )(·, ·), see Definition 2.1.
The function < )(·, ·) defines a metric on the Grassmannian G(n, m). The topology induced by this metric agrees with the standard quotient topology of G(n, m). We list several properties of < ) below. They will become useful for Hölder estimates of the graph parameterizations of Σ in Section 3.3.
since C 3 (m) ≥ 4 for all m ∈ N; see the definition of C 3 (m) at the end of the proof of Proposition 2.5. Hence Proposition 2.5 is applicable to the orthonormal basis (ê 1 , . . . ,ê m ) of V , and we conclude Since we assumed (2.14) we can divide both sides by 1 − C 3 (ε + C 2 δ) reaching the estimate Finally we set .
Angles and intersections of tubes.
The results of this subsection are taken from our earlier work [SM11b]. We are concerned with the intersection of two tubes whose m-dimensional 'axes' form a small angle, i.e. with the set where H 1 = H 2 ∈ G(n, m) are such that π H1 restricted to H 2 is bijective. Since the set {y ∈ R n : dist(y, H i ) ≤ 1} is convex, closed and centrally symmetric 4 for each i = 1, 2, we immediately obtain the following: is a convex, closed and centrally symmetric set in R n ; π H1 (S(H 1 , H 2 )) is a convex, closed and centrally symmetric set in For the global tangent-point curvature K tp , the next lemma and its corollary provide a key tool in bootstrap estimates in Section 3.3.
For the proof, we refer to [SM11b, Lemma 2.6]. It is an instructive elementary exercise in classical geometry to see why this lemma is true for m = 2 and n = 3.
The next lemma is now practically obvious.
for each a ∈ H and each s > 0.
Proof. Writing each y ∈ S ∩ B n (a, s) as y = π W (y) + (y − π W (y)), one sees that S ∩ B n (a, s) is contained in a rectangular box with (m − 1) edges parallel to W and of length 2s and the remaining edge perpendicular to W and of length 2d. Note that for any (m + 1)-dimensional simplex T the volume is given by The faces fc i (T ) are lower-dimensional simplices themselves, so that a simple inductive argument yields the estimate Fix two indices i 1 , i 2 ∈ {1, 2, . . . , m + 1} such that i 1 = i 2 . We shall estimate the height h i1 (T ). Without loss of generality we can assume that x i2 is placed at the origin. Furthermore, permuting the vertices of T we can assume that i 1 = 1 and i 2 = 2. We need to estimate h 1 (T ). Set so all we need to do is to estimate < )(P,P ) from above unless < )(P,P ) = 0, in which case we are done anyway.
2.4
Other auxiliary results. The following theorem due to Haj lasz gives a characterization of the Sobolev space W 1,p and is now widely used in analysis on metric spaces. We shall rely on this result in Section 3.4.
Theorem 2.13 (Haj lasz [Haj96, Theorem 1]).
Let Ω be a ball in R m and 1 < p < ∞. Then a function f ∈ L p (Ω) belongs to W 1,p (Ω) if and only if there exists a function g ∈ L p (Ω) such that (2.22) In fact, Haj lasz shows that if f ∈ W 1,p , then (2.22) holds for g equal to a constant multiple of the Hardy-Littlewood maximal function M (|Df |) of |Df | defined as Conversely, where the infimum is taken over all g for which ( sup x∈Σ θ Σ (x, r) = 0.
The following proposition was proved by David, Kenig and Toro. We will rely on it in Section 3.1.
Then Σ is an m-dimensional C 1,κ -submanifold of R n without boundary. 6
Towards the W 2,p estimates for graphs
In this section we prove the harder part of the main result, i.e. the implications (2) ⇒ (1) and (3) ⇒ (1). We follow the scheme sketched in the introduction. Each of the four steps is presented in a separate subsection.
The decay of β numbers and initial C 1,κ estimates.
In this subsection we prove the following two results.
holds for all r ∈ (0, diam Σ] and all x ∈ Σ. The constant C is an absolute constant.
The argument is pretty similar in either case but it will be convenient to give two separate proofs.
For the proof of Proposition 3.1 we mimic-up to some technical changes-the proof of [Kol11, Corollary 2.4]. First we prove a lemma which is an analogue of [Kol11, Proposition 2.3].
Renumbering the vertices of T we can assume that h min (T ) = h m+1 (T ). Thus, according to (2.16) the largest m-face of T is conv(x 0 , . . . , x m ). Let H = span{x 1 − x 0 , . . . , x m − x 0 }, so that x 0 + H contains the largest m-face of T . Note that the distance of any point y ∈ Σ ∩ B(x, r) from the affine plane x 0 + H has to be less then or equal to h min (T ) = dist(x m+1 , x 0 + H), since if we could find a point y ∈ Σ ∩ B(x, r) with dist(y, x 0 + H) > h min (T ), then the simplex conv(x 0 , . . . , x m , y) would have larger H m+1 -measure than T , but this is impossible due to the choice of T . Since (3.24) Hence β Σ (x, r) ≤ 2h min (T ) r . (3.25) Now we only need to estimate h min (T ) = h m+1 (T ) from above. Of course, T is (η, 2r)-voluminous with η = h min (T )/(2r). Lemma 3.3 implies that which ends the proof of the proposition. Now we come to the Proof of Proposition 3.2. Fix x ∈ Σ and r ∈ (0, diam Σ]. We know by definition of the β-numbers that β ≡ β Σ (x, r) ≤ 1. We also know that for any z ∈ Σ ∩ B(x, βr/2) that where H z ∈ G(n, m) denotes the image of z under the mapping H : Σ → G(n, m). Furthermore, for any > 0 we can find a point y ∈ Σ ∩ B(x, r) such that On the other hand, we have by |y − z| ≤ |y − x| + |x − z| ≤ 3 2 r dist(y , z + H z ) ≤ 1 2 K tp (z)|y − z| 2 ≤ K tp (z) 9 8 r 2 , so that we obtain 9 8 which upon letting → 0 leads to
Moreover, we can find a radius R = R(n, m, p, A Σ , M Σ , E, diam Σ) and a constant K = K(n, m, p, A Σ , M Σ , E, diam Σ) such that for each x ∈ Σ there is a function where Graph f x ⊂ P × P ⊥ = R n denotes the graph of f x , and Assume without loss of generality that x = 0 and write κ := κ i for any i ∈ {1, 2} depending on the particular choice of integrand K (i) . We know from Propositions 3.1 or 3.2, respectively, that there is a constant (3.27) The Grassmannian G(n, m) is compact, so we find for each r ∈ (0, diam Σ] an m-plane H x (r) ∈ G(n, m) such that Taking an ortho-(r/3)-normal basis (v 1 (r), . . . , v m (r)) of H x (r) for any such r ∈ (0, diam Σ] we find by (3.27) for each i = 1, . . . , m, some point z i (r) ∈ Σ such that (3.28) see Definition 1.1. Now there is a radius R 0 = R 0 (A Σ , E, m, p, M Σ ) > 0 so small that we have the inclusion B(v i (r), M Σ C 1 r κ+1 ) ⊂ B(0, r/2) for each r ∈ (0, R 0 ) and each i = 1, . . . , m, which then implies by (3.26) that dist(z i (r), H x (r/2)) ≤ C 1 r κ+1 for all r ∈ (0, R 0 ). (3.29) The orthogonal projections u i (r) := π Hx(r/2) (v i (r)) for i = 1, . . . , m, satisfy due to (3.28) and (3.29) Hence there is a smaller radius 0 < R 1 = R 1 (A Σ , E, m, p, M Σ ) ≤ R 0 such that for all r ∈ (0, R 1 ) one has so that Proposition 2.6 is applicable to the (r/3, 0, 0)-basis (v 1 (r), . . . , v m (r)) of V := H x (r) and the basis (u 1 (r), . . . , u m (r)) of U := H x (r/2) with ϑ := C 1 r κ . (Notice that condition (2.14) in Proposition 2.6 is automatically satisfied since = δ = 0 in the present situation.) Consequently, , H x (r/2)) ≤ C 4 C 1 r κ for all r ∈ (0, R 1 ). (3.31) Iterating this estimate, one can show that the sequence of m-planes (H x (r/2 N )) is a Cauchy sequence in G(n, m), hence converges as N → ∞ to a limit m-plane, which must coincide with the already present tangent plane T 0 Σ at x = 0, and the angle estimate (3.31) carries over to Let y ∈ Σ be such that |y − x| = r/2 and set w i (r) = π Hy(r) (v i (r)). We have Applying once again Proposition 2.6-which is possible due to (3.30)-we obtain the inequality This together with (3.32) (which by symmetry also holds in y replacing x) leads to the desired local estimate for the oscillation of tangent planes where C = C(E, A Σ , m, p, M Σ ) and R 1 = R 1 (E, A Σ , m, p, M Σ ) do not depend on the choice of x, y ∈ Σ. Next we shall find a radius R 2 = R 2 (E, A Σ , m, p, M Σ ) such that for each x ∈ Σ the affine projection is injective. This will prove that Σ∩B(x, R 2 ) coincides with a graph of some function f x , which is C 1,κ -smooth by (3.33).
Assume that there are two distinct points y, z ∈ Σ ∩ B(x, R 1 ) such that π x (y) = π x (z). In other words (y − z) ⊥ T x Σ. Since y and z are close to each other the vector (y − z) should form a small angle with T z Σ, but then < )(T z Σ, T x Σ) would be large and due to (3.33) this can only happen if one of y or z is far from x. To make this reasoning precise assume that |x − y| ≤ |x − z| and set H x = H x (|y − x|). Employing (3.26) and (3.32) we get where C depends only on E, A Σ , m and p. The same applies to (z − x) so we also have Next we estimate Setting H z = H z (|y − z|) and repeating the same calculations we obtain This gives On the other hand, by (3.33 This shows that if (y − z) ⊥ T x Σ then the point z has to be far from x. We set R 2 = min 1, (C +C) −1/κ , and this way we make sure that π x : Σ ∩ B(x, The oscillation estimate (3.33) leads with standard arguments (as, e.g., presented in [SM11b, Section 5]) to the desired uniform C 1,κ -estimates for f x on balls in T x Σ of radius R 2 which depends on E, A Σ , p, m, M Σ , but not on the particular choice of the point x on Σ.
Remark 3.5. The statement of Corollary 3.4 can a posteriori be sharpened: One can show that one can make the constants R and K independent of M Σ . This was carried out in detail in the first author's doctoral thesis; see [Kol11, Theorem 2.13], so we will restrict to a brief sketch of the argument here. Assume as before that x = 0 and notice that β(r) = β(0, r) → 0 uniformly (independent of the point x and also independent of M Σ according to (3.26)). Since at this stage we know that Σ is a C 1,κ -submanifold of R n without boundary, it is clearly also admissible in the sense of [SM11b, Definition 2.9]. In particular Σ is locally flat around each point y ∈ Σ-it is actually close to the tangent m-plane T y Σ near y-and Σ is nontrivially linked with sufficiently small (n − m − 1)-spheres contained in the orthogonal complement of T y Σ. Let H x (r) for r ∈ (0, diam Σ] be as in the proof of Corollary 3.4 the optimal m-plane through x = 0 such that dist(y, x + H x (r)) ≤ β(r)r for all y ∈ Σ ∩ B(0, r). (3.35) One can use now the uniform estimate (3.26) (not depending on M Σ ) to prove that there is a radius R 3 = R 3 (E, A Σ , m, p) such that the angle < )(T 0 Σ, H x (r)) is for each r ∈ (0, R 3 ) so small that, for any given p ∈ H x (r) ∩ B(0, R 3 ), one can deform the linking sphere in the orthogonal complement of T 0 Σ with a homotopy to a small sphere in p + H x (r) ⊥ without ever hitting Σ. Because of the homotopy invariance of linking one finds also this new sphere nontrivially linked with Σ. This implies in particular by standard degree arguments the existence of a point z ∈ Σ contained in the (n−m)-dimensional disk in p+H x (r) ⊥ spanned by this new sphere; see, e.g. [SM11b,Lemma 3.5]. On the other hand, by (3.35) Σ ∩ B(0, r) is at most β(r)r away from H x (r) which implies now that this point z ∈ Σ must satisfy |z − p| ≤ β(r)r. This gives the uniform estimate θ(r) ≤ Cβ(r) for all r < R 3 and some absolute constant C.
Now we know that the estimates in Corollary 3.4 do not depend on M Σ . This constant may be replaced by an absolute one if we are only working in small scales.
In the next section we show that this can be further sharpened: R and K depend in fact only on m, p and E, but not on the constant A Σ .
Uniform Ahlfors regularity and its consequences.
In this section, we show that the L p -norms of the global curvatures K G and K tp control the length scale in which bending (or 'hairs', narrow tentacles, long thin tubes etc.) can occur on Σ. In particular, there is a number R depending only on n, m, p and E, where E is any constant dominating K G p L p or K tp p L p , such that for all x ∈ Σ and all r ≤ R the intersection Σ ∩ B n (x, r) is congruent to Graph f x ∩ B n (x, r), where f x : R m → R n−m is a C 1,κi function (with small C 1 norm, if one wishes). Note that R does not at all depend on the shape or on other properties of Σ, just on its energy value, i.e. on the L p -norm of K G or of K tp .
By the results of the previous subsection, we already know that Σ is an embedded C 1 compact manifold without boundary. This is assumed throughout this subsection.
The crucial tool needed to achieve such control over the shape of Σ is the following.
Theorem 3.6 (Uniform Ahlfors regularity). For each p > m there exists a constant C(n, m, p) with the following property. If K G L p or K G L p is less than E 1/p for some E < ∞, then for every where R 0 = C(n, m, p)E −1/(p−m) and ω m = H m (B m (0, 1)).
The proof of Theorem 3.6 is similar to the proof of Theorem 3.3 in [SM11a] where Menger curvature of surfaces in R 3 has been investigated. This idea has been later reworked and extended in various settings to the case of sets having codimension larger than 1. GAFA CHARACTERIZING W 2,P SUBMANIFOLDS 963 Namely, one demonstrates that each Σ with finite energy cannot penetrate certain conical regions of R n whose size depends solely on the energy. The construction of those regions has algorithmic nature. Proceeding iteratively, one constructs for each x ∈ Σ an increasingly complicated set S which is centrally symmetric with respect to x and its intersection with each sphere ∂B n (x, r) is equal to the union of two or four spherical caps. The size of these caps is proportional to r but their position may change as r grows from 0 to the desired large value, referred to as the stopping distance d s (x). The interior of S contains no points of Σ but it contains numerous (n − m − 1)-dimensional spheres which are nontrivially linked with Σ. Due to this, for each r below the stopping distance, Σ ∩ B n (x, r) has large projections onto some planes in G(n, m). However, there are points of Σ on ∂S, chosen so that the global curvature K G (x), or K tp (x), respectively, must be 1/d s (x).
To avoid entering into too many technical details of such a construction, we shall quote almost verbatim two purely geometric lemmata from our previous work that are independent of any choice of energy, and indicate how they are used in the proof of Theorem 3.6. Proposition 3.7. Let δ ∈ (0, 1) and Σ be an embedded C 1 compact manifold without boundary. There exists a real number η = η(δ, m) ∈ (0, 1) such that for every point x 0 ∈ Σ there is a stopping distance d = d s (x 0 ) > 0, and an (m + 1)-tuple of points (x 1 , x 2 , . . . , x m+1 ) ∈ Σ m+1 such that
Moreover, we can provide a lower bound for all stopping distances. For this, we need an elementary consequence of the definition of voluminous simplices: Observation 3.9. If T = conv(x 0 , . . . , x m+1 ) ∈ V (η, d) then by (2.17) (3.39) The key to Theorem 3.6 in the case of K tp global curvature is to observe that high energy couples and large projections coexist on the same scale.
Assume that Σ is an arbitrary embedded C 1 compact manifold without boundary. For every x ∈ Σ there exist a number d ≡ d s (x) > 0 and a point y ∈ Σ such that and therefore For the proof of this lemma (for a much wider class of m-dimensional sets than just C 1 embedded compact manifolds) we refer the reader to [SM11b, Section 4].
Lemma 3.13. If Σ ⊂ R n is an embedded C 1 compact manifold without boundary, p > m and then the stopping distances d s (x) of Proposition 3.12 satisfy where c depends only on n, m and p.
As for Corollary 3.4 also here we do not enter into the details of construction of the graph parametrizations f x . These are described in [SM11b,Section 5.4] and in [Kol11, Section 3].
Remark 3.15. Note that shrinking a(n, m, p) if necessary, we can always assume that for an arbitrary small ε 0 = ε 0 (m) > 0 that has been a priori fixed.
3.3 Bootstrap: optimal Hölder regularity for graphs. In this subsection we assume that Σ is a flat m-dimensional graph of class C 1,κi , satisfyinĝ Σ K (i) (z) p dH m (z) < ∞ for i = 1 or i = 2, recall our notation from before: K (1) := K G and K (2) := K tp . The goal is to show how to bootstrap the Hölder exponent κ i to τ = 1 − m/p.
Relying on Corollary 3.14 and Remark 3.15, without loss of generality we can assume that for a fixed number R > 0, where for some number ε 0 to be specified later on. The ultimate goal is to show that osc B m (b,s) Df ≤ Cs τ with a constant C depending only on the local energy of Σ; cf. (3.50). The smallness condition (3.43) allows us to use all estimates of Section 2 for all tangent planes T z Σ with z ∈ Σ ∩ B n (0, 20R). Let F : P → R n be the natural parametrization of Σ ∩ B n (0, 20R), given by F (ξ) = (ξ, f (ξ)) for ξ ∈ P ; outside B n (0, 20R) the image of F does not have to coincide with Σ. The choice of ε 0 guarantees where ε 1 (m) is the constant from Lemma 2.8. As in our papers [SM11b, Section 6], [SM11a,Kol11], developing the idea which has been used in [SSM10] for curves, we introduce the maximal functions controlling the oscillation of Df at various places and scales, where the supremum is taken over all possible closed m-dimensional balls B of radius that are contained in a subset A ⊂ B n (0, 5R) ∩ P , with ≤ 5R. Since f ∈ C 1,κ with κ = κ 1 or κ = κ 2 we have a priori for some constant C which does not depend on , A.
To show that f ∈ C 1,τ for τ = 1 − m/p, we check that locally, on each scale ρ, the oscillation of Df is controlled by a main term which involves the local integral of K (i) (z) p and has the desired form Cρ τ , up to a small error, which itself is controlled by the oscillation of Df on a much smaller scale ρ/N . The number N can be chosen so large that upon iteration this error term vanishes.
Corollary 3.17 (Geometric Morrey-Sobolev embedding into C 1,τ ). Let p > m and Σ ⊂ R n be an m-fine set Then Σ is an embedded closed manifold of class C 1,τ , where τ = 1 − m/p. Moreover we can find a radius R 2 = a 2 (n, m, where a 2 (n, m, p) is a constant depending only on n, m and p, and a constant K 2 = K 2 (n, m, p) such that for each x ∈ Σ there is a function f : T x Σ =: P ∼ = R m → P ⊥ ∼ = R n−m of class C 1,τ , such that f (0) = 0 and Df (0) = 0, and where Graph f ⊂ P × P ⊥ = R n denotes the graph of f , and we have The rest of this section is devoted to the proof of Lemma 3.16 for each of the global curvatures K (i) . We follow the lines of [Kol11,SM11b] with some technical changes and necessary adjustments.
and consider the set of bad points where the global curvature becomes large, We now estimate the curvature energy to obtain a bound for H m (Y 0 ). For this we restrict ourselves to a portion of Σ that is described as the graph of the function f .
The last equality follows from the choice of K 0 in (3.52). Thus, we obtain and since the radius of B equals t, we obtain Now, select two good points u j ∈ B m (z j , t/N) \ Y 0 (j = 1, 2). By the triangle inequality, (3.56) Thus, we must only show that for good u 1 , u 2 the last term in (3.56) satisfies This has to be done for each of the global curvatures K (i) . (It will turn out that for K tp one can use just the second term on the right hand side of (3.57).)
Angles between good planes: the 'tangent-point' case.
We first deal with the case of K tp which is less complicated. To verify (3.57), we assume that Df (u 1 ) = Df (u 2 ) and work with the portion of the surface parameterized by the points in the good set (3.58) (3.59) To conclude the whole proof, we shall derive-for each of the two global curvatures-an upper estimate for the measure of G, where α := < )(H 1 , H 2 ) = 0 and H i := T F (ui) Σ denotes the tangent plane to Σ at F (u i ) ∈ Σ for i = 1, 2. Combining (3.60) and (3.59), we will then obtain (By an elementary reasoning analogous to the proof of Theorem 5.7 in [SM11b], this also yields an estimate for the oscillation of Df .) Following [SM11b, Section 6] closely, we are going to prove the upper estimate (3.60) for H m (G).
3.4 W 2,p estimates for the graph patches. We now show that Corollary 3.17 combined with the result of Haj lasz, cf. Theorem 2.13, easily yields the following. Definition 4.1. Let Σ ⊂ R n . We say that Σ is an m-dimensional, W 2,p -manifold (without boundary) if at each point x ∈ Σ there exist an m-plane T x Σ ∈ G(n, m), a radius R x > 0, and a function f ∈ W 2,p (T x Σ ∩ B n (0, 2R x ), R n−m ) such that We will use this definition only for p > m. In this range, by the Sobolev imbedding theorem, each W 2,p -manifold is a manifold of class C 1 .
Theorem 4.2.
Let p > m and let Σ be a compact, m-dimensional, W 2,p -manifold. Then the global curvature functions K G [Σ] and K tp [Σ] are of class L p (Σ, H m ). Remark 4.3. As already explained in the introduction, here we assume that K tp is defined for the natural choice of m-planes H x = T x Σ. As we mentioned before, if Σ is a C 1 manifold and H x = T x Σ on a set of positive H m -measure, then the global curvature K tp defined for H x instead of T x Σ has infinite L p -norm. 4.1 Beta numbers for W 2,p graphs. We start the proof with a general lemma that shall be applied later to obtain specific estimates for K G and K tp in L p (Σ). Proof . Fix s ∈ (m, p). Then, f ∈ W 2,s (B m (0, 2R)). Since s > m we have the embedding Of course Ψ x is in W 2,p (B m (0, 2R), R n ) and therefore also in W 2,s (B m (0, 2R), R n ). We now fix another point y in B m (x, R) and estimate the oscillation of Ψ x . Set U := B m x + y 2 , |x − y| .
By two consecutive applications of the Sobolev imbedding theorem in the supercritical case (cf. [GT01,Theorem 7.17]), keeping in mind that U is a ball of radius |x − y|, we obtain Here M denotes the Hardy-Littlewood maximal function and the constant C =Ĉ(n, m, s) depends on n, m, and s. Since m < s < p we have p s > 1 and |D 2 f | s ∈ L p/s (B m (0, 2R)). Hence we also have M (|D 2 f | s ) ∈ L p/s (B m (0, 2R)). Therefore M (|D 2 f | s ) 1/s ∈ L p (B m (0, 2R)). | 11,988.2 | 2013-05-07T00:00:00.000 | [
"Mathematics"
] |
Development of an HPTLC-based dynamic reference standard for the analysis of complex natural products using Jarrah honey as test sample
In this paper, we describe a novel approach to the development of a reference standard for the quality control of complex natural products, which will assist in the assessment of their authenticity and purity. The proposed method provides a template for the selection of samples, which can be pooled to obtain a reference standard. A shortfall of such an approach is, however, that the pooled sample is static in nature and therefore unable to capture difference in processing conditions or natural variations triggered by geographical or climatic impacts over time. To address this, the paper also outlines the development of a dynamic reference standard, which allows for ongoing adjustments to future variations. The method employs High-Performance Thin Layer Chromatography (HPTLC) derived extract profiles processed by multivariate analysis. The development of the dynamic reference standard is illustrated using honey, a complex natural matrix, as an example.
Introduction
Natural products of plant and animal origin have been investigated physically, chemically or organoleptically for thousands of years [1,2]. In particular for those that are used as medicinal, food or flavouring agents, a consistent phytochemical profile and with this predictability and reliability in appearance, taste, smell and also bioactivity are paramount [3][4][5][6]. The development of appropriate reference standards has therefore been a focus of quality control efforts in order to assess the authenticity, purity and potency of natural products. Many quality assurance methods for natural products rely on the qualitative and / or quantitative analysis of meaningful marker compounds [7][8][9]. Standardisation of these marker compounds, however, poses its own challenges, for example when the natural product's bioactivity levels (along with its organoleptic characteristics) cannot easily be tied to a single or a few compounds [10] are the result of a complex interplay of a variety of constituents [11][12][13], or in cases where key constituents have not yet been chemically identified [14]. The use of profile chromatograms, which reflect a natural product's typical phytochemical composition, is therefore a common approach [15]. Furthermore, seasonal and geographical variations introduce an additional layer of complexity for the authentication and quality control of complex natural matrices. Rather than evaluating an extract against a profile chromatogram derived from a single reference sample of the natural product, pooling samples might therefore be more appropriate [16][17][18]. In this approach a number of samples, deemed to adequately represent the natural product extract, even across seasons or a wider geographical spread, are blended to create a pooled reference sample. Although there will necessarily be some variations between individual samples within the blend, the overall 'picture' that emerges from this pooled reference sample and its associated profile chromatogram will capture the extract's typical phytochemical characteristics; pooling will 'dilute out' unusual constituents and amplify those that are common across the samples and so facilitate adequate quality control of complex natural products. Two core challenges remain nonetheless. First, how to select samples for inclusion in this pooled reference sample and second, how to ensure that the pooled reference standard remains 'current' and continues to adequately reflect a natural product extract, which might change over time due to a range of external factors (e.g. climate change, change in growing or processing condition).
In this paper, we describe a novel method for the development of a reference standard, which is able to address both of these challenges. It provides a template for the selection of samples and, due to its dynamic nature, also allows for ongoing adjustments to future variations. The approach is based on High-Performance Thin Layer Chromatography (HPTLC) extract profiles and their multivariate analysis. The development of such a dynamic reference standard is illustrated using honey, which is a complex natural matrix, as an example.
The phytochemical composition of honey, and with this its organoleptic and bioactivity profile, is directly related to its floral origin [19][20][21], namely the flowers bees visit and the nectar they collect. Variations in composition are reflected in a honey's organic extract and can be captured in the respective HPTLC profile [22][23][24]. Monofloral honeys, which are predominately derived from a single floral source, are highly sought after and priced accordingly [25,26]. However, wild harvested honeys are never 100% monofloral in their origin as bees cannot be restricted to a particular foraging area and will collect nectar opportunistically based on preferences and nutritional needs [27,28]. Furthermore, geographical and environmental variations of nectar producing plants, differences in harvesting methods and post-harvest processing as well as variations in storage conditions can also impact on the final phytochemical composition of honey [29][30][31]. This complexity makes honey an ideal model natural product to investigate the development of a dynamic reference standard for authentication and quality control.
Specifically, this study focuses on Jarrah honey, which originates from Eucalyptus marginata, a tree endemic to the south west of Western Australia [32]. This highly antibacterial and antioxidant honey [33] is mainly harvested from native forests and nature reserves, which means that Jarrah honeys might be mixed with other floral sources. To ensure a quality product, the authentication of the honey's predominant nectar source against a representative reference standard is therefore an important undertaking. Over the years a range of authentication methods for honey have been developed [34]. For example, melissopalynology is commonly used to authenticate honeys, although in the specific context of Australian eucalypt honeys this approach is not without its challenges [35][36][37][38][39]. The method introduced in this paper outlines how a dynamic reference standard can be developed based on the multivariate analysis of HPTLC profiles of Jarrah honey organic extracts, which might then be used as an alternative authentication tool.
It needs to be emphasised that the combination of HPTLC and multivariate analysis is not new, not even in the context of honey analysis [24,[40][41][42]. What is novel about this study is the way, outlined below, how multivariate analysis of HPTLC profiles can be used to derive a dynamic, representative reference standard for quality control purposes. Two steps are proposed to derive this reference standard: 1. Identify similarities in the HPTLC profile to determine the target cluster, which constitutes an aggregation of samples with similar constituent profiles. This step assists in defining the target cluster by removing extreme outliers as well as samples that are of multifloral origin.
2. Additional screening of the target cluster to remove diluted samples as well as those that have moderate quantities of other floral sources present. This step assists with the definition of the core cluster.
In the first step, the HPTLC fingerprints of the target samples are analysed alongside other samples of a different floral origin and thus with different HPTLC fingerprints. This assists in defining target cluster characteristics common to all target samples by discriminating from samples with different HPTLC profiles. Thus, this initially identified target cluster will only contain samples with similar characteristics; extreme outliers or samples of multifloral origin will be removed from the target cluster at this stage. The samples constituting this target cluster are then carried forward into the second analysis step.
In the second step, samples forming the target cluster will be analysed again. As in this analysis round no additional samples are introduced, the target cluster will be refined with dilute samples and those that contain moderate quantities of other floral origins shifting towards the periphery of the cluster. This will allow to identify those samples that constitute the core cluster. Reiterations of the second step are possible in order to further refine the core cluster.
Samples in the identified core cluster can then be pooled and the blend be used as a reference tool for quality control purposes as the representative fingerprint and chromatographic profile of the combined sample will capture all the characteristics and natural variations of the natural product extract. However, such a physical reference sample is static in nature and might no longer be able to capture and reflect externally driven changes (e.g. change in growing or processing conditions, climate change). An alternative to this pooling approach is therefore to work with a dynamic reference sample, which continues to reflect even subtle changes to the natural product extract's phytochemical composition over time, in fluent, or dynamic, cluster boundaries.
Using Jarrah honey as case example, we will explore the various steps leading to the identification of the target and core clusters and then assess three Jarrah honeys against the pooled reference sample as well as the dynamic reference standard, which were both developed on the basis of multivariate analysis, in order to determine their floral authenticity.
Reagents, chemicals and samples
All reagents and chemicals used in this study were of analytical grade. Honey samples (n = 104) were collected from beekeepers of Western Australia (Table 1). They were classified according to the information provided on the label and no further initial tests were carried out to confirm their floral identity.
To obtain the organic honey extracts for HPTLC fingerprinting, 1 g of each honey was dissolved in 2 ml of deionised water. The aqueous honey solution was extracted three times with 5 ml of dichloromethane. After drying with anhydrous MgSO 4 the combined organic extracts were evaporated at ambient temperature and stored at 4˚C until further analysis.
High-Performance Thin Layer Chromatography (HPTLC) fingerprinting
To obtain the honey extracts' respective chromatographic profiles, the method described by Locher et al. [22,23] was followed. In brief, after reconstituting in 100 μL of dichloromethane
Data acquisition
The four sets of fingerprints of each sample (at 254 nm and 366 nm, and at white light and 366 nm after derivatisation) were converted into their respective chromatograms to derive values for migration distances (Rf) and corresponding intensities (AU). Furthermore, the colour (as RGB values) of the corresponding HPTLC bands was also recorded. Only bands with a Rf value between 0.05 and 0.60 were considered as this captured the majority of bands. While some additional bands with higher Rf values can be seen in the respective HPTLC fingerprint (Fig 1) they are not specific to a honey's floral source and thus will not contribute any important bands towards the development of the reference standard. Given the lipophilic nature of the extraction solvent, these bands most likely represent waxy honey constituents, which are more reflective of the honey's processing conditions (e.g. to what extent filtration was used to remove waxes and other debris from raw honey) rather than its floral source. For the ensuing two-step multivariate analysis, band intensities (AU) were multiplied with their corresponding RGB values (as red, green and blue pixels) and the result plotted against the corresponding Rf values. A 1248 x 104 data matrix was derived from this approach and multivariate analysis (Principal Component Analysis) was performed on this dataset using R and R Studio [43,44].
Visual assessment of fingerprints
The obtained HPTLC profiles of the various honey extracts consisted of four sets of fingerprints and their corresponding chromatograms. While the chromatograms hold two-dimensional information (Rf vs Intensity), the fingerprint itself is richer as the various bands also differ in colour. When placed side by side visual differences and communalities in the respective HPTLC fingerprints can be assessed. Fig 1a exemplifies the diversity in fingerprints prior to clustering. This richness in data can be seen as one of the advantages of HPTLC analysis over other methods (e.g. HPLC) that can also be employed to derived chromatographic profiles. Individual compounds can be accounted for after development in two different conditions (254 and 366 nm) as well as after derivatisation, again in two different conditions (white light and 366 nm), with the different band colours captured in their respective RGB values. With this wealth of data even compounds with very similar or even identical chromatographic behaviour (i.e. Rf value) can be distinguished from each other.
Cluster analysis
Unsupervised non targeted multivariate analysis (Principal Component Analysis) was conducted in order to position all samples in a simple cluster diagram. In the first step of the analysis, aimed at identifying the target cluster, the fingerprints of 104 honeys, were analysed. They Table 1). The cluster diagram shown in Fig 2 demonstrates that several clusters formed in this first round of multivariate analysis and that the target cluster (JAR) is clearly separated from the rest of the analysed samples. There are some samples which are situated between the JAR target cluster and the BAS cluster and visual inspection of the fingerprints of those particular samples confirmed that they were of mixed floral origin. Similar observations were made for samples found between the JAR target cluster and the BAM cluster. Some samples, for instance BAG-23, POW-127, BAM-82, BAM-331, MEL-60 and BAN-229 (Fig 2), appeared within the JAR target cluster although they were not identified as Jarrah honeys by the beekeepers. Visual inspection of their corresponding HPTLC profiles confirmed that these were of multifloral origin with evidence of nectar sources other than Jarrah. On the other hand, some JAR samples (e.g. JAR-271, JAR-205) were found outside the JAR target cluster. In this case visual inspection of the respective HPTLC profiles confirmed that they were outliers and most likely misclassified by the beekeepers.
To prepare for the second step of the analysis, aimed at defining the JAR core cluster, a 60% probability circle was placed around the target cluster, which contained 38 samples representing the JAR target cluster.
In a second step the fingerprints of the 38 samples constituting the JAR target cluster were analysed again by multivariate analysis . Fig 3 illustrates that in this step the initial JAR target cluster was re-arranged to form a new cluster pattern where some samples (e.g. JAR 173, JAR 305) had shifted towards the periphery of the cluster. A visual inspection of their HPTLC profiles confirmed that those samples contained moderate quantities of other floral sources. Again, a 60% probability circle was placed around the cluster, which now contained 24 samples representing the preliminary JAR core cluster. Interestingly, two samples MEL-60 and BAN-229 were still found within the JAR core cluster. Visual inspection of their HPTLC profiles confirmed that their fingerprints were closely related to the typical fingerprint of JAR, which might indicate that their predominant floral origin was misclassified by the beekeepers.
In order to further refine the cluster, another multivariate analysis was performed on the 24 samples constituting the preliminary JAR core cluster. Fig 4 demonstrates that the samples in the preliminary JAR core cluster again re-arranged to form a new cluster pattern. Those samples, which were dilute JAR samples or contained minor quantities of other floral sources, shifted towards the periphery of this refined JAR core cluster, which was marked again with a 60% probability circle and contained 13 JAR samples. It is interesting to note that this refined JAR core cluster no longer contains MEL-60 and BAN-229. A visual inspection of the HPTLC profiles of the samples constituting this refined core cluster presented a consistent fingerprinting pattern (Rf values, colour) and band intensities (representing the respective compound concentrations) in all four HPTLC derived images (254 nm, 366 nm as well as 366 nm and white light after derivatisation).
We argue that these 13 JAR samples represent the characteristics of the refined JAR core cluster and therefore can be used to prepare a pooled sample in order to obtain a JAR reference standard for quality control purposes.
Preparation of pooled reference standard
Equal amounts of the 13 JAR samples identified as representing the refined JAR core cluster were pooled and warmed to 37˚C to assist with the preparation of a homogenous mixture. This mixture constitutes the JAR reference standard. To obtain the HPTLC profile of this reference standard, 1 g of the mixture was dissolved in 2 ml of deionised water and the aqueous honey solution extracted three times with 5 ml of dichloromethane. The combined extracts were dried at ambient temperature and then analysed as described in the Methods section. The obtained fingerprints and associated chromatograms of this pooled sample extract could be used in honey quality control to confirm the floral identity of a sample claimed to be JAR honey.
Development of a dynamic reference standard
As described in the following section in more detail, instead of preparing a physical pooled reference standard for quality control purposes, it is also possible to generate a dynamic reference standard from the collated data, based on the above described multivariate analysis. An advantage of this approach is that when clustering statistically, samples are not mixed physically, leaving a pathway for the future addition of new samples into the clustering process. Those samples might bring additional minor information, which might reflect changes in growing or processing conditions or climatic changes that impact on the phytochemical composition of the samples.
Proof of concept: Confirmation of floral source of Jarrah honey samples using a dynamic reference standard
Three honeys, declared by beekeepers as Jarrah honeys (here referred to as JAR-A, JAR-B and JAR-C) were extracted and HPTLC fingerprinted as described in the Methods section. The obtained information was then included in the data matrix and clustering performed on the new data set. JAR-C was found in a central position within the JAR target cluster, and subsequently also in the preliminary and refined core clusters (Figs 5, 6a and 6b) but the other two samples (JAR-A and JAR-B) were outside the target cluster's boundary. Visual comparison of the HPTLC fingerprints obtained for the three samples with those of the 13 JAR samples previously identified as representing the refined JAR core cluster demonstrate very close agreement for JAR-C. While containing all the characteristic fingerprinting features of the 13 JAR refined core cluster samples, JAR-A and JAR-B, however, present additional bands, indicating that these two honeys contain mainly JAR nectar, but also small amounts of other floral sources.
As can be seen from Fig 6a and 6b, JAR-C not only clustered relatively central within the preliminary JAR core cluster, which contained a total of 39 samples, but also in the refined core cluster (25 samples). On this basis, JAR-C can be considered to represent an authenticated JAR honey, which thus can be added to the dynamic reference standard. A careful comparison between the refined JAR core cluster, obtained prior to the inclusion of JAR-C, and the new refined JAR core cluster (including JAR-C) illustrates the dynamic nature of the standard and its slightly fluid and evolving cluster boundaries. This can be seen in subtle shifts in the cluster position of some samples. For instance, sample JAR-345, which was included in the initial refined core cluster (Fig 4) has moved just outside the new core cluster's 60% probability circle (Fig 6b). The slight shift is due to the addition of three new samples (JAR-A, JAR-B and JAR-C) in the analysis and ultimately the addition of a new sample (JAR-C) to the refined core cluster, which demonstrates the dynamic nature of the method. It needs to be emphasised that the above dynamic reference is currently based on the analysis of only 49 JAR samples and contains only 13 JAR core cluster samples. With the addition of new samples in the future and continued multivariate analysis, the refined core cluster's boundaries might shift slightly, capturing the dynamic nature of the reference standard. This will allow to reflect, much more easily than could be done with the use of a pooled reference standard, natural diversity triggered, for example, by environmental, geographical, seasonal or processing variations.
The paper also proposes a step-wise approach in determining the core cluster. How many iterations of the clustering will be carried out to ultimately derive at the final core cluster (i.e. in this study two iterations were carried out) is flexible and thus allows the method to be designed to be fit-for-purpose. The same applies to the decision at what level the cluster borders are set (i.e. in this study the probability circle was set at 60%). We envisage that this process requires stakeholder input (e.g. industry standards, internal quality control requirements) to determine how narrow or extended the cluster boundaries need to be in order to derive meaningful pooled or dynamic reference standards that meet stakeholder requirements. It might even be possible with this approach to determine samples of different quality. For instance, it might be decided that samples that fall into the target cluster meet the requirements of the respective Food Codex standard, whereas samples that are earmarked for use as (complementary) medicines and thus need to fulfil certain Monograph standards, will need to fall within the core cluster.
There are some limitations to the preparation of such a dynamic reference standard: An adequate number of target samples (here JAR) should be available to derive HPTLC fingerprints and corresponding chromatograms that adequately represent the cluster and the target samples should also be more numerous than 'other' samples that, from the onset, are outside the target cluster (here e.g. BAN, BAM, MEL-see Table 1). Furthermore, the target samples should be of an acceptable purity as a large number of highly contaminated or diluted samples might lead to a misrepresentation of the core cluster.
Conclusion
Assessment of authenticity and purity of complex natural products is a challenging undertaking, in particular in cases where key bioactive constituents that could act as marker compounds for standardisation are not (yet) identified or where a complex interplay of a variety of key constituents characterises the extract. In such cases quality control commonly relies on profile chromatograms to adequately capture the complexity of the natural product. Given natural variations in composition, it is advisable to prepare such profile chromatograms from pooled reference samples. This paper outlined a new method for how samples for such a pooled reference can be selected on the basis of HPTLC fingerprinting followed by multivariate analysis. Employing the same analysis approach, the study also described the development of a dynamic reference standard as an alternative to a static pooled reference sample, which is able to better capture seasonal, geographical, environmental or processing variations. The approach was illustrated using Jarrah honey, but the developed method provides a template that can be also used for the preparation of quality control standards (pooled samples and / or dynamic references) of other natural products.
Where available, an initial single botanical reference material (BRM) can be included in the analysis as a starting point from which the dynamic reference standard can be developed. Further, while this study has based its multivariate analysis on HPTLC derived data, future research should explore if, in other contexts, a similar clustering can also be achieved using different analytical input data. Here, the analysis has been based on individual constituent bands' Rf values, colour and peak intensities and it would be interesting to explore if a combination of constituents' retention times, peak areas and spectral data derived by High Pressure Liquid Chromatography (HPLC), for example, might provide equivalent discrimination power. | 5,304.6 | 2021-07-20T00:00:00.000 | [
"Environmental Science",
"Chemistry"
] |
Abandoned Object Detection Using Dual Background Model from Surveillance Videos
— with increase in threats and concerns in security, detection of suspicious activities in public areas has attracted an enormous level of attention. In general, video processing system are been employed for post-event analysis. However, there is a need to build an intelligent video surveillance system so as to find ways to prevent such events. The proposed system is used todetect the abandoned object from the surveillance videos with the use of dual background model. The division of video into frames is done and are pre-processed. In this approach, dual background method is used to subtract the foreground objects from the background, which generates two backgrounds called buffered background and current background. The foreground blobs are generated using subtraction of the two backgrounds and it is tracked to detect the abandoned objects. Tracking is done by maintaining a Track set which includes blobProperties, namely Area, Centroid, Major Axis length, Minor Axis Length and Convex Area, and two separate count set. The system is tested on various videoswhich are publically available.
II. RELATED WORK
Wahyono, Alexander Filonenko, and Kang-Hyun Jo [3] have presented their work on abandoned objects detection from crowded ccenes of surveillance videos using adaptive dual background model. In this paper, a new framework is presented to detect abandoned object using dual background model subtraction. Major contributions of their work includes: A new background model is introduced based on statistical information of image intensity. Dual background model subtraction is performed in order to extract candidate abandoned region which is robust against lightening changes. Matching-based tracking algorithm is employed to detect abandoned object under occlusion. Human and vehicle detection are integrated to classify human, vehicle and other objects.Quan Wei, Zhang Yuqiang, Ge Wei and LI Hialan [8] have presented their work on research on stationary object detection technique based on dual-Background. A new stationary object detection algorithm is proposed in this paper which includes dual background subtraction to get foreground image based on the approximated median filtering using the adaptive threshold method and detection of stationary object through morphological processing. The target detection algorithm is used the current background and buffer background difference to detect stationary object, then analyse the connected region to abstract the stationary target.Rajesh Kumar Tripathi, Anand Singh Jalal and CharulBhatnagar [10] have presented their work on a framework for abandoned object detection from video surveillance. In this paper,proposed method is used to detect abandoned object from surveillance video. Here, foreground objects are extracted by using background subtraction where background modelling is done through running average method. The objects which are static are detected by using contour features of foreground objects of consecutive frames. Edge based object recognition is used to classify detected static objects into human and non-human objects.A. Singh, S. Sawan, M.Hanmandlu, V.K. Madasu and B.C. Lovell [12] have presented their work on an abandoned object detection system based on dual background segmentation. In this paper, the system is based on a simplistic and intuitive mathematical model. The proposed system consists of a novel self-adaptive dual background subtraction technique based on the approximate median model framework. Tracking is performed on the detected block. A track set is maintained with three variables blobProperties, hitCount and miscount. If hitCount goes above the user defined threshold value, an alarm is triggered indicating the abandoned object is detected. Kevin Lin, Shen-Chi Chen, Chu-Song Chen, Daw-Tung Lin and Yi-Ping Hung [18] have presented their work on abandoned object detection via temporal consistency modelling and back-tracking verification for visual surveillance. Temporal dual-rate foreground integration method is proposed for static-foreground estimation for single camera video images. Subsequently, method introduced a simple pixel-based finite-state machine (PFSM) model that is used to temporal transition information to identify the static foreground based on the sequence pattern of each object pixel. The merits of their system include the dual-rate background modelling framework with temporal consistency which is better than single-image based double background models. It is superior in handling temporary occlusions and is still highly efficient to implement.
III. PROPOSED APPROACH In the proposed system, abandoned object detection is carried out from various scenarios. The abstract model of the proposed system is shown in the Fig. 2.
A. Pre-Processing
A video clip is provided as an input to the system. The input video is then extracted into frames for further processing. Pre-processing is applied on the extracted frames including resizing the video frames then converting frames from RBG to Gray-scale and later applying median filter in order to remove noise and sharpen the edges.
B. Dual Background Generation
In the proposed approach, Dual Background concept is used rather than the conventionally used simple background subtraction method. In this method, two different backgrounds are maintained-Buffered Background and Current Background. The buffered background is initialized by only the first frame of the input video. This background is stored and is not updated. On the other hand, current background is initialized by the first frame and subsequently each pixel of this current background is compared with the corresponding pixel of the next incoming frame. The mathematical model for update strategy is given below: Where CB is the pixel value of current background and I is the pixel value of each frame that has been read and t represents time.
C. Object Detection
In order to detect the object, difference between the current background and buffer background is calculated after every 10 seconds. The image pixels values are traversed from top to bottom, from left to right. CB i, j as current background pixel value and BB i, j as the buffer background pixel value, then the background subtraction B i, j is represented as: After the difference between the two backgrounds is calculated, the result is then binarized depending upon the threshold so as to detect the corresponding suspicious activity. This binarization is shown as follows: Here the value 1 is assigned for those pixels classified as foreground and 0 for those classified as background. Foreground pixels can be grouped into by means of connectivity properties.
D. Object Tracking
As from the above step a binary image is obtained, this binary image is divided into number of legitimate blobs i.e., rectangular regions enclosing continuous regions of foreground. Firstly, blobs along with their various properties such as area, centroid, position etc is been generated and later tracking algorithm is applied. Mathematically, it is assumed that after blob analysis N number of blobs are generated with enclosing regionR t, l, h, w , having area A , centroid C i, j , major axis length Maj , minor axis length Min and convex area CA , where t is top position value of the pixel, l is the left position value of the pixel, h gives the height of the blob and w is the width of the blob; and 1 n N. A set of tracked blobs is maintained. 'T' is the set of tracked blob defined as, Where, M is the number of blob tracked. Two count arrays are maintained namely count1 and count2. Count1 is the set of all individual blobs detected throughout the video frames maintaining total number of times it appeared, centroid values, frame number etc., and count2 is a set maintaining the blobs' records for the current 10 seconds including the blobs that weren't being tracked previously. The new incoming blob detected in count2 is added in the Count1 set if not present already. The next step in object detection is to track the different blobs so as to detect which blob corresponds to abandoned objects. Tracking involves the following steps: Create a set, Track, whose elements have six properties: Area, Centroid, Bounding Box, Major axis length, Minor axis length and Convex area collectively called as them blobProperties. This Track set stores properties of all the blobs detected after every 10 seconds interval. Also, two counts sets are maintained. For the initial first 10 seconds, add centroid values of each identified blob into the set count1. For every interval of 10 seconds analyze the incoming image for all the blobs and store their centroid values into another count set count2. If this set introduces new blobs which are not present in the set count1, then make their entry in count1. After 10 seconds is elapsed, comparison is made between the new entries in the Track set with the previous one. The comparison is made to check if all the blobProperties centroid, Area, Major axis length, Minor axis length and Convex area of two blobs are equal or not. If the match is found, the count value is incremented in the count1 set or else the count retained as it is. If the value of count reaches a threshold, here 2 indicating 20 seconds, the detected blob is marked with red boundaries indicating it to be potentially abandoned object. These steps are repeated until there are no incoming images.
A. Implementation Platform Details
The hardware and software specifications of the platform on which the proposed approach is implemented and tested is given below:
B. Tools and Technology
The whole approach is implemented in MATLAB R2012a. MATLAB is a fourth generation programming language which provides multi-paradigm numerical computing environment. The functions of computer vision system toolbox provide facilities to design and simulate video processing systems. Object detection and tracking, feature extraction and matching, estimation of motion can be done using it.
C. Dataset Design
In order to evaluate the presented work, the surveillance video datasets are collected from various resources. The work has been evaluated using 16 video sequences. Video Sequences includes various scenarios: indoor, outdoor, detection in light and crowd. The duration, length, frame rate and scenarios of these video sequences are specified in Table I below.
D. Experimental Results
The video1 video sequence is chosen for testing which contains outdoor scenario. The duration of the video is 73 seconds having 2189 frames with frame rate is 29.97. As per the ground truth, 1 abandoned object is present in the video. The first phase of the system includes: Extraction of first frame, resize it, convert from RGB to Gray and initialize it to Buffered and Current Background.
The next phase is to run the video in segments of size 10 seconds. Here since the duration of video is 73 seconds thus the segments obtained are 8. Frame extraction is carried out and the pixel values of next incoming video frame are compared with that of the current background for the each segment i.e., for the every 10 seconds of the video. Figure 3 shows the experimental result for the last segment as we detect abandoned object in that segment. Fig. 3(a) shows the buffered background, Fig. 3(b) shows the updated current background and Fig. 3(c) shows the binarized difference image. Here, three blobs are obtained whose blobProperties are listed in the Table II below: The values in array count 2 are updated as shown in the Table III below: TABLE III Now here, the centroid of blob1, blob2 and blob3 matches with the centroid of 67th, 70th and 71th entries in the set count1 respectively. Thus their values are overwritten by these new values. No new entries are included in count1. Below is Table IV showing the updated count1 set from 67th position. The comparison between the blobProperties of recently obtained blobs is made with the ones obtained in the previous segment. Comparison of the three blobs is shown is shown in the Table V along with their respective matches from the previous segment. Here, it is observed that all the three blobs in this segment match with previously obtained blobs in terms of area, centroid, major axis length, minor axis length and convex area. Thus the count of blob1 in set count1 is incremented by 1 making it a total of 2. Similarly, count of blob2 and blob3 are also incremented by 1. The Table VI is shown below with the incremented values of the count: The threshold set in the proposed system to label the object as abandoned is 20 seconds. Here, the count of value 2 indicates 20 seconds, meaning that the object is left abandoned for 20 seconds. Once the object is detected as abandoned, the boundary surrounding the object is changed to red colour. Figure 4 shows the three identified objects with two marked with green bounding box while one marked with red bounding box, indicating it to be abandoned. Table VII shows the summary of the detection results on outdoor, indoor and detection in night. Here, total of 7 videos are used. Ground truth is provided with every video having one abandoned object. Here, GT = Ground Truth, TN = True Negative, TP = True Positive, FN = False Negative and FP = False Positive. The detection results from the above table shows that the abandoned objects are successfully detected for all the video sequences with precision of 77.78% and recall being 100%. Only two false positives are obtained from video sequence 5 which is mainly due to unclean buffered background.Similarly, experiment performed on crowded scenario is shown in the below Table VIII. Here total of 9 videos are used each having crowded scene. Ground truth is provided with every video containing one abandoned object except for videos 4 and 5, having no abandoned object. From the above table it is observed that all the abandoned objects are accuratelydetected but also few false positives are detected because of the crowded nature of the videos and unclear first frame resulting in the unclean buffered background. The precision observed is 53.85% while recall remains 100%. Combining all the video sequences, the overall precision is calculated to be 63.63% and the recall is 100%.
V. CONCLUSION AND FUTURE WORK
This paper presents an approach based on dual background model which detects abandoned object from the surveillance videos. Dual background model maintains two separate backgrounds one called buffered background and other called current background.Experiments are performed on various video sequences for different scenarios including indoor, outdoor, detection in night and crowded scenes. The experimental results for video sequences having outdoor, indoor and detection in night scenario has precision of 77.78% and recall of 100%. For crowded scenario the precision measured is 53.85% and the recall measured is 100%. The overall precision for all the video sequences is measured to be 63.63% with 100% recall.Though the proposed system works well but in future it can be extended to work better even in densely crowded places. Occlusion of the objects continues to be an issue, which can be solved if way to update the buffered background is improved, thus enhancing the object detection by the system. | 3,423 | 2017-07-17T00:00:00.000 | [
"Computer Science"
] |
Differential Z + jet cross section measurements at 8 TeV
The measurement of differential cross section of a Z boson produced in association with jets is presented. The cross section is presented with respect to various jet kinematic variables where the Z bosons are reconstructed from opposite sign lepton pairs. The analysis is based on data of proton proton collisions with the centre of mass energy of 8 TeV collected in 2012 by the CMS experiment at LHC corresponding to 19.8 /fb of integrated luminosity. Obtained results are compared with different generators and are shown to be consistent with the Standard Model predictions.
Introduction
The large center-of-mass energy of pp collisions at the LHC allows the production of events with high jet transverse momentum, p T , and high number of jets, N jet , with a Z boson. Z bosons decaying to opposite sign lepton pairs (e, µ) provide an almost background free signal. Measurements of these processes provide stringent tests of pQCD predictions, and they are backgrounds to many Standard Model (SM) measurements such as single top, tt, vector boson fusion, WW scattering, Higgs boson production, as well as Beyond the Standard Model (BSM) searches such as supersymmetry (SUSY).
CMS collaboration [1] reported the first cross section measurements of Z boson production in association with jets (Z + jets) [2,3] at a center-of-mass energy of √ s = 8 TeV using full 2012 data of 19.6 fb −1 of integrated luminosity. In sections 2 and 3 the double and single differential Z + jet cross section measurements are given respectively. The cross sections are presented after deconvoluting the detector effects by an unfolding procedure. The measurements presented cover several kinematic regions in jet rapidity, and hence provide stringent tests of perturbative QCD predictions merging parton shower with matrix element calculations at leading (LO+PS) and next-to-leading (NLO+PS) order.
They also provide tests of the Parton Distribution Functions (PDFs) mainly at these large rapidities.
Double Differential Z+jet Cross Section Measurements
The double differential cross section, d 2 σ/d p j T dy j , is measured with respect to the transverse momentum (p T ) and the rapidity (y) of the highest p T jet in the di-muon channel. The muons are required to have p T greater than 20 GeV and pseudo-rapidity (η) less than 2.4. Particle-Flow [4] jets are selected in the calorimeter acceptance of |y| < 4.7 using the anti-k T jet clustering algorithm with a cone size of ∆R = 0.5. The jets are required to have p T > 30 GeV for jets in the region |y| < 2.5, and p T > 50 GeV for |y| > 2.5. The jets with ∆R( j, µ) < 0.5 are not considered in the analysis.
In figure 1 and 2, the double differential cross section results versus leading jet p T and the ratio of theory predictions to measurements are given respectively.
Single Differential Z+jet Cross Section Measurements
Single differential cross section of Z + jet process is measured in the di-electron and di-muon final states. The measurements are carried out with respect to the exclusive and inclusive jet multiplicity, jet p T , jet |η| and jet transverse momentum scalar sum (H T ) . The leptons are required to have p T greater than 20 GeV and |η| less than 2.4. A threshold of 30 GeV on jets p T is applied to reduce the pileup contamination as well as the large jet energy correction uncertainty. The jets overlapping with the leptons with ∆R( j, l) < 0.5 are not considered in the analysis.
Cross section results as a function of exclusive jet multiplicity and the 1st jet p T distributions are shown in figures 3 and 4 respectively.
Conclusion
Single differential cross section measurements have been made as a function of exclusive and inclusive jet multiplicities, as a function of the p T and η of the n th jet for n = 1 . . . 5, and as a function of the scalar sum of the jet transverse momenta for N jets ≥ n, for n = 1 . . . 5. Also, the double differential cross section measurement with respect to the rapidity and transverse momentum of the highest p T jet is presented in the di-muon final state, which is the first study of the double differential cross section in the Z + jet final state, and the first CMS measurement including forward jets up to |y| < 4.7 in this Z + jet event topology.
The measurements have been compared with two different calculations with different fixed order accuracy. Comparison is done with respect to tree level predictions from MadGraph [5], and sherpa2 [6]. MadGraph is a tree level matrix element calculator which generates Z bosons associated with up to four partons. pythia6 [7] is used to add the remaining QCD radiation via parton showering algorithm. sherpa2 is a multi-leg NLO generator. Events with up to two partons along with the Z boson are generated at NLO and merged with LO matrix element calculations up to configurations with a Z and four partons.
An excess of the cross-section contribution in the region p j 1 T ≈ 150 − 450 GeV with respect to the rest of the phase space in the MadGraph + pythia6 calculations is observed in both measurements, whereas sherpa2 calculations predict a slightly harder spectrum than the measurement. An overall agreement is seen between sherpa2 predictions and the data, except some discrepancies in different y and p T regions in the double differential cross section measurements. On the overall scale, the measurements are in agreement with the theoretical predictions within uncertainties. | 1,324.4 | 2014-10-22T00:00:00.000 | [
"Physics"
] |
Tailored second harmonic generation from self-organized metal nano-wires arrays
, Abstract: Here we report the second harmonic emission properties of self-organized gold nanowires arrays supported on dielectric substrates with a sub-wavelength periodic pattern. The peculiar morphology of the nanowires, which are locally tilted with respect to the average plane of the substrate, allows to generate maximum second harmonic signal at normal incidence with a polarization direction driven by the orientation of the wires (perpendicular to the wires). The generation efficiency was increased by tailoring the growth process in order to tune the metal plasmon resonance close to the pump field frequency and also by increasing the local tilt of the nanowires.
Introduction
Metal nanostructures supported on dielectric substrates have attracted great interest as building blocks of nanoscale optical devices. Large interest was devoted in developing molecular sensors, by using metal enhanced fluorescence [1][2], surface enhanced Raman scattering [3][4] or second harmonic (SH) emission from nanostructures synthesised by e-beam lithography [5][6][7][8][9]. The interest in the development of metallo-dielectric substrates providing high SH conversion efficiency is due to the possibility of realising new optical (multiphoton) microscopy schemes where vertical illumination and detection are adopted.
Here we studied the SH emission properties of a self-assembled gold nanowire arrays supported on sub-wavelength (160 nm) patterned glass templates produced recurring to a novel self-organised maskless approach. Different morphologies were here investigated in order to highlight and overcome the typical constraints which frustrate SH generation on flat metal surfaces: the emission is forbidden at normal incidence and it is always polarized along the plane of incidence, when the pumping light is set to be either s-or p-polarized; these peculiarities arise because most metals posses cubic crystal structure and the electric dipole term in the Maxwell equations, responsible for the standard SH signal, vanishes when inversion symmetry is present in the lattice structure. In a metal, the SH source terms consist of a magnetic dipole term, originating from the Lorentz force on the conduction electrons, and of an electric quadrupole contribution, through the Coulomb force. The expression of the nonlinear polarization at frequency 2ω which acts as a source term for the SH field was calculated by considering a free electron model for the metal [10,12]. Starting from the equation of motion for the free electrons, within a perturbative approach we can write: where e is the modulus of the electron charge, m is the electron effective mass, γ is a damping coefficient taking into account ohmic losses. The contribution of the second term on the right hand side of Eq. (1) is limited by the weak penetration of the electric current inside the metal due to the skin effect (≈15 nm at optical frequencies); the first term gives a nonzero contribution only at the surface [12] (≈ 1 nm, much smaller than the skin depth). We note that both terms in Eq. (1) are always polarized in the incidence plane (p-polarized) when the pump is either s-or p-polarized. Moreover, pumping at normal incidence, the transverse component of the nonlinear polarization (responsible for collinear SH generation) is zero. We experimentally demonstrate that the nonlinear properties of our samples, consisting of a tilted array of self-organized gold nanowires (NW) with sub-wavelength separation, are characterized by maximum SH emission at normal incidence with a polarization direction driven by the orientation of the wires (perpendicular to the wires). On the contrary, measurements of SH generation from reference samples (flat gold layer, corrugated gold layer, untitled wires) are in agreement with the expectations of ordinary centro-symmetric metal films i.e. they exhibit a minimum in the SH generation efficiency at normal incidence.
Sample fabrication
Nanowire arrays have been fabricated by combining ion beam sputtering (IBS) [13] to kinetically controlled deposition (KCD) [14][15]. The dielectric substrates (0.2 mm standard microscope glass slides) were patterned via IBS. The substrates were irradiated by a 800 eV Ar + defocused ion beam at an incidence angle of 35 deg from the surface normal. Under such conditions we obtained the formation of a nanoscale ripple pattern with a periodicity of 160 +/-20 nm and an amplitude of 16+/-5 nm (samples A,B,C,D,G). Then the synthesis of the metal nanowires is performed by means of glancing angle deposition of gold (80 deg with respect the surface normal). In this way, due to the shadowing effect imposed by the glass ripples, agglomeration of a disconnected array of metal nanowires with a tilt of 12 deg takes place onto the illuminated ridges of the glass ripple pattern. The derivative of the AFM image in the inset of Fig. 1(a) highlights the contrast between the unexposed glass and the polycrystalline structure of the gold NWs. In Fig. 1(b) a comparison between the derivative of two line profiles (before and after Au deposition) is shown, in order to retrieve information on the nanowire lateral size and disconnection.
Second harmonic generation measurements
We then performed SH measurements at nm 400 2 = ω λ on all the samples as a function of the incidence angle of the pumping beam for two different orientations of the samples, with the wires perpendicular or parallel to the incidence plane, named ⊥ and // configuration respectively. The fundamental beam was provided by the output of a p-polarized mode-locked laser system with pulse duration 150 fs, λ=800 nm, repetition rate ~1 kHz. The generated beam propagating along the forward direction is spectrally filtered to isolate the SHG contribution, then an additional polarizer is placed in front of the photomultiplier tube allowing to analyze the polarization of the emerging SHG emission. The fundamental intensity I ω was set to be lower than 4.5 GW/cm 2 in order to avoid noise from multiphoton processes. The SH measurements result affected by an overall uncertainty of 20%. In Figs. 2(f)-2(i) we plot the SH conversion efficiency ω ω η I I 2 = as a function of the incidence angle for the NW test samples A,B,C,D. In all cases the SH polarization state is perpendicular with respect to the wires orientation despite the fact that a standard metal surface generates SH signal only with p-polarization. More important, the SH signal presents a maximum efficiency when pumped at normal incidence. The conversion efficiency increases as the plasmon resonance is shifted closer to the pump wavelength reaching the maximum value of 11 10 2 . 1 − × for the sample D. We then fabricated a different glass template (sample E) were the ripple facets are more tilted (20 deg) with respect the previous four samples. In this case, even if the absorption peak is centred far from the pump wavelength (as the samples A,B), the SH measurements (Fig. 2(l)) show a maximum conversion efficiency of 11 10 6 . 1 − × at normal incidence, further demonstrating the importance of a local tilt of the nanowires. Other three samples, with a 20 nm gold thickness each, were prepared in order to provide a reference for the SH measurements. Sample F (Fig. 3(a)) is a flat gold film on a flat substrate. Sample G (Fig. 3(b)) was obtained by fluxing gold at normal incidence with respect to the sculpted glass template, resulting in the deposition of a connected Au film which conformally preserves the ripple shape of the underlying substrate. Finally, sample H (Fig. 3(c)), an array of Au nanowires locally parallel with respect to the glass substrate, was obtained by IBS etching a 150 nm thick gold film deposited on a flat glass substrate [16][17]. In Figs. 3(d)-3(f) we report the curves of the SH conversion efficiency as a function of the incidence angle, obtained by measuring the three reference samples F,G,H. In all cases the SH polarization state is p-polarized regardless the sample orientation and the angular dependence shows a negligible efficiency at normal incidence (less than 13 10 behaves very similarly to sample F (flat gold) both in the linear (transmission and absorption spectrum) and nonlinear regime, presenting a very small anisotropy. Sample H (Fig. 3(f)), similarly to the previous two examples, gives only a negligible contribution to the SH signal at normal incidence though for this sample, due to the presence of disconnected nanowires, a stronger dependence with respect to the pump polarization state is found both in the linear and nonlinear regime.
Numerical simulations
Numerical simulations were performed in order to calculate the linear fields and then to retrieve the origin of the nonlinear response by using a dedicated numerical algorithm based on Eq. (1). In Fig. 4 the calculated radiative nonlinear polarization terms are shown for two configurations of the wires, tilted ( Fig. 4(b)) and un-tilted ( Fig. 4(a)), respectively corresponding to the tilted nanowire arrays (Figs. 2(a)-2(d)) and to the un-tilted nanowire array (Fig. 3(c)) when the p-polarized pump is set to normal incidence. We remind the reader that the nonlinear polarization vector acts as a source term for the SH field and we note that, in the un-tilted case (i.e. H sample), the polarization contribution from one wire is balanced by a reverse contribution of the adjacent wire ( Fig. 4(a)). Thus it is possible to qualitatively predict a vanishing macroscopic SH signal at normal incidence, in agreement with experimental results (Fig. 3(f)). On the contrary, in the tilted case, the net contribution is different from zero due to the asymmetry of the system on a subwavelength scale, thus producing a radiative SH signal (Figs. 2(f)-2(l)). The linear fields have been retrieved by comparing experimental and numerical transmission spectra. The spectral behaviour is strongly dependent on the wire thickness, periodicity and degree of disconnection. For instance, the absorption spectrum for each sample has been performed revealing the direct correlation between the resonance in the transmission spectrum (E field perpendicular to wires) and the absorbance. Numerical results are in agreement with experiments; enhanced absorption (black curves in Fig. (5)) is obtained as long as wires are sufficiently separated from each other (Figs. 5(a)-5(b)). On the contrary, when distance between wires is less than 10 nm, interaction between wires is responsible for increased reflectivity (red curves) and lower absorption (Fig. 5(c)).
Conclusions
In conclusion our experiments demonstrate that it is possible to fabricate low cost metal nanowire arrays of subwavelength periodicity and size, which are supported on locally tilted transparent glass substrates. Their SHG has maximum emission efficiency at normal incidence with a polarization direction driven by the orientation of the wires (perpendicular to the wires). The efficiency of the SHG can be optimized by tailoring the growth process in order to tune the metal plasmon resonance close to the pump field frequency. The SHG efficiency increases by two orders of magnitude with respect to planar films or to un-tilted NWs due to the strong field localization at the dielectric-metal interfaces, as demonstrated by the theoretical and numerical calculations. A further increase of the SH generation efficiency at normal incidence was obtained by increasing the local tilt of the nanowires, thus demonstrating that adaptable effective medium supported over large areas can be synthesized by the proposed self-organised method. These results appear of clear interest in view of applications in the field of high sensitivity bio-sensing where multiphoton confocal microscopy detection schemes are employed for the study of biological fluorescent samples supported on glass substrates. The amplification of the SH signal, enhanced in the near field of the gold nanoparticles at normal light incidence, provides in fact an efficient way for boosting fluorescence emission from fluorochromes located at the surface of the nanoparticles. | 2,665.6 | 2009-03-02T00:00:00.000 | [
"Physics"
] |
Modeling of orientational polarization within the framework of extended micropolar theory
In this paper the process of polarization of transversally polarizable matter is investigated based on concepts from micropolar theory. The process is modeled as a structural change of a dielectric material. On the microscale it is assumed that it consists of rigid dipoles subjected to an external electric field, which leads to a certain degree of ordering. The ordering is limited, because it is counteracted by thermal motion, which favors stochastic orientation of the dipoles. An extended balance equation for the microinertia tensor is used to model these effects. This balance contains a production term. The constitutive equations for this term are split into two parts, one , which accounts for the orienting effect of the applied external electric field, and another one, which is used to represent chaotic thermal motion. Two relaxation times are used to characterize the impact of each term on the temporal development. In addition homogenization techniques are applied in order to determine the final state of polarization. The traditional homogenization is based on calculating the average effective length of polarized dipoles. In a non-traditional approach the inertia tensor of the rigid rods is homogenized. Both methods lead to similar results. The final states of polarization are then compared with the transient simulation. By doing so it becomes possible to link the relaxation times to the finally observed state of order, which in terms of the finally obtained polarization is a measurable quantity.
temporal evolution of polarization obtainable within the framework of extended micropolar theory. The paper will end with a summary and an outlook into further applications based on the presented results.
1.1 Introductory remarks: Benefits of the concept of the microinertia tensor Traditionally the microinertia tensor of a continuum particle, J, plays an important role only in context with its rotational degrees of freedom. In combination with the angular velocity vector, ω, it characterizes the spin of the continuum element. The details are outlined in Eringen's theory of micropolar media, see for example [11]. There it is shown that the microinertia tensor obeys a kinematic constraint in form of a rate equation, which expresses the possibility of material continuum particles to undergo rigid body rotations. This feature is captured by means of three rotating rigid directors. Within the framework of this theory the shape of the microinertia tensor does not change; rather, it can only rotate rigidly. Eringen calls such materials micropolar media. However, as we shall demonstrate in this paper, describing the particle spin is not the only use of the microinertia tensor. If generalized, the concept of a changing microinertia can be beneficial for describing processes in certain materials, for example, electromagnetic ones, such as the development of electric polarization, which may already occur under the absence of an angular velocity. Some other applications of micropolar theory can be found, for example, in [3,4].
In fact a radical change of the concept of the microinertia tensor has been presented recently in [14]. There the microinertia tensor is treated as a completely independent field variable for solid and fluid matter alike. In this formulation closed as well as open systems are allowed. This means that in-and outflux of matter in a Representative Volume Element (RVE) can be taken into account and the concept of a material particle is not imperative. Moreover, a structural change due to external forces becomes possible. The microinertia tensor becomes a fully independent field variable with its own balance requiring additional constitutive quantities. More specifically, in contrast with the balance of mass, the balance for the micro-inertia tensor is not conserved. It contains a production term, χ , which could be specified by following the rules of constitutive theory or be motivated by physics and intuition, such that fundamental principles are not violated.
In the following subsections it will be demonstrated that this extended theory allows for the modeling of processes accompanied by a considerable structural change characterized by a changing microinertia within a representative volume element, such as the development of orientational polarization in matter under the action of an external electric field, E. In this context the multi-disciplinary aspect of the present formulation should be stressed. Potentially it can be used fruitfully to synthesize new innovative materials [34], which combine mechanical and electrical behavior. For example, the use of piezoelectric patches can provide reduction in vibrations or energy harvesting (see, e.g., [2,12]). Moreover, for a recent thermodynamically consistent treatment of electro-mechanical problems see [1].
The balances of micropolar media
The motion and state of micropolar media in spatial description are described by the following coupled system of differential equations: • balance of mass, δρ δt = −ρ∇ · v, (1.1) • balance of momentum,
2)
• balance of spin, ρ J · δω δt = −ρω × J · ω + ∇ · μ + σ × + ρm, (1.3) • balance of internal energy, ρ δu δt = σ : ∇ v + I × ω + μ : ∇ ω − ∇ · q + ρr, (1.4) where ρ is the field of mass density, v and ω are the linear and angular velocity fields, σ is the non-symmetric Cauchy stress tensor, f is the specific body force, J is the specific micro-inertia tensor, μ is the non-symmetric couple stress tensor, (a b) × = a × b is the Gibbsian cross, m are specific body couples, u is the specific internal energy, q is the heat flux, and r is the specific heat supply. By the colon we denote the outer double scalar product between tensors of second rank, A : is the substantial derivative of a field quantity, d(·) /dt the total derivative, and w the mapping velocity of the observational point (see [13]). It was already indicated that traditional micropolar theory assumes that each material point or "particle" of a micropolar continuum is phenomenologically equivalent to a rigid body. It can rotate but the state of the rotational inertia in the principal axes system does not change. In other words the micro-inertia tensor will not change its form nor shape, see, for example, [9], [32], [19], [11]. Even if a so-called micromorphic medium is considered, which in principle allows an intrinsic change of micro-inertia (following [8], [11], [10]), many publications use only the following additional equation for the conservation of inertia (e.g., see [23], [5]), which is an identity of rigid body kinematics: Note again that the terms on the right-hand side characterize the change of the inertia tensor, which is exclusively due to rigid body rotation. An extension to this approach was suggested in [7], where it was proposed that the microinertia of polar particles may change as the continuum deforms. This idea was then further elaborated in [14], where it was clearly stated that the tensor of microinertia should be treated as an independent field. Within that approach a fixed and open elementary volume V was treated as a micropolar continuum (macro-) region, as it is customarily done in spatial description. Then its microinertia tensor J (in units of m 2 ) as a property on the continuum scale is obtained by homogenization as follows. Within the elementary volume V there are i = 1, ..., N microparticles of mass m i and inertia tensorĴ i (in units of kgm 2 ) such that: where m is the average mass within V . If the linear and angular velocities of the particles are denoted by v i and ω i , then the specific linear and angular momenta are given by: The specific linear momentum is nothing else but the translational velocity on the continuum scale. Equation (1.8) 1 simplifies considerably if all the microparticles have the same mass: This will be the case for the dielectric medium considered in this paper. Moreover, we will also assume that the inertia tensors of the microparticles are the "same." This means that the three principal values of the inertia tensor are the same for each particle,Ĵ j i =Ĵ j , but its eigensystem vectors e * i, j , j = 1, 2, 3 are not, because the microparticles are randomly oriented. Thus, in such a case we can only say that Only for a spherical inertia tensor, or if all microparticles are aligned in the same manner, the last relation would turn into an equality. This also means that in all other cases of "equal" inertia tensors we must conclude from the last relation in (1.8) that Because of the movement of the medium, the elementary volume contains different microparticles as time passes, and the microinertia tensor assigned to the volume will change due to the incoming or outgoing flux of inertia. However, internal structural transformations are also possible. These can be due to (a) the combination or fragmentation of the particles during mechanical crushing, to (b) chemical reactions, or to (c) changes of the anisotropy of the material, for example by applying external electromagnetic fields. Such effects are explained in greater detail in [22], [21], [20], or [33]. In a nutshell, on the continuum scale all of this can be taken into account by adding a source or production term, χ, to the right-hand side of Eq. (1.6), which now reads: On the continuum level this source term must be considered as a new constitutive quantity for which an additional constitutive equation has to be formulated. The form of the constitutive equation depends on the problem under consideration and can be a function of many physical quantities. A suitable form for the modeling of orientational polarization in polarizable matter under the influence of an external electric field will be discussed in the next section. Finally it should be emphasized once more that the field of microinertia, i.e., the rotational inertia of the continuum influences the development of the angular velocity ω. The temporal development is dictated by the spin balance (1.3), and this is usually the only purpose of J. In this paper it is different: Because of the extended balance (1.12) J can also be used to characterize structural changes of the micropolar medium, without the presence of an angular velocity. We proceed to explain this in more detail in the next section.
Introductory remarks on polarization
For didactical reasons we recapitulate a few facts from electrical engineering in this section. In this field one distinguishes between electrically conducting and non-conducting or insulating materials. On a microscopic scale the former possess freely movable electric charges, for example the electron gas in metals. In case of the latter charges cannot move around freely. Positive and negative charges must stay together. They are bound within a molecule or other basic atomic units, for example within a crystal lattice. Materials in which an electric current cannot flow are also known as dielectrics. In the absence of external electric fields they are electrically neutral. However, one of their basic properties is the ability to polarize if an external electric field E is applied. This leads to the creation of surface charges, which on the continuum scale are described by the polarization vector P. Indeed, ∂ V P · n d A allows to compute that charge, provided the field P is known.
The question arises how the polarization can be measured, at least in principle, since a direct measurement of charges, in particular surface charges, is difficult. A simple school experiment can be used. Consider a plate capacitor, which is first charged by a battery, so that the plates of surface A at a distance d are loaded with the electric charges ±Q. The battery is then detached and replaced by a voltmeter. If there is vacuum in between the plates, the voltmeter will show a voltage U vac , say. If we now place a dielectric body in between this voltage decreases down to U pol < U vac . The stronger the decrease, the more surface charges are created, and the stronger the polarization P will be. In order to quantify the effect in terms of a material constant, let us assume for simplicity that the dielectric material between the plates is isotropic and the polarization vector can be described by a linear constitutive equation of the type: where ε 0 = 8.854 × 10 −12 As Vm is the electric field constant and χ > 0 is the dielectric susceptibility, which in this simple case is a material-dependent, dimensionless constant. In fact, application of the static Maxwell [16] equations to the case of the plate capacitor described above yields: The combination ε r = 1 + χ is also known as relative permittivity, which is also dimensionless. It is equal to one for the case of vacuum. Then Eq. (2.2) allows to determine ε r or χ if the the two voltages before and after filling the vacuum are measured: Note that if the dielectric is anisotropic and if the electric field is not too high, the dielectric susceptibility constant can simply be replaced by a constant second rank dielectric susceptibility tensor, χ. For large electric fields the dielectric susceptibility is a nonlinear function of the electric field, χ(E), which is sometimes expressed in a power series. Moreover, analogously to viscoelasticity, which makes use of a frequency-dependent complex shear modulus during harmonic loading, it becomes necessary to introduce a frequency-dependent and complex valued dielectric susceptibility when harmonically alternating electric fields are applied.
It should be emphasized that we made these remarks just to illustrate the measurement principle. In practice (frequency dependent) susceptibilities and relative permittivities are measured dynamically, for example, by using microwave waveguide systems, see [35]. Figure 1 presents cartoons of the various polarization mechanisms encountered in materials on the microscale.
Inset (a) refers to electronic polarization. Due to the electric field the positive charge of the atomic nucleus and the negative charge of the surrounding electron cloud are shifted with respect to each other so that an atomic dipole results. If the field is removed, the electron cloud and the nucleus move reversibly into their old position. The atom is electrically neutral and no longer a dipole. It is a very weak effect in (more or less isolated) atoms or ions with spherical symmetry. It can be a strong effect in, e.g., covalently bonded materials, such as Silicon, Germanium or diamond [17,24].
Inset (b) illustrates ionic polarization. It emerges due to a shift in the positive and negative ion centers of gravity. A typical example are sodium chloride crystals [31].
Inset (c) illustrates orientational polarization, which will be modeled in this paper. It results from field stimulated orientation of atomistic aggregates that already carry a dipole moment before the external electric field is switched on. It is pertinent to polar liquids, but it can also be observed in solid polar organic substances. In this case, the polarization is usually not caused by the rotation of the molecule itself, but of the polar radicals present within it in relation to the molecule. In this context hydrochloric acid or water should be mentioned, because the charge distributions in these molecules are skewed so that a net permanent dipole moment arises. Moreover, in cellulose, the polarity is explained by the presence of OH and oxygen hydroxyl groups. In addition, crystals with a molecular lattice and weak van der Waals bonds can also orientate larger particles. A typical engineering example of materials that show orientational polarization are electrets [16].
Finally inset (d) presents spatial (or space) charge polarization. It is observed in dielectrics with a heterogeneous interlayer structure. Hence, it occurs when there is an accumulation of charge at an interface between two materials or between two regions within a material because of the external field. This can occur in compound dielectrics, or when there are two electrodes connected to a dielectric material [30].
It should be noted that the measurable dielectric constant is usually the result of several microprocesses that differ in the way and time at which a stationary state is reached. In particular, a distinction must be made between deformation (elastic) and thermal (relaxation) polarization. Elastic polarization relates to the rotation of molecules with constant dipoles relative to the equilibrium position under the influence of an external electric field. Dipole-elastic polarization is characteristic of those types of polar dielectrics in which the dipole moments of molecules cannot change their orientation significantly, but only oscillate with a small amplitude relative to the equilibrium position. In this case, the dipoles must be sufficiently rigidly coupled so that an elastic restoring force arises when the direction of orientation changes. This type of polarization is characteristic of liquid crystals and pyroelectrics. We shall not take elastic polarization into account in the model we are about to present and leave this to future work.
Thermal polarization is observed in dielectrics that contain weakly bound polar molecules that can move randomly during thermal motion. An external electric field leads to some order in the particle orientation, but, in general, thermal motion prevents the creation of a totally ordered orientation of all dipoles. Only at extremely low temperatures all the dipoles may be be aligned along the lines of force. Thus, only a partial orientation of the electric dipoles occurs under the influence of the field, i.e., depending on the strength of the electric field the dipoles tend to align toward it more or less but not completely (see Fig. 2, top right). We will now look into this in more detail.
The microscopic and the continuum viewpoint
The pictures in Fig. 2 relate to our model and show an RVE of matter capable of orientational polarization. The picture on the top left illustrates the situation before an external electric field was applied. We assume that on the microscopic or atomistic scale the material consists of rigid rods with positive and negative charges q at their ends, such that the dipole moment of one rod is given by p = ql, where the length vector l points from the negative to the positive head. The dipoles are chaotically oriented. Therefore, the total dipole moment on a continuum scale is zero. We also refer to it as the averaged or homogenized polarization vector of the ensemble of rods within the RVE, p . In the literature this quantity is sometimes also referred to as micropolarization. When multiplied by the continuum field of particle density n(x, t) = N /V we obtain the aforementioned local polarization vector P = n p .
Moreover, note that due to the requirement of isotropy before the electrical field acts, the microinertia tensor, J, which is also a continuum quantity, must be a spherical tensor, see Fig. 2, bottom left, which unlike P is not zero.
Under the influence of an external electric field, E = E n, the polarized microparticles, i.e., the rigid rods, tend to align in the direction n of that field, in order to reduce the electrostatic energy of the material: Fig. 2, top right, n being the unit vector in electric field direction. Then the substance will carry a dipole moment on the continuum scale, which is no longer equal to zero, and which coincides with the direction of the electric field vector, p = p n = 0. Moreover, the microinertia tensor will change from spherical to transversal anisotropy in the direction of n, as indicated in Fig. 2, bottom right. The idea is to model the time development of homogenized polarization, p = q l (t), through the time development of the microinertia, J = J (t), which will be used to compute a homogenized dipole length, l = l (t). In order to capture this time development the kinetic equation (1.12) may serve. Of course, for its integration the production term needs to be specified, so that it mimics thermal polarization. These issues will be clarified in the next subsection by presenting a suitable mathematical framework.
Compilation of relevant inertia tensor expressions and homogenization
Recall from dynamic textbooks the inertia tensor with respect to the center of gravity per unit mass for a rigid rod of length l oriented in e * 3 -direction of its normalized eigenbase e * i , i = 1, 2, 3: For future calculations we decompose this expression into a spherical and into a deviatoric part:
5)
Clearly this is an expression related to the microscopic scenario. It holds for each microparticle shown in Fig. 2, top left. However, it can also be used to characterize the situations on the continuum level shown on the bottom right of that figure. The key to this is homogenization by averaging over the particle population. For this purpose we introduce the so-called probability density for transversal anisotropy, P(ξ, ϑ) as follows (see [15], Section 5.3.5 for variations in the equation in the case of a semi-sphere): electric field. 0 ≤ ϑ ≤ π is the polar angle of the unit sphere . The probability density is normalized with respected to integration over , 0 ≤ ϕ ≤ 2π being the azimuthal angle: as can be demonstrated easily by using computer algebra programs. It is illustrated for different choices of ξ in Fig. 3. The case ξ = 0 corresponds to a constant value of P, such that all direction ϑ are equally possible. However, even for relatively small positive values of ξ = 0 one departs from this case and runs into transversal anisotropy, which favors small values of ϑ. We will use it now for homogenization. In the first place we want to calculate the average length vector l ∞ of the ensemble shown in Fig. 2, top right. The index ∞ is supposed to indicate that this is the effective, homogenized length after sufficient time has passed since the electric field was switched on. The directed length of an arbitrary rigid rod is given by l = le * 3 . However, the unit vector e * 3 is now arbitrarily oriented in space. In order to emphasize this point we assign e * 3 → N, N being an arbitrarily oriented unit vector. To make this even more obvious we recall the representation of the unit vector N in spherical coordinates, N = cos ϕ sin ϑ e 1 + sin ϕ sin ϑ e 2 + cos ϑ e 3 , where ϕ and ϑ can vary as indicated before, so that all directions in space are addressed by points on the unit sphere. The vector N is spanned with respect to a special Cartesian base e i , i = 1, 2, 3 located in the center of the RVEs shown in Fig. 2, such that the vector e 3 is oriented in the direction of the external electric field, n. Hence we write e 3 = n, and e 1 and e 2 are arbitrarily oriented perpendicularly to it within the corresponding plane of isotropy. Then l ∞ can be calculated by averaging as follows: d being the surface element of the unit sphere. Clearly within the plane of isotropy no average length contribution must arise. Everything points in the direction of transversal anisotropy, n. Note that for the case of perfect disorder ξ = 0 we obtain zero effective length, as expected. Moreover, for perfect alignment ξ = ∞ the homogenization yields l ∞ = ln as could have also be expected. We can use (2.9) to compute the effective final dipole moment on the continuum scale from p ∞ = q l ∞ . However, note once more that all these homogenizations characterize only the final state. The temporal development of how to get from the initially isotropic to the non-isotropic state cannot be analyzed within this approach. Next we homogenize the inertia tensor (2.5) of partially aligned rods within the RVE. To this end we assign e * 3 → N and carry out various integrations by using computer algebra programs. The final result reads: Obviously the deviatoric part vanishes for a chaotic arrangement of the rods, ξ = 0 and it turns into J dev 0 = l 2 /36 (I − 3n n) if all the rods are aligned. It should be emphasized that by its very construction J ∞ is the microinertia tensor on the continuum scale, however, after a very long time, so that there was ample of opportunity for the rods to arrange and find an equilibrium between the two concurring forces, the electric field, that wants them to align, and the disorientation effect due to a temperature different from absolute zero. We may refer to this by writing J ∞ ≡ J(t → ∞).
We are now in a position to compare two homogenized lengths, first, l ∞ from Eq. (2.9) and, second,l(ξ ) from Eq. (2.11) 3 as a function of the scattering parameter. The result is shown in Fig. 4. It is fair to say that the difference between the two approaches is small. The average length predicted by the microinertia approach is slightly less.
Moreover, we can compare the final result (2.11) with the microinertia tensor of a spheroidal ellipsoid with minor axes a ∞ = b in e * 1 and e * 2 directions, respectively, and the major axes c ∞ in e * 3 ≡ n direction. It is given by: J se = J se,sp + J se,dev (2.12) with spherical and deviatoric parts, By comparison of both expressions we conclude that (2.14) The ∞ signs indicate that we consider the situation after a long time. In the absence of an E-field, i.e., for total chaos, we find a ∞ = c ∞ , and for complete orientation a ∞ = 0, c ∞ = √ 5 /12l, as it should be. The latter result had been obtained before in [21] in context with the concept of an equivalent rod length. On first glance it is surprising that c ∞ = l /2 does not hold. This is because in an ellipsoid in contrast with the rod the mass must be considered as not evenly spread along the main axis.
Summarizing we may say that homogenization allowed us to analyze the final stage of the development of the microinertia. We now turn to the modeling of its temporal development.
The continuum model for the microinertia tensor
Note that the spherical part of the microinertia tensor cannot change in time, because the microparticles in the representative volume are rigid. Hence, temporal development of anisotropy is only characterized by the deviatoric part of the microinertia tensor, J dev . Consequently, the production term must be deviatoric, χ = χ dev , and be expressed in terms of deviators of microinertia. Hence, by using the nomenclature established in context with Eq. (2.11) we have (2.15) and the balance (1.12) for the inertia tensor reduces to a(t) is the semiaxis of the spheroidal ellipsoid in the plane of isotropy, c(t) is the semiaxis of the spheroid in the direction of the external field, n. They are time dependent as indicated.
The disappearance of the linear and angular velocity parts in Eq. (1.12) is worth a comment. First note that the translational velocity v must be zero. To prove this we argue as follows: The body force is given by the resulting Coulomb force within the RVE of volume V , namely ρ f = N (q + +q − )E/V . However, it vanishes because q − = −q + . Moreover, the medium is quasi "dust." Hence the stress tensor σ vanishes. Therefore, by virtue of Eq. (1.2) we must conclude that v = 0. On the other hand and with this in mind, if we now look at Eq. (1.9), we must conclude that all the velocities v i of the elementary particles are erratic and remain so during the polarization process. This is also understandable, because the Coulomb force on each of the micro-dipoles is also zero. Their centers will not be accelerated in the direction of the field E and, hence, no macroscopic velocity v will result.
Second, similar to the stress tensor, σ , there will be no couple stress tensor μ in Eq. (1.3). There are also no volume couples on the macrolevel, because they result from the vector product ρm = P × E. However, both P and E align with n, so that the vector product vanishes. To put it differently: We would expect the dipole macroparticle to rotate only if is misaligned with respect to the electric field, so that a moment couple is created. But this is not the case in our arrangement.
Nevertheless, this still leaves the term −ω × J · ω in Eq. (1.3), and in it obviously only the deviatoric part J dev might contribute to a temporal development of the angular velocity ω: This equation is identically satisfied and does not lead to internal contradictions, if for the physical reasons presented above ω = 0 is set. Unlike the case of the microvelocities v i we cannot support this conjecture from Eq. (1.8) where the angular momenta of the microparticles were averaged. Indeed, we can represent the angular velocity ω i of a microparticle in the eigensystem of its inertia tensor, ω i = ω i, j e * i, j . Then according to Eqns. (2.4), (1.8) and (1.10) we find: However, each microdipole will be subjected to a non-vanishing moment because of the applied electric field so that its angular velocity ω i will develop in time in contrast with its translational velocity v i . The production χ dev is additively split into two contributions, one to account for the effect of the external field, called χ E , and one to account for the impact of temperature, called χ T , as follows: Thermal polarization occurs rather slowly. In a constant external field equilibrium is established after some time τ p , which is known as the relaxation time of the polarization process. That is, a steady state during thermal polarization occurs when the external influence is compensated by internal thermal movement. Thus, Fig. 5 Change of the source term χ E vs. t /τ T for τ T/τ E =0.0001 (blue), 0.1 (red), 1 (green), 10 (magenta) the production term consists of a part that corresponds to the alignment of all microparticles in the direction of the external field without thermal movement, where J dev ∞ = l 2 /36 (I − 3n n) is the deviator of the microinertia that would be obtained if the electric field is infinitely strong and all microparticles would be forcefully aligned, cp., Eq. (2.11) 2 for ξ → ∞. J dev (t) will strive toward this value but never quite reach it. τ E is a (positive) relaxation time decreasing with increasing E 0 and characteristic of the intensity of the external effect, in agreement with experimental evidence. All of this indicates that the production χ E has the character of a source, i.e., it is always positive.
The second part of the production characterizes the thermal movement, where τ T is the time it takes for the material to return to an isotropic state due to temperature when the external field is turned off. The smaller the τ T -value, the faster the complete disorientation of the microparticles. Since the disorientation of particles is associated with thermal motion, τ T should be a decreasing function with temperature. Note that the production χ T is actually a sink term, since it is always less or at most equal to 0, i.e., essentially negative. The integration of Eq. (2.16) with the initial condition J dev = 0 yields the temporal development of the inertia tensor: In here J ∞ denotes the limit value of the moment of inertia for t → ∞. Note that the stationary value of (2.22) for t → ∞ does not coincide with the moment of inertia of the microparticle (2.5). The difference is the factor τ T τ E +τ T . This makes sense because not all of the dipoles are aligned in the n-direction due to thermal motion. Thus, this quantity characterizes the equilibrium distribution of dipoles over orientations. In fact by comparison with (2.11) we must conclude that: (2.23) Consider the first limit case, which is ξ = 0, i.e., total disorder of the particles. Then the right hand side of (2.23) is equal to zero. Consequently, τ T → 0 and the thermal sink term, χ T , creating chaos will dominate. The second case, total alignment, results for ξ → ∞. Then the right-hand side of (2.23) is equal to one, which is achieved for τ E → 0. Then the influence of the E-field related source term, χ E , is dominant. Figure 5 illustrates the behavior of the factor in front of the normalized source term (2.20), i.e., essentially the component e 1 · χ E · e 1 (e 1 ⊥ n) vs. normalized time t /τ T . Recall that if τ T/τ E << 1, then the source term should be small, because the chaotic effect of temperature will overcome the ordering imposed by the electric field. This is demonstrated by the blue and red lines. More mathematically speaking, we find that if τ T/τ E → 0 then 2χ E τ T/J 0 → 0, i.e., temperature dominance, and if τ T/τ E → ∞, then 2χ E τ T/J 0 → 1, i.e., electric field dominance. Figure 6 illustrates the behavior of the analogous factor in front of the normalized sink term (2.21) vs. normalized time t /τ E . Again recall that if τ T/τ E << 1, then the absolute value of the sink term should be large, because the chaotic effect of temperature will overcome the ordering imposed by the electric field. This is demonstrated by the blue and red lines. Moreover, we find that if τ T/τ E → 0 then 2χ T τ E/J 0 → −1, i.e., temperature dominance, and if τ T/τ E → ∞, then 2χ E τ E/J 0 → 1, i.e., electric field dominance.
It should also be noted that by comparison of the result shown in (2.22) with (2.15) 3 and (2.17) we find for the semi-axes: (2.24) We conclude that: This result is consistent with Eqs. (2.14) and (2.23). Also in the case of temperature supremacy τ T/τ E → 0 it follows that a ∞ = c ∞ , in other words isotropy. The deviator of the time-developing microinertia (2.22) can also be written in the form: where an effective lengthl τ (t) was defined: Obviously we obtain for very long times:l 28) and this result is consistent with (2.11) 3,4 and (2.23). The stationary length is plotted in Fig. 7. Clearly, for dominant thermal disorder (τ T << τ E ) the effective length goes to zero and chaos prevails, whereas with a strong electric field (τ E << τ T ) saturation can be reached. It is curious to note that the average length is not equal to 0.5 for τ E = τ T but rather to the square root of it. Mathematically speaking this is due to the equation of length identification (2.27). The microinertia itself favors the square.
Alternating electric field and dispersion
It was emphasized in context with Eq. (2.20) that the relaxation time τ E depends on the electric field E. More specifically it decreases with increasing electric field. So far τ E was treated as a constant. If we now wish to study the impact of an electric field alternating in magnitude but not changing its direction in space on the development of the microinertia tensor and therefore on the development of polarization, consequently, we have to allow that τ E changes with time. Let us write: where τ 0 E is a true constant. Because of the square we do not repolarize, however, the ordering effect of the electric field will not be optimal at all times. The cosine function was chosen for pure convenience. It is a smooth function and leads to no problems during the numerical integration. Then the thermal production shown in Eq. (2.21) will take over even more and has additional opportunity to reestablish chaos. Consequently, the effective lengthl τ and thus the molecular polarization will fluctuate more or less heavily depending on the chosen frequency ω. Such a dependence on frequency is known as dispersion. Moreover, between the applied alternating electric field and the varying polarization there may also be a phase shift.
If Eq. (2.29) is used in context with (2.20) and (2.21), the differential equation (2.16) can numerically be solved: Fig. 8 shows the effective length as a function of normalized time for τ T/τ 0 E =0.1 (top left), 1.0 (top right), 5.0 (bottom left), 10.0 (bottom right) for four choices of normalized frequency ω /τ T =0 (blue), 1 (red), 2 (green), and 5 (magenta). Of course, just numerical solutions of the differential equation (2.16) are possible in the alternating case. The following is observed: • The smaller τ T/τ 0 E , the smaller the effective polarization l τ , because then the thermal effect prevails (resulting in smaller values of τ T ) or the electric field is too weak (resulting in larger values of τ E ).
• The undulating polarization curves stay below the blue one for the non-alternating electric field. In other words, the thermal effect is more effective. • The larger the frequency of the ω of the alternating electric field, the closer the effective polarization comes to the one when the electric field does not alternate: The temperature has less time to take effect and dispersion is strongly visible. However, even at very high frequencies the effective polarization does not quite reach the one for a non-alternating field.
The effect of dispersion is further analyzed in Fig. 9. The curve and corresponding dots are for τ T/τ 0 E = 0.2 (red), 0.5 (green), 1.0 (blue), 2.0 (black), and 10.0 (magenta). Note that: • Increasing ωτ T from zero results in an initially steep decline followed by an increase that finally leads to saturation. • The higher the τ T/τ 0 E , the smaller the difference between the value for polarization at ωτ T = 0 and the saturation level. The particles have time to adjust. However, the average length of the non-transient case is never fully reached.
• The dispersion effect becomes more pronounced if τ T/τ 0 E is increased.
Conclusions and outlook
In this paper the following were achieved: • The importance of micropolar media for studying electric phenomena, such as polarization was emphasized, because they allow modeling materials with an internal structure. • The phenomenon of dielectric polarization was discussed in terms of micromodels. In particular the microphenomenon of orientational polarization was linked to the continuum level from a new viewpoint, namely to an extended version of micropolar theory. • The process of developing orientational polarization was analyzed by introducing two production terms in the extended balance of microinertia, one for the chaotic effect of temperature and one for the ordering effect of the electric field. • The final stage of polarization obtained from the microinertia model was compared to results obtained from homogenization both traditionally by calculating the effective length of oriented rigid dipoles and non-traditionally by calculating their average inertia tensor.
It is fair to say that the homogenization technique applied to orientational polarization in this paper captures the essential physics features of this process in a novel way, but it seems rather crude when compared to more sophisticated methods, for example the ones described in [18]. The authors of that paper focus on the electromagnetic side of the problems; in other words, they consider polarization and magnetization in terms of Maxwell's equations. The applications of their techniques to the mechanical viewpoint of extended micropolar media should be subject of further studies. Further research in the field of extended micropolar theory will surely include a similar investigation of the magnetic susceptibility. Both will potentially lead to an investigation of cross-property connections as follows. Note that the classical approaches, which are based on averaging according to p = q l , allow only the polarization of the material to be estimated. In contrast with that the approach proposed in this work, associated with a change in the tensor of inertia at the macrolevel, makes it possible to establish relationships between various physical and mechanical processes. In particular the reorientation of microparticles from a chaotic to an ordered state transforms an initially isotropic heterogeneous material into a transversally isotropic one, which, in turn, leads to a change in the effective elastic, or conductive (electro, heat, diffusion) properties of the material.
In the future our research might also be helpful for modeling structural transitions in nematic crystals. Surely, the interaction between the microparticles in such materials will be more complicated than the dust type of interaction that was assumed in our present work. Nevertheless, the orientational transitions under the action of electro-magnetic fields are similar to ours, as can be seen in a recent publication, where such modeling was attempted numerically [29]. If such coupled problems of nematic crystals are studied, it will also become necessary to reconsider the balance of internal energy (1.4) to account for effects of electro-magnetic dissipation (Joule heating).
Also a remark should be made regarding the attempts of researchers to include elastic effects to dielectrics. As it was mentioned so far we did not study truly coupled interaction between all field equations. Instead we specialized to "dust," which led to a balance of spin that was identically satisfied. The foundations of a more sophisticated electro-micropolar theory were laid very early in a seminal paper by Dixon and Eringen [6]. The methods explained in there now need to be used in the extended version of micropolar media. In particular it will be worthwhile to address the question as to whether the idea of higher electric moments (quadropoles) are in some way equivalent or go beyond to our idea of a dynamic microinertia following its own balance.
In the same context it should also be asked as to whether the concept of micromorphic continua is equivalent or goes beyond our concept of a microinertia modeling structural change. A starting point could be a comparison with results from [25][26][27], and [28]. To begin with it will become necessary to discuss the differences between the microinertia tensor of micromorphic continua and our microinertia for rigid body points. Then the striking mathematical similarity between the former and the quadropole tensor must be examined and, finally, the question must be answered as to whether the production of our microinertia describing structural change can be linked to the additional freedom of deformation inherent to micromorphic continua.
Funding Open Access funding enabled and organized by Projekt DEAL.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. | 10,187.8 | 2021-01-28T00:00:00.000 | [
"Physics"
] |
The Bayes Factor for the Misclassified Categorical Data
This article addresses the issue of misclassification in a single categorical variable, that is, how to test whether the collected categorical data are misclassified. To tackle this issue, a pair of null and alternative hypotheses is proposed. A mixed Bayesian approach is taken to test these hypotheses. Specifically, a bias-adjusted cell proportion estimator is presented that accounts for the bias caused by classification errors in the observed categorical data. The chi-square test is then adjusted accordingly. To test the null hypothesis that the data are not misclassified under a specified multinomial distribution against the alternative hypothesis they are misclassified, the Bayes factor is calculated for the observed data and a comparison is made with the classical p-value.
Introduction
The problem of misclassification is a major issue in observational epidemiologic studies.Not long after Bross (1954) pointed out that the non-differential misclassification would bias the corrected odds ratio toward the null hypothesis, Diamond and Lilienfeld (1962a-b) has extended the result to various types of epidemiologic studies.A 2 × 2 case-control studies with a single exposure variable being misclassified has been widely studied (Fleiss et al 2003, Chapter 17;Gustafson 2004, Chapter 5;Kleinbaum et al 1982, Chapter 12;Rothman et al 2008, Chapter 19).Yet, almost no authors pay attention to investigate the effect of misclassification in the analysis of a single categorical variable except Mote and Anderson (1965).Mote and Anderson primarily takes a deductive approach to account for the bias caused by the classification errors.Yet, the shortcoming with a deductive approach is that it does not take the sampling errors into consideration.As a result, the issue on how to deal with the misclassification in the analysis of categorical data still remains unsolved.This article addresses another important issue, that is, whether the observed categorical data are misclassified.Instead of using a deductive method, an inductive approach is employed to account for the misclassification bias embedded in the collected data.First, the inverse way is taken by equating the expected value of the estimated sample cell proportion with its population parameter conditional on that the misclassification probabilities are given.Then the bias-adjusted estimator is presented for the population cell proportion parameter by inverting the misclassification matrix.Second, the appropriate misclassification probabilities are calculated depending on if the misclassification is possibly made either from one category to all other categories (scenario I) or merely to its neighboring categories (scenario II).Third, in order to test the null hypothesis that the data are not misclassified under a specified multinomial distribution, a mixed Bayesian approach is used to calculate the Bayes factor and compare it with the traditional p-value.
Methodology & Background
Given that X is a categorical variable with K (≥ 3) categories and the data are collected through a simple random sampling of size N, where 1).The crude estimator, j p ˆ, for the population cell proportion p j in the j th category is then given by Assume that j p ˆis distributed as a multinomial distribution with the population size N and the cell proportion of the j th Suppose that the observed data are misclassified.Let w jk (j k) be the misclassification probability of an observation belonging to the j th category being incorrectly classified into the k th category and w jj the correct classification probability that an observation belonging to the j th category being correctly classified into the j th category.Then, it is easily shown that the expected value of p ˆis Eq. 2 shows that the crude estimator k p ˆ is no longer unbiased for the population parameter p k , provided that I W ,where I is the K × K identity matrix.A set of misclassification probabilities {w jk } is said to be feasible if the misclassification matrix W in Eq. 2 is invertible (or nonsingular) for 0 < w jk < 1.
Assume that W is invertible.Then bias-adjusted cell proportion (BACP) estimators ( where . Note that by using Eqs. 2 and 3 it's easily shown: The misclassification matrix W has two possible forms depending on how the categorical variable X is misclassified.
There are two possible scenarios that are given as follows: Scenario I: The misclassification occurs after classifying one category incorrectly into all other categories.Also, because misclassification can occur equally likely from any one of the j th correct category to the k th (observed) wrong category, we thus have, for fixed j , k ≠ j, and Scenario II: The misclassification occurs after classifying one category incorrectly only into its neighboring categories.Therefore, we have, for fixed j w jk = 0 for |k -j| > 1, and When K = 3, the associated misclassification matrix with its determinant and its inverse matrix for scenarios I and II are hereby obtained respectively.An explicit form of the misclassification matrix W I and its inverse V I for scenario I are given respectively by and By using Eqs.6b and 7, the feasibility and admissibility constraints for the misclassification probability and BACP estimator are given respectively as follows: ) and (8b) For scenario II, an explicit form of the misclassification matrix W II and its inverse V II are given respectively by and The BACP estimator for scenario II is thus given by By using Eqs.9b and 10, the feasibility and admissibility constraints for the misclassification probability and BACP are given respectively as follows: (11b) To test whether the data in table 1 are misclassified, we need to test the following (sharp) null hypothesis that the data has no misclassification under p = p 0 versus the alternative hypothesis that the data are misclassified (Berger and Selleke 1987) H 0 : p = p 0 , ω = 0 versus H 1 : p ≠ p 0 , ω > 0, ( where , {w jk } are the entries of the misclassification matrix W given by Eq. 2. To test Eq.12 the bias-adjusted chi-square test (BACST) is given by where , v jk denotes the entry of the j th row and the k th column of the inverse matrix V of the misclassification matrix W in Eq. 2 and For large samples, Eq. 13 is distributed under H 0 asymptotically as the central chi-square distribution with K -1 degrees of freedom (df).Yet Eq. 13 is distributed asymptotically under H 1 as the noncentral chi-square distribution with K -1 degrees of freedom and the non-centrality parameter given by (Lancaster 1969) When w jk = 0 for all j and k, Eq. 13 reduces to Reject the null hypothesis H 0 if 0 ˆC K , where K ˆ is given by Eq. 15 and C 0 is the critical value of the central chi-square distribution with K -1 df at the significance level α As is well known from the Bayesian viewpoint, the p-value is not an adequate measure for the evidence to support the null hypothesis (Goodman 1999a-b).Hence the Bayes factor is calculated as a comparison with the p-value.To formulate the hypothesis-testing problem in a Bayesian setting we begin with the data ) ,..., , ( and assume that its probability distribution follows in a family of distributions which are parameterized by is the K-dimensional simplex.To test the hypotheses of 0 , : (Eq.12), it is assumed that there exist a prior probability density function (PDF) ) ( 0 where g is a prior PDF on p ϵ Σ which assigns mass π 0 to {p = p 0 } and 1 -π 0 to {p ≠ p 0 }.Define , the Bayes factor is given by (Kass and Raftery 1995) where g m is given by 17b is the PDF of the noncentral chi-square distribution with K -1 degrees of freedom and the non-centrality parameter given by Eq. 14.
of Eq. 17b is calculated for Scenario I with the assumption of where c is the upper bound on the admissible BACP for scenario I and obtain where an approximation to the noncentral chi-square distribution is provided by using the central chi-square distribution (Cox and Reid 1987).The lower bound for the Bayes factor after using a symmetric Dirichlet's prior for g(p) are obtained under scenario I and II: The details for obtaining the value of ) max( i , i = I or II, are given in the appendix.
Example
The data in The issue of concern here is whether the data are misclassified separately for males and females.Because we do not have any prior belief on the values of p 0 in Eq. 12, they are thereby determined empirically from the observed data.As a result, the values of p 0 are chosen differently for males and females.For females the values of p 0 in the null hypothesis are chosen to be that of equiprobability, ˆ = 0.47 (p-value = 0.79) for males and females.Therefore, the null hypothesis H 0 is not rejected at the significance level of 0.05 for both males and females.Yet, we would like to test the above hypotheses from the Bayesian perspective by calculating the Bayes factor as a comparison with the p-value.
For both males and females under scenarios I or II, Eq.A10 in the appendix has three negative and one positive real, and a pair of conjugate complex roots.Due to the constraint that τ > 0, only the positive root is a stationary point for Eq.A9.Eq.A9 for males has only under scenario II a unique positive local maximum (Figure 1), while Eq.A9 has a unique positive local maximum at its stationary point for females only under scenario I (Figure 2). given by Eq.A9 is for CF model 12 under scenario I for females
Discussion
Some interesting observations are worthy to be mentioned below: 1.So far, this author is not aware of any guideline available in the literature on deciding how large the lower bound for the Bayes factor should be so that we're confident the evidence provided by the data surely supporting H 1 rather than H 0 .Yet, since the lower bounds for the Bayes factor from the cancer data for both genders were not large enough, a tentative conclusion was that the cancer data in table 2 seemed unlikely to be misclassified.Although H 0 was not rejected for both gender in table 2 either according to their p-values (table 3, column 6), the p-value is, strictly speaking, not an appropriate measure for assessing the evidence provided by the data due to its inherent fallacy (Goodman 1999a-b).2. From the analysis of the Bombay cancer data, the existence of Bayes factor seems to depend not only on the scenario (I or II) (the misclassification pattern), but also the multinomial distribution of p 0 (table 3).To clarify this issue, another data set related to the degree of severity for the clinical condition of myocardial infarction patients was studied (Snow 1965), where the distribution of p 0 for the treated and control groups are respectively specified as (0.4, 0.4, 0.2) and (0.3, 0.4, 0.3).It was found that the Bayes factor existed for the treated group under scenario I, but not under scenario II, whereas for the control group it exists under both scenarios.It seems that a crucial condition for the existence of Bayes factor is whether the BACST value (Eq.13) is positive.As far as the existence of the Bayes factor is concerned, I'd like to make a conjecture which is given as follows: "For any data set under either scenario I or II the lower bound of of Eq. 13 is positive for K ≥ 3."
Conclusion
This paper addresses an issue: "how to test whether the collected categorical data are misclassified."A mixed Bayesian approach is used to test the null hypothesis that the collected data are not misclassified under a specified multinomial distribution for the studied categorical variable.The Bayes factor is employed as the main instrument to assess the evidence provided by the data.The lung cancer from all hospitals in the city of Bombay, Australia was used as an example for illustration.Based on the result of the Bayes factor in this study, the p-value was shown again not an appropriate measure to assess the evidence provided by the data.
Appendix A
With an assumption of .
By substituting Eq.A1 into Eq.13, we have where By Eq. 14, we have of Eq. 18 with a choice of ) ( 0 h which equals to the pdf of uniform distribution over [0, c 1 ] is reduced to By substituting Eqs.A2 and A3 into the above equation and integrating with respect to θ, we have after algebraic simplification where With an assumption of By using Eq.A6, we have By substituting Eq.A7 into Eq.13 and integrating where If the prior distribution function for g(p) is taken to be a symmetric Dirichlet's distribution with the flattening constant (or hyper-parameter) τ (τ > 0) (Good 1975), then Eq.A5 is reduced to and set it equal to zero, we have after simplification a set of misclassification error probabilities {w jk } is said to be admissible if the corresponding BACP estimators { k p } are admissible.
for scenario I are given by Since p and ω are a priori independent under H 1 , we have
F
and w jk > 0, while that of p 0 in the null hypothesis for males are set up as follows: > 0. Because the misclassification probabilities of {w jk }, j, k = 1, 2, 3 are zero under the null hypothesis, the BACST values of Eq. 15 are then given respectively by M
To avoid the use of hyper-prior distribution on τ(Good and Crook 1974), the non-Bayesian approach is used to find the stationary point max(.)an elementary technique in calculus to calculate the first derivative of
Table 1 .
Observed data for the categorical variable X table 2 are taken from table C.1 inWoodward's book, pp.756-760 (Woodward 2005).It represents the lung cancer data collected by the Bombay Cancer Registry from all cancer patients registered in the 168 government and private hospitals and nursing homes in Bombay, Australia, and from death records maintained by the Bombay Municipal Corporation.The survival times of each subject with lung cancer from time of first diagnosis to death (or censoring) were recorded over the period 1 st January 1989 to 31 st December 1991.Here we are only concerned with type of tumor of 682 subjects grouped by gender.
Table 3 .
A comparison of the lower bound for Bayes factor (Eq. 19) with the p-value for admissible CF models | 3,374 | 2018-06-28T00:00:00.000 | [
"Mathematics"
] |
Bitcoin price prediction using ARIMA and LSTM
. The goal of this paper is to compare the accuracy of bitcoin price in USD prediction based on two different model, Long Short term Memory (LSTM) network and ARIMA model. Real-time price data is collected by Pycurl from Bitfine. LSTM model is implemented by Keras and TensorFlow. ARIMA model used in this paper is mainly to present a classical comparison of time series forecasting, as expected, it could make efficient prediction limited in short-time interval, and the outcome depends on the time period. The LSTM could reach a better performance, with extra, indispensable time for model training, especially via CPU.
Introduction
Finance Field has long been regarded as a prospective field in Machine learning, considering the price of financial assets is always non-linear, dynamic and chaotic, namely, it is difficult to predict. [1] Many famous organizations, including American Accounting Associates(AAA), EMERJ have all developed their own research areas. Models including RNN, LSTM have all proven to be efficient in predicting the future trend of finance grows in stocks, shares and currency flow.
Bitcoin is a special type of virtual currency, it is broadly used in series of online trading systems. In the past decades, the price of Bitcoin has went through series of fluctuation. Nowadays, the average price of Bitcoin is about 7000 from BTC to USD. It is an ideal platform to test the machine learning models as well as traditional time series prediction as its relatively young age and resulting volatility. [2] ARIMA has been shown to be one of the most commonly used algorithms in time-series data prediction. It is applied to forecast prices and performs satisfied [3]. Comparing to ARMA, it is more precise, and take less time to make calculation. In addition, LSTM have proven to be an efficient tool in making price prediction, risk-recognition due to the temporal nature of bitcoin data.
Dataset
Bitfinex have provided an API for users to reach the realtime pricing information about Bitcoin, it can automatically collect data from this API and result will show in its homepage. Pycurl is a commonly used python library in collecting online data, which support users to request information communication between server and terminal, suitable for receiving data from Bitfinex website. In order to obtain a trainable, considerable price dataset, data is collected from the API, after extract the information (in JSON format), change the Dataframe format, initial data will finally convert to a suitable dataset for later different scenarios analyzation. Based on the method described above, by using 5seconds interval trading data on the website Bitfinex, 10000 prices information, include price between BTC/USD, ETH/BTC, ex cetera is collected. And then it is splinted into training set and testing set, each contains first 8000 and last 2000 values, use price of each 5 second for training model. Table 1 shows some fundamental attributes of the information of BTC/USD.
ARIMA model
In statistics and econometrics, and particular in time series analysis, an autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. The 'integrated' refers to the number of times need to difference a series in order to achieve stationary, which is required for ARMA models to be valid. In other words, ARMA models is equivalent to an ARIMA model of the same MA and AR orders [4] In this section, the description of the proposed ARIMA model and the general statistical methodology are presented as follows:
Data Pre_requisition
Since ARIMA model is used for forecasting a time series which can be made to be 'stationary', after gaining the dataset. In most of the competitive electricity markets this series presents: high frequency, nonconstant mean and variance, and multiple seasonality. [4] Therefore the stationarity and seasonality of price data should be checked, performing differencing if necessary and choosing model specification ARIMA(p,d,q).
Considering the tiny gap between two neighbor price, an average price in a time pried can be adopted, the plot constructed by results that take an average for every 12 prices, which denoted the average price each minute, then its relative autocorrelation plot is also presented to show the stationarity of dataset.
A stationary series roams around a defined mean and its ACF plots reaches to zero fairly quick, while for the original price series, its ACF is slow-decaying, PACF first bar 1 , both implying price data is nonstationary. As previous result denotes that the initial time series is non-stationary, it is necessary to perform transformations to make it stationary, the most common way is to difference it, the right order of differencing is the minimum differencing required to get the near-stationary series to avoid over-difference. After lag-1 differencing, the result (Fig.2) and correspondent ACF describes its fast-decaying feature, which is a convenient evidence to support the stationarity of differencing data. Simultaneously, both ACF and PACF eventually decayed exponentially to zero, shows refined data is able to construct an ARIMA model. To avoid high random probability, Lagrange multiplier statistic test for heteroscedasticity. The p-value is 5.8137286e-14, much less than 0.05, ruled out the possibility of white noise.
Forcasting
After data pre-processing, the refined dataset contains 733 points in training set and 100 points in testing set separately. Model is autocorrelated, ARIMA(1,1,0), which is used for differenced first-order autoregressive model, is suitable for forecasting, by regressing the first difference of Y(in this case is the bitcoin price), on itself lagged by one period. The model would yield the following prediction equation:
LSTM model
Long short-term memory (LSTM) is developed from Recurrent neural network (RNN) model to solve the vanishing gradient problem. Comparing to the traditional Front forward neural network (FNN), the RNN adds a self-connecting edge to every node in the network, and thereby allowing the neural network to utilize the prediction result from the last run, to make time-series prediction. [5] This characteristic allows programmers to process various data, including handwriting recognition, speech recognition and anomaly detection. LSTM could be regarded as an improved version of RNN, it adds the input gate, output gate and forget gate to the existing cell units. These additional gates allow the cell unit to discard useless information, and memorizing important information in the training process. These gates could also handle with the exploding and vanishing gradient problems. In nowadays, LSTM is the most broadly-used tool to making classifying, processing and making predictions based on time series data. The forget gate takes the h and x as input, and output a decision (0~1) to the other parts. 0 represents "forget all", whilst 1 represents "keep all". In the input gate, the sigmoid function would decide which information to renew. Finally, the output gate would decide which value to output. It will combine the information from different parts, and decide which information to keep, and which information to output.
The model is trained 100 epochs with 10 pieces of continuous data in each round, the loss plot ( fig.7) recorded from each epoch shows that loss initially be large and then convergence immediately. The loss close to 0.02 at first, after 5 epochs, it becomes around 3 10 and reduce its decaying rate. With different input training shape, which is the time length for predicting next step's value, loss growth as time period stretch. Loss based on different strategy of input time series are also presented in the figure. In the training process, it is obvious that at the beginning of training, the loss is relatively high, but it could decrease sharply as the epoch goes up. After 3~4 epochs, the loss is very close to zero already.
(a)prediction based on 1 previous data (b) error distribution Trained LSTM model performs a satisfying prediction of testing set. The average Error rate is 0.4765938, with a standard deviation of 2.092208. This is ignorable since the original data is quite large. Model that use 5 and 10 previous data is also tried in testing set and comparing to single previous point, 5 or 10 points considered for forecasting is actually having negative effect, even to capture the fluctuation of data, the predicted result is not as precisely as expected.
(a) prediction based on 5 previous data (b) prediction based on 10 previous data In Dec 14th, another test set, containing captured 3752 pieces of information from the Bitfinex, is also tried for the model. The prediction result shows that LSTM is also performing well in datasets collected from various time periods.
Conclusion
Although both ARIMA and LSTM could perform well in predicting Bitcoin price, the LSTM would take extra amount of time to train the neural network model for about 42 minute an epoch via 4 core CPU or 1 minute 12 seconds via 2 core GPU. However, after training, the LSTM could make prediction more efficiently, and the precision rate is also higher. In general case, taking less previous data to make prediction in LSTM could lead to better result. ARIMA is quite efficient in making prediction in short span of time; but as the time grows, the precision rate would decrease. | 2,108.4 | 2020-11-01T00:00:00.000 | [
"Computer Science",
"Business"
] |
The Role of Localized Compressional Ultra‐low Frequency Waves in Energetic Electron Precipitation
Typically, ultra‐low frequency (ULF) waves have historically been invoked for radial diffusive transport leading to acceleration and loss of outer radiation belt electrons. At higher frequencies, very low frequency waves are generally thought to provide a mechanism for localized acceleration and loss through precipitation into the ionosphere of radiation belt electrons. In this study we present a new mechanism for electron loss through precipitation into the ionosphere due to a direct modulation of the loss cone via localized compressional ULF waves. We present a case study of compressional wave activity in tandem with riometer and balloon‐borne electron precipitation across keV‐MeV energies to demonstrate that the experimental measurements can be explained by our new enhanced loss cone mechanism. Observational evidence is presented demonstrating that modulation of the equatorial loss cone can occur via localized compressional wave activity, which greatly exceeds the change in pitch angle through conservation of the first and second adiabatic invariants. The precipitation response can be a complex interplay between electron energy, the localization of the waves, the shape of the phase space density profile at low pitch angles, ionospheric decay time scales, and the time dependence of the electron source; we show that two pivotal components not usually considered are localized ULF wave fields and ionospheric decay time scales. We conclude that enhanced precipitation driven by compressional ULF wave modulation of the loss cone is a viable candidate for direct precipitation of radiation belt electrons without any additional requirement for gyroresonant wave‐particle interaction. Additional mechanisms would be complementary and additive in providing means to precipitate electrons from the radiation belts during storm times.
Introduction
Energetic electron losses are a critical component of electron dynamics in the inner magnetosphere and outer radiation belt. Although electron dynamics in this region are only partially understood, electron losses can essentially occur either when their drift trajectories intersect with the magnetopause, termed magnetopause shadowing (e.g., Ozeke et al., 2014;Turner et al., 2012;West et al., 1972), or when their bounce trajectories lead them to be lost to the upper atmosphere (e.g., Millan et al., 2002). Traditionally, wave-particle interaction and in particular gyroresonant interaction with plasmaspheric hiss (e.g., Meredith et al., 2007) or whistler mode waves (Horne et al., 2003) are invoked as being responsible for pitch angle scattering of electrons into the loss cone and enhanced precipitation (e.g., Kennel & Petschek, 1966;Millan & Thorne, 2007;Rodger et al., 2012). Indeed, whistler mode chorus waves are thought to provide the source of the lower-energy diffuse aurora (e.g., Thorne et al., 2010), and observations of whistler mode chorus have been shown to be clearly linked to modulation of the diffuse aurora (e.g., Nishimura et al., 2010). However, large whistler mode chorus amplitudes are waves typically limited to the nighttime and morning sectors of the magnetosphere Meredith et al., 2012), whereas diffuse auroral processes occur at all magnetic local times (MLTs). More recently, other gyroresonant interactions have also been identified as being a major loss mechanism for relativistic electrons (Breneman et al., 2015), first invoked by Thorne and Kennel (1971). Electromagnetic ion cyclotron (EMIC) wave-driven electron loss is now considered to also be a significant contributor to radiation belt losses (e.g., Hendry et al., 2012Hendry et al., , 2016Hendry et al., , 2017Rodger et al., 2015;Zhang et al., 2016). The source of auroral particle precipitation across all MLT sectors remains to be determined.
Ultra-low frequency (ULF) waves have been proposed to provide both resonant (e.g., Elkington et al., 1999;Mann et al., 2013) and diffusive (e.g., Brautigam & Albert, 2000;Schulz & Lanzerotti, 1974) acceleration and transport of electrons. ULF wave precipitation signatures have been observed since the early 1960s (e.g., Anger et al., 1963;Brown, 1964;Ziauddin, 1960) and have been observed in riometer (e.g., Beharrell et al., 2010;Heacock & Hunsucker, 1977;Olson et al., 1980;Spanswick et al., 2005), auroral (e.g., Rae, Mann, Dent, et al., 2007;Roldugin & Roldugin, 2008), and X-ray-related precipitation (e.g., Brito et al., 2012;Halford et al., 2015;Motoba et al., 2013). However, although ULF wave signatures have been observed in precipitation across a wide range of energies from keV to MeV, these waves have only been proposed to be indirectly involved in energetic electron losses. This ULF modulation of precipitation in the Pc4-Pc5 frequency range (e.g., Jacobs et al., 1964) is often discussed in terms of the ULF modulation of other wave modes, principally ULF modulation of whistler mode wave growth rates (Breneman et al., 2015;Li et al., 2011;Millan & Thorne, 2007;Nishimura et al., 2013;Rae, Mann, Dent, et al., 2007;Spanswick et al., 2005;Watt et al., 2011). In these circumstances, ULF modulation of VLF wave intensities would provide an energy-dependent response where those electrons that are able to resonate with specific VLF wave frequencies would be precipitated. However, the remaining part of the phase space density (PSD) would most likely be unchanged, at least over ULF wave periods (~minutes) where pitch angle diffusion time scales are usually very long (hours to days; e.g., Horne et al., 2005). Hence, any broadband precipitation must also be explained in full, again at all local times. Recently, Brito et al. (2012Brito et al. ( , 2015 proposed a new mechanism whereby global ULF waves could be directly implicated in radiation belt losses. The radial motion of relativistic electrons within global-scale compressional ULF waves would mean that electrons would experience larger magnetic fields and shorter field line lengths during the inward motion phase, where conservation of the first and second adiabatic invariants would lead to a gain of parallel energy, altering pitch angles of some electrons sufficiently such that they move into the local loss cone. Although not discussed explicitly by Brito et al. (2012Brito et al. ( , 2015, this mechanism may work over a large range of electron energies. In this paper, we explore a related but new mechanism of electron precipitation directly driven by highly localized compressional ULF waves simply by modulating the equatorial loss cone appreciably from its average, or typical, value. We apply this mechanism initially at geosynchronous (GEO) orbit and find that the average geosynchronous loss cone can increase by up to 50% during large-amplitude compressional ULF waves. Depending upon the shape of the PSD close to the loss cone, this mechanism can provide a significant additional amount of precipitating flux without the requirement for any wave-particle interaction processes. We show clear experimental evidence of ULF wave-modulated precipitating electron fluxes across a wide range of energies (20-400 keV) and conclude that compressional ULF waves should be considered a direct, rather than an indirect, candidate precipitation mechanism for radiation belt electrons, or indeed all electrons close to the loss cone with bounce periods less than the wave period. This mechanism has the potential to directly drive electron precipitation across the entire outer radiation belt and over a wide range of energies and is not limited to geostationary magnetic latitudes where our observations are concentrated.
Instrumentation
In this paper, we primarily utilize data from the GOES fluxgate magnetometers at 0.512 s cadence (Singer et al., 1996). However, we also augment this with ground magnetometer data from the CARISMA (Canadian Array for Realtime Investigations of Magnetic Activity; Mann et al., 2008), together with Northern Solar Terrestrial Array (NORSTAR) riometer data (http://aurora.phys.ucalgary.ca/norstar/rio/), both at 1 s cadence. We further utilize southern hemispheric measurements of bremsstrahlung X-rays, related to the precipitation of energetic electrons from the Balloon Array for Radiation belt Relativistic Electron Loss (BARREL; Millan et al., 2013) Campaign 1, Payload 1H (1H) at both 50 ms resolution (fast X-ray spectrum channel 1 at <180 keV X-ray energy) and 32 s cadence (slow X-ray spectrum, for~30 keV-10 MeV X-ray energies).
hemisphere immediately conjugate to the NORSTAR Island Lake (ISLL) riometer, determined using the T96 magnetic field model. At the period of interest, 1930-2130 UT, GOES 13 is at slightly higher latitudes and around 1 h of magnetic local time (MLT) to the east.
From top to bottom, Figure 2 shows (a) the GOES 13 and conjugate ground magnetometer magnetic field magnitudes, with (b) the modulation of the loss cone using measured and modeled ionospheric magnetic fields (to be discussed later). Figure 2c shows channel 1 from the BARREL fast spectra of <180 keV X-rays, and Figure 2d shows BARREL 1H slow spectra from 50 to 300 keV X-rays. Figure 2e shows riometer absorption from ISLL. Figure 2f shows the normalized frequency content of each of these data sets calculated within the vertical lines using Fast Fourier Transform (FFT) analysis of the respective time series from GOES 13 (black), BARREL fast (blue) and slow (green and yellow) spectra, and the ISLL riometer (red). Figure 2a shows that large-amplitude (25 nT peak to valley on a back-ground~85 nT) compressional ULF waves are observed at geosynchronous orbit between 4 and 5 mHz (Figures 2a and 2f) in a temporally localized period between~1950 and 2030 UT. Around 20-25 min later in UT (2015-2050 and in the southern hemisphere, BARREL 1H measures a clear and large-amplitude ULF-modulated electron precipitation event (Figures 2c, 2d, and 2f), as does the ISLL riometer, which is conjugate in the northern hemisphere (Figures 2e and 2f). Fourier analysis of these time series for the respective periods of modulation (denoted by the dashed vertical black lines) reveals that GOES magnetic field and BARREL 1H precipitation signatures share a dominant common frequency of 4-5 mHz, and the ISLL riometer a slightly lower dominant frequency of 3-4 mHz. Hence, there are common frequencies observed in both geosynchronous magnetometer data and modulated precipitation in the ionosphere. In section 4 we discuss the relevance of the slightly lower frequency observed in the precipitation seen through riometer absorption changes. We note that the precipitation signatures actually correlate best with the compressional ULF wave signature if shifted by 0:30 UT, which suggests that there is in fact a localized source of ULF wave activity drifting slowly westward or sunward, for example, ULF waves driven via an internal source such as unstable ion distributions drifting through that region . Further observations from the GOES 15 magnetometer, and McMurray (MCMU) riometer stations (not shown), both located further west from the GOES 13, ISLL, and BARREL-1H measurements also indicate that the ULF wave activity is localized in space and persists for at least 2 h of universal time.
We calculate the linear correlation coefficients for the period of ULF wave activity, noting that there is a large background perturbation to both the ISLL and BARREL data, and that a slightly lower frequency is observed at ISLL for reasons we discuss in the section 7, but which are primarily due to an ionospheric decay effect. Peak correlation coefficients between GOES and ISLL are 0.5, and between GOES and BARREL is 0.57. Correlation between both ionospheric measurements is significantly better given that both are ionospheric measurements and hence are subject to the same ionospheric decay, peaking at 0.87 between ISLL and BARREL slow spectra at 53 keV.
In summary, this case study exhibits localized compressional ULF wave observations from GOES at~20 UT and~1430 MLT in addition to localized ULF wave-modulated precipitation at ISLL and BARREL 1H at 2015 UT at~1315 MLT. Given that the ULF wave signatures are at the same frequency, our hypothesis is that a localized ULF wave field drives ULF-modulated precipitation. The changes in MLT of the localized ULF wave activity as time progresses indicate that these ULF wave signatures must be slowly moving westward, in keeping with an ion-generated compressional ULF wave.
What Processes could Drive Localized ULF-Modulated Precipitation?
Given that the ULF signatures are observed in the same local time region, but are temporally limited in extent, we interpret these combined measurements as clear evidence of a large-amplitude, spatially localized ULF wave field in a highly limited spatial range in the postnoon sector (14-15 MLT). We discuss the potential (Tsyganenko, 1995). During this event, the BARREL 1H balloon, situated in the southern hemisphere, was immediately conjugate to the ISLL NORSTAR riometer, at dipole L of~5.2, with the geostationary GOES 13 satellite around 1 h of local time to the east.
Journal of Geophysical Research: Space Physics 10.1002/2017JA024674 source of these waves in section 7 but conclude that whatever mechanism leads to the ULF-modulated precipitation event is highly localized in space, and not in time. The question then becomes, what drives this ULF-modulated precipitation?
Whistler mode waves are invoked to drive precipitation across a wide range of energies (e.g., Miyoshi et al., 2015). In the case of ULFmodulated precipitation, whistler mode waves are assumed to already exist, and the ULF waves modulate the growth rates of the waves due to a preexisting source of free energy (e.g., Coroniti & Kennel, 1970). Alternately, the VLF spectral distribution is modified via wave-wave interaction between ULF and VLF waves (e.g., Chen, 1974) leading to a ULF-modulated precipitation signature being observed. However, Figure 2 demonstrates that precipitation is not observed by BARREL or ISLL riometer outside of the bounds of the ULF event above the background level, implying that whatever processes cause the precipitation only exist inside the region of ULF waves, indicated in this figure by vertical dashed lines. If whistler mode waves are present outside of this spatial window, then one would certainly expect to observe unstructured, or differently structured, precipitation to be occurring when the ULF wave field is not present.
In this case study, we show that large-amplitude ULF wave fields are localized to only a fraction of the drift trajectory of an electron, meaning that an energetic electron will encounter a rapid step change in local magnetic field as it undertakes gradient-curvature drift. If the time scale of this wave is shorter than the drift period, the third adiabatic invariant is likely to be violated. We explore the effects of localized perturbations in magnetic field on the conservation or otherwise of all invariants.
The equatorial bounce loss cone (BLC) characterizes the maximum pitch angle of particles that would precipitate into the ionosphere within one bounce period and is defined as where α G is the equatorial bounce loss cone angle and B G is the magnetic field strength in the equatorial plane. The value of B G is approximated by the magnetic field magnitude at GOES situated close to the equatorial plane, and B I is the magnetic field strength at the particle mirror point close to the ionosphere. Throughout this paper, we assume that the variation in magnetic field strength observed by GOES can be interpreted as the temporal variation of minimum magnetic field strength along the field line that threads its location. The values of magnetic field in this definition should be understood to be averages over time scales greater than the electron bounce time, which is short compared to a ULF wave period. To estimate the time evolution of equatorial BLC using the observed equatorial magnetic field at GOES for B G , we must first estimate the magnetic field strength at the ionosphere B I . Note that of the two magnetic field strengths required for equation (2), B G ≪ B I . It is likely that both B G and B I vary as a result of the ULF wave, but the variations in B G are a significant fraction of B G , whereas the variations in B I are very small compared to the magnitude of B I . Therefore, the average B I in the vicinity of the field line foot point mapped from the Geostationary Operational Environmental Satellite (GOES) spacecraft could be used in equation (2) with very little loss in accuracy. In this case study, we have compared two estimates for B I : the projected International Geomagnetic Reference Field (IGRF) at 100 km of the location of the magnetic field foot point of the GOES position, as mapped using the Tsyganenko T89 (Tsyganenko, 1989) magnetic field model, and the magnetic field strength measured at the Sanikiluaq (SNKQ) ground-based magnetometer (being the magnetometer closest to the foot print of GOES West). Figure 2b shows the estimated modulation of α G when using the IGRF field (black) and the measured field at SNKQ (blue). Regardless of the source of the conjugate ground magnetometer magnetic field magnitudes, (b) modulation of the loss cone using measured and modeled ionospheric magnetic fields (to be discussed later), (c) channel 1 from the BARREL fast spectra of <180 keV X-rays, (d) BARREL 1H slow spectra from 50 to 300 keV X-rays, (e) riometer absorption from ISLL, and (f) the normalized frequency content of each of these data sets calculated within the vertical lines using FFT analysis of the respective time series from GOES 13 (black), BARREL fast (blue) and slow (green and yellow) spectra, and the ISLL riometer (red).
Journal of Geophysical Research: Space Physics
10.1002/2017JA024674 estimated ionospheric field, there is little difference to the modulation of the loss cone; it is only the average size of the loss cone that is different. Since we are interested in the modulation of the loss cone, we will for simplicity use the IGRF field at the location of the GOES foot print to determine B I in the subsequent analysis, noting that this simplification of dipolar L shell determination of the first and second adiabatic invariants illustrates the utility of this calculation for enhanced modulation of precipitation, and which becomes increasingly appropriate for locations inside geosynchronous orbits and closer to the radiation belt region.
We now consider how the ULF wave alone could affect the pitch angle of individual particles. Since ULF wave time scales are of order minutes, we can assume that the first and second adiabatic invariants are conserved, but the third is not. Previous studies have investigated how conserving the first and second invariants affects the change in pitch angle and loss cone, under the assumption of a relatively dipolar magnetic field (e.g., Foster et al., 2015;Halford et al., 2015;Li et al., 1993;Wygant et al., 1994). For example, Halford et al. (2015) showed that the change in the equatorial pitch angle of a particle in a slowly changing and dipolar magnetic field configuration was independent of mass or energy and could be written as sin α eq;f ¼ ÀL where α eq0 and α eq,f are the initial and final equatorial pitch angles and L 0 and L f are the initial and final L values of the particle in dipolar L. This equation is valid for the action of a sufficiently low-frequency ULF wave. We use this idealized equation to make a comparison between the changes in particle pitch angle due to a slowly changing magnetic field and the changes in loss cone due to the same slowly changing magnetic field. We note here that at the location of GOES, a dipolar approximation is a simplification of the real measured magnetic field. However, as can be seen from Figures 2 and S1 in the supporting information, this is a reasonable assumption given that the measured magnetic field magnitude is~100 nT during the event at geosynchronous orbit. Figure 3 shows how the equatorial pitch angles α eq,f vary in a ULF wave-modulated magnetic field according to equation (1), where both the first and second adiabatic invariants are conserved. These changes (solid lines) are shown relative to the changes in the BLC α G according to equation (2) (dashed lines). Figure 3a shows a range of low particle pitch angles (colored lines). The expected change in the BLC is a dashed line, and pitch angles that fall within the BLC are shaded in grey. For a slowly varying magnetic field, the change in BLC is far greater than any change in particle pitch angle conserving the first and second invariants. Figure 3b shows selected "important" pitch angles for the case study shown in Figure 2. If only the average magnetic field is considered, the vertical location where the blue (upper) solid line crosses the dashed line would indicate the largest particle pitch angle to be lost into the BLC. The vertical location where the green (lower) solid line crosses the dashed line indicates the largest pitch angle that would be lost under the action of the ULF wave, which in this case has an amplitude of 13 nT. We will discuss in section 5 how even these small changes in equatorial loss cone can lead to large changes in precipitating flux. Figure 3c shows the fractional change in α eq,f (solid lines) and α G (dashed line) to demonstrate that the changes in the BLC are indeed much larger than the changes in the particle equatorial pitch angles and that for larger ULF wave fields, this effect becomes increasingly pronounced.
Implications for Precipitating Electron Flux
The previous section showed that compressional ULF waves can significantly modify the size of the equatorial BLC. In this section, we discuss the implications for driving or enhancing electron precipitation across all energies, likely impacting radiation belt electron dynamics. Figure 4 illustrates the concept of localized ULF wave-driven precipitation, and how this precipitation mechanism is affected by the localization of the wave and shape of the equatorial distribution in pitch angle. Figure 4a shows a schematic demonstrating how drifting electrons might interact with localized compressional ULF waves and result in electron precipitation, with the Sun to the right of the figure. Electrons undergoing gradient curvature drift around the Earth will encounter a localized region of compressional ULF wave activity, such that electrons that were previously just outside of the bounce (and potentially drift) loss cones Journal of Geophysical Research: Space Physics 10.1002/2017JA024674 and hence were trapped, then find themselves within the loss cone. We reiterate that this is a consequence of conservation of the first and second invariants and the violation of the third adiabatic invariant due to the spatially localized nature of the ULF waves.
If there are no additional electron sources to replenish those electrons that have been precipitated, and the region of ULF wave activity persists over time scales longer than a drift period, a range of resultant effects may be experienced, from a large precipitation spike into the atmosphere to a longer-lived ULF modulated precipitation signature (see Figure 4b). The precipitation signature as detected in the ionosphere depends upon the energy of the electron (i.e., how much time it spends within the ULF wave region) and the phase of its drift orbit relative to the phase and localization of the ULF oscillation. A single pulse of precipitation would indicate that a compressional ULF wave is acting over a large range of MLT such that electrons across a large fraction of the drift orbit at all energies within the enhanced loss cone would precipitate within the first wave cycle. For more localized compressional wave activity, the ionospheric electron precipitation signature may depend upon (i) the azimuthal wavenumber of the wave, (ii) the phase of the wave as the electron passes through the active region, and (iii) the azimuthal extent of the localized wave region. Hence, each drift Figure 3. Demonstration of how equatorial pitch angles α eq,G vary in a slowly varying magnetic field under the assumption of conservation of the first and second adiabatic invariants but not the third invariant (after Halford et al., 2015). (a) The range of small particle pitch angles (colored lines) and their variation according to equation (1). The expected change in the BLC due to a ULF wave with an amplitude of 13 nT is denoted as a dashed line, with pitch angles less than that and hence within the BLC shaded in grey. Colored lines denote sample pitch angles and their variation due to conservation of the first and second. (b) Important pitch angles for the case study shown in Figure 2. If only the average magnetic field is considered, the pitch angle where the blue (upper) solid line that crosses the dashed line would indicate the largest particle pitch angle to be lost into the BLC, and where the green (lower) solid line that crosses the dashed line indicates the largest pitch angle that would be lost under the action of the ULF wave. (c) The fractional change in α( eq,f ) (solid lines) and α G (dashed line) to demonstrate that the changes in the BLC are indeed much larger than the changes in the particle equatorial pitch angles and that for larger and larger ULF wave fields, this effect becomes more and more pronounced.
Journal of Geophysical Research: Space Physics 10.1002/2017JA024674 shell up to α G, max will not necessarily be fully depleted after a single drift period. For localized ULF wave activity, the ULF modulated precipitation signature would be maintained as long as the ULF wave was maintained, and until the flux in each drift shell is fully depleted.
The expected precipitation signatures also depends upon whether electrons with pitch angles close to the edge of either the typical or enhanced BLC are replenished from elsewhere in the magnetosphere, that is, there are additional processes providing a source of electrons on particular drift shells (e.g., the source/seed populations discussed in Jaynes et al., 2015). Substorm injections (e.g., Reeves et al., 1990) and enhanced convection (e.g., Walach & Milan, 2015) can be responsible for the refilling of drift shells. Electron flux can also be replenished through local wave-particle interaction processes (e.g., Summers & Thorne, 2003).
Note that precipitation as measured in the ionosphere by a riometer or any other instrument which senses atmospheric ionization changes will not necessarily depend upon time in the same manner as the precipitating flux. The ionospheric recovery times for the conductivity changes must also be taken into account Rodger et al., 2007). In this instance, each periodic enhancement in the precipitation flux magnitude would have an associated ionospheric decay time, such that additional pulses of precipitation would add to the previous ionospheric enhancement. ULF modulation in the riometer signal would therefore appear as only a small perturbation on a background enhancement as shown in Figure 4b. In addition, a long ionospheric decay time relative to the period of wave would result in the ULF modulation of the riometer signal having a slightly lower frequency response than the original ULF wave. We propose this simple explanation for the results shown in Figure 2: a 4-5 mHz precipitation signature is observed by BARREL, but a slightly lower frequency signature is observed in the precipitation as measured by a ground-based riometer.
Naively, for an isotropic distribution, one might expect that a given percentage increase in α G might result in a similar percentage increase in the amount of precipitating flux. However, magnetospheric electron distributions are not generally isotropic with respect to pitch angle, particularly close to the loss cone (e.g., Gu et al., 2011). Typically, electron flux at a constant energy varies as f = f 0 sin n α where n can take a range of values, for example, n = 0, 0.1, 0.25, 0.5, 1, 2, 3… and f 0 indicates the value of the flux at 90°. For example, n = 0 would correspond to the naïve isotropic assumption discussed above. However, Figure 4c shows how the pitch angle variations due to compressional ULF waves can drive increased precipitation for increasing values of n, using the compressional wave example shown in Figure 1, where α G = 2.8°and α G, max = 3.3°. From Figure 4c, it can be seen that varying the shape of the pitch angle distribution close to the loss cone can drive significantly more precipitation loss than that implied by the given percentage increase in α G . For a close to isotropic distribution, that is, for n values between n = 0 and n = 0.5, an 18% increase in α G would render a similar~18% increase in precipitation. However, if the shape of the PSD is closer to the n = 3 example, an 18% increase in α G would render significantly larger percentage increase in precipitating flux, closer to a 100% increase.
Statistical Results of GOES Bounce Loss Cone Variations
We employ 14 of geosynchronous Geostationary Operational Environmental Satellite (GOES) magnetometer measurements at 1 min cadence (Singer et al., 1996) to statistically study the variation in the BLC during compressional ULF wave events. Since the GOES satellites are in the geographic equatorial plane, we limit our statistical analysis to satellites located at the GOES West location, since these satellites are closer to the magnetic equator than their GOES East counterparts. As in the previous section, we calculate the variation in BLC using equation (2). The equatorial magnetic field strength B G is obtained from the GOES measurements, and the ionospheric magnetic field strength B I is estimated from the IGRF. In order to compile a large database of compressional wave events, we use a 14 year (1995-2008 years) database of GOES data (Ozeke et al., 2012). We limit our analysis to the dayside magnetosphere (06-18 MLT) to concentrate specifically on ULF wave activity and avoid the large-scale topological changes associated with magnetospheric substorms that occur on time scales in the ULF wave band. However, we note that, in principle, our analysis is also relevant to any significant and localized geomagnetic field magnitude variation (as discussed in Section 7).
We define a localized compressional ULF wave event as a quasi-periodic modulation in the magnetic field magnitude above a given amplitude threshold during a 1 h analysis window. We calculate the wave amplitude from the power spectral density at each frequency and identify discrete peaks above a 2 nT threshold using a peak finding algorithm. The 2 nT threshold minimizes the chance of the detection of any sudden impulses, or small ULF wave packets, using the same approach adopted in Watt et al. (2011). Any 1 h window with a discrete peak is flagged as an event containing a compressional ULF wave. In order to avoid overlapping windows or double counting, if the hour analyzed contains a compressional ULF wave that fits this criteria within it, this 1 h analysis window is shifted by an hour. If the hour analyzed does not contain a compressional ULF wave, the analysis window is stepped by 15 min in order to identify the highest number of unique ULF wave events possible. Finally, any hour for which the GOES-measured magnetic field contained a geosynchronous B ZGSM < 30 nT was considered to be potentially affected by magnetopause encounters and were thus discarded (cf. Watt et al., 2011). In total, through this approach we find 3,591 compressional wave events that satisfy our criteria over this 14 year period.
For each of the 3,591 identified events, we determine the median and maximum magnetic field magnitude from the GOES 60 min observations, as well as the median and maximum BLC angle α G,MAX during the hour. In order to determine the relationship between the equatorial loss cone variations with compressional ULF wave activity, we express the percentage change in the BLC (i.e., the maximum change in BLC as a fraction of the median BLC angle) during an hour as a function of compressional wave amplitudes normalized to the background magnetic field magnitude (dB/B 0 ). Note that the maximum magnetic field strength observed at GOES is equivalent to B G = B 0 + dB, and so dB/B 0 is a direct measure of the ULF wave amplitude, but not a direct measure of the change in the loss cone. Figure 5a shows the ULF wave amplitudes as a function of background field strength and their corresponding change in α G , on a log-log scale. There is a strong linear relationship between α G and dB/B 0, demonstrating that the changes in α G are indeed linearly related to the fractional change in the magnetic field magnitudes from localized compressional wave activity. Figure 5b reinforces this relationship by displaying a twodimensional histogram of these points. Finally, Figure 5c shows a probability distribution function (PDF) of these events as a function of dB/B 0 , where each (vertical) column sums to 100%. Figure 5c shows that there is a strong linear correlation between the size of the compressional wave activity and a most likely given change in the equatorial loss cone. From Figure 5 it can be seen that in the 14 year period studied there are certainly events whereby a narrowband ULF fluctuation occurs that is of order the background magnetic field strength, and which would correspond to around 50% increase in the size of the ambient BLC. Although fluxes are small at these small pitch angles relative to the core radiation belt population which have pitch angles closer to 90°, we discuss how a direct ULF modulation of the BLC can provide additional precipitation.
Discussion
Traditionally, ULF waves are not considered a direct precipitation mechanism for energetic electrons, and instead, the ULF modulation of VLF growth rates is invoked to explain precipitation modulated at ULF frequencies (Coroniti & Kennel, 1970). This is despite clear observational links between ULF magnetic field oscillations and a variety of auroral , riometer (Spanswick et al., 2005) and bremsstrahlung-related (Breneman et al., 2015;Halford et al., 2015) electron precipitation signatures. A primary reason for this is that, essentially, global-scale ULF wave fields vary much more slowly than electron bounce times and therefore cannot force bouncing electrons to violate their second adiabatic invariant (e.g., Olson et al., 1980). However, in the case where localized ULF wave fields exist only for a fraction of an electron's drift orbit, it is likely that drifting electrons would rapidly encounter magnetic fields that are not varying smoothly or slowly enough to satisfy conservation of the third adiabatic invariant.
Previous work has focused upon resonant global ULF wave processes such as field line resonance-driven auroral particle precipitation (e.g., Milan et al., 2001;Rae, Mann, Dent, et al., 2007;Rae et al., 2014;Rankin et al., 2005Rankin et al., , 2007Samson et al., 1991Samson et al., , 1996Samson et al., , 2003Xu et al., 1993), as opposed to any direct modulation of the conditions for particle precipitation by the ULF wave itself. Under these circumstances, it is largely electrons with energies less than a few keV that are involved in the Field Line Resonance (FLR)-electron interaction. FLRs have been shown to be linked to periodic auroral arc structuring (e.g., Rae, Mann, Dent, et al., 2007;Samson, 1994;Samson et al., 1991Samson et al., , 1996, are capable of modulating existing auroral arcs (e.g., Lotko et al., 1998), or are directly powering auroral displays via parallel electric fields accelerating auroral energy electrons (e.g., Rankin et al., 2005Rankin et al., , 2007. More complex auroral structuring can also be explained as a result of two harmonically related FLRs that result of field-aligned current element "braiding" (Milan et al., 2001). However, it is unlikely that electrons above approximately keV energies could be accelerated in the field-aligned direction in any of these scenarios, as toroidal mode FLRs have no compressional component, although they have recently been postulated to play a secondary role (e.g., Motoba et al., 2013).
At electron energies above approximately keV, a plethora of observations exist that link ULF waves in ground magnetometer and riometer absorption (e.g., Anger et al., 1963;Beharrell et al., 2010;Brown, 1964;Heacock & Hunsucker, 1977;Olson et al., 1980;Rae, Mann, Dent, et al., 2007;Roldugin & Roldugin, 2008;Spanswick et al., 2005;Ziauddin, 1960). Spanswick et al. (2005) used statistics of NORSTAR riometer measurements to investigate the relationship between Pc5 wave power observed in riometer data and FLRs observed in ground magnetometer data, finding that when significant ULF wave power was observed in riometer absorption, there was always generally a corresponding Pc5 wave signature in ground magnetometer data. In addition, it was found that FLR Pc5 activity was more efficient at producing the riometer modulation than non-FLR Pc5 activity. Spanswick et al. (2005) concluded that the most likely scenario was that when a suitable energetic electron population in the inner magnetosphere was present, resonant ULF waves could play a role in their precipitation but that pitch angle scattering from some other plasma wave (for example whistler mode waves) was required as well before both ground magnetometer and riometer would observe a ULF modulated signal. From a theoretical perspective (Coroniti & Kennel, 1970;Watt et al., 2011), a variation in magnetic field strength (i.e., a compressional component of the wave magnetic field) is required to Journal of Geophysical Research: Space Physics 10.1002/2017JA024674 modulate VLF growth rates. Moreover, a variation in magnetic field strength that is in direct antiphase with the cold plasma number density (cf. Li et al., 2011 andWatt et al., 2011) is required to modify VLF growth rates sufficiently to account for the changes in precipitation. Since FLRs are where energy from a propagating compressional wave couples to the shear mode (Samson et al., 1992), it is not clear whether the wave properties necessary to modify VLF wave growth rates are satisfied in an FLR. We postulate in this study that the reason is that the compressional component of the FLR driver may be the direct generator of ULF-modulated riometer absorption, rather than the action of the FLR itself. Specific case studies of a simultaneous compressional ULF wave and an FLR have been presented in the literature (e.g., Rae, Mann, Dent, et al., 2007). The evidence presented here suggests that an alternative explanation for the modulation of ULF-precipitation in this and other cases is the direct modulation of the equatorial BLC by the compressional component of the ULF wave.
Direct enhancement of the local equatorial bounce loss cone enhances other mechanisms for precipitation of electrons from the magnetosphere. Brito et al. (2012Brito et al. ( , 2015 used MHD simulations to show that the radial displacement of electrons due to global-scale compressional ULF waves can itself lead to enhanced precipitation. The radial motion of the electrons encountering a compressional ULF wave causes their trajectories to move closer to the Earth into a stronger magnetic field, where the loss cone is larger. Additionally, the inward radial motion of the electrons leads them into regions with shorter field lines, where they gain perpendicular energy due to conservation of the first adiabatic invariant and parallel energy due to conservation of the second adiabatic invariant. In this paper we show additional precipitation effects if these ULF wave fields are localized; under these circumstances, the loss cone is locally and abruptly modified as a function of time through the action of the compressional ULF waves themselves. Compressional magnetospheric ULF waves at geosynchronous orbit can have sufficient amplitudes to locally enhance the size of the bounce loss cone by over 50%. Of course, this effect (shown in Figure 4) depends upon the ratio of the wave amplitude to the background magnetic field, and the background magnetic field varies as a function of radial distance r as roughly r À3 . Our observations are confined to geosynchronous orbit, to which the majority of riometer absorption modulation also map (Spanswick et al., 2005). However, closer to the heart of the outer radiation belts at L = 4-5, where the field strength increases and ULF modulated precipitation is often seen (e.g., Breneman et al., 2015;Brito et al., 2015), the fractional enhancement in the traditional loss cone will become smaller for a given ULF wave amplitude. However, again, there are competing effects to be considered, given that equatorial BLC also increases with decreasing radial distance; this means that both the equatorial loss cone and compressional ULF wave amplitudes must be computed across all radial distances in order to determine their effect across the entire outer radiation belt region.
The direct enhancement of the BLC by a localized compressional ULF wave will also greatly enhance any precipitation mechanism that is due to pitch angle scattering. Whistler mode chorus (see Millan & Thorne, 2007, for a comprehensive review) is often invoked to pitch angle scatter radiation belt electrons outside of the plasmapause, with plasmaspheric hiss acting in a similar way inside of the plasmapause (e.g., Breneman et al., 2015). Electromagnetic ion cyclotron (EMIC) waves have also been shown to play a role in enhanced relativistic electron precipitation (e.g., Carson et al., 2013;Clilverd, Duthie, et al., 2015;Rodger et al., 2008) through cyclotron resonant interactions. Pitch angle scattering rates depend upon the wavenormal angle and power spectral densities of the whistler mode chorus (e.g., Ni et al., 2011). However, pitch angle diffusion rates for a 30 keV electron at geosynchronous orbit range from 10 À3 to 10 À4 s À1 , which is comparable to Pc5 ULF wave frequencies. By contrast, inside the plasmasphere, plasmaspheric hiss can have pitch angle diffusion rates of 10 À2 to 10 0 s À1 (e.g., Breneman et al., 2015). As EMIC waves are the left-hand counterpart of whistler mode waves, there would be no reason not to expect that EMIC wave growth would also be affected by large-amplitude monochromatic changes of the magnetic field magnitude and number density either, as Loto'aniu et al. (2009) discussed.
Whistler mode precipitation will be enhanced by a temporally varying loss cone for two reasons. First, pitch angle scattering increases the flux at pitch angles close to the bounce loss cone, while our mechanism increases the size of the bounce loss cone thus leading to enhanced loss. Second, by increasing the amount of precipitation, the anisotropy that drives whistler mode waves unstable may also increase during different phases of the wave leading to either enhanced wave amplitudes or longer lifetime and thus increased precipitation. This explanation provides additional insight into events discussed by Halford et al. (2015) and Breneman et al. (2015), where ULF waves were proposed to be modulating the resonance condition, Journal of Geophysical Research: Space Physics 10.1002/2017JA024674 leading to both an enhanced background level of precipitation and modulation at ULF frequencies. This symbiotic relationship, comparable to that espoused by Baumjohann et al. (2000) regarding whistler mode waves inside mirror mode waves in the dawn sector magnetosphere (e.g., Rae, Mann, Watt, et al., 2007), is ripe for further exploration.
Most importantly with regard to the results in this paper, it remains to be established whether ULF waves and ULF-modulated precipitation are observed without the presence of whistler mode chorus (e.g., Nishimura et al., 2013) or plasmaspheric hiss (e.g., Breneman et al., 2015). Our results suggest that such a precipitation mechanism is possible in theory and offers a suggested mechanism for the case study shown in Figure 2, in a region typically associated with limited VLF wave activity and where no enhanced precipitation outside of the compressional ULF wave region is observed. Future work will explore the wealth of ground and space-based observations available in the Van Allen Probe era to identify whether ULF-modulated precipitation can indeed exist without any VLF pitch angle scattering mechanism.
The localization of the ULF pulsation appears to be very important for the precipitation of electrons. Localized dayside ULF wave fields are often referred to as drift-bounce resonance or "storm time Pc5 waves" and are thought to be driven by unstable ion distributions emanating from magnetotail injections (e.g., Lanzerotti et al., 1969;Southwood et al., 1969;Wright et al., 2001). They are detected mainly in the afternoon/evening sector of the magnetosphere (e.g., Anderson et al., 1990). Our case study ( Figure 1) shows ULF compressional wave activity in the afternoon sector. However, in our statistical study, we show observations of compressional pulsations at geosynchronous orbit across all of the dayside magnetosphere, and so other generation mechanisms may also play a role (e.g., mirror mode waves in the dawn sector) (e.g., Constantinescu et al., 2009;Liu et al., 2016;Rae, Mann, Watt, et al., 2007;Vaivads et al., 2001;Zhu & Kivelson, 1994). We recognize that mode structure along the field is important for determining changes in BLC at any point along the geomagnetic field due to ULF wave modulation (e.g., Ozeke & Mann, 2004;Perry et al., 2005;Takahashi et al., 1987). Indeed, it is interesting to note that localized compressional waves (e.g., Liu et al., 2016; would act to trap particles primarily with pitch angles closer to 90°in magnetic bottles via the mirror effect. Hence, trapping of high pitch angle particles may act in concert with the enhanced precipitation of low pitch angle particles. To confirm that our assumptions are correct, future work will use electric, magnetic, and plasma density measurements to characterize mode structure and perform more accurate calculation of the change in the equatorial BLC in each case. Future work will utilize a more realistic three-dimensional magnetospheric wave model (Degeling et al., 2010) where localization of the waves in magnetic local time and realistic field-aligned structures can be reproduced. By doing this, electrons can then be traced through to see how their behavior is modified and the loss cone is modified due to the presence of the localized, compressional ULF waves.
Conclusion
This paper explored the potential role of localized compressional ULF waves as a candidate mechanism to directly enhance electron precipitation by simple modulation of the local bounce loss cone. Periodic magnetic compression of a localized magnetospheric region on long period time scales relative to the gyration and bounce allows conservation of the first and second adiabatic invariants but a clear opportunity to violate the third invariant. We demonstrate that the change in pitch angle of a given electron due to the conservation of the first and second invariants (Figure 3) is far smaller than the change in loss cone due to the localized ULF wave (Figures 2 and 4. In this way, we show that localized compressional ULF waves can directly contribute to electron precipitation. Previous studies (e.g., Brito et al., 2012Brito et al., , 2015 have focused on the role of global compressional ULF waves in driving radial motion of radiation belt electrons to additionally precipitate. Direct modulation of the loss cone differs from any other mechanism traditionally invoked to explain, in particular, radiation belt electron losses during active times. ULF modulation of the bounce loss cone would be enhanced during active times, such as during a storm main phase where compressional ULF wave amplitudes are largest and up to~2 orders of magnitude higher than statistically found . We note here that this mechanism will also operate across all electron energies, but with subtly different observational characteristics, potentially explaining how low-energy auroral (e.g., Samson et al., 1991), keV (e.g., Spanswick et al., 2005), hundreds of keV (e.g., Breneman et al., 2015), and MeV (e.g., Foat Statistically, we show that large-amplitude highly localized compressional ULF waves can modulate the loss cone by ±20%, which in turn allows a significantly greater fraction of the electron PSD to precipitate than previously thought. Importantly, this requires no other wave-particle interaction to cause precipitation of energetic electrons with pitch angles outside of the traditional loss cone, although this mechanism would be enhanced by local pitch angle scattering to refill the near-loss cone population. Hence, what fraction of this distribution is locally precipitated depends upon the strength of the perturbation, local magnetic field magnitude, shape of the pitch angle distribution close to the traditional loss cone, and the nature of any additional sources of energetic electrons into the ULF region (e.g., substorm injections) or near the loss cone (e.g., pitch angle scattering due to whistler mode waves). Since this mechanism does not require the presence or the absence of VLF wave-particle interaction, we simply point out that localized compressional waves should be considered along with other precipitation mechanisms within the current literature.
We show direct evidence of ULF wave modulated precipitation across the energy ranges measured by riometers and BARREL, which is spatially correlated with localized large-amplitude (~15% of the ambient magnetic field) compressional ULF wave activity in the afternoon sector. Within this case study we show clear evidence that the ULF wave fields are spatially localized, although we note here that there is no means to investigate other precipitation sources for this case which would be expected from pitch angle scattering mechanisms such as whistler mode chorus or plasmaspheric hiss. | 11,124.4 | 2018-01-16T00:00:00.000 | [
"Physics"
] |
Assessing the barriers to lean manufacturing adoption in the furniture industry of Bangladesh: a fuzzy-DEMATEL study
Purpose – The objective of this study is to investigate the barriers hindering the integration of lean manufacturing (LM) practices within the furniture industry of Bangladesh. The traditional operational paradigmsinthissectorhaveposedsubstantialchallengestotheeffectiveimplementationofLM.Inthisstudy,thebarriersofimplementingLMinthefurniturebusinessareexamined,aimingtoprovideasystematic understandingofthebarriersthatmustbeaddressedforasuccessfultransition. Findings – The research reveals that “ Fragmented Industry Structure, ” “ Resistance to Lean Practices ” and “ Inadequate Plant Layout and Maintenance ” , emerged as the foremost barriers to LM implementation in the furnitureindustry.Additionally, “ InsufficientExpertManagement, ”“ LimitedTechnicalResources ” and “ Lack of Capital Investment ” play significant roles. Research limitations/implications – The outcomes of this study provide valuable insights into the furniture industry, enabling the development of strategies for effective LM implementation. One notable challenge in lean implementation is the tendency to revert to established practices when confronted with barriers. Therefore, this transition necessitates informed guidance and leadership. In addition to addressing these internal challenges, the scope of lean implementation should be broadened. Originality/value – This study represents one of the initial efforts to systematically identify and assess the barrierstoLMimplementationwithinthefurnitureindustryofBangladesh,contributingtotheemergingbody of knowledge in this area.
Introduction
Lean has its origins in Henry Ford, who established an impressive Highland Park Manufacturing Company's production process in 1913 (Diego Fernando and Rivera Cadavid, 2007).The term "lean" is derived from Japanese manufacturing and refers to a way of thinking that detests waste in all its forms and works tirelessly to eradicate errors (Dickson et al., 2009).LM, often known as lean production, is a rigorous strategy to remove waste from a manufacturing process.Promote lean production as a multifaceted approach that integrates several management techniques, such as just-in-time manufacturing, quality control, workgroups, cellular manufacturing and management of supplier (Dhiravidamani et al., 2018).The Japanese had instead created a new method of production management called LM (Wu, 2003).LM aims to produce excellent products in the most effective and inexpensive way possible by using fewer space, less inventory, less time to develop things and less human labor (Chauhan and Singh, 2012).
In Bangladesh, individuals typically opt for stylish furniture that is also long-lasting, cozy and simple to keep.People from various socioeconomic backgrounds react differently to the elements that influence their household goods purchasing decisions.Customers typically conduct pre-purchase research despite the fact that local and national brands are available to them.Because of this, retailers must fully comprehend the buying habits of their customers (Nigar, 2021).Bangladesh's furniture business has grown.The business standard reported that the country's furniture industry generates more than 10,000 crores in income annually (Gautam et al., 2022).In addition to satisfying local clients' needs, manufacturers are currently exporting their products abroad.In order to lower production costs, speed up delivery and improve quality while maintaining competitiveness in a market that is becoming more globally diversified, wood manufacturers have been under pressure to embrace innovative manufacturing techniques and management strategies.Continuous improvement encourages a continual effort to improve quality and productivity for the wood products business.The complicated manufacturing structure of the furniture business, along with its many difficulties and other distinctive characteristics, make it a strong candidate for the adoption of LM.This study focuses on the areas that the furniture sector has to prioritize to successfully implement LM.Furniture sector managers and decision-makers can learn crucial lessons that will help them adopt LM effectively, particularly in emerging markets where resources are scarce (Debnath et al., 2023a).
In Bangladesh's garments sector there are many works on it.Due to issues with their recent production planning and management methods, many private Bangladeshi garment manufacturing enterprises are either running well below their probable capacity or facing a high level of late deliveries (Chakraborttya and Paul, 2011).The Bangladeshi economy relies heavily on its garment industry, a dominant force in the country's exports.To address the challenges faced by this sector, LM principles and techniques have gained prominence (Bashar and Hasin, 2018).Similarly, the footwear industry in Bangladesh, benefiting from abundant raw materials and labor, presents opportunities for growth.Various engineers, researchers and institutions have developed lean goals and concepts, focusing on enhancing processes, products and services.Lean principles encompass a set of tasks aimed at delivering value to customers through accurate, sequential and timely execution (Science, 2017).The adoption of LM practices is now a focal point for businesses striving to reduce waste and enhance competitiveness.Bangladesh's industrial output has surged, and its small-scale industries have played a pivotal role in the nation's economic progress (Sushil et al., 2020).The ready-made garments (RMG) sector generates more than 70% of Bangladesh's total export earnings and employs over 40% of the country's manufacturing workforce (Islam and Halim, 2022).As a result, government involvement is essential to ensure the sector's success.One of Bangladesh's major achievements is that IJIEOM RMG enterprises produce goods at low labor prices.LM principles are widely used in many countries, and they are also used in Bangladesh's numerous textile factories (Karim and Rahman, 2012).
One of the primary factors contributing to the limited adoption of LM practices is a lack of awareness among manufacturers.When manufacturers lack adequate understanding and information about LM technologies, they are less inclined to invest in them.This diminished interest and reduced investment can, in turn, hinder the advancement of the manufacturing sector (Mathiyazhagan et al., 2022).However, a lot of research has been done on the crucial variables and barriers to LM adoption (Maware and Parsley, 2022;Robertsone et al., 2022;Qureshi et al., 2022;Leite et al., 2022;Abu et al., 2022;Rathi et al., 2022).LM implementation barriers based on the Malaysian wood and furniture industry have been identified by Abu et al. (2022), and their analyses highlighted four dominant challenges which are related to culture and human attitude issues, i.e. lack of employee commitment, lack of senior management's interest and support, difficult to implement stands out as the most significant.A framework for implementing sustainable lean manufacturing in the electrical and electronics component manufacturing industry has been developed by Mathiyazhagan et al. (2022).
As the literature review indicates, there exists a dearth of research specifically addressing the barriers to LM adoption within the Bangladesh's furniture industry.The present study seeks to bridge this gap by systematically identifying and analyzing these barriers, thereby contributing novel insights into the body of knowledge in the field of LM implementation.Several studies such as (Maware and Parsley, 2022;Robertsone et al., 2022;Qureshi et al., 2022) examined the benefits and drawbacks of LM adoption in manufacturing industries and textile industries, but few have modeled paths specific into the Bangladesh's furniture industry.The existing research on LM implementation generally lacks sector-specific modeling that accounts for Bangladesh's furniture sector's unique difficulties and potential.It is also significant to note that no earlier research has looked at the barriers associated with applying LM in the furniture industry of Bangladesh (Chowdhury et al., 2015;Jannat et al., 2009).The Bangladeshi furniture industry faces numerous barriers in implementing LM practices.These barriers include such as fragmented industry structures, resistance to lean practices, inadequate plant layout and maintenance, insufficient expert management, limited technical resources, inefficient production times and a lack of capital investment (Darabi et al., 2023;Feldmann, 2022;Darabi et al., 2023, ;Mawlood et al., 2022).The corporations are excited to introduce LM in their industry.Following their analysis, the authors attempt to provide a framework for identifying the obstacles to implementing LM and attempt to respond to the subsequent research questions (RQs): RQ1.What are the pivotal barriers to implement lean manufacturing in the furniture industries of Bangladesh?
RQ2.How can a framework be created to model and examine the interdependence of those barriers for implementing lean practices?
RQ3.How the proposed framework helps the furniture industry to adopt lean manufacturing in the furniture industry?
By looking at the barriers to LM in the furniture sector, the current study has theoretically enhanced the body of knowledge on LM in an effort to respond to those RQs.The goal is to overcome the barriers and implement a proper framework for lean in the furniture industry.
For assessing the barriers, a novel framework incorporating questionnaires and a fuzzy-DEMATEL technique has been presented.The questionnaires and literature were utilized to determine the relevant barriers in the framework of Bangladesh's furniture industry.A fuzzy-DEMATEL model has been presented to investigate the significant interactions between the obstacles.The fuzzy-DEMATEL technique was used for this investigation, because it can map the barriers with influential linkages from imprecise data.In terms of practical implications, the study's findings may assist furniture producers in making judgments about establishing distinctive lean implementations and changing current systems into competitive ones.The fuzzy-DEMATEL model also aids industrial managers in developing successful LM implementation strategies.
The following is an outline of the article: Section 2 offers a comprehensive analysis of existing literature on LM methods and the barriers to using LM techniques in the furniture sector.Section 3 describes the data gathering procedure as well as the computational phases of the proposed fuzzy-DEMATEL framework.The results of using the suggested framework are shown in Section 4 of the paper.Section 5 highlights the significance of the findings and the insights gained from the investigation.Section 6 concludes the study by discussing its weaknesses and extents for further study.
2. Literature review 2.1 Lean manufacturing in furniture industry of Bangladesh Many wood products companies have already integrated LM components and tools in full or in part or they are considering doing so.In fact, the adoption of lean has helped a number of industry participants successfully alter their operations.Some received the Shingo Prize for operational excellence in manufacturing, the highest honor given each year to the top USA manufacturers (Horbach, 2013).The Bangladeshi furniture industry, a prominent player in the nation's economy, has been actively exploring the integration of LM principles and tools (Debnath et al., 2023b).This strategic shift is aimed at addressing various challenges and enhancing the sector's overall efficiency.Within the Bangladesh's furniture industry, there are notable success stories where LM practices have brought about substantial improvements.While not on the same scale as global manufacturing giants, these achievements are significant within the context of the local industry.
One such example is HATIL Furniture, which has made remarkable strides in LM adoption.The company's commitment to lean principles resulted in impressive outcomes, including notable cost reductions and streamlined production processes (Habib et al., 2023).The Bangladesh's furniture industry, with its unique strengths and challenges, has demonstrated its potential for growth (Habib et al., 2023).Unlike larger manufacturing nations, Bangladesh's furniture sector offers distinct advantages, such as abundant raw materials, a strategic location and a skilled labor force.The nation hosts a substantial number of furniture companies, employing a significant workforce.This sector's growth trajectory aligns with Bangladesh's economic development plans, making it a pivotal player in the country's industrial landscape (Khan, 2019).Despite these promising prospects, the industry faces its own set of challenges (Ahsan et al., 2022).This study on the Bangladeshi furniture industry is conducted in the context of addressing the specific challenges and opportunities within this industry.The Bangladesh's furniture sector holds significant economic potential due to its abundance of raw materials, skilled labor force and strategic location.However, despite its promise, this sector faces several unique challenges, including issues related to design, quality control, skilled manpower shortages, research and development, industry fragmentation and limited government support.Such as limited access to modern design, issues with quality control, skilled manpower shortages, inadequate research and development, fragmented industry structure, limited government support and many more (Debnath et al., 2023b;Habib et al., 2023).These barriers have underscored the need for LM practices as a means to address and overcome these IJIEOM challenges effectively (Jahan et al., 2022).As a result, the study aimed to fill this research gap by providing valuable insights into the barriers and opportunities for implementing LM practices within the context of Bangladeshi furniture manufacturing.So, the Bangladeshi furniture industry's journey toward LM signifies a proactive approach to addressing industry-specific challenges and enhancing competitiveness.While it may not match the scale of global furniture manufacturing giants, the industry's efforts to embrace lean principles are crucial for its sustained growth and contribution to Bangladesh's economy (Debnath et al., 2023b).
Barriers for implementing lean in context of furniture industry of Bangladesh
The LM implementation barriers were explored through the extensive literature review.In order to identify the barriers, the authors conducted a thorough literature review.Between 2012 and 2022, the Scopus database, Web of Science and Google Scholar were used for this literature search.The LM implementation challenges and barriers were explored through the extensive literature review.In order to identify the challenges, the authors conducted a systematic literature review (SLR).Table 1 displays the SLR approach's inclusion and exclusion criteria.The inclusion and exclusion criteria are based on the studies of Keung et al. (2020).
After reviewing the relevant literature, the authors came up with a list of barriers from (Maware and Parsley, 2022;Platin and Konuk, 2022;Wicaksono et al., 2022;Silvius et al., 2021;Teknologi et al., 2021;Abu et al., 2021;Ratnasingam et al., 2019;Inayatullah and Narain, 2017;Guerrero et al., 2017;Belhadi et al., 2016;Sharma et al., 2016;Velarde et al., 2011;Yu et al., 2011), which consists of several barriers to LM implementation.The complicated manufacturing structure of the furniture business, along with its many difficulties and other distinctive characteristics, make it a strong candidate for the adoption of LM.This study focuses on the areas that the furniture sector has to prioritize to successfully implement LM.Furniture sector managers and decision-makers can learn crucial lessons that will help them adopt LM effectively, particularly in emerging markets where resources are scarce (Debnath et al., 2023a).Identified barriers to the adoption LM were selected based on the mentioned articles are shown in Table 2. Authors have categorized the barrier table into three distinct contexts: managerial, technical and financial.These categorizations were determined through a comprehensive analysis of the barriers identified in the study.Each barrier was assessed based on its characteristics, including its relationship with management practices, technical aspects and financial implications.After careful consideration, the authors have assigned the barriers to the respective categories, ensuring that they align with the appropriate context.
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affect the adoption of LM.DEMATEL is particularly suited for analyzing complex systems with multiple interconnected variables (Jodlbauer and Tripathi, 2023).It allows us to examine the cause-and-effect relationships among barriers, providing insights into how each barrier influences others.This is valuable when dealing with intricate issues such as LM adoption.Fuzzy-DEMATEL extends the traditional DEMATEL method by accommodating fuzzy logic (Ahmed et al., 2021).In real-world scenarios, data and relationships are often imprecise and uncertain.Fuzzy-DEMATEL can handle this fuzziness effectively, allowing for a more realistic representation of the system under study.FAHP, Fuzzy VIKOR and BWM methods may not offer the same level of flexibility in handling fuzzy data (Kushwaha and Talib, 2020;Raut et al., 2019;Bouzon et al., 2016;Prakash and Barua, 2015).Fuzzy-DEMATEL has been successfully applied in various studies involving complex decision-making problems, including those related to barriers and obstacles (Ponnambalam et al., 2023;Murugan and Marisamynathan, 2022;Feldmann et al., 2022;Govindan et al., 2022).Its effectiveness in revealing hidden relationships and dependencies among variables makes it a suitable choice for our research context.Fuzzy-DEMATEL excels over methods like graph theory and fuzzy-TISM, due to its nuanced handling of uncertainties in causal relationships (Geekiyanage et al., 2023).It utilizes fuzzy logic to capture subtle influences between factors, accommodating experts' subjective input for decisions.Unlike the binary graph theory and less flexible fuzzy-TISM, fuzzy-DEMATEL thrives in ambiguous contexts, ideal for analyzing complex and uncertain relationships (Kumar et al., 2023).While the graph theory or fuzzy-TISM, FAHP, fuzzy-VIKOR and BWM methods are valuable in their own rights for multi-criteria decision-making, the specific characteristics of our research problem, which involve complex interrelationships and fuzzy data, make fuzzy-DEMATEL a suitable and advantageous choice for analyzing the barriers to LM adoption in the furniture industry of Bangladesh.
In order to identify the barriers to LM implementation in Bangladesh's furniture business, which is a developing economy, our study intention is to offer a framework.Lack of understanding of the connections between the barriers is preventing many furniture industries from successfully implementing the LM idea.Figure 1
Study design, data collection and validation
The fuzzy-DEMATEL is used in this study to examine the main motivations for implementing LM.Three distinct methods of getting expert feedback were used in the data collection procedure.In the initial stage, a survey questionnaire (attached in appendix) was sent via Google Form to 21 experts with the intention of validating and improving the significant barriers that had been identified.During the data validation process in our study, a purposive sampling method was employed to select a group of 21 experts with diverse backgrounds in both industry and academia.3 includes an overview of the profiles of the experts who took part in the study.Table 4 shows the finalized barriers of furniture industries that were developed by the experts.Following the meticulous evaluation process and thorough consideration of expert suggestions, a total of 12 key barriers, aligned with the scope of this investigation, were identified.Initially, the experts considered the broader context of LM adoption and condensed the initial list of 16 barriers identified in the literature review to 13.In the subsequent round, the experts further refined the list of barriers, concentrating specifically on cognitive and human psychological factors, ultimately selecting 12 barriers.These barriers, presented in Table 4 introduced by the panel of experts by using the Delphi technique.
In this study, the three-stage Delphi methodology is used to pinpoint the important barriers affecting LM adoption.Figure 2 (adopted from H. M. Taqi et al., 2023)
Fuzzy-DEMATEL method
Fuzzy-DEMATEL technique includes seven basic steps: Step 1: Objectives and evaluation criteria with respect to them are determined.
Step 2: Decision-makers are questioned to determine their judgments about the relationship between criteria.Since human judgments on evaluation criteria include uncertainty, five linguistic terms "Very high influence, High influence, Low influence, Very low influence, No influence" are determined.Then these linguistic terms are expressed as positive triangular fuzzy numbers as shown in Table 5.The answers of decision-makers in terms of linguistic terms are converted to triangular fuzzy numbers.
Step Step 2 A group of experts from different but related fields were chosen Step 3 Round 1 of Delphi: Discussion centered on the chosen barriers Step 4 Round 2 of Delphi: Refine the contributing barriers and get rid of the ones that don't matter Step 5 Round Step 4: In this step, average value of p evaluators normalized fuzzy decision matrix is found.Step 5: After finding initial direct relation matrix and normalizing it, total relation fuzzy matrix ( e T) is defined as follows: Step 6: In this step D and R are calculated.D is the sum of the row and R is the sum of the column of T. Then D and R are defuzzified separately.Best nonfuzzy performance (BNP) value was used as a defuzzification procedure.The BNP value can be found using the following equation: BNP ij represents the defuzzified value of D and R. We call defuzzified value of D and R as D and R, respectively.In order to determine causal relationships between critical success factors, D þ R and D À R are calculated.While D þ R represents degree of central role (how much importance the criteria have), D À R shows the degree of relation.Relation divides the criteria in to cause and effect group.If D-R is positive then criteria belong to cause group.If D À R is negative then criteria belong to effect group.
Step 7: Causal diagram is constructed.In this diagram, the horizontal axis represents D À R while vertical axis represents D þ R. In this diagram, the criteria above the horizontal axis mean that they belong to cause group.Criteria below the horizontal axis mean that they belong to effect group.
Results of the study
This segment summarizes the results of using the fuzzy-DEMATEL method to understand the relations between the barriers to lean implementation in the Bangladesh's furniture sector.An expert group comprised of academic and industrial specialists was formed to examine the interrelationship between the aspects related to the study work's aim (Step 1).The direct-relation matrix T is established, as shown in Table 6, based on expert responses.According to (Step 2) the language variable, the study examines the following responses to the human logic variable: no influence, very low influence, low influence, strong influence and very high influence.The linguistic scale is given in Table 5.
In the study, triangular fuzzy numbers are computed using the method of converting fuzzy data into crisp score (CFCS).The surveys are defuzzified to provide a crisp number.The initial direct-relation matrix F is computed by the logistic method to produce the initial directrelation matrix F displayed in Table 7 (Step 3).
In (Step 4) with the use of the formula, the author creates a generalized direct-relation matrix S, whose main diagonal elements are all between 1 and 0. As shown in the generalized direct-relation matrix, presented as Table 8.
By applying equation to the generalized direct-relation matrix, the total-relation matrix M is obtained.Table 9 displays the total-relation matrix (Step 5).Within the total-relation matrix M, the sum of the rows and the sum of the columns are represented individually as D and R (Step 6).Following the DEMATEL method, the matrix is found from using R code.
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We also figure out the D, R, D þ R, D À R value by using R code.Here D & R show us the relation among them.Table 10 provides the results (Step 7).Here, we rank the obstacles based on the values of (D þ R), which represent the degree of centrality from Table 10.The ranking is given in Table 11.
From Table 10 we can see the value of (D À R).There we can find both positive and negative value.We can define these values into effective group and cause group.Effective group refers the values which are (D À R) < 0. The rest of the values mean positive values go under the cause group.
Relationship between criteria
Lean manufacturing adoption managers can make informed decisions, allocate resources effectively and prioritize actions to improve LM adoption within their industry.
Validation of results
In this part of the study, the ranking of the barriers, causal diagrams were further validated with the help of industry practitioner.A series of focus group discussions were conducted in three phases, which involved 12 industrial managers to validate the research findings.
Lean manufacturing adoption
The selection criteria for the participants included their years of working experience, current organizational affiliation and area of expertise.Specifically, participants were chosen based on having at least 15 years of working experience, currently working in a manufacturing organization, and possessing knowledge of LM principles.In the first phase, the ranking of lean implementation barriers was given to the participants for validation.After the discussion, the participants reached a consensus on the ranking of barriers.During the second phase, the participants were asked to validate the barriers within context of the barriers.This was done to ensure that the barriers identified in the first phase were accurately categorized.Finally, the causal diagram and causal interactions diagram was presented to the participants.The participants were asked for their opinions on the direct and indirect
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relationships among the barriers, and whether they were appropriate in the context of furniture industry of Bangladesh.The participants expressed that they found the direct and indirect relationships among the barriers to be appropriate and relevant in the current context.Overall, this phase helped to further validate and refine the identified barriers and provided a deeper understanding of the relationships among them.
5. Discussion and implications of the study 5.1 Discussion of the findings The findings of our LM study hold substantial significance in the context of the furniture industry in Bangladesh.Just as Industry 4.0 (I4.0) technologies have transformed manufacturing, the adoption of LM practices can revolutionize the furniture industry's operations.However, understanding the barriers to LM adoption and their implications is essential for fostering this transformative change.This study sheds light on the elements obstructing LM implementation and analyzes their impact on the industry's journey towards efficiency and sustainability.Our study contributes to the growing body of research on LM adoption, particularly within the context of the furniture industry in Bangladesh.In comparing our findings with existing studies, we can draw attention to the distinctive aspects and significance of the research.Our study stands out as one of the few initiatives to investigate LM implementation barriers in the Bangladeshi furniture industry.While previous studies have addressed LM adoption in various contexts, such as manufacturing and service sectors (Ponnambalam et al., 2023;Robertsone et al., 2022;Leite et al., 2022;Mathiyazhagan et al., 2022), none have specifically focused on the furniture industry in Bangladesh.This specificity is vital as different industries often face unique challenges in LM implementation.Therefore, our research fills a critical gap in the literature by shedding light on the barriers specific to this industry.Similar to broader studies on LM, we recognize the intricate web of interdependencies among LM adoption criteria in the furniture industry.Our utilization of the fuzzy-DEMATEL method allows us to understand these complexities better.By delving into the causal relationships among various factors, we can pinpoint which criteria exert the most influence and which are most vulnerable to external influences.This sophisticated approach sets our study apart from simpler analyses in the LM literature.In contrast to general LM studies, our research within the furniture industry of Bangladesh reveals that "Fragmented Industry Structure," "Rejection of Lean Practice" and "Inadequate Plant Layout and Maintenance" are the top three barriers.This contrasts with studies in other sectors (Abu et al., 2022;Qureshi et al., 2022), where barriers may differ in significance.These unique findings underline the industry-specific nature of LM challenges, emphasizing the importance of tailoring strategies to address these particular obstacles.Our study offers practical insights into how the furniture industry in Bangladesh can overcome LM adoption barriers.The focus on "Insufficient Expert Management" highlights the need for knowledgeable leadership during the transition phase.Additionally, addressing "Limited Technical Resources" and "Lack of Capital Cost" becomes crucial.These findings guide industry practitioners in crafting targeted strategies, showcasing the real-world relevance of our research.In summary, our study bridges the gap in the literature by addressing LM adoption barriers in the Bangladeshi furniture industry.While drawing on established LM concepts, our research provides industry-specific insights that can guide strategies for successful adoption.The authors have noticed that the outcomes under various circumstances do not significantly change.It demonstrates how reliable our model is.LM adoption of Bangladesh furniture sector is primarily influenced by three barriers.These are the "Fragmented Industry Structure," "Rejection of Lean Practice," and "Inadequate Plant Layout and Maintenance".The rest of the barriers are being influenced by these three barriers.However, the technique used in this study enabled them to be combined, producing a framework that all the decision-makers involved could utilize to recognize and comprehend cause-and-effect links between groups of decision criteria.By comparing and contrasting our findings with existing studies, we emphasize the uniqueness of our contribution and underscore the need for industry-tailored approaches in LM implementation.This study lays the foundation for further research on LM in emerging markets, where such insights are crucial for industries striving for growth and competitiveness.
Theorical implications
The results of this study, from the standpoint of a practitioner, aid in comprehending the barriers and their interaction.Using our methodology, it is possible to prioritize the barriers and direct attention toward them in the proper order.Before implementing lean, the company must make sure that the management is dedicated and has the knowledge and abilities to recruit personnel.Another key barrier to lean deployment is Resistance to Changes and absence of awareness of the benefits.The biggest problem with lean implementation is the propensity to fall back into old routines when barriers arise.Therefore, knowledgeable inspiration and leadership are required during the shift phase.Along with fixing these internal issues, lean implementation needs to be broadened.Despite the fact that this study primarily employs case studies from wooden furniture companies, the created technique can be applied to other industries.As a result, overcoming a number of pertinent difficulties can be considerably linked to the offered structural framework of this research.Application of lean practices can directly contribute to the achievement of SDGs 12 (responsible consumption and production), eight (decent work and economic growth), 13 (climate action), 9 (industry innovation and infrastructure) and others, because it improves and augments production processes while taking into account effects on the environment, the workplace and natural resources.The literature already available on the application of lean gains various theoretical insights from this study, including: (1) Highlighting the main barriers that the emerging market furniture sector will face in implementing LM.
(2) Using the fuzzy-DEMATEL technique to assess and rank the main obstacles.
(3) To have a thorough understanding of how LM deployment might affect productivity and lessen any unfavorable effects on the furniture business (4) Laying the groundwork for further, in-depth research to give decision-makers a better understanding of the barriers facing the introduction of LM in many other manufacturing sectors.
Practical implications
The explanation given above exemplifies the observations made from the research, which will aid the furniture industries in understanding the barriers that are most important, least important and how they are related.Administrators will be better able to recognize the barriers in implementing lean as a result of this understanding.The study would be interesting to lean practitioners since it might be applied in organizations to focus on the interaction of obstacles needed for the effective adoption of LM.If manufacturers, researchers and politicians had a better understanding and understanding of these barriers, they could remove important obstacles to the implementation of lean projects.Scholars from different fields of industrial management could also follow the findings and discussions on the results.Managers will utilize the analysis as a starting point to boost their lean initiatives within their manufacturing organizations.By focusing on the largest barriers, the study might help managers in manufacturing organizations use their resources as efficiently as possible.They can choose which obstacle to concentrate on first by taking into account how this study analyzes the barriers and shows the hierarchical relationships between them.Since lean utilization and resource management are listed first among all the barriers, managers and policymakers should first focus on these issues.This study offers valuable practical insights for stakeholders in the furniture industry.The findings provide actionable guidance for industry practitioners, making our research directly relevant to real-world challenges.The practical implications are highlighted below: Addressing fragmented industry structure: Given that "Fragmented Industry Structure" is a significant barrier, furniture manufacturers should consider strategies to collaborate and consolidate their operations.This could involve forming alliances, sharing resources or creating industry associations to collectively address common challenges.
Overcoming resistance to lean practice: Since "Rejection of Lean Practice" is a top barrier, it is essential to focus on change management and employee engagement strategies.Implementing lean practices should involve educating and involving the workforce in the process to minimize resistance.
Improving plant layout and maintenance: "Inadequate Plant Layout and Maintenance" is another critical barrier.Manufacturers should prioritize investments in facility upgrades, layout optimization and regular maintenance to create an environment conducive to lean manufacturing.
Policy implications
Industry consolidation support: Policymakers can encourage furniture manufacturers to collaborate and consolidate their operations by offering incentives, tax breaks or grants for joint ventures or mergers that promote efficiency and competitiveness.
Change management training: Government-backed programs can provide training and resources for change management, emphasizing the importance of employee buy-in and participation when transitioning to lean practices.
Plant infrastructure development: Policies should support infrastructure development in the furniture industry, including incentives for upgrading plant layouts and ensuring regular maintenance to enhance efficiency.
Quality standards and certification: Establish industry-specific quality standards and certification programs that incentivize manufacturers to maintain high standards in plant layout and maintenance, aligning with lean principles.
Knowledge sharing platforms: Create platforms for knowledge sharing and best practice dissemination within the fragmented industry.Government-sponsored initiatives or industry associations can facilitate this exchange.
Research and development grants: Encourage R&D initiatives that focus on innovative solutions for overcoming barriers related to plant layout and maintenance.Grants and funding support can be provided for such projects.
By prioritizing these practical and policy implications based on the top three barriers, the furniture industry in Bangladesh can systematically address the challenges it faces in adopting lean manufacturing practices, leading to enhanced productivity and competitiveness.This study could be helpful to firms by helping them prioritize the lean implementation based on the performance measurements they think are more strategically crucial to improve.
Conclusion and future scopes of the study
In conclusion, this research has provided valuable insights into the challenges and opportunities surrounding the adoption of lean manufacturing practices in the Bangladeshi Lean manufacturing adoption furniture industry.By employing the DEMATEL technique, we have uncovered a nuanced understanding of the barriers faced by this sector.The study's conclusions indicate that there are numerous managements, technical and financial-related obstacles in the Bangladeshi furniture industry, making the application of lean a difficult procedure.This study has revealed several managerial, technical and financial barriers, rendering the implementation of lean practices a complex endeavor in the Bangladeshi furniture industry.Notably, both lean and non-lean organizations identified financial constraints as the primary obstacle.This underscores the critical role of financial resources in lean adoption.Moreover, a lack of expertise and knowledge emerged as a major impediment, emphasizing the need for training and skill development in lean methodologies.These conclusions enhanced our understanding of the deficiency of lean implementation in the furniture business in Bangladesh.It is shown that because the furniture companies have limited resources and capital, they can't employ all lean tools and methods simultaneously.Additionally, it highlights the significance of addressing management gaps and promoting specialized production processes, design and workmanship.To navigate those barriers and foster the efficient implementation of lean principles, it is imperative for the Bangladeshi furniture industry and relevant stakeholders to take deliberate actions.These actions encompass cultivating expertise among management, enhancing quality control mechanisms, investing in research and development and addressing structural inefficiencies.
While this study provides valuable insights, it acknowledges certain limitations.Authors have derived some barriers from expert opinions, leaving room for additional research to explore a more comprehensive range of barriers.Although authors have applied the fuzzy-DEMATEL approach to enhance result acceptance, other criteria-ranking methods (i.e.fuzzy-AHP, fuzzy-TISM, fuzzy-VIKOR etc.) warrant exploration in future work.The future research landscape in this domain is promising.It could encompass a more comprehensive investigation into barriers affecting the furniture industry's lean implementation.Additionally, exploring alternative fuzzy aggregation methods may offer deeper insights.Future studies should also focus on the broader industry ecosystem and outreach strategies tailored to different sectoral perspectives.This study contributes to the growing body of knowledge on lean adoption in the furniture sector of Bangladesh.It underscores the industry-specific challenges and offers valuable insights for practitioners and policymakers alike.Further research in this sector holds great potential for improving lean implementation and enhancing the competitiveness of the industry on a global scale.
The purposive sampling method, a nonprobability sampling technique, involves the deliberate selection of specific respondents based on characteristics or attributes relevant to the research objectives(Moktadir et al., 2018).To maintain the privacy of these experts, their names are not disclosed in this study.The carefully chosen individuals were actively involved and directly involved in the furniture sector.The specialists were chosen based on requirements that they are well knowledgeable about lean manufacturing and have working knowledge of the furniture sector, and at least six years of experience.The selection criteria for these experts were meticulously applied through panel sessions to ensure their qualifications for providing insights into the adoption of LM.The criteria for expert selection encompassed: (1) Expertise in LM adoption, (2) Sufficient understanding of lean concept and (3) Familiarity with the Bangladeshi furniture industry.The resulting panel of experts included individuals who held positions as Figure 1.Flowchart of the current research 3: Let e O k is the k.evaluators' fuzzy decision matrix about the criteria expressed in terms of fuzzy triangular numbers.25,0.50,0.75)High influence (H) (0.50,0.75,1.00)Very high influence (VH) (0.75,1.00,1.00)Source(s):Table courtesy of X 3 of Delphi: Review, consolidation, and confirmation of the barriers Source(s): Figure courtesy of H. M. Taqi et al. (2023) Figure 2. Steps of the three-stage Delphi technique
Figure
Figure 3. Causal diagram of (D À R) vs (D þ R) (Han and Deng, 2018)as formerly applied in 1973, by the Geneva Research Center of the Battelle Memorial Institute.The DEMATEL technique is a more advanced way to create and examine a structural model for examining the interactions between influences among complicated criteria(Han and Deng, 2018).However, it is difficult to separate complex variables when making decisions in a fuzzy situation.In the current work, a fuzzy-DEMATEL technique is applied to generate a more accurate analysis.The furniture industry of Bangladesh, like many industries, involves complex and interrelated factors that depicts the stages of this study.
Table 3 .
illustrates the Profiles of experts steps in the three-stage Delphi method.The figure illustrates how a thorough literature study is used to first identify the pertinent barriers. involved
Table 5 .
Fuzzy linguistic scale
Table 7 .
Initial direct-relation matrix F | 8,450.4 | 2023-11-28T00:00:00.000 | [
"Business",
"Engineering"
] |
A New Sufficient Condition for Checking the Robust Stabilization of Uncertain Descriptor Fractional-Order Systems
We consider the robust asymptotical stabilization of uncertain a class of descriptor fractional-order systems. In the state matrix, we require that the parameter uncertainties are time-invariant and norm-bounded.We derive a sufficient condition for the systemwith the fractional-order α satisfying 1 ≤ α < 2 in terms of linear matrix inequalities (LMIs). The condition of the proposed stability criterion for fractional-order system is easy to be verified. An illustrative example is given to show that our result is effective.
Introduction
Descriptor systems arise naturally in many applications such as aerospace engineering, social economic systems, and network analysis.Sometimes we also call descriptor systems singular systems.Descriptor system theory is an important part in control systems theory.Since 1970s, descriptor systems have been wildly studied, for example, descriptor linear systems [1], descriptor nonlinear systems [2][3][4], and discrete descriptor systems [5][6][7].In particular, Dai has systematically introduced the theoretical basis of descriptor systems in [8], which is the first monograph on this subject.A detailed discussion of descriptor systems and their applications can be found in [9,10].
It is well known that fractional-order systems have been studied extensively in the last 20 years, since the fractional calculus has been found many applications in viscoelastic systems [11][12][13][14], robotics [15][16][17][18], finance system [19][20][21], and many others [22][23][24][25][26]. Studying on fractional-order calculus has become an active research field.To the best of our knowledge, although stability analysis is a basic problem in control theory, very few works existed for the stability analysis for descriptor fractional-order systems.
Many problems related to stability of descriptor fractional-order control systems are still challenging and unsolved.For the nominal stabilization case, N'Doye et al. [27] study the stabilization of one descriptor fractional-order system with the fractional-order , 1 < < 2, in terms of LMIs.N'Doye et al. [28] derive some sufficient conditions for the robust asymptotical stabilization of uncertain descriptor fractional-order systems with the fractional-order satisfying 0 < < 2. Furthermore, Ma et al. [29] study the robust stability and stabilization of fractional-order linear systems with positive real uncertainty.Note that, in Example 1, by applying Theorem 2 [27], it is harder to determine whether the uncertain descriptor fractionalorder system (6) is asymptotically stable.Therefore, it is valuable to seek sufficient conditions, for checking the robust asymptotical stabilization of uncertain descriptor fractional-order systems.
In this paper, we study the stabilization of a class of descriptor fractional-order systems with the fractional-order , 1 ≤ < 2, in terms of LMIs.We derive a new sufficient condition for checking the robust asymptotical stabilization of uncertain descriptor fractional-order systems with the fractional-order satisfying 1 ≤ < 2, in terms of LMIs.It should be mentioned that, compared with some prior works, our main contributions consist in the following: (1) we assume that the matrix of uncertain parameters in the uncertain descriptor fractional-order system is diagonal.Thus, compared with the results in [28], our conclusion, Theorem 8, is more feasible and effective and has wider applications; (2) compared with some stability criteria of fractional-order nonlinear systems, for example, in [9,22], our method is easier to be used.
Notations: throughout this paper, R × stands for the set of by matrices with real entries, stands for the transpose of , {} denotes the expression + , denotes the identity matrix of order , diag( 1 , 2 , . . ., ) denotes the diagonal matrix, and • will be used in some matrix expressions to indicate a symmetric structure; i.e., if given matrices
Preliminary Results
Consider the following class of linear fractional-order systems: where 0 < < 2 is the fractional-order, () ∈ R is the state vector, ∈ R × is a constant matrix, and 0 represent the fractional-order derivative, which can be expressed as where Γ(⋅) is the Euler Gamma function.For convenience, we use to replace 0 in the rest of this paper.It is well known that system (2) is stable if [30][31][32] arg (spec ()) > 2 where 0 < < 2 and spec() is the spectrum of all eigenvalues of .
The next lemma, given by Chilali et al. [33], contains the necessary and sufficient conditions of (4) in terms of LMI, when the fractional-order belongs to 1 ≤ < 2.
It is well known that the following system Further we have that the uncertain descriptor fractionalorder systems ( 6) is normalizable if and only if the nominal descriptor fractional-order system ( 9) is normalizable.
Lemma 3 (see [28], Theorem 1).System ( 6) is normalizable if and only if there exist a nonsingular matrix and a matrix such that the following LMI is satisfied.In this case, the gain matrix is given by Assume that ( 6) is normalizable; by applying LMI (11), we obtain ∈ R × such that rank( + ) = .Consider the feedback control for (6) in the following form: where ∈ R × is one gain matrix such that the obtained normalized system is asymptotically stable.Then we have the closed-loop system: that is, where To facilitate the description of our main results, we need the following results.
In [28], N'Doye et al. derive a sufficient condition for the robust asymptotical stabilization of uncertain descriptor fractional-order systems with the fractional-order satisfying 1 ≤ < 2 in terms of LMIs.
Lemma 6 (see [41]).Let , , and be real matrices of appropriate sizes.Then, for any
Main Result
In this section, we present a new sufficient condition to design the gain matrix .In the following theorem, Δ and Δ are given nonsingular matrices, such that From now on, we denote Δ = Δ −1 ΔΔ −1 , M = 1 Δ , and N = Δ .It is obvious that ΔΔ ≤ .Thus, for any 1 > 0 and 2 > 0, by using Lemmas 5 and 6 and ΔΔ ≤ , we have and that is, Remark 7. Note that, when = 2, we have 1 + 2 ≤ 2 and That is, for any real scalar > 0, and two matrices ∈ R × 1 and ∈ R 2 × , we cannot obtain real scalars 1 > 0 and 2 > 0 such that where Theorem 8. Assume that ( 6) is normalizable; then there exists a gain matrix such that the uncertain descriptor fractionalorder system (6) with fractional-order 1 ≤ < 2 controlled by the controller ( 13) is asymptotically stable, if there exist matrices ∈ R × , = > 0 ∈ R × and two real scalars 1 > 0 and 2 > 0, such that where with = − (/2) and matrices and are given by LMI (11).Moreover, the gain matrix is given by Proof.Suppose that there exist matrices ∈ R × , = > 0 ∈ R × and two real scalars 1 > 0 and 2 > 0 such that (29) holds.It is easy to derive that By using the Schur complement of ( 29), one obtains Write = −1 .It follows from applying (25) that By using the above inequality (34) and Lemma 1, we obtain Therefore, system ( 6) is asymptotically stable.This ends the proof.
Note that if we choose Δ = and Δ = in LMI (29), It is easy to see the following: (1) For given , when 1 − > 0, it is always true that 1 + 2 − > 0; that is, there do not exist 1 and 2 such that < 0. Therefore, Theorem 8 is not a special case of Lemma 4 [28, Theorem 2], when Δ = and Δ = . (
A Numerical Example
In this section, we assume that the matrix of uncertain parameters Δ in the uncertain descriptor fractional-order system (6) is diagonal.We provide a numerical example to illustrate that Theorem 8 is feasible and effective with wider applications.
Example 1.Consider the uncertain descriptor fractionalorder system described in (6) with parameters as follows: where = 1.23.
It is easy to check that rank() = 2 < 3; that is, is singular.By applying the LMI (11) It follows from ( 16) that Based on those results, it is debatable whether or not system (6) is stable.
In the second way, we compute 0 , , 1 , 2 , and by using Theorem 8; we choose It is easy to check that (51) Therefore, system (6) is stable.
Conclusion
In this paper, the robust asymptotical stability of uncertain descriptor fractional-order systems (6) with the fractionalorder belonging to 1 ≤ < 2 has been studied.We derive a new sufficient condition for checking the robust asymptotical stabilization of (6) in terms of LMIs.Out results can be seen as a generalization of [28,Theorem 2].By adding appropriate parameters into LMIs, our result has wider applications.One special numerical example has shown that our results are feasible and easy to be used.
11361009], High level innovation teams and distinguished scholars in Guangxi Universities, the Special Fund for Scientific and Technological Bases and Talents of Guangxi [Grant no.2016AD05050], and the Special Fund for Bagui Scholars of Guangxi.The second author was supported partially by the National Natural Science Foundation of China [Grant no.11701320] and the Shandong Provincial Natural Science Foundation [Grant no.ZR2016AM04]. | 2,123.8 | 2018-07-18T00:00:00.000 | [
"Engineering",
"Mathematics"
] |
Diffany: an ontology-driven framework to infer, visualise and analyse differential molecular networks
Background Differential networks have recently been introduced as a powerful way to study the dynamic rewiring capabilities of an interactome in response to changing environmental conditions or stimuli. Currently, such differential networks are generated and visualised using ad hoc methods, and are often limited to the analysis of only one condition-specific response or one interaction type at a time. Results In this work, we present a generic, ontology-driven framework to infer, visualise and analyse an arbitrary set of condition-specific responses against one reference network. To this end, we have implemented novel ontology-based algorithms that can process highly heterogeneous networks, accounting for both physical interactions and regulatory associations, symmetric and directed edges, edge weights and negation. We propose this integrative framework as a standardised methodology that allows a unified view on differential networks and promotes comparability between differential network studies. As an illustrative application, we demonstrate its usefulness on a plant abiotic stress study and we experimentally confirmed a predicted regulator. Availability Diffany is freely available as open-source java library and Cytoscape plugin from http://bioinformatics.psb.ugent.be/supplementary_data/solan/diffany/. Electronic supplementary material The online version of this article (doi:10.1186/s12859-015-0863-y) contains supplementary material, which is available to authorized users.
Background
In the early days of Systems Biology, when molecular interaction data was still relatively sparse, all interactions known for a model organism were typically added to a single large interaction network. Such an integrated view would combine data from the proteome, transcriptome and metabolome [1][2][3][4]. While such studies certainly proved valuable to gain insights into the general characteristics of molecular networks, they lack the level of detail required to analyse specific response mechanisms of the interactome to changing conditions or stimuli. Consequently, differential networks have been introduced to model the dynamic rewiring of the interactome under specific conditions [5,6]. Differential networks only depict the set of interactions that changed after the introduction of a stimulus. Most current research in this field has focused on a single interaction type such as expression data [7,8], genetic interactions [9] or protein complexes [10]. Further, the analysis is usually limited to the comparison of only two networks [11][12][13]. At the same time, several promising studies have constructed multiple condition-specific networks such as time-course data [14,15], tissue-specific networks [16,17] or stressinduced co-expression networks [18]. These studies analyse general network statistics such as connectivity scores or employ machine-learning techniques to identify significantly rewired genes. However, due to the black-box behaviour of the methods and because these studies do not actually generate and visualise differential networks, the resulting prioritised gene lists cannot be easily interpreted by domain experts. By contrast, we believe it to be crucial that researchers can visualise and further explore the rewiring events in their network context. Unfortunately, there is currently no standardised methodology that would allow to integrate heterogeneous conditionspecific networks on the one hand, and produce intercomparable differential networks on the other hand.
Here, we introduce a novel ontology-based framework to standardise condition-specific input networks and to allow an arbitrary number of such networks to be used in the inference of a differential network. The network algorithms are designed to cope with a high variety of heterogeneous input data, including physical interactions and regulatory associations, symmetric and directed edges, explicitly negated interactions and edge weights. Depending on the application, these weights may be used to model the strength of an interaction, determined for instance by the expression levels of the interacting genes, or they may represent the probability that an interaction occurs when dealing with computationally inferred networks such as regulatory associations derived from co-expression analysis.
To the best of our knowledge, our integrative framework named 'Diffany' (Differential network analysis tool) is unique in the emerging field of differential network biology, and we hope its open-source release will facilitate and enhance differential network studies. As one such example, we will present how the reanalysis, with Diffany, of a previously published experimental dataset has unveiled a novel candidate regulator for plant responses to mannitol. Experimental validation confirmed that this regulator, HY5, might indeed be involved in the mannitolresponsive network in growing Arabidopsis leaves.
Framework
In this section, we detail the various parts of the Diffany framework (Additional file 1).
Network terminology
To perform a differential network analysis, two types of input data sources are required. First, a reference network R models an untreated/unperturbed interactome, serving as the point of reference to compare other networks to. Second, one or more condition-specific networks each represent the interactome after a certain treatment, perturbation or stimulus. We denote them as N i with i between 1 and c, and c the number of distinct conditions that are being compared to the reference state.
Both types of input networks may have edges with a certain weight associated to them. Such weights in the networks may be interpreted differently according to the application for which the framework is used. For instance, they may model the strength of physical interactions as determined by expression levels of the interacting genes. In other cases, when dealing with network data inferred through computational methods, such as regulatory associations derived from co-expression data, these weights may instead model the probability/confidence that an interaction really does occur. Whichever the case, the Diffany framework assumes the weights assigned to the edges are sensible and comparable to each other.
The two input sources are used to generate a differential network D (Fig. 1) that depicts the rewiring events from the reference state to the perturbed interactome. Further, an inferred consensus network C models the interactions that are common to the reference and conditionspecific networks, sometimes also called 'housekeeping' interactions. We do not adopt the latter terminology, because while some unchanged interactions may indeed provide information about the cell's standard machinery (i.e. housekeeping functions), others may simply refer to interactions that change under some other condition than the one tested in the experimental setup.
Interaction ontology
The interaction ontology is a crucial component that assigns meaning to heterogeneous input data types. Analogous to the Systems Biology Graphical Notation (SBGN) [19], this structured vocabulory provides a distinction between ' Activity Flow' interactions and 'Process' interactions, modelling regulatory associations and physical interactions separately. However, in contrast to SBGN, these complementary interaction classes can be freely mixed within one network, allowing for a varying level of modelling detail combined into one visualisation.
In the Diffany framework, a default interaction ontology is available, covering genetic interactions, regulatory associations, co-expression, protein-protein interactions, and post-translational modifications (Fig. 2). This ontology was composed specifically to support a wide range of use-cases, and is used throughout this paper. However, the ontology structure itself, as well as the mapping of spelling variants, can be extended or modified based on specific user demands. Additionally, when unknown interaction types are encountered in the input data, they are transparently added as unconnected root categories.
Network inference
The interaction ontology defines the root categories for which consensus and differential edges can be inferred. For the sake of simplification of the formulae in the following, we define R = N 0 , and we thus have a set N of c + 1 input networks. The union of all nodes in these c + 1 input networks is represented by G, and an edge of semantic root category S between two nodes X and Y in an input network N i as I sxyi . Notice that I sxyi may also refer to a non-existing or 'void' edge when the two nodes X and Y are not connected by any edge of that semantic category S in the network N i . Edge thickness refers to the weight of an edge. In Subfigure (c), the top connection (A-B) shows a negative differential edge ('decreases_regulation') occurring because of a switched polarity from positive (green) to negative (red) regulation, while the second and third links (M-N and X-Y) show a negative differential edge because the original positive edge was decreased or even entirely removed in the condition-specific network. The thickness of the differential edge represents the difference in weight between the reference and condition edge. Column (d) depicts the corresponding 'consensus' edges: both input networks are found to have a regulatory edge between nodes A and B and a positive regulation edge between M and N, but there is no consensus edge between X and Y A differential network is then inferred by considering each possible node pair (X, Y ) in (G × G) and, for each such pair, constructing the set of input edges I sxy for each semantic category S. The calculation of differential and consensus edges E from that set of input edges I sxy involves the determination of the following edge parameters: • edge negation: neg(E) is a boolean value • edge symmetry: symm(E) is a boolean value
Differential networks
The hierarchical structure of the interaction ontology forms the backbone for the inference of differential networks. First, all (affirmative) condition-specific edges in I sxy for a specific category S are processed to construct a support tree (Fig. 3). Such an edge provides support not only for the category it belongs to (e.g. 'inhibition'), but also for all super-categories in the tree (in casu, 'negative regulation' and 'regulation' , cf. left tree in Fig. 3). From the support tree that is thus generated, it becomes possible to synthesize the number of condition-specific networks that support a certain category, and by which weights they do so (cf. right tree in Fig. 3).
Negated edges in I sxy are interpreted as explicit recordings of links that are not present in the interactome, but otherwise do not influence the support tree. A differential edge D sxy is always affirmative (Formula (1)), and is only symmetrical when all input edges in I sxy are symmetrical (Formula (2)). When only some of the edges in I sxy are symmetrical while others are directed, the symmetrical ones are unmerged into two opposite directed edges of equal type and weight.
To further determine the type and weight of a differential edge D sxy , the reference edge R sxy is compared to the produced support tree of the condition-specific networks. If the set of values in the support tree (e.g. {0.6, 0.7, 0.8} for 'regulation') contains values both below as well as above the weight of R sxy , no meaningful differential edge D sxy can be deduced, as the response varies in directionality between the different conditions. This is also the case when the edges in C sxy all appear to be equal to R sxy . Otherwise, when all conditions support a higher weight than the weight of R sxy , the minimal difference to those Fig. 3 Evidence summarisation. Example of how the evidence from four different condition-specific networks ((a): C1-C4 from top to bottom) is summarised using the default edge ontology as backbone (shown only partially). Each condition-specific edge provides support not only for the category it belongs to (e.g. inhibition), but also for all super-categories in the tree (e.g. regulation (b)). After processing all condition-specific edges (c), the support tree summarises the number of condition-specific networks that support a certain category, and with which weights they do so supporting edges determines the increase value shared among all conditions and is thus used as the weight of D sxy (Formula (3)). Similarly, when all conditions support a lower weight, the minimal difference determines the decrease value shared among all conditions. For example, if R sxy would be a regulation edge of weight 0.9, D sxy would be of type decrease_regulation and weight 0.1 according to the support tree of of Fig. 3. If R sxy would have weight 0.4 instead, D sxy would be of type increase_regulation and weight 0.2.
While a Process edge expresses a physical interaction and has no polarity, an Activity flow edge can be determined to have a general 'positive' or 'negative' effect. This means that for an edge in the Activity flow category (e.g. 'positive regulation') also edges of the opposite category can be compared (in casu 'negative regulation'). While in principle edge weights are positive, in this case the weights of the opposite category will be converted to negative values only for calculation purposes. As such, the differential edge between 'negative regulation' of 0.2 (interpreted as −0.2 for calculation purposes) and 'positive regulation' of 0.3 would be of weight 0.5.
Consensus networks
The inference of consensus networks follows a similar procedure. To calculate a consensus edge C sxy from a set of affirmative input edges I sxy , the reference edge R sxy is first added to the support tree in a similar fashion as done previously for the condition-specific edges. The mostspecific edge type with highest weight that is supported by all input networks is then chosen to define the consensus edge. In the case when all edges in I sxy are negated, we construct a similar support tree, but one where the support travels downwards to sub-categories instead of upwards (e.g. 'no regulation' also implies 'no inhibition').
In this case, the least-specific edge type with the highest weight that is supported by all, will represent the consensus edge, which will also be negated (Formula (4)).
When I sxy contains both affirmative and negated edges, no consensus edge will be deduced between nodes X and Y. As described above, consensus edges are defined by retrieving a weight value that is supported by all input, thus effectively applying a 'minimum' operator to the input weights (Formula (6)). However, it is also possible to apply the maximum operator, which will identify the highest weight that is supported by at least one input network, thus simulating a 'union' operation rather than an 'intersection' between the given input edges. More sophisticated weighting mechanisms will be implemented in the future, depending on the applications in which the framework will be used.
Post-processing
An optional post-processing step is to automatically remove all inferred edges in the differential and/or consensus networks below a user-defined weight threshold. The exact value of this threshold should be chosen based on the input data and the edge weight normalisations of the original resources. For example, the differential weights could be indexed against the null distribution of values expected when the reference and conditionspecific networks would represent equal replicates [6].
Fuzzy inference
The differential inference methods as described above can identify a rewiring event that is common to all conditions, as compared to one reference network. However, in some cases it might be beneficial to allow for one or more mismatches. Such a relaxed constraint enables for instance the retrieval of rewiring events that occur in three out of four conditions, thus allowing a more 'fuzzy' or less stringent mode of comparison.
For the calculation of consensus networks, similar relaxed criteria can be applied. In this case, it can be specified whether or not the reference network always needs to 'match' or not. If this is set to 'true' , a consensus edge will always need support from the reference network specifically. Otherwise, all input networks are treated as equals.
Implementation
Diffany is implemented in Java 1.6 and the code, released under an open-source license, contains extensive in-line documentation as well as detailed javadoc annotations a . JUnit tests ensure proper behaviour of the algorithms also after code refactoring. A GitHub repository provides version control, public issue tracking and a wiki with documentation. For instance, the framework could be extended by adapting more complex statistical scoring strategies [7,12] into the ontology-based backbone. As this is a non-trivial task, we encourage others to contribute to this effort through the online GitHub repository.
The code base is structured in a modular fashion, with various methods for network cleaning, building and refining the ontology structure, applying custom edge filters, and so on. It is straightforward to extend the available functionality with additional network algorithms or filtering steps. By keeping semantics separate from functionality throughout the code, it becomes straightforward to create a custom ontology for any given project. On top of this core library, we have also implemented a Cytoscape plugin ('app') for the new Cytoscape 3 framework [20], providing an intuitive user interface and allowing straightforward integration with other network inference/analysis tools such as ClueGO [21], BINGO [22] or GeneMANIA [23]. Finally, a commandline interface supports large-scale bioinformatics studies through the generation of differential networks in straightforward tab-delimited file formats.
Results
By design, the framework presented here can deal with any mixed input networks of negated edges, different edge weights, directed as well as symmetrical edges and a variety of edge types. Herein lays the main strength of our framework that is thus applicable to a wide range of comparative network studies.
Genetic networks
To evaluate the implementation of our novel framework, we have applied it first to a small, artificial network available in previous literature (Fig. 4). Using the original inference as inspiration (Fig. 4a) to model the input networks (Fig. 4b-c), Diffany produced differential and consensus networks (Fig. 4d-e). Remarkably, compared to the inference of [6], the consensus network generated by Diffany contains one additional edge: the (weak) unspecified genetic interaction (gi) between A and B. Indeed, because our framework is ontology-driven, it can recognise the fact that 'positive gi' and 'negative gi' are both subclasses of the more general category 'genetic interaction' . As a result, there is an edge of type 'unspecified genetic interaction' between nodes A and B in the consensus network.
In cases where such general, unspecified edges without polarity are unwanted, it is trivial to remove them from the network in a post-processing filtering step. However, we believe this additional information can be valuable when combined with the information in the differential networks themselves, as the presence or absence of such a generic consensus edge helps distinguishing between the three different cases as depicted in Fig. 1. Specifically, this generic regulatory edge provides evidence for the fact that both the reference and condition-specific network contain a regulatory edge between nodes A and B, but with opposite polarity, as is the case in the top example in Fig. 1. Given that the differential edge presents an increase in regulation, this means that the reference network contained a negative (down-) regulation, and the condition-specific network a positive (up-) regulation. When instead the consensus edge would not have this general, unspecified edge, as in the case of the bottom example in Fig. 1, this would mean that the conditionspecific network simply did not have any link between the two nodes.
Heterogeneous data
The second example presents the application of the Diffany inference tool to heterogeneous input networks, further illustrating the power of the Interaction Ontology. Here, a differential and a consensus network are generated Fig. 4 Artificial differential network of genetic interactions. A comparison of Diffany results with a previously published (artificial) differential network involving positive (alleviating) and negative (aggrevating) genetic interactions. a: The original picture by [6]. The reference network is denoted as 'Condition 1' and the condition-specific network as 'Condition 2'. The differential network is displayed at the right, and the consensus network at the bottom ('Housekeeping interactions'). b-e: The differential d and consensus networks e produced by Diffany from the same input data. Because they do not contribute to an enhanced understanding of the molecular rewiring, unconnected nodes are not included in the networks from reference and condition-specific networks obtained through integrating various interaction and regulation types (Fig. 5). Notice how directionality, different edge types and weights can all be mixed freely in the networks.
Mannitol-stress in plants
To demonstrate the practical utility of our framework, we have used Diffany to reanalyse a previously published experimental dataset measuring mannitol-induced stress responses in the model plant Arabidopsis thaliana [24]. In this study, nine-days-old seedlings were transferred to either control medium, or medium supplemented with 25 mM mannitol. At this developmental stage, the third true leaf is very small and its cells are actively proliferating. RNA from these young leaves was extracted at 1.5, 3, 12 and 24 h after transfer. The expression data were processed with robust multichip average (RMA) as implemented in BioConductor [25,26]. Further, the Limma package [27] was applied to identify differentially expressed (DE) genes at two FDR-corrected P-values: 0.05 and 0.1, giving rise to two sets of DE genes for each time-point (Table 1 and Additional file 2).
Input networks
To determine the set of genes (nodes) relevant to this study, we have first taken all differentially expressed genes across all time-points, using the strict 0.05 FDR threshold. Next, all the PPI neighbours of these genes were extracted from CORNET [28,29] and added, with the exception of non-DE PPI hubs, as the inclusion of such hubs would extend our networks to irrelevant nodes. Analysis showed that for instance 10 % of all nodes account for 70 % of all PPI edges, and we have removed the bias towards such generic hubs by automatically excluding proteins with at least 10 PPI partners. Note that such hubs will still appear in the networks when they are differentially expressed themselves. Subsequently, all regulatory neighbours of the extended node set were added, using both the AGRIS TF-target data [30] and the kinase-target relations from PhosPhAt [31]. From the kinase-target relations, hubs with at least 30 partners were excluded, removing mainly MAP kinase phosphatases (MKPs) which are involved in a large number of physiological processes during development and growth [32]. Finally, we also added DE genes from the Artificial differential network of heterogeneous data. More complex calculation of differential (c) and consensus (d) networks from the reference (a) and condition-specific (b) networks. Notice how directionality, different edge types and weights can all be mixed freely in the networks second, less stringent result set (FDR cut-off 0.1), if they could be directly connected to at least one of the genes found up until that point. This approach allows us to explore also those genes that are only slightly above the strict 0.05 FDR cut-off, while reducing noise by excluding those that are not connected to our pathways of interest. In general, this two-step methodology as well as the hub filtering was found to produce more meaningful results. However, both steps are optional and can be removed from the pipeline when using the Diffany library in other studies.
The reference network was then defined by generating all PPI and regulatory edges between the node set as determined in the previous steps. All edges in the reference network were given weight one, a default value used when no overexpression is measured (yet). This resulted in a reference network of 1393 nodes and 2354 non-redundant edges, of which 56 % protein-protein interactions, 24 % TF regulatory interactions and 20 % kinase-target interactions.
Subsequently, each time-specific network was constructed by altering the edge weights according to the expression levels of the corresponding nodes/genes measured at that time point. All interactions with at least one significantly differentially expressed gene as interaction partner is thus down-or upweighted. To define differential expression, the less stringent criterium (0.1 FDR) is used here. For instance, the activation of a non-DE gene by a gene that is differentially expressed at that specific time point, would get a weight proportional to the fold change of that differentially expressed activator. By contrast, an edge would be removed (weight zero) when the edge does not fit the expression values at this time point, for instance when an activator is overexpressed but the target is underexpressed. This allows us to remove the interactions that, even though reported in the public interaction data, are probably not occurring in this specific context.
As a final result, the information on differentially expressed genes has now been encoded in the edge weights of the time-specific networks. By comparing them to the generic reference network, the Diffany algorithms will now be able to produce differential and consensus networks which depict the changes in expression values across the time measurements. In the following, we describe these results and provide interpretations that show-case how this type of analysis may lead to novel insights.
Differential network for one condition
With the statistically significant DE values translated into input networks, the differential networks can then be generated by either comparing the reference network to each time-specific network individually, or by comparing all time-specific networks against the reference network simultaneously.
As an example of the first mode of comparison, Fig. 6 depicts the differential network after 1.5 hours, illustrating the rewiring events occurring in this short time frame after the induction of mannitol stress. At this early time point, it is rather unlikely that the expression of the DE genes was affected by subsequent transcriptional cascades. By including transcription factors upstream of the DE genes in the network even if they are not DE themselves, it is possible to identify new putative regulators as compared to previous analysis methods. For example, HY5 and PIL5 might be suitable candidates, as they contain a putative phosphorylation site and are thus likely to be posttranslationally regulated.
To further investigate the possibility that HY5 would be a transcriptional regulator under mannitol stress, we validated the Diffany results by measuring the expression level of the proposed HY5-target genes in the growing leaves of WT and HY5 loss-of-function mutants. These genes, except ARL, were all underexpressed in hy5 mutants as compared to WT, confirming that HY5 is indeed involved in the regulation of the MYB51, EXO, RAV2 and TCH3 expression in growing Arabidopsis leaves (Additional files 3 and 4).
To further explore if HY5 is involved in leaf growth regulation under mannitol stress, phenotypic analysis was performed on hy5 mutants under both long term and short term mannitol treatment. The hy5 seedlings were clearly hypersensitive to stress, with decreased leaf size under long term and short term stress, and showed complete bleaching upon long term mannitol stress (Fig. 7, Additional file 4). These biological results demonstrate that HY5, which has been identified with Diffany as a putative regulator of mannitol stress, might indeed be involved in the mannitol-responsive network in growing Arabidopsis leaves.
Next to the identification of new putative regulatory links, the differential PPI edges make it possible to understand complex formation under specific conditions. For example, the EBF2 sub-complex presents a nice example of how the induction of one protein is sufficient to increase the activity of a whole complex. The EBF2 is a stress-responsive E3-ligase involved in the posttranslational regulation of the ethylene-responsive factors EIN3 and EIL1 [33,34]. In this differential network, EBF2 forms a complex with these two targets, which are induced by mannitol as well. However, some of the other members of the SCF-complex, such as CUL1, SKP1, ASK1 and ASK2, are missing from the differential network. As these SCFcomplexes are involved in many cellular processes, their specificity being defined by the E3-ligase, we can speculate that the other members of the complex are highly abundant and not specific to mannitol-stress. Their automatic removal from the differential network thus allows the user to focus on the truly interesting genes for this specific stress condition.
Differential network for all conditions
The second mode of comparison allows to simultaneously compare all condition-specific networks to one reference network. In this specific case, such an analysis models the stress-specific, but time-independent response. Fig. 8 shows these rewiring interactions. Strikingly, mainly the overexpressed genes (yellow nodes) remain differentially expressed throughout the time-course experiment, while this is only the case for a few of the underexpressed genes (blue nodes). This implies that in this context, the upregulation of genes is a more stable and long-term process.
For instance, the upregulation of TCH3 by HY5 is present because TCH3 is overexpressed at all time points and its upregulation by HY5 may thus play a significant role in the overall stress response. To validate this biologically, the expression level of TCH3 and other previously mentioned HY5 target genes was measured in WT and hy5 mutants, 24 h upon transfer to control or mannitol-supplemented medium (Additional file 4). While the induction of TCH3, MYB51 and ARL could be clearly observed in WT plants, a more variable but less pronounced upregulation was observed in hy5 mutants. Thus, HY5 might be involved in the regulation of TCH3, MYB51 and ARL under mannitol, although it is probably not the sole regulator of these targets, but instead acts in Fig. 6 Mannitol-induced stress response at 1.5 h. Analysis of the mannitol-induced stress response, depicting the generated differential network at the 1.5 h time point: increase/decrease of regulation in dark green and red respectively, increase/decrease of PPI in light green and orange, increase/decrease in phosphorylation in blue and purple. It is important to note that in these differential networks the arrows point to rewiring events: a decrease of regulation for instance (red arrows) does not necessarily point to an inhibition, but may also indicate a discontinued activation. Diamond nodes represent proteins with a known phosphorylation site, and proteins with a kinase function are shown with a black border. Blue and yellow nodes identify underexpressed and overexpressed genes respectively parallel with other regulators previously identified in the early mannitol-response of growing Arabidopsis leaves [24,35].
Finally, we can apply a less stringent criterium to the inference of differential networks by only requiring that three out of four time points need to match for a rewiring event to be included in the differential network (Fig. 9). This results in more robust network inference, as the differential network would remain the same when some noise would be introduced at one of the time points. Additionally, this method provides a more complete view on the rewiring pathway occurring in response to osmotic stress in plants. All these different settings and options are also available when generating the differential networks through the Cytoscape plugin.
Discussion and conclusion
We have developed an open-source framework, called Diffany, for the inference of differential networks from an arbitrary set of input networks. This input set always contains one reference network which represents the interactome of an untreated/unperturbed organism, while all other networks are condition-specific, each modelling the interactome of the same organism subjected to a specific environmental condition or stimulus. Differential networks allow focusing specifically on the rewiring of . Analysis of the mannitol-induced stress response, showing the differential network generated by comparing the reference network to all four time points simultaneously, and calculating the overall differential rewiring. Color coding as in Fig. 6 the network as a response to such stimuli, by modelling only the changed interactions. At the same time, interactions that remain (largely) the same are summarised in a 'consensus' network that provides insight into the basic interactions that are not influenced by changes of internal or external conditions. The analysis of these differential and consensus networks provides a unique opportunity to enhance our understanding of rewiring events occurring for instance when plants undergo environmental stress, or when a disease manifests in the human body. Fig. 9 Mannitol-induced stress response across all time points, allowing for one mis-match per edge. Analysis of the mannitol-induced stress response, showing the differential network generated by comparing the reference network to all four time points but allowing a match when only three out of four time points share the same response. Color coding as in Fig. 6, pink arrows depict an increase in dephosphorylation. In this figure, only regulatory interactions are shown as the addition of PPI data would obscure the visualisation Further, the fact that the framework can compare an arbitrary number of condition-specific networks to one reference network at the same time, forms a powerful tool to analyse distinct but related conditions, such as different human diseases that may share a defected pathway, or various abiotic stresses influencing a plant in a similar fashion.
In comparison to previous work in the emerging field of differential network biology, Diffany is the first generic framework that provides data integration functionality in the context of differential networks. To this end, we have implemented an Interaction Ontology which enables seamless integration of different interaction types, provides semantic interpretation, and deals with heterogeneous input networks containing both directed and symmetrical relations. This ontology forms the backbone for the implementation of the network inference methods that produces differential networks. As in any Systems Biology study or application, a known challenge involves the issue of non-existing edges: an interaction may be missing from the network because it was experimentally determined that no association occurred, or it may simply be that there is a lack of evidence for the interaction, not actually excluding its existence. To deal with these cases, Diffany allows the definition of negated edges, which are explicit recordings of interactions that were determined not to happen under a specific condition.
To provide easy access to the basic functionality of inference and visualisation of differential and consensus networks, we have developed a commandline interface and a Cytoscape plugin. The Cytoscape plugin allows to generate custom differential networks as well as reproduce the use-cases described in this paper. All relevant code is released under an open-source license.
Finally, we have illustrated the practical utility of Diffany on a study involving osmotic stress responses in Arabidopsis thaliana. The resulting differential networks were found to be concise and coherent, modelling the response to mannitol-induced stress adequately. The analysis of these differential networks and a preliminary experimental validation has led to the identification of new candidate regulators for early mannitolresponse, such as PIL5 and HY5, which likely contribute to the fast transcriptional induction of mannitol-responsive genes. Further detailed biological validation, including for instance ChIP experiments and experimental systems biology approaches, are necessary to confirm the role of HY5 in this context and fully unravel the early stress-induced rewiring events of this complex regulatory network. | 7,848.4 | 2016-01-05T00:00:00.000 | [
"Biology",
"Computer Science"
] |
Fluid flow lifting a body from a solid surface
If a body is at rest on horizontal ground and a sudden horizontal flow of fluid is applied, the body either remains on the ground (rocking, rolling, sliding or spinning) or is lifted off impulsively. This lift-off is followed by a return to the ground or by a fly-away in the sense of continued departure from the ground. Related phenomena arise in the lift-off of an air vehicle from, effectively, moving ground. The present investigation seeks fairly precise mechanistic conditions under which lift-off and subsequent return or fly-away occur for a thin body or more generally for any thin gap of fluid between a body and the ground. Nonlinear fluid–solid interaction takes place in which the motion of the body and the surrounding fluid affect each other. Small-time analysis on lift-off and a numerical study are presented, followed by large-time analysis showing a critical flow speed for fly-away for any shape of the body. The changes in ground effect, from being dominant during lift-off to diminishing in fly-away, are explored together with relevant applications.
Introduction
The interest here is in an impulsive fluid flow removing a body originally stationary on a fixed solid surface. The body is supposed to be much denser than the fluid, such that gravity can affect the body movement appreciably whereas the fluid flow feels almost no gravity effect over the current time frame. The mechanisms for a single body in two-dimensional flow are studied by modelling, analysis and related computation, with a view to understanding lift-off followed by either a return to the surface (ground) or complete fly-away of the body. Experimental results including saltation, take-off, entrainment are quite plentiful as in [1][2][3][4][5][6] and further pioneering experiments and related work are in [7][8][9]. Of special interest are the studies of body shape effects experimentally and numerically in [7], of turbulent-flow effects on the threshold of motion in [8] and of shearedflow effects for spherical particles in [9]. This last interesting recent paper (also see [10,11]) on experiments and related modelling pointed out that, in quantitative terms, the conditions required for fluid-driven removal of a particle from a solid surface were not well established and that there existed then no analytical results for configurations where fluid inertia is important (as is the case here).
The approach taken in the present paper is an alternative approach which is based on describing quantitatively the physical response of the thin layer of fluid supporting a body as lift-off occurs, our description being by means of model analysis supported by reduced computations and certain experimental links. This follows the fascinating results and motivation above and is intended to be complementary to the previous studies. A significant aspect of the present investigation is the ground effect coupled with the sudden horizontal flow. The present contribution is also associated with the model in [12], a paper which mentions many other applications including the relevance to the movement of dust on the planet Mars. The work in [12] is for unsteady interactions prior to lift-off: however, after lift-off, the fluid gap opens up and so there is no contact point in the present setting.
This paper considers phenomena that are dominated by unsteady, momentum and pressure forces. Applications arise in the removal of debris, grain segregation, dust blowing, leaf-blowers, sand movement, ski jumping or aircraft take-off. See for example [13][14][15].
The fluid is taken to be incompressible and Newtonian with uniform density (area density) ρ * , where the asterisk ( * ) refers to a dimensional quantity. The motion of the fluid and the immersed thin body (see figure 1) is expressed in terms of non-dimensional flow velocities (u, v), corresponding Cartesian coordinates (horizontal x, vertical y), time t and pressure p, such that the dimensional versions are u * (u, v), l * (x, y), l * t/u * and ρ * u * 2 p, respectively. Here u * is the freestream fluid velocity, while l * is the length of the body and the temporal factor l * /u * is the typical transport time. In particular (u, v) is given by (1,0) in the far field and the leading edge of the solid object can be taken as the origin. The Reynolds number Re = u * l * /ν * , where ν * is the kinematic viscosity of the fluid, is assumed large, in line with experiments. As a first model or approximation, an inviscid separation-free theory is applied, given that in many situations of real concern wall layers are turbulent and less prone to separate [16][17][18] than are laminar layers. A subsequent model for the laminar regime using ideas similar to those employed here would be called upon to cope with local flow separation perhaps by means of free-streamline theory.
Our interactions are governed by a nonlinear evolutionary system for the unknown scaled functions h, θ , u, p. Here h(t) is the vertical y-location of the centre of mass of the body, while θ (t) is the small angle the body chord makes with the horizontal. Also, x = σ is the prescribed x-location of the centre of mass and the initial contact point with the ground. Similar interactions arise in [19][20][21] in various different contexts of fluid-solid interplay.
Section 2 presents the model in detail including the description of the fluid-body interaction. The reasoning here is mostly expressed in terms of a thin body nearly aligned with the uniform incoming fluid flow but similar considerations apply for a thicker body provided that the gap between the under surface of the body and the ground is relatively small. This is followed by §3 which studies the behaviour for small times. Section 4 examines the lift-off criterion for different body shapes by means of the general formula derived which is then applied to specific examples. If the body does lift off, it returns to the ground within a finite time or flies away at large time ( § §5 and 6). We focus on the latter, finding a criterion for fly-away. The final §7 provides the conclusions including discussion of flow separation and other features concerning the physical validity of the lift-off and fly-away criteria.
The fluid-body interaction
The body is assumed to have a smooth shape with a non-dimensional horizontal length of unity and is thin, of vertical scale O(δ) for δ 1. The incoming flow moving from left to right is the uniform stream with (u, v) = (1, 0). Thus, the incoming vorticity of the flow is predominantly zero, with the majority of the thin body being assumed to be located in a region outside any oncoming turbulent or laminar boundary layer beneath the oncoming free stream, or possibly inside the outer portion of a turbulent boundary layer where the velocity deficit from the free-stream value is small. The present setting contrasts with that in the recent work [22,23] where non-zero incoming vorticity due to a boundary layer or channel flow is included. In the present setting, the body is initially in contact with the fixed horizontal surface y = 0 at its centre of mass whose x-location is x = σ as shown in figure 1.
Concerning figure 1, the scaled body mass is represented asM and moment of inertia asÎ (see details below) whileĝ denotes the scaled acceleration due to gravity. We should remark that in effect the mass and other quantities involved are non-dimensionalized first and then if necessary (to take account of any small or large parameters present) are scaled in order to be nominally of order unity. Thus, hereMĝ is the scaled weightŴ of the body. It is assumed that the typical y scale in the gap underneath the body is also of order δ, small compared with the O(1) length scale of x, but still large compared with the representative viscous thickness at large Reynolds numbers Re (that thickness being typically of order Re −1/2 in the laminar regime). In consequence, the flow itself is described formally by the classical boundary layer equations without a viscous contribution, yielding the so-called thin layer or, in another context, the shallow-water system for an effectively inviscid fluid. It is assumed in addition that the body, moving in response to the forces from the fluid motion, does so over time scales that are comparable with the time scales of the fluid motion and thereby has an appreciable effect on the fluid flow. The present assumptions imply that the flow over the horizontal length scale of order unity remains irrotational to leading order almost everywhere (since vorticity is conserved along particle paths) and so the scaled vorticity is zero. Thin-layer dynamics in which the vorticity is dominated by its ∂u/∂y component therefore require that u = u(x, t) does not depend on y, which forces v through continuity to change in y from zero at zero y to a value consistent with the kinematic condition at the unknown position of the moving lower surface of the thin body. Thus, the governing equations are Here H(x, t) denotes the unknown scaled thickness of the thin gap depending on the lower surface shape of the body and its orientation defined in (2.1c) above; f u (x) is the prescribed shape of the underbody. The contributions h(t) and θ(t) are owing to changes in the lateral location and orientation of the body, respectively, and are prescribed at the beginning in (2.1d). We remark that the real orientation angle is small, being θδ where θ can take any finite value in principle. Considering (2.1a-c) further, the kinematic condition yields (2.1a) while (2.1b) is the dominant streamwise momentum balance, with p being dependent only on x, t by virtue of the normal momentum balance, as in boundary layer theory. Concerning initial and boundary conditions, at the initial contact point x = σ the constraints (2.1d) below come from the requirement of zero minimum gap width for the smooth shapes considered herein. Also, the condition (2.1e) below allows for a jump across the leading-edge Euler zone at x = 0+. Since there is a quasi-steady local Euler flow around the leading edge [12,24], the quasi-steady Bernoulli condition (2.1e) is valid in the present unsteady flow scenario. The reason for the (Kutta) requirement (2.1f) below at the trailing edge of the body is that on top of the body the pressure varies typically by only a small amount of order δ throughout the external flow compared with its characteristic O(1) variation within the gap. Physically, the leading-edge jumps are induced by the necessity of the equi-pressure condition at the trailing edge (see [12,24]). The flow behind the body has no effect here to leading order. In consequence, we have the conditions These conditions are coupled with the body-motion equations in (2.1g,h). The unknowns C L (t), C M (t) are, respectively, the scaled evolving lift and moment coefficients. The dimensional mass is ρ * l * 2M /δ, while the dimensional moment of inertia is ρ * l * 4Î /δ. Also the acceleration due to gravity is δu * 2ĝ /l * in dimensional terms. The Froude number is (δĝ) −1 , whereas the Richardson number is δĝ. HereÎ <M/4 from its definition. Thus, the equations for the body motion arê The task in general is to solve the nonlinear system (2.1a)-(2.1h) for h, θ, u, p and this is addressed successively for early times t, O(1) times and late times in the following sections.
Early behaviour
An investigation of the behaviour of the system at small times t proves to provide insight. This not only leads on to a comparison with direct numerical work (in figure 2 and in appendix A) but also yields a lift-off criterion. The body is assumed to be initially at rest on the surface when the fluid flow is begun impulsively at time t = 0. Two flow regions are present at small positive t: one is affected by the complete underbody shape for x of order unity, specifically for 0 < x < σ , σ < x < 1, and the other closely surrounds the original contact point where the local body shape, being smooth, is O((x − σ ) 2 ) and is comparable with the initially small gap width which is O(t 2 ) because the initial body acceleration is expected to be uniform. The reason for the uniformity rests in an argument based on orders of magnitude. In the two spatial dimensions present here, the boundary conditions in (2.1e,f ) suggest that generally the pressure p should be of order unity at most and that implies pressure force contributions of order unity on the right-hand sides of the body movement balances in (2.1g,h). The left-hand sides then indicate that bodyacceleration responses (d 2 h/dt 2 , d 2 θ/dt 2 ) of order unity are likewise to be expected in general. Detailed working subsequently shows that u is of order t in the current setting in order to balance the pressure gradient in (2.1b) against the acceleration term ∂u/∂t and this confirms the O(1) pressure estimate above. We now investigate the fluid-body interaction as the lifting starts and in particular clarify the contributions from the inner and outer regions, which in one respect turn out to have similar degrees of importance. The main details are described in sections (a)-(c). In physical terms, the outer region in (a) suffers only small perturbations in height and inclination of the body compared with the initial state but these turn out to be sufficient to cause significant pressure forces to act over the majority of the underbody. The small inner region in (b) by contrast has height and inclination effects of order unity relative to the initial state as anticipated earlier in this paragraph and the pressure response is found to be logarithmically large but it acts only over the small length scale where x − σ is of order t in region (b) and so contributes only a comparatively minor influence on the lift and moment exerted on the body early on. The matching between the two regions is presented in (c) together with the resulting predictions for the changes in height and inclination of the body at small times.
(a) Outer region
In view of the initial state and the uniform body accelerations d 2 h/dt 2 , d 2 θ/dt 2 anticipated in the previous paragraph, we should expect the small-time expansions of the height h and inclination θ to contain contributions of order unity (from the initial fluid-filled gap) and t 2 (from acceleration).
For most x of O(1), the gap width, velocity and pressure thus develop at small times according to with the dominant term of the gap width being defined by while the tu 1 term is inferred from the balance in (2.1a). Here the unknown constants h 2 , θ 2 are proportional to the body acceleration coefficients. Substituting (3.1) into (2.1a) and integrating in x leads to the velocity in the outer region, of the form where c 1 is the integration constant. Next, integrating the momentum equation (2.1b) with respect to x at leading order and considering (2.1e,f ) yields the leading term of the pressure as Matching below implies that c 1 is zero, leaving negligible inertial effects here. Also we observe the singular behaviour (3.5) and the known constant B = f u /2 from the expression for the gap width near the original contact point. Next, the inner region near the initial contact x = σ needs to be studied.
(b) Inner region
In the inner region a nonlinear effect asserts itself in terms of the gap width, with the solution taking the form for x near the lift-off point: The scalings stem directly from those in the outer region. From substitution into (2.1a-d) and matching, the leading contributions satisfy and The prime ( ) denotes an ordinary derivative with respect to ξ . Here the constant α = −2h 2 /B in (3.7d) for matching. The leading order terms in the local velocity and pressure expansion from (3.7a-c) are therefore as follows, and where c * 0 , p * 0 (0) are integration constants to be determined.
Similarly, p * 0 (0) can be found, and this completes the u, p solutions. Only the outer region controls the main body motion at leading order but, to clarify, the inner region completes the starting condition for numerical work as well as ensuring complete physical sense. Here the body movement relations (2.1g,h) yield the leading order contributions in the scaled height and inclination of the body at small times in the form We need the right-hand side of (3.11a) to be positive in order that the body can lift off from the surface. Substitution of p 0 (x) from (3.4) into the system (3.11a,b) then leads to two linear equations with constants for the two unknowns h 2 , θ 2 . If the body is symmetric with σ = 1/2, then I 2 is identically zero. Comparisons between the early-time predictions and the results of numerical simulations are presented in figure 2 for the particular case of scaled massM equal to 0.5 and scaled gravityĝ equal to 0.24, with the scaled moment of inertia kept as 1/5 of the scaled mass. Further results and comparisons are shown in appendix A, where the numerical procedure is also described. The comparisons show quite close agreement at small times and tend to support both the direct numerical work and the asymptotic analysis.
In summary, the investigation of the early behaviour has shown a multi-structure occurring, with relatively large pressures and substantial flow velocities being induced very close to the original contact point with the ground. Elsewhere between the body and the ground substantial pressure variations are also provoked but with relatively minor flow velocities. The latter pressures act to drive the early movement of the body at the leading order. The next issue concerns, quantitatively, the question of whether lift-off actually occurs or not.
Lift-off criterion
The lift-off requirement is simply that h 2 needs to be positive because of the nature of the gap width near its minimum value as displayed in (3.7c). If we consider a body having a general Figure 3. The right-hand side of (4.2) versus the original contact location σ for varyingÎκ (shown as I κ ) ranging from 0.02 to 0.5. Body has a parabolic shape.
shape, using the relationship We note that I 1 < 0, I 3 < 0, α > 0, β > 0, while I 2 can either be negative or positive. If the scaled massM and moment of inertiaÎ are sufficiently large that γ > 0, then from (4.1) lift-off requireŝ Mĝ < σ/2 − σ 2 /4βI 2 by virtue of h 2 > 0. As a main example, for a parabolic-shaped body f u (x) = κx(1 − x) with curvature 2κ constant, for any σ , the criterion in (4.1) becomeŝ Figure 3 shows the right-hand side of (4.2) versus σ for a range ofÎκ. At small σ valuesMĝ has to be small for lift-off, whereas σ near unity allows lift-off for largerMĝ. In between there is a significant range of σ for which lift-off does not occur. Further, at σ = 1/2, the lift-off requirement isMĝ < 1/4 in scaled terms, in keeping with (3.12a), i.e. the dimensional incident flow speed must exceed a critical value.(Other shapes lead to a more complex response.) Figures 4 and 5 show numerical evolutions of the system (2.1a-h). These numerical solutions were obtained by use of a finite-difference scheme similar to that in [24]. Appendix A describes the scheme used. The results in figure 4 are for cases where the body, having a sinusoidal shape, lifts off but, depending on the conditions, either returns to the ground after a finite time or flies away as time increases. This tends to confirm that different outcomes can occur for an underbody shape which is less simple than the parabolic shape. In the examples shown in figure 4c,d, each gradual dip of the minimum gap width with time indicates that a return to the ground almost occurs at some finite time, after which the trend towards a fly-away event takes control. Figure 5 is for the parabolic underbody shape where the given constant curvature allows comparison with the prediction (4.2) at early times, and similarly with the prediction (4.1) for any other shapes. In the former case, if the prediction (4.2) is not satisfied then the body cannot lift off. For the configurations in figure 5, however, the prediction is satisfied, the body lifts off and indeed the departure from the ground continues to large times and, similarly to the behaviour found in figure 4c,d,
For large mass and moment of inertia
and This yields two coupled ordinary differential equations [24] for h, θ in the case of the parabolic underbody shape. More significantly, however, even in the case of an arbitrary shape (5.1a,b) themselves suggest a large-t response in which h, θ grow like t 2 at large times. (5.2) This produces integrands of order unity in (5.1a,b) and also gives independence from the shape f u (x) since, from (2.1c), H is dominated by the contributions h + (x − σ )θ of order t 2 for almost all x values. We pursue this below in the general case.
Large-time behaviour
This analysis applies for t 1 and general values of the parametersM,Î,ĝ. Guided by the idea in the previous section, we see that the response at large times is that h, θ are of O(t 2 ) as p typically must be O(1) by virtue of (2.1e). The resulting asymptotic description takes the form (H, h, θ , u, p) = (t 2 H 2 (x), t 2 h 2 , t 2 θ 2 , u 0 (x), p 0 (x)) + · · · . (6.1) Hence in (2.1a,b), the time derivatives H t , u t are negligible and simple quasi-steady relations hold again. The body shape contribution f u (x) likewise becomes negligible compared with the h, θ contributions. Also the Kutta condition (2.1f) leads to u 0 (1) = 1. The leading-order velocity u 0 is therefore Substituting (6.2) into (2.1e) then gives the pressure Hence the body-balance equations in (2.1g,h) yield and With the solutions h 2 , θ 2 thus determined, the leading-order terms in gap width, velocity and pressure solutions can now be determined. Figure 5 shows a sample comparison between the numerical and the analytical solutions for the height h and angle θ. The analytical ones use the large-time asymptotic expansions in (6.4a,b). A close match is seen for both h, θ , with the near-constant differences between the numerical and the large-time asymptotic results being attributable to effects of higher order in the latter approach including an arbitrary constant shift in the origin of time. In this example, and others not shown here, the body lifts off and rotates but does not impact on the ground, instead continuing to depart from the ground.
Concerning the fly-away criterion, figure 6 plots the coefficients h 2 , θ 2 versus scaled weight. A critical valueŴ =Ŵ c (= 1 2 ) emerges. We put Mĝ = 1 2 − with small and positive, (6.5) and then expand h 2 , θ 2 in powers of such that (h 2 , θ 2 ) = (ĥ 2 ,θ 2 ) + · · · . It is found withM = 1, for example, that (h 2 , θ 2 ) = 2 , − + · · · . (6.6) The critical value 1/2 applies for any shape of the body. In the critical case, the main balance of forces is between weight and the pressure force driven by the Bernoulli pressure head since h 2 , θ 2 are small. The asymptotic predictions agree well with those in figure 6 as t increases. For a symmetric body for example, the (h 2 + (1 − σ )θ 2 ) contribution in (6.4b) implies that the trailing edge stops rising, whereas the leading edge height is still increasing.
Summary
The lift-off of a single solid body from a flat surface has been modelled, analysed and calculated and this leads to certain experimental links as discussed below. The critical value of scaled weight is found to be 1/4 for any symmetric body in order that the body can initially lift off from the surface. A lift-off criterion is also found for non-symmetric body shapes although the criterion in this case is more complex as it is very shape-dependent. The body can subsequently return to the surface for a range of scaled mass, moment of inertia, gravity and body shapes, but alternatively fly-away occurs. This depends to a large extent on a competition between the vertical force and the rotating force on the body at earlier times. The critical value of the scaled weight such that the body can fly away is found: the critical value 1/2 applies irrespective of the shape of body, which potentially may seem a powerful result although it is subject of course to the assumptions involved, including the thinness of the body and the lack of separation. Non-dimensionally the 1/4 factor at early times is due to Bernoulli pressure acting only on the front half of the underbody in contrast with the complete underbody at late times due to the body being far from the wall which yields the 1/2 factor.
If the leading edge of the body goes up that generally implies an increased lift whereas a descending leading edge is associated with downforce. Likewise, the body rotation produced can lead to an impact on the ground or continued departure from the ground. Here the ground effect reduces the possibility of lift-off by reducing the lift-off force due to a given fluid flow in comparison with the fly-away case. In dimensional terms for a body mass represented as ρ * B h * B l * where ρ * B is the body density and h * B is the mean body thickness the lift-off and fly-away criteria on the incident velocity can be written, respectively, (for a symmetric body in the case of (7.1a) with g * denoting gravity). We remark again that the overall results derived here are mostly illustrated by specific examples and that the parameter space is large. Nevertheless, (7.1a,b) appear to represent quite general criteria. Beyond a few significant experiments and observations (see in next paragraph), there tend to be limited comparisons possible with experiments and direct simulations owing to the different parameter ranges involved as well as the model assumptions.
Two particular points stand out in regard to experimental links and observations. The first is that the criteria above are on effective Froude numbers and are akin to Shield's condition [25][26][27] in sediment processes but without shear stresses, given the present model has negligible viscous effects and corresponding friction forces are small compared with the form forces due to pressure.
Our study incorporating ground effect shows an evolution towards or away from fly-away and determines a precise coefficient (4 or 2) rather than the order of magnitude estimate of Shield, although this is for thin bodies. The second particular point is that, in a quite different setting, the comparison and broad agreement concerning the scalings associated with dust movement on the planet Mars still hold for the present work as in [12] since the present post-lift-off result agrees exactly in terms of its orders of magnitude with that in the previous pre-lift-off work based on normal force.
A basic explanation of fly-away is also provided by the present study via the original governing equations (2.1a,b) where the H t , u t contributions diminish when t 1. Hence the quasisteady Bernoulli relation holds for p. So then the body-motion balance involvingMḧ leads to the requirementMĝ < 1/2 in scaled terms, which simply balances weight against lift. In addition the lift-off condition is different from the fly-away condition because of the ground effect, implying that symmetric bodies for instance which are subject to flow velocities between the two values in (7.1) satisfy the fly-away condition but are unable to lift off, while a body that lifts off can either fly away or return to the ground.
Among the various major assumptions are the body thinness (or the gap thinness in the case of a thicker body), the given quasi-inviscid fluid and the flow irrotationality over the scales present. The assumptions are made in a first-go broad approximation for the nonlinear fluidbody interaction arising in lift-off, return or fly-away. These seem to yield results relevant to some applications in addition to further understanding, subject to the comments and caution above.
Other interesting matters have still to be addressed. The effect of incident shear in the oncoming flow has not been considered yet in the present context and neither have threedimensionality or viscous effects: see the latter in the recent analyses of [22,23] and shear effects in the recent experiments of [9]. We have supposed thin turbulent wall layers but we can certainly expect separation to take place in the laminar regime. The assumption of separationfree flow in the context of any laminar wall sublayers is certainly open to question on physical grounds if a more detailed model is to be developed and explored, given that sublayer separation may influence substantially the flow dynamics over a wide range of parameters and alter the conditions for lift-off of the body and return to the ground, if not the conditions for fly-away where the ground effect is reduced. The influence is dependent, however, on the body surface and ground conditions in detail, for example, whether the body is moving horizontally relative to the ground and whether the solid surfaces involved are rough or smooth. On a larger time scale, the normal pressure gradient within the fluid flow comes into play significantly as the ground effect diminishes. The incorporation of non-symmetric bodies as mentioned previously and likewise more complex bodies such as those with concavities offer interesting challenges for the future. Other possible extensions might be to reptation, clashes, body flexibility, and investigating the effects of the surface shape on which the body lies initially. The extension to several bodies is of further concern.
Data accessibility. This article does not contain any additional data. Authors' contributions. S.B. conducted the analysis and computation jointly with F.T.S. Both of the authors gave their final approval for publication.
Competing interests. We declare we have no competing interests. Acknowledgements. Thanks are due to Professor Danny Feltham for pointing out the relevance to Shield's condition. We also thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme The Mathematics of Sea Ice Phenomena when part of the work on this paper was finalized, supported by EPSRC grant number EP/K032208/1. Thanks are due to EPSRC for support through grant numbers GR/T11364/01, EP/D069335/1, EP/G501831/1, EP/H501665/1, EP/H500278/1 during part of this research. Additional thanks are due to Roger Gent and Richard Moser of AeroTex UK for very helpful discussions on body and particle movement in near-wall flow. Very helpful comments from the referees are acknowledged with much gratitude from the authors.
Appendix A. Numerical study of the complete interaction
The numerical treatment uses finite differencing. A brief overview of the algorithm is as follows. advances the body to its new position based on (2.1g,h) and finds the velocity and pressure of the fluid using (2.1a-f ). The scheme checks for the body returning to the surface and then either finds the body's new position, fluid velocity and pressure as above or stops when the body returns to the surface.
We expand on this description in a little more detail as follows. Initially, the body is placed horizontally on the surface. To proceed by a specified small time step δt (typically 5 × 10 −5 ) to the next time step, the scaled trailing-edge pressure is forced to zero in the following manner. Having performed an integration in (2.1a), discretization yields which is solved for u = u i values at the next time step from x = 0 to x = 1 (i = 1 to i = N) as we are only interested in this region where the body is located. The constant c is to be found. The spatial steps δx are taken typically as 0.01 (N = 101 steps) or smaller. The c value is found directly using the trailing-edge pressure condition. Next, (2.1b) is discretized using: Here the subscript and superscript denote a variable's spatial and time indexing, respectively, while K is the total number of time steps. The pressure values p i are therefore determined via (A 2). The trailing-edge pressure constraint is then addressed using a secant method. Next, the starting value u 1 is updated by carrying out iterations and continuing these until the difference between the required value of the trailing-edge pressure and p N is sufficiently small. Here all the terms dh/dt, h, dθ/dt, θ are renewed by integrating (2.1g,h) with an implicit Euler method and using the trailing-edge pressure constraint p N = 0. To advance to the next time step, the same to u j i and so on. The procedure is performed until the body either returns to the surface or in effect flies away. A range of scaled mass and moment of inertia values (M,Î) are accommodated in the treatment as well as the effect of the scaled acceleration due to gravityĝ.
Checks on the influences of the spatial and temporal step sizes are presented in detail in [24]. The sets of finite-difference solutions there are found to be robust as the step sizes are refined gradually.
Results and comparisons between the finite-difference solutions and the small-time analysis are shown in figures 7 and 8 (in addition to the solutions given in figures 2-6). The results in figures 7 and 8 enlarge the parameter range presented here, and again, as in figure 2, the agreement between the numerical and analytical findings seems encouragingly close. | 7,987 | 2018-11-01T00:00:00.000 | [
"Physics",
"Engineering"
] |
Validation of ligands in macromolecular structures determined by X-ray crystallography.
Better metrics are required to be able to assess small-molecule ligands in macromolecular structures in Worldwide Protein Data Bank validation reports. The local ligand density fit (LLDF) score currently used to assess ligand electron-density fit outliers produces a substantial number of false positives and false negatives.
Introduction
The quality of small-molecule ligands in Protein Data Bank (PDB) entries has been, and continues to be, a matter of concern for many investigators (Kleywegt & Jones, 1998;Kleywegt et al., 2003;Kleywegt, 2007;Davis et al., 2008;Liebeschuetz et al., 2012;Pozharski et al., 2013;Smart & Bricogne, 2015;Deller & Rupp, 2015). Correctly interpreting whether electron density observed in a binding site is compatible with the soaked ligand or represents water or buffer molecules is sometimes far from trivial. It is particularly challenging when ligands are relatively small or bind with only partial occupancy (Pearce et al., 2017). Low-resolution structures also tend to be more problematic to interpret unambiguously, particularly below 3 Å resolution, where any waters mediating interactions between ligand and protein are unlikely to be clearly observed. Furthermore, fitting a ligand into electron density and subsequently refining the model so that it has reasonable stereochemistry, while also fitting the experimental data well, can be challenging, particularly for inexperienced crystallographers (Smart & Bricogne, 2015). The details of ligand binding are often of crucial importance to the use of a structure, for instance for structure-guided drug discovery (Scapin et al., 2015). This makes it important to establish dependable metrics that can be used to assess whether a ligand modelled with a macromolecular structure can be relied upon.
The Worldwide PDB (wwPDB) validation report (VR; Gore et al., 2012Gore et al., , 2017 provides a mechanism to highlight any major issues concerning the quality of the data or the model at the time of deposition and annotation, so the depositors can fix issues, resulting in improved data quality. In addition, it is useful to help nonspecialist users and referees assess the quality of the coordinate model and supporting experimental data presented in a PDB entry or a manuscript. The first wwPDB/Cambridge Crystallographic Data Centre/Drug Design Data Resource Ligand Validation Workshop (LVW; Adams et al., 2016) has made recommendations as to how to improve ligand validation.
This paper investigates how the ligand-validation procedures and metrics currently included in the VR work in practice for structures determined by X-ray crystallography.
Methods
Analysis of the distribution of ligand-specific metrics reported in the VR was initially performed using the ValTrends DB website (http://ncbr.muni.cz/ValTrendsDB). A current limitation of ValTrends DB is that analysis is performed per PDB entry, with all ligand metric values for that entry being averaged. To get around this limitation, further analysis was performed on an individual ligand basis using NumPy (http:// www.numpy.org) and Matplotlib (https://matplotlib.org/) to plot graphs. The Jupyter Notebook (https://jupyter.org; Shen, 2014) for the analysis is included in the Supporting Information.
The electron density around selected ligands was visualized using the ligand's page on the PDBe website (https://pdbe.org) that incorporates the versatile LiteMol program (Sehnal et al., 2017) for interactive three-dimensional visualization of PDB structural models and Electron Density Server (EDS)-style electron-density maps (Kleywegt et al., 2004) within a web browser.
Validation of ligand geometric features
To assess ligand geometry, the wwPDB validation pipeline uses the Mogul program (Bruno et al., 2004) from the Cambridge Crystallographic Data Centre (CCDC). For each bond length and bond angle in the ligand, a search is performed for small-molecule crystal structures in the Cambridge Structural Database (CSD) that have a similar chemical environment.
Part of the Mogul search can be thought of as providing for ligands a CSD survey equivalent to that performed by Engh & Huber (2001) for ideal values of bond lengths and angles for standard amino acids in proteins. Currently, the VR reports Mogul bond-length and bond-angle deviations in terms of Z-scores: this is defined as the difference between an observed value and its expected or average value, divided by the standard deviation of the latter. The Mogul root-meansquared Z-scores (RMSZ) for all of the bond lengths and angles are calculated for each ligand to allow overall assessments. Fig. 1 and Supplementary Fig. S1 show the Mogul bond-length and bond-angle RMSZ values for PDB structures released in the past 20 years, separated by ligand size. It can be noted that the bond-length RMSZ values depend on ligand size. For ligands with 6-10 non-H atoms recent depositions have a median bond-length RMSZ below 0.5, whereas larger ligands with more than 20 non-H atoms have a median bondlength RMSZ around 1.5. This does not necessarily imply that large ligands are 'worse' than small ones, only that bond restraints are relatively easily satisfied in smaller ligands with typical data resolution and electron density. RMSZ values smaller than one are probably caused by the use of the same molecule crystal structures as a source of restraint information and in Mogul validation. It can be noted that novel CSD structures could be expected to have RMSZ values for bonds and angles around one, and that values lower than this are not 'better'. This is particularly important in the fair treatment of structures refined with ligand restraints derived from highlevel quantum-chemical procedures (Moriarty et al., 2009), using a force field (Bell et al., 2012;Janowski et al., 2016) or through the direct use of quantum-chemical methods (Borbulevych et al., 2014;Smart et al., 2016) to represent the ligands. We conclude that Mogul bond-length and bond-angle RMSZ values are not sufficient as ligand-geometry quality metrics and hence cannot be used to assess whether the quality of ligands in the PDB is improving.
It is useful to analyse Mogul bond-length and bond-angle results by listing individual bond lengths and angles whose Z-score exceeds a threshold value, as is performed in the VR, where ligand bond lengths and angles with an absolute Z-score above 2.0 are flagged as 'outliers'. This value is consistent with that used by Liebeschuetz et al. (2012), but is much lower than the Z-score threshold value of 5.0 recommended by the X-ray VTF (Read et al., 2011) for protein and nucleic acids and used in the corresponding parts of the VR. Using radically different thresholds results in ligand bond lengths and angles being judged far more strictly than those in proteins and nucleic acids, with the routine reporting of a number of moderate 'outliers' for well placed ligands refined with reasonable restraints. It would be useful to use a classification that distinguishes between moderate and severe distortion from the Mogul expectation, in a similar way to Ramachandran plot analysis (Ramachandran et al., 1963), where a classification of 'favoured', 'allowed' and 'outliers' is routinely used (Chen et al., 2010). The LVW recommends that Mogul results be presented in the VR using a coloured two-dimensional stick representation, as developed in Buster-Report (Global Phasing Ltd, 2011), that allows the extent of disagreement to be shown clearly.
A complication in interpreting Mogul outliers at present is that it is not possible to assess whether an outlier arose because the restraints used in refining the ligand had target values that were not in accord with Mogul assessment or because there was a problem in the ligand fit that caused research papers geometric strain in the model. Inclusion of the ligand-related refinement restraints in the structure deposition, as recommended by the LVW , will enable the disambiguation of these factors by using Mogul to analyse the restraint target values separately from the model. Read et al. (2011) note that for protein and nucleic acid structures the analysis of bond-length and bond-angle outliers provides only limited geometric validation information, as normally these parameters are tightly restrained using harmonic restraints to ideal values from Engh & Huber (2001) (for amino acids) or Parkinson et al. (1996) (for nucleotides). Instead, the most useful geometric validation criteria use structural features that are usually not tightly restrained during refinement such as (combinations of) torsion angles or nonbonded contacts (Kleywegt & Jones, 1995;Kleywegt, 2000). The MolProbity program (Chen et al., 2010) provides an analysis of the Ramanchandran plot of main-chain torsionangle combinations (Ramachandran et al., 1963), as well as an analysis of allowed side-chain rotamers and all-atom nonbonded short contacts; all three criteria are used in the validation slider plots in the VR and are used in the combined overall quality metric (described in x3).
Mogul analysis of torsion angles and ring puckers has the potential to provide informative validation information for ligand structures (Liebeschuetz et al., 2012;Smart & Bricogne, 2015). The current VR includes Mogul torsion-angle and ringpucker analysis, but at present the outlier identification criterion used is loose and only very distorted groups are ever reported. The CSD-Mercury (Macrae et al., 2008) and Buster-Report (Global Phasing Ltd, 2011) tools show how Mogul torsion-angle and ring-pucker analysis can be usefully applied in practice.
A limitation in using CSD-derived information from Mogul arises when no or too few related small-molecule crystal structures are identified for a particular geometrical feature (for instance a particular bond angle). When this occurs, no assessment can be made of that feature. The current VR does not include information to show which features have Mogul statistics and which do not. Coloured two-dimensional stick diagrams will clearly show this information. When no Mogul information is available, comparison to the restraints used in refinement becomes particularly important. Indeed, it would be useful if the deposition could include information as to the source of the information used to define a particular restraint, for instance derived from a particular quantum-chemical procedure, so that this could be included in the VR.
Analysis of ligand-protein contacts provides a further means of geometric validation. Currently, the VR uses the MolProbity (Chen et al., 2010) all-atom clash procedure to Plots showing how the RMSZ value from Mogul analysis of bond lengths for ligands in all PDB depositions solved by X-ray crystallography varies with deposition date and ligand size. The boxes show the upper and lower quartile range, with the thick line marking the median value. The whiskers mark the 10th and 90th percentile of the data, following Kleywegt & Jones (2002). identify contact distances between the biomacromolecule and ligand that are unreasonably short once H atoms have been added to both. There is the potential to widen validation to include analysis of whether the different functional groups of the ligand make favourable interactions with the biomacromolecule, such as hydrogen bonds or hydrophobic contacts. The LIGPLOT (Wallace et al., 1995) and PoseView (Stierand & Rarey, 2010) programs provide means to display this information in two-dimensional diagrams. The IsoStar program (Bruno et al., 1997) could potentially be used to assess numerically whether the pose and conformation of a ligand are complementary to the protein binding site. Beshnova et al. (2017) have shown how a semi-empirical force field, based on that used by AutoDock (Huey et al., 2007;Morris et al., 2009), can be used to detect 'questionable' ligands in PDB ligand-protein complex structures.
Assessing ligand fit to electron density
In addition to assessing the geometric quality of a ligand modelled in a protein, it is crucial to assess whether the electron density supports the placement (that is the presence, location, orientation and conformation) of the ligand (Kleywegt, 2007;Davis et al., 2008;Pozharski et al., 2013;Smart & Bricogne, 2015;Adams et al., 2016). It should be noted that the deposition of X-ray structure-factor data only became mandatory in 2008 (Berman et al., 2013). Because of this, it is not possible to calculate electron-density maps for the 10 409 X-ray PDB entries that were deposited before 2008 without structure-factor data. In these cases, validation is necessarily limited to geometric criteria.
Visual inspection of the ligand/protein model together with the electron-density maps provides a powerful way to assess ligand placement (Kleywegt et al., 2004;Emsley et al., 2010) and this is particularly important for nonspecialist users of structures. Fig. 2 shows screenshots of LiteMol (Sehnal et al., 2017) visualizations of ligands in PDB entries and the corresponding EDS-style electron-density maps. Fig. 2(a) shows PDB entry 4tzt (He et al., 2006), solved at 1.86 Å resolution, where visual inspection confirms that the ligand is well placed in the electron density and that there is little difference density near it. The electron density fully supports ligand placement and conformational details such as ring puckers. In contrast, Fig. 2(b) shows the diclofenac ligand DIF in PDB entry 3ib0 (Mir et al., 2009) solved at 1.4 Å resolution with an R free value of 0.219. The diclofenac ligand modelled in this entry has been classified by Pozharski et al. (2013) as 'absent', with the patches of electron density in the region instead being consistent with water molecules (Smart & Bricogne, 2015). Visual inspection of the ligand together with the electrondensity maps is informative and supports this alternative interpretation (Fig. 2b). The LVW recommends that informative images of the electron-density maps around ligands, as pioneered in Buster-Report (Global Phasing Ltd, 2011), should be provided in the VRs.
Inspection of electron-density maps is useful, but it is highly desirable to have numerical measures to quantify ligand reliability, to enable for instance ranking of ligands in search results and for the selection of sets of reliable protein-ligand complex structures for assessment of the performance of docking programs (Warren et al., 2012). Currently, the VR provides three numerical metrics to assess how well a ligand fits the EDS 2mF o À DF c map calculated for that entry.
(i) Real-space R value (RSR; Jones et al., 1991), a measure of how well 'observed' and calculated electron densities agree for a ligand. The wwPDB validation pipeline computes RSR using the MAPMAN program (Kleywegt et al., 2004), which compares 2mF o À DF c and DF c maps calculated by REFMAC5 (Murshudov et al., 2011). From a user perspective, it is important to note that the range of RSR is from 0 meaning 'perfect agreement', with values approaching or above 0.4 indicating a poor fit and/or low data resolution. A comprehensive description and review of the various approaches to the calculation of RSR values is given by Tickle (2012). (ii) Real-space correlation coefficient (RSCC; Jones et al., 1991). This is an alternative measure of how well the calculated density for a ligand matches the observed electron density. RSCC varies between 1.0 meaning 'perfect correlation' and À1.0 meaning 'perfect anticorrelation', with values of 0.8 and below indicating a poor fit. The VR User Guide (wwPDB, 2016) includes a 'rule of thumb' for interpreting ligand RSCC based on that used in Buster-Report (Global Phasing Ltd, 2011): A value above 0.95 normally indicates a very good fit. RSCC around 0.90 are generally OK. A poor fit results in a value around or below 0.80 that may well indicate the experimental data do not accord with the ligand placement.
(iii) Local ligand density fit (LLDF) compares the RSR value of a ligand with the mean and standard deviation of the RSR values of the neighbouring polymeric standard amino acids and nucleotides. The CCP4 program NCONT is used to identify standard amino acids and nucleotides that have an atom within 5.0 Å distance of a ligand atom. The mean (hRSR site i) and standard deviation [(RSR site )] of the RSR values is then calculated for these neighbouring residues and this is compared with the RSR value of the ligand (RSR ligand ) to calculate the LLDF score: If there are fewer than two neighbouring residues within 5.0 Å of the ligand then the LLDF cannot be calculated. The LLDF measure was introduced in the VR to provide a measure similar to the normalized RSR values used for polymeric proteins and nucleic acids, RSRZ (Kleywegt et al., 2004): where RSR resolution,residue is the set of RSR values found for that residue type (for example arginine) and resolution range in the PDB. In the VR, amino acids and nucleic acids are reported as electron-density fit outliers if the RSRZ value is above 2.0, and this generally works well. For most ligand molecules, it would be impossible to calculate RSRZ values as there would be few (and possibly no) occurrences of the ligand type in the PDB. In the absence of any comparable measures in the field, LLDF was introduced as a stop-gap metric where the normalization is against neighbouring standard residues in the binding site. Thus, the 'normalization' is carried out internally to a structure, as opposed to externally using many other structures as is the case for RSRZ. In the VRs, all three values (RSR, RSCC and LLDF) are reported. Ligands for which the LLDF value exceeds 2.0 are classified as 'electron-density fit outliers' (this value was chosen because it was used as an RSRZ cutoff for standard amino acids). The two examples shown in Fig. 2 are classified correctly using both the LLDF-based classification and the RSCC 'rule of thumb' described above.
However, a number of depositors have reported that the LLDF-based classification marks ligands with reasonable electron-density fit as 'outliers' (private communications), and Naschberger et al. (2016) note that LLDF misclassifies reasonably placed solvent molecules such as PEG fragments and glycans. To assess whether these problems are isolated or are more general, an analysis of the LLDF-based classification and the RSCC 'rule of thumb' was undertaken for all PDB ligands where the VR includes both values (Table 1). Table 1 shows that around a third of PDB ligands are currently classified as 'outliers' because they have LLDF values above 2.0. This is a matter of concern, as it indicates either that the PDB ligands are routinely badly placed by crystallographers or that Table 1 The fraction of PDB ligands classified as outliers by the LLDF and RSCC 'rule of thumb' criteria.
Analysis of 589 965 ligands in PDB entries, determined by X-ray crystallography and released up to 28 June 2017, where the wwPDB validation report includes values for both LLDF and RSCC. For further details, see the Supporting Information.
Figure 3
LLDF is plotted versus RSCC for all ligands in the PDB for which both values are available (see Table 1). Box plots and whiskers are as in Fig. 1.
the LLDF-based metric is not reliable. In contrast, just over 11% of the ligands have RSCC lower than 0.8. Fig. 3 examines the distribution of LLDF as a function of RSCC. As expected, values of RSCC below 0.8 indicating a poor ligand fit typically correspond to high values of LLDF. As RSCC increases, LLDF generally decreases as both measures reflect that the fit generally improves. Although this is the general trend, the box plots show that there is a wide variation in LLDF values for the same RSCC. Considering ligands with a RSCC value above 0.95 (indicating a very good fit by the 'rule of thumb'), 14% of these have LLDF values above 2.0 (Table 1) and thus the ligand involved would be marked as an 'electron-density fit outlier' in the VR. To investigate the origin of this anomaly, the EDS electron density for a number of these cases was examined. Curiously, they were often found to be ligands from high-resolution structures with excellent electron-density fits. Fig. 4(a) shows an example where the data resolution is 1.0 Å and the electron density consequently shows atomic detail, with individual separated peaks for each atom (for a review, see Rupp, 2010). The RSCC for the ligand is 0.99, reflecting its excellent electron density, but since the LLDF value for the ligand is over 4 this ligand is nevertheless marked as an 'electron-density fit outlier' in the VR. An explanation for cases like these could be that the RSR values for both the ligand and its surrounding residues are all low and similar in value so that (1) involves division by a very small number (the standard deviation of the RSR values of the surrounding residues) and therefore the computed LLDF values, although correct, become high and are therefore misleading.
Further analysis was performed to check whether high LLDF values for reliably placed ligands are a common occurrence for high-resolution structures. Fig. 5(a) shows that the median and upper-quartile LLDF values for ligands in the PDB increase with higher resolutions. Indeed, at 0.8 Å resolution the median LLDF value is around 2, showing that around half the ligands in such high-resolution structures are marked as electron-density fit outliers. The LLDF criterion suggests that structures with a resolution around 2.6 Å have ligands with the fewest 'electron-density fit outliers'. Although it is possible for ligand placement in high-resolution structures to be problematic, atomic resolution structures are in general the most reliable structures available (Berkholz et al., 2008;Rupp, 2010). Hence, LLDF is not a reliable statistic for identifying ligands with poor fit to the electron-density map for high-resolution structures. In contrast, both RSCC and RSR tend to improve for higher resolution structures (Figs. 5b and 5c) as ligand electron density becomes more reliable.
A further problem with using LLDF as an 'outlier' measure occurs when the electron density of both the ligand and the surrounding residues is poor; an example is shown in Fig. 4(b). This can lead to a low value of LLDF in cases where it would be sensible for the ligand to be marked as an electron-density fit outlier. This phenomenon is caused by the fact that LLDF is an internal measure that expresses how much better or worse the ligand fit is compared with that of its polymeric neighbours. Table 1 shows that this situation is reasonably common, with around one in four ligands having a poor fit by the RSCC 'rule of thumb' being judged as not being outliers by LLDF.
Discussion and conclusions
The PDB is a treasure trove of data on the interactions between small-molecule ligands and macromolecules. The assessment of ligand geometry using Mogul in the VRs has increased awareness of the issues with ligand geometry, but further work is required to clearly present Mogul validation information. The reports also attempt to help with the assessment of electron density for bound molecules and the electron-density model fit quality by providing the LLDF, RSCC and RSR metrics. Our analysis shows that the LLDF metric has drawbacks and is not a reliable metric in several Visualization of two ligands from the PDB together with electron-density maps where LLDF values provide misleading indications. (a) Example of a false positive: the map for PDB entry 1kcc at atomic resolution (1.0 Å ; Shimizu et al., 2002) shows electron density for a well placed ligand GTR where each atom is individually resolved. The high RSCC value reflects the good fit. In contrast, the LLDF value is high so that the ligand is incorrectly marked as an electron-density fit outlier in the current VR. (b) Example of a false negative: the ligand FER in PDB entry 1kyz (Zubieta et al., 2002) has a poor fit to the electron density, resulting in large amounts of difference density. The LLDF value of 1.3 results in the ligand not being marked as an electron-density fit outlier in the current VR, whereas the low RSCC value suggests a problem. Distribution of (a) LLDF, (b) RSCC and (c) RSR for structures by data resolution for the set of ligands in Table 1. Box plots and whiskers are as in Fig. 1. scenarios: (i) for high-resolution structures when all the residues in a binding site have a very good fit to the density and similar numerical values for RSR, (ii) when the electrondensity fit for both the ligand and the surrounding residues is poor and (iii) when the ligand has only a small number of surrounding polymeric residues. In such cases, both false positives (good ligands listed as outliers) and false negatives (ligands of questionable quality not identified as outliers) may occur.
There is a clear need for the community to develop better and well tested measures so that they can be incorporated into the wwPDB validation pipeline in the future. The presence of difference electron density close to a ligand may be an indicator of subtle issues of ligand placement such as a chiral inversion or placement of a ring in a reversed orientation (Smart & Bricogne, 2015). Such difference density can be picked up by visual examination, but metrics that are sensitive to it, such as those provided by DDQ (van den Akker & Hol, 1999), EDSTATS (Tickle, 2012) or EDIAscorer (Meyder et al., 2017), need to be employed .
Ligands in low-resolution structures provide particular challenges for validation. As the resolution worsens, the quality of the electron-density map will necessarily deteriorate (Rupp, 2010). Ligand placement becomes increasingly ambiguous and it is important to take into account geometric considerations: at 3 Å resolution there is no information from the X-ray data to determine the pucker of a ring (Smart & Bricogne, 2015) and so it is sensible to make sure that the ring is modelled with a geometrically low-strain pucker. Water molecules can be crucial in mediating ligand-protein interactions but are unlikely to be observed at resolutions lower than 3 Å , although refinement exploiting information from higher resolution structures can help (Smart et al., 2012). It is important to note that even if a ligand fits the available electron density well, has good internal geometry and makes sensible interactions with the protein, it does not necessarily mean that the proposed binding mode is correct. How to convey such information to the users of structures in a meaningful and intuitive way is a challenge.
Another issue is how to treat partially ordered ligands where part of the ligand is well defined by the electron density but where another part cannot be defined or unambiguously modelled. At present, depositors take several approaches to modelling the ambiguous part of a ligand: not including the atoms in the model, modelling the atoms but setting the atomic occupancies to zero, or modelling the ligand with normal occupancies and letting the B values become very high during refinement. The VR handles these cases by applying normal geometric validation and density-fit validation to all of the atoms that are included in the model. The VR reports the number of zero-occupancy and alternative-conformation atoms in a ligand as well as the number of missing atoms. The LVW has made a recommendation that the PDBx/mmCIF dictionary item _atom_site.calc_flag be used to identify non-experimentally defined atoms instead of using the atom occupancy. This has advantages, particularly for H atoms included in the model to indicate the modelled charge stage and tautomerization of ligands.
The recent LVW and the second wwPDB X-ray VTF meeting have resulted in recommendations to improve the assessment of ligands and have suggested different metrics to use in the validation reports. These will be implemented in the wwPDB validation pipeline. | 6,206.2 | 2018-03-01T00:00:00.000 | [
"Chemistry"
] |
(In)homogeneous invariant compact convex sets of probability measures
It is proved that for any iterated function system of contractions on a complete metric space there exists an invariant compact convex sets of probability measures of compact support on this space. A similar result is proved for the inhomogeneous compact convex sets of probability measures of compact support. Анотація. Математичні підвалини теорії фракталів запропонував Дж. Гатчінсон у 80-х роках минулого століття. Зокрема, він означив поняття атрактора (або інваріантного об’єкта) для ітерованої системи стискуючих відображень (скорочено IFS) на повному метричному просторі і довів існування таких атракторів у гіперпросторі (просторові непорожніх компактних підмножин) та просторі ймовірнісних мір з компактними носіями на повному метричному просторі. Доведення Гатчінсона використовують принцип стискуючих відображень і, зокрема, потребують відповідної метризації простору ймовірнісних мір. Незабаром аналогічні результати було отримано і для неоднорідних атракторів (тобто атракторів з приєднаними ущільнюючими множинами), які є природними узагальненнями інваріантних множин та інваріантних мір. У цій статті ми запроваджуємо поняття інваріантного об’єкта для IFS у просторі компактних опуклих множин ймовірнісних мір з компактними носіями у повному метричному просторі. Такі компактні опуклі множини мір мають численні застосування у теорії очікуваної корисності. На відміну від гіперпростору компактних опуклих підмножин повного метричного простору, інваріантні об’єкти в якому виглядають регулярними, атрактори IFS у просторі компактних опуклих множин мір зберігають іррегулярність, притаманну фрактальним множинам. Одним з основних результатів є теорема існування та єдиності інваріантної компактної опуклої множини ймовірнісних мір з компактними The authors are indebted to the referee for his/her valuable comments. 2010 Mathematics Subject Classification: 37E25, 54E35 UDC 515.12
INTRODUCTION
Hutchinson [7] proved the existence of invariant sets and invariant probability measures for the iterated function systems in the complete metric spaces. The structure of these two proofs is similar and it exploits, in particular, the functoriality of the constructions involved (i.e., the hyperspaces and spaces of probability measures) as well as existence of special metrizations. This led to several generalizations of the existence results, in particular, to the cases of inclusion hyperspaces (i.e., two-valued measures) [11] and idempotent measures on ultrametric spaces [9].
Another approach is applied in [10] and it is proved therein that there exists an invariant idempotent measure (see [18] for topological aspects of the theory of idempotent measures) for an iterated function system on a complete metric space.
Recently, a related notion of inhomogeneous invariant set and measure was introduced in [15]. The properties of these sets and measures were studied in various publications (see, e.g., [5,1,13]).
The compact convex sets of probability measures are used in the maxmin expected utility (MEU) theory [6].
2. PRELIMINARIES 2.1. Hyperspaces. Let exp X denote the set of all nonempty compact subsets of a Tychonov space X. A base of the Vietoris topology on exp X consists of the sets of the form where n P N and U 1 , . . . , U n are open sets in X. The obtained space is called the hyperspace of X.
Actually, exp is a functor in the category of Tychonov spaces and continuous maps. Given a map f : X Ñ Y , the map exp f : exp X Ñ exp Y acts as follows: exp f (A) = f (A), A P exp X.
If (X, d) is a metric space, then the Vietoris topology on exp X is induced by the Hausdorff metric d H , where O r (C) stands for the open r-neighborhood of a subset C.
By u X : exp exp X = exp 2 X Ñ exp X we denote the union map. This map is known to be well defined and, in the case of metric space, nonexpanding.
2.2. Kantorovich metric. By P (X) we denote the space of probability measures on a compact Hausdorff space X. We regard the set of probability measures on X also as a set of normed linear functionals on the Banach space C(X) of continuous real-valued functions on X. Given µ P P (X), we let µ(φ) = ş X φdµ, φ P C(X). The set P (X) is endowed with the weak* topology. A base of this topology is comprised by the sets of the form Let (X, d) be a compact metric space. By 1-LIP(X) we denote the set of all nonexpanding functions on X, i.e. functions φ : X Ñ R satisfying for all x, y P X. The Kantorovich metric d K on the space of probability measures P (X) is defined as follows: Every continuous map f : X Ñ Y between compact spaces induces the map P (f ) : P (X) Ñ P (Y ) defined by P (f )(µ)(A) = µ(f´1(A)) for any µ P P (X) and any measurable subset A Ă Y . In terms of functionals, P (f )(µ)(φ) = µ(φf ) for all µ P P (X) and φ P C(Y ).
Actually, P is a functor in the category Comp of compact Hausdorff spaces.
There is a procedure of extensions of functors from the category Comp to the category of Tychonov spaces [4]. In the case of the functor P , this procedure gives the space of probability measures of compact support. Recall that the support of µ P P (X) is the minimal closed set A Ă X such that µ(XzA) = 0. Alternatively, the support of µ is the minimal closed set A Ă X with the property that, for all φ, ψ P C(X), φ| A = ψ| A implies µ(φ) = µ(ψ).
Convex sets of probability measures.
Let X be a compact Hausdorff space. Denote by ccP(X) the hyperspace of closed convex subsets of the space P (X). Given a continuous map f : X Ñ Y between compact spaces, we define the map ccP(f ) : ccP(X) Ñ ccP(Y ) as follows: It is known that ccP is a functor on the category Comp (see, e.g. [16]). Given A P ccP(X), we say that the set Ytsupp(µ) | µ P Au is the support of A (denoted supp(A)). (Hereafter, for any set Y in a topological space, we denote by Y its closure). Again, applying construction from [4] we extend the functor ccP onto the category of Tychonov spaces. We preserve the notation ccP for this extension.
For any metrizable space X, the space ccP(X) is exactly the hyperspace of closed convex subsets A of P (X) such that supp(A) is compact. Now, assume that X is compact and define a map as follows, see [12]. First, for any compact convex subset K of a locally convex space, denote by b K : P (K) Ñ K the barycenter map. Since P (X) is a subset of the dual space C(X) 1 endowed with the weak* topology, the hyperspace ccP(X) can be regarded as a compact convex subset of a locally convex space [14] and therefore one can consider the barycenter map b ccP(X) : P (ccP(X)) Ñ ccP(X).
Finally, define θ X by the formula Note that the continuity of θ X is a consequence of the continuity of the barycenter map [3, Chapt. III, §3, Corollary of Proposition 9] and the union map [17,Proposition 5.2].
In the case when B is a compact convex subset of the convex hull of a set tM 1 , . . . , M n u, where M 1 , . . . , M n P P (ccP(X)), we have Now, let (X, d) be a metric space. We endow ccP(X) with the Hausdorff metric induced by the Kantorovich metric on P (X). By [8, Proposition 3.2], the map θ X : ccP 2 (X) Ñ ccP(X) is nonexpanding.
Let c¨d(x, y) for all x, y P X. As mentioned above, the 1-Lipschitz maps are also called nonexpanding.
RESULTS
Let (X, d) be a complete metric space and tf 1 , f 2 , . . . , f n u be a finite family of contractions on X (that is, an iterated function system, IFS). Let us consider the discrete topology on the set t1, 2, . . . , nu. Then the space P (t1, 2, . . . , nu) can be regarded as the standard (n´1)-dimensional simplex ∆ n´1 in R n , For B P ccP(t1, 2, . . . , nu) define the map Φ B : ccP(X) Ñ ccP(X) as follows. Let A P ccP(X) and g A : t1, 2, . . . , nu Ñ ccP(X) be the map sending i to ccP(f i )(A). Then we set Φ B (A) = θ X (ccP(g A )(B)).
We say that A P ccP(X) is an invariant set of probability measures for tf 1 , f 2 , . . . , f n u and B whenever A = Φ B (A). Proof. We first consider the case of compact space X. Note that the map Φ B is a contraction. This follows from the fact that the functor ccP preserves c-maps and the map θ X is nonexpanding. By the Banach Contraction Principle, there exists a unique A P ccP(X) such that A = Φ B (A).
In the case of noncompact space X, consider the map Ψ : exp X Ñ exp X defined as follows: is compact for any D P exp X. Now, consider an arbitrary C P ccP(X) and let K = supp(C). Then the the above arguments show that there exists an invariant closed convex set of probability measures A 0 P ccP(Y ) Ă ccP(X). □ Suppose that we are given an IFS tf 1 , f 2 , . . . , f n u on X, B is an element of ccP (t0, 1, . . . , nu), and C P ccP(X). For any A P ccP(X) let g 1 A,C : t0, 1, 2, . . . , nu Ñ ccP(X) be defined by the formulas: . Then the set A satisfying A = Φ 1 (A) is called an inhomogeneous invariant convex set of probability measures. Proof. Let B = tµu P ccP(t1, 2, . . . , nu), for some µ P P (t1, 2, . . . , nu), We start with A 0 = tν 0 u P ccP(X). Then clearly and this easily implies that the invariant set of probability measures A 8 in this case is tν 8 u, where ν 8 is the invariant measure in the sense of [7] corresponding to the IFS tf 1 , . . . , f n u and µ = A similar statement can be formulated and proved in the inhomogeneous case. Therefore our considerations are in some sense extensions of known results from [7] and [15] on probability measures.
FUNCTIONAL APPROACH
Let X be a compact Hausdorff space. Every A P ccP(X) determines a functional F A : C(X) Ñ R defined as follows: Proof. Denote by Without loss of generality one may assume that there exists µ P AzB. Since B is compact, there are φ 1 , . . . , φ k P C(X), for some k P N, such that Since p(B) is compact and convex, it follows from the hyperplane separation theorem that there exists a linear functional l : that sup νPB l(p(ν)) ă l(p(µ)).
Then there exists (l 1 , . . . , l k ) P R k such that Let τ˚be the weak* topology on the set F = tF A | A P ccP(X)}, i.e., the topology induced from the product topology on R C(X) . A base of this topology is comprised by the sets of the form where A 0 P ccP(X), φ 1 , . . . , φ n P C(X), ε ą 0.
If maxtµ(φ 0 ) | µ P Au = µ 0 (φ) for some µ 0 P A, then there exists i P t1, . . . , nu such that µ 0 P Oxµ i ; φ 0 ; εy. Then One can similarly prove that Proof. Due to compactness of X, the space ccP(X) is compact, and the assertion follows from the hausdorffness of F and Proposition 4.1. □ Now the mentioned functional representation A Þ Ñ F A of compact convex sets of probability measures allows us to obtain a purely functional proof of the main results of this paper in the spirit of [10, Theorem 1].
REMARKS
In the case when X = R n and the maps f 1 , . . . , f n are similarities, one can find many pictures of invariant and inhomogeneous sets in the literature.
The invariant probability measures can be visualized in a gray scale by using the random iteration algorithm (see [2, Chapt. IX] for details). An open problem is that of visualization of invariant convex sets of probability measures. | 2,986.2 | 2020-05-06T00:00:00.000 | [
"Computer Science"
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Pharmacological Effects of a Novel Bradykinin-Related Peptide (RR-18) from the Skin Secretion of the Hejiang Frog (Ordorrana hejiangensis) on Smooth Muscle
Bradykinin (BK) and bradykinin-related peptides (BRPs), which were identified from a diversity of amphibian skin secretions, exerted contractile and relaxing effects on non-vascular and vascular smooth muscle, respectively. Here, we report a novel bradykinin-related peptide with a molecular mass of 1890.2 Da, RVAGPDKPARISGLSPLR, which was isolated and identified from Ordorrana hejiangensis skin secretions, followed by a C-terminal extension sequence VAPQIV. The biosynthetic precursor-encoding cDNA was cloned by the “shotgun” cloning method, and the novel RR-18 was identified and structurally confirmed by high-performance liquid chromatography (HPLC) and tandem mass spectrometry (MS/MS). Subsequently, the myotropic activity of the synthetic replicate of RR-18 was investigated on the rat bladder, uterus, tail artery and ileum smooth muscle. The peptide was named RR-18 in accordance (R = N-terminal arginine, R = C-terminal arginine, 18 = number of residues). In this study, the synthetic replicates of RR-18 showed no agonist/antagonism of BK-induced rat bladder and uterus smooth muscle contraction. However, it displayed an antagonism of bradykinin-induced rat ileum contraction and arterial smooth muscle relaxation. The EC50 values of BK for ileum and artery, were 214.7 nM and 18.3 nM, respectively. When the tissue was pretreated with the novel peptide, RR-18, at the maximally effective concentration of bradykinin (1 × 10−6 M), bradykinin-induced contraction of the ileum and relaxation of the arterial smooth muscle was reduced by 50–60% and 30–40%, respectively. In conclusion, RR-18 represents novel bradykinin antagonising peptide from amphibian skin secretions. It may provide new insight into possible treatment options for chronic pain and chronic inflammation.
Introduction
Bradykinin nonapeptide, RPPGFSPFR, was first reported from Rana temperaria frog skin in the 1960s [1]. Subsequently, the bioactive components in the skin secretion of amphibians, especially biologically active peptides, such as antimicrobial peptides and pharmacological peptides, have been extensively studied during the past several decades [2,3]. Bradykinin (BK) and bradykinin-related peptides (BRPs), representing one of the major pharmacological peptides, have been widely isolated and identified in skin secretions of 5 families of amphibians, Leiopelmatidae, Ascaphidae, Bombinatoridae, Hylidae, and Ranidae [4][5][6]. BK is regulated by the kallikrein-kinin system (KKS) in mammals [7]; however, the frog skin BK/BRPs are not the products of enzyme catalysis by the KKS. The products were secreted from amphibian skin glands as immune defence peptides. Interestingly, extensive reports on the derivation of BRPs revealed that several amphibian skin BRPs were found in their putative predators, such as birds and snakes, suggesting that BRPs are molecular evolutionary adaptations to species-specific predators.
Recently, more than 100 amphibian BRPs have been reported [8]. However, few Auran species have been reported to secrete BRPs. Additionally, unlike antimicrobial peptides which have been studied extensively, just very few BRPs have been identified in amphibian skin. Apart from that, there is also very little information about BRPs in Ranidae frogs belonging to the Ordorrana hejiangensis (O. hejiangensis). Furthermore, extensive studies demonstrated that most of the BRPs are BK receptors agonist with a dose-dependent contractile activity on non-vascular smooth muscle. Still, some are antagonists in inhibiting contractility of BK on vascular smooth muscle. For instance, the RVA-Thr6-BK showed vasorelaxant activity on rat arterial smooth muscle but exerted contractile activity on bladder, uterus, and ileum smooth muscle [9].
Usually, BK exerts its function in combination with two G protein-coupled receptors families, namely B1 and B2 receptors [10]. B1 receptors are upregulated during tissue damage by pro-inflammatory cytokines and the oxidative stress through the nuclear factor kappa B (NF-κB) pathway [11]. However, B2 receptors were widely distributed in multiple tissues. Recently, B1 and B2 receptors were thought to be involved in many diseases, such as cancer, chronic pain, and diabetes [12][13][14]. For instance, a previous report demonstrated that B1 and B2 receptors were significantly expressed in colorectal cancer cells [15]. Therefore, the development of B1 and B2 receptor antagonists is of great significance in pharmacology or clinical applications.
Here, we report a novel BRP, RR-18, which was first identified in the skin secretion of Hejiang Frog, O. hejiangensis, followed by a C-terminal extension sequence VAPQIV. Pharmacological assays revealed that RR-18 displayed an antagonism of bradykinin-induced contraction of the rat ileum and relaxation of arterial smooth muscle. Furthermore, our results indicated that RR-18 exerted its BK inhibition activity by mainly targeting B2 receptors. It has been revealed that activation of BK receptors can induce several downstream signalling pathways involved in inflammatory responses [16] suggesting the unique property of RR-18 may be used in the potential treatment of chronic pain and chronic inflammation.
Skin Secretion Acquisition
The specimens of the O. hejiangensis were captured, settled and skin secretion was acquired from the dorsal skin as described previously [17]. All the procedures were carried out according to the guidelines in the UK Animal (Scientific Procedures) Act 1986, project license PPL 2694, issued by the Department of Health, Social Services and Public Safety, Northern Ireland. Procedures had been vetted by the Institutional Animal Care and Use Committees (IACUC) of Queen's University Belfast, and approved on 1 March 2011.
"Shotgun" Cloning of cDNA Encoding RR-18 Biosynthetic Precursor from Skin Secretion
The cDNA encoding RR-18 biosynthetic precursor was evaluated by the "shotgun" cloning method as previously described [17]. A Nested Universal Primer A (NUP A) (Clontech, Palo Alto, CA, USA) and a sense degenerated primer (5 -GAWYYAYYHRAGCCYAAADATGTTCA-3 ; W = A + T, Y = C + T, H = A + C + T, R = A + G, D = A + G + T) were subjected to the 3 -RACE reaction, from which the products were cloned and subsequently sequenced.
Isolation and Structural Characterisation of RR-18 from Skin Secretion
The isolation and structural characterisation of RR-18 from the lyophilised O. hejiangensis skin secretion was carried out as previously described [17]. In brief, five mg of lyophilised skin secretion was dissolved in trifluoroacetic acid (TFA) ( The fractions were monitored at 214 nm at a flow rate of 1 mL/min. The molecular masses of peptides in the fractions were analysed by matrix-assisted laser desorption/ionisation, time-of-flight mass spectrometry (MALDI-TOF MS) (Thermo Fisher Scientific, San Francisco, CA, USA) using alpha-cyano-4-hydroxycinnamic acid (α-CHCA) (Sigma-Aldrich, Dorset, UK) as the matrix and the putative primary structure of RR-18 was analysed using Sequest algorithm against the self-defined Fasta database in proteome Discoverer 1.0 software (Thermo Fisher Scientific, San Jose, CA, USA).
Solid-Phase Peptide Synthesis of Peptides
RR-18 (RVAGPDKPARISGLSPLR) and BK were synthesised using a Tribute peptide synthesiser (Protein Technologies, Tucson, AZ, USA) according to our previous study [17]. The purity of the peptides (>95%) was determined by RP-HPLC (Cecil, Cambridge, UK). The peptides were further confirmed using an LCQ-Fleet electrospray ion-trap mass spectrometer (Thermo Fisher Scientific, San Francisco, CA, USA).
Myotropic Activity Evaluation on Smooth Muscles
The fractions were rotary dried and then performed to screen the myotropic activity on smooth muscle. The synthetic replicated of RR-18 was used to determine the myotropic activity on rat smooth muscle. Female Wistar rats (250-300 g) were euthanised by CO 2 asphyxiation based on institutional animal experimentation ethics and the UK animal research guidelines. The endothelium of rat tail artery was removed and the proximal rat tail artery ring was dissected about 2 mm in width and connected to a triangular hook. An approximately 0.5 cm-length ring of ileum was cut. After that, the tissues of rat tail artery, bladder, uterus and ileum were mounted into an organ bath (2 mL) containing a Krebs solution (118 mM NaCl, 1.15 mM NaH 2 PO 4 , 2.5 mM CaCl 2 , 25 mM NaHCO 3 , 4.7 mM KCl, 1.1 mM MgCl 2 , and 5.6 mM glucose). All chemicals were purchased from Sigma-Aldrich (Dorset, UK). The bladder, uterus, artery, and ileum tissues were stretched, maintaining the normal physiological tension of 0.75 g, 0.5 g, 0.5 g, and 0.5 g, respectively. Arteries were pre-contracted with phenylephrine (1 × 10 −5 M) for 10~20 min to achieve constriction plateaux. A range concentration of synthetic peptides (from 10 −11 -10 −5 M) was prepared in Krebs solution. Tissues were incubated with peptides in a cumulative manner for at least 5 min before reaching the equilibrium for 20 min. RR-18 (10 −6 M) was applied for 10 min prior to different concentration of BK (10 −11 -10 −5 M). The myotropic effects of RR-18 on smooth muscles were recorded using a tension sensor with a PowerLab System (AD Instruments Pty Ltd., Oxford, UK).
Statistical Analysis
Data was analysed using Prism 6 (GraphPad Software, La Jolla, CA, USA). The mean and standard error of responses were analysed by Student's T-test and the dose-response curves were constructed using a best-fit algorithm. EC 50 values were calculated from the normalised curves.
Molecular Cloning of RR-18 Precursor-Encoding cDNAs
The nucleotide and translated open reading frame amino acid sequences of the novel RR-18 precursor encoding cDNAs was cloned from Hejiang Odorous Frog, O. hejiangensis, skin secretions are shown in Figure 1. Specifically, the precursor encoding cDNA of the RR-18 contained 67 amino acids including a putative signal peptide domain, an acidic amino acid residue-rich (spacer) domain (21 amino acids), an 18 amino acids length of putative mature peptide and a C-terminal extension peptide domain (-VAPQIV-) ( Figure 1). The encoding RR-18 precursor has been deposited in the GenBank Database (accession code: MT522014). Data was analysed using Prism 6 (GraphPad Software, La Jolla, CA, USA). The mean and standard error of responses were analysed by Student's T-test and the dose-response curves were constructed using a best-fit algorithm. EC50 values were calculated from the normalised curves.
Molecular Cloning of RR-18 Precursor-Encoding cDNAs
The nucleotide and translated open reading frame amino acid sequences of the novel RR-18 precursor encoding cDNAs was cloned from Hejiang Odorous Frog, O. hejiangensis, skin secretions are shown in Figure 1. Specifically, the precursor encoding cDNA of the RR-18 contained 67 amino acids including a putative signal peptide domain, an acidic amino acid residue-rich (spacer) domain (21 amino acids), an 18 amino acids length of putative mature peptide and a C-terminal extension peptide domain (-VAPQIV-) ( Figure 1). The encoding RR-18 precursor has been deposited in the GenBank Database (accession code: MT522014).
Isolation and Identification and Structural Characterisation of RR-18
Reverse-phase HPLC (RP-HPLC) chromatogram of the O. hejiangensis skin secretion is shown in Figure 2. Subsequently, the primary structure, RVAGPDKPARISGLSPLR, was thus unequivocally determined by tandem mass spectrometry (MS/MS) fragmentation sequencing ( Table 1). The RP-HPLC chromatogram showed that the purity of RR-18 was above 95% and the molecular mass of RR
Isolation and Identification and Structural Characterisation of RR-18
Reverse-phase HPLC (RP-HPLC) chromatogram of the O. hejiangensis skin secretion is shown in Figure 2. Subsequently, the primary structure, RVAGPDKPARISGLSPLR, was thus unequivocally determined by tandem mass spectrometry (MS/MS) fragmentation sequencing ( Table 1). The RP-HPLC chromatogram showed that the purity of RR-18 was above 95% and the molecular mass of RR-18 was detected by Matrix-Assisted Laser Desorption/Ionization-Time of Flight (MALDI-TOF) mass spectrum ( Figure 3). A single peptide with a mass of 1890.2 Da (Figure 4), which was resolved in HPLC fractions of skin secretion displayed the bradykinin inhibitory activity on smooth muscle. Table1. Predicted tandem mass spectrometry (MS/MS) fragmentation b-and y-ion series ion series (singly-, doubly-, and triply-charged) of RR-18. Observed ions were shown in bold italic typeface.
Bioinformatic Analysis of Novel RR-18
BLAST analysis of RR-18 was performed using the National Center for Biotechnological Information (NCBI) on line portal, and demonstrated that the full length open reading frame of RR-18 displayed relative high amino acid sequence identity with the wuyiensisin-1 and other typical bradykinin antagonist (RVA-T6-BK and RAP-L1, T6-BK) precursor sequences. Specifically, the similarity between the primary sequence of RR-18 and wuyiensisin-1 was over 94%. Additionally, the primary structure of RR-18 showed high similarity with some other typical bradykinin antagonists. The highly-conserved amino acids are Arg 1 , Pro 5 , Pro 8 , Gly 13 , Pro 16 , and Pro 18 ( Figure 5).
Pharmacological Effects of RR-18 on Smooth Muscle
The purified RR-18 and BK were employed in the evaluation of myotropic activity on rat uterus, bladder, ileum and tail artery. Specifically, RR-18 produced no distinct myotropic action on
Bioinformatic Analysis of Novel RR-18
BLAST analysis of RR-18 was performed using the National Center for Biotechnological Information (NCBI) on line portal, and demonstrated that the full length open reading frame of RR-18 displayed relative high amino acid sequence identity with the wuyiensisin-1 and other typical bradykinin antagonist (RVA-T6-BK and RAP-L1, T6-BK) precursor sequences. Specifically, the similarity between the primary sequence of RR-18 and wuyiensisin-1 was over 94%. Additionally, the primary structure of RR-18 showed high similarity with some other typical bradykinin antagonists. The highly-conserved amino acids are Arg 1 , Pro 5 , Pro 8 , Gly 13 , Pro 16 , and Pro 18 ( Figure 5).
Bioinformatic Analysis of Novel RR-18
BLAST analysis of RR-18 was performed using the National Center for Biotechnological Information (NCBI) on line portal, and demonstrated that the full length open reading frame of RR-18 displayed relative high amino acid sequence identity with the wuyiensisin-1 and other typical bradykinin antagonist (RVA-T6-BK and RAP-L1, T6-BK) precursor sequences. Specifically, the similarity between the primary sequence of RR-18 and wuyiensisin-1 was over 94%. Additionally, the primary structure of RR-18 showed high similarity with some other typical bradykinin antagonists. The highly-conserved amino acids are Arg 1 , Pro 5 , Pro 8 , Gly 13 , Pro 16 , and Pro 18 ( Figure 5).
Pharmacological Effects of RR-18 on Smooth Muscle
The purified RR-18 and BK were employed in the evaluation of myotropic activity on rat uterus, bladder, ileum and tail artery. Specifically, RR-18 produced no distinct myotropic action on
Pharmacological Effects of RR-18 on Smooth Muscle
The purified RR-18 and BK were employed in the evaluation of myotropic activity on rat uterus, bladder, ileum and tail artery. Specifically, RR-18 produced no distinct myotropic action on rat bladder, ileum, uterus and tail artery in its own right. Additionally, RR-18 showed no antagonism of BK-induced rat bladder and uterus smooth muscle contraction. BK produced a dose-response curve in affecting rat ileum and rat tail artery. However, RR-18 mediated a potent inhibition of bradykinin-induced contraction and relaxation of rat ileum and tail artery smooth muscle ( Figure 6). Specifically, the EC 50 values of BK on rat ileum and tail arteries were 214.7 nM and 18.3 nM, respectively. However, when the tissue was pretreated with the novel peptide, RR-18, at the maximally effective concentration of bradykinin (1 × 10 −6 M), BK-induced contraction of the ileum and relaxation of the arterial smooth muscle was abolished by 50-60% and 30-40%, respectively. Additionally, the EC 50 values of BK+RR-18 (10 −6 M) on rat ileum and tail arteries were 1.54 µM and 79.83 nM, respectively. Moreover, RR-18 represented a typical BK competitive inhibitor and non-competitive inhibitor on rat ileum and tail artery smooth muscle, respectively.
Biomedicines 2020 , 8, 225 8 of 12 rat bladder, ileum, uterus and tail artery in its own right. Additionally, RR-18 showed no antagonism of BK-induced rat bladder and uterus smooth muscle contraction. BK produced a dose-response curve in affecting rat ileum and rat tail artery. However, RR-18 mediated a potent inhibition of bradykinin-induced contraction and relaxation of rat ileum and tail artery smooth muscle ( Figure 6). Specifically, the EC50 values of BK on rat ileum and tail arteries were 214.7 nM and 18.3 nM, respectively. However, when the tissue was pretreated with the novel peptide, RR-18, at the maximally effective concentration of bradykinin (1 × 10 −6 M), BK-induced contraction of the ileum and relaxation of the arterial smooth muscle was abolished by 50-60% and 30-40%, respectively. Additionally, the EC50 values of BK+RR-18 (10 −6 M) on rat ileum and tail arteries were 1.54 µM and 79.83 nM, respectively. Moreover, RR-18 represented a typical BK competitive inhibitor and non-competitive inhibitor on rat ileum and tail artery smooth muscle, respectively.
Discussion
Amphibian skin secretions contain a variety of active substances including peptides, proteins, steroids and alkaloids. In particular, peptides, such as bombesin and bradykinin, act as myotropic peptides and are critical to protecting amphibians from predators [8,18]. At the same time, BK and BRPs are associated with many diseases, such as chronic pain and cancer [13,19]. Recently, very few peptides from the Hejiang frog have been reported [9,20,21].
In this study, a novel octade-peptide, RR-18, was identified by de novo sequencing and isolated
Discussion
Amphibian skin secretions contain a variety of active substances including peptides, proteins, steroids and alkaloids. In particular, peptides, such as bombesin and bradykinin, act as myotropic peptides and are critical to protecting amphibians from predators [8,18]. At the same time, BK and BRPs are associated with many diseases, such as chronic pain and cancer [13,19]. Recently, very few peptides from the Hejiang frog have been reported [9,20,21].
In this study, a novel octade-peptide, RR-18, was identified by de novo sequencing and isolated from the skin secretion of the O. hejiangensis. Obviously, O. hejiangensis showed high homology compared with the precursors of Amolops wuyiensis. Additionally, the precursor encoding cDNA library of RR-18 was further determined. Interestingly, sequence analysis exhibited high similarity (up to 94.4%) between RR-18 and wuyiensisin-1 (RVAGPDEPARISGLSPLR-OH; AIU99945.1) which was identified from the Sanchiang sucker frog (Amolops wuyiensis). It was noted that the O. hejiangensis is a unique amphibian species in China, mainly distributed in the Sichuan, Guangxi, and Chongqing areas of China. At the same time, the Amolops wuyiensis are only found in the Fujian, Zhejiang, and Anhui areas of China. This may explain why the same group of peptides could be found in different species in similar regions [22], and this may be of benefit to the evolution of amphibians. Thus, the Hejiang frog and the Sanchiang sucker frog, at least with respect to their skin BRPs, appear to be more closely related to one another than to other ranid species that occupy similar geographical distributions [5]. The residue was substituted to a lysine (K) residue at position 7 from the N-terminal of the peptide.
Additionally, it is significant that RR-18 has a similar structure to that of BK, although its biological activity has not been determined. Besides, compared with another BRP, RVA-Thr6-BK, which was identified in the skin secretion of O. hejiangensis, as well [9], the differences between RR-18 and RVA-Thr6-BK are mainly reflected in the N-terminal region. Specifically, an R residue was submitted to G at position 4 from N-terminal. Interestingly, the commutation of a single amino acid residue in wasp kinins can result in significant differences in the action of the peptide. The factors that distinguished the encoded proprepeptides of RR-18 in this family are unclear. This phenomenon may be due to differences in species, regions and the living environments of frogs [5].
Unlike the majority of previously cloned ranid frog skin BRP precursors, which always encode multiple peptides [5], RR-18 only contained a single copy in the proprepeptides. Additionally, the propeptide convertase cleavage site(s) of RR-18 was found to be unusual when compared with other kininogens. Firstly, an acidic amino acid-rich spacer peptide domain of RR-18 has no typical prepropeptide convertase processing site (-KR-). Secondly, the N-processing sites of mature kinin are always RR and KR. However, the N-processing sites of RR-18 are KK and an R. The C-terminus of the mature kinin is flanked by the sequence -VAPQIV-that is cleaved from the maturing kinin by a post arginyl cleavage. These phenomena may be attributed to evolution amongst amphibians [5].
Many vasodilators exerted relax activity on rat artery smooth muscle, which is mediated by the endothelium and the release of nitric oxide (NO) [23]. However, previous studies demonstrated that arterial smooth muscle preparations which were pretreated with specific endothelium nitric oxide synthase (eNOS) inhibitor failed to cause significant effects on the dose-responsive relaxation of vasorelaxant indicating that BRPs exert the relaxing activity on rat artery smooth muscle is unlikely to involve the action of NO [24,25]. Our data showed that RR-18 displayed an antagonism of bradykinin-induced rat ileum contraction and arterial smooth muscle relaxation, which is consistent with previous studies, in that Phe at the penultimate position of BRP is the crucial site for activating BK receptors. The Phe at the penultimate position of BRP substituted with Leu could induce an antagonistic activity [26]. Interestingly, RR-18 represented a BK competitive inhibitor and non-competitive inhibitor on rat ileum and tail artery smooth muscle. Firstly, the EC 50 values of BK and BK+RR-18 in rat tail artery smooth muscle were virtually identical. Secondly, the Emax value of BK+RR-18 is lower to that of BK. However, the Emax values of BK and BK + RR-18 in rat ileum were overlapping, suggesting BK occupied receptor in ileum when the concentration of BK is increasing. Henceforth, RR-18 was overcome by BK in rat ileum. Apart from these, in comparison with original BK, the primary structure of RR-18 displayed multiple segment insertion sites, like -VAG-, -DE-, and -ARIS-, that were inserted between RP, PP, and PG, respectively. Due to RR-18 having exerted different BK antagonism on rat ileum and tail artery, we speculated that the changes of BRPs structure caused various kinds of ligand receptor binding pathways, which affected the pharmacological activity of BRPs [27]. Additionally, a previous study demonstrated that BK exerted its activity by regulating B1 and B2 receptors, especially mainly regulated by B2 receptor [24]. Moreover, RR-18 showed high similarity to some B2 receptor antagonists like RVALPPGFTPLR, QIPGLGPLR and RVA-Thr6-BK [9,24,28], henceforth, we speculated that RR-18 exerted its BK inhibition activity by mainly targeting B2 receptors. Nevertheless, further studies are required to determine whether B1 receptor interaction could explain the competition/non-competition features of RR-18 on ileum and tail artery. Previous reports revealed that Arg1, Pro2, Gly4, Phe5, Pro7, Phe8 and Arg9 are key residues for the biological activity of BK [29]. In this study, both Phe5 and Phe8 were substituted to leucine, which may improve/reduce the affinity between the peptides and receptors or even change an agonist to antagonist [30].
Taken together, a novel BRP, which contains 18 amino acids, was first isolated and identified from O. hejiangensis. The cDNA-encoded biosynthetic precursor of RR-18 showed high similarity with a BRP peptide (wuyiensisin-1) which was identified from Amolops. Our study demonstrated that RR-18 displayed competitive and non-competitive inhibition of BK on rat ileum and rat tail artery smooth muscle, respectively. Furthermore, RR-18 showed BK antagonist activity by mainly activating the B2 receptor. There is compelling evidence that BK is involved in the development of many diseases, such as pain and hyperalgesia [31,32]. Meanwhile, more recently, it has been suggested that BK B2 receptors were upregulated after a traumatic brain injury (TBI) and the inflammatory response was significantly reduced after treatment with a bradykinin B2 receptor inhibitor [33]. Hence, RR-18, as a BK B2 receptor antagonist, may have the potential for developing new drugs for chronic pain and chronic inflammation. Furthermore, the structural diversity of BRPs and its related BK inhibitory activity suggested that anuran is a rich source for the study of the structure-activity relationships between BRPs. Moreover, in addition to canonical research on the fossil record and morphological characteristics, with the in-depth study of molecular techniques and the precursor encoding cDNA sequencing of orthologous genes, it may give us a new understanding of the scope of evolution of amphibians. | 5,422.2 | 2020-07-01T00:00:00.000 | [
"Medicine",
"Biology"
] |
Study on the Influence and Optimization of the Venturi Effect on the Natural Ventilation of Buildings in the Xichang Area
: Natural ventilation is a way to reduce the energy consumption of building operations and improve the indoor living environment comfort. The venturi cap is designed with a roof, grille and wind deflector to intensify the natural ventilation of buildings. The structural parameters of the venturi cap were designed using an orthogonal design. Fluid analysis software was used for nu ‐ merical simulation, and variance analysis was used to study the importance of seven influence fac ‐ tors: the width of the roof opening, the roof slope, the height of the wind deflector, the horizontal width of the wind deflector, the angle of the wind deflector, the angle of the grille, and the spacing of the grille slices. The results show that the most significant influencing factor is the width of the roof opening, while significant influence factors include the angle of the grille and the horizontal width of the wind deflector. Additionally, the optimum parameter combination for ventilation per ‐ formance at the research level was put forward, with the proposed combination achieving a volume flow rate of 5.507 m 3 /s. The average temperature of the horizontal plane at a height of 1.2 m above the ground was 3.002 K lower than that without a venturi cap, which provides a reference for the optimization of indoor ventilation design in buildings in the Xichang area.
The Necessity of Natural Ventilation
The construction industry has been identified as one of the most energy-intensive industries, accounting for about 42% of global energy consumption [1].The total energy consumption of residential buildings accounts for 18% of the energy consumption in the construction industry, and is growing at a rate of 1.5% each year [2].Natural ventilation offers great potential with respect to the energy efficiency of buildings.One of the main measures employed to achieve indoor comfort while mitigating building energy consumption is the strengthening of natural indoor ventilation [3].The results reported in [4] suggest that the amount of energy saved using other ventilation modes is not high, representing only 0.03% of common natural ventilation.That is to say, the application of technology to enhance the efficiency of natural ventilation in buildings without an external environment is a way of saving energy in buildings [5].In the construction industry, building ventilation is one of the most important parameters to be considered in order to maintain a comfortable indoor environment and to provide better indoor air quality [6].According to research reported by Canada's Environmental Defense Organization, 68% of human diseases are caused by indoor air pollution [7].The best way to improve indoor air quality is to allow enough fresh air into the building and ensure that there is a reasonable air distribution inside the building [8].In addition, the outbreaks of sick building syndrome (SBS) in developed countries in the 1970s and 1980s, severe acute respiratory syndrome coronavirus (SARS) in Asia in 2003, and Corona Virus Disease 2019 (COVID- 19) that has been sweeping the world since late 2019 have led people to think deeply about the safety and health of their offices and living spaces, with suitable temperature and humidity being achieved in enclosed spaces by mechanical means in modern architecture.
The total wind energy resource reserves of China at the height of 10 m above the ground are about 4.35 billion KW, which ranks first in the world [9].Considering the abundance of wind energy resources, land use types, and landforms, and the variability of wind energy, the regions with the most abundant sources of wind energy are the Tibet Plateau, the Hexi Corridor, and Inner Mongolia [10].Xichang is located on the Anning River Plain of the Western Sichuan Plateau, which has the best wind resources in Sichuan Province.The buildings in Xichang pay special attention to the ventilation of the building, while little attention is paid to the performance of thermal insulation, which has little impact on the residents' living situation [11].Using a venturi cap to optimize ventilation reduces energy consumption and improves the ventilation conditions in the Xichang area, meeting the needs of residents on an environmentally sustainable basis.
Venturi Cap
The venturi effect is an application of natural ventilation that can be employed in both horizontal and vertical directions.Vertical applications (Figure 1) are implemented in the form of a venturi cap.Most local buildings in Xichang have sloped roofs, which also meet the structural requirements of venturi caps.As shown in Figure 1, the main structure of the venturi cap comprises a sloping roof, a wind deflector, and a grille.The sloping roof guides the airflow separated at the windward facade to the roof ridge, making it accelerate, forming negative pressure at the openings, where the negative pressure causes the indoor air to be sucked out.The addition of a wind deflector on the upper side of the roof ridge can form a complete "venturi tube" structure, which can collect more incoming outdoor air and reduce the cross-section, enhancing the acceleration effect and increasing the adsorption capacity.(Figure 2) The grille blocks out direct sunlight, reducing heat radiation in the summer and preventing small animals from falling through the openings.The grille can also be closed if necessary.While protecting traditional culture, making full use of renewable resources to create comfortable indoor environments is an indispensable part of the protection and renewal of residential buildings.It is also one of the crucial solutions for building energy conservation and emission reduction.
Research into Application of the Venturi Effect
The most representative application of the venturi effect is the venturi tube (Figure 3), which has been widely using in various fields due to its simple structure and low cost [12].Li et al. [13] studied the influence of the geometrical parameters of the venturi tube on the cavitation phenomenon and microbubble generation.Shi et al. [14] conducted experimental and numerical studies on the cavitation phenomena in venturi tubes with different geometric shapes.Bimestre et al. [15], Zhu et al. [16], and Long et al. [17] explored the cavitation characteristics of venturi tubes.The application of the venturi effect goes far beyond this.Gonzalez-Perez et al. [18] enhanced the absorption of steam waste in the absence of a mechanical compressor by using the venturi effect.Perez et al. [19][20][21] studied the important role played by the venturi effect in the production of O2 from H2O2.Ji et al. [12], Xu et al. [22], and Yu et al. [23] showed that the venturi effect could be applied to the nozzle to improve its performance.The venturi effect also plays a positive role in agricultural production.Lei et al. [24] studied the movement of rapeseed and wheat seeds in the venturi seed feeding device and provided suggestions for improving the operating performance of seed feeding devices.Moreover, Quiroz-Perez et al. [25] used CFD simulation to find that the venturi device was able to generate a gas-liquid flow, thus increasing the gas production in some types of gas wells.Pan et al. [26] optimized the outlet of a smoke exhaust fan based on the venturi effect using an orthogonal design, a comprehensive scoring method, and the range analysis method, improving its smoke exhaust performance.Li [27] used the venturi effect to strengthen the natural smoke exhaust.On the basis of theoretical analysis, CFD numerical simulation, and wind tunnel experiments, a natural smoke exhaust device under the venturi effect was designed.Oliveira, M. A. d. et al. [28] studied the influence of the venturi effect on the control and suppression of vortex shedding in a slightly rough cylinder using the discrete vortex method.Shishodia et al. [29] applied the venturi effect in helmet design to improve the local airflow velocity in the gap between the head and the helmet, increasing the thermal comfort of riders.
With decreasing cross-section area, the flow velocity in building passages increases, as has been widely recognized and disseminated [30].For integrated buildings with narrow gaps, building installations with divergent channels at intersecting angles can lead to the formation of the venturi effect [31].However, Blocken et al. [32] put forward a different view, doubting the feasibility of the venturi effect in urban wind environments, and suggesting that the wind-blocking effect leads to increases in near-surface wind speed.Li et al. [33] and Allegrini et al. [34] provided support for the views proposed by Blocken et al. [32] on the basis of experiments.Chong.et al. [35] and Wang et al. [36] studied a hybrid solar-wind-rain eco-roof system for buildings.The system enhanced the wind speed before the interaction between the wind and the wind turbine located between the roof, strengthening the effect of the wind turbine through a rational use of the venturi effect.Ameer et al. [37], inspired by the venturi effect, designed a narrow roof that could increase the wind speed when the wind passed between two obstacles on the roof.Blocken et al. and Hooff et al. [38][39][40] studied the effect of venturi roofs on ventilation and analyzed the effect of the venturi and wind-blocking effects on venturi roofs.Then, they discussed the relationship between the width of the venturi roof and roof performance.Kumar et al. [41] studied the use of the venturi effect to intensify the air pressure in the vertical void to enhance the lateral ventilation on the leeward side of a double-load apartment building.Li et al. [42] studied the venturi effect on the effect of transverse entrains on pollutant diffusion in a street canyon.Some studies have been devoted to finding the best window opening to effectively regulate indoor airflow intensity by using the venturi effect [43][44][45][46].Muhsin et al. [47] showed that the natural ventilation performance of multi-story residential units could be enhanced by implementing an appropriate void structure.Wang et al. [48] aimed to build a relationship between wind energy potential and the configuration of two vertical buildings by studying the wind accumulation phenomenon of the venturi effect in the building environment.In addition, the venturi effect was used in the design of the escape passage in order to adsorb the airflow and generate stable air movement in the room.This effect makes it possible to generate airflow in indoor areas such as basements [49].Paepe et al. [50] optimized the ventilation of a cowshed by enhancing the venturi effect by creating an opening along the ridge and adding a wind deflector in the cowshed.Therefore, it can be seen that the venturi effect has extensive application prospects in regions with abundant sources of wind energy, and the development of wind energy in the built environment will be a crucial topic for sustainable cities in the future.
Summary
To date, scholars have proposed many strategies and measures for effectively applying the venturi effect in order to improve the convenience of our lifestyles and production on the basis of studies of applications of the venturi effect.However, by reviewing the research into applications of the effect, it can easily be found that that: Many scholars have performed numerous studies analyzing applications of the venturi effect applications; however, there is no comprehensive study evaluating the degree to which structural parameters affect the ventilation performance of the venturi effect.
Therefore, in line with the above summary, in this paper, the application of the venturi effect in building ventilation and the influence of various parameters on ventilation effect will be studied, and a venturi cap structure suitable for use in the Xichang area will be proposed.
Physical Model
In the early days, the Yi people in Liangshan Prefecture lived together with poultry.Even now, this habit of habitation is still being preserved.Therefore, buildings have a high ventilation demand.The house structure, comprising raw soil and produced through wooden structure trusses, is a common building type for the middle class among the Yi in Liangshan [51].The building is made of columns, beams, and wooden structure roof trusses as the frame of the house, and the components are connected.The wall is made of a wall compacted with raw soil, with wall thickness reaching up to 350 mm [52].While investigating the residential forms in the town of Huanglianguan in Xichang, scholars found that buildings with a depth of 3500 mm-4200 mm and a face width of 5500 mm-6400 mm account for the largest proportion in the local area [53].Therefore, as shown in Figure 4, this study selected buildings with sizes of 6 m × 4 m for the study.The thickness of the building walls was 350 mm, while the height of the cornice was 3000 mm, and the roof was covered in wood with a thickness of 50 mm and grass much with a thickness of 30 mm.As is shown in Table 1, the building height was related to the sloping roof and the width of the roof opening.The venturi cap was arranged along the ridge of roof.The thickness of the grille was 10 mm.The width of the grille was equal to the width of the gap between the grilles, allowing the grille to close easily.There was also a door on the other wall of the room, which was 1200 mm wide and 2000 mm high, to provide airflow from the outside.
Numerical Scheme
The orthogonal experimental design is a method used to study multiple factors at multiple levels.It is an efficient, rapid, and economical experimental design method that selects representative points from comprehensive tests according to the principle of orthogonality.This paper studies the effects of seven factors: 1, each factor has four different levels.Because the full factor design required 4 7 = 16,384 experiments, the orthogonal experimental design was adopted to reduce the number of experiments and improve the experimental efficiency.Table 1 shows the results of the orthogonal experimental design using an IBM SPSS 25.0, which produced 32 simulation scenarios.To better show the changes in these parameters, the model was decomposed according to its structure.Figure 5 shows the changes in the roof, grille, and wind deflector.
Physical Properties of Building Materials and Boundary Conditions
Table 2 summarizes the physical properties of the building materials, and these materials were used to simulate the heat conduction in the structure.The grille of the venturi cap is made of wood, while the wind deflector is made from aluminum alloy, the indoor floor is concrete, the outdoor floor is earth, and the wall is rammed earth.All of the necessary thermophysical properties of the building materials and air are assumed to be constant, except for the air density, which is considered to be an ideal gas.The size of the air domain outside the model is 50 m × 36 m × 30 m.The inlet boundary condition of the model is velocity-inlet.The outlet is a pressure outlet, and the remaining surfaces are set to be symmetrical.The door and grille are set to the interior.The optimization of natural indoor ventilation in Xichang in summer is the main aspect under consideration.Therefore, the model adopts the predominant wind direction in Xichang during summer, and the predominant wind direction in Xichang is north-south [11].The meteorological data used for the weather energy of Xichang in the numerical simulation were obtained from Chinese Standard Weather Data (CSWD) files, which were downloaded from the website [54] and are suitable for China [55].In the numerical simulation, the meteorological data for summer days in the Xichang area were selected, and therefore the outside temperature was set at 300 K and the wind speed was 3.3 m/s.
Grid Division
To ensure the independence of the mesh, four grid sizes were used for the experiments: 1,347,614 (1#), 1,919,598 (2#), 2,269,404 (3#) and 2,651,469 (4#).Figure 6 shows the experimental convergence results under four different meshing conditions.The difference in the volume flow rate between 1# and 2# was 40.833%, that between 2# and 3# was 1.650%, and that between 2# and 4# was 0.259%.Finally, the partition method of 1,919,598 (2#) was selected.In addition, as shown in Figure 7, the poly-hex core grid type was adopted to mesh the model.The global minimum surface mesh was 48.828 mm, and the global maximum surface mesh was 1000 mm.The local surface mesh of the door, indoor floor, wall, and roof was set as 80 mm, and the local surface mesh of the grilles and wind deflector was set as 20 mm.The minimum mesh volume was 20 mm, the maximum mesh volume was 640 mm, and three layers of the boundary were set to achieve a reasonable transition of the mesh.
Computational Fluid Dynamics (CFD) Theory
Numerical simulation was performed using ANSYS Fluent 2020 R2 using a finitevolume hydrodynamics solver.The simulation follows the laws of conservation of mass, momentum, and energy.
The mass conservation equation of the continuity equation is expressed as follows: where ρ is the fluid density, V ⃗ is the velocity vector, and Δ ρV ⃗ is the velocity divergence.
The momentum equation of viscous fluid is a mathematical expression of the law of conservation of momentum, which is expressed as follows: where v ⃗ is the velocity component in the direction of i; P is the surface force vector, including static pressure and fluid viscous stress.g is the volume force acting on the direction of unit volume flow i; f is the resistance acting in the direction of unit volume flow.
The energy conservation equation is expressed as follows: where k is the effective thermal conductivity (k + kf) with kf being the thermal conductivity caused by turbulence, and ȷ ⃗ is the diffusion flux of component i.The first term on the right-hand side of the equation represents the energy transfer due to heat conduction.
The second term represents component diffusion, and the third term represents viscous dissipation.S contains the heat of the chemical reaction and any other definable volume heat source.
In Fluent, the solar radiation model was adopted, and solar ray tracing was activated.Then, parameters such as latitude and longitude were set so that the computer could automatically calculate solar radiation intensity.The wall thermal boundary was Heat Flux, and the calculation formula for this was as follows: where k is the heat conduction coefficient of a solid; Δn is the distance from the wall surface to the center of the unit of the first layer; Ts is the temperature of the solid wall surface; q is the input heat flux; and q is the radiant heat flux.In the numerical simulation, the realizable K-ε turbulence model was selected.The K-ε turbulence model is the most commonly used two-equation turbulence model [56].The realizable K-ε turbulence model is appropriate for complex shear flows involving rapid strain, slight rotation, vortex, and local transition flow.Therefore, the model is suitable for the study of indoor environments.
Analysis of Variance
Thirty-two scenarios were numerically simulated, and the volume flow of the venturi cap device is shown in Table 1.Range analysis and analysis of variance (ANOVA) are commonly used to analyze the experimental results of orthogonal design [56].ANOVA was chosen for this study, and the variance analysis table of the volume flow rate is given (see Table 3).Based on the ANOVA performed on the results of the numerical simulation, we obtained the optimal level for each factor.In addition, on the basis of the p-value, the influencing factors were ranked.If a factor has a p-value less than or equal to 0.01, then there is 99% or so probability that the factor has a highly significant impact on overall performance.If the p-value is between 0.01 and 0.05, the probability drops, and the factor can be regarded as having a significant impact on overall performance.If the p-value is greater than 0.05, the effect of this factor is not significant.
On the basis of the analysis of the simulation results of the venturi cap with different structural parameters, it can be observed that the width of the roof opening has a highly significant impact on the volume flow rate, followed by the angle of the grille, the horizontal width of the wind deflector, the wind deflector height, the spacing of the grille slices, the roof slope, and the angle of the wind deflector (see Tables 1 and 3).The specific order of influence is as follows: width of roof opening > angle of grille > horizontal width of wind deflector > height of wind deflector > spacing of grille slices > roof slope > angle of wind deflector.In the analysis of the orthogonal experiment results, the level of each factor can be regarded as good if it corresponds to a larger volume of flow rate.When the width of the roof opening, angle of the grille, horizontal width of wind deflector, height of wind deflector, spacing of grille slices, roof slope, and angle of wind deflector were assigned values of 1000 mm (A4), 15° (B1), 800 mm (C4), 200 mm (D1), 45° (E4), 75° (F3), and 40 mm (G2), respectively, this scenario was named N33 and the volume flow rate of the venturi cap was 5.220 m 3 /s.As seen in Figure 8, N33 provided the maximum volume flow rate for the indoor environment and was therefore regarded as the optimum choice among these 33 scenarios.The velocity cloud diagram is shown in Figure 9.At the same time, in the same scenario, without the venturi cap, the average temperature of the horizontal plane at a height of 1.2 m above the ground was 308.836K, while when the venturi cap was turned on, the average temperature of the plane was 305.997K, representing a reduction by 2.839 K.These results show that the venturi cap plays a definite role in improving the ventilation conditions.
Single Factor Study
On the basis of the results of the variance analysis, it can be seen that the only highly significant factor affecting the effect of the venturi cap is the width of the roof opening.The angle of the grille and the width of the wind deflector have significant effects, while the other factors have insignificant effects.To determine the optimal design, the highly significant factor and the significant factors were studied in these 33 scenarios.
In N33, a single factor study was carried out on the highly significant factor.Only the width of the roof opening was changed, and the other six factors were fixed.The volumetric flow rate of the venturi cap and the average temperature of the 1.2 m horizontal plane were obtained through numerical simulation, as shown in Figure 10.When the width of the roof opening was changed in the range between 0 mm and 2000 mm, the volume flow rate of the venturi cap was the best at 1000 mm, with a maximum flow volume of 5.220 m 3 /s.This indicates that N33(A4B1C4D1E4F3G2) is still the optimal combination when the width of the roof opening is within the range of 0 mm-2000 mm.Single factor studies were carried out for the significant factors.Only the horizontal width of the wind deflector was changed, and the other six factors were fixed.The volume flow rate of the venturi cap and the average temperature of 1.2 m high horizontal plane above the ground were obtained on the basis of numerical simulation, as shown in Figure 11.When the horizontal width of the wind deflector was changed in the range of 200 mm-1000 mm, the volume flow rate of the venturi cap had the best value at 400 mm, where the volume flow rate reached a maximum of 5.507 m 3 /s.This shows that when the horizontal width of the wind deflector was within the range of 200 mm-1000 mm, the volume flow rate first increased and then decreased with increasing horizontal width of the wind deflector.Similar to the analysis of the horizontal width of the wind deflector, the angle of the grille was studied.The results are presented in Figure 12.When the grille angle was 75°, the volume flow rate reached its maximum value.On the basis of the analysis of the above parameters, N34(A4B1C4D2E4F3G2) was obtained by adjusting the horizontal width of the wind deflector to 400 mm on the basis of N33, and the maximum volume flow rate achieved was 5.507 m 3 /s.At the same time, in the same scenario, without the venturi cap, the average temperature of the horizontal plane at a height of 1.2 m above the ground in the whole building was 308.836K, while when the venturi cap was turned on, the average temperature of the plane was 305.834K, which is a reduction by 3.002 K. Therefore, it can be seen that the venturi cap is able to improve the ventilation of indoor environments and reduce indoor temperatures.In summer, this could lead to a reduction in the use of air conditioning equipment, thus achieving an energy-saving effect.
Conclusions
The orthogonal experimental design and variance analysis were performed using SPSS, and the numerical simulation analysis was carried out using CFD.The feasibility of using a venturi cap in the Xichang area was verified.The main key factors influencing the venturi cap with respect to improving ventilation, and the degree of the effect were obtained.An optimized combination scheme was provided within the research scope and verified on the basis of numerical simulation.Therefore, the following conclusions can be drawn: 1. Variance analysis showed that the width of the roof opening had a highly significant effect on the ventilation performance of the venturi cap, while the angle of the grille and the horizontal width of the wind deflector had a significant impact.The height of the wind deflector, the spacing of the grille slices, roof slope, and the angle of the wind deflector were not significant.2. On the basis of the analysis of the highly significant factors and the significant factors, it was found that the best solution was N34, that is, the width of the roof opening, the angle of the grille, the horizontal width of wind deflector, the height of wind deflector, the spacing of the grille slices, the roof slope and the angle of wind deflector were assigned values of 1000 mm (A4), 15° (B1), 800 mm (C4), 400 mm (D2), 45° (E4), 75° (F3), and 40 mm (G2), respectively; the volume flow rate reached 5.507 m 3 /s, and the average temperature of the horizontal plane at a height of 1.2 m above the ground dropped by 3.002 K.
This research on building ventilation in the Xichang area showed that the structure is able to meet the needs of both residents and building characteristics, optimizing the ventilation conditions of local buildings while reducing indoor temperature and improving indoor air quality.
Outlook
In this study, the length-width ratio and shape of the venturi cap were not taken into consideration.The length of the venturi cap was set at a fixed length, and the area was converted into the width for the purposes of research.The thickness of the grille was also directly set at a fixed thickness, ignoring the possible influence of the change in the thickness of the grille on the ventilation conditions.The size and location of the air inlet were also fixed.In future research, these influencing factors should be further analyzed in order to put forward suggestions for the better application of the venturi effect in buildings and to provide design ideas and data references for the optimal design of building ventilation.
China's building energy consumption report 2020 reported that in 2018, China's total energy consumption was 2.147 billion tons of standard coal equivalent (tce), and its total carbon emissions were 4.93 billion t CO2.Rural residential buildings account for 24% of China's building energy consumption and 21% of its carbon emissions, which are huge numbers.The application of a venturi cap in architectural design can increase indoor ventilation, bring more fresh outdoor air into the room, and reduce indoor temperature.The reduction in the use of air-conditioning systems during the summer will help to achieve the aim of reducing building energy consumption.Research regarding the venturi cap could provide design ideas for the future reconstruction of old rural buildings in the Xichang area in the future.In addition, in the context of COVID-19, indoor ventilation has
Figure 1 .
Figure 1.Schematic diagram of a venturi cap.
Figure 2 .
Figure 2. Acceleration due to the venturi effect, simulated by computational fluid dynamics (CFD).
Figure 3 .
Figure 3. Schematic diagram of a venturi tube.
(A) width of roof opening; (B) roof slope; (C) height of wind deflector; (D) horizontal width of wind deflector; (E) angle of wind deflector; (F) angle of grille; (G) spacing of grille slices.As shown in Table
Figure 6 .
Figure 6.Volumetric flow rate under various grid sizes.
Figure 8 .
Figure 8. Volumetric flow and average temperature of a horizontal plane at a height of 1.2 m above the ground in 33 scenarios.
Figure 9 .
Figure 9. Velocity cloud diagram of the N33 scenario.(a) Side view; (b) plan view.
Figure 10 .
Figure 10.Volumetric flow and temperature values for different widths of roof opening.
Figure 11 .
Figure 11.Values of volumetric flow and temperature at different horizontal widths of the wind deflector.
Figure 12 .
Figure 12.Volumetric flow and temperature values at different angles of grille.
Table 1 .
Orthogonal design arrangements and results.
Table 2 .
Material properties of the venturi cap.
Table 3 .
Analysis of variance (ANOVA) table for volume flow rate. | 6,707.4 | 2021-08-17T00:00:00.000 | [
"Engineering",
"Environmental Science"
] |
Research on the Reasonable Strengthening Time and Stability of Excavation Unloading Surrounding Rock of High-Stress Rock Mass
This study is aimed at better understanding the deformation and failure mechanism of surrounding rock during excavation unloading of a high-stress rock mass and determining the reasonable reinforcement time for the surrounding rock. To fulfill this aim, true triaxial tests were carried out on different loading and unloading paths during the unilateral unloading of a high-stress rock mass. The variational condition for minimization of plastic complementary energy is obtained, the optimal reinforcement time is determined, and the range of the plastic zone in the surrounding rock reinforced by anchor mesh-cable-grouting is compared and analyzed. The results are as follows: (1) Based on the Mohr-Coulomb yield criterion and the deformation reinforcement theory of surrounding rock, the stable state with the minimum reinforcement force is obtained. (2) After the true triaxial tests on the unilateral unloading of the third principal stress were carried out under different confining pressures, loading continued to be performed. Compared with rock failure without confining pressure, in the conventional uniaxial compression test, the failure of samples is dominated by composite splitting-shear failure; the unilateral unloading stress-concentration failure is a progressive failure process of splitting into plates followed by cutting into blocks and then the ejection of blocks and pieces. (3) The relationship between the time steps of the surrounding rock stability and the excavation distance is obtained. The supporting time can be divided into four stages: presupport stage, bolt reinforcement stage, anchor cable reinforcement stage, and grouting reinforcement stage. (4) In the range of within 5m behind the tunneling face, the plastic zone of the surrounding rock with support is reduced by 7m as compared with that with no support. In the range of over 5m behind the tunneling face, the plastic zone of the roadway floor with support is reduced by 2.6m as compared with that without support, and the deformation is reduced by 90%. These results can serve as a reference for controlling the behavior of surrounding rock during excavation unloading of high-stress rock masses.
Introduction
After roadway/tunnel excavation, the surrounding rock suffers deformation, thus resulting in stress redistribution. In the process of constant stress adjustment, the internal structure of the rock mass changes. With time, the stress in the surrounding rock near the excavated rock mass reaches its critical failure strength, and overall failure occurs [1,2]. Therefore, understanding the failure characteristics and determining the rational supporting time of surrounding rock near the excavated rock mass can help effectively control the deformation of surrounding rock [3][4][5].
There have been many studies on the stability of surrounding rock of underground roadways from the perspectives of stress, deformation, energy, etc. using various research methods [6][7][8]. Wu et al. [9] adopted a variety of research techniques to analyze the zonal deformation and failure characteristics and stress distribution characteristics of the roof, floor, two sides, and four corners of a tilted stratum roadway. Besides, the stability control technology for controlling the nonhomogeneous deformation of the tilted stratum roadway was proposed with engineering verification. Zhang and Han [10] analyzed the magnitude, direction change, and distribution characteristics of crustal stress in mines based on the measured crustal stress data in the mining areas and studied the influence of crustal stress on roadway stability; they provided a reliable basis for the design of a reasonable support structure for roadways. Gou et al. [11] investigated the effect of horizontal tectonic stress on the stability of surrounding rock of a roadway by numerical simulation and showed that with an increase in the horizontal stress, the horizontal stress transfers to the deeper parts of the roadway roof and floor; this causes floor heave and fold failure of the roadway and shear deformation and wedge caving of the roof, with deformation and failure of the roof and floor being greater than that of the two sides of the roadway. Li et al. [12] mainly analyzed the stress distribution, deformation, and failure mechanism of surrounding rock in deep parts by using the elastic-brittle constitutive model and sliding failure theory. Yang et al. [13] showed that the rotation angle of the main roof was the main factor leading to roof deformation; the roof convergence could not be reduced by strengthening the roadway support, and the roof convergence, as well as the fracture direction, could be effectively controlled by increasing the roof cutting height and angle. Yao [14] is of the opinion that the surrounding rock support of a roadway is closely related to the initial stress, excavation mode and progress, surrounding rock grade, etc. Han et al. [15] studied the stress characteristics of rock strata experiencing roof cutting and pressure relief and determined the key parameters of roof cutting height, roof cutting angle, and hole spacing based on the theoretical analysis method of mine ground pressure. They showed that the roof cutting could significantly reduce roadway stress and deformation and improve roadway support and production efficiency. Xu et al. [16,17] conducted true triaxial tests to study the damage and fracture characteristics of marble under excavation unloading of a high-stress rock mass; they showed that for the excavation unloading surface, the main failure surface is near the free surface as the stress decreases. Dong et al. [18] studied the mechanical characteristics and failure mechanism of surrounding rock during excavation unloading of a deep circular roadway and established the strength criterion and a tension-compression damage model for dynamic unloading to obtain the failure characteristics of the excavation unloading surface. These scholars evaluated the failure characteristics, overall stability, and reasonable support structure of surrounding rock after excavation unloading of roadways from various perspectives; however, they did not propose a reasonable supporting time or specific measures according to the actual situation.
Based on the failure mechanism of the surrounding rock of roadways during excavation unloading, many scholars have put forward reasonable supporting times and supporting modes [19][20][21]. Su et al. [22] determined the primary support timing through the evolution of safety factors during tunnel excavation. Zhou et al. [23] analyzed the changes of stress in the plastic zone, displacement of the tunnel wall, and support pressure in the tunnel supporting process and proposed a reasonable supporting time for staged tunnel supporting. Sun and Zhang [24] put forward the layer model, obtaining the deformation process and supporting characteristics of the surrounding rock, and studied the synergistic supporting mechanism of the composite supporting layer. Yu [25] studied the space-time evolution of surrounding rock deformation under the disturbance of tunnel excavation and established a three-dimensional mechanical model to study the interaction between tunnel structure and surrounding rock. He also analyzed the supporting effects of various supporting structures and obtained the mechanical characteristics and practicability of composite supporting structures. Dong [26] and Hou et al. [27] mainly summarized three supporting technologies in terms of control technologies: the combined supporting technology with anchor bolt (cable) as the main part supplemented by other technologies, the integrated supporting technology with the integration of anchor bolt, and the combined technology with supports. However, they only analyzed the supporting effect from one aspect or through multiple ways and adopted a single or multiple supporting means for combined support; they, however, did not propose a reasonable supporting time and appropriate supporting mode from the optimal supporting time in different stages of surrounding rock of roadways under excavation unloading. Therefore, building on many previous studies, the reasonable supporting time and stability were explored in this study.
In this study, based on the Mohr-Coulomb yield criterion and the minimum plastic complementary energy, the failure and reinforcement time of surrounding rock were analyzed. True triaxial tests on different loading and unloading paths were conducted to investigate the stress failure characteristics of a rock mass during excavation unloading. Through 3DEC numerical simulation, the optimum supporting time for surrounding rock during excavation unloading at different stages was determined, and on-site verification was conducted.
Theoretical Analysis on Surrounding Rock
Reinforcement during Excavation Unloading 2.1. Mohr-Coulomb Yield Criterion. According to the method of calculating the safety coefficient of points in surrounding rock based on the Mohr-Coulomb theory, the Mohr-Coulomb yield function is expressed by the principal stress as follows: where σ 1 , σ 2 , σ 3 denote the first, second, and third principal stresses, respectively; φ denotes internal friction angle; and c denotes cohesion.
With the elastic theory as the basis, it is considered that yield occurs when the stress value meets certain conditions; 2 Geofluids to represent the safety degree of a rock mass, engineering researchers propose the concept of the safety coefficient [22]: where H denotes material parameter, which is the function of the internal variable χ of scalar, and F denotes the safety coefficient; F > 1 indicates no yield inside the yield surface, F = 1 indicates a critical state on the yield surface, and F < 1 indicates shear failure outside the yield surface. According to the Mohr-Coulomb yield criterion, the distance between the stress state at any point in the rock mass and the strength envelope curve is determined (shown in Figure 1).
If the strength envelope curve is translated downward, that is, corresponding to the reserve safety margin, then the safety coefficient based on the Mohr-Coulomb yield criterion is
Deformation Reinforcement Theory of Surrounding Rock.
It is supposed that for the action on an elastic-plastic structure, the body force is f = f i , the stress boundary is S σ , and the boundary condition is T = T I = σ ij n j . Then, regarding any given virtual displacement δu = δu i , the corresponding virtual strain is δε ij . Based on the virtual displacement principle, the following can be obtained: Considering any coordinated equilibrium stress field σ 1 and coordinated stable stress field σ, the difference between them is the plastic stress increment field Δσ p : Substitute Equation (5) into Equation (4), and through the transposition of terms, the following can be obtained: Δε p = C : By substituting Equation (8) into Equation (7) and noting that σ is on the yield plane, the final stress state σ can be determined, that is, Due to the deformation compatibility characteristic of σ 1 , it actually represents a certain deformation state. Therefore, Equation (6) can also be expressed as follows: an unstable deformation state can be stabilized by applying reinforcement force. There are many such reinforcement schemes. The stable stress field σ in accordance with the plastic constitutive equation (orthogonal flow rule and consistency condition) is determined as follows: everywhere within V0, σ 1 = σ, and σ is determined by using Equation (9) in each point within V1. It is clear that the stable stress field σ determined in this way is the stress field closest to the stress field σ 1 in the set S, i.e., L or ΔE is the minimum.
Thus, an important conclusion can be drawn as follows: for a specific rock mass with an unstable deformation structure, the plastic constitutive relation makes the structure approach the nearest stable state, or the plastic constitutive relation makes the structure approach the stable state requiring the minimum reinforcement force. The variational condition for minimizing the plastic complementary energy is For a specific rock mass with unstable deformation structure, it indicates δσ 1 ≡ 0. Due to the positive definiteness of C, the second-order variation of the plastic complementary energy is constantly positive: Thus, the following can be obtained:
Test Analysis of a High-Stress Rock Mass during Excavation Unloading
Rock masses usually exist in a certain stress environment, and they are in a three-dimensional stress equilibrium state before excavation. In both TMB excavation and boreholeblasting excavation, the original balance is broken, forming a free surface on the rock mass, and the stress state transforms from the original three-dimensional six-sided stress into a three-dimensional five-sided stress, leading to the redistribution of stress in the surrounding rock. Stress concentration occurs in the surrounding rock near the free surface. When the secondary stress exceeds the bearing limit of the surrounding rock, the rock mass suffers failure. Therefore, the use of a unilateral unloading and loading method can more truly reflect the failure state of surrounding rock in practical engineering.
Test Equipment.
The true triaxial disturbance unloading rock test system used in this study (see Figure 2) can expose a surface of the sample to simulate the phenomenon of a free surface occurring after excavation in underground engineering; this is achieved through an independent loading in three mutually vertical directions and sudden unloading in a single surface in the horizontal direction. In the vertical direction (Z) of the system, the maximum load of the loading cylinder is 5000 kN; the disturbance cylinder is installed on the lower beam of the vertical loading frame, with a maximum dynamic load of 500 kN; the maximum loads of the two loading cylinders in the horizontal direction (X, Y) are both 3000 kN; one of the cylinders is a dynamic cylinder, which is used for quick unloading; the loading and unloading are controlled by a fully digital servo controller, which provides the necessary means for determining the stress state of the rock mass when it suffers failure.
Test
Scheme. This test mainly simulates the stressconcentration failure test of unilateral unloading under a true triaxial, three-dimensional, and hexahedral stress state. A cuboid marble with good integrity and uniformity was used as the rock sample; it had an initial density of 2758 kg/m 3 , a water content of 0.02%, and a size of 100 mm × 100 mm × 200 mm.
Conventional Uniaxial Compression Test.
To obtain the conventional compressive strength, deformation parameters, and failure characteristics of the marble, and to serve as a reference for the unilateral unloading and loading tests under true triaxial, three-dimensional, and hexahedral stress states, the confining pressure of sample #1 was designed to be zero in this test (see Table 1). To better observe the variation in the postpeak curve, the deformation mode was used for loading in the test (see Figure 3(a)), with a loading rate of 0.05 mm/min and σ as the stress.
Unilateral Unloading Stress-Concentration Failure
Test. When simulating deep tunnel excavation, the surrounding rock that is originally in the three-dimensional stress state develops a free surface, and the mutual extrusion of the surrounding rock in the tangential direction inten-sifies the failure caused by stress concentration. The samples used in this test are numbered from #2 to #5, and the loading was controlled by loading at a loading rate of 0.5 MPa/s. The stress loading path during the test is shown in Figure 3(b). First, in the X, Y, and Z directions, the load is applied at 0.5 MPa/s to the set initial stress level (see Table 1). After reaching the initial stress level, the stress remains unchanged in the Y and Z directions, and transient unloading was performed on a surface in the X direction at a speed of 50 mm/s (see Figure 4(b)). Then, loading was performed in the Z direction at a speed of 0.5 MPa/s until failure.
Stress-Strain
Curve. The stress-strain curve for the true triaxial third principal stress with different confining pressures continuing to be loaded after unilateral unloading is shown in Figure 5. Compared with rock sample #1 without confining pressure failure, the stress-strain curve of the stress-concentration type has the following characteristics: in the case without confining pressure, the peak value is 88 MPa, and with the confining pressure increasing, the peak points increase to 151 MPa, 162 MPa, 200 MPa, and 264 MPa, respectively. The prepeak curve also shows notable yield points. With the increase in the confining pressure, the yield point and the peak point increase, and the slope of the curve between the yield point and the peak point is moderate. The corresponding failure phenomenon is the splitting failure in the free surface and the potential shear failure in 5 Geofluids the rock mass. The axial strain before the peak is larger than that after the peak, and the postpeak stress after the peak shows a brittle drop. The postpeak stress-strain curve is relatively steep and inclined. When the confining pressure is 30 MPa and 20 MPa, the postpeak curve is the steepest and the postpeak strain is the smallest. This shows that with an increase in the confining pressure, the failure changes from composite tensile-shear failure to splitting failure; with an increase in the confining pressure, the failure of the samples is the most severe, and the intensity of the rock burst is greater.
Failure Characteristic Analysis
3.4.1. Conventional Uniaxial Compression Test. In conventional uniaxial compression tests, the macroscopic failure type of marble samples is mainly a composite splittingshear failure (as shown in Figure 6). Because marble is a hard rock and has a relatively high brittleness coefficient, under the condition of no confining pressure, the lenticular angle of the cubic sample experiences a boundary constraint effect. In the failure process, there is a splitting failure surface at the upper part of the rock samples, which is almost parallel to the first principal stress surface. After failure, a peeling surface forms on the rock sample. There is a master shearing surface at the lower part of the rock sample, on which there is a large quantity of scratches and small fragments and powders of the rock sample. This is due to the secondary shear failure caused by stress concentration at resistance to load in the process of shear slip.
Unilateral Unloading Stress-Concentration Failure.
After the rock sample is maintained for a certain period of time from triaxial compression to the initial state, rapid unloading is performed on the unilateral third principal stress, and the rock sample is in the stage of microcrack development. The number of microcracks increases, but no macroscopic cracks occur on any of the rock samples. Afterward, loading continues to be performed on σ 1 ; when it is loaded to 70% of the failure peak, after plate crack and ejection occurs on the #2~#5 rock samples, plate failure occurs on the free surface, with the generation of fine white rock powder. Two larger shear oblique cracks appear inside the rock mass, and a large amount of fine white rock powder appears in the cracks. With the increase in the axial stress, the plate crack width increases, and the rock sample reaches the final failure mode (see Figure 7). The slabby splitting of the rock mass is dominated by a tensile fracture, with a local shear stress. It is a progressive failure process of splitting into plates, followed by cutting into blocks, and then the ejection of blocks and pieces. This indicates that in the unilateral unloading process of σ 3 and σ 2 restricts the lateral expansion of the rock samples under the action of σ 1 , leading to the development of rock samples towards the free surface. The continuous deformation causes the rock samples to transform from a state of compression to tension. When the tensile strength is reached, longitudinal cracks running through the rock samples are generated near the unloading surface, and rock plates parallel to the unloading surface form. With the continuous unloading of the unloading surface, the rock slab reaches the critical buckling value, and with the release of excess energy, rock burst failure occurs. The morphology of the rock samples after failure is shown in Figure 7. The #2~#5 rock samples all suffer plate cracks on the free surface, showing the three types of sheet shape, thin-plate shape, and wedge shape. This indicates that tensile failure occurs under true triaxial unilateral unloading conditions with confining pressure. With the increase in the confining pressure, the failure of rock samples shows dual characteristics, with tension failure occurring first followed by compression-shear failure. V-shaped failure pits appear on the free surface, and penetrating shear fractures appear in the areas far away from the free surface. When the confining pressure increases to a certain extent, the rock samples suffer splitting failure, and splitting and penetrating cracks form over the entire rock mass. This shows that in the excavation process of a deeply buried roadway with high crustal stress, the two sides will show an instantaneous "unloading" effect, with instantaneous rebound deformation occurring. With the stress redistribution and stress concentration in local regions, when the tensile strength of the surrounding rock is exceeded, accidents such as plate cracks, rib spalling, and rock bursts will gradually occur on the two sides.
Reasonable Supporting Time for Surrounding Rock of a High-Stress Rock Mass Under Excavation Unloading
After the excavation of a high-stress rock mass, with time, the bearing capacity of the surrounding rock itself decreases, creating a fractured zone with both depth and breadth. The stress concentration is caused by the bearing capacity of the rock mass itself. When the local high stress generated by the stress concentration exceeds the strength of the rock mass, the rock mass will deform towards the excavation surface, thus leading to failure. From the excavation surface to the deep part, it can be divided into three zones: failure zone (completely losing bearing capacity), plastic zone (having certain bearing capacity), and elastic zone (having intrinsic bearing capacity) (as shown in Figure 8). To reduce the range of the failure zone and the plastic zone and reasonably control the deformation of the surrounding rock, it is necessary to support the surrounding rock in a timely manner. According to the basic principle of NATM construction, as shown in Figure 9, selecting the best supporting time is the key after roadway excavation. The number of time steps is the number of iterative steps calculated through numerical simulation, and it is the number of steps needed to be calculated in the process of establishing the stress balance of surrounding rock. However, the measurement unit used in the actual construction is time. The establishment of the relationship between time and the number of steps facilitates the numerical simulation results to guide the site construction better and more effectively. In the process of numerical simulation, when the displacement field, stress field, and plastic zone do not change with the increase in the time steps, the calculation reaches equilibrium, and the surrounding rock reaches the equilibrium and stable state. In the excavation process of a high-stress rock mass, the effect of each excavation unloading on the displacement field, stress field, and plastic zone is the key factor for guiding the site construction. When the calculation reaches the equilibrium state, it indicates that the effect of excavation unloading ends. According to the displacement curve of the surrounding rock deep in the roof during roadway excavation in numerical simulation, the relationship between the number of time steps required to achieve surrounding rock stability and the excavation distance can be determined through Pre support rt rt sta sta ta sta sta a a a a a a a a sta sta ta sta a a a sta t t t st t s ge g g g g g g I I I I I I I I I I I I I I I I I I I II I I I I I I I I I I I I I I I I I I I I III I I I I I I I I I I I I IV I I I I IV I I I 8 Geofluids deformation of the surrounding rock. Reasonable reinforcement and supporting time should be the corresponding time when the surrounding rock displacement tends to be relatively stable. As can be seen from Figure 10, due to the influence of roadway excavation, the surrounding rock within 1 m away from the roadway roof is severely deformed and broken into blocks, showing large deformation, and the final deformation reaches 452 mm. Due to the inherent loadbearing capacity of the surrounding rock in the plastic zone, the surrounding rock that is 1 m-4 m away from the roadway roof is subjected to a declining convergence amount and convergence rate from the inner side to the outer side. The convergence amount of the surrounding rock within the range of 4 m to 5 m from the roof is basically the same. Therefore, it can be seen that, in the case with no support, the surrounding rock within 3 m and over 4 m from the roof shows a bed-separation phenomenon. Similar results can be obtained from the curves for convergence amount and convergence rate on the right side.
Analyzing the convergence amount and convergence rate of the surrounding rock at the top and right side of the excavation roadway with high-stress rock mass shows that the deformation of the surrounding rock at the top of the roadway changes dramatically in the first 520 steps of roadway excavation, and the convergence rate of the surrounding rock also shows a sharp change. The convergence amount of the roof tends to be relatively stable after 620 steps. When the number of time steps is 112, 236, and 520, the convergence rates of the surrounding rock of the roof all show the trend of increasing and decreasing, indicating that the plastic zone of the surrounding rock plays its own role of load-bearing during the time steps of 0-112, 192-236, and 482-520; during this time, the convergence rate of Grouting and reinforcement st Pre Pre Pre Pr P P P P P P P P P P P P P P P P P P P P P P P P P P P P P support stage Bolt support stage Anchor support stage I II I I I I I I I I I I I I I I I III IV I I I Step 9 Geofluids displacement decreases. With the increase in the displacement, the rock mass within the plastic zone loses its bearing capacity. The convergence rate of the surrounding rock displacement increases. Similar results can be obtained from the change curves of convergence amount and convergence rate on the right side. Thus, it can be seen that the optimal supporting time can be divided into four stages: (I) presupport stage: controlling the convergence amount of the displacement of the rock mass on the roadway surface to prevent the rock mass on the roadway surface from suffering tensile failure; (II) bolt reinforcement stage: increasing the strength of the plastic zone in the roadway and improving the bearing capacity of the plastic zone; (III) anchor cable reinforcement stage: further increasing the strength of the plastic zone in the roadway, enhancing its inherent bearing capacity, and reducing the deformation of the surrounding rock; and (IV) grouting reinforcement stage: carrying out grouting reinforcement on the rock mass within the plastic zone in the roadway to ensure the long-term stability of the roadway.
Technical Scheme for Surrounding Rock Reinforcement
and Support. After the excavation of a high-stress rock mass, with time, stress concentration will occur in the surrounding rock of the roadway, and stress release will occur within a certain range, making the surrounding rock suddenly suffer severe deformation and failure; this severe deformation and failure will gradually extend to the deeper parts of the surrounding rock.
Anchor bolt (mesh) support plays a positive role in improving the strength and stress state of surrounding rock. The higher prestress can improve the stress state and control the deformation of surrounding rock. The combination of anchor cable and anchor bolt can make the anchorage structure of the anchor bolt hang in the harder and more stable rock strata deep in the surrounding rock. Cement grout plays a bonding role and can penetrate the loose zone to improve the strength of the surrounding rock around a roadway. Therefore, an anchor mesh-cable-grouting reinforcement technology for deep roadways is proposed. The concept is as follows: (1) The deformation characteristics of high-stress roadways show that their support cannot reach the goal in one step; providing support is a process requiring secondary support or multiple supports (2) During roadway excavation, the surrounding rock can be permitted to suffer some loose deformation and release some deformation energy accumulated in the surrounding rock, but it is necessary to undertake measures like initial spraying to seal the surrounding rock in time (3) Anchor bolt-cable support with high strength and high prestress can be carried out on the roadway in a timely manner (4) According to the monitoring results, after the severe deformation stage of the roadway, grouting rein-forcement should be carried out on the surrounding rock of the roadway at the right time to strengthen the surrounding rock and improve its overall bearing capacity According to the special conditions of the air return cross-hole in the No. 81 mining area of the Xinhu Coal Mine that has a kilometer-deep well, a corresponding support scheme is put forward as follows: Supporting parameters: GM22/2600-490 rebar high-strength anchor bolt is used as anchor bolt; the row spacing between anchor bolts is 800 × 800 mm, with a rectangular layout; the anchor rod tray is 200 × 200 × 10 mm. Two rolls of the K2950 resin anchoring agent are used for each anchor bolt above the arch camber, and two rolls of the Z2950 resin anchoring agent are used for each anchor bolt at the sides. The anchor cable is prestressed steel strand anchor cable, with a specification of Φ 21:8 × 7300 mm; two rolls of the Z2950 type and one roll of the K2950 resin anchor agent are used for each anchor cable; the row spacing is set to be 1600 × 1600 mm; a 300 × 300 × 15 mm anchor tray is used for matching with each anchor cable; and the lockset at the outcrop of the anchor cable is 150~250 mm. Two rolls of the Z2950 resin anchoring agent are used for each anchor bolt on the side. The metal mesh is processed using Φ6.0 mm round steel, with length × width = 2400 × 900 mm, and mesh of 100 × 100 mm connected by hook, and with the stubble of 100 mm. The full-face shotcrete is 100 mm thick, and the concrete strength is C20. Grouting anchor bolts are laid out on the full face, and grouting anchor bolts are processed by using Φ25 × 2800 mm steel pipe, with the row spacing between them being 1600 × 1600 mm. At ≯70 m lagging behind the tunnel face, grouting anchor bolts are set up, and grouting is carried out. P.O42.5-type ordinary Portland cement is used as the cement for grouting, with a water : cement ratio of 1 : 1 and a grouting pressure of 2 MPa. Parameters of the supporting grouting and anchor cable are as follows: a hollow mine anchor cable is used as the anchor cable for grouting, with a specification of Φ22 × 7000 mm. The tray of the anchor cable is TPF300 × 300 × 15 mm, and the lockset at the outcrop of the anchor cable is 150~250 mm. 5 anchor bolts are laid out in each row along the roadway, with a row spacing of 2400 × 2400 mm. Two rolls of the Z2950 resin anchoring agent are used for each anchor cable for the grouting. P.O42.5-type ordinary Portland cement is used as the grouting cement with a water : cement ratio of 1 : 1. At ≯140 m lagging behind the tunnel face, the grouting anchor cables are set up and grouting is carried out with a grouting pressure of 3 MPa.
Analysis of the Support Effect of Surrounding Rock.
To obtain the deformation, failure, and stress distribution characteristics of the surrounding rock at the roof and floor and the two sides of a high-stress roadway, the mechanical characteristics of the surrounding rock of the roadway were analyzed through 3DEC numerical simulation as shown in Figure 11.
Three-dimensional failure field characteristics of the high-stress surrounding rock during excavation support. Figure 12 shows the failure diagrams for the areas 5 m in front of the tunneling face, at the tunneling face, 5 m behind the tunneling face, and the heading direction of tunneling. As can be seen from the figure, although the rock mass 5 m away from the tunneling face has not been excavated, the rock mass suffers failure due to the support factor.
After the roadway is excavated, the surrounding rock suffers failure quickly in a wide range under the action of high stress, but the deformation of the surrounding rock is restricted by the support. In the area within 5 m behind the tunneling face, the plastic zone of the surrounding rock in the entire surrounding rock roadway no longer expands, forming a circular plastic zone with an approximate radius of 2.2 m, which is 7 m smaller than that in the case without support. In the roadway, more than 5 m behind the tunneling face, the plastic zone range at the side no longer expands, but the plastic zone of the floor still continues to expand, and the final plastic zone range of the floor reaches 5.9 m, which is 2.6 m smaller than that in the case without support.
Field
Feedback on the Excavation Support Effect of Surrounding Rock. In this study, the deformation and failure characteristics of a high-stress rock mass were obtained through true triaxial tests on different loading paths.
According to the deformation reinforcement theory, a composite support scheme of anchor mesh and cable shotcrete +shallow and deep hole grouting is designed and proposed, and the support effect was verified through numerical simulation. Through field practice, with the support field drawing shown in Figure 13, the reliability of the test results was verified, which serves as a reference for related projects. Step
Conclusion
(1) True triaxial tests were carried out to compare and analyze the conventional uniaxial compression test results of a high-stress rock mass and the unilateral unloading stress-concentration failure tests; we obtained the progressive failure process of the surrounding rock, in which the failure characteristics of the rock mass under conventional uniaxial load is a composite splitting-shear failure, while the unilateral unloading stress-concentration failure characteristic follows the process of splitting into plates, followed by cutting into blocks, and then the ejection of blocks and pieces (2) The roadway tunneling process was simulated through numerical simulation to obtain a reasonable reinforcement time for surrounding rock. It can be divided into four stages, i.e., the presupport stage, the bolt reinforcement stage, the anchor cable reinforcement stage, and the grouting reinforcement stage (3) Under reasonable support, the plastic zone of the entire surrounding rock forms a circle of approximately 2.2 m, which is 7 m smaller than that without support. The plastic zone at the side no longer expands, but the plastic zone of the base plate still expands, finally reaching 5.9 m, which is 2.6 m smaller than that without support. The deformation is significantly reduced
Data Availability
The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.
Conflicts of Interest
The authors declared no conflicts of interest. | 8,152.2 | 2021-09-14T00:00:00.000 | [
"Engineering",
"Geology"
] |
Circulating miRNAs: cell–cell communication function?
Nuclease resistant extracellular miRNAs have been found in all known biological fluids. The biological function of extracellular miRNAs remains questionable; however, strong evidence suggests that these miRNAs can be more than just byproducts of cellular activity. Some extracellular miRNA species might carry cell–cell signaling function during various physiological and pathological processes. In this review, we discuss the state-of-the-art in the field of intercellular miRNA transport and highlight current theories regarding the origin and the biological function of extracellular miRNAs.
INTRODUCTION
MicroRNAs (miRNAs), a subclass of short non-coding RNAs, are expressed in all eukaryotic cell types and mediate posttranscriptional regulation of gene expression (Ambros, 2004;Bartel, 2004). The action of miRNAs is mediated by its binding to the 3untranslated region (3 UTR) of the target mRNAs and thus regulating targeted mRNAs stability and protein synthesis (Ambros, 2004;Bartel, 2004). There have been more than 2000 different human miRNA species discovered so far and this amount is increasing (http://www.mirbase.org/). In humans, endogenous miRNAs regulate at least 30% of genes (Lewis et al., 2005) and, thus, coordinate key cellular processes including proliferation, DNA repair, differentiation, metabolism, and apoptosis (Ambros, 2004;Bartel, 2004;Croce and Calin, 2005). Deregulation of certain miRNAs' expression in the cell was consistently observed during various pathologies including cancers (Lu et al., 2005). Every miRNA has a unique nucleotide sequence and unique expression pattern in certain cell type (Lu et al., 2005;Landgraf et al., 2007).
Several years ago, significant amounts of miRNA were detected in all biological fluids including blood plasma, urine, tears, breast milk, amniotic fluid, cerebrospinal fluid, saliva, and semen [reviewed in ]. These extracellular circulating miRNAs are surprisingly stable and survive unfavorable physiological conditions such as extreme variations in pH, boiling, multiple freeze thaw cycles, and extended storage. In contrast to miRNAs, common RNA species like mRNA, rRNA, and tRNA are degraded within several seconds after being placed in nuclease rich extracellular environment (Chen et al., 2008;Turchinovich et al., 2011). In their pioneering work Valadi et al. reported that cells in culture transport intracellular miRNAs into the extracellular environment by exosomes (Valadi et al., 2007). This finding was confirmed in many subsequent reports and mechanisms of miRNA transfer have been suggested. In this review, we discuss the state-of-the-art in the field of intercellular miRNA transport, and particularly the mechanisms involved in this process. We will highlight actual theories regarding the origin and the biological function of extracellular circulating miRNAs in body fluids.
miRNA BIOGENESIS AND MODE OF ACTION
All miRNAs are originally generated in the cell nucleus as long primary miRNAs (pri-miRNAs) transcripts containing 5 cap and a 3 polyA tail (Lee et al., 2004). The pri-miRNAs are further cleaved by a microprocessor complex consisting of Drosha and DGCR8 proteins into ∼70 nt hairpin precursor miRNAs (pre-miRNAs) (Lee et al., 2003;Landthaler et al., 2004). On the next step pre-miRNAs are actively transported into the cytoplasm (Yi et al., 2003) where they cleaved into ∼22 bp miRNA/miRNA * duplexes by Dicer/TRBP enzyme complex (Zhang et al., 2002;Chendrimada et al., 2005). Finally, miRNA/miRNA * duplexes separate leaving one of strands associated with an Argonaute (AGO) protein (Okamura et al., 2004;Ender and Meister, 2010). This AGO associated "mature" miRNA strand sequencespecifically binds to complementary mRNAs, promoting their decay and inhibiting translation (Figure 1). Surprisingly, some miRNAs activated both translation and steady state levels of target mRNAs during cell cycle arrest in quiescent mammalian cells and Xenopus oocytes (Vasudevan et al., 2007;Truesdell et al., 2012)-a mechanism which is yet to be explained.
Four human AGO proteins (AGO1, AGO2, AGO3, and AGO4) have been described so far; all of them can mediate both translation repression of mRNA on ribosomes and mRNA decay in P-bodies. However, only AGO2 is capable of directly cleaving mRNA in the cytoplasm (Hock and Meister, 2008). AGO carrying FIGURE 1 | The biogenesis of miRNAs starts in the cell nucleus with generation of primary miRNAs (pri-miRNAs) transcripts. Pri-miRNAs are cleaved by the microprocessor complex Drosha/DGCR8 into shorter miRNA precursors (pre-miRNA). The later are transported to the cytoplasm and further cut by the endonuclease Dicer into ∼22 nt miRNA/miRNA * duplexes. Finally, one of the miRNA/miRNA * strands is incorporated into a protein of the Argonaute family (AGO1, AGO2, AGO3, or AGO4). The mature miRNA strand eventually serves as the guide for RISC-mediated mRNA targeting resulting in either mRNA cleavage or translational interference. Extracellular miRNA can be either solely AGO protein-associated or additionally encapsulated into apoptotic bodies, microvesicles, and HDL particles. miRNA forms the RNA-induced silencing complex (RISC) by binding to GW182 via C-terminal domain of AGO protein (Lian et al., 2009;Braun et al., 2013). The RISC can be localized (1) diffusely in the cytoplasm; (2) in the dense cytoplasmic structures called GW-or P-bodies-the main localization for mRNAs which undergo decapping, deadenylation, and degradation (Kedersha et al., 2005). Importantly, only 1% of cytoplasmic AGO2 was found in P-bodies whereas the majority was diffusely distributed elsewhere in the cytoplasm (Leung and Sharp, 2013). When studying extracellular miRNA the researchers must take into account the particularities of miRNA biogenesis, its mode of action and localization in the cell. Importantly, neither mature miRNAs nor pre-miRNAs were ever found within the cells in non-protein bound forms.
EXTRACELLULAR miRNA
The pioneering observations that mature miRNAs are also present in cell-free blood plasma and serum was made in the year of 2008 by several independent research groups (Chen et al., 2008;Chim et al., 2008;Lawrie et al., 2008;Mitchell et al., 2008). Later, the existence of extracellular circulating miRNA in all other biological fluids was confirmed (Park et al., 2009;Hanke et al., 2010;Kosaka et al., 2010b;Weber et al., 2010). The mechanism which is responsible for the nuclease resistance of miRNA outside the cell remained enigmatic for quite a long period; however, the presence of miRNAs in the exosomes exported by cells in culture has been known before (Valadi et al., 2007). The theory that extracellular miRNA is protected by encapsulation into membrane-vesicles emerged after Hunter et al. detected miRNAs in peripheral blood microvesicles (Hunter et al., 2008). Together with the evidence that exchange of miRNA (and also mRNA) between cells can be accomplished through exosome-mediated transfer (Valadi et al., 2007) the finding of Hunter and co-authors led to a revolutionary hypothesis-the existence intercellular and inter-organ communication system in the body by means of microvesicles (MVs) encapsulated miRNAs.
In 2011, the assumption that only membrane-vesicles encapsulated miRNAs are present in biological fluids was challenged by two independent research groups who demonstrated that 90-99% of extracellular miRNA are MVs-free and associated with proteins of the AGO family both in blood plasma/serum and cell culture media (Arroyo et al., 2011;Turchinovich et al., 2011). The remarkable stability of AGO2 protein in protease rich environment elegantly explained the resistance of associated miRNAs in nucleases containing biological fluids (Turchinovich et al., 2011).
Since then, accumulated reports have consistently shown that extracellular miRNAs can be shielded from RNAse degradation by: (1) packaging in apoptotic bodies, shedding vesicles and exosomes; or (2) solely by complexing with AGO proteins (reviewed in Cortez et al., 2011;Chen et al., 2012; (Figure 1). Some miRNA species were also found in purified fractions of high-density lipoprotein (HDL) from human plasma (Vickers et al., 2011). The existence of HDL-associated miRNAs in the blood circulation have been recently confirmed by Dimmeler's group (Wagner et al., 2013), however, the analysed HDL-miRNAs constituted only minor proportion the total circulating miRNAs. Finally, synthetic miRNA can be protected from the degradation by RNAses when mixed with purified nucleophosmin 1 (NPM1) protein in vitro (Wang et al., 2010). Although NPM1 was indeed exported by cells in culture together with miRNA, neither intracellular nor extracellular miRNA association with NPM1 has been found in vivo (Wang et al., 2010;Turchinovich et al., 2011).
THE THEORY OF CELL-CELL COMMUNICATION VIA EXTRACELLULAR miRNA
The presence of miRNA in the extracellular environment ignited the hypotheses that cells selectively release miRNAs which mediate cell-cell signaling via paracrine or even endocrine routes (Valadi et al., 2007;Cortez et al., 2011;Chen et al., 2012). However, circulating miRNAs bound solely by AGO proteins are apparently non-specific remnants resulting from physiological activity of the cells and cell death (Turchinovich et al., 2011;. Thus, both AGO2 protein and miRNAs remain stable for prolonged periods after the parental cells die. Furthermore, there are no indications of either active release of AGO-miRNA ribonucleoprotein complexes from cells or their uptake by recipient cells in mammals. The opinion that many extracellular miRNAs are released non-selectively after cell death also accords with the fact that upon toxicity in certain tissues the level of tissue-specific miRNAs in the blood increases (Laterza et al., 2009;Corsten et al., 2010;Lewis and Jopling, 2010;Zhang et al., 2010a;Pritchard et al., 2012).
At the same time, a number of independent research groups have demonstrated that extracellular miRNAs entrapped within apoptotic bodies and exosomes can be transferred to recipient cells, alter gene expression and mediate functional effects (Valadi et al., 2007;Skog et al., 2008;Kosaka et al., 2010a;Pegtel et al., 2010;Mittelbrunn et al., 2011;Montecalvo et al., 2012). Patterns of mRNAs in exosomes and their donor cells correlate poorly, suggesting specific sorting of miRNA "for export" (Valadi et al., 2007;Skog et al., 2008;Collino et al., 2010;Pigati et al., 2010;Mittelbrunn et al., 2011). The mechanism behind this sorting needs to be investigated in more detail, however, certain clues may lie within the fact that miRNAs, GW182 and AGO proteins co-localize in the compartments which are strongly linked with endosomes and multivesicular bodies (MVBs) (Gibbings et al., 2009). Because exosomes are formed in the MVB and also contain high levels of GW182, these observations may be important findings for the understanding of the loading of RNA into exosomes (Gibbings et al., 2009). It is feasible that AGO-bound miRNAs which reside in the MVBs become encapsulated randomly into the newly formed exosomes. The fact that different miRNAs might possess different decay kinetics could partially account for the fact that certain miRNAs were expressed at higher levels in extracellular MVs than in the parental cells (Bail et al., 2010;Krol et al., 2010). Another possible methodological bias which has to be addressed when comparing extracellular versus intracellular miRNA profiles include preferential loss of certain miRNAs during extraction from samples with very low RNA content (e.g., extracellular fluids) (Kim et al., 2012). Nevertheless, there is mounting evidence that cells selectively package certain miRNAs into MVs and actively secrete them. However the exact mechanisms of vesicular miRNAs sorting and secretion are yet to be discovered.
Collino and co-authors have demonstrated that MVs exported by human bone marrow derived mesenchymal stem cells (MSCs) and liver resident stem cells (HLSCs) indeed contained both miRNAs and AGO2 protein (Collino et al., 2010). Furthermore, selected patterns of miRNAs in MVs suggested their specific compartmentalization. Bioinformatics analysis revealed that MV-expressed miRNAs could be involved in organ development, cell survival, cell differentiation, and regulation of the immune system. The authors further showed that pre-treatment with the inhibitor of actin polymerization cytochalasin B significantly reduced the release of MVs from both MSCs and HLSCs (Collino et al., 2010).
At the same time several research groups have further demonstrated that exosomal miRNA is released via ceramide-dependent secretory pathway which is controlled by the enzyme of ceramide biosynthesis neutral sphingomyelinase (nSMase) (Kosaka et al., 2010a;Kogure et al., 2011;Mittelbrunn et al., 2011). nSMase mediates hydrolysis of sphingomyelin to form ceramide and is indispensable for budding of intracellular vesicles into the MVB (Trajkovic et al., 2008). Inhibition of nSMase2 with the small molecule compound GW4869 and the appropriate siRNA decreased both exosomes and miRNA secretion (Kosaka et al., 2010a). Consistently, ectopic overexpression of nSMase2 resulted in higher amounts of extracellular miRNAs (Kosaka et al., 2010a). An independent group of authors further demonstrated that inhibition of nSMase does not alter intracellular miRNA levels but reduces miRNA in secreted exosomes (Kogure et al., 2011). While these data emphasize the importance of the MVBs and sphingomyelins for miRNA excretion, how exactly the selection and the loading of specific miRNA into exosomes occurs remains unknown. Finally, cell targeting has been hypothesized to be mediated by both exosomal surface proteins and receptors on the acceptor cells. The putative mechanisms of membrane vesicles uptake can be either direct membrane fusion or endocytosis (Thery et al., 2002;Cocucci et al., 2009;Simons and Raposo, 2009).
As it was mentioned before, some extracellular miRNA was co-purified with HDL from human blood (Vickers et al., 2011). HDL particles were able to deliver miRNAs to recipient cells and mediate direct targeting of mRNA reporters, while contrary to exosomes, cellular export of HDL associated miRNAs was negatively regulated by nSMase2. In addition, HDL mediated miRNA delivery was dependent on a cell surface HDL receptor SRBI, which binds HDL and mediates the uptake of cholesteryl ester from HDL. Because small RNAs can easily complex with zwitterionic liposomes it was hypothesized that HDL could simply bind to extracellular plasma miRNAs through divalent cation bridging (Vickers et al., 2011). This hypothesis, however, assumes the existence of naked mature miRNAs in the cell. Furthermore, targeting of mRNA by miRNA requires the latter to be associated with one of the AGO proteins. Importantly, neither formation of mature miRNAs nor their existence apart from AGO proteins has been found in vivo. It is, therefore, feasible that mature miRNAs in exosomes, MVs and HDL particles can be also bound to AGO proteins. Interestingly, recent evaluation of the HDL-bound miRNAs isolated from human blood revealed that the concentration of the most abundant HDL-bound miRNA miR-223 contributed to only 8% of the total miR-223 in the circulation (Wagner et al., 2013). Furthermore, no significant uptake of HDL-bound miRNAs was observed into endothelial cells, smooth muscle cells or peripheral blood mononuclear cells (Wagner et al., 2013).
EXTRACELLULAR miRNAs ASSOCIATED WITH MICROVESICLES
Two different types of extracellular MVs described so far are shedding vesicles and exosomes. Exosomes are 30-100 nm in size, formed within the MVBs and released upon fusion of MVBs with the plasma membrane (Thery et al., 2002). Unlike exosomes, shedding vesicles are formed by outward budding and fission of the plasma membrane and can vary in size from 0.1 to 1 μm (Cocucci et al., 2009). Both types of MVs contain various proteins, mRNAs and miRNAs in a proportion depending on the cell from which they originate (Simons and Raposo, 2009;Muralidharan-Chari et al., 2010). Due to the similar size of exosomes and small shedding vesicles, it is impossible to completely separate them using differential ultracentrifugation or other physical methods. It has to be mentioned that most current reports describing isolation of MVs-associated extracellular miRNA rely on using solely ultracentrifugation. As a result, such experiments inevitably characterize miRNAs in a mixed population of two MVs types. However, researchers often refer to the miRNA isolated from ultra-centrifuged MVs to as "exosomal" miRNA. To our knowledge, there are no reports describing specifically "shedding vesicles" miRNA or specifically "exosomal" miRNA.
Exosomes can have many cell-type specific functions which were attributed predominantly to exosomal surface proteins. For example, Fas ligand located on the surface of tumor exosomes induces apoptosis in T lymphocytes (Abusamra et al., 2005). The biological function of the exosomal RNA in vivo remains questionable. However, numerous experiments performed on cultured cells have demonstrated that exosomal miRNAs can affect gene expression in the recipient cells and mediate a physiological response. A growing body of evidence that miRNAs can play a role in intercellular communication suggests the paracrine function of miRNAs which are packed in extracellular MVs (reviewed in Cortez et al., 2011;Chen et al., 2012;. The Internet-based database, ExoCarta (http://www. exocarta.org/), currently lists 463 miRNAs which were found in exosomes from various cells. In addition, the phenomenon of cellcell communication via extracellular miRNAs has been shown in multiple cell culture models (Table 1).
Collino and co-authors incubated murine tubular epithelial cells (mTEC) with MSC-derived MVs and confirmed the transport of selected miRNAs by qRT-PCR (Collino et al., 2010). The abundance of extracellular miRNAs in acceptor cell increased progressively and correlated with the extent of MV internalization. Additionally, incubation of mTEC with MSC-derived MVs resulted in the reduction of proteins known to be targeted by some of the enriched miRNAs found in MVs including: PTEN (targeted by miR-21), cyclin D1 (targeted by miR-100, miR-99a, and miR-223) and Bcl-2 (targeted by miR-34, miR-181b, and miR-16).
Microvesicular miRNA from macrophages have been shown to enhance the invasiveness of breast cancer cells in culture (Yang et al., 2011). Specifically, macrophages activated by treatments with IL-4 secreted exosomes packed with miR-223 and were able to promote migration of SKBR3 and MDA-MB-231 breast cancer cells in a transwell invasion assay. Blocking miR-223 with antisense oligonucleotides prevented the observed increase of invasion capacity. In addition, (1) miR-223 targeted Mef2c mRNA level was reduced in the exosome-treated cells, and (2) the expression of β-catenin in the nucleus increased. Based on their observations, the authors suggested that miR-223 was transferred from macrophages to breast cancer cells via exosomes where it affected the Mef2c-β-catenin pathway leading to invasiveness of the breast cancer cells. For the first time it was suggested that prevention of the exosomal communication between macrophages and breast cancer cells may help preventing cancer metastasis and being potential target for cancer therapy (Yang et al., 2011).
The capacity of exosomal miRNA to facilitate viral infection was reported by Pegtel and co-authors. After infection of B-lymphoblastoid cells with Epstein-Barr virus (EBV) the viralspecific miRNAs (EBV-miRNAs) were secreted via exosomes and affected the expression of EBV-miRNA target gene CXCL11 in co-cultured non-infected cells (Pegtel et al., 2010). Viral miRNAs were present in both B-cell and non-B-cell fractions isolated from infected patients, while viral DNA was restricted to the circulating B-cell population. This indicated that viral
miRNAs transfer from infected to non-infected cells also occurs in vivo.
Another evidence for functional cell-to-cell miRNA transfer was found during investigation of the immune synapse formation. Mittelbrunn and co-authors showed that exosomes of T, B, and dendritic immune cells contained different miRNA repertoires. Furthermore, miRNAs were transported from T cells to antigen presenting cells unidirectionally and this transport was antigen-driven (Mittelbrunn et al., 2011). In addition, transferred miRNAs could modulate gene expression in recipient cells. The exosomal miRNA-based communication between different dendritic cells has also been reported, resulting in the repression of target mRNAs of acceptor dendritic cells (Montecalvo et al., 2012).
MVs produced by THP1 monocyte/macrophage cells have been shown to deliver FITC-labeled exogenous miR-150 to HMEC-1 endothelial cells in culture (Zhang et al., 2010b). In addition, the delivery of miR-150 correlated with the reduction of a validated miR-150 target c-Myb and was accompanied with an increase in HMEC-1 cells migration. Treatment of HMEC-1 cells with specific miR-150 inhibitor abrogated the observed increase in migration. While the effect was observed in cultured cells over-expressing miR-150, it remains unknown whether extracellular levels of endogenous miR-150 in body fluids is high enough to significantly affect gene expression in targeted cells in vivo. However, the observation that plasma MVs isolated from atherosclerotic patients contained elevated levels of miR-150 ignited a hypothesis that secreted endogenous miR-150 may play a role in regulating endothelial cell migration.
Multipotent mesenchymal stromal cells are known to interact with brain parenchymal cells and promote their functional recovery. In the work of Xin et al., mesenchymal stromal cells exported miR-133b to the ipsilateral hemisphere. In addition, miR-133b was highly abundant in the primary cultures of neurons and astrocytes treated with exosome-enriched fraction released by mesenchymal stromal cells (Xin et al., 2012). Authors further showed that gap junction intercellular communication was important for the reported exosome-based miRNA transfer.
The elegant approach was used by Skog et al. to prove that exosomal RNA originating from glioblastoma tumor cells is taken up by recipient cells (Skog et al., 2008). The authors incorporated mRNA encoding luciferase reporter into exosomes and monitored luminescence of the recipient cells. Glioblastoma-derived MVs stimulated proliferation of a human glioma cell line enhancing further tumor progression. Besides, the authors demonstrated that serum MVs from glioblastoma patients contain mRNAs and miRNAs characteristic for gliomas and thus provide a potential diagnostic use.
Interestingly, the miRNAs from the let-7 family were found within the exosomes exported from the cultured metastatic gastric cancer cell line AZ-P7a but not from less metastatic cell lines (Ohshima et al., 2010). Because these miRNAs are known to be tumor-suppressive, the authors suggested that their elimination via exosomal export can maintain the oncogenic properties of the metastatic cells.
Hepatocellular carcinoma cells (HCC) have been shown to produce exosomes with specific mRNA, miRNA, and protein content (Kogure et al., 2011). The miRNAs highly enriched within HCC exosomes were predicted to target transforming growth factor β activated kinase-1 (TAK1), which contributes to local spread, intrahepatic metastases, or multifocal growth of this type of carcinoma cells (Kogure et al., 2011). Indeed, HCC-derived exosomes modulated TAK1 expression and enhanced transformed cell growth in recipient HCC in culture.
Another cancer-based model was based on human renal cancer stem cells. Grange and colleagues reported that a subset of tumor-initiating MSCs from human renal cell carcinoma released MVs which triggered angiogenesis and promoted the formation of a pre-metastatic niche. Importantly, cancer stem cell MVs contained miRNAs implicated in tumor progression and metastases, and conferred an angiogenic phenotype to normal human endothelial cells, stimulating their growth and vessel formation (Grange et al., 2011). However, it remains uninvestigated whether the miRNAs were responsible for the observed physiological impact.
Hergenreider and co-authors have found that extracellular vesicles mediate miRNA transfer from human endothelial cells to smooth muscle cell in vitro. Specifically, membrane vesicles secreted by shear-stressed cultured endothelial cells were enriched with miR-143/145 and modulated gene expression in co-cultured smooth muscle cells (Hergenreider et al., 2012). Moreover, miR-143/145-containing vesicles inhibited atherosclerotic lesion formation in the aorta in a mouse model suggesting a potential therapy against atherosclerosis.
EXTRACELLULAR miRNAs ASSOCIATED WITH OTHER CARRIERS
The products of cell apoptosis (or programmed cell death) are apoptotic bodies (AB) 1-2 μm in size (Kerr et al., 1972;Hengartner, 2000;Hristov et al., 2004). Together with exosomes and MVs, some researchers consider ABs as carriers of cell-cell communication information. Thus, both viral and chromosomal DNA can be transferred between somatic cells by uptake of the apoptotic bodies (Holmgren et al., 1999;Bergsmedh et al., 2001). Zernecke et al. has shown that ABs inhibit atherosclerosis progression when injected into the blood circulation. The authors also proposed that miR-126 encapsulated into ABs may be responsible for this protective effect via induction of the chemokine CXCL12 expression. Indeed ABs contained miR-126 and delivered miR-126 to recipient vascular cells (Zernecke et al., 2009). Furthermore, injections of miR-126 containing apoptotic bodies reduced manifestations of atherosclerosis in mice, while apoptotic bodies isolated from miR-126-deficient animals did not have such an effect. The protective effect was accompanied by elevated expression of CXCL12 in the carotid arteries. It has to be mentioned that in their experimental model the authors describe incubation of carotid arteries with relatively high concentrations of ABs in vitro. It remains to be tested whether physiological levels of ABs would affect gene expression in a similar manner.
Solely AGO protein-associated miRNA represents by far the largest class of extracellular miRNA (Arroyo et al., 2011;Turchinovich et al., 2011;. It was hypothesized that the AGO-ribonucleoprotein complexes are passively released by all cells after either necrotic or apoptotic death and remain stable in the extracellular space due to the high stability of the AGO proteins (Turchinovich et al., 2011;. However, it cannot be completely excluded that certain cell membrane-associated channels or receptors mediate specific release of some AGO-miRNA complexes. Interestingly, in C. elegans, cellular uptake of dsRNA is mediated by a transmembane channel protein SID-1 (Feinberg and Hunter, 2003). In addition, SID-1 is capable of importing synthetic miRNA precursors and long hairpin molecules into the cell (Shih and Hunter, 2011). While the mammalian homologs of SID proteins do exist, it remains unclear whether they can uptake RNA from extracellular fluids (Duxbury et al., 2005;Wolfrum et al., 2007). Furthermore, it remains to be evaluated whether AGO-bound single stranded mature miRNA can be recognized by SID proteins in a similar manner as "naked" double stranded RNA. Amazingly, two recent research reports suggest that extracellular miRNA may work in non-canonical ways. Specifically, either dead cell-released or exosomes secreted miRNAs can act as signaling molecules to mediate intercellular communication via binding to extracellular or intracellular Toll-like receptors (TLRs) (Fabbri et al., 2012;Lehmann et al., 2012). TLRs are a family of innate immune system receptors which recognize various molecular patterns of microbial pathogens and induce antimicrobial immune responses (Takeda et al., 2003;Blasius and Beutler, 2010). In 2001, Alexopoulou and co-authors first showed that dsRNA binds to mammalian TLR-3, consequently leading to the activation of NF-kappaB and the production of type I interferon response (Alexopoulou et al., 2001). Later, Kleinman and co-authors reported that cell surface TLR-3 mediates extracellular siRNA-induced inhibition of angiogenesis independently of siRNA sequence (Kleinman et al., 2008). The intracellular TLRs located within endolysosomal compartments can also bind both double stranded and single stranded nucleic acids derived from viruses and bacteria (Heil et al., 2004). Among the major effects of the activation of intracellular TLRs is the induction of cytokines essential for innate immune responses. In their work, Fabbri et al. showed that miR-21 and miR-29a secreted by tumor cells are capable of binding to murine TLR-7 and human TLR-8 in immune cells, triggering secretion of prometastatic inflammatory cytokines that ultimately may lead to tumor growth and metastasis (Fabbri et al., 2012). The authors also concluded that extracellular miRNAs could function as key regulators of the tumor microenvironment by acting as paracrine agonists of TLRs (Fabbri et al., 2012). The recent report of Lehmann and colleagues provided further evidence in favor of the unconventional role for the extracellular miRNAs (Lehmann et al., 2012). Intrathecal injection of extracellular let-7b into the cerebrospinal fluid of wild-type mice, but not TLR7 knockouts, resulted in activation of microglia/macrophages and neurodegeneration. Furthermore, susceptibility to let-7-induced toxicity was restored in neurons transfected with TLR7 by intrauterine electroporation of Tlr7 −/− embryos. The authors also observed that: (1) dying neurons released let-7b in vitro; and (2) levels of let-7b were increased in CSF from patients with Alzheimer's disease (Lehmann et al., 2012). These results suggest that extracellular miRNAs can function as signaling via TLR-7 pathway and contribute to the spread of CNS damage.
In 2011, Vickers and colleagues reported that HDL complexes isolated from human blood plasma contain miRNA and could transmit this miRNA into other cells (Vickers et al., 2011). To examine whether miRNAs carried by HDL can alter gene expression in distant cells, HDL were isolated from hypercholesterolemia patients and healthy subjects. Treatment of human hepatocytes in culture with HDL derived from hypercholesterolemia subjects significantly increased the level of miR-105 in these cells, whereas HDL from healthy controls had no such effect. Further microarray analysis revealed that HDL from hypercholesterolemia patients induced profound alterations in mRNA expression including downregulation of multiple putative targets of miR-105 in cultured hepatocytes. Contrary to exosomes, cellular export of HDL-associated miRNAs was negatively regulated by nSMase2. In addition, HDL mediated miRNA delivery was dependent on a cell surface HDL receptor SRBI, which binds HDL and mediates the uptake of cholesterylester from HDL.
CONCLUSION AND FUTURE PERSPECTIVE OF THE FIELD
Despite a number of fascinating examples of intercellular communication via miRNA between cells in culture, the physiological significance of such paracrine or endocrine impact in the body is challenged by the fact that the vast majority of the extracellular miRNA are present in membrane-vesicle-free AGO proteinassociated form. Furthermore, the concentration of miRNA in the biological fluids is drastically lower than in the surrounding cells and might be below the threshold for triggering any significant physiological effect in vivo (Turchinovich et al., 2011;Williams et al., 2013). Finally, so far extracellular miRNA trafficking was consistently shown: (1) only in cultured cells; and (2) only for several miRNAs.
In their recent report Tuschl group argues against a hormonelike effect of extracellular miRNA in the blood (Williams et al., 2013). Deep sequencing experiments revealed that the concentration of total miRNA in the plasma is within 100 fM range, and the concentration of any individual miRNA is only a fraction of this number. However, even the lowest level trace hormones in the blood are present at least in the picomolar concentration range. The action of hormones implies receptor-binding and multimillion amplification of the transmitted signal within the cell. Unlike hormones miRNAs require intracellular levels of greater than 1000 copies per cell to exert measureable activity on their mRNA targets (Williams et al., 2013). Based on these calculations the authors concluded that it is unlikely that miRNAs can function as hormones unless they bind to a sensitive miRNA receptor (Williams et al., 2013).
The paracrine mode of cell-cell signaling for extracellular miRNA appears to be more feasible. Indeed most, if not all, current reports describe evidence of rather short distance communication of cells via extracellular miRNA. Unlike average miRNA levels in a biological fluid, the local concentrations of extracellular miRNAs could suffice to secure the delivery of physiologically relevant amounts of miRNA from donor to neighboring acceptor cell. Recent evidence of interaction of miRNA with TLRs provided additional complexities to distinguish sequence-specific effects of extracellular miRNA on the targeted mRNAs expression in acceptor cells and non-specific response of the innate immune system (Fabbri et al., 2012;Lehmann et al., 2012).
Despite the fact that extracellular miRNA circulating in biofluids has many properties of promising biomarkers for various pathological conditions, the concept of miRNA mediated cellcell signaling in vertebrates requires further validation. Among the central questions to be answered remains: (1) whether solely protein-bound extracellular miRNA can penetrate through the cell membrane and if so, which mechanisms are responsible; (2) whether concentrations of MVs-associated miRNAs are above the physiological limit to mediate any significant para-or endocrine signaling in vivo; (3) what are the mechanisms of selective export of miRNAs into extracellular space; (4) how many miR-NAs out of the total extracellular pool participate in cell-cell signaling. | 6,958 | 2013-06-28T00:00:00.000 | [
"Biology"
] |
A computational model of epidemics using seirx model
Epidemiology studies the spread and impact of infectious diseases within defined populations, focusing on factors such as transmission rate, infectious agents, infectious periods, and susceptibility. Computational epidemiology simulates these factors using basic compartmental models like Susceptible-Infected-Recovered (SIR), Susceptible-Exposed-Infected (SEI), and Susceptible-Exposed-Infected-Recovered (SEIR). However, these models inadequately address mortality and fatality rates. To enhance the accuracy of epidemic transmission models, we propose an expanded SEIR model by introducing a new compartment, denoted as X, representing the deceased population. This new model, Susceptible-Exposed-Infected-Recovered-Deceased (SEIRX), incorporates fatality and mortality rates, providing a more comprehensive understanding of epidemic dynamics. The SEIRX model demonstrates superior accuracy in inferring and forecasting epidemic transmission compared to existing models, offering a complete and detailed approach to studying infectious disease outbreaks.
INTRODUCTION
The raw data and comprehensive observational data are not enough to forecast the outbreaks of epidemics.In order to have more accurate and complete picture of transmission dynamics inference of epidemics the computational analysis can be used.Inference and forecasts of the outbreak can be used to make required arrangements of medicines and medical personnel.Mathematical modeling and Bayesian inference have been developed in the area of infectious disease modeling have enabled the assumption of key epidemiological characteristics related with the historical disease outbreaks.The deterministic and stochastic models were employed for both model specification and observational error by providing a better estimate of system behavior than simply analysis using the data or model alone.
Mathematical models can be used to forecast how pathogens progress, the current state, and expected results.These models consider few basic assumptions and mathematics to find factors for various infectious diseases and applies those factors to calculate the effects of possible interventions, like herd immunity and mass vaccination programs.There are three basic types of computational models that are available for infectious diseases which are spread among the defined population by person-to-person.Parameters are estimated and categorized for various kinds of diseases.These parameters are used to identify the herd immunity ratio and vaccination.The mathematical models are presented with notations, concepts, intuition and more refined models.
The SEIRX model is an extension of the classic SEIR (Susceptible-Exposed-Infectious-Recovered) epidemiological model, incorporating additional compartments to represent specific sub-populations or factors influencing disease dynamics.The term "X" typically denotes an extra compartment or a set of additional features beyond the core SEIR structure.The SEIRX model is widely used in infectious disease modeling to provide a more nuanced understanding of epidemic scenarios.
Here's a brief introduction to the key components of the SEIRX model: Susceptible (S): this compartment represents individuals who are susceptible to the infectious disease but have not yet been exposed.
Exposed (E): individuals in this compartment have been exposed to the pathogen but are not yet infectious.This stage accounts for the latent period between exposure and becoming infectious.
Infectious (I): this compartment includes individuals who are infectious and capable of transmitting the disease to susceptible individuals.
Recovered (R): individuals who have recovered from the infection and gained immunity are placed in this compartment.
X Compartment: the "X" compartment introduces additional complexity to the model.This could represent various sub-populations, such as asymptomatic carriers, hospitalized individuals, or those under specific interventions like vaccination.
Spreading of the epidemics among a defined population has been described by several types of computational models either stochastic or deterministic.The application of these models varies according to the kind of parameters consider and computational methods.The World Health Organization (WHO) observations are considered and are compiled with computational modeling and Bayesian inference to estimate the key characteristics of epidemiology and inference mortality levels and future case for the current Ebola outbreak in West Africa.We collected data of epidemic outbreak of Ebola for a week and used those collected data to assess inference and forecasting model performance. (14)
Related work
Ad-hoc balancing palliation solutions aim to maintain a self-balancing business pace after a specified mitigationfree period of time have been developed.They evaluated the impact of several balancing methods in the latter context in light of the COVID-19 outbreak in England and the Brazilian state of Amazonas. (1)For the model under study, two rumour existing-endemic equilibrium points one rumor-free have been developed.Then, using the fuzzy forward Euler and fuzzy nonstandard finite difference (FNSFD) methods, the model is numerically solved (2) The findings have significance for academics looking to use scaled populations in their work since they suggest that distinct regional dynamics of the spread of disease are particularly connected with varied population sizes (3) During a pandemic, the suggested framework offers regional and national authorities a useful tool for improved public health decisions, (4) Their findings suggest that healthcare overcapacity will develop when predicted economic effects are greater.But when the illness severity is low and the pandemic's predicted economic losses are high, a no-intervention policy might be preferred.The expense of intervention increases in direct proportion to the infection's severity.Along with the severity of the economic costs of interventions and the rate of illness infection, the death toll also rises.Our models recommend earlier mitigation tactics, often beginning before the healthcare system becomes saturated when illness severity is high (5) This model explains how infectious diseases spread and how a person can go from being vulnerable to becoming infected and then recovering (7) The results demonstrate the effectiveness of the two methods, with both achieving classification accuracy levels of over 70 %.Additionally, the trials we ran show how association rule mining can be used and is useful for Salud, Ciencia y Tecnología -Serie de Conferencias.2024; 3:.1107 2 categorizing images.This model accurately captures Nairobi's STD (Sexually Transmitted Diseases) prevalence and HIV prevalence temporal trend. (8)They proposed a straightforward technique to model dynamic networks of sex relationships.We study how the duration of infectiousness alters the effective contact network over which disease may spread using survey data on sexual views and lifestyles.Then, we mimic a number of control techniques, including behavioral treatments, immunization, and screening. (9,10)he Sustainable Development Goals (SDGs) place a priority on enhancing global health and well-being, as evidenced by their targets to eradicate AIDS, tuberculosis, and malaria epidemics, make important progression in maternal and children health, and combat the rising incidence of non-communicable diseases (NCDs).The primary findings of the Commission's report are that the HIV epidemic is not on course to be eliminated and that the instruments available today are inadequate.Notwithstanding the fact that anti-retro viral therapy (ART) has altered the immune system's response to HIV by reducing mortality, improving quality of life, and preventing new HIV infections, treatment for HIV itself will not stop the spread of HIV.The UNAIDS 90-90-90 strategy must be backed by a strong serious-mindedness to particular HIV interference that is scaled up, as well as to the creation of a impeding vaccine and a workable HIV cure.(11) They developed the SEAIHRDS adaptable mathematical framework, which stands for "Susceptible, E-exposed, A-asymptomatic, I-infected, H-hospitalized, R-recovered, d-dead from COVID-19 infection, S-susceptible."The framework can predict likely epidemic consequences, especially the necessary hospital capacity, and simulate various deployment scenarios for preventive approaches.(12) For the purpose of digital mammography tumour identification, some tests have been conducted.They looked into the use of several data mining methods, including neural networks and association rule mining, for the identification and classification of anomalies.The outcome demonstrate the effectiveness of the two methods, with both achieving classification accuracy levels of over 70 %.Additionally, they exploited association rule mining's efficiency for image categorization in their tests.(13) Deep learning algorithms are used for improving health using smart health care management systems and analysis of psychological disorder.(14,15) The SIR Model The Suspected-Infected-Recovered Model is used in epidemiology to figure out the amount of susceptible, infected, recovered people in a define population.
Assumptions
The models can be defines as good when they considers appropriate assumptions.The SIR model considers the basic and appropriate assumptions as follow: The basic factors considered in SIR model are susceptible, infected and recovered individuals at time t, for total population size N.The differential equation is given by: The total population is such a way give as: The figure 1 depicts general model for epidemics.Epidemic models serve as essential tools for explaining and predicting the rate at which infectious diseases spread.These mathematical and computational models are designed to capture the dynamics of disease transmission within a population, considering factors like transmission rates, recovery rates, and population demographics.There are two main types of epidemic models: deterministic models, which use fixed parameters to predict average epidemic behavior, and stochastic models, which introduce randomness to account for individual variations and events.
Several common epidemic models include the SIR model, which tracks the susceptible, infectious, and recovered populations; the SEIR model, which adds an exposed compartment for those exposed but not yet infectious; and compartmental models with age structure, considering the age distribution of a population.These models play a crucial role in epidemiology, helping researchers and public health officials understand how interventions like vaccination, social distancing, and healthcare capacity can influence the course of an epidemic.They are valuable tools for planning public health strategies, developing policies, and allocating resources during disease outbreaks.
The SEIR Model Assumptions
In figure 2, The SEIR Model is employed to estimate the population's exposure, susceptibility, infection, and recovery rates.The SEIR model's presumptions are the same as those in the SIR model.
There is a significant incubation period for many serious infectious diseases, during which the affected individual has been infected but is not yet contagious.The person is regarded as exposed throughout this time.With the assumption that the incubation period has an arbitrary exponential distribution with parameter and that vital dynamics occur when the death and birth rates are equal, the following model is obtained: The total population is such a way give as:
Basic Reproductive Ratio
In addition with the Susceptible, Exposed, Infected and Recovered compartment, an important factor to be considered is the Basic Reproductive Ratio, denoted as BR.The Basic Reproductive Ratio is used to tell us if a Salud, Ciencia y Tecnología -Serie de Conferencias.2024; 3:.1107 4 population is at risk from a disease.BR is affected by the infection and removal rates, i.e. β, k and is denoted by B R = β/kS 0 .The three conditions of disease impact are When BR > 1, the occurrence of the disease will increase.When BR = 1, the disease occurrence will be constant.When BR < 1, the occurrence of the disease will decrease and the disease will eventually be eliminated.Who will not fully contract the infection is also predicted by the basic reproductive ratio.The SIR model's behaviour facilitates this.
Herd Immunity Threshold
Herd immunity is a way to reduce the number of people who need to get vaccinated but have never experienced the disease that could start an epidemic.The Herd Immunity Threshold is a measurement that determines what proportion of the infectious population must be immune to stop the spread of a disease.Diekmann and Heesterbeek's formula for calculating the herd immunity threshold is: This can successfully halt the spread of disease throughout the neighbourhood.The herd immunity threshold rises with the number of vaccinations given.The herd immunity threshold lowers as the population of susceptible individuals increases.
Effective Reproductive Number
The Effective Reproductive Number aids academics and public health professionals in assessing how well their disease-control strategies are working.The fundamental reproductive ratio is multiplied by the population that is sensitive at time t to determine ERN.It's indicated as: Where BR is Basic reproductive ration and St is number of persons who are susceptible and N is the population size.
Proposed SEIRX model
An SEIR model stands for Susceptible-Exposed-Infectious-Recovered, and the additional "X" might indicate an extension or modification.
In the context of epidemic modeling, analyzing the results of an SEIRX model involves examining the trends and patterns in the susceptible, exposed, infectious, and recovered (and possibly additional) compartments.
Here's a general guideline for analysis: Initial Conditions: check the initial conditions of the model.The number of initially susceptible, exposed, infectious, and recovered individuals can significantly influence the epidemic dynamics.
Transmission Rate (Beta): analyze the impact of the transmission rate (beta).Higher values of beta typically lead to a faster spread of the disease, while lower values might result in a slower epidemic progression.
Incubation Period (Exposure Rate): evaluate the incubation period or exposure rate.This parameter influences the duration individuals spend in the exposed compartment before becoming infectious.
Recovery Rate (Gamma): examine the recovery rate (gamma).A higher recovery rate implies a shorter infectious period, potentially leading to a faster decline in the number of infectious individuals.
Additional Compartments (X): if the "X" in SEIRX introduces additional compartments (e.g., for asymptomatic carriers, hospitalized individuals, or other specific groups), analyze how these compartments contribute to the overall dynamics of the epidemic.
Interventions: assess the impact of interventions or changes in parameters over time.For example, introducing vaccination, social distancing, or other control measures can significantly alter the course of the epidemic.
Sensitivity Analysis: conduct sensitivity analyses to understand how changes in model parameters affect the results.Identify which parameters have the most significant impact on the outcomes.
Model Validation: validate the model results against real-world data if available.This step is crucial for ensuring that the model accurately reflects the observed epidemiological trends.
The Susceptible, Exposed, Infected, Recovered (SEIR) model was one of the parameters used in earlier Ebola epidemic modelling research.Although the aforementioned criteria are taken into account by the current models, they were insufficient, and it was unclear how epidemics were transmitted.Additional needed compartments are taken into consideration in order to more accurately and thoroughly define the Ebola transmission cycle and forecast the dynamics of outbreaks.In order to include integration of fatality rate and mortality data in addition to incidence data for the deceased population in this attempt, we introduce a new compartment called X. Marimuthu S, et al https://doi.org/10.56294/sctconf2024.1107 The following equations provide a description of the model: Where, X is the deceased person with respect to time and η is the case fatality rate.The stochastic variable for the transmission rate exerted by the live person is defined as: Where, R0 Mean is a mean reproductive number.R0 Amp is the maximum amplitude with which the daily reproductive number, R0(t) varies around R0Mean, and κ is a number collected randomly from the uniform distribution of range [-0,5, 0,5] To find reflection of epidemics in a defined group or village, R0(t) can be increased i.e., R0(t) R0Mean + 0,5 R0Amp.Same way the implementation of interventions and vaccinations the R0(t) can be decreased i.e., R0(t) R0Mean -0,5 R0Amp.The values of R0Mean, R0Amp can be applied to find the R0(t) as the time sequence of these discrepancy are unknown.This can be done by the stochastic formulation.
Initially the outbreak of epidemics will be limitad and hence the Ebola epidemics apeares erratically.This situation may lead report with errors.And also it may reflect discrepancy in the swelling of outbreaks to the new regions.This can be eradicated by the stochastic models.To conquer this issue SEIRX framework i.e., above mentioned equations and stochastic formulation can be employed to produce the occurrence time similar to these observations.
RESULTS
Methodology: susceptible-Exposed-Infected-Recovered-Deceased (SEIRX) Model: In epidemiology, the Susceptible-Exposed-Infected-Recovered-Deceased (SEIRX) model is a variation of the classic SEIR model that mimics the transmission of infectious diseases.By including fatality and mortality rates, this model incorporates a new compartment to represent the population that has passed away, offering a more thorough understanding of illness dynamics.
Simulation of 300 members with the SEIRX model was used with the observations of WHO of weekly cumulative occurrences, case fatality rate, mortality and Ensemble Adjustment Kalman Filter (EAKF).To make the observation to be smoothed the iterative simulation of EAKF algorithm were employed.By adjusting the EAKF, the variables and R(t) can be explicitly varied within the SEIRX model system.
Salud, Ciencia y Tecnología -Serie de Conferencias.2024; 3:.1107 6 3 shows the SEIRX of the instances collected from WHO of Ebola epidemics.The analysis starts with assumption that everyone being susceptible to the disease and then one person among the defined population suddenly becomes infected.To calculate the β, we know that: Table 4 shows the average beta value with respect to the table 2 and 3 values.
The Effects of Infectious Rate and the amount of Initial Infectious persons Calculation the infectious rate is very essential in disease modeling.Ebola's infection rate lies between 65-85 %.This number affects how long it takes until everyone that will get the disease, recovers from it and the amount of people in the susceptible, infected, exposed and recovered groups.The second set of graphs shows how the people in the susceptible, infected, exposed and recovered groups are by infectious rates.
Controlling for initial amount of people that are infected for our two cases (α=0,65 and β=0,85).
Effects of Infectious Rate
Figure 3. comparative analysis on amount of infected, susceptible, recovered, and population.3.1 Susceptible Group, 3.2 Exposed Group, 3.3 Infected Group, 3.4 Recovered Group, 3.5 Decreased group With higher and smaller alpha.From figure 3.1, the amount of susceptible people decreases faster than that of a smaller alpha.From figure 3.2, the population with the higher alpha has a higher peak, than that of a smaller alpha.3.3, with the increase in the people who are initially infected, the time it takes for the susceptible to converge is less.From figure 3.4, the recovered group of higher alpha increases soon than that of a small alpha.From figure 3.5, as we decrease the initial amount of infected people, the peak is increased.combined Results and Discussion section is often appropriate.Avoid extensive citations and discussion of published literature.
Using historical data from recent infectious disease outbreaks, such COVID-19 and Ebola, the SEIRX model was assessed.In comparison to the classic SIR, SEI, and SEIR models, a comparative analysis revealed that the SEIRX model obtained superior accuracy in predicting the course of the epidemic, including the number of killed individuals.The SEIRX paradigm significantly improved performance measures like Mean Absolute Error (MAE) and Root Mean Square Error (RMSE).
CONCLUSION
The SEIRX estimate calculates the number of individuals in a particular group who are susceptible, exposed, infected, recovered, or died at a given time in order to estimate epidemic outbreaks and their effects.Researchers and health officials simulate the model to forecast the medical requirements that people might have during an epidemic of a particular disease.Researchers and health administrators can determine various figures from the SEIRX model's results that indicate if activities and safety precautions are effective and Salud, Ciencia y Tecnología -Serie de Conferencias.2024; 3:.1107 8
Table 1 .
List of parameters using in modeling Parameter/ Notation Description S Number of susceptible individuals I Number of infected individuals R Number of recovered individuals α Probability of becoming infected by a disease β Average number of transmissions from an infected person in a time period η Case called fatality rate N Population size Z Average time with which the person becomes infected before exposed D Mean infectious period M Average time from symptom onset to deathSource: Wise S et al.(3)
Figure 1 .
Figure 1.General SIR model for epidemics
Figure 2 .
Figure 2. General SEIR model for epidemics including exposed phase
Table 2 .
The number of cases in each state per period for α=0,65
Table 3 .
The number of cases in each state per period for α=0,85 | 4,436.6 | 2024-08-13T00:00:00.000 | [
"Computer Science",
"Medicine"
] |
Numerical Assessment of Enhanced Coatings in Wire Mesh Volumetric Absorbers
. Two different wire mesh open volumetric receivers (OVRs) are studied together with six different coatings and two different working conditions in order to assess their effect on the performance of the OVR comparing them to the two baseline OVRs, uncoated and state-of-the-art. The results show that selective coatings produce the best OVR thermal results, having the best results when the solar absorptance is as high as possible and the thermal emittance is as low as possible.
Introduction
Among the different CSP technologies, central receiver systems (CRSs) do have the potential to increase the efficiency of the technology, make it more reliable and cost-effective, leading the future generation of CSP technologies.CRS can operate at very high temperatures and solar fluxes, and can be coupled with innovative power cycles and thermal energy storage (TES) systems, either commercially available or innovative ones [1,2].The most implemented CRS used molten nitrate salt technology, working at maximum temperatures of around 838K (565ºC).The hot molten salts are used to produce high-quality steam which drives a Rankine cycle to produce electricity [3].
Innovative new designs and alternatives to the reference tubular receivers are receiving research attention as possible solutions to increase solar-to-thermal/electrical efficiency, such as particle receivers [4], alternative point-focus designs [5] and volumetric receivers [6,7].Research on volumetric receiver's dates from the early 80s with the first volumetric concept proposed by Fricker [8].Recent work has focused on the search for new designs and solutions for coupling open volumetric receivers (OVRs) with combined cycles [9].Concerning the OVR, most of the literature studies deals with ceramic materials, as they withstand temperatures above 1073K [10].However, new metallic designs are able to achieve high efficiencies for temperatures up to 1273K [11].
Moreover, CRSs usually paint the receivers with a non-selective coating in order to increase their solar absorptance ( ), despite those coatings having a high thermal emittance ( ).Currently, significant research is being devoted to the improvement of high-temperature selective coatings (SCs) that could work in air, which will allow their use in CRSs.The CIEMAT-PSA has made some advances in this area, and this work will present data from two metal absorbers with six different coatings compared to two different baseline optical characteristics.
Baseline and coating descriptions
This work analyses how six different optical coatings affect the thermal performance of two metallic OVRs made of 310 stainless steel using a two-dimensional (2D) computational-fluiddynamic (CFD) model, comparing the performance of the coatings against two baselines, uncoated and state-of-the-art.Two of the coatings have been developed by CIEMAT-PSA and are SCs.Another one is the commercial Pyromak 2500 coating.Finally, three cases involve theoretical candidates with intermediate values between the two SCs that may guide future materials development.In detail, the cases analysed are as follows: • Case 1 (C1) refers to the baseline uncoated bare metallic mesh with the optical properties that have been validated with experiments and simulations: α s = ε T = 0.80 [12].• Case 2 (C2) adopts the state-of-the-art optical properties usually implemented in the numerical simulations, α s = ε T = 0.95, for oxidized metals or bare ceramic materials [13,14].• Case 3 (C3) is an SC developed for high temperature applications where all layers are deposited using a dip-coating technique.It presents a α s of 0.96 and a ε T of 0.16 at 973K.It is stable in air at temperatures up to 973K.It can be deposited on several stainless steel alloys and has the structure depicted in Figure 1.• Case 4 (C4) represents a second SC using dip-coating technology, initially developed for application on silicon carbide and alumina substrates during the NEXTOWER Project [15], but which should be able to be applied to stainless steel absorbers.It has a solar absorptance of 0.973 and a thermal emittance of 0.652 at 973K.The coating was stable at 973K, however both optical properties were reduced due to high temperature layer contraction.
The structure is shown in Figure 2. • Case 5 (C5) is the Pyromark 2500 coating.It is used as the reference coating implemented in commercial tower power plants due to its high solar absorptance and good thermal durability.It is coated by spraying and cured following a specific thermal protocol and is stable up to 1366K.The solar absorptance varies from 0.96 to 0.97, depending on the layer thickness, and the thermal emittance at 973K is 0.878.• Case 6 to 8 (C6-C8) have values that lie between SC1 (C3) and SC2 (C4) and help to provide a finer grained analysis of the effects of certain optical characteristics.
Numerical methodology
The continuum method has been adopted in this research as it focuses on the macroscopic phenomena involved.This modelling strategy is usually adopted because of the balance between accuracy and low computational resources needed [16].The main assumptions adopted are [17]: a) The air is an ideal gas; b) The flow is laminar; c) The thermal properties of the fluid and solid are temperature dependent; d) The radiative properties are isotropic; e) The incident radiation is collimated.
Conservative equations
Both phases (fluid and solid) energy equations have to be solved, especially when the temperature profiles of both phases are needed.In such a case, the local thermal non-equilibrium (LTNE) model is adopted, where the coefficient ℎ is responsible for coupling them.
The source term within the solid phase for the solar irradiation follows the Beer's law: To analyse the effect of the radiation inside the OVR, the Rosseland approximation is used [18].
Effective properties
The effective properties are parameters required to solve the energy equations, and their accuracy determines the feasibility of the numerical predictions.The main properties are the heat transfer coefficient, ℎ , the effective fluid and solid conductivities, , and , , and the radiative properties, .
Heat transfer coefficient
The heat transfer coefficient determines the rate of heat transferred from the solid porous structure to the fluid per unit volume and is the main parameter to couple both energy equations [19].
Fluid and porous conductivities
The conduction is modelled with the correlations from [20].
Radiative properties
The main radiative property is the extinction coefficient which is dependent of the wire mesh diameter and the porosity following the next equation [12]:
Boundary conditions
The conservative equations require the following boundary conditions in order to be solved: • The air temperature at the inlet boundary is fixed to 300 K together with a velocity of 1 m/s.• The air pressure at the outlet boundary is set to 0.
• The thermal losses to the ambient are computed following the Stefan-Boltzmann law.
Wire mesh parameters
For the CFD simulations, two commercial wire mesh screens with a diameter of 50 mm and a thickness of 20 mm are used.Table 2 presents the main properties [21,22]: d is the wire diameter, M is the mesh count, ∅ is the porosity, is the specific surface area and is the extinction coefficient.The coefficient a, b and c are those used in (5).
Results and discussion
Current SCs are able to work at temperatures up to 973K with a stable performance in air; however, OVRs require higher temperatures, especially for the solid phase of the volumetric receivers, which can reach temperatures of 1273K or higher.So, this study analyses two different working conditions, both having an inlet velocity of 1 m/s: a) the usual working conditions of OVRs of 600 kW/m 2 /s, and b) limiting the temperature of the solid phase to 973K.
Working condition 1: Solar flux equals 600 kW/m 2
This section studies two metallic OVRs (Table 2) with 70% and 62% porosity, with eight different optical properties (Figure 3 and Table 1) and a solar flux of 600 kW/m 2 .
Table 3 presents the main thermal results for the first working condition (WC1).It is worth noting that in all the cases, except C1, the frontal solid temperature (T s−in ) for both meshes exceeds the 973K limit for SCs.
Overall, the increase in means a higher solid temperature, and a higher air outlet temperature (T f−out ), while the decrease of with temperature results in lower radiative thermal losses (Loss) of the OVR frontal surface, which subsequently yields higher thermal efficiency (η OVR ).Thus, comparing C1 and C2, where both optical parameters ( , ) change from 0.80 to 0.95, higher T s−in and thermal losses (Loss) are observed, but an improvement of T f−out and η is also seen due to a higher and despite the higher thermal losses.If C1 (uncoated material) is compared to C5 (Pyromark), the relative thermal efficiency improvement (∆η OVR ) is 17%.Comparing with the different SCs, the better the optical properties �↑ and ↓ �, the better the thermal efficiency.It should also be noted that the better the thermal efficiency, the higher T s−in and T f−out .
Finally, the thermal performance of a stainless steel OVR can be improved greatly using a non-selective coating such as Pyromark 2500 (17%), and even more if a SC is used, ranging from 20.1 to 24.8%.Between the two mesh types (A & C), the results are better for mesh C, with the ∆η OVR of the different cases being similar.The value for mesh type C is slightly lower since the uncoated mesh (C1) has better performance, which makes the ∆η OVR lower.However, it is important to note that mesh type C could reach an efficiency of 89.6% with the Pyromark coating and even 92.3% with the first SC (C3).
Working condition 2: Variable solar flux
Given that the constant solar flux of 600 kW/m 2 produced T s−in above 973K, which is the current limit for selective coatings, in all but the baseline case, this working condition adjusted incident solar fluxes to limit the temperatures for all eight cases to that maximum.
Table 4 presents the main thermal results for the second working condition (WC2).It is worth noting that the solar flux (Flux) of all the cases with mesh type A, except C1, have a value lower than 600 kW/m 2 to achieve the target T s−in .On the other hand, all the cases with mesh type C require a much higher Flux value to achieve the same target temperature.
The cases with mesh A have a T f−out ranging from 681 to 690K, while η varies from 73.0 to 92.8% and the incident solar flux varies from 499 to 646 kW/m 2 .The cases with mesh C have a T f−out ranging from 874 to 878K, while η varies from 73.6 to 91.8 % and the incident solar flux varies from 499 to 971 kW/m 2 .The OVRs with mesh C have a higher T f−out , ~200K greater, than OVRs with mesh A, despite the η having similar values.In some cases η has higher values for mesh type A (C3; C6; C7), while in other cases OVRs with mesh type C have higher values (C1; C2; C4; C5; C8).Moreover, the thermal losses are almost the same in all cases for both mesh types, because they have the same T s−in , and the same optical properties, only varying in their physical properties (Table 2), which are similar in terms of ∅.
Conclusions
This numerical research analyses the performance of open volumetric receivers with two different designs and how they vary for eight different optical properties.It includes the optical properties of uncoated wire mesh screens, the usual properties adopted in numerical simula-tions ( = = 0.95), two selective coatings developed by CIEMAT-PSA, the commercial Pyromark 2500, together with three theoretical selective coatings.Moreover, two different working conditions have been adopted to account for the usual working conditions implemented for OVRs, taking into consideration the current temperature limit for the feasibility and stability of selective coatings in air.In summary, OVRs with mesh type C and a porosity of 62% tend to perform better than the OVRs with mesh type A. Concerning the different optical properties studied, the higher the solar absorptance and the lower the thermal emittance, the better the results, as happens with the selective coatings developed by CIEMAT-PSA.The best performance corresponds to the selective coating (case 3) with a solar absorptance of 0.96 and a thermal emittance of 0.16 at 973K, with an improvement with respect to the uncoated material (case 1) ranging from 22 to 27%.On the other hand, the improvement with the commercial Pyromark paint (case 5) varies from 17 to 19%.Despite the fact that using a selective coating clearly enhances OVR performance, further development of better coatings that can work at higher temperatures is required in order to increase the current temperature limit.
Figure 1 .
Figure 1.Layers of selective coatings designed for metallic receivers in CRSs
Figure 2 .
Figure 2. Layers of selective coating designed for ceramic receivers in CRSs
Figure 3 .
Figure 3. Thermal emittance of commercial Pyromark 2500, two selective coatings developed by CIEMAT-PSA and three theoretical selective coatings
Table 1 .
Main optical properties of the different cases analysed
Table 3 .
Working conditions 1 -Thermal results of OVRs with meshes A and C for the eight different cases studied
Table 4 .
Working conditions 2 -Thermal results of OVRs with meshes A and C for the eight different cases analysed | 3,059 | 2024-04-16T00:00:00.000 | [
"Engineering",
"Environmental Science",
"Materials Science",
"Physics"
] |
Frequency, amplitude, and phase measurements in contact resonance atomic force microscopies
Summary The resonance frequency, amplitude, and phase response of the first two eigenmodes of two contact-resonance atomic force microscopy (CR-AFM) configurations, which differ in the method used to excite the system (cantilever base vs sample excitation), are analyzed in this work. Similarities and differences in the observables of the cantilever dynamics, as well as the different effect of the tip–sample contact properties on those observables in each configuration are discussed. Finally, the expected accuracy of CR-AFM using phase-locked loop detection is investigated and quantification of the typical errors incurred during measurements is provided.
Introduction
A number of atomic force microscopy (AFM) variants have emerged since the introduction of the original technique in 1986 [1]. Besides topographical acquisition and spectroscopy, an important application nowadays is the measurement of conservative and dissipative interactions across nanoscale surfaces, which is highly relevant for viscoelastic materials such as polymers and biological samples. These measurements can be carried out through a combination of contact and dynamic AFM modes. Within the force modulation method [2], the tip and the sample are brought into contact at a prescribed tip-sample force setpoint (cantilever deflection setpoint, as in contact mode imaging) and the sample is excited with a sinusoidal oscillation in the vertical direction (atomic force acoustic microscopy (AFAM) configuration [3]), such that the tip oscillation amplitude and its phase with respect to the excitation can be measured and converted into a loss and storage modulus. In contact resonance AFM (CR-AFM) [3][4][5][6][7][8][9] a similar setup is used, supplying the sinusoidal excitation either at the base of the cantilever (in the so-called ultrasonic atomic force microscopy (UAFM) configuration [4]) or to the sample stage (in the AFAM configuration [3]). In both cases, the effective resonance frequency, amplitude, and phase of various eigen-modes of the cantilever-tip system are generally measured through excitation frequency "sweeps" for quantitative determination of the same elastic and viscous responses of the material. More recently, other methods have been introduced to more rapidly infer the frequency response (amplitude vs frequency curves) of the tip-sample contact. In the band excitation (BE) method, a time-dependent signal containing a band of frequencies around the desired resonance is applied at each pixel of the scan, such that the frequency response at that location can be rapidly obtained through a Fourier transform of the cantilever tip response and a fit to a Lorentzian curve [10,11]. This calculation allows mapping of the resonance frequency and quality factor across the sample, from which viscoelastic properties can also be inferred. In contrast, in the dual-amplitude resonance tracking (DART) method, the frequency response curve is rapidly inferred from the phase and amplitude response at two frequencies around the resonance frequency during a real-time scan [12].
Intermittent-contact methods have also been used to characterize conservative and dissipative tip-sample interactions simultaneously with topographical acquisition. This was originally performed using the tapping-mode (amplitude modulation) technique [13], within which variations in the phase contrast can be directly related to changes in energy dissipation [14,15]. Conservative and dissipative interactions are generally expressed in terms of the virial (V ts ) and the dissipated power (P ts ), respectively [15][16][17][18][19][20]. In the last ten years, intermittentcontact measurements have been enhanced through multifrequency excitation methods [21][22][23][24][25][26][27]. In multifrequency AFM, the fundamental cantilever eigenmode is typically controlled in conventional AM-or FM-AFM mode for topographical measurement, while one or more higher eigenmodes are driven simultaneously in order to also map compositional (viscoelastic) contrast. Since the higher eigenmodes are not directly affected by the topographical acquisition controls, they can be tuned independently to map V ts and P ts with high sensitivity. However, with the exception of small-amplitude FM-AFM [28,29] in which the tip-sample force gradient can be measured directly, the mapping of V ts and P ts in intermittentcontact imaging generally only provides a qualitative map of surface viscoelasticity.
In this work the focus is on the CR-AFM technique. Specifically, we analyzed the response variables for the two configurations currently in use (UAFM and AFAM), and restricted our analysis to the first two cantilever eigenmodes. Similarities and notable differences were observed in the signals and calculated variables (frequency, amplitude and phase) for the two cases, which require careful analysis for proper experimental setup and interpretation. As an example, we analyzed the errors intro- duced during resonance frequency tracking through the use of a phase-locked loop (PLL), which leads to different results in both configurations. This is a highly relevant practical consideration, since PLL techniques offer versatility and speed of characterization when they can be implemented accurately.
Results and Discussion
Equation of motion for a cantilever beam in UAFM and AFAM configurations In this work two CR-AFM configurations will be analyzed: UAFM [4], with the cantilever vibrated from its base (Figure 1a), and AFAM [3], with the sample vibrated from underneath ( Figure 1b). In both configurations the vibration is in the form of a mechanical oscillation of variable frequency and the detection is performed at the end of the cantilever where the tip is located. The dynamics of the cantilever-tip-sample system in each of these configurations was discussed by Rabe in [30]. We limit ourselves to briefly reviewing the equations necessary for our analysis. For simplicity, the vertical tip-sample coupling was modelled as a spring in parallel with a dashpot (Kelvin-Voigt model) and no lateral contact coupling was considered; vertical and lateral refer here to the normal and parallel directions to the sample surface, respectively.
The Euler-Bernoulli equation of motion for damped flexural vibrations of a cantilever beam in air is (1) where the cantilever is described by its Young's modulus E, second moment of area of its cross section I, mass density ρ, and cross-sectional area A, and η air characterizes the damping of the oscillations in air. The general solution of Equation 1 is in the form of y(x,t) = y(x)e iωt , with (2) with A 1 , A 2 , A 3 , and A 4 constants and α the complex wave number of a flexural oscillation, .
For the UAFM and AFAM configurations shown in Figure 1, the following boundary conditions are imposed to the general solution: (3) and (6) where L is the length of the cantilever, A d the driven amplitude, and Θ(α) is given by (7) Here k c = 3EI/L 3 is the cantilever spring constant, k* the contact stiffness, γ* the contact damping constant, and the dimensionless contact damping constant. With the above specified boundary conditions the solution further simplifies to (8) with the following constants for the two configurations: and (13) with M ± = sin αL cosh αL ± sinh αL cos αL, N(α) = (αL) 3 (1 + cos αL cosh αL) + Θ(α)M − , and Θ(α) given by Equation 7. In particular, the deflection of the end of the cantilever reduces to (14) The magnitude of the deflection and phase are given by: (15) and (16) respectively.
We illustrate our analysis with a rectangular Si cantilever of length L = 225.03 µm, width w = 30.00 µm, and thickness T = 4.89 µm. With mass density ρ Si = 2329.00 kg/m 3 and Young's modulus E Si = 130.00 GPa, the cantilever's spring constant was calculated as k c = 10.00 N/m. Using these parameters and considering η air = 2.50 s −1 in Equation 1, the first two eigenmodes are characterized by the dynamic parameters given in Table 1. The frequency dependences of the amplitude ratio and phase around resonance are shown in Figure 2 for the first two free eigenmodes of the cantilever. For calculations of the free-eigenmodes, the cantilever was vibrated in the UAFM configuration. In the following analysis we will characterize the contact damping by the dimensionless contact damping constant p rather than the actual contact damping constant γ*. The discussion is focused on the dynamics of the cantilever in the two CR-AFM configurations only and further consideration of various contact geometries would be required to convert the measured dynamic parameters into the elastic and viscous properties of the materials and structures probed [8,9,[31][32][33]. Amplitude and phase along the cantilever In Figure 3 are shown the amplitude ratio and phase of the first eigenmode along the cantilever for the UAFM ( Figure 3a) and AFAM ( Figure 3c) configurations for the same contact stiffness, k* = 20 N/m, and three different contact damping values: mild (p = 0.10), medium (p = 0.25), and strong (p = 0.50) contact damping. In both configurations, the calculated displacement along the cantilever shows the deformed shape of the first eigenmode with a node at the base of the cantilever (x = 0) and an antinode at the end of the cantilever (x = L), with smaller and smaller displacement values as the contact damping increases. In contrast to the displacements, the phase response is quite different in magnitude and shape. Thus, in the UAFM configuration, the phase of the first eigenmode (refer to Figure 3a) goes from 0 at the base of the cantilever to around 90 degrees at the end of the cantilever. The resonance state at the end of the cantilever for the UAFM configuration is detailed in Figure 3b in terms of amplitude and phase. From this, little change in the phase can be observed for the range of considered contact damping, from 91.1 degrees for p = 0.10 to 95.5 degrees for p = 0.50. Interestingly, as can be seen in Figure 3a, the phase is about 90 degrees at 87% of the length of cantilever, independent of the contact damping values. The key observation here is that the phase at the end of the cantilever in the UAFM configuration varies by a few degrees around 90 degrees depending on the magnitude of the contact damping. However, a completely different response in phase is shown in Figure 3c and 3d for the AFAM configuration. First, the phase of the first AFAM eigenmode is essentially constant (very small variation) along the cantilever. Second, its magnitude changes significantly with the considered contact damping. It decreases from essentially 90 degrees when no contact damping is present to 82.6 for p = 0.10, to 72.1 degrees for p = 0.25, and to 57.1 degrees for p = 0.50.
An analogous analysis can be carried out for the amplitude and phase of the second eigenmode shown in Figure 4. The shape of the second eigenmode of the cantilever exhibits two nodes (at the base of the cantilever and at 77% of the length of the cantilever) and two antinodes (at 46% of the length of the cantilever and at the end of the cantilever). Both the UAFM and AFAM configurations impose the same shape for the second eigenmode but the amplitude is about one order of magnitude larger in UAFM than in AFAM. As in the case of the first eigenmode discussed above, the phase of the second eigenmode differs substantially between the two configurations. In the UAFM configuration, the phase is 0 at the cantilever base, shows a 90 degrees plateau around the first antinode, goes through 180 degrees at the second node, and shows another plateau of 270 degrees at the end of the cantilever; 270 degrees is equivalent here to a resonance at −90 degrees. As observed in Figure 4a at the end of the cantilever and also in Figure 4b from the frequency dependences around the resonance, the phase of the second eigenmode at the end of the cantilever experiences small variations as a function of contact damping: 269.1 degrees for p = 0.10 to 265.4 degrees for p = 0.50. In the AFAM configuration, the phase resembles the shape of a two-step function with a sharp transition at the second node. At the end of the cantilever, the phase of the second AFAM eigenmode shown in Figure 4c and 4d varies substantially with the contact damping considered: From 72.6 degrees for p = 0.10, to 52.0 degrees for p = 0.25, and to 32.6 degrees for p = 0.50.
From the above discussion of the amplitude and phase of the first and second eigenmodes of the cantilever, we can conclude that for a given contact stiffness, the amplitude changes significantly with the contact damping and this change is qualitatively and quantitatively similar in UAFM and AFAM. However, the phases of the two configurations differ significantly from each other. In the UAFM configuration the phase experiences small variations as a function of contact damping, with values around 90 degrees (first eigenmode) or −90 degrees (second eigenmode). On the other hand, in the AFAM configuration, the phase is very sensitive to changes in contact damping and exhibits large variations. This analysis indicates that both the would not be a good measurement for it. However, as discussed later, the invariance of the UAFM phase to contact damping can be used to track the resonance state by phase-control techniques (i.e., PLLs) [34,35].
Contact resonance frequency, amplitude, and phase
To retrieve the contact stiffness and contact damping responses of a material, measurements are made in terms of resonance frequency, amplitude, and phase in any of the CR-AFM configurations. In the following we will analyze these various signals at the end of the cantilever as a function of contact stiffness and contact damping in UAFM and AFAM configurations and examine the differences between these two configurations.
The amplitude ratio, resonance frequency, and phase of the first eigenmode are shown as a function of the contact stiffness in Figure 5 for a small p = 0.05 contact damping and in Figure 6 for a medium p = 0.25 contact damping, respectively. All the cantilever parameters were taken to be the same as above, with k c = 10.00 N/m. As can be seen in Figure 5 and Figure 6, for each of the contact damping values considered, there is no significant difference between the UAFM and AFAM resonance frequencies (red and grey continuous lines) over the investigated contact stiffness range. This shows that in terms of contact stiffness measurements based on the shift in the resonance frequency the UAFM and AFAM configurations provide the same result. The differences between the two configurations are notable in terms of amplitude and phase. In the UAFM configuration, the amplitude (green continuous line in Figure 5 and Figure 6) slowly increases with the increase in contact stiffness. For the two contact damping values considered in Figure 5 and Figure 6, the overall increase in UAFM amplitude was about 40% between the initial value at k* = 0 N/m and end value at k* = 50 N/m. A more abrupt increase can be observed for the AFAM amplitude (green dotted lines in Figure 5 and Figure 6). In the AFAM configuration the amplitude is zero at k* = 0 N/m when the tip and the sample are basically uncoupled. In practice, however, small oscillations are induced in the cantilever when it is brought close to but still not in contact with the vibrated sample. So, in this case of very small contact stiffnesses, the theoretical AFAM configuration might not be reproduced in experiments. It is interesting to observe that the UAFM and AFAM amplitudes become comparable towards large contact stiffness couplings in both cases of small and medium contact damping. The phase variation as a function of contact stiffness is similar to the amplitude variation in each configuration. Thus, over the considered contact stiffness range, the UAFM phase (blue continuous line in Figure 5 and Figure 6) changes within one degree from its free value (90 degrees) in the case of a small p = 0.05 contact damping and within 4 degrees in the case of a medium p = 0.25 contact damping. However, a much larger variation is experienced by the AFAM phase (dotted blue line in Figure 5 and Figure 6) with the increase in the contact stiffness. From essentially zero degrees, in the absence of tip-sample coupling, the AFAM phase increases sharply in the range of small contact stiffnesses and has an asymptotical increase for contact stiffnesses comparable or larger than the cantilever stiffness. These asymptotic values of the AFAM phase however depend strongly on the actual contact damping. For the examples shown in Figure 5 and Figure 6, the AFAM phase approaches 87 degrees for a contact stiffness of p = 0.05 and 80 degrees for a contact stiff- ness of p = 0.25. This reiterates the above observation that the AFAM phase is sensitive to contact damping and could be used as a measure of the tip-sample contact damping.
The variations of the contact resonance frequency, amplitude, and phase as a function of both contact stiffness and contact damping were fully analyzed in the maps shown in Figure 7 for the first eigenmode and in Figure 8 for the second eigenmode of UAFM and AFAM, respectively. In terms of contact resonance frequency, large shifts were observed over the range of considered contact stiffness and damping: about 130 kHz for the first eigenmode (Figure 7a and 7e) and about 50 kHz for the second eigenmode (Figure 8a and 8e). As can be seen, the frequency shifts are almost insensitive to contact damping and mainly responsive to contact stiffness variations only. On the other hand, a pronounced contact damping dependence and moderate contact stiffness dependence can be observed in the amplitude maps (Figure 7b and 7f for the first eigenmode and Figure 8b and 8f for the second eigenmode), especially for the UAFM configuration. With the exception of the small contact stiffness range, the UAFM and AFAM amplitude values are comparable for the first eigenmode (Figure 7b and 7f). In the case of the second eigenmode, the UAFM amplitudes are consistently larger than the AFAM amplitudes, exhibiting a better amplitude detection of the second UAFM eigenmode than its counterpart in the AFAM configuration. A concurrent dependence on contact stiffness and contact damping can be observed in the maps of the phase at resonance (Figure 7c and 7g for the first eigenmode and Figure 8c and 8g for the second eigenmode). The UAFM phase response to the considered contact stiffness and contact damping variations is of order of a few degrees around 90 degrees for the first eigenmode and few degrees below 270 degrees (−90 degrees) for the second eigenmode. Thus, the UAFM phase of the first eigenmode (Figure 7c) is less than 90 degrees for compliant materials with either low or high contact damping and stiff materials with low contact damping. The phase goes above 90 degrees in the less realistic case of stiff materials with high damping. An even smaller variation of only 5 degrees below the free resonance phase was observed for the second UAFM eigenmode (Figure 8c). As inferred from the above discussion, the AFAM phase, either for the first eigenmode (Figure 7g) or second eigenmode ( Figure 8g) exhibits large variation as a function of contact stiffness and contact damping. Thus, the AFAM phase is around zero degrees at small contact stiffnesses and goes asymptotically towards 90 degrees as the contact stiffness increases. This asymptotic trend is progressively delayed with the increase in contact damping. An interesting behaviour is observed also in the maps of quality factor Q (Figure 7d and 7e for the first eigenmode and Figure 8d and 8e for the second eigenmode), calculated as the ratio of the resonance frequency to the width of the resonance peak, ω n /Δω. In general, the quality factor is directly associated with the damping response of the system. However, as it can be seen in Figure 7d and 7h, it depends on both the contact stiffness and contact damping. The Q-factor is almost independent of contact stiffness for the second UAFM and AFAM eigenmodes, in which case it can be used as a direct measurement of the tip-sample contact damping. Explicit relationships between the Q-factors of various contact eigenmodes and contact damping were intuitively proposed [36] and rigorously derived [37] previously for the AFAM configuration. The results shown in Figure 7h and Figure 8h are in agreement, within the common range of contact stiffness, with the Q-factor versus contact damping dependences shown in Figure 2 of [37] for the first two eigenmodes.
Phase-locked loop detection
By considering their specific dependences in either UAFM or AFAM configurations, the measured contact resonance frequency, amplitude, and phase can be converted into the stiffness and damping of the tip-sample contact coupling. One way of observing the fast change in the dynamics of a cantilever used in CR-AFM point measurements or scanning is to track the resonance state by PLL detection, similar with what is used in non-contact frequency modulation AFM. In non-contact AFM, PLL tracking has been implemented in either constant-excitation frequency modulation [17,18] or constant-amplitude frequency-modulation [19,20]. In the following we will refer only to the constant-excitation PLL setup in which the driving amplitude is constant and the frequency is adjusted continuously to maintain a constant phase difference between drive and response, φ PLL . In the case of an AFM cantilever brought into contact from air, the PLL reference phase would be the phase of the free oscillation of the selected eigenmode. However, as we discussed above, the phase of a vibrated cantilever that is in contact with a sample, even when it is driven at the resonance, is not constant but varies in accordance with the magnitudes of the contact stiffness and contact damping. This means that in PLL detection the true resonance condition will not be retrieved. Instead one would obtain the state having the predefined PLL phase, φ PLL . The error introduced by the PLL in measuring the resonance frequency will then by Δf = f resonance − f PLL , where f resonance is the dynamic resonance frequency and f PLL is the frequency at which the phase of the detected signal is φ PLL .
Based on its weak dependence on contact stiffness and contact damping, the UAFM phase can be used in a PLL detection [35,38] to maintain the cantilever-tip-sample system at the resonance and track the changes in the resonance frequency and amplitude. Figure 9 shows the errors introduced by the PLL in measuring the resonance frequency of the first and second eigenmodes when the locked phase was that of the free resonance of the respective eigenmode. As can be seen in Figure 9, the errors introduced by the PLL in determining the true resonance frequencies of the first two UAFM eigenmodes are within 1 kHz for low and medium contact damping (p < 0.25) over the contact stiffness range considered. In the case of very large contact damping, these errors extend to about 2 kHz or 3 kHz for some particular values of contact stiffness. Considering that these errors are for shifts of about 150 kHz for the resonance frequency of the eigenmode (refer to Figure 7a) and 50 kHz for the resonance frequency of the second mode (refer to Figure 8a), respectively, they result in negligible errors in the conversion of measured contact resonance frequencies into material elastic moduli.
A particular situation arises in the case of using PLL detection in the AFAM configuration. As was discussed above, large variations are experienced by the AFAM phase from out of contact to contact states. In the AFAM configuration the phase was found to be very sensitive to the stiffness and damping of the tip-sample contact. This phase sensitivity could be used directly for contact damping measurements [8] but would make impractical the PLL detection of the contact resonance of an AFAM eigenmode with respect to its free resonance. However, a moderate variation is experienced by the AFAM phase for contact stiffness comparable or greater than the stiffness of the cantilever (e.g., contact stiffnesses about or greater than 10 N/m in the examples considered in Figure 5 and Figure 6). It is therefore possible to perform PLL tracking even in the AFAM con-figuration by choosing a reference contact resonance state with respect to which moderate phase variations are experienced during contact measurements or scanning. This type of measurement has been performed also in the UAFM configuration of CR-AFM on Cu-low-k dielectric materials, with the PLL locked on the phase of a contact resonance state, after the tip was brought into contact at the desired applied force [35]. From a practical point of view, it is worth mentioning here that in the case of UAFM, the detection is very sensitive to the transfer function of the cantilever used and in some cases, depending on the cantilever used and tip-sample couplings, spurious resonances can mask or distort the real tip-sample coupling resonances [39,40]. On the other hand, in AFAM configuration, the frequency spectra are heavily overwritten by the transfer function of the excitation actuator (underneath the sample), which can provide cleaner spectra at the expense of a more aggressive tip-sample coupling.
Conclusion
The resonance frequency, amplitude, and phase of the first two eigenmodes of two contact resonance AFM (CR-AFM) configurations, namely a setup with sample stage excitation (AFAM) and one with cantilever base excitation (UAFM), were analyzed in detail. This allowed observing similarities and differences among the dynamic parameters of each of the CR-AFM configurations as a function of the mechanical coupling on different materials. Thus, while the contact resonance frequency is mostly sensitive to contact stiffness and less sensitive to contact damping, the resonance amplitude and phase exhibit a concurrent dependence on both contact stiffness and contact damping. Also, it was found that the two CR-AFM configurations differ greatly through their phase response. Thus, while the UAFM phase shows a reduced variation over a large range of material parameters, the AFAM phase is very sensitive to both contact stiffness and contact damping. These results suggest that, from an experimental point of few, UAFM would be the preferred CR-AFM configuration in phase-control detection applications. However, with appropriate use of their specific frequency dependences, both amplitude and phase are theoretically available for elastic modulus and dissipation measurements in both UAFM and AFAM configurations. | 6,055 | 2014-03-12T00:00:00.000 | [
"Physics"
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Sitagliptin‐mediated preservation of endothelial progenitor cell function via augmenting autophagy enhances ischaemic angiogenesis in diabetes
Abstract Recently, the dipeptidyl peptidase‐4 (DPP‐4) inhibitor sitagliptin, a major anti‐hyperglycaemic agent, has received substantial attention as a therapeutic target for cardiovascular diseases via enhancing the number of circulating endothelial progenitor cells (EPCs). However, the direct effects of sitagliptin on EPC function remain elusive. In this study, we evaluated the proangiogenic effects of sitagliptin on a diabetic hind limb ischaemia (HLI) model in vivo and on EPC culture in vitro. Treatment of db/db mice with sitagliptin (Januvia) after HLI surgery efficiently enhanced ischaemic angiogenesis and blood perfusion, which was accompanied by significant increases in circulating EPC numbers. EPCs derived from the bone marrow of normal mice were treated with high glucose to mimic diabetic hyperglycaemia. We found that high glucose treatment induced EPC apoptosis and tube formation impairment, which were significantly prevented by sitagliptin pretreatment. A mechanistic study found that high glucose treatment of EPCs induced dramatic increases in oxidative stress and apoptosis; pretreatment of EPCs with sitagliptin significantly attenuated high glucose‐induced apoptosis, tube formation impairment and oxidative stress. Furthermore, we found that sitagliptin restored the basal autophagy of EPCs that was impaired by high glucose via activating the AMP‐activated protein kinase/unc‐51‐like autophagy activating kinase 1 signalling pathway, although an autophagy inhibitor abolished the protective effects of sitagliptin on EPCs. Altogether, the results indicate that sitagliptin‐induced preservation of EPC angiogenic function results in an improvement of diabetic ischaemia angiogenesis and blood perfusion, which are most likely mediated by sitagliptin‐induced prevention of EPC apoptosis via augmenting autophagy.
Introduction
Diabetes is a disease that is strongly associated with both microvascular and macrovascular complications, including retinopathy, nephropathy, and neuropathy (microvascular) and ischaemic heart disease, peripheral vascular disease and cerebrovascular disease (macrovascular), resulting in organ and tissue damage in approximately one-third to one-half of people with diabetes [1,2]. Vascular complications associated with diabetes are the leading causes of morbidity and mortality for diabetic patients. Vascular complications in diabetes are associated with dysregulation of vascular remodelling and vascular growth, decreased responsiveness to ischaemic/hypoxic stimuli, impaired or abnormal neovascularization, and a lack of endothelial regeneration. Thus, there is a great need for therapeutic interventions aimed at accelerating the repair of dysfunctional endothelium and restoring blood flow in damaged organs and tissues [3].
Endothelial progenitor cells (EPCs) are found in bone marrow, peripheral blood and certain organs, such as the spleen and liver. In the event of endothelial injury or tissue ischaemia, EPCs are mobilized into the circulation from the bone marrow, home to the site of injury, differentiate into mature endothelial cells and incorporate into the endothelium, replacing apoptotic or damaged cells and mediating neovascularization. However, the number of EPCs in diabetic patients is reduced, and the function of EPCs is attenuated as a consequence of exposure to the dysmetabolic diabetic environment [4]. An efficient therapeutic strategy includes mobilizing more EPCs into peripheral blood and promoting EPCs homing to ischaemic tissue to enhance angiogenesis with pharmacological agents.
Dipeptidyl peptidase 4 (DPP-4), a membrane-bound extracellular peptidase, also designated CD26, has been demonstrated to cleave cytokines and chemokines [5]. Stromal-derived factor-1a (SDF-1a), one of the chemokine substrates of DPP-4 [5], serves as a chemoattractant for EPCs and stem/progenitor cells and plays critical roles in EPCs and stem cell mobilization and homing [6]. Previous studies have reported that inhibition of DPP-4 activity in the blood leads to an increase in the circulating number of EPCs [7][8][9], enhancing angiogenesis and blood flow in hind limb ischaemia (HLI) [8,9] and protecting the heart in models of myocardial infarction [10,11]. However, the direct effects of DPP-4 inhibition on EPCs function remain elusive.
In this study, sitagliptin, a DPP-4 inhibitor that is widely used in the clinic, was used to treat HLI in db/db type 2 diabetic mice in vivo and EPCs under high glucose (HG) conditions in vitro. We aimed to evaluate (1) the therapeutic effects of sitagliptin on HLI; (2) the mobilization of EPCs induced by sitagliptin; (3) and the proangiogenic effects and mechanisms of sitagliptin on EPCs under HG conditions, which was used to mimic a dysmetabolic environment.
Materials and methods
Animals db/db (FVB background) male mice at 2-3 months of age were used in this study. All animal procedures were approved by the Animal Policy and Welfare Committee of Wenzhou Medical University and/or the Institutional Animal Care and Use Committee of the University of Louisville, which conform to the Guide for the Care and Use of Laboratory Animals published by the US National Institutes of Health (publication No. 85-23, revised 1996).
HLI and sitagliptin treatment
The db/+ founder mice [FVB.BKS(D)-Lepr db/+ /ChuaJ, FVB background] were purchased from the Jackson Laboratory (Bar Harbor, ME, USA) and maintained under specific pathogen-free conditions at the University of Louisville Animal Facility (Louisville, KY, USA) or the Wenzhou Medical University. The db/db mice were generated by breeding male db/+ to female db/+ mice following Jackson Laboratory's instructions. Twelve-week-old male db/db mice were equally divided into two groups (n = 16/group) to develop the HLI model as described in our previous report [12]. One group was pretreated with sitagliptin (25 mg/kg, daily) for 1 week before HLI surgery and continually treated with sitagliptin for an additional 7 or 35 days after surgery via gavage administration. Another group was treated with H 2 O as the vehicle control. At 7 or 35 days after surgery, eight mice from each group were sacrificed to collect blood and gastrocnemius muscle samples. The HLI procedure is briefly described below: under sufficient anaesthesia with isoflurane (1-3% isoflurane in 100% oxygen at a flow rate of 1 l/min.), the hind limbs were shaved and the entire right superficial femoral artery and vein (from just below the deep femoral arteries to the popliteal artery and vein) were ligated with 6-0 silk sutures, cut and excised with an electrical coagulator (Fine Science Tools Inc., Foster City, CA, USA). The overlying skin was closed with 4-0 silk sutures.
Measurement of blood flow perfusion with a Pericam perfusion speckle imager (PSI)
To evaluate the limb perfusion ratio [ischaemic limb (right)/normal limb (left)], real-time microcirculation imaging analysis was performed using a Pericam PSI based on laser speckle contrast analysis technology (Perimed Inc., Kings Park, NY, USA) before surgery and at day 0, 3, 7 14, 21, 28 and 35 post-surgery.
Quantification of circulating EPCs by flow cytometry
At days 3 and 7 after surgery, blood samples were collected in 0.1 mol/ l EDTA-2Na-coated tubes from the tail vein. Whole blood was incubated with CD34-PE and VEGFR-2-APC antibodies [13,14] (BD Pharmingen, San Jose, CA, USA) for 1 hr, then lysed and fixed in FACS TM lysing solution (BD Biosciences, San Jose, CA, USA) for 5 min. Flow cytometry analysis was performed with a BD FACS (BD Biosciences) to count VEGFR-2 and CD34 double-positive EPCs. Isotype control IgG (BD Pharmingen) was used to exclude false-positive cells.
Histological assessment
The extent of angiogenesis at day 35 post-ischaemic surgery was assessed by measuring capillary density using isolectin B4 staining. Ischaemic gastrocnemius muscle tissues were fixed with 4% paraformaldehyde and embedded with paraffin. Paraffin sections (5 lm) were stained with Alexa Fluor â 594 conjugated isolectin GS-IB4 antibody (Thermo Scientific, Waltham, MA, USA) to evaluate the capillary density. The capillaries were counted in randomly selected fields for a total of 20 different fields (940 magnification) per section and three sections per animal. The capillary density is presented as capillary number per muscle fibre.
Isolation and culture of bone marrow-derived EPCs
EPCs were isolated from the bone marrow of wild-type (WT) FVB mice and cultured according to our established methods with minor modifications [15]. Briefly, bone marrow mononuclear cells (MNCs) were isolated from the femurs and tibias of the mice by density gradient centrifugation with histopaque-1083 (Sigma-Aldrich, St. Louis, MO, USA). After two washes, MNCs were plated on vitronectin-coated culture dishes (Sigma-Aldrich) and maintained in endothelial growth factor-supplemented media (EGM-2 bullet kit; Lonza, Basel, Switzerland) with 10% foetal bovine serum. Cells were cultured at 37°C with 5% CO 2 in a humidified atmosphere. EGM-2 medium was replaced after the first 24 hrs and every 3 days thereafter. Cell colonies appeared after 7 days of culture and were expanded to the fourth or fifth passage for further analysis.
Characterization of bone marrow-derived MNCs
After 14 days of culture in endothelial-specific media and the removal of non-adherent MNCs, the remaining cells were characterized by uptake of Dil-Ac-LDL and ulex europaeus lectin-1 binding. For the uptake of Dil-Ac-LDL and ulex europaeus lectin-1 binding assay, cells were seeded on a vitronectin-coated 8-well l-slide (ibidi, Martinsried, Germany) one day before the procedure, and then, the cells were incubated with 5 lg/ml acetylated DiI lipoprotein from human plasma (Dil-Ac-LDL, Thermo Fisher Scientific, Waltham, MA, USA) at 37°C for 4 hrs, followed by three washes with Dulbecco's phosphate-buffered saline (DPBS) and fixed with 4% paraformaldehyde. Then, the cells were incubated with 10 lg/ml fluorescein isothiocyanate-labelled ulex europaeus lectin-1 (FITC-UEA-1; Sigma-Aldrich) for 1 hr at room temperature. After incubation, the cells were rinsed with DPBS three times and were visualized via confocal microscopy.
To further confirm the identity of these cells, immunofluorescence staining was performed to analyse the expression of specific cell markers VEGFR2 and Sca-1. For the immunofluorescence staining, cells were seeded on a vitronectin-coated 8-well l-slide one day before the procedure and then fixed with 4% paraformaldehyde after three washes with DPBS. The fixed cells were incubated with PE-VEGR2 and FITC-Sca-1 [16,17] antibodies (Abcam, Cambridge, MA, USA) overnight at 4°C. DAPI (4 0 ,6-diamidino-2-phenylindole, dihydrochloride) was used to label nuclei.
DPP-4 enzymatic activity assay
DPP-4 enzymatic activity was assayed in the culture medium of EPCs under different treatment conditions using a DPP-4 Activity Assay Kit (Sigma-Aldrich). EPCs were seeded on 12-well plates and maintained under basal culture conditions with or without HG (25 mmol/l) for 24 hrs [18] in the presence or absence of different concentrations of sitagliptin. The culture medium was collected for the DPP-4 enzymatic activity assay. Briefly, a 50 ll volume of medium was diluted with 48 ll of DPP-4 assay buffer, mixed with 2 ll substrate gly-pro-7amino-4-methylcoumarin (AMC) and then incubated at 37°C for 30 min. The release of AMC from the substrate was measured with a fluorescence spectrophotometer at 360 nm excitation and 460 nm emission.
Apoptosis assay
EPCs were seeded on 12-well plates (1 9 10 5 cells/well) and maintained under basal culture conditions or with HG (25 mmol/l) for 24 hrs in the presence or absence of sitagliptin. Non-adherent cells were removed by washing with PBS. In some experiments, cells were pretreated with the autophagy inhibitor 3-methyladenine (3-MA, 5 mmol/l; Sigma-Aldrich) or the autophagy activator rapamycin (10 lmol/l; Sigma-Aldrich) for 30 min. and then continually exposed to HG for the indicated durations in the presence or absence of sitagliptin. Subsequently, adherent cells were released with 0.25% trypsin without EDTA. EPCs were collected by centrifugation and stained with an APC-conjugated Annexin V Apoptosis Detection Kit according to the manufacturer's instructions (Biolegend, San Diego, CA, USA). Apoptotic EPCs were detected by flow cytometry. Early apoptotic cells were defined as AnnexinV + /PI -.
Tube formation assay
The in vitro angiogenic capability of EPCs was determined by a Matrigel tube formation assay. Briefly, 48-well plates were coated with growth factor-reduced matrix gel (150 ll/well, BD Biosciences). EPCs (5 9 10 4 cells/well) in 200-ll basal culture medium or medium containing HG in the presence or absence of different concentrations of sitagliptin were incubated at 37°C with 5% CO 2 for 12 hrs to form tubes. In some experiments, cells were pretreated with 3-MA (5 mmol/l) or rapamycin (10 lmol/l) for 30 min. and then continually exposed to HG for the indicated durations in the presence or absence of sitagliptin. Images of tubes in each well were acquired using an inverted microscope (Nikon Eclipse E600, Nikon, Kanagawa, Japan). The tube lengths were calculated by ImageJ software (National Institutes of Health, Bethesda, MD, USA).
Quantitative determination of oxidative stress
To detect the reactive oxygen species (ROS) levels of EPCs with HG treatment in the presence or absence of different concentrations of sitagliptin, a dihydroethidium (DHE; Molecular Probes, Eugene, OR, USA) probe was used to stain EPCs. DHE is cell permeable and able to react with superoxide to form ethidium, which in turn intercalates with DNA
Autophagic signalling assay
Autophagic signalling was assayed by detecting microtubule-associated protein 1A/1B-light chain 3 (LC3) and p62 protein expression levels and LC3-bound puncta formation. For the LC3 and p62 protein expression assay, EPCs were seeded on 6-well plates (1 9 10 5 cells/well) and maintained under basal culture conditions with or without HG for 24 hrs in the presence or absence of sitagliptin. Non-adherent cells were removed by washing with PBS. In some experiments, cells were pretreated with AMPactivated protein kinase (AMPK) inhibitor compound C (10 lmol/l; Sigma-Aldrich) for 30 min. and then continually exposed to HG for the indicated durations in the presence or absence of sitagliptin. Then, EPCs were harvested for a Western blot assay of LC3 and p62 protein expression levels. For the LC3-bound puncta assay, EPCs were seeded on an 8well microculture chamber (2 9 10 4 cells/well) and maintained under basal culture conditions with or without HG for 24 hrs in the presence or absence of sitagliptin. Non-adherent cells were removed by washing with PBS. The remaining cells were stained with a LC3B primary antibody (1:100; Novus Biologicals, Littleton, CO, USA) and an appropriate FITCconjugated secondary antibody. LC3 puncta were observed with immunofluorescence microscopy.
Statistical analysis
All data are presented as the mean AE S.D. Statistical analysis was performed using Origin 7.5 (OriginLab data analysis and graphing software, Northampton, MA, USA) with one-way or two-way ANOVA, followed by post hoc multiple comparisons with Scheffe's test. Statistical significance was considered P < 0.05.
Results
Sitagliptin enhances blood perfusion and angiogenesis in HLI in type 2 diabetic mice To evaluate the angiogenic effect of DPP-4 inhibition in diabetes, db/db mice were pretreated with sitagliptin (Januvia) for 1 week; then, the mice were subjected to HLI surgery and continually treated with sitagliptin for an additional 5 weeks until to the end of the experiments. Blood flow was evaluated by PSI at day 3, 7, 14, 21, 28 and 35 after surgery. The results showed that sitagliptin treatment time dependently improved blood perfusion in db/db mice underwent HLI (Fig. 1A), which was accompanied by promoted angiogenesis mirrored by increased capillary density (Fig. 1B).
Sitagliptin increases proangiogenic factor expression levels and enhances EPCs mobilization in type 2 diabetic mice
To evaluate the effect of DPP-4 inhibition on the expression levels of proangiogenic factors in plasma and ischaemic tissue, peripheral blood and gastrocnemius muscles in ischaemic limbs were collected at day 7 after surgery. The ELISA results showed that mice that received sitagliptin had elevated levels of GLP-1 and SDF-1 in plasma ( Fig. 2A and B). Proangiogenic factors in gastrocnemius muscle were detected by Western blotting, and the results showed that VEGF and SDF-1 increased significantly in sitagliptin-treated mice (Fig. 2C).
At days 3 and 7 after surgery, peripheral blood was collected to evaluate the number of EPCs in circulation. A flow cytometry assay showed that the number of circulating EPCs (CD34+/VEGFR2+) significantly increased in sitagliptin-treated mice (Fig. 2D), indicating that sitagliptin promoted EPCs mobilization from bone marrow to peripheral blood.
Characterization of bone marrow-derived EPCs
MNCs isolated from bone marrow were cultured in EGM-2 medium on vitronectin-coated culture dishes. By 14-21 days of culture, endothelium-like cells with the cobblestone-like morphology of late EPCs were nearly confluent. Late EPCs were further characterized by Dil-ac-LDL uptake and FITC-UEA-1 lectin binding. As shown in Figure 3A, most late EPCs were positive for Dil-ac-LDL and FITC-UEA-1 lectin staining. To further confirm the identity of these cells, immunofluorescence staining was performed to analyse the expression of specific cell markers (Fig. 3B, upper panel). The results showed that the majority of cells are both VEGFR2 and Sca-1 positive (Fig. 3B, lower panel).
Sitagliptin improves the survival and angiogenic function of EPCs treated with HG
To validate the potency of sitagliptin, DPP-4 activity was measured in the medium of EPCs using a DPP-4 Activity Assay Kit. As expected, HG increased the DPP-4 activity of EPCs, which was inhibited by sitagliptin treatment in a dose-dependent manner (Figure S1). To determine whether DPP-4 inhibition could restore the survival and angiogenic function of EPCs under diabetic conditions, EPCs were exposed to HG to mimic the dysmetabolic stress of hyperglycaemia. The results demonstrated that HG significantly increased EPC apoptosis, as measured by Annexin V/PI staining (Fig. 4A). Sitagliptin treatment dose dependently prevented HGinduced apoptosis of EPCs within the lower dose range, although this protection was blunted at higher doses (Fig. 4A). Tube formation assays were used as one measure of angiogenic function in vitro. Similarly, HG significantly impaired the tube formation abilities of EPCs, and sitagliptin treatment significantly prevented the detrimental effects of HG on EPCs function at the same dose levels that prevented apoptosis (Fig. 4B).
Sitagliptin attenuates ROS levels in EPCs treated with HG
Oxidative stress is a major factor responsible for the dysfunction of diabetic EPCs [19,20]. We used DHE staining to show superoxide production in EPCs. The results demonstrated that HG significantly increased superoxide production levels, whereas sitagliptin treatment attenuated HG-induced superoxide production in EPCs at the same optimal dose level that prevented apoptosis and protected angiogenic function (Fig. 4C). Therefore, the optimal dose of sitagliptin at 3 lmol/l in EPCs protection was used in the following mechanistic studies.
Sitagliptin improves the survival and function of EPCs treated with HG via augmenting autophagy
Under diabetic conditions, impaired autophagy contributes to endothelial dysfunction, and restoration of autophagy can improve endothelial cell survival and function [21]. In this study, we found that sitagliptin improved the survival and function of EPCs treated with HG. Therefore, we investigated whether the protective effects of sitagliptin on EPCs were mediated by autophagy activation in the following studies. EPCs were treated with HG (25 mmol/l) in the presence or absence of sitagliptin (3 lmol/l), and cells treated with 5.5 mmol/l glucose plus 20.5 mmol/l mannitol were used as a control. Immunofluorescence staining analysis demonstrated that elevated glucose levels reduced the number and distribution of LC3 puncta staining, suggesting a reduction in autophagosome formation, which was significantly prevented by sitagliptin treatment (Fig. 5A). In addition, we also detected the expression of p62 and the ratio of LC3II to LC3I by Western blotting. The results showed that the ratio of LC3II to LC3I decreased in EPCs with HG treatment, which was reversed by sitagliptin, whereas p62 expression exhibited the opposite pattern (Fig. 5B). These results indicate that sitagliptin activates autophagy in EPCs under HG treatment conditions.
To confirm whether the protective effects of sitagliptin on EPCs were dependent on augmented autophagy, the autophagy inhibitor 3-MA and the activator rapamycin were tested against the protection of sitagliptin. The result showed that inhibition of autophagy by 3-MA completely abolished the sitagliptin-stimulated increase in LC3II and decrease in p62 expression in EPCs (Fig. 6A), resulting in complete abolishment of sitagliptin-induced cell survival (Fig. 6B) and tube formation (Fig. 6C) in EPCs under HG treatment conditions, whereas activation of autophagy by rapamycin almost completely prevented HG-induced pathological changes in EPCs, which are comparable to that of sitagliptin treatment ( Fig. 6A-C). These results suggest that sitagliptin preserves EPC function via restoring autophagy in EPCs.
Sitagliptin restores autophagy in EPCs treated with HG via activating the AMPK/ULK1 signalling pathway AMPK/ULK1 signalling is critical for autophagy regulation under diabetic conditions [22,23]. A previous study has shown that sitagliptin can activate AMPK [24]. Therefore, we first detected AMPK activation in EPCs. The results showed that HG inhibited AMPK activity, as estimated by the decreased phosphorylation of AMPK, whereas sitagliptin treatment prevented HG-induced decreases in the phosphorylation of AMPK (Fig. 7A). Meanwhile, we also found that sitagliptin prevented HG-induced phosphorylation of mTOR, which was accompanied by an increase in the phosphorylation of ULK1 at Ser555 (Fig. 7A). To further confirm the critical role of AMPK activation in sitagliptin- Fig. 4 Sitagliptin improves the survival and angiogenic function of EPCs treated with high glucose (HG). EPCs were exposed to HG (25 mmol/l) with or without different doses of sitagliptin. (A) The apoptosis of EPCs was analysed by flow cytometry using Annexin V/propidium iodide (PI) staining after exposure to HG for 24 hrs. Apoptotic cells were defined as Annexin V + /PI -. (B) The effects of sitagliptin on the angiogenic function of EPCs after HG treatment for 12 hrs were determined by a tube formation assay. Tube length was normalized to the mannitol control group. (C) The anti-oxidative effect of sitagliptin was determined by fluorescent probe DHE staining after exposure to HG for 6 hrs, and the fluorescence intensity of DHE was measured by a fluorescence microplate reader. Three independent experiments were performed for each study. Data shown in graphs represent the means AE S.D. *P < 0.05, vs mannitol control group; # P < 0.05, vs HG treatment group. induced augmentation of autophagy in EPCs, the AMPK inhibitor compound C was tested against sitagliptin-induced activation of autophagy. The result showed that compound C completely abolished the sitagliptin-stimulated increase in LC3II and decrease in p62 expression in EPCs (Fig. 7B). These results suggest that AMPK is a critical mediator of the protective effects of sitagliptin on EPC function via augmenting autophagy.
Discussion
The present study provides three new lines of evidence demonstrating the benefits of sitagliptin in ischaemic angiogenesis in type 2 diabetic mice in vivo and the angiogenic function of EPCs in vitro. The first novel finding is that sitagliptin treatment enhances blood perfusion and angiogenesis in HLI in db/db type 2 diabetic mice by increasing the circulating number of EPCs; the second innovative finding is that sitagliptin protects EPCs against diabetic stress conditions, which is mediated by restoring the autophagy of EPCs; and the third novel finding is that sitagliptin restores EPC autophagy, which is mediated by the AMPK/mTOR/ULK1 signalling pathway.
Previous studies have shown that DPP-4 inhibitors can improve blood flow recovery and angiogenesis in critical limb ischaemia models, which are accompanied by an increase in circulating EPCs [8,9]. In the present study, for the first time, we revealed that sitagliptin treatment improves blood perfusion and enhances angiogenesis in HLI in db/db type 2 diabetic mice (Fig. 1), which is consistent with previous findings in normal mice [9,25]. We also found that sitagliptin treatment increased the number of circulating EPCs (Fig. 2D) and elevated the expression of the chemokine SDF-1 in plasma (Fig. 2B). SDF-1 is a substrate of DPP-4, which proteolytically cleaves SDF-1 and attenuates the interaction of SDF-1 with its receptor CXCR4 [26,27]. SDF-1 is a critical factor in EPC mobilization from bone marrow to peripheral blood and homing to ischaemic sites via interacting with its receptor CXCR4 [28]. Therefore, sitagliptininduced enhancement of EPC mobilization and promotion of ischaemic blood perfusion and angiogenesis are most likely mediated by protecting SDF-1 from DPP-4 cleavage. In addition, our study demonstrated that sitagliptin also increased the proangiogenic factor SDF-1 and VEGF expression in ischaemic tissue (Fig. 2C), indicating that sitagliptin-augmented ischaemic angiogenesis may also attribute to a proangiogenic factor-mediated paracrine mechanism.
Accumulating studies have demonstrated that the beneficial effects of DPP-4 inhibition on vascular damage are mainly mediated by mobilization of EPCs [7,8,25]; however, the direct effects of DPP-4 inhibition on EPCs biological function have been largely neglected, especially under diabetic conditions. In a previous study, researchers have presented preliminary data showing the direct effects of the DPP-4 inhibitors sitagliptin and vildagliptin on human EPCs under basal conditions [29]. The authors found that DPP-4 inhibition prevented the spontaneous apoptosis, enhanced cell proliferation and the expression levels of VEGF, VEGFR-2 and eNOS in EPCs, which were accompanied by SDF-1/CXCR4 signalling activation, and blockade of the SDF-1/CXCR4 signalling pathway by AMD3100 resulted in increased apoptosis and the inhibition of cell proliferation and the expression levels of VEGF, VEGFR-2 and eNOS in EPCs [29]. In the present study, we further evaluated the direct effects of sitagliptin on EPC survival and angiogenic function under diabetic conditions for the first time (Fig. 4). We found that direct incubation of EPCs with sitagliptin significantly attenuated HG-induced apoptosis and angiogenic dysfunction (Fig. 4A and B), which is consistent with previous findings that direct incubation of mesenchymal stem cells with sitagliptin remarkably attenuates hypoxia-induced apoptosis [30]. More recently, Pujadas et al. [31] found that teneligliptin, another DPP-4 inhibitor, reduced pro-apoptotic gene expression levels and ameliorated oxidative stress in human umbilical vein endothelial cells under HG conditions. In the present study, we also found that sitagliptin attenuated the ROS accumulation in EPCs induced by HG (Fig. 4C).
These results indicate that sitagliptin-mediated improvement of the survival and angiogenic function of EPCs may attribute to sitagliptininduced attenuation of ROS production and accumulation under HG conditions.
Autophagy plays an important role in cellular homeostasis through the degradation and recycling of organelles, such as mitochondria or the endoplasmic reticulum, that are closely related to the pathogenesis of diabetes [32,33]. Autophagy can be induced by conditions such as starvation or inflammation but can also occur constitutively under non-starvation conditions in basal autophagy, a process critical for the maintenance of cellular homoeostasis in the vasculature [33]. The level of autophagy in EPCs from diabetic Fig. 6 Sitagliptin improves the survival and function of EPCs treated with high glucose (HG) via augmenting autophagy. EPCs were pretreated with or without the autophagy inhibitor 3-MA (5 mmol/l) or the autophagy activator rapamycin (10 lmol/l) for 30 min. and then exposed to HG in the presence or absence of sitagliptin (3 lmol/l). (A) The LC3 and p62 expression levels in EPCs were evaluated by Western blotting. (B) The apoptosis of EPCs was analysed by flow cytometry using Annexin V/PI staining. (C) The angiogenic function of EPCs was determined by a tube formation assay, and the tube length was normalized to the mannitol control group. Three independent experiments were performed for each study. Data shown in graphs represent the means AE S.D. *P < 0.05, vs mannitol control group; # P < 0.05, vs HG treatment group. patients is decreased, and upregulating autophagy can improve the survival and function of EPCs under diabetic conditions [34]. Recently, the DPP-4 inhibitor vildagliptin has been reported to reduce acute mortality after myocardial infarction with the restoration of autophagy in type 2 diabetes [11]. In the present study, we found that HG treatment decreased the autophagy level in EPCs and that sitagliptin could restore the autophagy levels ( Fig. 5A and B). Furthermore, the protective effects of sitagliptin on EPCs are orchestrated by the induction of autophagy as the autophagy inhibitor, 3-MA, abrogated sitagliptininduced protection against apoptosis and angiogenic dysfunction under HG conditions (Fig. 6).
However, the role of ROS in the induction of autophagy still remains controversial. For example, recent studies have found that ROS inhibits autophagy [35,36], whereas other studies have shown that natural compounds can protect cells against ROS damage via elevating autophagy [37,38]. In our study, we found that sitagliptin induced the autophagy of EPCs under HG conditions, which was accompanied by reduced ROS levels, indicating a possible link between sitagliptin-induced autophagy and the reduced ROS levels of EPCs. The underlying mechanism needs to be investigated in future studies.
AMPK is a serine/threonine kinase that stimulates catabolic processes and inhibits anabolic processes to restore ATP levels when cellular energy is low [39]. It is well-known that activation of AMPK promotes starvation-induced autophagy through interactions with mTORC1 and/or ULK-1 [40,41]. However, whether AMPK regulates basal autophagy in the excess nutrient environment is controversial. He et al. [42] found that activation of AMPK overcomes the autophagy impairment in myoblasts induced by HG; in addition, the authors also found that activation of AMPK restores autophagy in rodent macrophages exposed to palmitate, following stimulation with lipopolysaccharide [43]. However, in human aortic endothelial cells, AMPK activation cannot restore autophagy impaired by HG and palmitate [44]. In the present study, we showed that sitagliptin preserved the phosphorylation of AMPK and ULK1 and inhibited the phosphorylation of mTOR under HG treatment conditions, eventually resulting in the restoration of autophagy in EPCs, which could be blocked by the AMPK inhibitor compound C (Fig. 7). These findings indicate that sitagliptin-induced restoration of autophagy in EPCs under HG conditions is mediated by the activation of the AMPK signalling pathway. However, how sitagliptin activates AMPK-mediated Fig. 7 Sitagliptin restores autophagy in EPCs treated with high glucose (HG) via activating the AMPK/ULK signalling pathway. EPCs were pretreated with or without the AMPK inhibitor compound C (10 lmol/l) for 30 min. and then exposed to HG in the presence or absence of sitagliptin (3 lmol/l) for 24 hrs. (A) The phosphorylation of AMPK, mTOR and ULK1, and (B) the expression levels of p62 and LC3 were evaluated by Western blotting. Three independent experiments were performed for each study. Data shown in graphs represent the means AE S.D. *P < 0.05, vs mannitol control group; # P < 0.05, vs HG treatment group. | 6,750.8 | 2017-08-10T00:00:00.000 | [
"Biology",
"Medicine"
] |
Regge trajectory relations for the universal description of the heavy-light systems: diquarks, mesons, baryons and tetraquarks
Two newly proposed Regge trajectory relations are employed to analyze the heavy-light systems. One of the relations is $M=m_1+m_2+C'+\beta_x\sqrt{x+c_{0x}}$, $(x=l,\,n_r)$. Another reads $M=m_1+C'+\sqrt{\beta_x^2(x+c_{0x})+\frac{4}{3}\sqrt{{\pi}{\beta_x}}m^{3/2}_2(x+c_{0x})^{1/4}}$. $M$ is the bound state mass. $m_1$ and $m_2$ are the masses of the heavy constituent and the light constituent, respectively. $l$ is the orbital angular momentum and $n_r$ is the radial quantum number. $\beta_x$ and $c_{0x}$ are fitted. $m_1$, $m_2$ and $C'$ are input parameters. These two formulas consider both of the masses of heavy constituent and light constituent. We find that the heavy-light diquarks, the heavy-light mesons, the heavy-light baryons and the heavy-light tetraquarks satisfy these two formulas. When applying the first formula, the heavy-light systems satisfy the universal description irrespective of both of the masses of the light constituents and the heavy constituent. When using the second relation, the heavy-light systems satisfy the universal description irrespective of the mass of the heavy constituent. The fitted slopes differ distinctively for the heavy-light mesons, baryons and tetraquarks, respectively. When employing the first relation, the average values of $c_{fn_r}$ ($c_{fl}$) are $1.026$, $0.794$ and $0.553$ ($1.026$, $0.749$ and $0.579$) for the heavy-light mesons, the heavy-light baryons and the heavy-light tetraquarks, respectively. Upon application of the second relation, the mean values of $c_{fn_r}$ ($c_{fl}$) are $1.108$, $0.896$ and $0.647$ ($1.114$, $0.855$ and $0.676$) for the heavy-light mesons, the heavy-light baryons and the heavy-light tetraquarks, respectively. Moreover, the fitted results show that the Regge trajectories for the heavy-light systems are concave downwards in the $(M^2,\,n_r)$ and $(M^2,\,l)$ planes.
I. INTRODUCTION
There is a vast amount of experimental data on the spectra of different types of hadrons [1].One of the widely used approaches in studying the hadron spectra is the Regge trajectory .The study of Regge trajectories of hadron spectra is beneficial for gaining insights into the strong interactions from various perspectives [22][23][24][25][26][27][28][29][30][31].Clearly, an unified dynamic mechanism will lead to the universal description of Regge trajectories for hadrons [25][26][27].
The meson Regge trajectories exhibit structures that vary in different energy regions [32,33].This variability is expected to hold true for other hadrons with a similar dynamic mechanism, such as baryons and tetraquarks in the diquark picture.For the light-light systems, it is wellknown that they can be well described by the renowned linear Regge trajectories [3,4].In case of the heavy-heavy systems, an universal description is presented in Refs.[34,35].Regarding the heavy-light systems, the authors provide an universal description of the orbitally excited heavy-light mesons and baryons in Ref. [28].In Ref. [36], we present the heavy-light diquark Regge trajectories.The proposed Regge trajectory relations can universally describe the heavy-light mesons and the heavy-light diquarks.In this study, we apply the Regge trajectory where M 0 = ω 1 + ω 2 .M is the bound state mass (diquark, meson, baryon and tetraquark).Ψ d,m,b,t (r) are the diquark wave function, the meson wave function, the baryon wave function, and the tetraquark wave function, respectively.V d,m,b,t are the diquark potential, the meson potential, the baryon potential, and the tetraquark potential, respectively.ω 1 is the relativistic energy of constituent 1, and ω 2 is of constituent 2, m 1 and m 2 are the effective masses of heavy constituent 1 and light constituent 2, respectively.
In the present work, the Cornell-like potential is considered [37,38,44,45], where V c ∝ 1/r is the color Coulomb potential or a Coulomb-like interaction for different hadrons [37,44].
The second term is the linear confining potential and σ is the string tension.C is a fundamental parameter [46,47].
From Eqs. ( 1) and ( 3), we see that the heavy-light diquarks, the heavy-light mesons, the heavy-light baryons, and the heavy-light tetraquarks are described in an unified approach [37,38].Therefore, it is expected that these heavy-light systems can be described universally by the Regge trajectory approach.
B. Regge trajectory relations
The mass of the light constituent is assumed to approach zero, m 2 → 0 in Refs.[15,28] or is considered by correction term in Refs.[16,27,[48][49][50].In the limit m 1 → ∞ and m 2 → 0, Eq. ( 1) is reduced to be By employing the Bohr-Sommerfeld quantization approach [51,52], we have from Eq. ( 5) where Using Eq. ( 6), the parameterized formula can be written as [36] The parameter in Eq. ( 8) reads as [32] The constants c x [c nr and c l ] and c c are Both c f l and c f nr are theoretically equal to one and are fitted in practice.For the heavy-light mesons, the common choice of m R is [15,28,32,[48][49][50]53] m R , c x and σ are universal for the heavy-light systems.c f x and c 0x , which vary with different Regge trajectories, are determined by fitting the given Regge trajectory.
The usual Regge trajectory Eq. ( 8) with (11), which is obtained in the limit m 1 → ∞ and m 2 → 0, cannot give agreeable results of the heavy-light diquarks.Corresponding to different ways to include the light constituent's mass, two modified formulas are proposed in Ref. [36], which can describe universally both the heavylight mesons and the heavy-light diquarks.One is Eq. ( 8) with where Another reads if m 2 ≪M , where where β x is in (9).( 8) with ( 12) is an extension of M = m 1 + m 2 + a(n r + αl + b) [16], while (14) with ( 15) is based on the results in [27,48].As m 2 = 0, these two modified formulas, formulas (8) with ( 12) and ( 14) with (15), become identical.As m 2 = 0 and C is neglected, these two modified formulas reduce to the usual Regge trajectory formula for the heavy-light mesons, i.e., (8) with (11).In this work, we apply these two modified formulas to the heavy-light systems: diquarks, mesons, baryons, tetraquarks.
III. UNIVERSAL DESCRIPTION OF THE HEAVY-LIGHT SYSTEMS
In this section we present the universal description of different types of heavy-light systems by employing (8) with ( 12) and ( 14) with (15).The Regge trajectories for the heavy-light systems are fitted individually.
A. Parameters
The parameters are [54][55][56] where { } denotes the axial-vector diquark and [ ] the scalar diquark.c 0x and c f x vary with different Regge trajectories.
The values in Eq. ( 16) are used to calculate the masses of tetraquarks [54], baryons [55] and mesons [56].In Ref. [28], the values are used to give an universal description of the heavy-light mesons and baryons.The values are also used to discuss diquarks [35,36].
In case of Eq. ( 8) with ( 12), the heavy-light diquarks satisfy the universal description irrespective of both mass of the light constituents and mass of the heavy constituent.In case of Eq. ( 14) with ( 15), the heavy-light diquarks satisfy the universal description irrespective of mass of the heavy constituents.
C. Heavy-light mesons
By using Eqs.( 8) with ( 12) and ( 14) with (15) and data in Table I, the radial and orbital Regge trajectories for the heavy-light mesons D * , D * ± s , B * and B * s are obtained, see Fig. 1.The fitted values are listed in Table II.In Fig. 1, the Regge trajectories (the red dashed lines) obtained by employing ( 14) with (15) lie above the Regge trajectories (the black lines) obtained by applying ( 8) with (12).It is because m R for these two Regge trajectories are different, see Eqs. (12) and (15).The figures show that the heavy-light mesons satisfy both of these two Regge trajectory relations.
From Fig. 2 and the fitted values in Table II, we can see that both of the radial and orbital Regge trajectories in the ((M − m 1 − m 2 − C) 2 , x) planes almost overlap with each other irrespective of both the light quark flavor and heavy quark flavor.It shows an universal description of these heavy-light mesons.For the heavy-light mesons, the Regge trajectories in the ((M − m 1 − C) 2 , x) plane are universal only irrespective of heavy quark flavor.
As employing Eq. ( 8) with (12), the average values of c f nr and c f l are 1.026 and 1.026 for the heavy-light mesons, respectively.When applying Eq. ( 14) with (15), the average values of c f nr and c f l are 1.108 and 1.114, respectively.
From Table II, we can see that the fitted values of c f nr and c f l decrease in the majority of cases as the masses of the constituents increase when employing (8) with (12).However, the fitted values of c f nr and c f l obtained by using ( 14) with ( 15) frequently decrease with the increase of the masses of the heavy constituent and rise with the increase of the masses of the light constituent.This trend aligns with the results in [28].
D. Heavy-light baryons
In the diquark picture, the baryons consisting of one light quark and one heavy diquark or consisting of one heavy quark and one light diquark are denoted as the heavy-light baryons and belong to the heavy-light systems.Employing ( 8) with ( 12) and ( 14) with ( 15) to the heavy-light baryons, the Regge trajectories are fitted.The used data are listed in Table III and the fitted values are in Table II.The fitted Regge trajectories are in Fig. 3.
The difference of m R for two Regge trajectory relation leads to that the Regge trajectories (the red dashed lines) obtained by employing ( 14) with (15) lie above the Regge trajectories (the black lines) obtained by applying (8) with (12), see Fig. 3. From Fig. 4 and the fitted values in Table II, we can see that the heavy-light baryons satisfy both of these two Regge trajectory relations.We also notice that some fitted Regge trajectories by employing (8) with (12) are better than the fitted Regge trajectories by applying ( 8) with (12), for example, the Regge trajectory for Ω c , see 3(m).
Similar to the meson case, from Fig. 4 and the fitted values in Table II, we can see that both of the radial and orbital Regge trajectories for the heavy-light baryons plotted in the ((M − m 1 − m 2 − C) 2 , x) planes almost overlap with each other irrespective of both the light constituent and the heavy constituent.This shows an universal description of these heavy-light baryons.For the heavy-light baryons, the Regge trajectories in the ((M − m 1 − C) 2 , x) plane are universal only irrespective of heavy constituent.
As employing Eq. ( 8) with (12), the average values of c f nr and c f l are 0.794 and 0.749 for the heavy-light baryons, respectively.When applying Eq. ( 14) with (15), the average values of c f nr and c f l are 0.896 and 0.855, respectively.The fitted c f nr and c f l for the heavy-light baryons are smaller than that for the heavy-light mesons.8) with ( 12) (Fit1) and ( 14) with (15) (Fit2).The used data are in Tables I, III, IV and V.The fitted values for the doubly heavy baryons approximate the fitted values for the heavy-light mesons because the doubly heavy baryons strongly resemble the heavylight mesons.
E. Heavy-light tetraquarks
The heavy-light tetraquarks denote tetraquarks consisting of one heavy diquark and one light antidiquark FIG. 1: The radial and orbital Regge trajectories for the heavy-light mesons by employing formulas ( 8) with ( 12) (the black lines) and ( 14) with ( 15) (the red dashed lines).The PDG data (the dots and the filled squares) and the theoretical data (the circles and the empty squares) are listed in Table I. mR for the black lines and for the red dashed lines are different, see ( 12) and ( 15).The used data are listed in Table I. or consisting of one light diquark and one heavy antidiquark.The tetraquarks composed of a diquark and antidiquark in color 3 and 3 configurations are considered.
Applying Eqs. ( 8) with ( 12) and ( 14) with ( 15) and using data in Table V, the radial and orbital Regge tra-jectories for the heavy-light tetraquarks are obtained, see Fig. 5.The fitted values are listed in Table II.Similar to the heavy-light mesons and the heavy-light baryons, the Regge trajectories (the red dashed lines) obtained by employing ( 14) with (15) lie above the Regge trajectories FIG. 4: Same as Fig. 2 except for the heavy-light baryons and Tables III and IV.
From Fig. 6 and the fitted values in Table II, we can see that the heavy-light tetraquarks satisfy both of these two Regge trajectory relations.Moreover, we can see that the universal description of the heavy-light tetraquarks approximately holds.We notice that the fitted results are not reliable enough because the experimental data is lack and the theoretical data on the λ-excited states are scarce.[The theoretical data on the λ-excited states of the tetraquarks are scarce because the masses of these states lie above the corresponding thresholds.]As employing Eq. ( 8) with (12), the average values of c f nr and c f l are 0.553 and 0.579 for the heavy-light tetraquarks, respectively.When applying Eq. ( 14) with (15), the mean values of c f nr and c f l are 0.647 and 0.676, respectively.The fitted c f nr and c f l for the heavylight tetraquarks are smaller than that for the heavy-light mesons and the heavy-light baryons.
IV. CONCAVITY OF THE REGGE TRAJECTORIES
The Regge trajectories take different forms in different energy regions [32,33].In this section, the Regge trajectories are depicted in the (M 2 , x) (x = n r , l) planes.In Refs.[35,36,67], it is shown that the Regge trajectories for all types of diquarks (including the doubly heavy diquarks, the heavy-light diquarks and the light diquarks) are concave downwards.
In Ref. [68], it is shown that the meson Regge trajectories are concave downwards for the doubly heavy mesons and the heavy-light mesons.In the case of the light mesons, the Regge trajectories assume a linear form when the masses of the light quark and antiquark are taken as zero.However, upon taking into account the masses of the light quark and antiquark, the Regge trajectories for the light mesons also adopt a concave shape, see Refs.[27,48].
In Ref. [34], we show that the Regge trajectories for the heavy-heavy baryons and tetraquarks are also concave downwards.In this work, we observe that the Regge trajectories for the heavy-light baryons and the heavylight tetraquark also display a concave shape.Taking into account the masses of the light constituent, it is expected that the Regge trajectories for the light baryons and the light tetraquarks will similarly be concave.
The curvature of the Regge trajectories holds significant importance [68].In potential models, the curvature is related to the dynamic equation and the confining potential.Based on the discussions in this section, we assume that, when considering the mass of the light constituent, all Regge trajectories for the diquarks, mesons, baryons and tetraquarks are concave downwards in the (M 2 , n r ) and (M 2 , l) planes.Future experimental data will either validate or challenge the concavity conjecture.It will improve understanding of hadron dynamics and promote the study of hadron spectra.
FIG. 3 :
FIG.3: Same as Fig.1except for the heavy-light baryons and Tables III and IV.
TABLE I :
[56]experimental values[1]and the theoretical values (EFG)[56]for the charmed and bottom mesons.The values are in GeV.
TABLE II :
The fitted values of parameters c f nr , c f l , c0n r , and c 0l by employing formulas (
TABLE III :
The experimental and theoretical data for the radially excited states1 | 3,654 | 2023-02-14T00:00:00.000 | [
"Physics"
] |
α-Mangostin inhibits LPS-induced bone resorption by restricting osteoclastogenesis via NF-κB and MAPK signaling
Background Excessive osteoclast activation is an important cause of imbalanced bone remodeling that leads to pathological bone destruction. This is a clear feature of many osteolytic diseases such as rheumatoid arthritis, osteoporosis, and osteolysis around prostheses. Because many natural compounds have therapeutic potential for treating these diseases by suppressing osteoclast formation and function, we hypothesized that α-mangostin, a natural compound isolated from mangosteen, might be a promising treatment as it exhibits anti‐inflammatory, anticancer, and cardioprotective effects. Methods We evaluated the therapeutic effect of α-mangostin on the processes of osteoclast formation and bone resorption. The receptor activator of nuclear factor-κB (NF-κB) ligand (RANKL) induces osteoclast formation in vitro, and potential pathways of α-mangostin to inhibit osteoclast differentiation and function were explored. A mouse model of lipopolysaccharide‐induced calvarial osteolysis was established. Subsequently, micro-computed tomography and histological assays were used to evaluate the effect of α-mangostin in preventing inflammatory osteolysis. Results We found that α-mangostin could inhibit RANKL-induced osteoclastogenesis and reduced osteoclast‐related gene expression in vitro. F-actin ring immunofluorescence and resorption pit assays indicated that α-mangostin also inhibited osteoclast functions. It achieved these effects by disrupting the activation of NF-κB/mitogen-activated protein kinase signaling pathways. Our in vivo data revealed that α-mangostin could protect mouse calvarial bone from osteolysis. Conclusions Our findings demonstrate that α-mangostin can inhibit osteoclastogenesis both in vitro and in vivo and may be a potential option for treating osteoclast-related diseases. Supplementary Information The online version contains supplementary material available at 10.1186/s13020-022-00589-5.
bone resorption, disrupts the balance between bone resorption and bone formation, and causes a variety of bone disorders including osteoporosis, rheumatoid arthritis, periodontal disease, and metastatic cancers [4,5]. Therefore, inhibiting osteoclast activity might be and effective treatment strategy for such diseases.
Receptor activators of nuclear factor-κB (NF-κB) ligand (RANKL) and macrophage colony-stimulating factor have been shown to mediate osteoclast differentiation by activating different signaling cascades, such as NF-κB and mitogen-activated protein kinase (MAPK) pathways [6][7][8]. These signaling pathways promote the expression of transcription factors including activator protein-1 and nuclear factor of activated T cells c1 (NFATc1), which are the key transcription factors for osteoclast differentiation, and finally promote the differentiation and activation of monocyte-macrophage precursors into osteoclasts [9,10]. As such, drugs that suppress RANKL-induced signaling have great potential to prevent these osteoclast-related diseases. Here we explored the effect of α-mangostin on RANKL-induced NF-κB activation and osteoclastogenesis was explored.
α-mangostin is the most representative xanthone isolated from the pericarp of mangosteen and was reported to have a variety of pharmacological effects [11]. Specifically, α-mangostin has potential usage as an anticancer treatment and can be regarded as a chemopreventive agent for oral cancer, colon cancer, pancreatic cancer, breast cancer, and cutaneous carcinoma [12,13]. It also has reported anti-inflammatory, anti-bacterial, antimalarial, and anti-obesity effects action [11,[14][15][16]. Furthermore, α-mangostin has been shown to improve cardiovascular and digestive system health, as well as controlling free radical oxidation [17][18][19]. Recent research has shown that α-mangostin can inhibit osteoarthritis (OA) progression by suppressing mitochondrial apoptosis of chondrocytes induced by NF-κB pathway activation [20]. Nevertheless, there are few studies on the effects of α-mangostin on osteoclasts and osteolytic diseases [21]. Based on previous results showing that α-mangostin had potential therapeutic value in the treatment of OA through inhibiting the production of nitric oxide (NO) and prostaglandin E2, as well as interleukin (IL)-1β-induced phosphorylation of the NF-κB signaling proteins, we hypothesized that α-mangostin might be a novel candidate for treatment of osteoclast-related diseases based on its ability to inhibit osteoclastogenesis.
Here we studied the effects of α-mangostin on the induction and outcomes of RANKL-induced osteoclastogenesis, then explored its mechanism and discovered that its affects two key signaling pathways: NF-κB and MAPK. Finally, the bone protective effect of α-mangostin was verified in a lipopolysaccharide (LPS)-induced osteolysis calvarial mouse model.
Bone marrow-derived macrophage isolation and osteoclast differentiation
PBS and DMSO (Sigma-Aldrich) were used as vehicle and negative control for all treatments. Bone marrow cells were acquired from the long bones of 6-week-old male C57BL/6 mice, as described previously [22], and the bone marrow cells in femurs and tibias were flushed out and cultured in α-MEM supplemented with 10% FBS, 100 U/mL penicillin, 100 µg/mL streptomycin, and 25 ng/mL M-CSF at 37 °C for 5 days to differentiate into bone marrow-derived macrophages (BMMs). Next, cells were respectively seeded into 48-well plates (~ 1 × 10 4 cells/well in triplicate) and treated with different concentrations of α-mangostin (0, 0.5, 1, or 2 μmol/L) in the presence of 25 ng/mL M-CSF and 50 ng/mL RANKL. The culture medium was replaced every 2 days. After culturing for 5 days, the cells were fixed with 4% paraformaldehyde (PFA) and then stained for TRAP based on the instructions. TRAP-positive multinucleated cells with ≥ 3 nuclei were counted using a light microscope (BX51; Olympus, Tokyo, Japan).
Cell viability assay
To test the effects of α-mangostin on BMM viability, Cell Counting Kit 8 (CCK8) assays were performed. Based on the manufacturer's instructions (Dojindo, Shanghai, China), cells were seeded in 96-well plates (8 × 10 3 cells per well) and cultured in complete α-MEM medium for 48 or 96 h with different concentrations of α-mangostin (0-4 µM). Next, CCK8 reagent (10 µL) was added to each well, and the plate was incubated for another 2-4 h. The optical density (OD) was measured using a MR7000 microplate reader (Dynatech, Melville, NY, USA) at 450 nm. The viabilities of BMMs exposed to α-mangostin are expressed as a percentage of untreated cells.
Constructing stable overexpression cell lines (transfection)
To validate that ACP5 gene was involved in α-mangostin inhibitory on osteoclagenesis. An ACP5 gene overexpression plasmid and negative control (NC) plasmid were purchased from Genepharma Corporation (Shanghai, China). All the procedures were followed with the manufacture protocols. The transfected cells were treated with 2 μg/mL puromycin until all the cells in the control group died (untransfected cells). The transfection efficiency of the cells was further confirmed by western blot before they were used in experiments.
Hoechst 33342 staining
Cells (4 × 10 5 cells per well) were placed in six-well plates and treated with different concentrations of α-mangostin for 5 days with the medium changed every 2 days, then cells were incubated with Hoechst 33342 for 20 min. A fluorescence microscope (Olympus) was utilized to visualize morphological changes of apoptotic cells at 365 nm.
Apoptosis flow cytometry assay
Apoptosis was measured using Annexin V-fluorescein isothiocyanate/propidium iodide (FITC/PI) apoptosis kits (Multi-Sciences, Hangzhou, Zhejiang, China). BMMs (2 × 10 5 per well) were seeded in six-well plates and cultured with different concentrations of α-mangostin (0, 0.5, 1, 2 μmol/L) for 24 h. After washing the cells with phosphate-buffered saline (PBS), they were collected and incubated with the reagents for 20 min in the dark. All
In vitro osteoclast differentiation
BMMs were planted into a 96-well plate at a density of 8 × 10 3 cells per well, and cultured in complete α-MEM supplemented with 25 ng mL × 1 M-CSF, 50 ng mL × 1 RANKL, and different concentrations of α-mangostin (0, 0.5, 1, and 2 µM). The culture medium was replaced every 2 days. After 5 days, the cells were washed twice with PBS, fixed with 4% PFA, and stained for TRAP. TRAP-positive cells with ≥ 3 nuclei were counted as mature osteoclasts under a light microscope.
RNA extraction and quantitative polymerase chain reaction (PCR)
Total RNA from cultured cells was extracted using the TRIzol reagent (Invitrogen, Carlsbad, CA, USA) according to the manufacturer's protocols. Complementary DNA was synthesized from 1 µg of total RNA using Pri-meScript RT Master Mix (TaKaRa Biotechnology, Otsu, Japan). Real-time PCR was performed using the TB Green Premix Ex Taq kit (TaKaRa Biotechnology) on a StepOnePlus Real-Time PCR System (Applied Biosystems, Foster City, CA, USA). Each reaction was run at the following conditions: 95 °C for 60 s and then 40 cycles of 95 °C for 10 s, 60 °C for 20 s and 72 °C for 20 s. Glyceraldehyde 3-phosphate dehydrogenase (GAPDH) served as the endogenous control. The mouse primer sequences are shown in Table 1.
F-actin ring immunofluorescence and resorption pit assays
In order to visualize F-actin rings, BMMs were treated with 25 ng/mL M-CSF and 50 ng/mL RANKL for 4 days. We seeded differentiated osteoclasts (2 × 10 3 cells/cm 2 ) onto bovine bone slices and allowed them to adhere overnight. Then cells were treated with different concentrations of α-mangostin (0, 0.5, 1, or 2 µM) for another 2 days. The cells were then fixed with 4% PFA for 15 min, permeabilized with 0.4% Triton X-100 for 10 min, then stained with rhodamine-conjugated phalloidin (1:200; Invitrogen) diluted in 0.5% bovine serum albumin (BSA)-PBS for 30 min. Fluorescent images were captured utilizing a fluorescence microscope (EU5888, Leica, Wetzlar, Germany) and analyzed by ImageJ software [National Institutes of Health (NIH), Bethesda, MD, USA]. To observe resorption pits, the bone slices were washed twice with PBS, and adhered cells were removed by mechanical brushing. Bone slice images were acquired with a scanning electron microscope (SEM; S-4800, Hitachi, Japan) and analyzed by ImageJ software.
Western blotting
The main signaling pathways affected by α-mangostin were detected by western blotting. Cells were treated with or without 2 µM α-mangostin for 4 h, then stimulated with 50 ng mL × 1 RANKL for 0, 5, 10, 20, 30, or 60 min. To explore the effects of α-mangostin on c-Fos and NFATc1 expression, BMMs were seeded in sixwell plates (1 × 10 5 cells per well) and cultured with 25 ng mL × 1 M-CSF and 50 ng mL × 1 RANKL in the presence or absence of 2 µM α-mangostin for 0, 2, 4, or 6 days. Then the cells were collected and lysed with radioimmunoprecipitation assay buffer (Sigma-Aldrich) containing a protease inhibitor and phosphatase inhibitor cocktail (Sigma-Aldrich). According to the steps in the manufacturer's protocols, the supernatant was collected. Bicinchoninic acid protein assay kits (Beyotime, Shanghai, China) were used to quantify the total amounts of protein. Equal amounts of protein samples were separated by 8-15% sodium dodecyl sulfate-polyacrylamide gel electrophoresis at 75 V for 1.5 h and subsequently transferred onto 2.2-µm polyvinylidene fluoride membranes (Millipore, Burlington, MA, USA) at 250 mA for 2 h in a humid atmosphere. The membranes were blocked with 10% milk or 5% BSA (Sigma-Aldrich) and incubated with the primary antibody overnight at 4 °C. After three washes in Tris-buffered saline with Tween 20 (10 min each), the membranes were incubated with horseradish peroxidase-conjugated secondary antibodies (Huabio, Hangzhou, Zhejiang, China) for 1 h at room temperature. The target bands were developed with enhanced chemiluminescence kits (Millipore).
Mouse model of LPS-induced calvarial osteolysis
All animal care and experimental protocols were designed and performed in compliance with the NIH Guide for the Care and Use of Laboratory Animals and the Guide of the Animal Care Committee of Zhejiang University. Thirty 6-week-old male C57BL/6 mice weighing 18-22 g was purchased from Experimental Animal Center of Zhejiang University. A mouse model of LPSinduced calvarial osteolysis was established, as described previously, to explore the effects of α-mangostin on inflammatory bone loss in vivo. After acclimatizing to the laboratory for 1 week, mice were randomly divided into the following three experimental groups (n = 5 each): sham, LPS (vehicle), and LPS + α-mangostin groups (both LPS and α-mangostin were first dissolved in dimethyl sulfoxide and then diluted with PBS). After anesthetization with intraperitoneal sodium pentobarbital (50 mg/kg), the cranial periosteum of mice was separated, and 5 mg/kg body weight (50 μl 10 mM) LPS (Sigma-Aldrich) in PBS was embedded under the periosteum at the middle suture of the calvaria in the LPS (vehicle) and LPS + (100 μl 5 mM) α-mangostin groups on days 1 and 4, while PBS was injected in the sham group. Mice in the LPS + α-mangostin group also received daily subcutaneous injections of 10 mg/kg α-mangostin for 7 days. Mice in the sham and LPS groups were administered PBS as a control. Α-mangostin doses were determined according to previous studies [17,27]. All the mice were sacrificed on day 7, and their calvaria were harvested for subsequent analysis.
Micro-computed tomography (CT) scanning
Calvaria were measured (n = 5 per group) by a high-resolution micro-CT (Skyscan 1072, Aartselaar, Belgium). The scanning protocol was set at an isometric resolution of 9 µm and X-ray energy settings of 80 kV and 80 µA. Then, three-dimensional reconstruction was performed, and a 3 mm × 3 mm region of interest surrounding the midline suture was selected for further qualitative and quantitative analyses. Bone volume/tissue volume (BV/ TV), number of porosities, and porosity percentage for each specimen were measured as reported previously [23].
Hematoxylin and eosin (H&E) and TRAP staining
Fixed tissue samples (n = 5 per group) were decalcified in 10% ethylenediaminetetraacetic acid (pH = 7.4) for 2 weeks and then embedded in paraffin. Next, the calvaria were cut into 4-μm-thick histological sections for H&E and TRAP staining. The sections were photographed under a light microscope (TE2000-S; Nikon, Tokyo, Japan). Histomorphometric parameters of BV/TV, erosion area, the number of TRAP-positive osteoclasts, and surface area of osteoclasts per bone surface (OcS/BS) were assessed for each sample.
Statistical analysis
All data are expressed as mean ± standard deviation (SD). Each experiment was repeated at least three times, and the results were analyzed with Prism 6.01 (GraphPad Software, San Diego, CA, USA). Two-tailed, unpaired Student's t-tests were used for the comparisons between two groups. One-way analyses of variance with post hoc Newman-Keuls test were performed to analyze differences in multiple comparisons. Differences were considered significant at P < 0.05.
Preventive effect of α-mangostin on RANKL-induced osteoclast differentiation in vitro
Cell viability assays were performed to evaluate a potential cytotoxic effect of mangostin on BMMs. The cells were treated with different concentrations of mangostin (0, 0.5, 1, 2, 4 µmol/L) for 48 or 96 h. The CCK-8 results revealed that mangostin caused no obvious BMM cytotoxicity at concentrations ≤ 2 μmol/L (Fig. 1B). Flow cytometry showed that mangostin administered at a concentration of 0-2 μmol/L did not cause BMM apoptosis, which was also confirmed by the absence of significant changes in apoptosis-related proteins (Fig. 2). When the concentration of mangostin reached 4 μM, the flow cytometry results indicated that 64.94% of BMMs were apoptotic. In addition, Hoechst 33342 staining, as a classic method for observing apoptotic cell nucleus shrinkage, also showed obvious cell apoptosis under 4 μM α-mangostin. There were also corresponding changes in apoptotic protein expression levels (Additional file 1: Fig. S1). Based on these results, we choose 2 μmol/L as the highest concentration for subsequent experiments.
To explore the preventive effect of α-mangostin against osteoclastogenesis, BMMs were treated with different concentrations of α-mangostin (0, 0.5, 1, 2 μmol/L) in the presence of M-CSF (25 ng/mL) and RANKL (50 ng/mL). After 5 days of incubation, the osteoclasts had differentiated into BMMs as confirmed by TRAP staining. Notably, α-mangostin reduced osteoclast differentiation in a dosedependent manner (Fig. 1C and D). There were numerous mature TRAP-positive multinucleated osteoclasts in the control group, but the number and area of osteoclasts were significantly decreased in a dose-dependent manner in the α-mangostin groups. Next, α-mangostin was added at different stages of osteoclast formation to clarify which stage of osteoclast formation is affected by α-mangostin. Specifically, cells were treated with 2 µM α-mangostin at early (day 1-2), middle (day 3-4), late (day 5-6), and final stage (day 1-6). Compared with the other groups, the numbers and sizes of osteoclasts were significantly reduced in the final stage and early-stage groups ( Fig. 1E and F). Correspondingly, there was a slight decrease in the middle stage group, but this inhibition effect was not significant in the late stage α-mangostin group. Finally, we explored whether the inhibitory effect of α-mangostin would be offset in BMMs overexpressing the TRAP gene (ACP5). We constructed stable transfected cells overexpressing ACP5 (S2A), and again evaluated osteoclast numbers and sizes. Despite the presence of α-mangostin, osteoclasts overexpressing ACP5 were able to regain the physiological function of bone resorption. This result confirmed TRAP as a key pathway for α-mangostin to hamper osteoclastogenesis. After overexpression of ACP5, despite the inhibitory effect of α-mangostin, BMMs could still be induced to differentiate into osteoclasts, but the sizes and numbers were reduced compared to the control group (Additional file 1: Fig. S1D4). Overall, these data demonstrate that α-mangostin had a suppressive effect on osteoclast formation, especially at the early stage of differentiation.
Preventive effect of α-mangostin on bone resorption in vitro
α-mangostin was previously shown to inhibit osteoclast formation, so we wondered if it could also inhibit their function. BMMs (1 × 10 4 cells/well) were seeded on Osteo Assay Plates and then incubated with RANKL and M-CSF and different concentrations of α-mangostin for 5-6 days. The tight F-actin ring is necessary for osteoclasts to perform bone resorption and can be used to evaluate whether mature osteoclasts are functioning. The immunofluorescence results showed that the shape and size of the F-actin ring were destroyed by α-mangostin in a dose-dependent fashion (Fig. 4A). Extensive bone resorption areas and larger pits were observed in the control group, while α-mangostin treatment significantly decreased the pit area, and almost no resorption pits were found on bone slices treated with 2 µM α-mangostin ( Fig. 4B and C). Similarly, we verified the effect of ACP5 overexpression on α-mangostin's inhibition of osteoclast function. Despite the presence Figure S2B3). Together, our results indicate that α-mangostin suppresses the F-actin ring formation and bone resorptive activity of mature osteoclasts in vitro.
α-mangostin inhibits RANKL-induced NF-κB and MAPK signaling
First, we verified that α-mangostin could inhibit the expression of osteoclast-related proteins induced by RANKL in a dose-dependent manner ( Fig. 5A and B). Due to the presence of RANKL in the control group, the osteoclast-related proteins NFATc1, c-Fos, CTSK, and TRAP were significantly increased, while α-mangostin obviously inhibited their expression, especially 3-5 days after adding RANKL.
NF-κB signaling is regarded as having a key role in osteoclast differentiation, so we wondered whether the effect of α-mangostin on RANKL-stimulated osteoclastogenesis was regulated via NF-κB activation [5]. In this study, the phosphorylation and protein levels of NF-κB p65 and IκBα were measured by western blot. Before 1 h stimulation with 50 ng/mL RANKL, the BMMs were preincubated with different concentration of α-mangostin for 4 h. Cells treated with α-mangostin showed less phosphorylation of NF-κB p65 and IκBα, and degradation of IκBα protein was also significantly decreased ( Fig. 5C and D). In addition, MAPKs (ERK, JNK, and p38) were phosphorylated by stimulation with RANKL, while α-mangostin treatment significantly suppressed the phosphorylation levels of these proteins (Fig. 5E), which was confirmed by the quantitative analysis (Fig. 5F). We used the JNK agonist anisomycin to carry out the reverse experiment. The results suggested that α-mangostin indeed inhibited JNK pathway activation, but the ability of α-mangostin to attenuate osteoclast formation and function was not completely eliminated (Additional file 1: Fig. S1D5 and Additional file 2: S2B4, C). These results revealed that α-mangostin inhibits RANKL-induced activation of NF-κB and MAPK signaling in vitro.
Effect of α-mangostin on LPS-induced osteolysis in a mouse calvarial model
To investigate effects of α-mangostin on pathological osteolysis in vivo, an LPS-induced murine calvarial osteolysis model was established. LPS was embedded under the periosteum at the middle suture of the calvaria with or without α-mangostin (10 mg/kg) in the LPS (vehicle) and LPS + α-mangostin groups. Mice in the LPS + α-mangostin group were intragastrically administered 10 mg/kg α-mangostin every day for 7 days. Mice in the sham and LPS (vehicle) groups were administered PBS intragastrically as a control. After 7 days, the calvaria were collected and fixed in 4% PFA, then analyzed by micro-CT and histology (Fig. 6A). Micro-CT images showed that calvaria bone loss was decreased by α-mangostin treatment, while extensive Data are shown as mean ± SD. *P < 0.05, **P < 0.01, ***P < 0.001, compared with the controls bone erosion was observed in the LPS (vehicle) group compared with the sham group. Quantitative analysis indicated that decline of BV/TV and increased porosity induced by LPS were all attenuated by α-mangostin treatment (Fig. 6B).
Histological assessments further confirmed the results from Micro-CT showing that α-mangostin had a therapeutic effect against osteolysis. H&E staining showed that LPS induced severe osteolytic changes in the LPS (vehicle) group, but a significantly reduced extent of bone erosion was found in the α-mangostin group (Fig. 6C). Moreover, the number of osteoclasts was decreased in the α-mangostin group compared with LPS (vehicle) group as shown by TRAP staining (Fig. 6E). Finally, we extracted protein samples from calvaria tissue from each group to examine the expression of pathway-related proteins. Similar to previous results, the expression levels of these proteins were significantly inhibited by mangosteen. These data suggest that α-mangostin hindered LPS-induced osteolytic bone loss in vivo.
Discussion
Increased osteoclast-induced bone resorption is an important factor leading to periprosthetic osteolysis and osteoporosis [2,24]. The balance between osteoblastmediated bone formation and osteoclast-mediated bone resorption is critical for appropriate bone turnover and remodeling, so it is important to identify strategies to treat bone diseases [5]. In our study, we demonstrated for the first time that α-mangostin could inhibit RANKLinduced osteoclastogenesis by inhibiting NF-κB and MAPK signaling in vitro and hinder LPS-induced osteolytic bone loss in a mouse calvarial model. α-mangostin has extensive biological activities and pharmacological properties; it is antioxidant, antineoplastic, antiproliferation, and induces apoptosis [14,25,26]. A recent report described the use of α-mangostin in treating rheumatoid arthritis and a α-mangostin-loaded self-micro emulsion was designed [26]. Recently, it was reported that α-mangostin can block LPS-induced activation in RAW264.7 cells, thereby inhibiting the secretion of IL-1β, IL-6, NO, and cyclooxygenase 2 [27]. The resorption area of bone discs and the size of F-actin rings were quantified using the ImageJ software, N = 3. Error bar = mean ± SD. **P < 0.01, ***P < 0.001, compared with the controls Α-mangostin was also reported to inhibit the activation of TAK1-NF-κB to exert anti-inflammatory effects, which makes it a potential choice for treating inflammatory diseases [28]. Previous studies have shown that α-mangostin has an inhibitory effect on the osteoclast differentiation of RAW264.7 cells. However, it is more scientific to use mouse BMMs as the research object for in vitro experiments as the results are more credible. We also confirmed the role of α-mangostin in inhibiting osteoclasts at the animal level. Our current research confirms that α-mangostin has great potential for treating osteoporosis.
We examined whether α-mangostin had a toxic effect on BMMs and if it could inhibit the osteoclast differentiation. The CCK-8 results showed that α-mangostin had no obvious inhibitory effect on BMMs at concentrations < 2 μmol/L. To clarify whether the effect of α-mangostin on osteoclast formation is indeed achieved by inhibiting their differentiation rather than The protein expression levels of NFATc1, c-Fos, TRAP and CTSK in BMMs treated with 50 ng/mL RANKL with or without 2 µM α-mangostin for 0, 1, 3, or 5 days, N = 3. B The expression of these proteins were quantified using the ImageJ software, N = 3. C, E BMMs were pretreated with or without 2 µM α-mangostin for 4 h and then cultured with RANKL for the indicated periods. D, F The gray levels of phosphorylated p65, ERK, JNK, and p38 were quantified and normalized relative to their total protein counterparts. The gray levels of p-IκBα and IκBα were normalized to β-tubulin, N = 3. Data are presented as mean ± SD. *P < 0.05, **P < 0.01, ***P < 0.001, compared with RANKL alone promoting apoptosis, we performed flow cytometry and western blotting, and the results were consistent with our previous conclusions. Additional file 1: Fig. S1 clearly shows that when the α-mangostin dose reached 4 μM, apoptosis-related protein expression was significantly increased. The flow cytometry results suggested that there was apoptosis in BMMs, and Hoechst staining further confirmed this conclusion. This was the basis to select the drug dosage for our follow-up studies. TRAP staining showed that at concentrations below cytotoxic levels, α-mangostin had a significant protective effect against RANKL-induced osteoclast differentiation. As the concentration of α-mangostin increased, the number of TRAP-positive cells decreased, and mature osteoclasts were rarely observed in the high concentration (2 μmol/L) treatment group. Based on the conclusions of previous studies of natural compounds, the inhibitory effect of berberine on osteoclast formation was used as our positive control [29]. To further determine when osteoclastogenesis was inhibited by α-mangostin, we added α-mangostin (2 μmol/L) at different stages of osteoclastogenesis. The experimental results were in line with our expectations. As shown in Fig. 1D, the earlier the α-mangostin intervention, the stronger the effect of obstructing osteoclast formation. Compared with the control group, osteoclastogenesis inhibition of α-mangostin was hardly seen in the latestage group. Based on these results, we concluded that α-mangostin could inhibit osteoclast formation, especially in the early stage of osteoclastogenesis.
Under RANKL stimulation, the upregulation of the expression of several specific genes is closely related to osteoclast differentiation [8]. Real-time PCR was then utilized to measure the inhibitory effect of α-mangostin on RANKL-induced mRNA expression of these genes (TRAP, NFATc1, CTSK, V-ATPase d2, CTR, and DCstamp). As expected, α-mangostin blocked RANKLstimulated osteoclast-related gene expression in a dose-and time-dependent manner. This proved from another aspect that α-mangostin indeed suppressed osteoclast differentiation. After verifying the inhibitory effect of α-mangostin on osteoclast formation and RANKL-induced osteoclastic marker gene expression, we explored whether α-mangostin could also affect osteoclast bone resorption. The results showed marked bone resorption in the control group that was attenuated in the α-mangostin group, again demonstrating that α-mangostin hinders osteoclast function.
NF-κB signaling is a classic pathway investigated in osteoclastogenesis studies [7]. When RANKL activates downstream signaling, the phosphorylation of NF-κBp65 and IκBα and the degradation of IκBα promote the activation and nuclear translocation of NF-κB p65, which will increase the expression of osteoclast-specific genes and promote osteoclast formation and function [30,31]. Based on this status quo, many researchers currently focus on pharmacological interventions for NF-κB signaling related checkpoints. In our current study, we found that α-mangostin restricted the degradation of IκBα and phosphorylation of NF-κB p65 and IκBα induced by RANKL stimulation. Furthermore, previous studies have shown that RANKL-induced osteoclastogenesis usually involves the activation of both NF-κB and MAPK signaling pathways. We therefore explored whether α-mangostin could also inhibit MAPK pathway activation. Not surprisingly, the phosphorylation of all three MAPK pathways (ERK, JNK, and p38) in RANKL-stimulated BMMs was blocked by α-mangostin at non-cytotoxic concentrations.
Previous studies reported that JNK1 regulates RANKLinduced osteoclastogenesis by activating the Bcl-2-Bec-lin1-autophagy pathway, and our findings suggest that the JNK pathway is regulated by α-mangostin [32]. For this reason, we used the JNK activator anisomycin to explore whether α-mangostin-mediated inhibition of osteoclastogenesis could be reversed. The results confirmed that anisomycin indeed reversed the effect of α-mangostin on the JNK pathway, but the inhibitory effect of α-mangostin on osteoclast formation and function was not affected. This may be due to the fact that α-mangostin works through all three MAPK pathways, so simply altering one of them does not make a significant difference. When the LPS pathway is activated, TRAF-TBK1-IRF3 signaling also changes [33]. We used western blots to detect the expression of TBK1 and IRF3 proteins and found that α-mangostin did not affect the pathways affected by stimulation of RANKL. Therefore, we concluded that MAPK and NF-κB pathway activation was inhibited by α-mangostin, except for IRF3 (Additional file 2: Figure S2D).
Because previous results indicated that α-mangostin obstructed RANKL-induced osteoclast formation and decreased the expression of osteoclastic-related genes by blocking the NF-κB and MAPK signaling cascades in vitro, we investigated whether α-mangostin could inhibit pathological osteolysis in an LPS-induced murine calvarial osteolysis model [34]. Micro-CT scan results and histological examinations led us to conclude that α-mangostin reduced LPS-induced osteolysis in vivo. Regarding the choice of in vivo drug dosage and administration method, we referred to methods in previous studies [35,36]. At first, we chose 20 mg/kg as the in vivo dose, but we observed inflammatory hyperplasia under the skin of the mouse skull. We the reduced the dose to 10 mg/kg, which is consistent with the effective dose in another study [37]. These results provide the first evidence that α-mangostin could be a potential treatment for osteoclast-related diseases.
Nevertheless, there are several limitations of the current study. First, because there is a balance between osteoclastic bone resorption and osteoblastic bone formation, further research on the effect of α-mangostin on osteoblasts is needed. The present study proved that α-mangostin markedly suppressed RANKL-induced osteoclast formation by inhibiting the pathway in vitro. We still need to study whether α-mangostin also exerts its anti-osteoclastogenic effect through this pathway in vivo. Unfortunately, we did not explore the exact binding target of α-mangostin. Identifying this target should explain why α-mangostin blocks NF-κB and MAPK signaling induced by RANKL. In the early stage of the RANKL pathway, after RANKL binds to RANK, tumor necrosis factor receptor-related factor 6 (TRAF6) is recruited to form a complex that further activates the MAPK and NF-κB pathways [38,39]. Because the MAPK and NF-κB pathways share the same upstream promoter in TRAF6, it is reasonable to speculate that α-mangostin interferes in the binding process between TRAF6 and RANK.
Conclusion
Our results demonstrate that α-mangostin inhibited RANKL-induced osteoclastogenesis and bone resorption in vitro. These inhibitory effects were mediated by suppressing RANKL-induced NF-κB and MAPK signaling. In addition, α-mangostin exerted a protective effect against LPS-induced inflammatory bone loss in vivo, indicating that it can be used as a potential drug to prevent or treat osteoclast-related diseases. | 6,869.8 | 2021-12-13T00:00:00.000 | [
"Biology",
"Medicine"
] |
Decision Tree Integration Using Dynamic Regions of Competence
A vital aspect of the Multiple Classifier Systems construction process is the base model integration. For example, the Random Forest approach used the majority voting rule to fuse the base classifiers obtained by bagging the training dataset. In this paper we propose the algorithm that uses partitioning the feature space whose split is determined by the decision rules of each decision tree node which is the base classification model. After dividing the feature space, the centroid of each new subspace is determined. This centroids are used in order to determine the weights needed in the integration phase based on the weighted majority voting rule. The proposal was compared with other Multiple Classifier Systems approaches. The experiments regarding multiple open-source benchmarking datasets demonstrate the effectiveness of our method. To discuss the results of our experiments, we use micro and macro-average classification performance measures.
Introduction
Multiple Classifier Systems (MCS) are a popular approach to improve the possibilities of base classification models by building more stable and accurate classifiers [1]. MCS are one of the major development directions in machine learning [2,3]. MCS proved to have a significant impact on the system performance, therefore they are used in many practical aspects [4][5][6][7].
MCS are essentially composed of three stages: generation, selection and fussion or integration. The aim of the generation phase is to create basic classification models, which are assumed to be diverse. This goal is achieved, inter alia, by methods of dividing the feature space [8]. In the selection phase, one classifier (the classifier selection) or a certain subset of classifiers is selected (the ensemble pruning) learned at an earlier stage. The fusion or the integration process combines outputs of base classifiers to obtain an integrated model of classification, which is the final model of MCS. One of the commonly used methods to integrate base classifiers' outputs is the majority vote rule. In this method each base model has the same impact on the final decision of MCS. To improve the efficiency of MCS the weights are defined and used in the integration process. The use of weights allows to determine the influence of a particular base classifier on the final decision of MCS. The most commonly used approach to determining the weights uses probability error estimators or other factors [9][10][11]. A distance-weighted approach to calculating the weights is also often used in many problems, were the weights are determined [12][13][14]. In general, this approach is based on the query where the appropriate object is located. In this article, we use the feature subspace centroid in the definition of the distance-weighted approach.
There are, in general, two approaches to partition a dataset [15]. In horizontal partitioning the set of data instances is divided into a subset of datasets that are used to learn the base classifiers. Bagging bootstrap sampling to generate a training subset is one of the most used method in this type of datasets partitioning. In the vertical partitioning the feature set is divided into feature subsets that are used to learn the base classifiers. Based on vertical partitioning feature space the forest of decision trees was proposed in [16]. Contrary to the types of dataset partitioning mentioned above, the clustering and selection algorithm [17] is based on the clustering. After clustering, one classifier is selected for each feature subspace. In this algorithm the feature space partition is an independent process from the classifier selection process and precedes this selection. The non-sequential approach to clustering and selection algorithm was probesed in [18,19].
In this work, we propose a novel approach to determining the division feature space into the disjoint feature subspace. Contrary to the clustering and the selection method described above in our proposal the proces of partitioning the feature space follows base classifier learning. Additionally, the proposed approach does not use clustering to define a feature subspace. The partiotion of the feature space is defined by base classifier models, and exactly through their decision boundaries. According to our best knowledge the use of the decision boundary of base models for partitioning feature space is not represented in MCS. Finally, the centroids of proposed feature subspace are used in the weighted majority voting rule to define the final MCS decision.
Given the above, the main objectives of this work can be summarized as follows: • A proposal of a new partitioning of the feature space whose split is determined by the decision bonduaries of each decision tree node which is a base classification model.
•
The proposal of a new weighted majority voting rule algorithm dedicated to the fusion of decision tree models.
•
An experimental setup to compare the proposed method with other MCS approaches using different performance measures.
The outline of the paper is as follows: In Section 2 related works are presented. Section 3 presents the proposed approach to MCS fusion process. In Section 4 the experiments that were carried out and the discusion of the obtained results are presented. Finally, we conclude the paper in Section 6.
Related works
Classifier integration using the geometrical representation has already been mentioned in [20]. Based on transformations in the geometrical space spread on real-valued, non-categorical features this procedure has proven itself to be more effective in comparison to others, commonly used integration techniques such as majority voting [21]. The authors have studied and proved the effectiveness of an integration algorithm based on averaging and taking median of values of the decision boundary in the SVM classifiers [22]. Next, two algorithms for decision trees were proposed and evaluated [23,24]. They have proven themselves to provide better classification quality and ease of use than referential methods.
Polianskii and Pokorny have examined a geometric approach to the classification using Voronoi cells [25]. Voronoi cells fulfill the role of the atomic elements being classified. Labels of the nearest training objects are assigned to the boundaries. The algorithms walks along the boundaries and integrates them with respect to the associated class. SVM, NN and random forest classifiers were used in evaluation.
The nearest neighbor algorithm can be used to test which Voronoi cell an object belongs to [26]. By avoiding the calculation of the Voronoi cells geometry, the test appears to be very efficient. On that basis a search lookup was described by Kushilevitz et al. [27]. A space-efficient data structure is utilized to find an approximately nearest neighbor in nearly-quadratic time with respect to the dimensionality.
However, the nearest neighbor algorithms are difficult. The number of prototypes needs to be specified beforehand. Using too many causes high computational complexity. Too few, on the other hand, can result in an oversimplified classification model. This matters especially when datasets are not linearly separable, have island-shaped decision space, etc. There are several ways to solve this problem that can be found in the literature. Applying Generalized Condensed Nearest Neighbor rule to obtain a set of prototypes is one of the possible solutions [28]. In this method a constraint is added, that each of the prototypes has to come from the training dataset. A different approach was proposed by Gou et al. [29]. Firstly, kNN algorithm is used to obtain a certain number of prototypes for each class. Afterwards the prototypes obtained in the first step are transformed by the local mean vectors. This results in a better representation of the distribution of the decision space.
Decision trees are broadly used due to their simplicity, intuitive approach and at the same time good efficiency. The way they classify the objects is by recursive partitioning of the classification space [30]. Although they have first appeared more than three decades ago [31], the decision tree algorithm and its derivatives are in use in a range of industry branches [32].
At some point it has been noticed that the local quality of each of the base classifiers is different. The classifier selection process was introduced in order to choose a subset of base classifiers that have the best classification quality over the region. The selection is called static, when the division can be determined prior to the classification. In the opposite scenario the new pattern is used to test the models' quality [33]. Kim and Ko [34] have shown a greater improvement in the classification when using local confidence over averaging over the entire decision space.
Another approach to the classifier integration is by using a combination of weighting and local confidence estimation [35]. The authors noticed, that using only a subset of points limited to a certain area in the training process results in a better classification performance.
An article [36] discusses a variation of the majority voting technique. A probability estimate is computed as the ratio of properly classified validation objects over certain geometric constraints known a priori. Regions that are functionally independent from each other are treated separately. The proposed approach provides a significant improvement in the classification quality. The downside of this method is that the knowledge of the domain is necessary to provide a proper division. Additionally, the split of the classification space has to be done manually. The performance of the algorithm was evaluated using a retinal image and classification in its anatomic regions.
An improvement in the weighted majority voting classification can be observed for class-wise approach covered in [37]. For each label weights are determined separately for the objects in the validation dataset.
Random forest, introduced by Breiman in 2001 [38] is one of the most popular ensemble methods. It has proven itself to be very effective and many related algorithms were developed since then. Fernandez et al. studied 179 different classifications algorithms using 121 datasets [39]. The random forest outperforms most of the examined classifiers. It uses decision trees trained on distinct subsets of the training dataset. A majority voting over classifications of every model for an object under test is calculated as the final result.
Numerous algorithms involving gradient boosting and decision trees have emerged. Extreme Gradient Boosting (XGB) is an implementation of one of the most widely spread stacking techniques. It is used especially in machine learning competitions [40][41][42]. In theory subsequent decision trees are trained. Consecutive models minimize the value of loss function left by their predecessors [43]. Another implementation of Gradient Boosting Decision Tree designed with performance in mind, especially when working with datasets with many dimensions, is LightGBM [44]. Compared to the previous library, statistically no loss of performance in the classification is observed, but the process of training can be up to 20 times faster.
Vertical or horizontal partitioning can be used to force the diversity between base classifiers [30]. The datasets of extreme sizes are classified better using horizontal partitioning compared to bagging, boosting or other ensemble techniques [45].
Proposed Method
The proposed method is based on previous works of authors, but suggests a slightly different approach [23,24]. While the cited articles used static division into regions of competence, this paper presents an algorithm with a dynamic approach. The main goal of introducing the dynamically generated Voronoi cells is to achieve better performance than with other referential methods of the decision tree commitee ensembling: majority voting and random forest.
Before proceeding with the algorithm, datasets are normalized to the unit cube (every feature takes values in range of [0, 1]) and two most informative features are extracted. Feature extraction is conducted using ANOVA method.
The first step of the presented algorithm is training a pool of base decision trees. To make sure the classifiers are different from one another, they are trained on the random subsets of the dataset. Having a commitee of decision trees trained, we are extracting rectangular regions that fulfill the following properties: • Their area is maximal. • Every point they span is labeled with the same label by every single classifier (labels can differ across different classifiers). In other words regions span over the area of objects equally labelled by the classifier points.
In practice this means, that the entire space is divided along every dimension at all the split points of every decision tree. This way the regions are of the same class as indicated by every model. Having the space divided into subspaces, midpoints are calculated. Let us denote by S the set of obtained subspaces and by (x s,1,min ; x s,1,max ) and (x s,2,min , x s,2,max ) the range of subspace s along axis x 1 and x 2 respectively. The midpoint of subspace s will be denoted as x s,mid . For every subspace and every label the weight is calculated using the following formula: where d(p 1 , p 2 ) is the euclidean distance between the points p 1 and p 2 , c s,Ψ i is the number of classifiers that classify the subspace s with the label Ψ i , σ is the correction which purpose is to make the sum of weights equal 1 and δ(s 0 , s) is a function that returns 1 if s 0 and s are neighbors and 0 otherwise, i.e., 1 if x s 0 ,1,min = x s,2,max or x s 0 ,1,max = x s,1,min or x s 0 ,2,min = x s,2,max or x s 0 ,2,max = x s,2,min 0 otherwise (2) It's important to notice, that according to the Formula (2), δ(s, s) = 0 for every subspace s. This is because the contribution of the subspace itself is reflected by the second summand of the Equation (1). The term 2n was chosen in the denominator, because then the subspace s 0 makes up half of the weight's value, i.e., The process of obtaining subspaces is depicted in the Figure 1. Let us suppose, that all the base decision trees (colorful lines on subfigure a) are oriented in the same way -all the points below the decision boundary are classified by the given decision tree with a single label, different from all the objects above the line. As it was stated before, the competence regions are obtained by splitting the entire space at the splitpoints of all the decision trees (subfigure b). When calculating the weight of the label for each region, the region itself (filled with dark grey in subfigure c) together with its neighbors (lightgrey in subfigure c) are considered. Whereas the region itself contributes to half of its weight, contributions from every neighbor depend on the distance between its midpoint and the midpoint of the considered region. The entire procedure is presented in Algorithm 1. Algorithm 1: Classification algorithm using dynamic regions of competence obtained from decision trees. Input : K -number of base classifiers (Ψ 1 , Ψ 2 , . . . , Ψ K ) Output : Integrated decision tree Ψ i 1 Normalize the dataset and select two most informative features. 2 Split dataset into K + 1 subsets (K for training every base decision tree and 1 for testing). 3 Train base classifiers Ψ 1 , Ψ 2 , . . . , Ψ K and obtain their geometrical representation (splits and labels). 4 Divide the feature space using splits of all the decision trees. 5 For every region and every label calculate the weight using formula (1). 6 Classify every region by picking the label with the highest weight value.
Experimental Setup
The algorithm was implemented in Scala. Decision tree and random forest implementation from Spark MlLib were used [46]. The statistical analysis was performed with Python and libraries Numpy, Scipy and Pandas [47][48][49]. Matplotlib was used for plotting [50]. In Spark's implementation the bottommost elements (leaves) are classified with a single label. The algorithm performs a greedy, recursive partitioning in order to maximize the information gain in every tree node. Gini impurity is used as the homogeneity measure. Continuous feature discretization is conducted using 32 bins.
The experiments were conducted using open-source benchmarking datasets from repositories UCI and KEEL [51,52]. Table 1 describes the datasets used with the number of features, instances and imbalance ratio. The imbalance ratio was given to stress the fact that accuracy is not a reliable metric when comparing the performance of the presented algorithm and the reference. It is calculated as the quotient of the count of objects with the major label (most frequent) and the objects with minor label (least common): Imb = #major class objects #minor class objects [53]. If the value of Imb equals 1, then the dataset is balanced-all classes have the same amount of instances. The larger the value, the more imbalanced the dataset is. Some of the datasets are highly imbalanced, because of the low imbalance ratio, so other metrics other than average accuracy should be considered when comparing the performance of classifiers. The reason is explained in the following example. Suppose Imb = 9 for a binary classification problem. When a classifier labels all the test objects with the label of the major class, its accuracy is ACC = 9 9+1 = 90%. In the parentheses, together with the names, abbreviations of the datasets names were placed by which they will be further referenced for brevity.
The experiments were conducted according to the procedure described in Section 3 and repeated 10 times for each hyperparameter set. Together with integrated classifiers, referential methods were evaluated: majority voting of the base classifiers and random forest. The results were averaged. K = 3 was taken as the number of base classifiers.
Results
The purpose of the experiments was to compare the classification performance measures obtained by the proposed algorithm (with the subscript i) with the known methods as references: majority voting (subscript mv) and random forest (subscript r f ). The experiments were conducted 10 times for each setup and the results were averaged. Because we conducted experiments on the multiclass datasets, as the classification evaluation metrics we use micro-and macro-average precision, recall and F-score which is the harmonic mean of precision and recall. For this reason F-score takes both false positives and false negatives into account. Additionally, we present the results for overall accuracy. The F-score was computed alongside the accuracy because of the high imbalance of multiple datasets used, as it was indicated in Section4. The F-score describes the quality of a classifier much better than the overall accuracy for the datasets with a high imbalance ratio and gives a better performance measure of the incorrectly classified cases than the overall accuracy. Accuracy can be in this case artificially high. The metrics are calculated as defined in [54]. In the Table 2 the results are gathered: average accuracy, micro-and macro-average F-score, while the Tables 3 and 4 show results for microand macro-average respectively. Together with the mentioned metrics, Friedman ranks are presented in the last row -the smaller the rank, the better the classifier performs. However, it should be noted that for micro-average performance measures the result obtained for precision and recall are the same. This result is justified by the micro-averaging disadvantage, because for the frequent single-label per instance problems Precision µ = Recall µ [55]. Table 2. Average accuracy and f-scores for the random forest, the majority voting and the proposed algorithm together with Friedman ranks. Table 3. Micro-average precision and recall for the random forest, the majority voting and the proposed algorithm together with Friedman ranks.
Discussion
For the proposed weighting method of the decision tree integration all the calculated classification performance measures are better than of the referrential algorithms as indicated by the Friedman ranks. This statement holds true for all the classification performance measures that have been used. Post-hoc Nemenyi test after Friedman ranking requires the difference in ranks of 0.38 to define a significant statistical difference between the algorithms. For F-score µ performance measure this condition is met, which means that the proposed method Ψ i achieves statistically better results than the reference methods Ψ r f and Ψ mv . Whereas for F-score M performacne measure there is no such property as shown in the Figure 2. The micro-average measure counts the fraction of instances predicted correctly across all classes. For this reason the micro-average can be a more useful metric than macro-average in the class imbalance dataset. Thus, the results show that the proposed method improves the classification results, in particular of imbalanced datasets. This conclusion is confirmed by the values obtained for other performance measures. And so for micro-avarage precision and recall the difference in ranks betwenn Ψ i and Ψ r f indicated the statistical differences in the results. The corresponding difference for Ψ i and Ψ r f algorithms is very close to being able to state the statistical differences in the results because it is equal 0.36 (see Table 3). In case of macro-avarage precision the obtained results do not indicate significant difference in this performance measure. Whereas for macro-avarage recall (see Table 4) the obtained avarage Friedman ranks are equal for Ψ i and Ψ r f algorithms.
Conclusions
This paper presents a new approach for determining MCS. Contrary to the clustering and selection method we propose that the feature space partition is based on decision bonduaries defined by base classifier models. It means that we propose to use learned base classification models instead of clustering to determine the feature subspace. The centroids of the proposed feature subspace are used in the weighted majority voting rule to define the final MCS decision. In particular, a class label prediction for each feature subspace is based on adjacent feature subspaces.
The experimental results show that the proposed method may create an ensemble classifier that outperforms the commonly used methods of combining decision tree models-the majority voting and RF. Especially, the results show that the proposed method statistically improves the classification results measured by the mico-avarage F 1 classification performance measure.
According to our best knowledge the use of the decision boundary of base models to partition feature space is not represented in MCS. On the other hand, the proposed approach has also a drawback, because it uses geometrical centroids of defined feature subspaces. Consequently, our future research needs to be aimed at finding centroids of objects belonging to particular feature subspaces. Additionally, we can consider another neighborhood of a given feature subspace necessary to determine the decision rule. This neighborhood may, for example, depend on the number of objects in particular the feature subspace. | 5,191.2 | 2020-10-01T00:00:00.000 | [
"Computer Science"
] |
Increased Depth of Cellular Imaging in the Intact Lung Using Far-Red and Near-Infrared Fluorescent Probes
Scattering of shorter-wavelength visible light limits the fluorescence imaging depth of thick specimens such as whole organs. In this study, we report the use of four newly synthesized near-infrared and far-red fluorescence probes (excitation/emission, in nm: 644/670; 683/707; 786/814; 824/834) to image tumor cells in the subpleural vasculature of the intact rat lungs. Transpelural imaging of tumor cells labeled with long-wavelength probes and expressing green fluorescent protein (GFP; excitation/emission 488/507 nm) was done in the intact rat lung after perfusate administration or intravenous injection. Our results show that the average optimum imaging depth for the long-wavelength probes is higher (27.8 ± 0.7 μm) than for GFP (20 ± 0.5 μm; p = 0.008; n = 50), corresponding to a 40% increase in the volume of tissue accessible for high-resolution imaging. The maximum depth of cell visualization was significantly improved with the novel dyes (36.4 ± 1 μm from the pleural surface) compared with GFP (30.1 ± 0.5 μm; p = 0.01; n = 50). Stable binding of the long-wavelength vital dyes to the plasma membrane also permitted in vivo tracking of injected tumor cells in the pulmonary vasculature. These probes offer a significant improvement in the imaging quality of in situ biological processes in the deeper regions of intact lungs.
INTRODUCTION
Physiologists understood early that the study of life is better in the living than in fixed cells, tissues, or organs. The ultimate question is not what happens in the test tube or in a frozen moment of time, but what happens kinetically in live cells in situ. It is now evident that fluorescence imaging techniques of live cells and organs have been and will continue to be of major help in answering this question.
Using an experimental metastasis model that involves intravenous injection of tumor cells in animals, we study the interaction of tumor cells with the endothelial cells in the target organ such as the lung and monitor their fate within and outside the blood vessels. Green fluorescence protein and fluorescence probes emitting in the 500-600 nm range have been used to label and detect the tumor cells in the pulmonary circulation in situ [1][2][3]. With probes in this wavelength range, there is substantial tissue scattering of both exciting light and emitted fluorescence. It was demonstrated that long-wavelength (> 600 nm) probes give the best signal levels in mammalian tissue due to lower absorption in tissue [4]. Scattering in tissues may result from photon interactions with sub-wavelength size structures, such as individual molecules (Raleigh's scattering), or from interaction with supra-wavelength size structures, such as cells, organelles, and cytoskeleton (Mie scattering) [5,6]. Raleigh scattering is inversely proportional to the fourth power of wavelength; therefore, scattering at 480 nm excitation and 510 nm emission for GFP is 6.97 and 6.36 times more than at 780 nm excitation and 810 nm emission, respectively. Maximum usable imaging depth in the intact lung is less than 30 μm with a ×60 objective and GFP as a fluorophore due to significant limitation of the penetration depth by scattering. The purpose of these studies was to use far-red and near-infrared fluorescence probes to enhance penetration and increase usable imaging depth in the intact lung. Although hardware for imaging in the near-IR and far-red wavelengths is available off-the-shelf or is easily made to order, there has been limited use of any such fluorescent probe in research use for assessing cellular function in an intact organ [7][8][9][10]. We have evaluated four newly developed fluorescent probes of near-IR and far-red range to test their utility for imaging tumor cells at greater depths in the intact rat lung. Our results indicate that, compared with GFP, these dyes offer the advantage of high-resolution imaging of tumor cells at depths greater than 30 μm from the pleural surface of the intact lung. These vital dyes also appear to be suitable for in vivo tracking of injected tumor cells in the pulmonary vasculature because of their stable binding to the plasma membrane.
Fluorescence probes and filter sets
The vital probes PTIR271, PTIR272, PTIR273, and PTIR274 are membrane-intercalating dyes developed at PTI Research, Inc. (Exton, Pa). Like the visible membrane dyes PKH26 and PKH67, the PTIR dyes label cells by partitioning into lipid regions of cell membranes [11,12]. However, the PTIR dyes are both excited and fluoresce in the far-red to near-infrared region of the spectrum ( Figure 1). Spectra were all run on the HORIBA fluoromax instrument and at settings where there was not significant light-scattering artifact for PTIR272 (spectra currently in this figure were taken on the PTI instrument). Based on these spectra, high-quality bandpass interference filters for use in a Nikon TE2000 inverted widefield epifluorescence microscope were custom made for the dyes PTIR272-274 by Chroma Technologies (Rockingham, Vt) and are described in (Table 1). For PTIR271, the Cy5 filter set was readily usable.
Cells and labeling
A GFP-expressing murine breast cancer cell line was used to compare the PTIR dyes with the GFP fluorescence for tumor cell localization, depth estimation, and image quality (signal-to-noise ratio). 4T1-GFP cells were trypsinized from T75 flasks, pelleted and washed with Hanks' buffer, and then labeled with PTIR dyes at 5 μM final concentration in Diluent C (Sigma -Aldrich Chemical Co., St. Louis, Mo) for Abu-Bakr Al-Mehdi et al. 3 5 minutes, after which staining was stopped by addition of serum. The cells were washed again with Hanks' buffer before being administered in the isolated lung or injected intravenously in animals. To assess the effect of the PTIR dyes on viability, labeling was performed in 35 mm Petri dishes. After washing with Hanks' solution, viability was assessed by exclusion of the fluorescent probe propidium iodide, 10 μM, after 30-minute incubation. The cells did not exhibit signs of loss of viability at 1 or 5 μM of PTIR dyes (one nonviable cell per about 300 cells). Five μM concentration was not only nontoxic for these probes, but the resultant fluorescence intensity also allowed high-quality imaging of the cells in the pulmonary vessels of the intact lung, yielding S/N of greater than 10. Signal-to-noise ratio, a measure of the inherent "noisiness" of the region of interest in the picture, was calculated by dividing the background-subtracted average intensity value in the region of interest containing fluorescent cells by the standard deviation of mean pixel intensity for the same region, using the image analysis functions of Meta-Morph.
Fluorescence imaging of 4T1-GFP cancer cells in subpleural microvessels in situ in the intact rat lung
An established intact organ microscopy method was utilized to observe and image subpleural pulmonary vessels in situ in the isolated, ventilated, blood-free lungs in real time using an epifluorescence microscope [1,13]. In brief, for lung isolation, the animal was anesthetized with intraperitoneal injection of 60 mg/kg body weight sodium pentobarbital. A tracheostomy was performed and artificial ventilation with 95% air +5% CO 2 was started through a cannula. The abdomen was opened and the animal was exsanguinated by transection of major abdominal vessels. A cannula was inserted into the main pulmonary artery via a puncture in the right ventricle and another was inserted into the left atrium. The lung was cleared of blood by gravity perfusion via the pulmonary artery with an artificial medium (Hanks' solution with 5% dextran and 10 mM glucose at pH 7.4). The flow-through perfusate left the lung via the left atrial cannula. Once the lung became visibly cleared of blood, the heart-lung preparation was dissected en bloc and was placed in a specially designed Plexiglas chamber with ports for the tracheal, pulmonary, and left atrial cannulae. The cardiovascular ports were connected to a peristaltic pump that recirculated 40 ml of perfusate through the pulmonary vascular bed. The lung was suspended sideways over a coverslip window at the bottom of the chamber with the posterior surface of the lung gently touching the coverslip. The subpleural vasculature of the lungs was directly visualized at high magnification (×600) by epifluorescence microscopy. For imaging the morphological and functional dynamics of PTIR probe-labeled 4T1-GFP cancer cells in the subpleural pulmonary circulation, we used a high-resolution digital fluorescence video microscopy system consisting of a Nikon TE2000 inverted fluorescence microscope, ×60 water immersion (NA is 1.2) and ×60 oil immersion (NA is 1.4) objectives, automated 10-position filter wheels for both excitation and emission (Sutter Instruments, Lambda 10-2), automated dichroic filter cube changer (Nikon), xy-axis automated stage (Prior Scientific, Inc.), z-axis motor (Prior), a high-resolution, Far-Red and near-IR-sensitive 12bit C4742-95-12ERG IEEE 1394 digital CCD camera with acquisition rate of 18 frames/s with 2 × 2 binning (Hamamatsu Inc.), and MetaMorph image acquisition, processing and analysis software with 3D reconstruction, and point-spreadfunction (PSF) -based deconvolution capabilities (Universal Imaging Corp., Downingtown, Pa). For 3D reconstruction, images of the same area were acquired along 40 μm of z-axis at 0.5 μm intervals (optical slicing) over 40 seconds. However, since this was a widefield fluorescence microscope system, there was some out-of-focus light at each of the planes of acquisition. To eliminate the out-of-focus light, standard 0.1 and 0.5 μm fluorescent beads were used as point sources of light and z-axis image stacks were acquired at 0.5 μm intervals for 20 μm above and below the plane of sharp focus. These stacks of images were used by the PSF-based deconvolution function of the software to calculate and apply the PSF to the experimental stacks of images for deconvolution. The deconvolved stacks were then used to create noise-free 3D reconstructions to determine the relationship of the tumor cells to their surrounding structures. The excitation light source was a 120 watt metal halide lamp (X-Cite120, EXFO Photonics Solutions, Mississauga, ON) with 5% relative output above 600 nm. The camera's CCD is characterized by linear decrease in quantum efficiency from 70% at 450-600 nm to 50% at 700 nm, to 30% at 800 nm, and to 20% at 850 nm.
The PTIR dye-labeled 4T1-GFP cells were either infused directly into the perfusate of the isolated lungs or injected intravenously 3 and 5 days before lung isolation and imaging. Most of the posterior and lateral aspects of the left lung were scanned for the deepest-lying cells that could be focused on in the PTIR dye channels, and the same cells were then imaged in the GFP fluorescence channel. The left lung was chosen because, in the rat, it consists of a single lobe, and thus provided a large surface area that allowed unobstructed scanning for cells.
Statistical analysis
Data analysis was done by SigmaStat (SPSS Inc.) using one way analysis of variance and Bonferroni's test. Data are expressed as means ±SE. Differences were considered significant with P < 0.05.
RESULTS
The mesothelial monolayer of the visceral pleura is transparent with UV and visible light excitation/emission. PTIR dyelabeled 4T1-GFP cells could be readily visualized in the capillaries and pre-and postcapillary vessels of the lungs using both the GFP filter set and the appropriate PTIR dye filter set (Table 1). Lung tissue did not exhibit detectable autofluorescence in the filter windows used to collect emission from the PTIR dyes (S/N= 16 ± 0.4; 17.3 ± 0.6; 16.8 ± 0.5; and 17.5 ± 0.9 for PTIR271, PTIR272, PTIR273, and PTIR274, respectively versus 12.5 ± 0.6 for GFP; P < 0.05 for all PTIR probes; n = 4). Decreased light scattering was seen with the PTIR dyes than with GFP, as expected due to their longer wavelengths, and was evidenced by increased sharpness and improved edge detection in the PTIR images of tumor cells (Figure 2). The visual quality of pictures was considered optimum when the S/N was higher than 10. The depth at which the cell pictures had S/N of more than 10 was defined as the optimum imaging depth. The average optimum imaging depth for all of the PTIR dyes was higher (27.8 ± 0.7 μm) than for GFP (20 ± 0.5 μm; p = 0.008; n = 50). The maximum depth at which the cells were still visible (but with S/N < 10) was significantly more for the PTIR dyes (36.4 ± 1 μm) compared with GFP (30.1 ± 0.5 μm; p = 0.01; n = 50). (Figure 3) shows the values of S/N ratios and imaging depths separately for individual PTIR probes. Figure 2 shows representative pictures of PTIR dyelabeled 4T1-GFP cells lodged in subpleural lung vessels. As can be readily seen, the long-wavelength probes improve the sharpness and visibility of cells at depths greater than 30 μm. The PTIR dyes not only improved the quality and depth of images of cells administered acutely in the isolated lung in vitro, but they also survived the challenges in vivo for up to 5 days of study (Figures 2(e) and 2(f)). Although the signal intensity of the PTIR dyes decreased by up to 50% after 5 days in vivo, presumably due to cell division, many tumor cells were still found to generate higher-quality images in the PTIR wavelengths than in the GFP wavelength.
DISCUSSION
Visualizing biological processes in the living tissue or cells in situ has always been the goal of fluorescence imaging. The collection of such information depends on the optimum Abu-Bakr Al-Mehdi et al. combination of light sources, optics, detection system, image processing, analysis and acquisition hardware and software along with the proper fluorescence probes. The ability to reconstruct the living dynamism in 3D and over time by zaxis and time-lapse microscopy has yielded many important insights into the cell biological processes. An important approach more recently taken is the fluorescence imaging of thick living specimens: explant tissues, cells in situ in isolated organs, and whole organisms (e.g., translucent nude mice with GFP-expressing tumor colonies) [14][15][16][17][18][19][20][21][22]. The major problem encountered in thick tissue imaging is the significant loss of signal at depth due to scattering. Both the excitation light and the emitted light can be absorbed and scattered by the elements of the tissue, thus reducing image quality and limiting the depth of visualization. The maximum depth of imaging allowed by a ×60objective (Nikon PlanApo with a numerical aperture of 1.4 and a working distance of 210 μm) using a standard 1(1/2) coverslip (170 μm thickness) is 40 μm into the tissue. GFP and other visible short-wavelength excitation/emission limit the usable depth of imaging to 20 μm due to significant scattering and interference caused by autofluorescence.
Using long-wavelength PTIR dyes for imaging intravascular tumor cells in the rat lung instead of GFP increased the effective depth for high-quality imaging from 20 to 28 μm. This corresponds to a 40% increase in the volume of tissue accessible for imaging. The increase in maximum imaging depth from 30 to 36 μm results in 20% more sampling volume. The most significant increase in the depth of optimum imaging was associated with the PTIR271 dye as compared with GFP. Shifting to longer wavelengths (PTIR272-274) beyond that led to only minor improvements in the imaging parameters in our system, as expected based on the declining spectral sensitivity of the camera and decreasing light output by the lamp at wavelengths above 700 nm. The data presented herein are not designed for comparative assessment of the efficiencies of the probes because of nonuniform detector sensitivity and illumination. However, our results clearly show that these dyes are suitable for imaging at their far-red and near-IR wavelengths using conventional instrumentation and appropriate filters. Using these new probes in addition to GFP, it should be possible to obtain high-quality images of up to five distinct colors in a single study, a capability that will contribute greatly to the goal of being able to follow biological processes involved in the interactions of multiple cell types.
Retention of the dyes by the plasma membrane permits cell tracking in vivo for up to 5 days in our study. Although permanent expression of GFP or the like is more suitable for very-long-term in vivo tracking, availability of these new FR/NIR dyes will be helpful in multicolor studies. The principle of dye dilution might help estimate the extent of cell division, something that cannot be done with GFP alone [11,12]. Furthermore, the better tolerance of FR/NIR excitation by cells and fluorescent probes due to lower photon energy and decreased phototoxicity should permit long-term time-lapse imaging.
CONCLUSION
Use of FR/NIR fluorescent probes offers significant advantages over blue-green fluorophores for live cell imaging in intact organs. Increased depth of imaging, possibility of multicolor imaging, and lesser phototoxicity promise better assessment of different cellular structure and function by fluorescence microscopy. 6 International Journal of Biomedical Imaging
ACKNOWLEDGMENTS
We would like to thank Mr. Arthur Groy of PTIR for his assistance in preparing these compounds. Work on this project was supported by NIH Grants R43 CA86692 and R44 EB 00228. | 3,889.2 | 2006-03-08T00:00:00.000 | [
"Biology"
] |
PERFORMANCE EVALUATION OF DRIP IRRIGATION SYSTEM ACCORDING TO THE SUGGESTED STANDARDS SH
A field experiment was conducted during autumn season 2017 at Al-Saqlawia, far about 50km northwest of Baghdad/Iraq, aimed to a periodic evaluation for drip irrigation system to obtain best values of the suggested standards. The experiment included two factors; first, emitters' discharge (d) at two levels using emitters with 4Lh -1 design discharge (d4) and emitters with 8Lh -1 design discharge (d8). While the second factor; operational pressure at three levels, first level, operational pressure 0.5 bar(P1), second, operational pressure 0.7 bar(P2), and the last, operational pressure 1.0 bar (P3), the experiment was designed according to randomized complete block design. The results showed a decrease in values of both uniformity coefficient and emission uniformity, while the rate of actual discharge and variation ratios have been increased with the increase of operational pressure and for both discharge, where the reduction ratios at uniformity coefficient reached 3.02%, 4.25%, while at emission uniformity 6.52%, 7.18%, then actual discharge ratios increased about 10.75%, 20.25%, while the discharge variation ratios increased to reach 389.36%, 490.48%; while at depending an emitter 8Lh -1 actual discharge, the reduction ratios at uniformity coefficient reached 1.33%, 2.64%, then at emission uniformity, they reached 3.91%, 2.85%, while actual discharge ratios increased to reach 11.73%, 21.44%, then the increase ratios of discharge variation were about 122%, 199.22% when comparing above values with the effect of operational pressure mentioned previously.
INTRODUCTION
Water is considered the first determining factor of agricultural production. And with the increase of its scarcity problems, it is become necessary to reconsider the traditional irrigation methods, with the aim of using modern systems and technologies in irrigation that achieve an increase in productivity of water volume unit by reducing the water gates during irrigation process, so water and its provision are considered the tasks and priorities of many researchers and specialists in this domain, that is the increase of food production per water unit is one of the most important challenges that confront the researchers especially in the arid and semi-arid regions whose limited water resources (15). Alamoud (2) indicated that this challenge will open the door to discovery of modern and economical technologies that helps to rationalize and provide water in the suitable quality and quantities. The same researcher above showed that to preserve the achievements of agricultural development, a serious program of scientific researches should be adopted which is interested in the transfer of modern technology and taking care to select, design, evaluate, and develop this technique of drip irrigation systems. As its management and maintenance is a priority in the rationalize of water for agricultural proposes. Drip irrigation is one of the main methods in field irrigation, and it's also a relativity modern method, which frequently gives or supplies water to or below the soil surface as a discrete drops or ling stream by small devices called "emitters" installed along the water supply line (5), and this requires a periodic evaluation for the standards of this system and depend these standards in the use of this system to irrigate field areas as plant type and soil nature. Rain Bird (14) indicated that the uniformity of water distribution is one of the important parameters to describe the emitters and design the drip irrigation system, and the operation of water uniformity for a particular areas starts with irrigation process and the perfusion uniformity may be expressed from 0 to 100%, and it's impossible to achieve a uniformity of 100%, so the same researcher indicated to uniformity values of water distribution as follows, less than 70% is weak and 70% to 90% is good and higher than 90% the uniformity perfusion is excellent, while according to (8) the uniformity coefficient is excellent if its value is greater than 90% and good if the value is between 80% and 90%, while it is weak from 60% to 80% and unacceptable if its value is less than 60%. Deba (10) showed that the uniformity of water distribution in drip irrigation system depends on the manufacturing difference of the emitters. the operational pressure, and length of the sub-line, To get best uniformity of irrigation water distribution in the field, being by efficient evaluation and design for the system. Al-Mehmdy (3) has got best value of uniformity coefficient of water distribution, where it was 96.77% and 96.21% at 50kps operational pressure using drip irrigation system carrying emitters type "Turbo" which have an actual discharge 3.94 and 7.88Lh -1 , the same researcher added that the increase of operational pressure increases the velocity of water in the tube as a result of reducing the friction with stability of the cross-section area and therefore increasing the discharge. Al-Obiedy (1) showed that emitter's discharge in the lateral lines increases by increasing the operational pressure and decreases by increasing length of the side tube, while Malooki (6) indicated that the values of uniformity coefficient decrease with the increase of operational pressure, where the values were 98.94%, 95.63%, and 94.66%, while the values of emission uniformity were 98.40%, 91.69%, and 90.87%, while the values of discharge variation were 5.37%, 26.23%, and31.65% at operational pressure 50, 70, and 100 kps respectively. This was attributed to the emitters used in the evaluation are designed to operate according to low operational pressures, and any increase in pressure may cause irregular outflow and water distribution, the same researcher above indicated that the best results that were obtain are by depending an operational pressure of 50 kps. Wu and Gitlin (11) classified the variation values in discharge (q var ), when they are less than or equal to 10, they are preferred when they are between 10% to 20%, they are acceptable, while they unacceptable if they exceed 20%. Al-Kateeb and Al-Shameri (4) showed that the variation ratios in emitter's discharge increase with increasing of pressure, then they have attributed that the emitters used in evaluating the system are basically designed to operate according to low operational pressures about 50 Kps or less. So this study aims to a periodic evaluation for the drip irrigation system to achieve best values of the depended standards through which the practical and scientific procedures are depended to rationalizing the water use and raising the value of the invested water unit.
MATERIALS AND METHODS Experiment's site
A field experiment was conducted to study performance evaluation of drip irrigation system during autumn 2017 in Al-Saqlawia region far about 50 Km north-west 24ˊ 57 41ˊ 23 east. Study factors and experimental design 1. Emitter discharge (d): In this study, the emitters type GR were used whose design discharge as follows: a. Emitters whose design discharge 4 Lh -1 (d 4 ). b. Emitters whose design discharge 8 Lh -1 (d 8 ). 2. Operational pressure, the following were selected: a. Operational pressure of 0.5 bar (P 1 ). b. Operational pressure of 0.7 bar (P 2 ). c. Operational pressure of 1.0 bar (P 3 ). The experiment was conducted according to randomized complete block design (RCBD) and for three repeaters, table 1 shows the symbols of treatment and its details.
Preparing the experiment land
An area of 768 m 2 (dimensions 32 m*24 m) was selected and plowed by the mold board, it was smoothed and settled then divided into three sectors where dimensions of each one of it (9 m*24 m) with leaving a guardian region which its dimension (2.5 m*24 m), there're 6 treatments in each sector, according to the study factors, dimensions of each terrace are (1.5 m*24 m) Components of drip irrigation system and its install 1. Main tube with diameter 3ʺ and length 50m. 2. Filter with diameter 3ʺ 3. End line lock with diameter 3ʺ, (No.2). 4. Lateral lines carrying emitters type GR and the distance between emitters is 0.40 m, as following: a. Lateral lines length 180 m carrying emitters whose discharge 4 Lh -1 . b. Lateral lines length 180 m carrying emitters whose discharge 8 Lh -1 . 5. Plugs of end line and locks of start line whose diameter 16 mm with 18 for each. Figure 1 illustrates how to install a drip irrigation system and according to its components, and the treatments were distributed randomly according to the design depended in the experiment. Relationship between emitter's discharge and operational pressure Three operational pressures 0.5, 0.7, and 1.0 bar were selected to get best two actual discharges of the design discharges depended in the experiment, and they are (4,8)Lh -1 by Table 1. Treatments symbol and details.
Details Symbol Treatment
Emitter whose design discharge 4Lh -1 at operational pressure 0.5 bar d 4 P 1 T1 Emitter whose design discharge 4Lh -1 at operational pressure 0.7 bar d 4 P 2 T2 Emitter whose design discharge 4Lh -1 at operational pressure 1.0 bar d 4 P 3 T3 Emitter whose design discharge 8Lh -1 at operational pressure 0.5 bar d 8 P 1 T4 Emitter whose design discharge 8Lh -1 at operational pressure 0.7 bar d 8 P 2 T5 Emitter whose design discharge 8Lh -1 at operational pressure 1.0 bar d 8 P 3 T6 Fig. 1. Field experiment scheme controlling the rotational velocity of the engine(rpm), reading the pressure on the meter at the beginning of installing the main tube to the lateral lines and the tube of returning the excess water to the source. This was done by applying the volumetric method when time is constant (0.25 h), and knowing the volume of water reaching the water collection cans scattered below the emitters, using the equation mentioned by (5), and as following: ( ) Where: emitter's discharge (Lh -1 ). V = volume of water received in the cans (L). t = operating time (h). Tables 2 , 3 show the volumes of water received to the cans and actual discharge for each emitter according to the selected operational pressure. Uniformity coefficient was calculated using equation of "Christiansen" (12) and mentioned in (7), and as follows: Where: Uc = Uniformity coefficient (%). ∑x i= Total absolute deviations by the overall discharge rate (Lh -1 ). M = Overall discharge average of the emitters (Lh -1 ). n = Number of emitters Then the variation ratio in the emitter's discharge was calculated according to the equation mentioned in (9),as following: ( ) Where : ɋ var =variation ratio of emitter's discharge(%) maximum discharge of emitters (Lh -1 ) . ɋ max ɋ min = minimum discharge of emitters (Lh -1 ). while emission uniformity was calculated according to (3), the following equation :
( )
That is : Eu = Emission Uniformity (%) ɋ 25% =discharge rate of the lowest quarter (Lh -1 ) . ɋ =overall discharge rate of the emitters(Lh -1 ) RESULTS AND DISCUSSIONS Actual discharge of emitters: Figure2 illustrates that the actual discharges of emitters is directly proportional to the operational pressure, where actual discharge rates reached 4.00, 4.44, and 4.81 Lh -1 for the emitter whose design discharge 4 Lh -1 , while they reached 7.93, 8.6, and 9.63 Lh -1 for the emitter whose design discharge 8 Lh -1 at the operational pressures 0.5, 0.7, and 1.0 bar respectively. And the increase percentage reached about 10.75% and 20.25% when comparing the values of the actual discharge at the operational pressure 0.5 bar with the two operational pressures 0.7 and 1.0 bar respectively, by depending a design discharge 4 Lh -1 , while the increase percentage when depending a design discharge 8 Lh -1 reached 11.73% and 21.44% respectively. Then the increase of values in the actual discharge with the effect of operational pressure and for both emitter's discharge was significant according to the values of lowest significant difference (L.S.D). Increasing the operational pressure increases the speed of molecules inside the side tube section and therefore the friction decreases with stability of the cross-section area of this tube, and that's considered a reason of the increase of discharge, this is consistent with what mentioned by Al-Obiedy(1) and Al-Mehmdy(3) who indicated that the discharge in lateral lines increases by the increase of operational pressure due to the increase of water flow inside the tube, and reducing the friction and the discharge decreases by the increase of the lateral lines. Table 3
. Water Volumes Received in Collection Cans and Emitters' Discharges at Different
Operational Pressures with Time 0.25 h Using Emitters whose Actual Discharges 8 Lh -1 001. Figure 3 illustrates that the uniformity coefficient is inversely proportional to the operational pressure when depending emitters type GR whose actual discharge 4 and 8 Lh -1 , where it has reached 98.85%, 95.86%, and 94.65% when increasing the operational pressure from 0.5 bar to 0.7 bar and 1.0 bar by depending emitters whose emitter's discharge 4 Lh -1 respectively. And the decrease percentage has reached 3.02% and 4.25% when comparing the value of uniformity coefficient at the operational pressure 0.5 bar with the value of uniformity coefficient for the two operational pressures 0.7 bar and 1.0 bar respectively, while values of the uniformity coefficient when depending emitters whose actual discharge 8 Lh -1 have reached 97.17%, 95.88%, and 94.60% for the operational pressures 0.5 bar, 0.7 bar , and 1.0 bar respectively, and for a decreasepercentages about 1.33% and 2.64% when comparing the value of uniformity coefficient at 0.5 bar operational pressure with the values of uniformity coefficient of the two operational pressures previously mentioned, respectively. And the values of L.S.D at level 0.05 showed a significant decrease, by the effect of study factors "discharge and operational pressure" and the interference between them. And that may be due to the increase of operational pressure causing irregular water outflow and therefore leads to irregular water distribution, and this is consistent with what mentioned by Al-Mehmdy (3) that the best value of uniformity coefficient was obtained at the operational pressure 0.5 bar, and this also agrees with what mentioned by Malooki (6) that the emitters used in the evaluation process were deigned to operate according to low operational conditions, and that the operational pressure caused an irregular outflow and distribution of water. Figure 4 illustrates that the variation percentage are directly proportional to the operational pressure when depending emitters type GR whose discharge 4 and 8 Lh -1 , where it has reached the values 5.36%, 26.23% and 31.65% by increasing the operational pressure from 0.5 bar to 0.7 bar and 1.0 bar when depending emitters whose actual discharge 4 Lh -1 , respectively, and the increase percentage in the values of discharge variation have reached 389.36% and 490.48% when comparing the value of discharge variation at operational pressure 0.5 bar with the values of the discharge variation for the two operational pressures 0.7 bar and 1.0 bar, respectively. while the values of discharge variation have reached 41.54%, 25.62%, and 34.53% when depending emitters whose actual discharge 8 Lh -1 at the operational pressure 0.5 bar, 0.7 bar and 1.0 bar, respectively, and with decrease values about 122% and 199.22% when comparing the value of discharge variation at the operational pressure 0.5 bar with the value of discharge variation of the two operational pressure 0.7 bar and 1.0 bar, respectively. When the values of lowest significant difference at level 0.05 showed a significant differences in the decrease values of discharge variation by the effect of study factors and the interferences between them. This is due to the increase in velocity of water flow inside the lateral drip tubes and therefore reducing the friction effect between the flowing water molecules, which was a reason in the raise in values of discharge variation as well as the raise of actual discharge for both emitter's discharges by increase of operational pressure, and this is consistent with what mentioned by Al-Kateeb and Al-Shameri (4) that the variation percentage increases by the increase of operational pressure, then they attributed this that the emitters used to evaluate the system were basically designed to operate according to low operational pressures (about 50 kps or less). Figure 5 illustrates that the values of emission uniformity are inversely proportional to the operational pressure when depending emitters type GR whose discharge 4 and 8 Lh -1 , where it reached 97.82%, 91.44%, and 90.85% by increasing the operational pressure from 0.5 bar to 0.7 bar and 1.0 bar when depending emitters whose discharge 4 Lh -1 , respectively, while it reached 94.45%, 91.76%, and 90.76% when depending emitters whose actual discharge 8 Lh -1 at the operational pressures 0.5 bar, 0.7 bar, and 1.0 bar, respectively. Then the values of lowest significant difference (L.S.D) showed a significant decrease in the values of emission uniformity by the effect of discharge and operational pressure and the interference between them. And this may be attributed that as the values of emission uniformity increase, water distribution in the field is regular, and that occurred when depending an operational pressure 0.5 bar for both discharge. This is consistent with what mentioned by Ortega etal.(13) who defined the emission uniformity as the ratio between discharge rate of the lowest quarter to the overall discharge rate of the emitters Conclusion and recommendations The emitters used are designed to endure low operational pressures (about 0.5 bar), where it gave highest values of uniformity coefficient and emission uniformity and lowest values of variation percentage in the emitter's discharge, so it is recommended to depend those emitters and for both discharge at the minimum operational pressure and the conditions of work similar to that study to distribute water in the field regularly, which may have a positive effect on the moisture distribution in the soil profile within the boarders of plant root. | 4,114.6 | 2018-12-06T00:00:00.000 | [
"Physics"
] |
An Automatic Observation Management System of the GWAC Network I: System Architecture and Workflow
The GWAC-N is an observation network composed of multi-aperture and multi-field of view robotic optical telescopes. The main instruments are the GWAC-A. Besides, several robotic optical telescopes with narrower field of views provide fast follow-up multi-band capabilities to the GWAC-N. The primary scientific goal of the GWAC-N is to search for the optical counterparts of GRB that will be detected by the SVOM. The GWAC-N performs many other observing tasks including the follow-ups of ToO and both the detection and the monitoring of variable/periodic objects as well as optical transients. To handle all of those scientific cases, we designed 10 observation modes and 175 observation strategies, especially, a joint observation strategy with multiple telescopes of the GWAC-N for the follow-up of GW events. To perform these observations, we thus develop an AOM system in charge of the object management, the dynamic scheduling of the observation plan and its automatic broadcasting to the network management and finally the image management. The AOM combines the individual telescopes into a network and smoothly organizes all the associated operations. The system completely meets the requirements of the GWAC-N on all its science objectives. With its good portability, the AOM is scientifically and technically qualified for other general purposed telescope networks. As the GWAC-N extends and evolves, the AOM will greatly enhance the discovery potential for the GWAC-N. In the first paper of a series of publications, we present the scientific goals of the GWAC-N as well as the hardware, the software and the strategy setup to achieve the scientific objectives. The structure, the technical design, the implementation and performances of the AOM will be also described in details. In the end, we summarize the current status of the GWAC-N and prospect for the development plan in the near future.
INTRODUCTION
In the last decade, a new type of network emerged. Thanks to the modern computing and communication technologies, these telescopes are designed to form a general-purpose observation network, such as Las Cumbres Observatory Global Telescope (LCOGT, Brown et al. 2013), the Global Relay of Observatories Watching Transients Happen (GROWTH, Kasliwal et al. 2019), the All-Sky Automated Survey for Supernovae (ASAS-SN, Shappee et al. 2014), the Robotic Optical Transient Search Experiment (ROTSE, Akerlof et al. 2003), the Pan-STARRS Survey (Chambers et al. 2016), the Rapid Action Telescope for Transient Objects (TAROT, Boër et al. 1999), and the Master-Net (Lipunov et al. 2010)... Such inclusions of individual facilities into a global interconnected network is a key to largely enhance the discovery potentials and take up the challenge of the multi-messenger astronomy of the next decade. However, netting telescopes, organizing and scheduling for the general-purpose network are the common problems in modern observational astronomy, since these facilities with limited resource are designed only for given purposes, which requires different size, photometry parameters and controlling technics. A huge human intervention is still involved in the schedule process for most modern observation networks (Mora & Solar 2010).
Under the framework of the Chinese-French Space Variable Object Monitor (SVOM) mission, an array consisted of a set of 9 Ground-based Wide-Angle Cameras (GWAC-A, hereafter) is designed to simultaneously search for the optical prompt emission of Gamma Ray Bursts (GRBs) detected by the SVOM on-board gamma-ray instruments (ECLAIRs and GRM, Cordier et al. 2015;Wei et al. 2016). Furthermore, several robotic, multi-band, small Field of View (FoV) telescopes are also deployed for automatically validating and following up candidates detected by the GWAC-A. In fact, combining these wide FoV telescopes and fast-slewing, multi-band, small FoV telescopes in a well organized network can permits to obtain a better observational coverage and detection performances useful for multiple tasks such as, large-sample surveys, periodic and quasi-periodic objects, transient targets, moving objects. But successfully performing these observations depends not only on instrument properties but also on a network combining robotic telescopes, communication, observation scheduling, observation controlling and data processing. Besides, in order to catch the nature of different scientific targets, different optimized observation strategies must be implemented. The optimization of observation strategy should balance between the fruitful scientific returns and the limited telescope resource. Therefore, we develop an automatic observation management system to integrate the facilities and software into a network named as the GWAC network (GWAC-N hereafter), since the GWAC-A, is the majority of this network. The automatic observation management system contains functions of observation target management, fully-automated dynamic observation scheduling and autonomous telescope dispatching, data management. The system enhances the efficiency of uses of the GWAC-N to a great level by automatized carrying out multi-target, multi-telescope, simultaneous joint observations, all the routine observations for each telescope, and keeping the manual observing function. With standard datalink, this system can be easily adapted to other similar subjects in time-domain astronomy and extended to the collaborative telescopes.
In 2014, 12 mini-GWAC, the pathfinder telescopes of the GWAC-A started operation in the GWAC dome at Xinglong observatory (Huang et al. 2015). Two 60-cm follow-up telescopes (GWAC-F60A/B) were installed in 2015 and achieved first light in the same year. The first GWAC mount equipped with 4 Joint Field of View (JFoV) cameras and 1 Full Field of View (FFoV) camera were installed and tested in 2017. In 2018, 2 fully equipped GWAC mounts, 2 GWAC-F60A/B, 1 GWAC-F30 were in operation. Figure 1 shows the dome and telescopes of the GWAC-N. Although the telescopes were in place, they were still not connected as a network. The telescopes were operated separately and manually controlled by two observation assistants during night observations. Responding speed and observation efficiency were low. Observation capability for scientific targets was limited. Paving a small part of sky with the GWAC-A and monitoring several targets with the GWAC-F60A/B and the GWAC-F30 were the pattens of the routine observations at this stage. Thus, the automatic observation management (AOM) system had been developed in 2019 to integrate the hardware and software of the GWAC-N to fulfill the scientific requirements described in the Section 4. In the late 2019 and early 2020, the Tsinghua-NAOC (National Astronomical Observatories of China) Telescope (TNT) at Xinglong Observatory, and the Chinese Ground Follow-up Telescope (CGFT) at Jilin Observatory started to work collaboratively with the GWAC-N as external partners by taking advantage of the ToO alert processing and managing capability of AOM. The GWAC-N can functionally perform the observation tasks to meet all the scientific requirements of the network by adopting the AOM as of the date of this writing (December 2020). A complete GWAC-N will comprise 9 mounts equipped with 36 JFoV and 9 FFoV cameras and several associated follow-up telescopes. Two world-wide sites and advanced CMOS detectors are foreseen to be applied to the GWAC-N in a near future. The development timeline depends on the future funding and maturity of new technology. Since the GWAC-N is still under development and evolution, this paper describes the structure of network based on the current stages.
In this paper, we present the GWAC-N's telescopes, the AOM system and the opportunities / science outputs from the GWAC-N. The remainder of the paper is organized as follows. Section 2 describes the system structure of the GWAC-N and the instruments of the GWAC-N, including internal telescopes and the extend partners. In Section 3 We then present the AOM of the GWAC-N that we developed for performing for the multi-purpose, flexible, highly efficient observations. We will describe the scientific opportunities of the GWAC-N and achievement of the network in Section 4. In Section 5, we summarize the current status of the GWAC-N and describe network prospects for the near future.
SYSTEM STRUCTURE OF THE GWAC-N
The whole system of the GWAC-N (shown in the Figure 2) comprises three main parts: the target input interfaces, the AOM system and the telescopes. In this section, we describe the target input interfaces and the telescopes. The AOM system is described in the Section 3.
Target Input Interfaces
The GWAC-N provides multiple external interfaces connected with a variety of alert streams, survey/catalogue planners, the GWAC-A self-detected transient validation system (Xu et al. 2020A) and scientists. All automatic or manual observation requests are inserted into the system via these external interfaces. Figure 2. The GWAC-N is composed of interfaces for the target inputing, the multiple telescopes and the AOM system. The ToO alert interface can receive the alerts of GW, GRB and neutrinos from the external CMM server . The TNT and the CGFT telescopes are connected with the GWAC-N as external partners.
During the O3 run of LIGO/Virgo, the SVOM team develops the Gravitation Wave Skymap Processor (GWSP) at Irène Joliot-Curie laboratory (IJCLab at CNRS/IN2P3), France. The GWSP digests the GW skymap and optimizes the tiling observation strategy based on the telescope parameters for the GWAC-A, the GWAC-F30 and the CGFT. Using the Mangrove galaxy catalog (Ducoin et al. 2020A), the GWSP can create optimized galaxy lists for small FoV telescopes like the GWAC-F60A/B. The format of the tiling coordinates and galaxy lists are standard, therefore, it can also be applied to other telescopes, i.e. the GRANDMA (the Global Rapid Advanced Network Devoted to the Multi-messenger Addicts) network (Antier et al. 2020). The tiling and galaxy lists are sent to the Chinese Multi-Messenger (CMM) server using the VOEvent protocol via brokers. The CMM Service can receive the GRB or Neutrino alert streams from GCN public access by using the pygcn code (Leo Singer 1 ). The GWAC-N provides an interface to automatically receive the GW alerts from the CMM in real time.
Several observation planning codes are running to create target/pointing list for all telescopes to perform routine observations. Each planner can insert the target/pointing list into the AOM using a client provided by the GWAC-N. The GWAC-N also accepts observation applications from scientists. A tool allows the scientists to customize the observational parameters and to generate complex observation programs. The GWAC-N has another type of targets, the self-detected transient candidates of the GWAC-A validated by the Real-time Automatic transient Validation System of the GWAC-N (RAVS, Xu et al. 2020A). The target needs to be quickly identified and followed-up by the GWAC-F60A/B. Therefore, an interface has been developed for real-time communications between the RAVS and the AOM.
The telescopes
The GWAC-A telescopes are the main instruments of the GWAC-N. Two GWAC-A telescopes are being operated (two more are under testings) at the Xinglong Observatory (lat = 40 • 23'39"N, lon = 117 • 34'30"E) and founded by the National Astronomical Observatories (NAOC, Chinese Academy of Sciences). Each GWAC-A mount is equipped with two types of cameras: Figure 3. The sky, in Equatorial coordinates, is partitioned into 148 grids of equal area fitting the mount's FoV. The GWAC-A telescope points to the center of a grid (blue dot), so it can cover the sky field (red square) with its wide FoV.
• the Joint Field of View (JFoV) camera, a refractive lens with an aperture of 180 mm, is equipped with 4k x 4k CCD camera. The FoV of a JFoV camera is ∼ 12.8 • x 12.8 • . The CCD camera is composed with a 4K E2V chip and a customized liquid cooler system, which allows the CCD works in -50 • Celsius with respect to the local environment temperature. 4 cameras are installed on a connection frame with angle adjustment mechanism. By carefully adjusting the pointing angles of the JFoV, the four JFoVs cameras are paved in a square sky field. The joint field of view for one mount (four JFoV cameras) reaches about 25 • x 25 • . The limiting magnitude of the JFoV camera reaches R ∼ 16 magnitude for a single image (10 seconds of exposure) in a dark night without cloud. From the stacking images, a typical limiting magnitude of R ∼ 18 magnitude is obtained.
• the Full Field of View (FFoV) camera, a SIGMA 50mm F1.4 lens with aperture of 3.5 cm, is equipped with an Apogee U9000X 3k x 3k CCD camera. The FoV of a FFoV camera is ∼ 30 • x 30 • , which covers the approximately same sky field of the joint FoV of the four JFoV cameras.The FFoV carries out guiding and extending the optical flux coverage to R ∼ 6 magnitude at bright end.
Both types of cameras work on the clear band and variable image cadences depending on objectives (15 or 25 seconds typically). An automatic focusing mechanism developed by Huang et al. (2015) is used on the JFoV and the FFoV cameras to keep the images at their best qualities during the observations. We define a pre-planed grid format, which the all sky is partitioned into 148 fixed grids whose sizes fit the GWAC-A mount's FoV, see Figure 3. The grid format is adopted for the GWAC-A telescopes to carry out all types of observation modes.
The remote controlling datalink is available for these automatized GWAC-A telescopes. The above features make the GWAC-As being well suited for the optical follow-up of multi-messenger events. The real-time catalog cross-matching and stacking image analysis and transient classification pipeline give to the GWAC-A the capabilities of independently detecting both fast and slow optical transients.
Two robotic GWAC-F60A/B telescopes and one robotic GWAC-F30 telescope are installed inside of the GWAC dome. The GWAC-F60s are used for the automatic validation of the GWAC OT candidates. They have ∼ 10 degree/second slewing speed and 18'x18' of FoV with the 2Kx2K Andor iKon-L 936 CCDs. The GWAC-F30 with a FoV of 1.8 • x1.8 • can complete the gaps of flux coverage and the FoV between the GWAC-A and the GWAC-F60A/B. All the three telescopes are equipped with the Johnson UBVRI filters. With remote controlling and real-time data processing, they can be integrated into the GWAC-N. As a whole, the GWAC-N obtains the capabilities for multiple objectives from survey, queue observations to follow-up observations for many types of targets. The parameters of each type of telescope are summarized in Table 1.
By using customized datalink, the GWAC-N can collaborate with external telescopes to extend the network. The external network currently includes two telescopes: the 80-cm Cassegrain reflecting TNT telescope located at the Xinglong Observatory of NAOC and the 1.2-meter CGFT at the Jilin Observatory of NAOC. The parameters of the TNT can be found in Zheng et al. (2008), Huang et al. (2012). The parameters of the CGFT is being tested, as the telescope is under hardware updating.
AOM SYSTEM
For a highly efficient telescope network, a strong and smart observation management is a key factor. The automatic observation management is the only way to integrate tens of telescopes into a complete network, the GWAC-N. Figure 4. All the sub-systems or modules of the AOM system are shown in the red color. The ToO follow-up sub-system obtains the alerts of the ToO from the CMM database as input targets. The target management sub-system receives all other types of observation requests, and converts them as input targets. For the internal telescopes of the GWAC-N, a client running in the telescope side can monitor the observation and data statues, and transmit them back to the AOM. For the external telescopes, the datalink is customized for different telescopes. No client is installed in the telescope side in current stage.
Otherwise, the huge workload during observations is unacceptable for our scientists on duty, not to mention the slow response and inefficient observation. Therefore, we developed the AOM system for the GWAC-N to manages all input targets, distributes them to all telescopes and organizes observations with all types of strategies. The system consists of the following sub-systems: the ToO follow-up, the target management, the scheduler, the dispatcher sub-systems and the communication center. The architecture of the AOM is shown in the Figure 4. The functions of each sub-system is given in the following sub-sections.
ToO follow-up sub-system
The ToO follow-up sub-system monitors the CMM database for the newly arriving alerts. Currently, three types of events, including the LIGO/Virgo GW, the Swift GRB and the Fermi GRB, are selected by the ToO follow-up sub-system. The sub-system generates a target or a sequence of targets with observation parameters for the alert that meets the alert selection criteria. The observation parameters (such as instrument, observation mode, exposure, etc. ) are set based the observation strategies dedicated to different cases. The alert selection criteria, observation strategies are defined regarding the physical variable behavior of the target and the telescope detection capability to increase the chance of detecting the optical counterpart of the ToO. The details of the selection criteria and observation strategies will be described in another paper (Han et al. in preparation). For the external partners of the GWAC-N, the datalink is customized for a dedicated telescope. A dispatcher sends a target or target sequence to the TNT and the CGFT Figure 5. The workflow of target management starts from the target inputting via automatic/manual submission interfaces. The format validation, manual correction, adding, updating, deleting of targets and duplicate target checking are supported by the target management sub-system.
Target Management Workflow
regarding an alert of the Swift GRB or the LIGO/Virgo GW event. By design, no feedback is returned to the AOM from external partners in current stage. A two-side datalink is planned to be implemented between the GWAC-N and the CGFT in the next stage.
Target management sub-system
The target management sub-system is to manage the inputs from all interfaces to prevent conflicts or duplication processes during the target inputting. The workflow of the target management sub-system is shown in the Figure 5. The sub-system automatically checks the format of the inputs and allows scientists and operators to make the corrections. A target input message can be either adding new target or updating, deleting target from the sub-system. During observation and testing, different interfaces or different users could attempt to repeatedly input targets into the sub-system. These duplicated inputs will be rejected by the sub-system to avoid the waste of the telescope resources. On the other hand, the sub-system allows the users to perform the repeated observations for a target by adopting a specific observation mode.
Dynamic scheduling sub-system
The goal of the scheduler of the GWAC-N is to dynamically generate observation plans for all the telescopes. The principle of scheduling of the GWAC-N is the prioritization of targets. The scheduler satisfies the observation requests for targets with the highest priorities as much as the telescope resources allow to do. The targets with higher priorities can interrupt observations of targets with lower priorities. Multiple levels of grading standards are pre-defined to deal with the complex relation among the target, the observation mode and the telescope. The top level of them is the observation mode, such as, the manual observation, the automatic ToO follow-up, the calibration etc. In this level, each mode of observation is given a range of scores based on its importance. The standard of grading can be changed from telescope to telescope. For example, if a telescope is preferred for a certain observation mode, the score of this mode will be increased for this telescope. Basically, the grading is following the standard definition shown in Table 2. We give each mode a range of priority numbers for different cases. For instance, in the automatic ToO follow-up mode, the priority of updated GRB alert is higher than the priority of the initial alert. We define the second and/or third level priorities to indicate the sequence of all targets with the same priority in the top level. For different observation modes, the second and third levels can refer to different parameters. Here, we describe two strategies to define the second and third level priorities as examples. For the ToO follow-up observations mode, the rankings need to be adopted in both tiling and galaxy targeting strategies. In our system, the probabilities of tiles and galaxies are defined as the second level priority, while the altitude angle is the third level. For the validation mode, the trigger time (receiving time of target in the system) is the second level priority. No third level is needed in this mode. Using these methods, we can generate observation plans with many complex strategies. The scheduler makes a re-sorting process for target list for each telescope based on the priorities, the observability, the status of observation and the telescope, when any update for the target is made in the database. The tables in the Figure 6 demonstrates the sorting sequence for the target list during observations. The most important target is listed in the top of the table in the right side. All targets observable in time after the re-sorting are shown in the green cells. The yellow row shows the target being observable later on. Other targets including the ones already completed or no observation time window in that night are not scheduled, which are shown in grey. After re-sorting, the observation plans are refreshed with new order of target list and probable new observation parameters. Each time, the dispatcher picks up the first target in the list for a given telescope. The priority, observability, status of observation and telescope are constantly updated by other sub-systems, which makes the scheduling dynamically.
Dispatching sub-system
The scheduler does not send any observation command to the telescope controller. A dispatching system does that. Two types of dispatchers are developed for the telescopes inside of the GWAC-N and for the external partners. The technologies used for the external dispatchers depend on the interfaces of the external telescopes.
The internal dispatcher is dealing with the telescopes inside of the GWAC-N. The observation commands are sent to the telescope controller via a one-way link. The observation status is obtained through a link between the monitor server and a client. The dispatcher starts multiple threadings to different telescopes. The work flow is shown in the Figure 7. The dispatcher gets an observation plan from scheduler and then it will check the availability of the assigned telescope. If the telescope is available, the dispatcher will check the observability of the target. If yes, an observation command will be sent to the telescope controller. For another case, when the telescope is under observation, the dispatcher Figure 6. The original target list is shown in the left table. The sorted target list is shown in the right table. The first target in the right table enters the observation procedure. The target under observation is in the red row. The targets observable in the moment of scheduling are in the green rows. The targets that are currently not observable, but will be observable in the following hours of the night, are in the rows in the light yellow.
compares the priorities of targets. The new target with higher priority can interrupt the on-going observation of an old target. The dispatcher constantly monitors the observation status feedbacked from the observation status monitor. The actions of the dispatcher are based on that real time status. The client of the observation status monitor running on the telescope side sends the status back to the server, including the command reception, observation status and completeness. An error code is also sent back to the server, which can be used for system error analysis.
Communication center
The AOM system is composed of many sub-systems and a database. The communications are very complex and frequent among external interfaces, sub-systems and telescopes. To avoid the conflicts and sequential confusion in the communications, a sequential control mechanism is crucial for the AOM system. In the earlier version, all sub-systems are directly communicating to the database. When a large number of concurrency entries occur in the database, a protecting mechanism will be triggered in the databases from preventing damages of data. These chance faults are Figure 7. Top: The workflow of the AOM dispatching procedure. The tasks of dispatcher are drawn in red color, while scheduler and observation controller sub-system are marked in green. Bottom: The workflow of the AOM observation status monitoring procedure, which is drawn in red.
rare but fatal to our system. Another key point is for the scheduling. Unlike the multi-instance dispatcher, only one instance of scheduler can be run at time, because to deal with the dynamic information by multiple schedulers easily causes the information confusion. The AOM system must ensure that the scheduling is well organized in such a complex situation. A sequential controller can solve those communication issues. Therefore, we developed a communication center (CC) combined with communicating and sequential controlling functions and a communication client deployed on each sub-system. The CC runs a server and many instances (communication modules). An instance is launched when a connect request is created by a server or a client running on a sub-system. All messages between the server and the clients are marked with flags to indicate different types of the messages. In the server side, the messages will be classified and distributed to the dedicated clients in the proper orders. The procedures of observation scheduling and dispatching depend on the ordering of the messages. In the client side, each message will be treated as an independent message, and be processed only in order of arrival. In this paper, we simulate four scenarios to show how the observational procedures are executed smoothly in the GWAC-N. These scenarios are the most typical cases of communication time sequences during the scheduling and dispatching (see the Figure 8): Case 1. Communication time sequence for normal observation procedure. In the normal case, the procedure starts at the point, which a target is added into the target list. The next steps are the scheduling, the dispatching, and the observation. The final step is a re-scheduling process. To be specific, after a new target is put into the target list from an interface (TC1), the target management client will process it, format it and send a message (TM1) with observation parameters of the target to the CC. The message will be added to a message list organized by a sequencer in the CC. The target message is instantaneously sent to an instance of the scheduler (SC1) that will start to make an observation plan. The scheduler generates the observation plans not only for that new added target but also for all observable targets in the target list. After the scheduling is done, a message with a status of scheduling (SM1) is returned back to the CC, then a command of dispatching will start an instance of dispatcher client (DC1). The dispatcher client decides to choose a target with top priority from the target list for the next observation or to wait the completeness of the current observation. There are multiple instances of dispatcher clients running simultaneously to control different telescopes. The client of the dispatcher sends messages (DM1) to inform the CC when the observation is started and finished. After the observation is done, the scheduler client receives a command from the CC to start re-scheduling to update the observation plans. The instance of dispatcher client is closed then. The procedure ends at this point.
Case 2. When a target is added into the target list, the scheduler will firstly compute the observational time window. The one without the observational time window from TC2 will not be scheduled. The instance of the scheduler (SC2) will still communicate to the CC for the scheduling status (SM2) to inform the dispatcher (DC2) that the update of target list. The procedure ends at the dispatcher (DC2).
Case 3. Multiple telescopes are needed to observe one target. This situation usually occurs when synchronized multi-band photometry is performed for the target. In the Figure 8, we assume that two telescopes are used in that scenario. After receiving the target information from an interface (TC3), the instance of the scheduler (SC3) generates two observation plans for two telescopes respectively. Then the CC starts the first instance of a dispatcher client (DC3), while the second instance of a dispatcher client (DC4) will not be started, until the CC gets the feedback message (DM3, the starting status of observation) from the DC3. Then the DC4 sends an observation command to the second telescope and observation status message (DM4, the starting status of observation) to the CC. When the DC3 obtains the complete status of the observation, the SC3 will start re-scheduling process. In the meantime, the DC4 obtains the status of the second observation, but the message transmission (from DM4 to an instance of SC4) will be put on hold until the observation plans are refreshed by the SC3. Then the SC4 is started. The procedure is finished when the SM4 is received.
Case 4. In this case, dozens or even hundreds of targets/pointings are added into the system at nearly same time. This situation happens frequently during the Multi-Messenger follow-up observations. We simulate the scenario when two targets (TC5 and TC6) are inserted in the same time. An instance of scheduler (SC5) is started immediately when the message of target (TM5) is transmitted. The SC5 and a dispatcher client (DC5) are executed successively. The message (TM6 ) for the second target (TC6) will be transferred after the status message (DM5, the starting status of observation for the TC5) is received. Then the second instance of scheduler (SC6) and a dispatcher client (DC6) are executed for the TC6. When the observations and re-scheduling are finished for the TC5 and the TC6, the procedures end.
In the procedure of above cases, both actions of scheduling and actions of dispatching are triggered by the dedicated messages. The sequential controller can organize the messages in proper orders, which prevents the confliction and sequential confusion during observations. 3.6. AOM system workflow Combining with above sub-systems, the overall workflow of the AOM system is described as follows. The targets are manually/automatically inserted into the system by using interfaces provided by the AOM system (all observation request are treated as targets). All the targets are processed and classified by the target management sub-system, then are inserted into the target database. Some targets are sent by the external dispatcher to trigger the follow-up observations with external telescopes. The targets for the GWAC-N will be initially scheduled in order to compute the observation time windows and to make the initial observation plans. The targets having the observation time windows are added in the daily target list and are stored in the database. This daily target list contains all the targets to be observed in a given night. This list is kept updated during the night, since new targets come in, the observation parameters and status of targets are updated, and some targets are removed from the list. Triggered by the CC, the dynamic scheduler makes observation plans for the target in the target list, and the dispatcher selects a Target A Target B Figure 8. The figure demonstrates the four typical scenarios of the message sequences in the AOM system. A functioning communication center (CC) consists of a message sequential controller, multiple instances that one of each is launched and communicates with a given connected client. The message sequential controlling of the CC is shown in the grey box. The incoming and outputting message flows for the controller are drawn in red and green colors respectively. To clarify the message sequencing procedure, we use yellow, red and blue colors to mark the actions of target management (shorten with TC and TM), scheduling (SC and SM) and dispatching (DC and DM). A green circle and a black circle represent the starting point and the ending point of a message flow.
target to observation command based on the observation plan, status of observation and the status of telescopes. The observation status monitor keeps observation status updated in the target list, so the scheduling and dispatching can be fully dynamically. The system completes a closed control loop (shown in the Figure 9) 3.7. Performance of the AOM system With the AOM, the GWAC-N integrates 5 telescopes and collaborates with 2 external telescopes. By using the standard link provide by the AOM, the telescopes can easily join the network. The AOM also provides the customized link for external telescopes, which is very useful for those telescopes willing to join the ToO follow-up campaigns without developing their own follow-up system. The AOM can perform complex observations with currently 10 observation modes and 175 strategies. To add or modify the observation modes or strategies, the users only need to edit the configuration file rather than change the code of the system. During the operations, the routine survey, the target monitoring, the GWAC OT validation and the ToO follow-up observations are done automatically. The operators (1) Re-scheduling after any update in the current target/pointing list.
AOM System Workflow
(2) Adding new pointings or re-sequencing the pointing list.
(3) Updating observation status of pointings Observation Status Monitoring Figure 9. The workflow of a complete observation management sequence controlled by the AOM system that is drawn in red color. The target management sub-system receives all the targets from the interfaces (in yellow). The external dispatcher deals with the external telescopes (in the grey box) of the GWAC-N. The system fully controls the internal telescopes (in the green box) with the scheduling, dispatching and status monitoring sub-systems.
are needed for monitoring the operation status and manually importing the targets with the special observation requirements into the system. The communication mechanism and system structure of the AOM ensure the stability of the system, which is another key factor for a robotic telescope network. The AOM has been implemented in the GWAC-N since August 2019. During the observation season of 2019-2020 (from October to April, weathers are better and night time is longer comparing with the rest of year), the AOM is working with a high duty cycle and a stable behavior. The AOM produced 622 observation plans per clear night on average (in December 2020), with failure-free. On the 7th of December, the AOM produced 1064 observation plans, which is the highest working load in the month.
The efficiency of the AOM can be valued by the time delay between the target inserting and the observation command sending. Shortening the time delay is very important for a ToO orientated observation network. The time delay is usually caused by the communication delays, the scheduling process and the observation status monitoring process. In the AOM, the main time consuming is from the scheduling process, which depends mainly on the number of targets in the target list. Because once an observation is finished, the AOM will start a re-scheduling process for all the targets in the list and send an observation command to a telescope. During December 2020, the list contains an average number of 1500 targets in a night. On the 7th of December 2020, the AOM handled 3955 targets, which is the largest number for a night among the month. We tested the time delay of each re-scheduling process during the night. The longest time delay is less than 2 seconds, which is negligible comparing with the time delay in the telescope side between stopping the previous exposure and starting new observation. We simulated the extreme scenario of observing 10000 targets for 10 telescopes. The time delay is less than 4 seconds, which makes the AOM qualified for all types of the ToO follow-up tasks and for a large telescope network.
SCIENTIFIC OPPORTUNITIES AND OUTPUT TO THE GWAC-N
The primary goal of the GWAC-N is to observe the prompt emission of GRBs in optical bands. We emphasized the role of the telescopes of the GWAC-A because of their key features of large sky coverage, high time resolution and real time transient detection capability. These features allow the GWAC-A to independently search for optical transients with a high cadence. Furthermore, the GWAC-A can be also used for follow-up observation of multi-messenger event.
The associated multi-band small FoV telescopes in the GWAC-N are originally designed for the real-time automatic validation for the optical transients detected by the GWAC-A. These telescopes can be also used for other purposes, such as photometry of variable object, galaxy targeting observation for multi-messenger events and supernova survey.
Gamma-Ray Burst
The prompt emission of GRB in optical bands is difficult to be observed, since its very fast temporal decay. To obtain the prompt emission, the speed of response of telescopes to a GRB alert is highly desired. The idea behind the design of the GWAC-A is to eliminate the response time to a GRB alert. The total sky coverage of full GWAC-A is as large as 5000 square degrees, which can cover the same sky area being monitored by the ECLAIRs telescope, the main GRB detector of SVOM (Wei et al. 2016). This extreme large sky coverage guarantees that the GWAC-A simultaneously discovers the optical counterparts for about 30% SVOM detected GRBs at tigger time (T0). It can also make the GWAC-A to be a suitable instrument to follow up the GRBs detected by other gamma-ray instruments, which cannot provide accurate localizations (the Fermi Gamma-ray Space Telescope and SVOM/GRM, etc.).
The two GWAC-F60A/B telescopes and the GWAC-F30 telescope in the GWAC-N robotically follow-up the GRBs detected not only by SVOM but also by the Swift satellite. Since 2016, these 3 telescopes manually followed up 6 Swift GRBs (Xin et al. 2016. Since 2020, the AOM automatically followed up 3 Swift GRBs by using GWAC-A, GWAC-F60 and TNT telescopes (Xin et al. 2020B, Xin et al. 2020C, Xin et al. 2020D, Xin et al. 2021 . For GRB 201223A, the optical counterpart was detected in a GWAC-A image taken at 2 seconds after the burst. The GWAC-F60A started the follow-up observations for the counterpart 23 seconds after receiving the alert of the burst and 44 seconds after the burst trigger. These observations can provide consecutive lightcurve from the prompt emission phase to the afterglow phase (Xin et al. 2020C, Xin et al. 2020D).
Multi-Messenger Target of Opportunities astronomy (gravitational wave, neutrino)
The poor localization of the Multi-Messenger Target of Opportunities (ToO-MM) alert is a great challenge for all the optical follow-up facilities. To quickly search for the optical counterparts in a large sky area, two observation strategies are widely used by most of the optical telescopes for the ToO-MM follow-ups, which are either by tiling the large localization regions or by performing galaxy-targeted observations. By using all the telescopes by the AOM, the GWAC-N can conduct efficient follow-up observations with both strategies. Taking advantage of the wide field of view of telescopes, GWAC-A can cover a significant portion of the ToO-MM localization regions in a very short amount of time by using the tiling strategy. In the meanwhile, the GWAC-F60A/B and GWAC-F30 carry out galaxy targeting observations. As a group, three telescopes can search ∼500 galaxies in a clear night. During the O2 and O3 GW run, the pathfinder telescopes mini-GWAC array and the GWAC-A performed follow-ups of large sky covering for 25 of GW events (8 in O2 and 17 in O3, Dornic et al. 2019, Ducoin et al. 2020B, Ducoin et al. 2020C, Gotz et al. 2019, Lachaud et al. 2019, Leroy et al. 2017, Mao et al. 2020 Thanks to the large sky coverage of the GWAC-A, the fast follow-up capability of the GWAC-F60A/B and GWAC-F30 and the dedicated online data processing pipeline of each telescope, the GWAC-N is not only capable to independently detect optical transients in the sky but also to identify the types of the candidates in realtime. Since 2018, the GWAC-N has detected several super stellar flares (Han et al. 2018B, Wang et al. 2020C, Xin et al. 2020E). The GWAC 181229A, a supper flare with an amplitude of ∆R ∼ 9.5 mag was detected by the GWAC-A and was classified as a ultracool M9 type star by the photometry follow-ups of GWAC-F60A and spectroscopic observations of the NAOC 2.16m telescope (Xin et al. 2020E). This is a good example to demonstrate the capability of the GWAC-N.
The routine survey mode of the current GWAC-A covers ∼20000 square degree of observable sky (galactic plane not included) on a clear night. The center of the sky coverage of the survey shifts ∼ 1 degree along the longitude each day, while most of survey area is consistent in successive observation nights, which means a supernova survey with 1 day cadence can be made using the GWAC-A data. We adopt the ASAS-SN supernova detection relation (Fig 6. in Holoien et al., 2017) to estimate the detection rate of the GWAC-A. With a limiting magnitudes of m R ∼ 16 in a single image and ∼ 200 clear nights per year at the GWAC site, we estimate that the GWAC-A is capable to detect about 30 bright, nearby supernovae per year by using a dedicated pipeline.
Variable and Periodic object
The most of sky coverages of the GWAC-A's survey are consistent in successive observation nights, which means one given sky area can be monitored for days or dozens of days. With a high cadence observation mode (15 seconds per image), the GWAC-A can monitor the variables or the periodic objects in the sky area and obtain their variation. The online data processing pipeline of the GWAC-A can measure the photometric features for all sources in the images. Using neural network mechanism, researchers analyze the massive data of the GWAC-A to detect and to classify variable and periodic sources (Qiu et al. 2018.
Moving object
With its large field of view and high cadence, the GWAC-A can monitor hundreds asteroids on an observation night. The GWAC-A also has the capability to detect the decameter asteroids and meteors (Shugarov 2019. They are valuable for the researchers in these fields. Our team works on the algorithm and database to recognize and morphology analyze them from the GWAC data. The Figure 10 shows some moving objects automatically detected in the GWAC-A images by an algorithm for selecting moving objects. The accuracy over 85% can be reached for the meteor candidate selections by using the algorithm (Xu et al. 2020B).
SUMMARY AND PERSPECTIVE
The GWAC-N is currently composed of two GWAC telescopes, two GWAC-F60 telescopes and one GWAC-F30 telescope. It is also collaborating with two external telescopes: the CGFT and the TNT telescope. By implementing the AOM, those telescopes can work as a network smoothly. Besides of routine observations, the GWAC-N performed follow-up observations of the LIGO/Virgo GW, the Fermi GRB, the Swift GRB events. During the LIGO/Virgo O3 campaign, using the AOM system described in this paper, the GWAC-N observed 17 GW events and published 23 GCN circulars.
In the next two years, the complete GWAC-N will be installed at two observatories. The number of telescopes in the GWAC-N will be extended to nine GWAC-A telescopes and five 60cm class telescopes. More external telescopes are also foreseen to join the network. The AOM will fully support the operations of the GWAC-N and greatly enlarge the scientific return of the GWAC-N. Its technology and mechanism, or as a whole, the AOM can be adapted to other world-wide, general purposed, telescope networks. The code of the whole AOM system is available at the Github 2 for public download.
The AOM is not only used to manage the operations of telescopes but also to manage the data. A server named the Data Center (DC) is installed inside of the AOM. In the past, the massive data taken from the GWAC-N telescopes bring huge workload to the scientists and operators to collect and find images for certain observations. Currently, the data of the ToO follow-up observations taken by the GWAC-F60, the GWAC-F30 are automatically collected and uploaded to the DC by the AOM. It allows we centralized the data processing in the DC rather than the data processing distributed in the telescope side. In the future, we plan to integrate the data processing pipeline in the AOM system, as well as the data product release.
ACKNOWLEDGEMENT
The GWAC team at the NAOC is grateful for financial assistance from the National K&D Program of China (grant No. 2020YFE0202100) and the National Natural Science Foundation of China (Grant No. 11533003, 11973055, U1831207, 11863007). This work is supported by the Strategic Pioneer Program on Space Science, Chinese Academy of Sciences, grant Nos. XDA15052600 & XDA15016500 and by the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No.XDB23040000. Damien Turpin acknowledges the financial support of the CNES postdoctoral program. We thank the staffs of the Xinglong and the Jilin observatories at which the TNT and the CGFT telescopes are operated. We would like to thank Sarah Antier, David Corre, Jean-Grégoire Ducoin for their very helpful discussions during the developments of the AOM system. | 10,376.8 | 2021-02-05T00:00:00.000 | [
"Physics",
"Engineering"
] |