content stringlengths 86 994k | meta stringlengths 288 619 |
|---|---|
PE: Redistribution
The focus of today’s lecture will be on redistribution as discussed in Chapter 3(Mueller, 2003). Additionally, we will discuss papers quantitatively assessing the situation (De Haan & Sturm , 2017;
Sturm & de Haan, 2015).
A justification for the state can be redistribution. But redistribution itself can be argued for based on different reasons. In this post, we will illuminate the main arguments. First three voluntary
redistribution arguments will be covered, then we will have a look at involuntarily redistribution.
Redistribution as insurance
If one assumes Rawls’ veil of ignorance (Rawls, 2009), redistribution can be seen as an insurance against the uncertainties of what kind of role one will assume in society. Insurance can be covered
privately, so at first state intervention may seem inadequate. However, since people can assess their risk, high-risk individuals would select the insurance whereas low-risk individuals would shun
the insurance. To overcome the issue of adverse selection, public insurance is introduced. The issue of adverse selection has been introduced by Akerlof (Akerlof, 1970) and shows that information
asymmetry can break markets. The public insurance overcomes this issue by forcing a pareto-optimum on a societal level. Typical cases for this are health care insurance, unemployment insurance, and
retirement insurance.
Redistribution as public good
Another justification comes from altruism or empathy (“warm glow”). The utility equation is expanded to [latex]max U_m + \alphaU_o[/latex] where [latex]0\leq\alpha\leq1[/latex].
Redistribution as fairness norm
The assumption that fairness is an important norm, is the basis for this redistribution argument. The classical example is the dictator game, where anonymous individuals are paired and one gets an
amount of money and may share it with the other. Usually, any individual share around 30% with the other despite being able to keep everything and not knowing anything about the other. So far, the
assumption is that the random element of the game let people share their gain because they also could have ended up on the other side.
Redistribution as allocative efficiency
If two individuals ([latex]P[/latex] and [latex]U[/latex]) work a fixed amount of land. The productivity of [latex]P[/latex] is 100 whereas [latex]U[/latex]’ productivity is 50. The connecting curve
describes the production possibility frontier. Any initial allocation (e.g. [latex]A[/latex] may not be optimal on a societal level (i.e. [latex]A[/latex] is not tangential on a [latex]45°[/latex]
line), the societal optimum would be in [latex]B[/latex], which is however unacceptable for [latex]U[/latex]. The inefficient allocation would end up at [latex]A'[/latex]. The state could either
redistribute land to reach [latex]B[/latex] or production to reach [latex]C[/latex]. Note that C in the graph should amount to a value above 100. Alternatively, private contracting could reach the
same result given that the state enforces property rights and contracts.
The example is based on (Bös & Kolmar, 2003).
Redistribution as taking
Groups can lobby to increase their utility [latex]U[/latex] by increasing their income [latex]Y[/latex] based on their political resources [latex]R[/latex] available. However, if two antagonistic
groups lobby their policies may cancel each other leaving them only with the additional cost of lobbying without any gains.
Measuring redistribution
To measure redistribution, inequality needs to be measured first. A typical measure of inequality is done via the Lorenz curves and the Gini coefficient (Gini, 1912). The Gini coeffcient is the ratio
of areas under two curves. The Gini market coefficient (before taxes) and the Gini net coefficient (after taxes and subsidies) are subdivisions that taken at ratio help to assess redistribution.
The causation of inequality is difficult to assess. Some argue for politics (Stiglitz, 2014), whereas others argue for the market-based economies (Muller, 2013). A new line of inquiry attributes
inequality to ethno-linguistic fractionalisation reducing the interest in redistribution (Desmet, Ortuño-Ortín, & Wacziarg, 2012).
Sturm and de Haan (Sturm & de Haan, 2015) follow up on the argument and examine the relationship between capitalism and income inequality. A large sample of countries is analysed using an adjusted
economic freedom (EF) index as proxy for capitalism and Gini coefficients as proxy for income inequality. Additionally, they analyse the relation between income inequality and fractionalistion given
similar capitalist systems. For the first analysis, there is no conclusive evidence that capitalism and income inequality are linked. However, if fractionalisation is taken into account, than
inequality can be explained based on the level of fractionalisation. The more fractionalised a society is, the less redistribution takes place and consequently inequality remains high.
In a second paper de Haan and Sturm (De Haan & Sturm , 2017) analyse how the financial development impacts income inequality. Previous research on financial development, financial liberalisation and
banking crises (theoretical and empirical) has been ambiguous. TBC.
Akerlof, G. A. (1970). “The market for” lemons”: Quality uncertainty and the market mechanism. The Quarterly Journal of Economics, 488–500.
Bös, D., & Kolmar, M. (2003). Anarchy, efficiency, and redistribution. Journal of Public Economics, 87(11), 2431–2457.
De Haan, J., & Sturm , J.-E. (2017). Finance and Income Inequality: A review and new evidence. European Journal of Political Economy, Forthcoming.
Desmet, K., Ortuño-Ortín, I., & Wacziarg, R. (2012). The Political Economy of Linguistic Cleavages. Journal of Development Economics, 97(2), 322–338.
Gini, C. (1912). Variabilità e mutabilità. In E. Pizetti & T. Salvemini (Eds.), Memorie di metodologica statistica (p. 1). Rome: Libreria Eredi Virgilio Veschi.
Mueller, D. C. (2003). Public Choice III. Cambridge, UK: Cambridge University Press.
Muller, J. Z. (2013). Capitalism and inequality: What the right and the left get wrong. Foreign Affairs, 92(2), 30–51.
Rawls, J. (2009). A theory of justice. Harvard university press.
Stiglitz, J. (2014). Inequality is not inevitable. New York Times, pp. 1–2.
Sturm, S., Jan-Egbert, & de Haan, J. (2015). Income Inequality, Capitalism and Ethno- Linguistic Fractionalization. American Economic Review: Papers and Proceedings, 105(5), 593–597. | {"url":"http://blog.gruebel.io/2017/03/13/pe-redistribution/","timestamp":"2024-11-13T21:18:10Z","content_type":"text/html","content_length":"66887","record_id":"<urn:uuid:5cfffcf8-10c5-40d8-a64d-1ff8e279f794>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00830.warc.gz"} |
K5 Math Worktext, 5th ed. | BJU Press
K5 Math Worktext, 5th ed.
The BJU Press K5 Math Student Worktext includes practice problems, a colorful layout, STEM activities, manipulatives, differentiated instruction, and review questions.
Christian School Pricing
This new product is not yet available.
The Math K5 Student Worktext, 5th ed. teaches students to learn math through a biblical worldview. These students will develop a better understanding of numbers by solving real-life problems,
analyzing money, identifying dates and time, solving addition and subtraction problems, and identifying fractions. Follow the adventures of Farmer Brown, Mrs. Brown, and Cheddar as they learn more
about math!
Key Features of the K5 Math Worktext
• Essential questions in each chapter
• Practice problems to enhance understanding of numbers
• Biblical worldview shaping themes
• Cyclical approach to review
• STEM lessons
• Differentiated instruction boxes included for each chapter
• Use of manipulatives
• Engaging stories about math in each chapter opener | {"url":"https://www.bjupress.com/k5-math-worktext,-5th-ed./5637431185.p","timestamp":"2024-11-04T07:39:06Z","content_type":"text/html","content_length":"365093","record_id":"<urn:uuid:741e5079-dd4e-4203-a537-aa1eecab3b64>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00275.warc.gz"} |
Synchronization of spatially extended chaotic systems with asymmetric coupling
In this paper, we report the consequences induced by the presence of asymmetries in the coupling scheme on the synchronization process of a pair of one-dimensional complex fields obeying Complex
Ginzburg Landau equations. While synchronization always occurs for large enough coupling strengths, asymmetries have the effect of modifying synchronization thresholds and play a crucial role in
selecting the statistical and dynamical properties of the highly coupled synchronized motion. Possible consequences of such asymmetry induced effects in biological and natural systems are discussed.
Synchronization of spatially extended chaotic systems with asymmetric coupling
S. Boccaletti^I; C. Mendoza^I; J. Bragard^II
^IIstituto Nazionale di Ottica Applicata, Largo E. Fermi, 6, I-50125 Florence, Italy
^IIDepartamento de Física y Matemática Aplicada, Universidad de Navarra, E31080 Pamplona, Spain
In this paper, we report the consequences induced by the presence of asymmetries in the coupling scheme on the synchronization process of a pair of one-dimensional complex fields obeying Complex
Ginzburg Landau equations. While synchronization always occurs for large enough coupling strengths, asymmetries have the effect of modifying synchronization thresholds and play a crucial role in
selecting the statistical and dynamical properties of the highly coupled synchronized motion. Possible consequences of such asymmetry induced effects in biological and natural systems are discussed.
1 Introduction
The synchronization of coupled chaotic systems has been a topic of intense study since 1990 [1]. Interest has now moved to the study of synchronization phenomena in space-extended systems, such as
large populations of coupled chaotic units and neural networks [2-4], globally or locally coupled map lattices [5,6], coupled map networks [7] as well as other space-extended systems [8-13]. Most of
the studies have considered synchronization due to external forcings, or to bidirectional symmetric or to unidirectional master-slave coupling configurations. In many practical situations, however,
one cannot expect to have purely unidirectional, nor perfectly symmetrical coupling configurations. As a result, recent interest has focused on detecting asymmetric coupling configurations [14], and
quantifying asymmetries in the coupling scheme in relevant applications (such as the study of the human cardiorespiratory system) [15], and then to characterize the effects of asymmetric coupling on
synchronization (for example between pairs of one-dimensional space extended chaotic oscillators [16]). In particular, Ref. [16] has shown that asymmetry in the coupling of two one-dimensional fields
obeying Complex Ginzburg-Landau Equations (CGLE) enhances complete synchronization, and plays an important role in controlling the properties of the final synchronized state.
This paper presents an account of the synchronization of a pair of non identical CGLE with an asymmetric coupling, for both small and large parameter mismatches. We will analyze the type of
synchronized dynamics occurring in the presence of asymmetric coupling in all possible dynamical states emerging from CGLE, and we will show that in all cases the threshold for the appearance of
synchronized motion depends non trivially on the asymmetry in the coupling. We will demonstrate that the selection of the dynamics within the final synchronized manifold is always crucially affected
by the asymmetry. The process leading to synchronization is anticipated by defect-defect synchronization, inducing the simultaneous appearance in the coupled fields of phase singularities, even in
the cases in which the uncoupled dynamics of both fields does not include the presence of defects.
2 Model equation for synchronization
We will consider a pair of one-dimensional fields obeying Complex Ginzburg-Landau Equations (CGLE). This equation has been extensively investigated in the context of space-time chaos, since it
describes the universal dynamical features of an extended system close to a Hopf bifurcation [17], and therefore it can be considered as a good model equation in many different physical situations,
such as occur in laser physics [18], fluid dynamics [19], chemical turbulence [20], bluff body wakes [21], or arrays of Josephson's junctions [22].
We will consider a pair of complex fields A[1,2](x,t) = r[1,2](x,t) [1,2](x,t) and phases f[1,2] (x,t), whose dynamics obeys
Here, dots denote temporal derivatives, x < L (L being the system extension), a and b[1,2] are suitable real parameters, c represents the coupling strength and q is a parameter accounting the for
asymmetry in the coupling. The case q = 0 describes the bidirectional symmetric coupling configuration, whereas the case q = 1 (q = 1) recovers the unidirectional master slave scheme, with the field
A[1] (A[2]) driving the response of A[2] (A[1]).
When c = 0 (the uncoupled case), different dynamical regimes occur in Eqs. (1) for different choices of the parameters a, b [23-25]. The full parameter space for the dynamics of the CGLE is shown in
Fig. 1. In particular, Eqs. (1) admits plane wave solutions (PWS) of the form
Here, q is the wavenumber in Fourier space, and the temporal frequency is given by w = b (a b) q^2. The stability of such PWS can be analytically studied below the Benjamin-Feir-Newel (BFN) line
(defined by ab = 1 in the parameter space). Namely, for ab > 1, one can define a critical wavenumber
such that all PWS are linearly stable in the range q[c] < q < q[c]. Outside this range, PWS become unstable through the Eckhaus instability [26].
When crossing from below the BFN line in the parameter space, Eq. (3) shows that q[c] vanishes and all PWS become unstable. Above this line, Refs. [23-25] identify different turbulent regimes, called
respectively Amplitude Turbulence (AT) or Defect Turbulence, Phase Turbulence (PT), Bi-chaos, and a Spatiotemporal Intermittent regime. The borders in parameter space for each one of these dynamical
regimes are schematically drawn in Fig. 1, together with the BFN line. In this work, we will mainly concentrate on PT and AT, since they constitute the fundamental dynamical states for the evolution
of the uncoupled fields, and their main properties [27] have received considerable attention in recent years including the definition of suitable order parameters marking the transition between them
[28], as well as for the study of synchronization in bidirectional symmetrical coupling configurations [11,29-31].
PT is a regime where the chaotic behavior of the field is mainly dominated by the dynamics of f(x,t), the amplitude r(x,t) changing only smoothly, and being always bounded away from zero. On the
other hand, AT is the dynamical regime wherein the fluctuations of r(x,t) become dominant over the phase dynamics. Here, the complex field experiences large amplitude oscillations which can (locally
and occasionally) cause r(x,t) to vanish. As a consequence, at all those points (hereinafter called space-time defects or phase singularities) the global phase of the field F º arctan
3 Characterization of synchronized states
The purpose of our paper is to report the different synchronization states that are selected when an asymmetric coupling takes place between the two CGLE fields. In order to be as exhaustive as
possible, we will consider different regimes for the two CGLE. The reference as a starting point is the case treated in Ref. [16] (i.e. a = 2, b[1] = 0.7 and b[2] = 1.05). For this parameter
choice, the two fields are originally prepared to display PT and AT, respectively. As a consequence, hereinafter we will denote this situation as PT-AT(I). Another possible choice for an initial
PT-AT configuration, whose relevance will be momentarily clear, is to consider a = 2, b[1] = 0.95 and b[2] = 1.2 (we will denote such a situation as PT-AT(II)). Finally, we will consider also cases
of small parameter mismatch, where the two systems start from the same initial dynamical state, such as a = 2, b[1] = 0.75 and b[2] = 0.9 (denoted by PT-PT) and a = 2, b[1] = 1.05 and b[2] = 1.2
(denoted by AT-AT).
In all cases, we consider values of the asymmetry parameter q Î [ 1,+1], and highlight the effects of asymmetry in the synchronization properties (c ¹ 0) of system (1). Simulations were performed
with a Crank-Nicholson, Adams-Bashforth scheme (which is second order in space and time [32]), with a time step dt = 10^ 2 and a grid size dx = 0.25, for L = 100 (corresponding to 400 grid points)
and spatial periodic boundary conditions [A[1,2] (0,t) = A[1,2](L,t)].
A crucial parameter in all our investigations, that dictated the choice of the parameters in the different cases, is the natural average frequency of the single CGLE. Such a frequency is calculated
from the numerical simulations of a single CGLE by averaging in space the unfolded phase f defined in
where < ... > [x] represents for a spatial average.
Figure 2 shows w vs. the parameter b at a = 2. In order to construct Fig. 2, we have integrated the CGLE for a very long time (t[f] = 15,000) after eliminating transient behaviour (T = 5,000). Two
different initial conditions for each value of b were chosen in order to measure the sensitivity of w with respect to selection of different initial condition. It should be emphasized that all
initial conditions were chosen to have a zero average phase gradient [28], because the frequency in the PT regime is highly sensitive to the average phase gradient as shown by [28].
From Fig. 2 one clearly realizes that w reaches a maximum for b » 0.98, close to the transition from the PT to the AT regime. This transition has been extensively studied by several authors
[28,33,34], and it has been shown that it depends on the spatial extension on which the Eqs.(1) are integrated, as well as on the average phase gradient. In addition, it is interesting to notice (see
Fig. 2) that on the right hand side of the maximum (PT regime) the two different initial conditions lead to nearly the same value for the averaged frequency, while on the left hand side of the
maximum (AT regime) the two initial conditions lead in general to two different values for w. This fact could serve as an alternative indicator for the characterization of the PT-AT transition.
Furthermore, the frequency difference between the prediction given by the dispersion relation of the PWS (dashed line) and the numerical simulations can be evaluated quite accurately in the PT regime
(right hand side of the maximum) by using the modified Kuramoto-Sivashinsky equation [35,36].
Considerations based on Fig. 2 dictate the choice for the parameters b's in the rest of the presentation. Indeed, a question to be clarified is how crucial is the role of the natural frequency for
the selection of the dynamics for the two coupled CGLE in the synchronized state. A previous study with bidirectional symmetrical coupling configuration (q = 0) between a PT and a AT regime [11]
pointed out that the final synchronized dynamics occurs in a PT state. The above result was obtained for a parameter choice for which the frequency w[PT] of the initial PT state was smaller than the
one (w[AT]) of the initial AT state. This was also the situation of the case PT-AT(I) treated in Ref. [16] (see Fig. 2). We will show that, in the absence of asymmetries, the dynamics in the final
synchronized state is always selected to correspond to that state having an originally smaller value of w. This property has dictated the choice of parameters for the case PT-AT(II) considered in the
present Manuscript (b[1] = 0.95 and b[2] = 1.2). In this case Fig. 2 shows that w[PT] > w[AT], and we will see that the synchronized motion at q = 0 develops onto a AT regime.
Let us now discuss how to characterize the synchronization properties of the coupled fields by means of suitable indicators [13]. As we are dealing with extended chaotic fields that may be in defect
turbulence, concepts of phase synchronization may be hindered by the presence of phase singularities in such regimes, that make average phases difficult to define properly in AT.
On the other hand, complete synchronization (CS) states can be detected by the use of Pearson's coefficient defined as
where áñ denotes a full space-time average (in order to avoid getting spurious values, we allow in general some transient time T to elapse before evaluating this coefficient). g measures the degree
of cross correlation between the moduli r[1] (x,t) and r[2] (x,t): When g = 0 the two fields are linearly uncorrelated, while g = 1 marks complete correlation and g = 1 indicates that the fields are
negatively correlated.
Another indicator characterizing the disorder in the system is the number of phase singularities (or defects) N. Theoretically, a defect is a point (x,t) for which r(x,t) = 0. This implies that
defects are intersections of the 0-level curves in the (x,t) plane of the real and imaginary parts of A[1,2] (x,t). In practice, because of the finite size of the mesh and of the finite resolution of
the numerics, we must introduce a method for the detection of a defect. A reliable criterium is to count as defects at time t those points x[i] where the r(x[i],t) is smaller than 0.025 and that are
furthermore local minima for the function r(x,t).
It is well known [33,34] that N is an extensive quantity of both time and space, and therefore it is sometimes convenient to refer to the defect density n[D], that is calculated as the defect number
N per unit time and unit space.
In the following, we will describe the important effects of asymmetries in the coupling of system (1), for different values of the parameters b[1] and b[2], while a = 2 will be hereinafter fixed.
4 Asymmetry Enhanced Synchronization
A striking effect of asymmetry in the coupling that has already been highlighted in our previous analysis for the case PT-AT (I) [16] is that one can improve dramatically the synchronization
threshold by selecting a suitable level of asymmetry in the coupling. Conversely, one can also achieve desynchronization of the two coupled systems by varying the asymmetry level in the coupling
4.1 Large Parameter Mismatch
By selecting in (1) a sufficiently large parameter mismatch in the equations for A[1,2], one can set the uncoupled evolutions of A[1] and A[2] to be in PT and AT, respectively. By doing that, one
still has three possibilities of choosing the parameters b accordingly to the natural frequencies of the two separate CGLE.
The first case (PT-AT(I)) corresponds to system 1 in the PT regime (b[1] = 0.7) with a lower natural frequency than system 2 in the AT regime (b[2] = 1.05). The natural frequencies are
approximately equal to w[1]» 0.7 and w[2]» 0.87 > w[1] (see Fig. 2). This situation has been extensively studied in [16] where both complete and frequency synchronization features were discussed and
The second case (PT-AT(II)) corresponds to preparing system 1 in the PT regime (b[1] = 0.95) with a higher natural frequency than system 2 in the AT regime (b[2] = 1.2). The natural frequencies are
approximately equal to w[1]» 0.9 and w[2]» 0.84 < w[1] (see Fig. 2). For this case, we will show how asymmetry enhances the setting of complete synchronization.
Notice that a further situation could be studied where the two systems are prepared in the PT and AT regimes respectively, but they have approximatively the same natural frequency. This more complex
case, where one might expect some kind of resonance coming into play in the process of synchronization, will be dealt with elsewhere.
Figure 3a reports g vs. the parameter space (c,q) for the PT-AT(II) case, and shows the non trivial dependence of the threshold for synchronization on the asymmetry parameter q. A better way to
visualize such a dependence is by making a cut of the surface at a fixed value of the coupling (e.g. c = 0.25, see Fig. 3b). Both in the PT-AT(II) case and in the PT-AT(I) case (already reported in
Fig. 1b of Ref. [16]), a better synchronization level is obtained for the unidirectional configuration where the system in the PT regime is driving the system in the AT regime (q = 1). The surfaces
and curves of Fig. 3a;b) have been obtained by making averages over a time t[f] = 15,000 after a large transitory has elapsed (T = 6,000) in order to ensure that we are measuring stationary
synchronization states.
4.2 Small Parameter mismatch
The very same scenario of asymmetry enhanced synchronization occurs when we select small parameter mismatches in Eqs.(1), i.e. we set the parameters so as the two uncoupled fields are both either in
PT or AT, thus confirming that this feature generally characterize the emergence of the synchronized motion in our system.
4.2.1 AT-AT Case
In this case, we set b[1] = 1.05 and b[2] = 1.2. Both systems now are in the AT regime, with system 1 having a natural frequency higher than the one of system 2.
Figs.4 shows Pearson's coefficient vs. the parameter space (c,q) (a), as well as a cut of the g-surface at c = 0.17 (b), showing that asymmetry in the coupling is still playing an important role in
modifying the level of synchronization for a fixed value of the coupling strength c. It is not surprising that the complete synchronization threshold is now lower compared to the PT-AT cases. This,
indeed, is related to the fact that smaller parameter mismatches induce closer initial dynamics, which are therefore easier to synchronize.
4.2.2 PT-PT Case
Finally, in order to complete this first part of the discussion, we examine the PT-PT case. Now, parameters are b[1] = 0.75 and b[2] = 0.9, determining an initial PT state for both uncoupled
fields, with system 1 having a lower natural frequency with respect to system 2.
Figures 5a;^b describe the behavior of g as a function of the coupling c and the asymmetry q. Once again, asymmetry plays a decisive role in enhancing the appearance of a synchronized motion in
system (1). Notice that here the values of c required for a synchronized motion are smaller than in any of the previous cases, reflecting the fact that the present situation corresponds to the
smallest parameter mismatch.
At variance with all the other cases, an interesting feature of ^Fig. 5b is that an increase in the asymmetry does not always yield a monotonic increase of g.
At this stage, we can already draw some interesting conclusions. We have seen that changing asymmetry in the coupling configuration for the same coupling strength has the effect of enhancing the
appearance of a synchronized motion or destroying synchronization, regardless of the initial uncoupled state of the dynamics. We conjecture that this may have relevant consequences in biological
systems, where changes in asymmetry of the interactions could be a way to efficiently synchronize-desynchronize the dynamics for the same strength of interaction.
Furthermore, in Eqs.(1) the coupling is a mapping of all the grid points of system 1 on their corresponding grid points of system 2. We could, in fact, imagine more complicated and probably more
realistic configurations where couplings, besides being asymmetric, would be spatially dependent or even asynchronous. While it is likely that real systems show combinations of asymmetric,
asynchronous and spatially dependent coupling schemes to control and synchronize in an optimal way their dynamical regimes, here we only focused on the effects of asymmetries, since the scenario of
emerging dynamics is already extremely rich in this ßimplified" approach.
5 Selection of the Final State
Next, we move to describe how asymmetries play a crucial role in setting the state of the dynamics within the synchronized regime, which occur for large values of the coupling strength. Let us recall
the methods adopted for our investigation of the dynamics within the synchronized regime. Initially (t = 0) we begin a trial simulation of the two Eqs.(1) connected with a non-zero value of c. We
impose random initial conditions on both systems, which in general will have different parameters. As a consequence, the dynamics usually attains synchronized motion only after a transient time T.
Since we are not here interested in characterizing the dynamics in the transient stage, we let a certain transient time T elapse (we have verified that T = 6,000 is large enough for reaching such
asymptotic state) before starting to calculate the indicators of any asymptotic synchronized state. In this way, we can measure such indicators within the statistically stationary state represented
by the asymptotic synchronized motion.
While it is not surprising that when coupling two initially PT states (AT states) the final synchronized motion will persist in the PT regime (AT regime), a relevant point concerns what mechanisms
control the selection of the synchronized motion, once the two fields originally start from different regimes. To address such an issue, we will focus in the present section on the two PT-AT cases.
In these cases, it is not trivial to predict a priori what will be the resulting dynamical state for the synchronized motion.
Figures 6a;^b show the total number of defects counted for a time t[f] = 15,000 in the parameter space (c,q) for the PT-AT(II) case. Namely, Fig. 6a (^Fig. 6b) corresponds to the defects appearing in
system 1 (in system 2) that was set initially in the PT regime (in the AT regime) at c = 0. One clearly sees that both systems exhibit a large number of defects for non-zero coupling. Furthermore,
for asymptotically large values of the coupling (c » 0.5) leading to a synchronized motion, the asymmetry parameter q plays a crucial role in setting the synchronized dynamics on either a PT regime
or an AT regime. The defect number vs. the parameter space for the case PT-AT(I) was already reported by us in Fig. 2 of Ref. [16], where again was emphasized the role of the asymmetry in the
selection of the synchronized dynamical regime.
Let us compare and discuss more fully these two cases. In Section (3), we have already seen that the main difference between the cases PT-AT(I) and PT-AT(II) is in terms of the initial natural
frequencies of the two subsystems. Namely, in the PT-AT(I) (the PT-AT(II)) case the natural frequency of the subsystem originally set in AT is larger (smaller) than the one of the subsystem
originally set in PT. In Fig. 7 we summarize the result of the comparative study of the two cases. We choose a sufficiently large value of the coupling strength so as to ensure a synchronized state,
and we have represented with a dashed region (a blank region) the range of q-values for which the synchronized motion develops into an AT (a PT) regime.
First of all we observe that at q = 0 (i.e. in the bidirectional symmetrical case) the system with a lower natural frequency is the dominant one at the moment of selecting the final synchronized
state. Furthermore, in Fig. 7 we observe a very different scenario for the two PT-AT cases. In the PT-AT(I) case a final state in PT is selected for most of the values of the asymmetry parameter
(until q = 0.84, below which a final state in AT takes over). In contrast, in the PT-AT(II) case for most of the asymmetry values (up to q = 0.64) the final state is selected in the AT regime.
The conclusion of the present Section is that asymmetries in the coupling configuration play a decisive role in the selection of the dynamics and the statistical properties of the synchronized state.
This feature may have relevant consequences in biological and natural systems, where small changes in the asymmetry of the interactions could be used as an efficient way to select the synchronized
state of an ensemble of interacting complex units.
6 Conclusions
In conclusion, we have reported and discussed several asymmetry induced effects in the process of synchronization of a pair of coupled complex space extended fields. While synchronization always
occurs for large enough values of the coupling strength, the threshold for the setting of synchronized motion crucially depends on the asymmetry in the coupling configuration. Furthermore, the
asymmetry controls in relevant cases the statistical and dynamical properties of the synchronized motion, as is the case when the coupled subsystems start from statistically different dynamical
regimes. In this latter situation we have shown that a bidirectional symmetrical coupling configuration leads to a synchronized motion where the statistical properties of the subsystem having
originally a lower natural frequency prevail, whereas asymmetries can drastically change such a scenario.
We argue that such features may have relevant consequences in biological and natural systems, where small changes in the asymmetry of the interactions could be used as an efficient way to synchronize
or desynchronize the dynamics, as well as select the main statistical properties of the synchronized motion in ensembles of interacting complex units.
Work partly supported by MCYT project (Spain) n. BFM2002-02011 (INEFLUID).
Received on 18 January, 2005
• [1] For a comprehensive review on the subject, see: S. Boccaletti, J. Kurths, G. Osipov, D. Valladares, and C. Zhou, Phys. Rep. 366, 1 (2002), and references therein.
• [2] S.H. Strogatz, S.E. Mirollo, and P.C. Matthews, Phys. Rev. Lett. 68, 2730 (1992).
• [3] A. Pikovsky, M. Rosenblum, and J. Kurths, Europhys. Lett. 34, 165 (1996).
• [4] D.L. Valladares, S. Boccaletti, F. Feudel, and J. Kurths, Phys. Rev. E65, 055208 (2002).
• [5] V.N. Belykh and E. Mosekilde, Phys. Rev. E54, 3196 (1996).
• [6] A. Pikovsky, O. Popovich, and Yu. Maistrenko, Phys. Rev. Lett. 87, 044102 (2001).
• [7] S. Jalan and R.E. Amritkar, Phys. Rev. Lett. 90, 014101 (2003).
• [8] G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994).
• [9] L. Kocarev, Z. Tasev, and U. Parlitz, Phys. Rev. Lett. 79, 52 (1997).
• [10] R.O. Grigoriev, M.C. Cross, and H.G. Schuster, Phys. Rev. Lett. 79, 2795 (1997).
• [11] S. Boccaletti, J. Bragard, F.T. Arecchi, and H.L. Mancini, Phys. Rev. Lett. 83, 536 (1999).
• [12] H. Chaté, A. Pikovsky, and O. Rudzick, Physica D131, 17 (1999).
• [13] L. Junge and U. Parlitz, Phys. Rev. E62, 438 (2000).
• [14] M.G. Rosenblum and A. Pikovsky, Phys. Rev. E64, 045202 (2001).
• [15] M.G. Rosenblum, L. Cimponeriu, A. Bezerianos, A. Patzak, and R. Mrowka, Phys. Rev. E65, 041909 (2002).
• [16] J. Bragard, S. Boccaletti, and H. Mancini, Phys. Rev. Lett. 91, 064103 (2003).
• [17] For a comprehensive review on pattern dynamics emerging from space-time bifurcations, see: M. Cross and P. Hohenberg, Rev. Mod. Phys. 65, 851 (1993), and reference therein.
• [18] P. Coullet, L. Gil, and F. Roca, Opt. Commun. 73, 403 (1989).
• [19] P. Kolodner, S. Slimani, N. Aubry, and R. Lima, Physica D85, 165 (1995).
• [20] Y. Kuramoto and S. Koga, Prog. Theor. Phys. Suppl. 66, 1081 (1981).
• [21] T. Leweke and M. Provansal, Phys. Rev. Lett. 72, 3174 (1994).
• [22] B.D. Josephson, Phys. Lett, 1, 251 (1962).
• [23] B.I. Shraiman, A. Pumir, W. van Saarlos, P.C. Hohenberg, H. Chaté, and M. Holen, Physica D57, 241 (1992).
• [24] H. Chaté, Nonlinearity 7, 185 (1994).
• [25] H. Chaté, in: Spatiotemporal Patterns in Nonequilibrium Complex Systems, edited by P.E. Cladis and P. Palffy-Muhoray (Addison-Wesley, New York, 1995).
• [26] B. Janiaud, A. Pumir, D. Bensimon, V. Croquette, H. Richter, and L. Kramer, Physica D55, 269 (1992).
• [27] A. Torcini, H. Frauenkron, and P. Grassberger, Phys. Rev. E 55, 5073 (1997).
• [28] A. Torcini, Phys. Rev. Lett. 77, 1047 (1996).
• [29] S. Boccaletti, J. Bragard, and F.T. Arecchi, Phys. Rev. E 59, 6574 (1999).
• [30] J. Bragard and S. Boccaletti, Phys. Rev. E62, 6346 (2000).
• [31] J. Bragard, S. Boccaletti, and F.T. Arecchi, Int. J. of Bifurcation and Chaos. 11, 2715 (2001).
• [32] W.H. Press, et al., Numerical Recipes in Fortran 90 (Cambridge University Press, 1992).
• [33] D.A. Egolf and H.S. Greenside, Phys. Rev. Lett. 74(10), 1751 (1995).
• [34] L. Brusch, M.G. Zimmermann, M. van Hecke, M. Bär, and A. Torcini, Phys. Rev. Lett. 85, 86 (2000).
• [35] H. Sakaguchi, Prog. Theor. Phys. 83, 169 (1990).
• [36] H. Sakaguchi, Prog. Theor. Phys. 84, 792 (1990).
Publication Dates
• Publication in this collection
06 Sept 2005
• Date of issue
June 2005 | {"url":"https://www.scielo.br/j/bjp/a/HXhbTNwTHvNBdRXngyrYzYM/?lang=en","timestamp":"2024-11-11T05:28:12Z","content_type":"text/html","content_length":"117176","record_id":"<urn:uuid:8f93d691-e9a9-4745-8253-7fdce37b1089>","cc-path":"CC-MAIN-2024-46/segments/1730477028216.19/warc/CC-MAIN-20241111024756-20241111054756-00059.warc.gz"} |
Semiconductors in Magnetic fields
The application of magnetic fields is one of the more powerful methods for investigating the properties of charge carriers. It was first shown by Landau in 1930 that the energy levels of a population
of free electrons will become quantised into a set of magnetic sub-bands (landau levels). These levels are separated by the cyclotron frequency, with energies given by
where w[c ]=eB/m*[ ]is the cyclotron frequency and k[||] is the component of the wavevector parallel to the magnetic field.
Towards the bottom of each Landau level, the density of states develops a series of singularities known as Van Hove singularities. This divergence is often expressed in a parabolic approximation
$D(E)=\frac{eB}{h}(2m^\star)^{1/2}\sum_{n}\left(E-\left(n+\frac{1}{2}\right)\hbar w_{c}\right)^{-1/2}$
The two expression above are depicted in the figure below.
If the energy separation between two of the levels (hw[c]) is equal to a well defined energy, such as the optic phonon energy, resonant absorption and emission of phonons will take place. This is
known as the Magnetophonon effect and lead to the spectrum shown in figure 2.
At low temperatures, in degenerate materials, conduction takes place within a small region around the Fermi energy. As the magnetic field is varied, the singularities at the bottom of each Landau
level cross the Fermi level in succession, and thus give rise to a series of structures in the resistivity which are periodic in 1/B.
The first experimental demonstration of this effect was the observation by Shubnikov and de Haas of small oscillations in the magnetoresistance of bismuth. These become known subsequently as
Shubnikov de Haas oscillations and are shown in Figure 3.
Figure 3: Experimentally observed SdH oscillations. Taken from J. P. Freire et al, Braz. J. Phys. 34 (2004) | {"url":"https://warwick.ac.uk/fac/sci/physics/current/postgraduate/regs/mpagswarwick/ex5/mag/","timestamp":"2024-11-13T14:57:38Z","content_type":"text/html","content_length":"37243","record_id":"<urn:uuid:05f4e535-14f8-4372-8e4f-2b8d933c5bf7>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00120.warc.gz"} |
Course syllabus
Electromagnetic Fields
Elektromagnetisk fältteori
EITF80, 9.0 credits, G2 (First Cycle)
Valid for: 2024/25
Faculty: Faculty of Engineering LTH
Decided by: PLED E
Date of Decision: 2024-04-02
Effective: 2024-05-08
General Information
Main field: Technology Depth of study relative to the degree requirements: First cycle, in-depth level of the course cannot be classified
Mandatory for: E3
Elective for: D4
Language of instruction: The course will be given in English
The student shall acquire fundamental knowledge of vector analysis and electromagnetic theory.
The student shall acquire a good ability to perform calculations on given problems.
The student shall acquire good knowledge of the electromagnetic concepts that are used in electrotechnical applications, e.g., electronics, measurement techniques and electric power techniques.
Learning outcomes
Knowledge and understanding
For a passing grade the student must
• be able to explain how electric charge and electric current generate and are affected by electric and magnetic fields.
• be able to use cylindrical coordinates, spherical coordinates, the nabla operator, Stokes´ theorem and Divergence theorem.
• be able to use equations such as Coulomb's law, Biot-Savart law, the law of induction and Maxwell's equations.
• be able to explain concepts such as capacitance, inductance, induction, wave propagation and antenna.
Competences and skills
For a passing grade the student must
• be able to analyse an solve basic problems of electrostatics, magnetostatics, quasistationary and general electromagnetic field theory.
• be able to explain how given problems of electromagnetic field theory can be solved.
Judgement and approach
For a passing grade the student must
• understand that electromagnetic field theory is fundamental for all technique and all science that involves electric, magnetic and electromagnetic fields.
• be able to describe the strength of and the possibilities of a mathematical model of the type that electromagnetic field theory is an example of.
Vector analysis, electrostatics, magnetostatics, induction and general time-dependence. Examples of what is treated in the course are divergence, curl, electric fields in vacuum and in materials,
capacitors, system of conductors, the image method, Biot-Savart law, force, inductance, the law of induction, Maxwell’s equations, plane waves and antennas.
Examination details
Grading scale: TH - (U, 3, 4, 5) - (Fail, Three, Four, Five)
Assessment: Compulsory written test and written examination.
The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination
equivalent to that of a student without a disability.
Code: 0117. Name: Written Examination.
Credits: 6.0. Grading scale: TH - (U, 3, 4, 5). Assessment: Passed written examination. Optional tasks can give bonus points to regular examination results. The module includes: Vector analysis and
electromagnetic field theory.
Code: 0217. Name: Control Examination.
Credits: 3.0. Grading scale: UG - (U, G). Assessment: Passed written examination. The module includes: Vector analysis and electromagnetic field theory.
Admission requirements:
• FMAB30 Calculus in Several Variables
Assumed prior knowledge: FMAA01 or FMAA05 Calculus in one variable, FMA420/FMAB20 Linear algebra.
The number of participants is limited to: No
Kursen överlappar följande kurser: ESS050 ETE055 ETEF01 FMFF01 EITF85
Reading list
• David K. Cheng: Field and Wave Electromagnetics (2nd Edition, Pearson New International Edition). Pearson, 2013, ISBN: ISBN-10:1292026561, ISBN-13: 978-1292026565.
Course coordinator: Buon Kiong Lau, buon_kiong.lau@eit.lth.se
Course homepage: https://www.eit.lth.se/course/eitf80
Further information | {"url":"https://kurser.lth.se/kursplaner/24_25-en/EITF80.html","timestamp":"2024-11-07T15:50:10Z","content_type":"text/html","content_length":"8548","record_id":"<urn:uuid:da4d01cc-1c0d-4e54-9309-a6bc55057313>","cc-path":"CC-MAIN-2024-46/segments/1730477028000.52/warc/CC-MAIN-20241107150153-20241107180153-00719.warc.gz"} |
Differential Equation problem
Differential Equation problem
• Thread starter hibernator
• Start date
In summary, the conversation is about solving a given differential equation using the substitution method and expressing the answer in terms of x and y. The attempt at a solution involves using the
properties of logarithms and integrating, but the final answer differs from the one given in the textbook. The conversation ends with the suggestion to plug the answer back into the original equation
to check its validity.
Homework Statement
Substituition y=vx , differential equation x^2dy/dx = y^2-2x^2 can be show in the form x dv/dx = (v-2)(v+1)
Hence , solve the differential equation x dv/dx = (v-2)(v+1) ,expressing answer in the form of y as a function of x in the case where y > 2x > 0 .
The Attempt at a Solution
I can only show the equation ,but can't solve the equation as the answer is y =x(2+Ax^2) / (1-Ax^2)
Show us what you tried so far.
vela said:
Show us what you tried so far.
I start after from my showing.
x dv/dx = (v-2)(v+1)
dv/dx = (v-2)(v+1) / x
dx/dv = x / (v-x)(v+1)
1/x dx = 1 / (v-2)(v+1) dv
Then I start to integrate , I am still new , so I don't know how to use to type the symbol.Sorry for the inconvenience.
1/x dx = 1/3 ( (1 / (v-2) )- ( 1/ (v+1) ) -----(1/3 from partial fraction )
ln x + c = 1/3 ln (v-2) - ln (v+1)
ln x + c = 1/3 ln (v-2)/(v+1)
Then I forgot know how to continue as i left my exercise book at home. I can only done so far.Then how could I continue ?
hibernator said:
I start after from my showing.
x dv/dx = (v-2)(v+1)
This is wrong. If y= xv then dy/dx= x dv/dx+ v, not just x dv/dx.
-dv/dx = (v-2)(v+1) / x
dx/dv = x / (v-x)(v+1)
1/x dx = 1 / (v-2)(v+1) dv
Then I start to integrate , I am still new , so I don't know how to use to type the symbol.Sorry for the inconvenience.
1/x dx = 1/3 ( (1 / (v-2) )- ( 1/ (v+1) ) -----(1/3 from partial fraction )
ln x + c = 1/3 ln (v-2) - ln (v+1)
ln x + c = 1/3 ln (v-2)/(v+1)
Then I forgot know how to continue as i left my exercise book at home. I can only done so far.Then how could I continue ?
HallsofIvy said:
This is wrong. If y= xv then dy/dx= x dv/dx+ v, not just x dv/dx.
no , I have done using dy/dx= x dv/dx+ v, from the equation x2dy/dx = y2-2x2 .
Use the properties of logarithms:
\log ab &= \log a + \log b \\
b \log a &= \log a^b
and exponentiate to get rid of the logs.
Applying the properties of logarithm, i get
y= x(2+Ax^3)/1-Ax^3
which is supposed to be 'Ax^2?' HmMm.
median27 said:
Applying the properties of logarithm, i get
y= x(2+Ax^3)/1-Ax^3
which is supposed to be 'Ax^2?' HmMm.
Same answer as mine.I got y= x(2+Ax^3)/1-Ax^3 .But the textbook's anwser is saying that 'Ax^2.The textbook probably wrong?
It's straightforward enough to check. Just plug your answer back into the original differential equation and see if it works.
vela said:
It's straightforward enough to check. Just plug your answer back into the original differential equation and see if it works.
I will try , thank you so much for your help ^^
FAQ: Differential Equation problem
1. What is a differential equation?
A differential equation is a mathematical equation that describes how a quantity changes and relates to its rate of change. It involves the use of derivatives to represent the rate of change of a
2. Why are differential equations important?
Differential equations are important because they are used to model and predict real-world phenomena in many fields, including physics, engineering, economics, and biology. They are also the
foundation for many advanced mathematical concepts and techniques.
3. How do you solve a differential equation?
The process of solving a differential equation involves finding a function that satisfies the given equation. This can be done analytically using mathematical techniques such as separation of
variables, substitution, or integrating factors. Alternatively, numerical methods can be used to approximate the solution.
4. What are the types of differential equations?
The main types of differential equations are ordinary differential equations (ODEs) and partial differential equations (PDEs). ODEs involve functions of one variable and their derivatives, while PDEs
involve functions of multiple variables and their partial derivatives.
5. What are some applications of differential equations?
Differential equations have a wide range of applications in fields such as physics, engineering, economics, and biology. They can be used to model and predict the behavior of systems and phenomena,
such as population growth, chemical reactions, and the motion of objects. | {"url":"https://www.physicsforums.com/threads/differential-equation-problem.508055/","timestamp":"2024-11-06T04:33:35Z","content_type":"text/html","content_length":"116536","record_id":"<urn:uuid:e57f3fe8-a640-4411-b91a-4e352d67927c>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00402.warc.gz"} |
A network to catch a fish in
A network to catch a fish in
by Lynn Fortin, 10 May 2019
‘See what you can do with this’ – these words, or certainly these sentiments, have preceded many significant mathematical breakthroughs. What if you were given the ‘problem’ of (re) designing a
mathematics curriculum and nothing but that phrase? What might you do?
William Thomas Tutte (1917 – 2002; generally pronounced ‘tut’) spent most of his life as a research mathematician working in the field of graph theory. Born in Newmarket, Suffolk, he completed his
PhD thesis An Algebraic Theory of Graphs at Cambridge University in 1948. He worked at the University of Toronto and then the newly founded University of Waterloo, Ontario, in 1962, becoming one of
the first members of its Department of Combinatorics and Optimization in 1967, where ‘he advanced graph theory from a subject with one text (D. König’s) toward its present extremely active state, and
he developed Whitney’s definitions of a matroid into a substantial theory’ (Hobbs & Oxley, 2004).
Tutte’s ground-breaking early work in graph theory resonates with those of us working on the Cambridge Maths project as we are using a graph database for the development of our Framework. This is
enabling us not only to capture the content of Mathematics education but, more importantly, to identify and show the connections and progression within that content as well as generating subsets of
the content depending on many different criteria. Our use of nodes, connected by edges, which may show direction, means our Framework is in fact a large, complex graph; Tutte’s work in this area
helped to make it a more mainstream part of mathematics which underpins much of modern research in all fields.
However, there was another part of Tutte’s life for which he should be far better known. ‘As a young mathematician codebreaker, he deciphered a series of German military encryption codes known as
Fish’* (Order of Canada citation, quoted in Younger, 2002). What the citation neglects to mention, however, is that this accomplishment was ‘probably the single biggest intellectual achievement at
Bletchley during World War Two’ (Murrell, 2014).
Most of us have heard of Alan Turing and the remarkable work he and his team at Bletchley Park carried out in breaking the German codes created by the Enigma machine. What is far less well known,
however, is that there was a second machine – Lorenz – which was used by the German Army High Command for its most top-secret communications. Where Enigma used three and eventually four rotors for
encryption, Lorenz used 12 rotors (two sets of five coding wheels and two motor wheels) with 1.6 million billion possible combinations. Throughout WWII – and for decades after the war – the codes it
created were believed by its users to have been unbreakable.
A Lorenz machine with its covers removed to show the rotors. Source: Matt Crypto [Public domain], from Wikimedia Commons
When the Lorenz-coded messages were first intercepted at Bletchley they certainly seemed to be so. Although they had been able to break one message which had carelessly been sent twice using the same
settings, Bletchley’s top cryptanalysts were unable to work out anything about the machine which had produced them. Unlike with Enigma, they had no captured machine or manual to tell them its design
or system – just this one broken message of 4,000 characters. They had ‘no clue as to how the Lorenz cypher worked, other than it produced a stream of key letters that were added to the message
letters … the problem of how those key letters were generated from the info entered by the operator remained’ (Farr, 2017). After several months of trying, they passed the job on to the quiet,
unassuming 24-year-old Bill Tutte with exactly the words we considered previously: ‘See what you can do with this’ (Tutte, 1998).
Captain Jerry Roberts worked in the same office as Tutte and remembered that he ‘saw him staring into the middle distance for extended periods, twiddling his pencil and making endless counts on reams
of paper for nearly three months, and I used to wonder whether he was getting anything done.’ (2017, p. 73). Suffice to say that he was. Using paper, pencils and his mathematical intellect alone,
Bill Tutte found the patterns in the coded sequence which enabled him to establish not only that Lorenz had twelve rotors but also their functions and how many teeth each had. The most challenging
part of cracking Lorenz was broken, but as Tutte himself later remarked somewhat wryly, his feat was hardly recognised at the time: ‘I suppose I would have been said to have broken the key by pure
analytic reasoning. As it was I was thought to have a stroke of undeserved good luck. There must be a moral in this.’ (1998).
Nor has his feat been sufficiently recognised to date. One reason for this is that the breaking of Lorenz remained classified until the 1990s: when Tutte visited Germany after the war and was shown a
Lorenz machine he had to grit his teeth and pretend to agree with the German intelligence officer showing it to him that it was unbreakable (Roberts, 2017, p. 74). Even now information about it is
still only slowly coming to light. What is known is that the broken Lorenz messages allowed the Allies to ‘read Hitler’s intentions and gave insight into his whole military planning and decision
making’ (ibid, p. 135). Roberts asserts that intercepted and decoded Lorenz messages helped to decide the successful Allied strategies for the Battle of Kursk and for the D-Day landings, among other
campaigns, and that General Dwight D. Eisenhower acknowledged they helped to shorten WWII by two years (ibid, p. 220).
It will doubtless never be known exactly how great the contribution the breaking of Lorenz was to the outcome of WWII. The proud tradition of mathematicians who rise tremendously to the occasion of
‘see what you can do with this’ remains, however, and the joy of tackling a problem with only one’s wits, paper and a pencil is an important part of mathematical creativity unlikely to change despite
the developments in technology (which Tutte’s efforts actually helped to bring about) that eventually revolutionised the codebreaking process.
*The workers at Bletchley Park did not know that the machine which produced these codes was called Lorenz. The official name given to it at Bletchley was “Tunny”, and the codebreakers called the
codes it produced “Fish”.
Farr, G (2017) ‘Remembering Bill Tutte: another brilliant codebreaker from World War II’, in The Conversation
Hobbs, Arthur M. and Oxley, James G (2004) ‘William T. Tutte (1917 – 2002)’ in Notices of the American Mathematical Society, Vol. 51, No. 3, pp. 320 – 330
Murrell, Kevin, founding trustee of The National Museum of Computing at Bletchley Park, quoted by the BBC on 10 September 2014
Roberts, J (2017) Lorenz: Breaking Hitler’s Top Secret Code at Bletchley Park. The History Press, Stroud, Gloucestershire
Tutte, W T (1998) ‘FISH and I’. Lecture at the opening ceremony of the Centre for Applied Cryptographic Research (CACR), University of Waterloo
Younger, D (2002) ‘Biography of Professor Tutte’ in Combinatorics and Optimization, University of Waterloo
Join the conversation: You can tweet us @CambridgeMaths or comment below. | {"url":"https://www.cambridgemaths.org/blogs/a-network-to-catch-a-fish-in/","timestamp":"2024-11-05T16:43:34Z","content_type":"text/html","content_length":"35558","record_id":"<urn:uuid:4600cc7d-54ef-49d0-9c45-4067ab13e747>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00353.warc.gz"} |
Recent Developments in Lie Algebras, Groups and Representation Theorysearch
Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
Please make all selections above before adding to cart
Recent Developments in Lie Algebras, Groups and Representation Theory
Hardcover ISBN: 978-0-8218-6917-8
Product Code: PSPUM/86
List Price: $139.00
MAA Member Price: $125.10
AMS Member Price: $111.20
eBook ISBN: 978-0-8218-9392-0
Product Code: PSPUM/86.E
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Hardcover ISBN: 978-0-8218-6917-8
eBook: ISBN: 978-0-8218-9392-0
Product Code: PSPUM/86.B
List Price: $274.00 $206.50
MAA Member Price: $246.60 $185.85
AMS Member Price: $219.20 $165.20
Click above image for expanded view
Recent Developments in Lie Algebras, Groups and Representation Theory
Hardcover ISBN: 978-0-8218-6917-8
Product Code: PSPUM/86
List Price: $139.00
MAA Member Price: $125.10
AMS Member Price: $111.20
eBook ISBN: 978-0-8218-9392-0
Product Code: PSPUM/86.E
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Hardcover ISBN: 978-0-8218-6917-8
eBook ISBN: 978-0-8218-9392-0
Product Code: PSPUM/86.B
List Price: $274.00 $206.50
MAA Member Price: $246.60 $185.85
AMS Member Price: $219.20 $165.20
• Proceedings of Symposia in Pure Mathematics
Volume: 86; 2012; 310 pp
MSC: Primary 17; 20
This book contains the proceedings of the 2009–2011 Southeastern Lie Theory Workshop Series, held October 9–11, 2009 at North Carolina State University, May 22–24, 2010, at the University of
Georgia, and June 1–4, 2011 at the University of Virginia.
Some of the articles, written by experts in the field, survey recent developments while others include new results in Lie algebras, quantum groups, finite groups, and algebraic groups.
Graduate students and research mathematicians interested in representation theory, Lie algebras, quantum groups, and algebraic groups.
□ Articles
□ Pramod N. Achar — Perverse coherent sheaves on the nilpotent cone in good characteristic
□ Christopher P. Bendel, Daniel K. Nakano and Cornelius Pillen — On the vanishing ranges for the cohomology of finite groups of Lie type II
□ Matthew Bennett and Vyjayanthi Chari — Tilting modules for the current algebra of a simple Lie algebra
□ Jon F. Carlson — Endotrivial modules
□ Shun-Jen Cheng, Ngau Lam and Weiqiang Wang — Super duality for general linear Lie superalgebras and applications
□ Jie Du — Structures and representations of affine $q$-Schur algebras
□ Andrew Francis and Lenny Jones — Multiplicative bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group
□ Robert L. Griess Jr. — Moonshine paths and a VOA existence proof of the Monster
□ Robert Guralnick and Gunter Malle — Characteristic polynomials and fixed spaces of semisimple elements
□ David J. Hemmer — “Frobenius twists” in the representation theory of the symmetric group
□ Jonathan Kujawa — The generalized Kac-Wakimoto conjecture and support varieties for the Lie superalgebra $\mathfrak {osp}(m|2n)$
□ Shrawan Kumar — An approach towards the Kollár-Peskine problem via the Instanton Moduli Space
□ G. Lusztig — On the representations of disconnected reductive groups over $F_q$
□ Brian J. Parshall and Leonard L. Scott — Forced gradings in integral quasi-hereditary algebras with applications to quantum groups
□ Brian J. Parshall and Leonard L. Scott — A semisimple series for $q$-Weyl and $q$-Specht modules
• Permission – for use of book, eBook, or Journal content
• Book Details
• Table of Contents
• Additional Material
• Requests
Volume: 86; 2012; 310 pp
MSC: Primary 17; 20
This book contains the proceedings of the 2009–2011 Southeastern Lie Theory Workshop Series, held October 9–11, 2009 at North Carolina State University, May 22–24, 2010, at the University of Georgia,
and June 1–4, 2011 at the University of Virginia.
Some of the articles, written by experts in the field, survey recent developments while others include new results in Lie algebras, quantum groups, finite groups, and algebraic groups.
Graduate students and research mathematicians interested in representation theory, Lie algebras, quantum groups, and algebraic groups.
• Articles
• Pramod N. Achar — Perverse coherent sheaves on the nilpotent cone in good characteristic
• Christopher P. Bendel, Daniel K. Nakano and Cornelius Pillen — On the vanishing ranges for the cohomology of finite groups of Lie type II
• Matthew Bennett and Vyjayanthi Chari — Tilting modules for the current algebra of a simple Lie algebra
• Jon F. Carlson — Endotrivial modules
• Shun-Jen Cheng, Ngau Lam and Weiqiang Wang — Super duality for general linear Lie superalgebras and applications
• Jie Du — Structures and representations of affine $q$-Schur algebras
• Andrew Francis and Lenny Jones — Multiplicative bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group
• Robert L. Griess Jr. — Moonshine paths and a VOA existence proof of the Monster
• Robert Guralnick and Gunter Malle — Characteristic polynomials and fixed spaces of semisimple elements
• David J. Hemmer — “Frobenius twists” in the representation theory of the symmetric group
• Jonathan Kujawa — The generalized Kac-Wakimoto conjecture and support varieties for the Lie superalgebra $\mathfrak {osp}(m|2n)$
• Shrawan Kumar — An approach towards the Kollár-Peskine problem via the Instanton Moduli Space
• G. Lusztig — On the representations of disconnected reductive groups over $F_q$
• Brian J. Parshall and Leonard L. Scott — Forced gradings in integral quasi-hereditary algebras with applications to quantum groups
• Brian J. Parshall and Leonard L. Scott — A semisimple series for $q$-Weyl and $q$-Specht modules
Permission – for use of book, eBook, or Journal content
Please select which format for which you are requesting permissions. | {"url":"https://bookstore.ams.org/PSPUM/86","timestamp":"2024-11-08T18:52:21Z","content_type":"text/html","content_length":"99824","record_id":"<urn:uuid:3f77e87e-85d6-4cc8-9dc6-f3fefb37aa08>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00808.warc.gz"} |
RD Sharma Class 6 Solutions Chapter 6 - Fractions (Ex 6.5) Exercise 6.5 - Free PDF
Free PDF download of RD Sharma Class 6 Solutions Chapter 6 - Fractions Exercise 6.5 solved by Expert Mathematics Teachers on Vedantu. All Chapter 6 - Fractions Ex 6.5 Questions with Solutions for RD
Sharma Class 6 Maths to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.
FAQs on RD Sharma Class 6 Solutions Chapter 6 - Fractions (Ex 6.5) Exercise 6.5
1. How to convert mixed fractions to proper fractions in questions from Class 6 chapter 6 fractions?
Class 6 students are often asked to convert the mixed fractions to proper fractions during their exams. Certain steps that can make these types of questions easy for class 6 students to solve are:
• Identify the whole number, the numerator, and the denominator of the proper fraction. The numerator is usually the number written on the top of the fraction while the denominator is the number
written at the bottom of the fraction.
• Now, for converting the mixed fraction to a proper fraction multiply the whole number to the denominator and then add the product to the numerator and divide the whole to the denominator.
2. How can I convert improper fractions to mixed fractions in Exercise 6.5 of Chapter 6, fractions?
Class 6 students are often asked to convert the improper fractions to mixed fractions during their exams. Certain steps that can make these types of questions easy for Class 6 students to solve are:
• Identify the numerator and the denominator of the improper fraction. The numerator is usually the number written on the top of the fraction while the denominator is the number written at the
bottom of the fraction.
• Now, to convert this improper fraction to a mixed fraction divide the fraction and write the quotient of the division as a whole number, the remainder of the division as the numerator while the
denominator of the fraction remains as it is.
3. How to represent fractions on a number line in Exercise 6.5 of Chapter 6 of Class 6?
Representation of fractions on the number line is one of the easiest questions that can be asked to Class 6 students in their exam. These types of questions require the students to remember the
concept of representation of whole numbers on a number line studied in the previous class. Suppose, you want to represent ½ on a number line, then simply draw a number line and locate the 0-1 region
on the number line. Now divide this line into two equal halves and denote it as ½. Now, suppose you want to represent ¼ on a number line, then fetch the 0-1 range on a number line and divide it into
four equal halves. The first half that is close to 0 denotes ¼.
4. What are like fractions and unlike fractions discussed in Class 6 Chapter 6 Fractions?
Class 6 students come across new terms, that is, like fractions and unlike fractions in their maths chapter 6, that is, fractions. Like fractions generally refer to fractions that have the same
denominator, for example, ⅓, ⅔, are like fractions and ¼, ¾ are also like fractions. The unlike fractions discussed in chapter 6 of class 6 are the fractions that have different denominators. For
example, ⅓, ⅖ are unlike fractions.
5. How can I compare fractions that have different denominators and the different numerators in Exercise 6.5 of Chapter 6 Class 6?
Exercise 6.5 of class 6 chapter 6, that is, fractions contains questions where the students are required to compare two fractions who have different numerators and denominators as well. This type of
comparison is simple if you keep the steps in mind. Comparing fractions with different numerators and denominators is solved using the technique of equivalent fractions. Each fraction in the
question is converted to an equivalent fraction such that they become like fractions and then one can simply compare both these fractions. To convert the fractions into equivalent fractions first
find the LCM of the denominators, then convert the fractions into equivalent fractions such that the denominator of both the fractions is the LCM. now, since both the fractions are equivalent to
each other, you can easily compare both the fractions. | {"url":"https://www.vedantu.com/rd-sharma-solutions/class-6-maths-chapter-6-exercise-6-5","timestamp":"2024-11-11T10:37:41Z","content_type":"text/html","content_length":"177104","record_id":"<urn:uuid:9c3f9873-5ecf-4633-9284-b0c5ee2692f4>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00435.warc.gz"} |
Convolution II: Impulse inputs | JustToThePointConvolution II: Impulse inputs
The scariest monsters are the ones that lurk within our souls, Edgar Allen Poe.
Differential equations
An algebraic equation is a mathematical statement that declares or asserts the equality of two algebraic expressions. These expressions are constructed using:
1. Dependent and independent variables. Variables represent unknown quantities. The independent variable is chosen freely, while the dependent variable changes in response to the independent
2. Constants. Fixed numerical values that do not change.
3. Algebraic operations. Operations such as addition, subtraction, multiplication, division, exponentiation, and root extraction.
Definition. A differential equation is an equation that involves one or more dependent variables, their derivatives with respect to one or more independent variables, and the independent variables
themselves, e.g., $\frac{dy}{dx} = 3x +5y, y’ + y = 4xcos(2x), \frac{dy}{dx} = x^2y+y, etc.$
It involves (e.g., $\frac{dy}{dx} = 3x +5y$):
• Dependent variables: Variables that depend on one or more other variables (y).
• Independent variables: Variables upon which the dependent variables depend (x).
• Derivatives: Rates at which the dependent variables change with respect to the independent variables, $\frac{dy}{dx}$
The Existence and Uniqueness Theorem provides crucial insight into the behavior of solutions to first-order differential equations ODEs. It states that if:
• The function f(x, y) (the right-hand side of the ODE) in y’ = f(x, y) is continuous in a neighborhood around a point (x[0], y[0]) and
• Its partial derivative with respect to y, $\frac{∂f}{∂y}$, is also continuous near (x[0], y[0]).
Then the differential equation y' = f(x, y) has a unique solution to the initial value problem through the point (x[0], y[0]) .
A first-order linear differential equation (ODE) has the general form: a(x)y' + b(x)y = c(x) where y′ is the derivative of y with respect to x, and a(x), b(x), and c(x) are functions of x. If c(x) =
0, the equation is called homogeneous, i.e., a(x)y’ + b(x)y = 0.
The equation can also be written in the standard linear form as: y’ + p(x)y = q(x) where $p(x)=\frac{b(x)}{a(x)}\text{ and }q(x) = \frac{c(x)}{a(x)}$
A second-order linear homogeneous differential equation ODE with constant coefficients is a differential equation of the form: y'' + Ay' + By = 0 where:
• y is the dependent variable (a function of the independent variable t),
• y′ and y′′ are the first and second derivatives of y with respect to t,
• t is the independent variable,
• A and B are constants.
This equation is homogeneous, meaning that there are no external forcing terms (like a function of t) on the right-hand side.
Laplace Transform
The Laplace Transform of a function f(t), where t ≥ 0, is defined as $\mathcal{L}(f(t)) = \int_{0}^{∞} f(t)e^{-st}dt = F(s)$.
One of the most important properties of the Laplace Transform is linearity, which states: $\mathcal{L}(af(t)+bg(t)) = a\mathcal{L}(f(t))+b\mathcal{L}(g(t))$
Function Laplace Transform
u(t) $\mathcal{L}(u(t)) = \frac{1}{s}, s > 0$
$e^{at}$ $\frac{1}{s - a}, s > a$
$e^{(a + bi)t}$ $\mathcal{L}(e^{(a + bi)t}) = \frac{1}{s - (a + bi)}, s > a$
$\cos(\omega t)$ $\mathcal{L}(\cos(\omega t)) = \frac{s}{s^2 + \omega^2}, s > 0$
$\sin(\omega t)$ $\mathcal{L}(\sin(\omega t)) = \frac{\omega}{s^2 + \omega^2}, s > 0$
$t^n$ $\mathcal{L}(t^n) = \frac{n!}{s^{n+1}}, s > 0$
$u(t-a)$ $\mathcal{L}(u(t-a)) = \frac{e^{-as}}{s}, s > 0$
$\delta(t-a)$ $\mathcal{L}(\delta(t-a)) = e^{-as}, a \geq 0$
$\frac{1}{t}$ $\mathcal{L}\left(\frac{1}{t}\right) = \text{not defined}$
$e^{-bt} \cos(\omega t)$ $\mathcal{L}(e^{-bt} \cos(\omega t)) = \frac{s + b}{(s + b)^2 + \omega^2}, s > -b$
$e^{-bt} \sin(\omega t)$ $\mathcal{L}(e^{-bt} \sin(\omega t)) = \frac{\omega}{(s + b)^2 + \omega^2}, s > -b$
$e^{at}f(t)$ $\mathcal{L}(e^{at}f(t)) = F(s-a)$
This is the Exponential Shift Theorem, indicating that multiplying a function by an exponential term shifts its Laplace Transform.
Besides, $\mathcal{L}(f’(t)) = sF(s)-f(0), \mathcal{L}(f’’(t)) = s^2F(s)-sf(0)-f’(0)$
Impulse inputs
In the study of differential equations and physical systems, impulse inputs represent sudden forces applied over a very short period of time. These impulses model events like a hammer strike or a
collision, where a large force is exerted briefly.
If f(t) is a force applied over time, the impulse delivered over the time interval [a, b] is defined as: Impulse = $\int_{a}^{b} f(t)dt$.
The impulse represents the total effect of a force applied over a time interval, accounting for both the magnitude and the duration of the force.
In the case where f(t) is a constant force F, then the impulse simplifies to: Impulse = $\int_{a}^{b} f(t)dt = F\int_{a}^{b} dt = F·(b-a)$. The total impulse is proportional to the magnitude of the
force and the duration over which it is applied.
Modeling an Impulse with the Box Function
Consider an undamped mass-spring system with mass m. When an impulse is applied, we can model the force over a small time interval, say [0, h], e.g., image applying a short burst of force to the mass
over this brief period (Refer to Figure i for a visual representation and aid in understanding it), by using a box function.
In mathematical terms, to represent an impulse of area 1 (a unit impulse), the height of the force during the interval must be: ^1⁄[h]. This reflects that as the time interval becomes shorter, the
magnitude of the force must increase to maintain the total impulse (area under the curve) as 1.
To represent an impulse of area 1 (a unit impulse), we define the force function f(t) as: $f(t) = \frac{1}{h}[u(t) -u(t-h)]$ where u(t) is the Heaviside Step Function, u(t) -u(t-h) is the unit box
function u[0h](t), which is 1 in the interval [0, h] and 0 elsewhere.
Impulse = $\int_{a}^{b} f(t)dt = \int_{0}^{h} \frac{1}{h}[u(t) -u(t-h)]dt = \int_{0}^{h} \frac{1}{h}dt = 1$.
• As the time interval h becomes very small, the force magnitude $\frac{1}{h}$ becomes very large to maintain a constant impulse of 1.
• This reflects the idea that an impulse is a very large force applied over an infinitesimally small time period.
Equation of Motion with an Impulse
The equation of motion for the undamped mass-spring system under the action of the impulse is: $y'' + y = {1}{h}[u(t) -u(t-h)]dt = \frac{1}{h}u_{0h}(t)$ where:
• y(t) is the displacement of the mass from its equilibrium position.
• y′′ +y = 0 is the homogeneous equation describing the natural oscillations of the system.
• u[0h](t) = u(t) - u(t-h) is a box function representing a force that turns on at t = 0 and turns off at t = h.
• The right-hand side, $\frac{1}{h}u_{0h}(t)$, represents the force of height ^1⁄[h] applied over the interval [0, h]
Laplace Transform Solution
Step 1: Laplace Transform of the Forcing Function
To solve this equation in the Laplace domain, recall the Laplace Transform of a step function: $u(t) \leadsto \frac{1}{s}, u(t-a) \leadsto e^{-as}\frac{1}{s}$
Thus, applying this to the box function $u_{ab}(t) = u_a(t)-u_b(t) = u(t-a)-u(t-b)$, a = 0, b = h:
$\frac{1}{h}u_{0h}(t) = \frac{1}{h}[u(t)-u(t-h)] \leadsto \frac{1}{h}[\frac{1}{s}-\frac{e^{-hs}}{s}] = \frac{1-e^{-hs}}{hs}$
$\frac{1}{h}u_{0h}(t) \leadsto \frac{1-e^{-hs}}{hs}, \mathcal{L}(\frac{1}{h}[u(t)-u(t-h)]) = \frac{1-e^{-hs}}{hs}$
Step 2: Taking the Limit as h → 0
As the width h of the impulse interval approaches zero (h → 0), we get: $\lim_{h \to 0} \frac{1-e^{-hs}}{hs} =[\text{Let u = hs}] \lim_{u \to 0} \frac{1-e^{-u}}{u} =[\text{L’Hospital’s rule }] \lim_
{u \to 0} \frac{e^{-u}}{1} = 1$.
On the other side of the Laplace Transform, as h approaches zero, the box function $\frac{1}{h}u_{0h}(t)$ approaches the Dirac delta function, denoted by δ(t).
Conclusion. The Laplace Transform of the Dirac Delta Function is $\mathcal{L}(δ(t)) = 1$.
As h → 0, the interval [0, h] get smaller and smaller and the value of the function at 0 goes to infinity.
The Dirac delta function δ(t), also known as the unit impulse, is not a function in the traditional sense but a a generalized function on the real numbers or distribution, whose value is zero
everywhere except at zero t = 0, and whose integral over the entire real line is equal to one, $\int_{-∞}^{∞} δ(t)dt = 1$ (Refer to Figure ii for a visual representation and aid in understanding it),
and for any continuous function f(t) = $\int_{-∞}^{∞} δ(t)f(t)dt = f(0)$ (🚀)
δ(t) is zero everywhere except at t = 0, where it is “infinite” in such a way that its integral over any interval containing t = 0 is 1.
The Sifting Property
The most important property of the Dirac delta function is the sifting property, which states that for any function g(t) that is continuous at t = a: $\int_{-∞}^{∞} δ(t-a)g(t)dt = g(a)$. In other
words, The delta function “picks out” the value of g(t) at t = a.
$δ_a = \begin{cases} ∞, &t = a \\ 0, &t ≠ a \end{cases}$
The Mean Value Theorem for Integrals states that if f(t) is continuous on the closed interval [a, b], then there exists a point c ∈ [a,b] such that: $\int_{a}^{b} f(t)dt = (b-a)f(c)$
The total area under f(t) from a to b equals the area of a rectangle with width b − a and height f(c).
Let δ[a, ε] be an approximation of the delta function (Rectangular Pulse Approximation) such that is zero outside [a, a + ε] and it has a constant height of $\frac{1}{ε}$
$δ_{a, ε} = \begin{cases} \frac{1}{ε}, &t ∈ [a, a + ε] \\ 0, &otherwise \end{cases}$
Let’s calculate: $\int_{0}^{∞} δ_{a, ε}(t)g(t)dt = \int_{a}^{a+ ε} \frac{1}{ε}g(t)dt =[\text{Th. Mean Value Theorem for Integrals}] ε·\frac{1}{ε}g(c) = g(c)$ where c ∈ [a, a + ε]
Taking the Limit as ε → 0, the interval [a, a+ε] shrinks to the point a, then c → a, hence $\int_{0}^{∞} δ_{a, ε}(t)g(t)dt → g(a)$.
Therefore, $\int_{0}^{∞} δ_a(t)g(t)dt = g(a)$
Special Case: a = 0, the Dirac delta function becomes δ(t), centered at the origin. f(t) = $\int_{-∞}^{∞} δ(t)f(t)dt = f(0)$
Since δ(t) is zero everywhere except at t = 0, the integral picks out the value of f(t) at t = 0.
Another property is: $\frac{d}{dt}u(t-a)=δ_a(t)$
Laplace Transform of the Dirac Delta Function
The Laplace Transform of the Dirac Delta Function is: $\mathcal{L}(δ(t)) = \int_{0}^{∞} e^{-st}δ(t)dt = e^{-s·0} = 1$. The delta function picks out the value of f(t) = e^-st at t = 0 🚀, which is 1.
This makes the delta function a powerful tool in modeling instantaneous forces or idealized impulses, as it encapsulates the idea of applying a force over an infinitesimally small time period (a
force that acts instantaneously at t = 0, e.g., if you strike a mass-spring system with a hammer), while still imparting a finite impulse.
Convolution with the Delta Function
In the context of the Laplace Transform, we typically deal with causal functions —functions that are defined to be zero for t < 0.
Next, we explore how the delta function behaves under convolution. Let f be an arbitrary function. The convolution of f(t) with the delta function δ(t) is defined as: (f * δ)(t) = $\int_{0}^{t} f(τ)δ
(t - τ)dτ = f(t)$
Since δ(t - τ) is non-zero only when τ = t. If t ≥ 0, τ = t is withing [0, t]. The integral 🚀 reduces to f(t).
In the Laplace domain, convolution becomes multiplication. The Laplace Transform of δ(t) is 1, so:
$u(t)f(t) * δ(t) \leadsto_{\mathcal{L}} F(s)·1, u(t)f(t)\leadsto_{\mathcal{L}} F(s)$. Therefore, u(t)f(t) * δ(t) = u(t)f(t). In other words, the delta function acts as the identity under
convolution,, effectively “sampling” the function at t. In other words, convolving any function with δ(t) simply reproduces the original function. This property reflects the nature of the delta
function as a mathematical “impulse” that isolates the behavior of a system at a specific moment in time.
Additionally, the derivative of the step function u(t) is the delta function: u’(t) = δ(t).
The step function jumps from 0 to 1 at t = 0, and its derivative is the delta function at that point.
Undamped Mass-Spring System with an Impulse
Consider an undamped mass-spring system where the mass m is attached to a spring. The system is subjected to (“kicked with”) an impulse of magnitude A applied at time t = ^π⁄[2]. The initial
conditions are given as: y(0) = 1, y’(0) = 0.
The goal is to solve the differential equation that governs the motion of the system using the Laplace Transform.
The assumption “kicked with impulse A at t = ^π⁄[2] can be expressed mathematically using the Dirac delta function $Aδ(t-\frac{π}{2})$, which models the instantaneous application of force at t = ^π⁄
Therefore, the model that control our motion is $y'' + y = Aδ(t-\frac{π}{2})$ where
• y is the displacement of the mass from its equilibrium position.
• The term y′′ +y = 0 describes the natural behavior of an undamped mass-spring system, which would oscillate without any external force.
• The term Aδ(t -^π⁄[2]) introduces the external force, modeled as an impulse of magnitude A applied at t = ^π⁄[2].
Solve the differential equation using Laplace Transforms to find y(t).
Using the standard Laplace Transform rules: $\mathcal{L}(y’’) = s^2Y(s) −sy(0) −y’(0), \mathcal{L}(y) = Y(s), \mathcal{L}(Aδ(t-\frac{π}{2})) = Ae^{\frac{-π}{2}s}$, the model’s equation Laplace
Transform is $s^2Y -s +Y = Ae^{\frac{-π}{2}s} ↭ (s^2+1)Y - s = Ae^{\frac{-π}{2}s}$. Then, we solve by $Y = \frac{s}{s^2+1} + \frac{Ae^{\frac{-π}{2}s}}{s^2+1}$.
We now take the Inverse Laplace Transform to find y(t) in the time domain. The expression for Y(s) consists of two terms that we can invert separately:
The first term is a standard Laplace Transform, and its inverse is: $\frac{s}{s^2+1} \leadsto_{\mathcal{L^{-1}}} cos(t)$
For the second term, we use the T-axis translation formula: $u(t-a)f(t-a) \leadsto e^{-as}F(s)$ where $F(s) = \frac{A}{s^2+1}$, and $\mathcal{L}^{-1}(\frac{A}{s^2+1}) = A·sin(t)$. Therefore, $\
mathcal{L}^{-1}(\frac{Ae^{\frac{-π}{2}s}}{s^2+1}) = u(t-\frac{π}{2})Asin(t-\frac{π}{2})$
Therefore y(t) = $cos(t) + Au(t-\frac{π}{2})sin(t-\frac{π}{2})$
Simplify the expression. $sin(t-\frac{π}{2}) = -cos(t)$
$sin(t-\frac{π}{2}) = sin(t)cos(\frac{π}{2}) -cos(t)sin(\frac{π}{2}) = sin(t)·0 -cos(t)·1 = -cos(t)$
$y = \begin{cases} cos(t), &0 ≤ t ≤ π/2 \\ cost(t) -Acos(t), &t ≥ π \end{cases}$
$y = \begin{cases} cos(t), &0 ≤ t ≤ π/2 \\ (1 - A)cos(t), &t ≥ π/2 \end{cases}$
Refer to Figure iii for a visual representation and aid in understanding it.
Interpretation. 0 ≤ t ≤ π/2, The system oscillates naturally with displacement y(t) = cos(t). No external force has been applied yet. At t = π/2, an impulse of magnitude A is applied. This causes an
instantaneous change in the amplitude of the oscillations. t ≥ π/2, The amplitude of the oscillations is scaled by (1 −A). The system continues to oscillate, but the amplitude is altered due to the
Solving a Second-Order Linear Differential Equation with Periodic Impulses Using Laplace Transforms
Consider an undamped mass-spring system where:
• Mass m: Attached to a spring with stiffness k k (for simplicity, set k = 1 for normalization).
• Displacement y(t): Represents the displacement of the mass from its equilibrium position at time t.
• Impulse Force f(t): External forces applied as impulses at specific times.
The system is subjected to impulses (e.g. a hammer) at times t = nπ for n = 0, 1, 2,…. These impulses can be modeled using the Dirac delta function δ(t− nπ), which represents an instantaneous force
applied at t = nπ.
Therefore, the differential equation governing the motion of the system is: $y'' + y = \sum_{n=0}^\infty δ(t-nπ)$. Initial conditions y(0) = y’(0) = 0. These conditions indicate that the system
starts from rest with no initial displacement or velocity.
The goal is to solve the differential equation that governs the motion of the system using the Laplace Transform.
Using the standard Laplace Transform rules: $\mathcal{L}(y’’) = s^2Y(s) −sy(0) −y’(0), \mathcal{L}(y) = Y(s), \mathcal{L}(δ(t-a)) = e^{-as}$, the model’s equation Laplace Transform is $\mathcal{L}
(y’’)+\mathcal{L}(y) = \mathcal{L}(y)(\sum_{n=0}^\infty δ(t-nπ)) ↭ s^2Y +Y = \sum_{n=0}^\infty e^{-nπs} ↭ (s^2+1)Y = \sum_{n=0}^\infty e^{-nπs}$. Then, we solve by $Y = \sum_{n=0}^\infty \frac{e^
Recall $u(t-a)f(t-a) \leadsto e^{-as}F(s)$, where F(s) = $\frac{1}{s^2+1}, \mathcal{L}^{-1}(\frac{1}{s^2+1}) = sin(t)$.
$Y(t) = \sum_{n=0}^\infty u(t -nπ)sin(t -nπ)$
Recall sin(t -nπ) = (-1)^nsin(t) and observe for any arbitrary t: nπ < t < (n+1)π, u(t -nπ) = 0 for t < nπ.
$Y(t) = sin(t)\sum_{n=0}^\infty (-1)^n·u(t -nπ)$
Y(t) = sin(t) -sin(t) + ··· + (-1)^nsin(t)
$Y(t) = \begin{cases} sin(t), &n,even \\ 0, &n,odd \end{cases}$
The system oscillates naturally with displacement y(t) = sin(t). An impulse is applied, instantaneously altering the system’s state. The system alternates between oscillating and being at rest due to
the periodic impulses.
General Second-Order Linear Differential Equation and Its Solution Using Laplace Transforms
In this explanation, we will explore how to solve a general second-order linear differential equation using Laplace Transforms.
We begin by considering the following general second-order linear differential equation: y’’ + ay’ + by = f(t) where:
• y(t) is the output or response of the system (e.g., the displacement of a mass, the voltage in a circuit, etc.).
• f(t) is the input or external forcing function (e.g., an applied force or voltage).
• a and b are constants related to the physical parameters of the system, such as damping coefficient or stiffness in mechanical systems.
• The initial conditions are given as y(0) = 0 and y′(0) = 0, meaning the system starts from rest.
Applying the Laplace Transform
Recall the following properties of the Laplace Transform: $\mathcal{L}(y’’(t))=s^2Y(s)-sy(0)-y’(0) =[\text{Applying initial conditions}] s^2Y(s), \mathcal{L}(y’(t)) = sY(s)-y(0) = [\text{Applying
initial conditions}] = sY(s), \mathcal{L}(y(t)) = Y(s), \mathcal{L}(f(t)) = F(s)$
The Laplace transform of the equation y’’ + ay’ + by = f(t) is $s^2Y +aSY + bY = F(s)$. Combining like terms: $(s^2 +aS + b)Y = F(s)$.
Solve for Y: $Y = F(s)·\frac{1}{s^2+as+b}$
The term $\frac{1}{s^2+as+b}$ is referred to as the transfer function of the system, denoted by W(s). The transfer function describes how the system responds to inputs in the Laplace (frequency)
The inverse Laplace transform of the transfer function, $\mathcal{L}^{-1}(\frac{1}{s^2+as+b}) = W(t)$ is called the weight function (or impulse response function). It represents the system’s response
over time to a unit impulse applied at t = 0.
Solution in the Time Domain Using Convolution
The solution y(t) in the time domain can be found by taking the inverse Laplace Transform of Y(s):
Taking the inverse Laplace transformation: $y(t) = f(t)*W(t)$. Thus, the solution in the time domain can be written as a convolution between the input function f(t) and the weight function W(t).
By the definition of convolution, this is written as: $y(t)= \int_{0}^{t} f(u)W(t-u)du$
To understand what W(t) represents, consider the following scenario: we subject the system to a unit impulse δ(t), which is a sharp “kick” (unit impulse) applied at t = 0. This is equivalent to
solving the differential equation with f(t) = δ(t)
So, the equation becomes: y’’ + ay’ + by = δ(t) with initial conditions y(0) = 0 = y’(0).
Taking the Laplace Transform yields: $s^2Y’’ + asY + bY = 1 ⇒[\text{Solving for Y}] Y = \frac{1}{s^2+as+b}$, and taking its inverse Laplace transform: $y(t) = δ(t)*W(t) = W(t)$. Therefore, the weight
function W(t) is the solution to to the system when it is subjected to an impulse at t = 0 and starts from rest. It characterizes how the system responds over time to a sudden or sharp impulse
This content is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License and is based on MIT OpenCourseWare [18.01 Single Variable Calculus, Fall 2007].
1. NPTEL-NOC IITM, Introduction to Galois Theory.
2. Algebra, Second Edition, by Michael Artin.
3. LibreTexts, Calculus and Calculus 3e (Apex). Abstract and Geometric Algebra, Abstract Algebra: Theory and Applications (Judson).
4. Field and Galois Theory, by Patrick Morandi. Springer.
5. Michael Penn, and MathMajor.
6. Contemporary Abstract Algebra, Joseph, A. Gallian.
7. YouTube’s Andrew Misseldine: Calculus. College Algebra and Abstract Algebra.
8. MIT OpenCourseWare [18.03 Differential Equations, Spring 2006], YouTube by MIT OpenCourseWare. | {"url":"https://justtothepoint.com/calculus/convolution2/","timestamp":"2024-11-14T04:03:44Z","content_type":"text/html","content_length":"40227","record_id":"<urn:uuid:a034e636-85d5-4339-bd90-e6b97c65f2d0>","cc-path":"CC-MAIN-2024-46/segments/1730477028526.56/warc/CC-MAIN-20241114031054-20241114061054-00178.warc.gz"} |
Find the number of subarrays where the even numbers appear odd number of times. - Codeforces
I was solving subarray problems the other day and came up with the above problem. I searched it online. I just wanted to solve it and submitted it to a judge. But I could not find such a problem. Do
you guys happen to have encounter such a problem somewhere?
4 weeks ago, # |
» +6
utkarsh_108 This problem is the same concept you want. You need to find subarray where even appears odd no time but in this problem you have to find odd number appears odd number of time because odd
number appeared odd times so the sum is odd
• » 4 weeks ago, # ^ |
» +6
Gismet Yes, indeed it is almost the same thing I want. Thank you.
4 weeks ago, # |
You can re-structure the problem like ->
» assign 0 to every odd number and 1 to every even number, now you just need to find the subarray which have XOR = 1, For this you can maintain prefix_XOR AND count of prefix XOR'S since
the XOR Value will either be 1 or 0 only.
Taking index i as the right end point of the subarray you will do ->
ans += prefix_count[prefix_xor[i]^1];
and u will update prefix_count[prefix_xor[i]]++;
• » 4 weeks ago, # ^ |
» ← Rev. 3 → 0
utkarsh_108 Damm!! this is a nice idea for solving these types of problems. thanks for the amazing approach
• » 4 weeks ago, # ^ |
» 0
Gismet That is a good idea. Thank you. | {"url":"https://codeforces.net/blog/entry/134916","timestamp":"2024-11-04T20:31:48Z","content_type":"text/html","content_length":"101255","record_id":"<urn:uuid:d792bf41-5080-48e1-8fd6-b94f54bf994a>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00119.warc.gz"} |
Advanced Mathematical Formulas using the M Language
By: John Miner | Updated: 2015-12-03 | Comments | Related: > Power BI
The Power BI desktop designer is a great tool and in this tip we will look at advanced mathematical formulas using the M language.
The first step of any Power BI project is to load data into the model. The image below explains the process flow for Power Query, but still applies to the Power BI desktop designer. Today, we will
connect to our Excel data source. We will be writing advanced mathematical formulas in the M language. Since we are working with only one dataset, there will be no combining of data. As a result of
our actions, the data is available (shared) for reporting.
Find the home menu on the Power BI desktop designer. Click the Get Data option on the ribbon. Click more at the bottom of the drop down box of most common selections. Choose the FILE option on the
left pane. Last but not least, select MS Excel as the import file type.
Browse to the location of the "advance-math.xls" file. This is a simple data set that I crafted for this tip. You can download the file from this link.
Clicking the OPEN button loads the data into a preview view window. Select the "Sample Data" worksheet as the source. The user can either LOAD the data without manipulation, EDIT the data or CANCEL
the current operation.
Please choose the EDIT option to manipulate the data using a set of steps in a query.
We can see that the last column needs to be removed from the data set. Also, the first row needs to be promoted as a header. When it is possible, fixing data at the source will reduce the number of
query steps. Each step can be equated to some amount of processing on your laptop. Thus, adding to the over time to load the data. In your Sample Data set, I already removed column 7.
Again, please promote the top most line to a header. Change the data type of the [ZeroSum], [Root] and [Power] columns to integers. Convert the data type of [Dividend] and [Divisor] columns to
decimals. This task can be done by right clicking the column and selecting change type action from the menu. Choose the correct type in the sub-menu.
The sample data set contains the following columns: [IsNumber] contains alpha numeric data; [ZeroSum] contains negative, positive, odd and even numbers; [Dividend] & [Divisor] contain real numbers
for division; and the [Root] & [Power] contain integer values.
We will be using this data with our advanced mathematical formulas.
If you followed the instructions correctly, the resulting M language query should look like the one above. The Excel.Workbook function tells the M language the content type of the file. Since there
can be multiple worksheet in any MS Excel file, the Source function selects the correct data.
Data Type Conversions in Power BI
Many times, a BI Developer needs to convert from a textual format to a numerical format. How can we accomplish this task?
The Number.From function allows for the conversion of a text value to a numeric value.
However, the results are just not appealing. Any value that is a number is correctly converted to a number. All null values result in a null value result. Any non-numeric characters in the input
results in a error value. In this format, we can not apply any aggregations during reporting.
Like most languages, the M language has implemented error handling. Start the computed column with the try clause and catch errors with the otherwise clause. To allow for aggregation, we will convert
the data to a number. If there is an error during conversion, we will return a zero value.
The [Convert2Number] column now contains data that we can report on. I just touched the tip of the iceberg when it comes to these functions.
Numerical Formulas in Power Query Formula Language
The Power Query formula language informally know as "M" supplies the developer with a bunch of functions on information and operations involving numerical data. Let us start looking at the
informational functions using the [ZeroSum] column. We will be adding computed columns to our Sample Data set to demonstrate each function.
M Language Number.IsOdd Function
We can determine if a number is odd by calling the Number.IsOdd function.
M Language Number.IsEven Function
We can determine if a number is even by calling the Number.IsEven function.
M Language Number.Abs Function
We can determine the magnitude (size) of a number by calling the Number.Abs function.
M Language Number.Sign Function
We can determine the sign a number by calling the Number.Sign function. It returns a value of -1 for negative numbers and 1 for positive numbers.
Most of the results seen below are what you expect from the functions.
The [OddNumber] column seems to have a odd nature. No pun intended. The function does not work with negative numbers. The definition of a odd number by www.mathisfun.com is "Any integer (not a
fraction) that cannot be divided exactly by 2."
I have submitted a bug request to the Microsoft Power BI team. However, how can we work around this bug right now?
The quickest fix to the problem is to re-write the formula as Number.IsOdd(Number.Abs([ZeroSum])). Another solution is to define a function in the M language that tests if the number is an integer
and determines if 2 does not evenly divide the number.
Numerical Operations in the M Language
Now, we can concentrate on non-trigonometric, numerical operations supported by the M language. We will be adding computed columns to our Sample Data set to demonstrate each function. Each function
can be used to solve a specific mathematical question.
M Language Number.IntegerDivide Function
How many times the [Divisor] divides into [Dividend] evenly? This question can be answered by calling the Number.IntegerDivide function.
M Language Number.Mod Function
What is the remainder of the [Dividend] divided by the [Divisor]? The answer to the question can be found by calling the Number.Mod function.
The results below are from a sample use of the Number.IntegerDivide and Number.Mod functions.
M Language Number.Power Function
The power (exponent) of a number says how many times to use the number (base) in a multiplication. The image below shows 2 raised to the fourth power.
How do we raise a number to the two's power? This is also know as squaring the number. We can use the Number.Power function on the [Power] column to investigate this question.
M Language Number.Sqrt Function
The opposite (inverse) of squaring a number is taking the square root of a number. I am only talking about positive squared results. Otherwise, we will have to talk about i imaginary numbers. In
short, every positive square has two roots, a positive one and a negative one. Thus, we can replace 3 with -3 in the image below and have the same balanced equation.
The image below depicts the use of the Number.Sqrt function on the [Root] column. Almost all languages return just the positive square root of any number.
M Language Number.Factorial Function
The factorial function, expressed with the ! symbol, is defined as the multiplication of a series of descending natural numbers. Thus, three factorial written as 3! = 3 x 2 x 1 = 6. The image below
illustrates the [Power] column expressed as a factorial using the Number.Factorial function.
The results below are from a sample calls to the Number.Power, Number.Sqrt, and Number.Factorial functions.
M Language Number.Exp Function
Euler's number, expressed as a lower case e, is an important mathematical constant and is the base of the natural logarithm. It is approximately equal to 2.71828. The exponential function raises e to
the power of x. This can be represented mathematically as (e ^ x).
The formula below defines the [Exp] column as the result of calling the Number.Exp function with the [Power] column.
M Language Number.Ln Function
The natural logarithm, expressed as ln, is the inverse function of exp. Therefore, ln (e^x) = x.
The formula below calls the Number.Ln function with the [Exp] column. Because we are applying the inverse, the result equals the original input, the [Power] column.
M Language Number.Log10 Function
The M language contains the common logarithm. It can be defined 10 raised to the x power equals the number y or 10 ^ x = y. The following equations are true: log10 (1000) = 3, log10 (100) = 2, and
log10 (10) = 1.
The formula below defines the [Log10] column as the result of calling the Number.Log10 function with the [Power] column.
M Language Number.Log Function
The M language contains the binary logarithm. It can be defined 2 raised to the x power equals the number y or 2 ^ x = y. The following equations are true: log2 (8) = 3, log2 (4) = 2 and log2(2) = 1.
The formula below defines the [Log2] column as the result of calling the Number.Log function with the [Root] column.
M Language Number.Combinations Function
In mathematics, a combination is a way of selecting k items from a total collection of n items. The order of the k items does not matter. However, the answer to this question can be expressed as the
equation below. We can finally use that factorial function that was introduced earlier. Thus, how many ways we can select 2 items for a set of 4. This is mathematically equal to 4! / (4-2)! 2! = 6
The formula below defines the [Combinations] column as the result of calling the Number.Combinations function with the [Power] column as the set size and 2 as the selection size.
M Language Number.Permutations Function
In mathematics, a permutation is a way of selecting k items from a total collection of n items. The order of the k items does matter! However, the answer to this question can be expressed as the
following equation. Again, the factorial function is used in expressing the answer. Thus, how many distinct ways we can select 2 items for a set of 4. This is mathematically equal to 4! / (4-2)! = 12
The formula below defines the [Permutations] column as the result of calling the Number.Permutations function with the [Power] column as the set size and 2 as the selection size.
The results below are from a sample calls to the above functions.
Numerical Constants in the M Language
The last topic to cover today is the numerical constants that are supplied by the M Language.
M Language Number.Epsilon Function
The Number.Epsilon function returns the smallest value in the M language.
M Language Number.E Function
The Number.E function returns Euler's number.
M Language Number.PI Function
The Number.PI function returns the ratio of a circles circumference to the diameter which is depicted by the Greek letter PI in mathematical literature.
M Language Number.PositiveInfinity and Number.NegativeInfinity Functions
The M language contains both a Number.PositiveInfinity and Number.NegativeInfinity functions. The definition of infinity describes something without limits. For instance, if we take a -1 and
continuously divide by 2. This sequence of numbers is infinite in size, approaches zero and never reaches zero.
The image below shows the use of the negative infinity function.
M Language Number.Nan and Number.IsNaN Functions
This next function is called Number.Nan which represents 0/0. Beginning programmers who have not coded defensively for division by zero might have been waken up in the night to fix such a bug. In
mathematics, division by zero is undefined. The is a informational function Number.IsNaN that returns true if the column contains this value. In short, I just do not see any real use of these
functions unless you are study some advanced mathematical structures.
The results below are from a sample calls to the above functions.
The Power BI desktop designer contains a rich set of advanced mathematical functions. We can combine these functions together in a computed column to solve numerical business problems. Some of these
functions are not readably applicable to our day-to-day issues. Having knowledge of these functions is a good foundation to draw upon.
Before I wrap up this tip, I want to talk about one real use of the log10 function called the Logarithmic scale. This technique is used to graph the magnitude of some variable that has a large range
of values.
One example that I can think of is the number of retail returns (R) over the course of weeks in a year. I can imagine that the numbers are relatively low for most weeks. However, I am sure there is a
big spike during the holiday season. If we graphed this value R on the dashboard, we might have values ranging from 100's of items to thousands of items. On the other hand, if we graph log10 (R) we
would have number between 0 an 5. The graph would be cleaner to show the spikes during special times of the year.
Next Steps
• Check out these other M language tips
Learn more about Power BI in this 3 hour training course.
About the author
John Miner is a Data Architect at Insight Digital Innovation helping corporations solve their business needs with various data platform solutions.
This author pledges the content of this article is based on professional experience and not AI generated.
View all my tips
Article Last Updated: 2015-12-03 | {"url":"https://www.mssqltips.com/sqlservertip/4107/advanced-mathematical-formulas-using-the-m-language/","timestamp":"2024-11-06T22:04:33Z","content_type":"text/html","content_length":"77560","record_id":"<urn:uuid:eee3c436-17c0-44fc-8492-99eb628bd85f>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00045.warc.gz"} |
Which of the following figures will continue the same series as establ
Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP
Board, Bihar Board, Rajasthan Board, MP Board, Telangana Board etc
NCERT solutions for CBSE and other state boards is a key requirement for students. Doubtnut helps with homework, doubts and solutions to all the questions. It has helped students get under AIR 100 in
NEET & IIT JEE. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year papers, NEET previous year papers, NCERT books for classes 6 to 12, CBSE, Pathfinder Publications, RD Sharma, RS
Aggarwal, Manohar Ray, Cengage books for boards and competitive exams.
Doubtnut is the perfect NEET and IIT JEE preparation App. Get solutions for NEET and IIT JEE previous years papers, along with chapter wise NEET MCQ solutions. Get all the study material in Hindi
medium and English medium for IIT JEE and NEET preparation | {"url":"https://www.doubtnut.com/qna/649158279","timestamp":"2024-11-01T20:49:16Z","content_type":"text/html","content_length":"187767","record_id":"<urn:uuid:bb0f5c97-6f7b-4d2e-bf28-6a8c85f10826>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00692.warc.gz"} |
Using classes of equivalence in the detecting and correcting errors in the wordcode
Jusufi, Azir and Beqiri, Xhevair and Imeri-Jusufi, Bukurie (2018) Using classes of equivalence in the detecting and correcting errors in the wordcode. Journal of Natural Sciences and Mathematics of
UT, 3 (5-6). pp. 152-156. ISSN 2671-3039
Download (1MB)
Developments in recent decades of the sector in digital communication have created a close relationship between mathematics and computer engineering. An important class of codes are linear codes in
the vector space V (n, q) , where GF (q), is a finite field of order q. Let C be a linear [n, k] code. A generator matrix of C is a k × n matrix such that the rows are basis vectors of C [n, k]. If
we specify V(n,q) as a vector space on then the linear binary code C[n,k] is nothing else, but a subspace of the vector space V(n,q). When transferring the wordcodes through different types of
obstacle channels, errors may occur, which we need to detect and correct. With classes a+C, where a is a vector from V(n, q), we construct the standard group, which we will use to detect and correct
the errors in the wordcode. If the word code c is sent, but the received vector is r, we define the error vector e = r − c. The error vector which will be corrected are precisely the coset leaders,
irrespective of which wordcode is transmitted. By choosing a minimum weight vector in each coset as coset leader, we ensure that standard array decoding is a nearest neighbour decoding scheme.
Actions (login required) | {"url":"https://eprints.unite.edu.mk/155/","timestamp":"2024-11-02T07:52:06Z","content_type":"application/xhtml+xml","content_length":"19408","record_id":"<urn:uuid:d8d8170e-6977-43de-be9d-646419fec5d4>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00875.warc.gz"} |
Definition: Diffusion Tensor Imaging (at Stand Out Publishing) - Netlab Loligo
Glossary of Neural Network Terms
Key Word Search
by term... Diffusion Tensor Imaging (DTI)
by definition... is an
for letter: "D" MRI
imaging technique that maps the diffusion tensor (i.e. diffusion of water). Its primary use is to map and characterize the directional diffusion of water
A B C D E F G H I as a function of its location in three dimensional space. The diffusion tensor describes the magnitude, the degree of anisotropy, and the orientation, of
J K L M N O P Q R directional differences in diffusion. Estimates of white matter connectivity patterns in the brain from white matter mapping may be obtained using the
S T U V W X Y Z # degree of diffusion, and the principal diffusion directions.
Results DTI is not
HARDI High Angular Resolution Diffusion Imaging versus Diffusion Tensor Imaging . . . . . . .
Sources & Resources
Also: MRI HARDI Imaging
Unless otherwise indicated, all glossary
content is:
(C) Copyright 2008-2022
Dominic John Repici
~ ALL RIGHTS RESERVED ~
No part of this Content may be copied
without the express written permision of
Dominic John Repici.
Web-based glossary software: (c) Creativyst, 2001-2022 | {"url":"https://standoutpublishing.com/g/Diffusion-Tensor-Imaging.html","timestamp":"2024-11-11T19:44:39Z","content_type":"text/html","content_length":"21196","record_id":"<urn:uuid:ffff4f04-644b-4a77-a44a-fdbc79c0e536>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00756.warc.gz"} |
Summer Football
Saturday 23rd November 2024 - kick-off 3pm
Scottish Premiership - St Mirren v Aberdeen
[[Template core/global/global/poll is throwing an error. This theme may be out of date. Run the support tool in the AdminCP to restore the default theme.]]
Absolute no brainer.
Impressed by the club actually asking the fans too.
Aye but its nae going tae happen
Do not need to see the need to change myself. We have had one bad winter in the last 30 and folk are over reacting to it. Have not seen any evidence that summer football will lead to any improvement
to the game.
The problem with Summer football is with the every 2nd year there is a world cup or Euro's.
Some MLS teams lost star players for 2 or 3 games during the world cup and that was with having a 3 week break. Without the break they normally lose a lot more.
Not that Aberdeen have many players to lose. Rangers and Celtic would be screwed. Oh maybe it is a good idea.
So we have a 4week break every 2 years.
Makes more sense than shutting down for 2 weeks in January (2 fucking limp wristed weeks?! At least shut down for the entire month if yer going to bang on about reducing the number of cancelled
And at least when we shut down for the euros etc we have something to watch.
Start 2-3 weeks earlier, get a few midweek games in then have a winter break for a few weeks during late Jan-early Feb but allow teams to play during that time if theres been lots of posponements
leading upto the break.
That way there more time to play games and teams get a few competitive games before European comps start.
Dinna like the thought of Summer fitba
Not really sure about this either way.
I think having the League Cup final or at least semi finals wrapped up by November is an idea to avoid congestion in the latter half of the season in case of Scottish Cup replays or cancelled
Summer football. Definitely. Fed up with the number of times I've nearly developed hypothermia.
Nae that it'll be exactly warm it still being Scotland, but I mind really enjoying the evening games at the youth World Cup back in the late 80s.
I don't see the point in summer football. I enjoy going out in the winter, but thats probably because I don't go very often.
Not really sure about this either way.
I think having the League Cup final or at least semi finals wrapped up by November is an idea to avoid congestion in the latter half of the season in case of Scottish Cup replays or cancelled
I much preferred the League Cup when the final was in November
I much preferred the League Cup when the final was in November
Me too, A nice way to end the year with a cup final at Hampden
I much preferred the League Cup when the final was in November
Me too.
It hasn't been just a "bad winter" that's made most folk's mind up I think, more likely the utter disgrace the pitches end up no matter what outlay is made on them or the extent of the weather. I
like the idea of not watching fitba freezing my nuts off and being played on a surface that it actually can be played on rather than the grassless fuck ups we have been offered.
As dave_min says, it really is a no brainer.
Summer football would be a boost. TV money would be more substantial as summer foobtall would fill the void when the EPL is shut down. We are competing with EPL for broadcasters money and it goes
without saying that it's a pointless contest. Add alcohol sales in to the mix and it makes for a more enjoyable experience.
Definite for me.
One of the reasons I didn't renew was sitting through the coldest winter in 30 years watching terrible football. At least I wouldn't get pneumonia if they took a winter break. | {"url":"https://www.donstalk.co.uk/topic/3092-summer-football/","timestamp":"2024-11-13T20:52:48Z","content_type":"text/html","content_length":"283138","record_id":"<urn:uuid:339faf4b-2afe-4066-8b8d-60664b038ee0>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00165.warc.gz"} |
Printable Multiplication Practice Sheets
Printable Multiplication Practice Sheets - Significant emphasis to mental multiplication exercises. 4 digits times 1 digit. On this page, you will find multiplication worksheets for practicing
multiplication facts at various levels and in a variety of formats. From the simplest multiplication facts to multiplying large numbers in columns. Web get 600+ multiplication worksheets. Master
basic times tables, decimal multiplication, & more with drill sheets, word problems, & other fun printables.
Multiplication Worksheets Printable Free
Master basic times tables, decimal multiplication, & more with drill sheets, word problems, & other fun printables. On this page, you will find multiplication worksheets for practicing multiplication
facts at various levels and in a variety of formats. From the simplest multiplication facts to multiplying large numbers in columns. Web get 600+ multiplication worksheets. 4 digits times 1 digit.
Multiplication Worksheets 6 7 8 9
Significant emphasis to mental multiplication exercises. From the simplest multiplication facts to multiplying large numbers in columns. Master basic times tables, decimal multiplication, & more with
drill sheets, word problems, & other fun printables. Web get 600+ multiplication worksheets. 4 digits times 1 digit.
Multiplication Practice Sheets PDF worksheetspack
4 digits times 1 digit. Master basic times tables, decimal multiplication, & more with drill sheets, word problems, & other fun printables. On this page, you will find multiplication worksheets for
practicing multiplication facts at various levels and in a variety of formats. Significant emphasis to mental multiplication exercises. From the simplest multiplication facts to multiplying large
numbers in columns.
Printable Multiplication, Multiplying Worksheets, Numbers 1 12 for Kindergarten 1st Grade Math
Web get 600+ multiplication worksheets. Master basic times tables, decimal multiplication, & more with drill sheets, word problems, & other fun printables. From the simplest multiplication facts to
multiplying large numbers in columns. 4 digits times 1 digit. Significant emphasis to mental multiplication exercises.
FREE PRINTABLE MULTIPLICATION WORKSHEETS + WonkyWonderful
4 digits times 1 digit. Web get 600+ multiplication worksheets. Master basic times tables, decimal multiplication, & more with drill sheets, word problems, & other fun printables. On this page, you
will find multiplication worksheets for practicing multiplication facts at various levels and in a variety of formats. Significant emphasis to mental multiplication exercises.
Printable Multiplication Practice
Significant emphasis to mental multiplication exercises. On this page, you will find multiplication worksheets for practicing multiplication facts at various levels and in a variety of formats. Web
get 600+ multiplication worksheets. From the simplest multiplication facts to multiplying large numbers in columns. 4 digits times 1 digit.
Multiplication Worksheets 8+ Examples, Format, Pdf Examples
On this page, you will find multiplication worksheets for practicing multiplication facts at various levels and in a variety of formats. Significant emphasis to mental multiplication exercises.
Master basic times tables, decimal multiplication, & more with drill sheets, word problems, & other fun printables. From the simplest multiplication facts to multiplying large numbers in columns. 4
digits times 1 digit.
Multiplication Times Tables Worksheets 2, 3, 4, 5, 6, 7, 8
4 digits times 1 digit. Master basic times tables, decimal multiplication, & more with drill sheets, word problems, & other fun printables. From the simplest multiplication facts to multiplying large
numbers in columns. Significant emphasis to mental multiplication exercises. Web get 600+ multiplication worksheets.
Free Printable Multiplication Practice Sheets
From the simplest multiplication facts to multiplying large numbers in columns. Web get 600+ multiplication worksheets. On this page, you will find multiplication worksheets for practicing
multiplication facts at various levels and in a variety of formats. Significant emphasis to mental multiplication exercises. 4 digits times 1 digit.
Free Printable Multiplication Practice Sheets
On this page, you will find multiplication worksheets for practicing multiplication facts at various levels and in a variety of formats. From the simplest multiplication facts to multiplying large
numbers in columns. 4 digits times 1 digit. Significant emphasis to mental multiplication exercises. Master basic times tables, decimal multiplication, & more with drill sheets, word problems, &
other fun printables.
4 digits times 1 digit. Master basic times tables, decimal multiplication, & more with drill sheets, word problems, & other fun printables. Significant emphasis to mental multiplication exercises. On
this page, you will find multiplication worksheets for practicing multiplication facts at various levels and in a variety of formats. From the simplest multiplication facts to multiplying large
numbers in columns. Web get 600+ multiplication worksheets.
Master Basic Times Tables, Decimal Multiplication, & More With Drill Sheets, Word Problems, & Other Fun Printables.
On this page, you will find multiplication worksheets for practicing multiplication facts at various levels and in a variety of formats. Web get 600+ multiplication worksheets. From the simplest
multiplication facts to multiplying large numbers in columns. 4 digits times 1 digit.
Significant Emphasis To Mental Multiplication Exercises.
Related Post: | {"url":"https://unser-herzstueck.de/printable/printable-multiplication-practice-sheets.html","timestamp":"2024-11-12T16:59:13Z","content_type":"text/html","content_length":"24674","record_id":"<urn:uuid:60b2778f-94ee-47bc-8675-db07d66ebada>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00416.warc.gz"} |
Generate Random Integers in Python
Getting random integers in Python
# import the function
from random import randint
# set your parameters
howmany = 10
min = 0
max = 100
# use a list comprehension to fill an array
rand_ints = [randint(min,max) for _ in range(howmany)]
Seems kinds of bulky, but you specify how many numbers you would like, what range to draw them from, and then call the radint() function over and over again until you have the numbers you need, using
a for loop with a throaway variable “_”.
But there’s a few ways to do this! If you have NumPy installed, it has a similar function for generating random integers, and the lines of code above, can be reduced to just two: import the library,
call the function.
from numpy.random import randint
The result is as follows:
array([42, 99, 30, 94, 60, 90, 7, 31, 91, 11])
Both of these methods would usually be preceded by a call to “seed” the random number generator, so that you can set a reproducible starting point for random number generation. The function has the
same name in each library, and calling seed for one does not set the seed for the other. But that’s more than you need to know for now.
You must be logged in to post a comment. | {"url":"http://www.phaget4.org/2021/02/25/generate-random-integers-in-python/","timestamp":"2024-11-09T12:57:02Z","content_type":"text/html","content_length":"32549","record_id":"<urn:uuid:655579cf-0607-4cd7-81ce-b1678a95e272>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00602.warc.gz"} |
160 oz to lb - How much is 160 ounces in pounds? [CONVERT] ✔
Conversion formula
How to convert 160 ounces to pounds?
We know (by definition) that: $1⁢oz = 0.0625⁢lb$
We can set up a proportion to solve for the number of pounds.
$1 ⁢ oz 160 ⁢ oz = 0.0625 ⁢ lb x ⁢ lb$
Now, we cross multiply to solve for our unknown $x$:
$x ⁢ lb = 160 ⁢ oz 1 ⁢ oz * 0.0625 ⁢ lb → x ⁢ lb = 10.0 ⁢ lb$
Conclusion: $160 ⁢ oz = 10.0 ⁢ lb$
Conversion in the opposite direction
The inverse of the conversion factor is that 1 pound is equal to 0.1 times 160 ounces.
It can also be expressed as: 160 ounces is equal to $1 0.1$ pounds.
An approximate numerical result would be: one hundred and sixty ounces is about zero pounds, or alternatively, a pound is about zero times one hundred and sixty ounces.
[1] The precision is 15 significant digits (fourteen digits to the right of the decimal point).
Results may contain small errors due to the use of floating point arithmetic. | {"url":"https://converter.ninja/mass/ounces-to-pounds/160-oz-to-lb/","timestamp":"2024-11-08T23:52:48Z","content_type":"text/html","content_length":"20681","record_id":"<urn:uuid:517f9218-9e6a-4f2c-9d9a-c041f6a2c958>","cc-path":"CC-MAIN-2024-46/segments/1730477028106.80/warc/CC-MAIN-20241108231327-20241109021327-00393.warc.gz"} |
Marginal cost pricing with a fixed error factor in traffic networks
It is well known that charging marginal cost tolls (MCT) from self interested agents participating in a congestion game leads to optimal system performance, i.e., minimal total latency. However, it
is not generally possible to calculate the correct marginal costs tolls precisely, and it is not known what the impact is of charging incorrect tolls. This uncertainty could lead to reluctance to
adopt such schemes in practice. This paper studies the impact of charging MCT with some fixed factor error on the system's performance. We prove that under-estimating MCT results in a system
performance that is at least as good as that obtained by not applying tolls at all. This result might encourage adoption of MCT schemes with conservative MCT estimations. Furthermore, we prove that
no local extrema can exist in the function mapping the error value, r, to the system's performance, T(r). This result implies that accurately calibrating MCT for a given network can be done by
identifying an extremum in T(r) which, consequently, must be the global optimum. Experimental results from simulating several large-scale, real-life traffic networks are presented and provide further
support for our theoretical findings.
Original language English
Title of host publication 18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019
Pages 1539-1546
Number of pages 8
ISBN (Electronic) 9781510892002
State Published - 2019
Externally published Yes
Event 18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019 - Montreal, Canada
Duration: 13 May 2019 → 17 May 2019
Publication series
Name Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
Volume 3
ISSN (Print) 1548-8403
ISSN (Electronic) 1558-2914
Conference 18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019
Country/Territory Canada
City Montreal
Period 13/05/19 → 17/05/19
• Congestion games
• Flow optimization
• Marginal-cost pricing
• Routing games
• Traffic flow
Dive into the research topics of 'Marginal cost pricing with a fixed error factor in traffic networks'. Together they form a unique fingerprint. | {"url":"https://cris.ariel.ac.il/en/publications/marginal-cost-pricing-with-a-fixed-error-factor-in-traffic-networ","timestamp":"2024-11-10T21:10:41Z","content_type":"text/html","content_length":"56539","record_id":"<urn:uuid:dbd35e98-490e-4835-900d-6847e576bab1>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00863.warc.gz"} |
Unveiling the Secrets: Extracting Position from Velocity Graphs
Unveiling The Secrets: Extracting Position From Velocity Graphs
To find position from a velocity graph, calculate the area under the curve using geometric shapes like rectangles and triangles. Identify points on the graph representing time intervals, and
determine the corresponding velocity values. Multiply the velocity by the time interval to obtain displacement. Sum the displacements for each interval to calculate the total displacement, which
represents the change in position from the starting point.
Understanding the Interplay between Velocity and Displacement
In the realm of physics, understanding the dynamics of objects in motion requires a firm grasp of two fundamental concepts: displacement and velocity. Displacement, measured in meters, quantifies the
change in an object’s position over a specified time interval. Velocity, on the other hand, measures the rate at which this displacement occurs. It is expressed in meters per second and encapsulates
both the speed and direction of an object’s movement.
To delve deeper, envision a car traveling along a straight road. The car’s displacement represents the distance it has covered, while its velocity describes not only the magnitude of its speed but
also the direction it is moving (e.g., north or south). For example, if the car has moved 100 meters to the north in 10 seconds, its displacement is 100 meters north, and its velocity is 10 meters
per second north.
Interpreting Velocity as a Vector Quantity: Understanding Direction and Magnitude
In the realm of motion, velocity stands as a pivotal concept, painting a vivid picture of an object’s journey through space. To grasp its true essence, we must delve into its vector nature, a duality
that encompasses both magnitude and direction.
Magnitude: The Measure of Swiftness
Envision a speeding car tearing down the highway. Its velocity is characterized by a scalar value: its speed. Speed measures how quickly an object traverses distance, expressing the rate at which
ground is being covered. However, it tells only half the story.
Direction: Charting the Course
Where speed describes how fast, direction reveals which way an object is headed. Velocity, being a vector quantity, embodies both aspects. Picture the same car careening down the road, its velocity
vector pointing forward. Positive velocities indicate movement in the direction of the vector, while negative velocities signal a reverse journey.
Positive vs. Negative: Unveiling Motion’s Directionality
The sign of a velocity tells a compelling tale. A positive velocity implies that the object is advancing along the vector’s path, such as a sailboat gliding westward with the wind at its back.
Conversely, a negative velocity signifies motion in the opposite direction, like a roller coaster descending a steep incline.
Embracing the Vector Nature
Understanding velocity as a vector quantity empowers us to fully comprehend an object’s motion. By embracing both magnitude and direction, we can accurately map its trajectory, predict its destiny,
and unravel the secrets hidden within its dynamic journey.
Calculating Acceleration from the Slope of the Velocity-Time Graph
• Define acceleration as the rate of change of velocity over time.
• Show how a positive slope indicates positive acceleration (increasing velocity) and a negative slope indicates negative acceleration (decreasing velocity).
Calculating Acceleration from the Slope of the Velocity-Time Graph
Understanding Acceleration
In the realm of motion, acceleration holds a pivotal role. It is the key to discerning how velocity changes over time, a phenomenon that can reveal much about an object’s journey. Mathematically,
acceleration is defined as the rate of change in velocity with respect to time.
Slopes and Acceleration
Now, let’s delve into the fascinating relationship between the slope of a velocity-time graph and acceleration. Just as a slope on a hill indicates its steepness, so too does the slope of a
velocity-time graph convey vital information about acceleration.
Positive Slopes and Increasing Velocity
When the slope of the velocity-time graph is positive, it implies that velocity is increasing with time. This means the object is accelerating. The steeper the slope, the greater the acceleration. In
other words, the object is gaining speed more rapidly.
Negative Slopes and Decreasing Velocity
Conversely, a negative slope on the velocity-time graph indicates that velocity is decreasing over time. This corresponds to deceleration, or slowing down. Again, the steeper the slope, the greater
the deceleration.
Example: Skydiver in Freefall
Consider a skydiver in freefall. As they plummet, their velocity increases steadily. This is reflected in the positive slope of the velocity-time graph, indicating positive acceleration due to
gravity. But when they deploy their parachute, their velocity begins to decrease. This is captured by the negative slope of the graph, showing that they are decelerating due to the drag force.
The slope of a velocity-time graph is an invaluable tool in understanding acceleration. It provides a graphical representation of how an object’s velocity changes over time, allowing us to infer the
presence and magnitude of acceleration and gain insights into the dynamic nature of motion.
Identifying Constant Velocity on Velocity-Time Graphs
In the realm of motion, one of the key concepts to understand is velocity – the rate at which an object changes its position over time. A velocity-time graph is a powerful tool that allows us to
visualize and analyze the motion of an object by plotting its velocity against time.
One of the most important things to look for on a velocity-time graph is constant velocity, which indicates that an object is moving at a uniform speed and in a constant direction. This is
represented as a horizontal line on the graph, parallel to the time axis.
Imagine a car traveling along a straight highway at a steady speed. On a velocity-time graph, the car’s motion would be represented by a horizontal line. The slope of the line would be zero,
indicating that the car’s velocity is not changing. This means that the car is neither accelerating nor decelerating, but simply maintaining a constant speed.
In contrast, if the velocity-time graph shows a sloped line, it means that the object’s velocity is changing, indicating acceleration* or **deceleration. A positive slope indicates that the object is
increasing in velocity (accelerating), while a negative slope indicates that it is decreasing in velocity (decelerating).
Understanding constant velocity on velocity-time graphs is crucial for analyzing motion. By identifying horizontal lines on the graph, we can easily determine the periods during which an object is
moving at a constant speed and in a constant direction. This information provides insights into the object’s movement and can be used to calculate key parameters such as displacement, distance, and
Recognizing Zero Velocity on Velocity-Time Graphs
Understanding motion is essential in physics, and velocity-time graphs are a powerful tool for visualizing and analyzing the movement of objects. Velocity, a vector quantity, describes the rate of
change in an object’s position over time and has both magnitude (speed) and direction.
On a velocity-time graph, zero velocity is a special case that provides valuable insights into an object’s motion. Zero velocity indicates the absence of motion, meaning the object is not moving.
This state is represented by a vertical line intersecting the time axis.
Imagine a car that starts from rest. As it accelerates, the velocity-time graph shows a sloping line, indicating increasing velocity. However, when the car reaches its peak speed, the graph becomes
horizontal, representing constant velocity. Once the car begins to decelerate, the graph slopes downward, indicating decreasing velocity.
Finally, when the car comes to a complete stop, the graph returns to a vertical line, indicating zero velocity. This line represents the moment when the car is no longer moving and its position
remains unchanged.
By identifying zero velocity on velocity-time graphs, we can determine when an object is not moving. This information is crucial for analyzing the motion of objects, understanding their behavior, and
predicting their future movement.
Leave a Reply Cancel reply | {"url":"https://www.biomedes.biz/extracting-position-velocity-graphs/","timestamp":"2024-11-02T02:19:34Z","content_type":"text/html","content_length":"85980","record_id":"<urn:uuid:ae6f2635-1cd4-4315-8bdf-da7168c3b2e9>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00391.warc.gz"} |
Application and Popularization of Energy Formula
1. Introduction
From mechanical energy, chemical energy, electric energy to nuclear energy has become the main subject of physics research.
The great energy we have now is the polymerization of hydrogen into helium. However, there is no unified formula for the calculation of energy.
In physics, there are two main energy formulas. One is kinetic energy formula. The another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can
only calculate light speed motion. The two formulas are not unified. We hope to get a unified formula. But it didn’t work. It’s difficult. Now let’s look at a formula:
Here (1.1) is called kinetic energy formula. w is kinetic energy. m is the mass. v is the velocity of the object.
For example,
let m = 2 kg, v = 100 M/s, calculated by (1.1)
This is the kinetic energy of an object under the action of an external force. There is motion mass. When the object moves at low speed, the motion mass is very small and can be ignored. Therefore,
this formula is suitable for energy calculation at low speed. But it is not suitable for energy calculation of large speed, especially the energy calculation of light speed.
In 1905, Einstein published his special theory of relativity and proposed an energy formula [1]:
Here (1.2) is called Einstein equation. E is energy. m[0] is the static mass. The speed of light c = 299,792,457.4 ± 0.1 M/s.
Obviously, the formula is not suitable for (1.1). Can there be a formula suitable for (1.1) and (1.2)? Einstein improved (1.1)
Let the rest mass m[0], the motion velocity v, the motion mass m[v],
$\sqrt{1-{v}^{2}/{c}^{2}}$ It’s called Lorentz contraction factor. It is not difficult to confirm that m[v] > m[0], so as to obtain the changed mass Δm
$\Delta m={m}_{v}-{m}_{0}=\frac{{m}_{0}}{\sqrt{1-{v}^{2}/{c}^{2}}}-{m}_{0},$
$\Delta m={m}_{0}\left(\frac{1}{\sqrt{1-{v}^{2}/{c}^{2}}}-1\right),$
Substituting (1.2) $E=\Delta m{c}^{2}$, the kinetic energy formula is obtained
$E=\Delta m{c}^{2}={m}_{0}\left(\frac{1}{\sqrt{1-{v}^{2}/{c}^{2}}}-1\right){c}^{2},$
Here (a) is Einstein’s improved kinetic energy formula. Let’s look at the scope of the kinetic energy formula. Let $v\ll c$, we get
$\frac{1}{\sqrt{1-{v}^{2}/{c}^{2}}}=1+\frac{{v}^{2}}{2{c}^{2}}+\cdots ,$
Take main item $1+\frac{{v}^{2}}{2{c}^{2}}$, by (a) get (1.1)
The kinetic energy formula (a) is suitable for (1.1). Let v = c, by (a) get
It tends to infinity. The kinetic energy formula (a) is not suitable for (1.2). It seems that it is difficult to obtain the formula which is suitable for (1.1) and (1.2).
Let’s look at the Journal of Shaanxi Normal University (volume 03.31, April, 3857.53)_ 03) Professor Chen Junfu’s research on kinetic energy formula.
Variable acceleration motion and new kinetic energy formula
Let the initial acceleration be a[0] and the final acceleration be a[v], then the average acceleration can be obtained.
Let the initial acceleration be a[0] and the final acceleration be a[v], then the average acceleration can be obtained
Can get ${v}^{2}=2\stackrel{¯}{a}s=\left({a}_{0}+{a}_{v}\right)s,$
Substituting ${a}_{v}={a}_{0}\frac{c-v}{c}$
From the above $s=\frac{c}{{a}_{0}\left(2c-v\right)}{v}^{2},$
Here (c) is the new kinetic energy formula, where E is kinetic energy. m[0] is the static mass. v is the speed of motion.
Let’s look at the scope of application of formula (c). We get
Let $v\ll c$, $v/c\approx 0$, we get (1.1)
Let v = c, we get (1.2)
Obviously, formula (c) is suitable for (1.1) and (1.2).
However, there is a problem in the reasoning of formula (c). $\frac{c}{2c-v}$ How is it obtained? Unclear.
Besides, $E={m}_{0}{a}_{0}s$, it’s not right. a[0] should be the average acceleration. It should be
From the front ${v}^{2}=2\stackrel{¯}{a}s$ get $\stackrel{¯}{a}s=\frac{{v}^{2}}{2}$, From this we get
It’s still formula (1.1). It’s not a new kinetic energy formula.
In this paper, we use Lorentz contraction principle [2] to generalize Einstein’s equation, and obtain generalized Einstein’s equation and new Einstein’s kinetic energy formula.
2. Lorentz Contraction Principle
In 1892, the physicist Lorentz, based on the practical research of Michelson and Murray, proposed that when an object moves, it shrinks in the direction of motion. This is the famous Lorentz
Let the length before the object moves be L[0], the length when the object moves be L[v], and the velocity be v get [1] [2] [3] [4]:
Here (2.1) is called Lorentz contraction principle. It’s called Lorentz contraction factor. L[v] is called motion length. The speed of light c = 299,792,457.4 ± 0.1 M/s.
for example,
Let L = 2 m, v = 100 M/s, calculated by (2.1)
The greater the speed, the smaller the movement length,
Confirmed by (2.1) L[0] > L[v], From (2.1) we get the length of the change ΔL
$\Delta L={L}_{0}-{L}_{v}={L}_{0}-{L}_{0}\sqrt{1-\frac{{v}^{2}}{{c}^{2}}},$(2.2)
By (2.2) get
$\Delta L={L}_{0}\left(1-\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}\right),$
Represents the length of an object as it moves. Let’s look at the length of motion of an object moving at the speed of light.
Let v = c, and the length of change is obtained from (2.2)
$\Delta L={L}_{0}\left(1-\sqrt{1-\frac{{c}^{2}}{{c}^{2}}}\right)={L}_{0},$
Represents the maximum length of change when an object moves at the speed of light.
3. Mass Shrinkage Formula
We generalize Lorentz length contraction to mass contraction. The length of motion L[v] is extended to motion Quality m[v].
Let m[0] be the mass before the object moves, m[v] be the mass when the object moves, v be the velocity, get
Here (3.1) is called motion mass, represents the mass of an object in motion. It was confirmed by (3.1) that m[0] > m[v],
Let the variable mass Δm be obtained from (3.1)
$\Delta m={m}_{0}-{m}_{v}={m}_{0}-{m}_{0}\sqrt{1-\frac{{v}^{2}}{{c}^{2}}},$
$\Delta m={m}_{0}\left(1-\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}\right),$(3.2)
Here (3.2) represents the variable mass of an object in motion.
For example,
Let m[0] = 2 kg, v = 100 M/s, calculated by (3.2)
$\Delta m=2\left(1-\sqrt{1-\frac{{100}^{2}}{\text{}{299792457.4}^{2}}}\right)=0.00000000000011126500605073307,$
The greater the speed, the greater the change of mass. Let’s look at the change of mass when an object moves at the speed of light.
Let v = c, and the variable mass is obtained from (3.2)
$\Delta m={m}_{0}\left(1-\sqrt{1-\frac{{c}^{2}}{{c}^{2}}}\right)={m}_{0},$
Represents the maximum mass that changes when an object moves at the speed of light. According to (1.2), we generalize Einstein’s equation [5], transform mass into energy, and get the generalized
Einstein’s equation [6].
4. Generalized Einstein Equation
We can get from (1.2) and (3.2) [7]
$E=\Delta m{c}^{2},$(4.1)
From (3.2) and (4.1), we can get [8]:
Here (4.2) is called generalized Einstein equation.
E is the energy released. m[0] is the mass of the object before it moves. The speed of light c = 299,792,457.4 ± 0.1 M/s.
For example,
Let m[0] = 2 kg, v = 100 M/s, calculated by (4.2)
The value is the same as the kinetic energy formula in (1.1). Let’s look at the scope of application. Let $v\ll c$, according to the previous
From this we get
Can get
Substituting (4.2)
$v/c\approx 0$, get
The formula (4.2) is suitable for (1.1). Let v = c, which can be obtained from (4.2)
This is formula (1.2). The generalized Einstein equation is suitable for both (1.1) and (1.2).
Let velocity v, mass m[0] = 1, E(a) denote formula (a), E(s) denote formula (4.2),
Partial calculation:
$\begin{array}{llll}v\hfill & E\left(a\right)\hfill & E\left(s\right)\hfill & E\left(a\right)/E\left(s\right)\hfill \\ 10000\hfill & \text{50000000}\hfill & \text{50000000}\hfill & 1\hfill \\ 200000\
hfill & \text{20000006675}\hfill & \text{20000002225}\hfill & \text{1}\text{.0000002}\hfill \\ 65000000\hfill & 2190023689283367\hfill & \text{2137928152810761}\hfill & \text{1}\text{.0243672}\hfill
\\ 299570000\hfill & 2243549820812118646\hfill & \text{86413821733172904}\hfill & \text{25}\text{.962858}\hfill \end{array}$
The value of formula E(a) is very close to that of formula E(s). However, when v approaches the speed of light, the deviation of E(a) is obvious.
Through the above discussion, it is not difficult to find that the key to the argument is Δm. Thus, a new Einstein kinetic energy formula is obtained.
5. Einstein’s Kinetic Energy Formula
Previously, we discussed the traditional kinetic energy formula (1.1)
When an object is in motion, its mass changes $\Delta m$, The total mass was obtained
$m={m}_{0}+\Delta m,$
Total energy
$W=\frac{m{v}^{2}}{2}=\frac{{m}_{0}+\Delta m}{2}{v}^{2},$
$W=\frac{{m}_{0}{v}^{2}}{2}+\frac{\Delta m{v}^{2}}{2},$(5.1)
By (3.2) get
$\Delta m={m}_{0}\left(1-\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}\right),$
We can get
$\frac{\Delta m{v}^{2}}{2}=\frac{{m}_{0}{v}^{2}}{2}\left(1-\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}\right),$
By (5.1) get
We can get
The results are as follows
Here (5.2) is called Einstein’s kinetic energy formula.
Let $v\ll c$, $v/c\approx 0$, and can be ignored
By (5.2) can get
Formula (5.2) is suitable for (1.1).
Let v = c and v/c = 1, we get
By (5.2) get
The formula (5.2) is suitable for (1.2).
In this way, formula (5.2) is suitable from low speed to light speed.
Let velocity v, mass m[0] = 1, E(W) denote formula (5.2), E (s) denote formula (4.2),
Partial calculation:
$\begin{array}{llll}v\hfill & E\left(W\right)\hfill & E\left(s\right)\hfill & E\left(W\right)/E\left(s\right)\hfill \\ 10000\hfill & \text{50000000}\hfill & \text{50000000}\hfill & 1\hfill \\ 200000\
hfill & \text{20000004451}\hfill & \text{20000002225}\hfill & \text{1}\text{.00000011}\hfill \\ 65000000\hfill & 2162751429396361\hfill & \text{2137928152810761}\hfill & \text{1}\text{.0116109}\hfill
\\ 299570000\hfill & 88013904766446535\hfill & \text{86413821733172904}\hfill & \text{1}\text{.0185165}\hfill \end{array}$
The value of formula E(W) is very close to that of formula E(s).
6. Conclusions
In this paper, according to Lorentz contraction principle and Einstein equation, we get
Here (6.1) is the generalized Einstein equation. It means that the mass of an object shrinks and releases energy. Also
Here (6.2) is Einstein’s kinetic energy formula. It means that the mass of an object expands and absorbs energy.
The generalized Einstein equation and Einstein’s kinetic energy formula are all correct.
The above energy formula is based on the theory of mass and energy conversion. According to this theory, the wave particle image can be interpreted. Particle is mass. Waves are energy. The conversion
of mass into energy is a wave. When energy is converted into mass, it is called a particle.
Light is a wave of mass and energy. When mass and energy are transformed, particles contract in the direction of motion and release energy. Then it absorbs the energy and the particles expand in the
direction of motion. Particles move through contraction and expansion.
It can also explain the speed limit of light. The mass of the particle shrinks to the minimum, the energy is the maximum, and the speed is the maximum. The mass of the particle shrinks to the limit,
the energy is the limit, and the speed is the limit. This speed limit is the speed of light.
The theory of mutual transformation between mass and energy can be regarded as the basis of relativity. This theory is correct. | {"url":"https://scirp.org/journal/paperinformation?paperid=107426","timestamp":"2024-11-13T18:33:34Z","content_type":"application/xhtml+xml","content_length":"158848","record_id":"<urn:uuid:95b9f6f6-002c-46c2-b8b3-4593d80deb37>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00787.warc.gz"} |
Rhythmomachia: The Philosopher's Game
A Strategy Game of High Mathematical Precision
To enjoy the full depth of Rhythmomachia, we recommend to read the rules on this page incrementally, and instantly try a few moves on the board. When you take a little time to discover its value,
Rhythmomachia really is just an incredible game!
Be sure to click the End Turn button at the end of each turn.
If your web browser does not display the board game above, download Rhythmomachia. Look at the button descriptions and further help if you are unsure what the buttons do. If the whole applet does not
show, make sure you have enabled Java support for your browser. A new implementation, Rhythmomachia 2, with much more features is available as a separate application for download or as Rhythmomachia
2 Webstart.
P.S. I implemented Rhythmomachia when I was in high school before I knew anything about computer science. But you may enjoy this fun game as much as I did back then.
See David Dyers' recent Rhythmomachia
The Rules of the Game
Startup position of game board
Rhythmomachia is a complex strategic game played on a board similar to a chessboard. It is an old game supposedly invented in the Middle Ages, and has several mathematical roots. Rhythmomachia is
played by two players. The program is based on a historical reconstruction.
Early, there were some theoretical and mathematical examinations. Some concerning the best strategies, and some analyzing how far Rhythmomachia's tactics might relate to ancient warfare. Though some
of these examinations might be mainly unproved or even mere fiction conserved over the centuries, one cannot doubt that Rhythmomachia makes use of certain mathematical connections known in number
Rhythmomachia is played by two players. Who wins and when? The player whose figures (pieces) are arranged in a regular mathematical order on the opposite yard, or has captured all opposite figures.
Who starts? The blue one does the first move. Then the two players alternate by turn.
The Moves
For making a move, use your mouse to drag pieces to their new position according to the following moves:
1. Infantry, represented by a circle, moves exactly 2 fields in horizontal or vertical direction.
2. Cavalier, represented by a triangle, moves exactly 3 fields in diagonal direction.
3. Chariot, represented by a square, moves exactly 4 fields in any direction, horizontally, vertically, or diagonally.
4. Pyramid, represented by a pyramidal tower, contains six or less units and can choose like which of its pieces it wants to move or attack, every time. If a figure contained in the pyramidal tower
is attacked successfully, then it is removed and cannot be used for moving, any more.
○ Important: The number of fields moved includes the starting and ending position! So a Cavalier has moved three fields if it has simply stepped over one empty field in between. This unusual
calculation is important for attacks.
○ Each figure has a rating that determines its combat values, whereas hardly any two figures have the same ratings.
If a pyramid looses one of its components and an identical duplicate of the same league is still in play, the player can choose to swap them out. The figure in the pyramid which was lost is removed
and the duplicate takes its place in the pyramid, instead.
The Attacking Options
Though every player can only do a single move per turn, each can attack as many times as possible, before and/or after their move. Each figure can attack as many times as possible and attacks can be
lead by as many figures as necessary. To attack an opponent's figure successfully, you must reduce its rating exactly to 0 (each figure that still has a negative or positive rating at the end of the
opponents turn, will regenerate to its full rating).
Various possibilities for a single attack of a figure do exist, each with the goal of reducing the target's rating to 0. They can be combined freely:
1. Direct confrontation is used if a movement of a figure would lead exactly onto the target figure and the ratings are equal.
2. Combat formation in joint attack
3. Ambuscade also allows multiple figures in a joint attack to contribute by Direct Confrontation if they could move directly to the target and their respective ratings add up to the target rating.
Enable this option via direct configuration->also joint.
4. Seige captures pieces that are fully surrounded by enemies (optional).
When attacking, you must respect that:
○ a figure can only lead an attack into those directions that it can move to. So for example, a Cavalier can only attack in diagonal directions.
○ a figure can attack one distinct figure only once, even though it may take part in attacks of any number of different figures each turn.
○ the distances are calculated like for moves (including the starting and ending position).
will also disable capture of pieces and remove pieces off the board after a successful attack instead.
The Winning Harmonies
A player can win if he has arranged three piecesin a distinct shape and a distinct order (according to their ratings). Such an arrangement must be located entirely on the opponent's yard (the half
the board where the opposite player starts). At most one of the three pieces can be an opponent's piece. The figures playing a role in such an arrangement must be located in a regular mathematical
shape without other pieces in between like:
• a regular triangle(i|j) and one at (i+n|j) and one at (i|j+m), with m,n being integers.
Place these figures in a right-angled triangle. Rotated triangles are allowed.
• a linen fields each, on the same vertical column or horizontal row, with n being an integer.
So place these piece on one vertical or horizontal line. Diagonal are allowed.
The ratings of these figures must be in a regular order like:
• Arithmetic order applies if the figures fit with an arithmetic sequence (a[n])
with a[n] := b + c*n. Then it is a[i] - a[i-1] = const.
Such as: {3,5,7}, {3,9,15}, {4,8,12} or {30,36,42}.
The name is derived from the arithmetic series b+c*.
• Geometric order applies if the figures fit with a geometric sequence (g[n])
with g[n] := c*q^n. Then it is g[i] / g[i-1] = const.
Such as: {4,16,64}.
The name is derived from the geometric series b+c*^i.
• Harmonic order applies if the figures fit with a harmonic sequence (h[n])
with h[n] := c / n.
Such as: {12,6,4}.
The name is derived from the harmonic series b+c*i^-r where mostly it is r=1.
○ At most one piece in a winning harmony can belong to the opponent.
Note the winning harmonies are not checked in the Java implementation, but you can still celebrate if you win.
Download Rhythmomachia
If you liked this game, you can also download it. Rhythmomachia 2 is very much like Rhythmomachia 1, but supports more rules (for example full pyramid support) and is customizable for several rule
variants at least to some extent. It has been rewritten completely, in order to flexibilize the rules and make use of more Java features than the original version for Java Virtual Machine 1.0
supports. This allowed beautifying the user interface. Also thanks to the integration in our game
, we can now start to implement a computer player. Some rudimentary steps have already been taken into this direction, but the overall player performance is still much worse than that for the Seti
game. The version 2 is recommended instead of Rhythmomachia 1. Rhythmomachia 2 is not available as a Java applet, though, but has to be downloaded and can be run using Java Virtual Machine 1.4+.
Comments & Puzzles
If you have found out any mathematical properties concerning Rhythmomachia, or know any alternative rules then please tell me. Also if you know about additional sources on the web, I can include a
link to them.
Some hints if try to solve some puzzles: a simple mathematical connection in Rhythmomachia concerns the starting arrangements of the figures. Some of the pieces' ratings follow up a sequence like:
• {n, n*n, n*(n+1), (n+1)*(n+1), (n+1)*(2n+1), (2n+1)*(2n+1) }
for example in
• {2, 4, 6, 9, 15, 25}
• {7, 49, 56, 64, 120, 225}
Can you find out further connections?
What pieces are the most effective ones? Which can attack the most opponents and which can be attacked by the least? Which pieces can be used best for winning harmonies? What ratings do these pieces
have then?
Can you compute a list of all possible combinations for winning orders? My computer printed out this list of winning orders.
There are quite a few books and descriptions on the deeper aspects, philosophy and strategy of Rhythmomachia play. Some of them further contain interesting historical motivations.
[Bell, 1983]
Bell, Robert Charles. The Boardgame Book. Bookthrift, 1983. ISBN 978-0671060305
[Illmer et al., 1987]
Illmer, Detlef & Gädeke, Nora, & Henge, Elisabeth & Pfeiffer, Helene & Spickler-Beck, Monika. Rhythmomachia. Hugendubel Verlag, 1987, ISBN 3-88034-3194-5 (in German)
[Borst, 1986]
Borst, Arno. Das mittelalterliche Zahlenkampfspiel. - Heidelberg : Winter, 1986. - 553 S. : Ill. (Supplemente zu den Sitzungsberichten der Heidelberger Akademie der Wissenschaften,
Philosophisch-Historische Klasse ; 5) Literaturverz. S. 495 - 498 ISBN 3-533-03750-9 ISBN 3-533-03751-7 SW: Zahlenkampfspiel ; Geschichte (in German)
[Barozzi, 1572]
Barozzi, Francesco (1538?-1587?) Il nobilissimo et antiqvissimo givoco Pythagoreo nominato rythmomachia cioe battablia de consonantie de nvmeri, ritrouato per vtilita & solazzo delli stidiosi, et
al presente in lingua volgare in modo di paraphrasi composto. Venetia, G. Perchacino, 1572 (in Italian)
[Fulke, 1563]
1563 translation by William Fulke of Boissiere's 1554/56 description of Rythmomachy. It is entry 15542a in the Short Title Catalog of Pollard and Redgrave, and on Reel 806 of the corresponding
microfilm collection. (The sources disagree, on whether the name is Fulke or Fulwood. He lived 1538-1589.)
[Moyer, 2001]
Moyer, Ann E. The Philosophers' Game: Rithmomachia in Medieval and Renaissance Europe. University of Michigan Press, 2001.
More bibliography on Rhythmomachia (in French). | {"url":"https://lfcps.org/applet/Rhythmomachia.html","timestamp":"2024-11-11T21:07:17Z","content_type":"text/html","content_length":"27527","record_id":"<urn:uuid:cd048197-9ebf-4760-8e85-99ccf50a1910>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00011.warc.gz"} |
27. Remove Element
Given an array nums and a value val, remove all instances of that value in-place and return the new length.
Do not allocate extra space for another array, you must do this by modifying the input array in-place with O(1) extra memory.
The order of elements can be changed. It doesn’t matter what you leave beyond the new length.
Confused why the returned value is an integer but your answer is an array?
Note that the input array is passed in by reference, which means a modification to the input array will be known to the caller as well.
Internally you can think of this:
// nums is passed in by reference. (i.e., without making a copy)
int len = removeElement(nums, val);// any modification to nums in your function would be known by the caller.
// using the length returned by your function, it prints the first len elements.
for (int i = 0; i < len; i++) {
Example 1:
Input: nums = [3,2,2,3], val = 3
Output: 2, nums = [2,2]
Explanation: Your function should return length = 2, with the first two elements of nums being 2.
It doesn't matter what you leave beyond the returned length. For example if you return 2 with nums = [2,2,3,3] or nums = [2,2,0,0], your answer will be accepted.
Example 2:
Input: nums = [0,1,2,2,3,0,4,2], val = 2
Output: 5, nums = [0,1,4,0,3]
Explanation: Your function should return length = 5, with the first five elements of nums containing 0, 1, 3, 0, and 4. Note that the order of those five elements can be arbitrary. It doesn't matter what values are set beyond the returned length.
class Solution {
int removeElement(vector<int>& nums, int val) {
for(int i=0; i<nums.size(); i++){
if(nums[i] == val){
return nums.size();
Runtime: 0 ms, faster than 100.00% of C++ online submissions for Remove Element.
Memory Usage: 8.7 MB, less than 68.23% of C++ online submissions for Remove Element. | {"url":"https://andreea337.medium.com/27-remove-element-315a11f4e774","timestamp":"2024-11-11T23:38:30Z","content_type":"text/html","content_length":"96358","record_id":"<urn:uuid:9a5b8cb0-4367-4ffe-af0b-5787450da636>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00163.warc.gz"} |
dask.array.stats.moment(a, moment=1, axis=0, nan_policy='propagate')[source]¶
This docstring was copied from scipy.stats.moment.
Some inconsistencies with the Dask version may exist.
Calculate the nth moment about the mean for a sample.
A moment is a specific quantitative measure of the shape of a set of points. It is often used to calculate coefficients of skewness and kurtosis due to its close relationship with them.
Input array.
orderint or 1-D array_like of ints, optional (Not supported in Dask)
Order of central moment that is returned. Default is 1.
axisint or None, default: 0
If an int, the axis of the input along which to compute the statistic. The statistic of each axis-slice (e.g. row) of the input will appear in a corresponding element of the output. If
None, the input will be raveled before computing the statistic.
nan_policy{‘propagate’, ‘omit’, ‘raise’}
Defines how to handle input NaNs.
○ propagate: if a NaN is present in the axis slice (e.g. row) along which the statistic is computed, the corresponding entry of the output will be NaN.
○ omit: NaNs will be omitted when performing the calculation. If insufficient data remains in the axis slice along which the statistic is computed, the corresponding entry of the output
will be NaN.
○ raise: if a NaN is present, a ValueError will be raised.
centerfloat or None, optional (Not supported in Dask)
The point about which moments are taken. This can be the sample mean, the origin, or any other be point. If None (default) compute the center as the sample mean.
keepdimsbool, default: False (Not supported in Dask)
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.
n-th moment about the `center`ndarray or float
The appropriate moment along the given axis or over all values if axis is None. The denominator for the moment calculation is the number of observations, no degrees of freedom correction
is done.
The k-th moment of a data sample is:
\[m_k = \frac{1}{n} \sum_{i = 1}^n (x_i - c)^k\]
Where n is the number of samples, and c is the center around which the moment is calculated. This function uses exponentiation by squares [1] for efficiency.
Note that, if a is an empty array (a.size == 0), array moment with one element (moment.size == 1) is treated the same as scalar moment (np.isscalar(moment)). This might produce arrays of
unexpected shape.
Beginning in SciPy 1.9, np.matrix inputs (not recommended for new code) are converted to np.ndarray before the calculation is performed. In this case, the output will be a scalar or np.ndarray of
appropriate shape rather than a 2D np.matrix. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or np.ndarray rather than a masked array with mask=False.
>>> from scipy.stats import moment
>>> moment([1, 2, 3, 4, 5], order=1)
>>> moment([1, 2, 3, 4, 5], order=2) | {"url":"https://docs.dask.org/en/stable/generated/dask.array.stats.moment.html","timestamp":"2024-11-04T14:07:15Z","content_type":"text/html","content_length":"36334","record_id":"<urn:uuid:cb300cdf-ddf9-4b2f-a0b3-39ea9244d0dd>","cc-path":"CC-MAIN-2024-46/segments/1730477027829.31/warc/CC-MAIN-20241104131715-20241104161715-00495.warc.gz"} |
The Theory of the Continuum
A continuum is a large range or group of things that gradually change, have no clear dividing points, and blend into each other. Continuums are used to describe many different things, including
color, political opinion, and the evolution of galaxies.
The continuum in mathematics is the set of all real numbers, whose size is infinite. It is the most important infinite set of numbers in the world, and has been the subject of much research.
One of the most famous mathematicians who worked on the problem was Kurt Godel. His work on the problem led to several important developments that have had a lasting effect on the theory of the
First, he introduced the idea that there is a macroscopic mathematical model of the fluid which contains infinitely small volumetric elements called particles. This is a fundamental part of continuum
mechanics, which is an important subdiscipline of applied mathematics.
This model is the basis for a wide range of studies, including air and water flow and the study of rock slides. It also explains the flow of blood and other body fluids as well as the evolution of
Next, he developed a technique for resolving the properties of this fluid at a macroscopic level that is smaller than the scale of molecular action, but larger than the size of individual particles.
He did this by defining a geometric volume of infinitesimally small size, which is known as the representative elementary volume (REV). The REV has perfect homogeneity and is essentially a sharp
cut-off filter.
The REV then serves as a sampling volume for the continuous model, a volume that is as small as necessary to resolve spatial variations in fluid properties and that is sufficiently large to capture
the behavior of a single particle.
Eventually, this sampling volume degenerates to a mathematical point which occupies every geometric point in three-dimensional space. This point has fluid properties that are remarkably similar to
those of the original fluid.
These fluid properties are governed by a system of equations derived from the continuum theory. This system of equations is known as the Godel-Hilbert model, and it is an important tool for studying
a variety of phenomena.
In fact, the Godel-Hilbert model is so widely used that it has become part of the standard machinery of mathematics. It is difficult to prove that it fails, and a number of theorems that depend on it
are not provably true.
When the theory of the continuum was first proposed, a significant amount of controversy surrounded it. In the nineteenth century, Georg Cantor, who invented the concept of the continuum in set
theory, met with strong opposition from those who were afraid to admit infinite objects into mathematics.
But, the concept of the continuum is now accepted as a basic theory in modern mathematics. It is a central part of the field of set theory, and it has played a pivotal role in the development of
other areas of mathematics. | {"url":"https://vegoodjani.com/the-theory-of-the-continuum/","timestamp":"2024-11-14T01:11:44Z","content_type":"text/html","content_length":"51313","record_id":"<urn:uuid:9cc7f168-1dbe-4fab-8b8f-d1b0088e9fef>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00025.warc.gz"} |
Kaggle Titanic - Data Analysis
Kaggle Titanic – Data Analysis
Today we start the Titanic Kaggle competition. Our objective is to build a classifier that predicts which passengers of the Titanic survived.
If you want a detailed description of the Titanic Kaggle competition, you find all information on the Kaggle website.
I separated the process of building the classifier in the following tasks:
1. Today we take the first step. We analyze the data to get a good understanding about the features in the given dataset.
2. The next part will be the data cleaning and preparation to get the most out of the machine learning algorithms.
3. The third step is the creation of our first basic machine learning models, starting from a very simple classifier to a 3 staged sklearn pipeline.
4. In the last step, we will build multiple advanced machine learning models including ensembled methods and analyzing the feature importance.
In this article we start with the first step in every machine learning project: the data analysis. Week by week I will publish the next article of the Titanic competition and put the link to all
articles at the end of every article.
I do almost all my work in a Jupyter Notebook. All notebooks are stored in a GibHub repository.
Import all Libraries
# pandas: handle the datasets in the pandas dataframe for data processing and analysis
import pandas as pd
print("pandas version: {}". format(pd.__version__))
# matplotlib: standard library to create visualizations
import matplotlib
import matplotlib.pyplot as plt
print("matplotlib version: {}". format(matplotlib.__version__))
# seaborn: advanced visualization library to create more advanced charts
import seaborn as sns
print("seaborn version: {}". format(sns.__version__))
# turn off warnings for better reading in the Jupyter notebbok
pd.options.mode.chained_assignment = None # default='warn'
The first step in almost every Python script is to import all necessary libraries that we need. One thing that I recommend is to print the installed version of all used libraries. This helps a lot
when you debug parts of your code or you copy a section of my code, but it does not compile, because your version of a library is outdated.
In total, I only use the standard libraries that you should already know:
• I use pandas to handle the whole dataset
• For visualizations I use seaborn because in my opinion the charts have a nicer and more modern look. And on top I use matplotlib to change details of the seaborn figures.
To make the code cleaner for this video, I turn off all warnings.
Load Training and Test Dataset
I already downloaded all files of the Titanic Kaggle competition in a folder named 01_rawdata. Therefore, I can read the training and test dataset and create a pandas dataframe for each dataset.
# load training and test dataset
df_train = pd.read_csv('../01_rawdata/train.csv')
df_test = pd.read_csv('../01_rawdata/test.csv')
With the training set, we train the classifier that we will build and with the test dataset, we create a submission file to get an official score from the Kaggle website. This official score shows
how good the final machine learning model is.
First Look at the Training and Test Dataset
To get a fist look at the training and test datasets, we plot the first few lines and create basic statistical reports.
Print the first lines of the dataset
The first step in my data analysis process is to get a feeling for the features. Therefore, I print the first 10 lines of the training and test datasets.
# print the first 10 lines of the training data
# print the first 10 lines of the test data
If you take a closer look to both datasets, you notice the following things:
• The PassengerId starts with 1 in the training set and with 892 in the test dataset. Therefore, the PassengerId looks like a consecutive numbering of individual passengers.
• The column Survived is only in the training set and should be predicted from the test dataset.
□ All other columns are available in the training data set as well as in the test data.
• The Ticket feature is very cryptic and maybe hard to process.
• And the Cabin column has a lot of NaN values that is short for “Not a Number” and represents empty cells in a pandas dataframe.
Create a Statistical Report of Numeric and Categorical Features
By printing out the first lines of the Titanic data, you get a first view of the data, but not a good understanding of all samples. Therefore, we create statistical reports including all numeric and
categoric features for both datasets.
To create such statistical reports, we use the pandas describe function. I use the transpose function to get the report for each feature in a row, because otherwise if you have a lot of features, you
get endless columns that are hard to visualize in a Jupyter notebook.
For all numeric features we get the following information in the statistical report:
• the number of non-empty rows
• mean and standard deviation
• the 25th, 50th, and 75th percentiles, where the 50th percentile is equal to the median
• and you get the minimum and maximum value of each feature
# create the statistic report of the numeric features of the training dataset
# create the statistic report of the numeric features of the test dataset
So, what are the results from the statistical report of the numeric features?
• From the number of non-empty rows, we see that the training dataset contains 891 samples and the test dataset 418 samples.
• The PassengerId is consecutively numbered and a false added afterwards information to the datasets.
• The feature Age has missing values (714 instead of 891 in the training dataset and 332 instead of 418 in the test dataset). We will handle the missing values in the next article during the data
cleaning and preparation.
• The mean of the Survived column is 0.38. Therefore, we already know that 38% of all passengers survived.
• 75% of all passengers are between 38 (for the training set) and 39 years old or younger (for the test set). There are a few older passengers with the oldest 80 years old.
• More than 75% of all passengers travel without parents or children because the 75th percentile of Parch is equal to 0.
• The minimum fare is 0. Therefore, it could be that children did not have to pay for their ticket.
• For the test dataset the feature Fare has missing values (417 instead of 418). We also handle this one missing value in the next article.
We got a lot of information from the statistical reports of the numeric features. There is also the possibility to create a slightly different report for all categorical features of the dataset. The
only difference is that we include the datatype object, short O.
# create the statistic report of the categoric features of the training dataset
# create the statistic report of the categoric features of the test dataset
The report of the categoric features include the information of the non-empty rows, the number of unique values, the most common value as “top” and the frequency of the most common value.
• We see that all passenger names are unique but not all ticket numbers. It could be possible that children or families share the same ticket number.
• There are in total 843 male passengers 577 in the training and 266 in the test set. Because the Sex feature has only two unique values (male and female), there must be 472 female passengers, the
difference between the total number of passengers in both datasets and the total number of male passengers.
• The feature Cabin has missing values (204 instead of 891 in the training dataset and 91 instead of 418 in the test dataset.
• Also the feature Embarked has missing values (889 instead of 891 in the training dataset).
Key Questions for the Data Analysis
Now let us remember our task for the Titanic competition. We want to build a classifier that predicts which passengers of the Titanic survived. The classifier must find patterns in the features to
separate the passengers that survived from the passengers that didn’t survive the Titanic.
For that reason, it makes sense to dive deeper into the features of the datasets and try to find features that have an impact on the survival rate of a passenger. You could just test each feature,
but I like to create some key questions that helps to clarify whether a feature is useful or not.
For every key question and for every feature, we will compute the survival rate of the passengers separated by this feature. Therefore, it makes sense to create a function that computes all this for
us and use this function in every key question.
def pivot_survival_rate(df_train, target_column):
# create a pivot table with the target_column as index and "Survived" as columns
# count the number of entries of "PassengerId" for each combination of target_column and "Survived"
# fill all empty cells with 0
df_pivot = pd.pivot_table(
df_train[['PassengerId', target_column, 'Survived']],
# rename the columns to avoid numbers as column name
df_pivot.columns = [target_column, 'not_survived', 'survived']
# create a new column with the total number of survived and not survived passengers
df_pivot['passengers'] = df_pivot['not_survived']+df_pivot['survived']
# create a new column with the proportion of survivors to total passengers
df_pivot['survival_rate'] = df_pivot['survived']/df_pivot['passengers']*100
The function is called pivot_survival_rate and has as arguments the training dataset and the feature that we want to analyze. In this function, we create a pivot table with the feature as index and
the “Survived” label as column. We count the number of passengers for each combination of the key question feature and the “Survived” label. To count the number of passengers, we use the
“PassengerId” column. Empty values are filled with 0 and we reset the index to rename our columns because we defined the “Survived” label as column for the pivot table with the values 0 for not
survived and 1 for survived.
Now we can compute the total number of passengers for each attribute of the feature we want to analyze and calculate the survival rate. In the last step of the function, we print the pivot table. If
you use the to_markdown function for the pandas dataframe, you get a beautiful, formatted table.
If you don’t understand every part of this function, it’s no problem, just wait after we used the function for the first time, and you see the output table.
Now let’s start with the key questions.
Had Older Passengers and Children a Higher Chance of Survival?
The first key question is: Had older passengers and children a higher chance of survival?
My main idea is to create a basic univariate distribution plot of the feature “Age” in the training data to find threshold values when the survival rate is changing, because I guess that children and
older passengers had a higher survival rate compared to adults.
# create univariate dirstribution plot for "Age" seperated by "Survived"
# common_norm=False: distribution for survived and not survived passengers sum up individually to 1
sns.kdeplot(data=df_train, x="Age", hue="Survived", common_norm=False)
#sns.kdeplot(data=df_train, x="Age", hue="Survived")
# limit the x-axes to the max age
plt.xlim(0, df_train['Age'].max())
To create the distribution plot, I use the kdeplot function from the seaborn library. On the x-axis I plot the age and on the y-axis the density separated by the “Survived” label. It is important to
set the common_norm attribute to false (default is true) so that each distribution for “Survived” sums up to 1.
From the distribution plot we can get the following information by comparing the differences between the line of survived (the orange line) and not survived (the blue line):
• Below 12 years, the chances of survival are higher than not to survive, especially for children around 5 years (see the peak in the survived curve).
• And if a passenger is older than the 60 years, the chance to survive reduces very fast (the gap between both curves get wider).
Computing the survival rate of each age does not make any sense, because there are too few samples for each age. That is the reason why we now create groups for the age as new feature, based on the
thresholds that we found in the distribution curve.
def age_category(row):
Function to transform the actual age in to an age category
Thresholds are deduced from the distribution plot of age
if row < 12:
return 'children'
if (row >= 12) & (row < 60):
return 'adult'
if row >= 60:
return 'senior'
return 'no age'
# apply the function age_category to each row of the dataset
df_train['Age_category'] = df_train['Age'].apply(lambda row: age_category(row))
df_test['Age_category'] = df_test['Age'].apply(lambda row: age_category(row))
I want to create in total three groups: children, adult and senior. Because we compute the new grouped age feature for the training and test dataset, it is handy to create a function that is
basically a multi if-else query. The thresholds when a passenger is a child, or a senior are based on our knowledge of the distribution plot. We must remember that there are missing values in the
“Age” feature. For these missing values we create a fourth class.
# show the survival table with the previously created function
pivot_survival_rate(df_train, "Age_category")
After we apply the age_category function to the training and test dataset we use our previous created pivot_survival_rate function to compute the survival rate for each age category.
From the table you see that children had a relatively high survival rate of 57% but senior passengers had a much lower survival rate of 27% compared to the mean survival rate of 38% that we got from
the statistical report.
Had Passengers of a Higher Pclass also a Higher Change of Survival?
The second key question is if passengers with a higher passengers class also had a higher change of survival?
# create a count plot that counts the survived and not survived passengers for each passenger class
ax=sns.countplot(data=df_train, x='Pclass', hue='Survived')
# show numbers above the bars
for p in ax.patches:
ax.annotate('{}'.format(p.get_height()), (p.get_x()+0.1, p.get_height()+10))
# show the ledgend outside of the plot
ax.legend(title='Survived', bbox_to_anchor=(1.05, 1), loc='upper left')
Before we compute the survival rate for each passenger class, lets create a countplot to see how many passengers survived and not survived for each passenger class. To show the numbers above the
bars, we use the annotate function. get_height returns the height of a bar and by iterating over all bars, we can write the number of passengers above each bar.
From the bar chart, we see that most passengers that survived are from the 1st class, but to get the exact numbers, we use the pivot_survival_rate function again.
pivot_survival_rate(df_train, "Pclass")
The exact survival rates from the table show that the higher the passenger class, the higher was the survival rate and that the highest survival rate had passengers in the first class (63%) compared
to the survival rate of the lowest class (24%).
Did Passengers that paid a higher fare also had a higher survival rate?
We could also assume that passengers that paid a higher fare had a higher chance for survival.
To see if the fare influences the survival rate, we create a basic univariate distribution plot of “Fare” for the training data because we need the information if the passengers survived not or. For
the distribution plot we use the kdeplot function of the seaborn library and separate the distribution by “Survived”.
Like for the first key question, if children and older passengers had a higher survival rate, it is important to set the common_norm attribute to false so that the distribution of each unique value
for “Survived” sums up to 1.
# create univariate dirstribution plot for "Fare" seperated by "Survived"
# common_norm=False: distribution for survived and not survived passengers sum up individually to 1
sns.kdeplot(data=df_train, x="Fare", hue="Survived", common_norm=False)
plt.xlim(0, 100)
From the distribution plot we see that a fare lower than 30 results in a very low survival rate. If a passengers paid a fare higher then 30, the chance to survive was higher than not to survive.
Did women have a higher chance of survival?
From the Birkenhead Drill, better known as the code of conduct: “Women and children first”, we also must prove if women had a higher chance of survival. Because the feature “Sex” has only two values
female and male, we can use our function pivot_survival_rate to get the survival rate for male and female passengers.
pivot_survival_rate(df_train, "Sex")
From the resulting table we see that the survival rate for female is 74% and for male 19%. Therefore, currently the feature “Sex” is the best feature for the classification algorithm, because it
separates the survived passengers best from the not suvrived passengers.
Did the port of embarkation influence the survival rate?
The last key question is if the port of embarkation influences the survival rate. The corresponding feature “Embarked” has three unique values so that we can use the pivot_survival_rate function
pivot_survival_rate(df_train, "Embarked")
The results are the following:
• There is a difference in the survival rate between the three different ports.
• The lowest survival rate had passengers that embarked in Southampton (S) with 34%.
• The highest survival rate had passengers that embarked in Cherbourg (C) with 55%.
Try to separate Survived and not Survived Passengers
In addition to the key questions, we can create different visualizations to see if one or a combination of features separate the survived and not survived passengers. This task gives an indication
which features could be important for the machine learning algorithm.
The advantage is that you can try out all features separated by numeric and categorical features in a loop. That saves a lot of time and can be fully automated. The disadvantage is that you do not
think much about each feature. That can hurt you to create new features in the feature engineering part.
My recommendation is to think about some key questions, answer the key questions like we did but also compute the influence of every feature on the target variable at the end of the data analysis
part, so that you are not missing some important influence.
Before we visualize the influence of all features, we combine different features that showed a high influence on the survival rate during the processing of the key questions.
Survival Rate for Sex and Pclass
The first two features are “Sex” and “Pclass”. Both features are categories, so we use the catplot of the seaborn library. Seaborn has no possibility to show the values of the y-axis in each bar of
the plot. But we can use the bar_label function from matplotlib. Note that this function is only available for matplotlib versions greater or equal v3.4.2.
g = sns.catplot(x="Sex", y="Survived", col="Pclass", data=df_train, kind="bar")
# loop over the three different axes crated by the col feature
for i in range(3):
# extract the matplotlib axes_subplot objects from the FacetGrid
ax = g.facet_axis(0, i)
# iterate through the axes containers
for c in ax.containers:
labels = [f'{(v.get_height()):.2f}' for v in c]
ax.bar_label(c, labels=labels, label_type='center')
First, we loop over each of the three axis of the passenger class and extract the axes_subplot from the FacetGrid. Now we iterate for each axis container, get the number of the y-axis from the
get_height function and use this number for the bar_label.
Let me know in the comments if you know another possibility to show the values of the survival rate in the chart.
From the categorial plot that shows the survival rate separated by the sex and passenger class, we get the following results:
• Almost all female passengers of the first class (97%) as well as the second class (92%) survived.
• Female passengers of the 3rd class had a higher chance of survival than male passengers of the first class -> the feature Sex has a higher influence of the survival rate than the Pclass.
• The survival rate for male passengers in the first class was more than twice as high compared to the second and third class.
• The survival rate of male passengers between the second and third class differs not much.
Survival Rate for Age and Pclass
We can also combine a categorical and numeric feature in a catplot by creating a swarmplott. I would like to find out if the age of the passenger in the different passenger classes has a significant
influence of the survival rate.
g = sns.catplot(x="Survived", y="Age", col="Pclass", data=df_train, kind="swarm")
From the swarmplot we see that almost all young passengers from the first and second passenger class survived, but there are a lot of young passengers from the third class that died. The second
observation is that older passengers had a higher change to survive if they are in a higher passenger class (imagine a horizontal line, starting around the age of 50).
Survival Rate for selected Categorical and Numerical Features
After we combined multiple features of the key questions, we want to visualize the influence of selected categorcial and numerical features on the survival rate.
For the categorical features we use the catplot and for the numerical features we use the kdeplot. You already know both seaborn functions from the key questions section.
For the categorical plots we use the same lines of code to create the bar labels that show the survival rate inside each category bar.
for feature in ["Sex", "Embarked", "Pclass", "SibSp", "Parch"]:
g = sns.catplot(x=feature, y="Survived", data=df_train, kind="bar")
# extract the matplotlib axes_subplot objects from the FacetGrid
ax = g.facet_axis(0, -1)
# iterate through the axes containers
for c in ax.containers:
labels = [f'{(v.get_height()):.2f}' for v in c]
ax.bar_label(c, labels=labels, label_type='center')
for feature in ["Age", "Fare"]:
g = sns.kdeplot(data=df_train, x=feature, hue="Survived", common_norm=False)
You already know the results for the first three categories “Sex”, “Embarked” and “Pclass” from the key questions. Only the results of the features “SibSp” and “Parch” are new.
• For “SibSp” the highest survival rate had passengers with 1 sibling or spouse (54%). The second highest survival rate had passengers with 2 siblings or spouses (45%) but the confidence interval
gets very wide. Therefore, the reliability of the results gets weaker.
• For “Parch”, passengers with 3 parents or children had the highest survival rate (60%) but with a wide confidence interval. Therefore, the result of passengers with 1 parch with a slightly lower
mean survival rate (55%) but also with a narrower confidence interval is more reliable.
Save the Analyzed Dataset
The last step in the data analysis Jupyter notebook is to save the training and test dataset as pickle files.
In the next article we will cover the data cleaning and preparation process, where you learn among other important things which additional features I created and how to deal with the missing values
in the datasets.
If you liked the article, bookmark my website and subscribe to my YouTube channel so that you don’t miss any new video.
See you next time and in the meantime, happy coding.
Leave a Comment | {"url":"https://datasciencewithchris.com/kaggle-titanic-data-analysis/","timestamp":"2024-11-08T14:19:30Z","content_type":"text/html","content_length":"85884","record_id":"<urn:uuid:cd59ffc0-12db-46bd-bce3-59effab9ab49>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00084.warc.gz"} |
DEoptim: Differential Evolution Optimization in DEoptim: Global Optimization by Differential Evolution
fn the function to be optimized (minimized). The function should have as its first argument the vector of real-valued parameters to optimize, and return a scalar real result. NA and NaN values
are not allowed.
lower, two vectors specifying scalar real lower and upper bounds on each parameter to be optimized, so that the i-th element of lower and upper applies to the i-th parameter. The implementation
upper searches between lower and upper for the global optimum (minimum) of fn.
control a list of control parameters; see DEoptim.control.
fnMap an optional function that will be run after each population is created, but before the population is passed to the objective function. This allows the user to impose integer/cardinality
constraints. See the the sandbox directory of the source code for a simple example.
... further arguments to be passed to fn.
the function to be optimized (minimized). The function should have as its first argument the vector of real-valued parameters to optimize, and return a scalar real result. NA and NaN values are not
two vectors specifying scalar real lower and upper bounds on each parameter to be optimized, so that the i-th element of lower and upper applies to the i-th parameter. The implementation searches
between lower and upper for the global optimum (minimum) of fn.
an optional function that will be run after each population is created, but before the population is passed to the objective function. This allows the user to impose integer/cardinality constraints.
See the the sandbox directory of the source code for a simple example.
The control argument is a list; see the help file for DEoptim.control for details.
The R implementation of Differential Evolution (DE), DEoptim, was first published on the Comprehensive R Archive Network (CRAN) in 2005 by David Ardia. Early versions were written in pure R. Since
version 2.0-0 (published to CRAN in 2009) the package has relied on an interface to a C implementation of DE, which is significantly faster on most problems as compared to the implementation in pure
R. The C interface is in many respects similar to the MS Visual C++ v5.0 implementation of the Differential Evolution algorithm distributed with the book Differential Evolution – A Practical Approach
to Global Optimization by Price, K.V., Storn, R.M., Lampinen J.A, Springer-Verlag, 2006. Since version 2.0-3 the C implementation dynamically allocates the memory required to store the population,
removing limitations on the number of members in the population and length of the parameter vectors that may be optimized. Since version 2.2-0, the package allows for parallel operation, so that the
evaluations of the objective function may be performed using all available cores. This is accomplished using either the built-in parallel package or the foreach package. If parallel operation is
desired, the user should set parallelType and make sure that the arguments and packages needed by the objective function are available; see DEoptim.control, the example below and examples in the
sandbox directory for details.
Since becoming publicly available, the package DEoptim has been used by several authors to solve optimization problems arising in diverse domains; see Mullen et al. (2011) for a review.
To perform a maximization (instead of minimization) of a given function, simply define a new function which is the opposite of the function to maximize and apply DEoptim to it.
To integrate additional constraints (other than box constraints) on the parameters x of fn(x), for instance x[1] + x[2]^2 < 2, integrate the constraint within the function to optimize, for instance:
fn <- function(x){ if (x[1] + x[2]^2 >= 2){ r <- Inf else{ ... } return(r) }
This simplistic strategy usually does not work all that well for gradient-based or Newton-type methods. It is likely to be alright when the solution is in the interior of the feasible region, but
when the solution is on the boundary, optimization algorithm would have a difficult time converging. Furthermore, when the solution is on the boundary, this strategy would make the algorithm converge
to an inferior solution in the interior. However, for methods such as DE which are not gradient based, this strategy might not be that bad.
Note that DEoptim stops if any NA or NaN value is obtained. You have to redefine your function to handle these values (for instance, set NA to Inf in your objective function).
It is important to emphasize that the result of DEoptim is a random variable, i.e., different results may be obtained when the algorithm is run repeatedly with the same settings. Hence, the user
should set the random seed if they want to reproduce the results, e.g., by setting set.seed(1234) before the call of DEoptim.
DEoptim relies on repeated evaluation of the objective function in order to move the population toward a global minimum. Users interested in making DEoptim run as fast as possible should consider
using the package in parallel mode (so that all CPU's available are used), and also ensure that evaluation of the objective function is as efficient as possible (e.g. by using vectorization in pure R
code, or writing parts of the objective function in a lower-level language like C or Fortran).
Further details and examples of the R package DEoptim can be found in Mullen et al. (2011) and Ardia et al. (2011a, 2011b) or look at the package's vignette by typing vignette("DEoptim"). Also, an
illustration of the package usage for a high-dimensional non-linear portfolio optimization problem is available by typing vignette("DEoptimPortfolioOptimization").
The output of the function DEoptim is a member of the S3 class DEoptim. More precisely, this is a list (of length 2) containing the following elements:
Members of the class DEoptim have a plot method that accepts the argument plot.type. plot.type = "bestmemit" results in a plot of the parameter values that represent the lowest value of the objective
function each generation. plot.type = "bestvalit" plots the best value of the objective function each generation. Finally, plot.type = "storepop" results in a plot of stored populations (which are
only available if these have been saved by setting the control argument of DEoptim appropriately). Storing intermediate populations allows us to examine the progress of the optimization in detail. A
summary method also exists and returns the best parameter vector, the best value of the objective function, the number of generations optimization ran, and the number of times the objective function
was evaluated.
Differential Evolution (DE) is a search heuristic introduced by Storn and Price (1997). Its remarkable performance as a global optimization algorithm on continuous numerical minimization problems has
been extensively explored; see Price et al. (2006). DE belongs to the class of genetic algorithms which use biology-inspired operations of crossover, mutation, and selection on a population in order
to minimize an objective function over the course of successive generations (see Mitchell, 1998). As with other evolutionary algorithms, DE solves optimization problems by evolving a population of
candidate solutions using alteration and selection operators. DE uses floating-point instead of bit-string encoding of population members, and arithmetic operations instead of logical operations in
mutation. DE is particularly well-suited to find the global optimum of a real-valued function of real-valued parameters, and does not require that the function be either continuous or differentiable.
Let NP denote the number of parameter vectors (members) x in R^d in the population. In order to create the initial generation, NP guesses for the optimal value of the parameter vector are made,
either using random values between lower and upper bounds (defined by the user) or using values given by the user. Each generation involves creation of a new population from the current population
members {x_i | i=1,...,NP}, where i indexes the vectors that make up the population. This is accomplished using differential mutation of the population members. An initial mutant parameter vector v_i
is created by choosing three members of the population, x_{r_0}, x_{r_1} and x_{r_2}, at random. Then v_i is generated as
where F is the differential weighting factor, effective values for which are typically between 0 and 1. After the first mutation operation, mutation is continued until d mutations have been made,
with a crossover probability CR in [0,1]. The crossover probability CR controls the fraction of the parameter values that are copied from the mutant. If an element of the trial parameter vector is
found to violate the bounds after mutation and crossover, it is reset in such a way that the bounds are respected (with the specific protocol depending on the implementation). Then, the objective
function values associated with the children are determined. If a trial vector has equal or lower objective function value than the previous vector it replaces the previous vector in the population;
otherwise the previous vector remains. Variations of this scheme have also been proposed; see Price et al. (2006) and DEoptim.control.
Intuitively, the effect of the scheme is that the shape of the distribution of the population in the search space is converging with respect to size and direction towards areas with high fitness. The
closer the population gets to the global optimum, the more the distribution will shrink and therefore reinforce the generation of smaller difference vectors.
As a general advice regarding the choice of NP, F and CR, Storn et al. (2006) state the following: Set the number of parents NP to 10 times the number of parameters, select differential weighting
factor F = 0.8 and crossover constant CR = 0.9. Make sure that you initialize your parameter vectors by exploiting their full numerical range, i.e., if a parameter is allowed to exhibit values in the
range [-100, 100] it is a good idea to pick the initial values from this range instead of unnecessarily restricting diversity. If you experience misconvergence in the optimization process you usually
have to increase the value for NP, but often you only have to adjust F to be a little lower or higher than 0.8. If you increase NP and simultaneously lower F a little, convergence is more likely to
occur but generally takes longer, i.e., DE is getting more robust (there is always a convergence speed/robustness trade-off).
DE is much more sensitive to the choice of F than it is to the choice of CR. CR is more like a fine tuning element. High values of CR like CR = 1 give faster convergence if convergence occurs.
Sometimes, however, you have to go down as much as CR = 0 to make DE robust enough for a particular problem. For more details on the DE strategy, we refer the reader to Storn and Price (1997) and
Price et al. (2006).
David Ardia, Katharine Mullen mullenkate@gmail.com, Brian Peterson and Joshua Ulrich.
Ardia, D., Boudt, K., Carl, P., Mullen, K.M., Peterson, B.G. (2011) Differential Evolution with DEoptim. An Application to Non-Convex Portfolio Optimization. R Journal, 3(1), 27-34. doi: 10.32614/
Ardia, D., Ospina Arango, J.D., Giraldo Gomez, N.D. (2011) Jump-Diffusion Calibration using Differential Evolution. Wilmott Magazine, 55 (September), 76-79. doi: 10.1002/wilm.10034
Mitchell, M. (1998) An Introduction to Genetic Algorithms. The MIT Press. ISBN 0262631857.
Mullen, K.M, Ardia, D., Gil, D., Windover, D., Cline,J. (2011). DEoptim: An R Package for Global Optimization by Differential Evolution. Journal of Statistical Software, 40(6), 1-26. doi: 10.18637/
Price, K.V., Storn, R.M., Lampinen J.A. (2006) Differential Evolution - A Practical Approach to Global Optimization. Berlin Heidelberg: Springer-Verlag. ISBN 3540209506.
Storn, R. and Price, K. (1997) Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces, Journal of Global Optimization, 11:4, 341–359.
DEoptim.control for control arguments, DEoptim-methods for methods on DEoptim objects, including some examples in plotting the results; optim or constrOptim for alternative optimization algorithms.
## Rosenbrock Banana function ## The function has a global minimum f(x) = 0 at the point (1,1). ## Note that the vector of parameters to be optimized must be the first ## argument of the objective
function passed to DEoptim. Rosenbrock <- function(x){ x1 <- x[1] x2 <- x[2] 100 * (x2 - x1 * x1)^2 + (1 - x1)^2 } ## DEoptim searches for minima of the objective function between ## lower and upper
bounds on each parameter to be optimized. Therefore ## in the call to DEoptim we specify vectors that comprise the ## lower and upper bounds; these vectors are the same length as the ## parameter
vector. lower <- c(-10,-10) upper <- -lower ## run DEoptim and set a seed first for replicability set.seed(1234) DEoptim(Rosenbrock, lower, upper) ## increase the population size DEoptim(Rosenbrock,
lower, upper, DEoptim.control(NP = 100)) ## change other settings and store the output outDEoptim <- DEoptim(Rosenbrock, lower, upper, DEoptim.control(NP = 80, itermax = 400, F = 1.2, CR = 0.7)) ##
plot the output plot(outDEoptim) ## 'Wild' function, global minimum at about -15.81515 Wild <- function(x) 10 * sin(0.3 * x) * sin(1.3 * x^2) + 0.00001 * x^4 + 0.2 * x + 80 plot(Wild, -50, 50, n =
1000, main = "'Wild function'") outDEoptim <- DEoptim(Wild, lower = -50, upper = 50, control = DEoptim.control(trace = FALSE)) plot(outDEoptim) DEoptim(Wild, lower = -50, upper = 50, control =
DEoptim.control(NP = 50)) ## The below examples shows how the call to DEoptim can be ## parallelized. ## Note that if your objective function requires packages to be ## loaded or has arguments
supplied via \code{...}, these should be ## specified using the \code{packages} and \code{parVar} arguments ## in control. ## Not run: Genrose <- function(x) { ## One generalization of the Rosenbrock
banana valley function (n parameters) n <- length(x) ## make it take some time ... Sys.sleep(.001) 1.0 + sum (100 * (x[-n]^2 - x[-1])^2 + (x[-1] - 1)^2) } # get some run-time on simple problems maxIt
<- 250 n <- 5 oneCore <- system.time( DEoptim(fn=Genrose, lower=rep(-25, n), upper=rep(25, n), control=list(NP=10*n, itermax=maxIt))) withParallel <- system.time( DEoptim(fn=Genrose, lower=rep(-25,
n), upper=rep(25, n), control=list(NP=10*n, itermax=maxIt, parallelType=1))) ## Compare timings (oneCore) (withParallel) ## End(Not run)
For more information on customizing the embed code, read Embedding Snippets. | {"url":"https://rdrr.io/cran/DEoptim/man/DEoptim.html","timestamp":"2024-11-05T01:30:41Z","content_type":"text/html","content_length":"38743","record_id":"<urn:uuid:e3003aa2-140c-40f0-a1ba-a77847c593ce>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00175.warc.gz"} |
Difference Between Sequence and Series
Sequence and Series is one of the important topics in Mathematics. Though many students tend to get confused between the two, these two can be easily differentiated. Sequence and series can be
differentiated, in which the order of sequence always matter in the sequence but it’s not the case with series.
Sequence and series are the two important topics which deal with the listing of elements. It is used in the recognition of patterns, for example, identifying the pattern of prime numbers, and solving
puzzles, and so on. Also, the series plays an important role in the differential equations and in the analysis process. In this article, let us discuss the key difference between the sequence and
series in detail. Before that, we will see the brief definition of the sequence and series.
Definition of Sequence and Series in Maths
Sequence: The sequence is defined as the list of numbers which are arranged in a specific pattern. Each number in the sequence is considered a term. For example, 5, 10, 15, 20, 25, … is a sequence.
The three dots at the end of the sequence represents that the pattern will continue further. Here, 5 is the first term, 10 is the second term,15 is the third term and so on. Each term in the sequence
can have a common different, and the pattern will continue with the common difference. In the example given above, the common difference is 5. The sequence can be classified into different types,
such as:
• Arithmetic Sequence
• Geometric Sequence
• harmonic Sequence
• Fibonacci Sequence
Series: The series is defined as the sum of the sequence where the order of elements does not matter. It means that the series is defined as the list of numbers with the addition symbol in between.
The series can be classified as a finite series and infinite series which depends on the types of sequence whether it is finite or infinite. Note that, the finite series is a series where the list of
numbers has an ending, whereas the infinite series is never-ending. For example, 1+3+5+7+.. is a series. The different types of series are:
• Geometric series
• Harmonic series
• Power series
• Alternating series
• Exponent series (P-series)
What is the Difference Between Sequence and Series?
Here, the list of major differences between the sequence and series are given below:
Sequence Series
Sequence relates to the organization of terms in a particular order (i.e. related terms follow each other) and series Series can also be classified as a finite and infinite series.
is the summation of the elements of a sequence.
In sequence, the ordering of elements is the most important In series, the order of elements does not matter
The elements in the sequence follow a specific pattern The series is the sum of elements in the sequence
Example: 1, 2, 4, 6, 8, . . . . n are said to be in a Sequence and 1 + 2 + 4 + 6 + 8 . . . . n is said to be in a A finite series can be represented as m1 + m2 + m3 + m4 + m5 + m6 + . . . . . +
series. mn
General Form: \([p_{i}]_{i=1}^{n}\). Unending sequence like p1, p2, p3, p4, p5, p6, . . . . , pn, . . . . . , is If m1 + m2 + m3 + m4 + m5 + m6 + . . . . . . + mn = Sn, then Sn is termed as the
known as an infinite sequence. sum to n elements of the series.
General Form: \([p_{n}]_{n=1}^{\infty }\). General Form: \(S_{n}=\sum_{r=1}^{n}m_{r}\).
The order of a sequence matters. Hence, a sequence 5, 6, 7 is different from 7, 6, 5. However, in case of series 5 + 6 + 7 is same as 7 + 6 + 5.
Frequently Asked Questions on Sequence and Series
What is meant by arithmetic sequence?
In maths, arithmetic sequence, also known as the arithmetic progression where the difference between the two consecutive terms in the sequence should be a constant.
Write down the next three terms in the given sequence 1, 4, 7, ….
The next three terms in the sequence are 10, 13, 16. In this sequence, The difference between 1 and 4 is 3, and 4 and 7 is 3. So, the common difference of this sequence is 3. Therefore, 7+3 = 10,
10+3 = 13, 13+3 = 16.
What are the different types of series in maths?
The different types of series in maths are arithmetic series, harmonic series and geometric series, P-series, exponential series and so on.
Define the finite sequence.
If the number of terms in the sequence is finite or fixed length, then it is called a finite sequence.
Define series with an example
The series is defined as the addition/sum of terms in a sequence. For example, 2, 4, 6, 8 is a sequence, then the series is written as 2+4+6+8.
To learn more difference between articles, register with BYJU’S – The Learning App and download it today. | {"url":"https://mathlake.com/article-314-Difference-Between-Sequence-and-Series.html","timestamp":"2024-11-05T22:01:52Z","content_type":"text/html","content_length":"14786","record_id":"<urn:uuid:ddd88c7c-3560-46f0-9e93-e75bea7aeb0e>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00614.warc.gz"} |
Foundations of Physics
Background Philosophy (top)
I am interested in the foundations of physics.
The goals are admittedly ambitious and bold.
Let's face it, life is short!
My belief is that most foundational research either assumes too much or is too focused on specific sub-fields of physics. For example, I do not believe that one can effectively study the foundations
of quantum mechanics and ignore probability theory, gravity, electromagnetism, and other related phenomena. The universe is a package deal, and to understand it requires understanding the package as
a whole. Certainly progress is made in relatively small steps, but if one is serious about solving the puzzle, one has to keep in mind the whole picture while one is trying to place a particular
I bring to this work my experience in machine learning, which amounts to effective and efficient problem-solving. The more that is assumed in a theory, the more likely it is to be wrong. And perhaps
more importantly, what is assumed cannot be understood. For example, studying the foundations of quantum mechanics by assuming all of the mathematics of a Hilbert space, basically assumes half the
problem, and in doing so prevents one from achieving deep insight.
I take the advice given by Galileo to heart:
"Measure that which is measurable, and make measurable that which is not so."
In my research to date, I have found that apt consistent quantification of any set of entities is often constrained by symmetries and order, and that the resulting constraint equations tend to
reflect what we conceive of as physical laws. That is, underlying order results in orderly laws. I, often in collaboration with others, have applied these ideas to probability theory, information
theory, quantum mechanics, space-time physics, and relativistic quantum mechanics. The progress my colleagues and I have made can be followed below in a series of papers.
How far this approach can take us is anyone's guess, but one must admit that it important to know just how much of physics is derivable as being contingent on underlying symmetry and order.
Quantification (top)
The topic of apt consistent quantification has a long history with many players and examples and I cannot begin to do it justice here. The main different in our approach, is that we treat this as a
central philosophy toward understanding foundations, and not simply a toolbox of disconnected examples throughout history.
Janos Aczel at the Universty of Waterloo and other researchers in the field of Functional Equations have clearly been aware of the critical importance symmetries in the derivation of laws. Perhaps
one of the first texts to treat quantification as a foundational principle is the book by Pfanzagl:
Pfanzagl J. "Theory of Measurement", John Wiley & Sons, 1968.
Our relevant papers range from early:
Knuth K.H. 2003. Deriving laws from ordering relations. In: G.J. Erickson, Y. Zhai (eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Jackson Hole WY 2003, AIP
Conference Proceedings 707, American Institute of Physics, Melville NY, pp. 204-235. arXiv:physics/0403031v1 [physics.data-an] (pdf 206K)
to more recent:
Knuth K.H. 2009. Measuring on lattices. P. Goggans, C.-Y. Chan (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Oxford, MS, USA, 2009, AIP Conference Proceedings
1193, American Institute of Physics, Melville NY, 132-144. (pdf 227K)
Inference and Probability Theory (top)
In many ways, physics is about making optimal inferences about the world around us. To understand this aspect of physics, which is critical to statistical mechanics and quantum mechanics, one must
properly understand the foundations of inference. The inspiration for this research approach came from Richard T. Cox's derivation of probability theory from the foundation of Boolean logic.
Cox R.T. 1946 “Probability, Frequency, and Reasonable Expectation”, American Journal of Physics, 14, 1-13.
Since then, these ideas have evolved and matured as we have employed the more general and powerful formalism of order theory to expose the relevant concepts and expand the applicability of the
Knuth K.H. 2005. Lattice duality: The origin of probability and entropy. Neurocomputing. 67C: 245-274. DOI: 10.1016/j.neucom.2004.11.039 (pdf 477K)
Knuth K.H., Skilling J. 2012. Foundations of Inference. 1(1), 38-73; doi:10.3390/axioms1010038 (Free Full-Text at Axioms)
Quantum Mechanics (top)
Philip Goyal and John Skilling and I have demonstrated that the concepts involved in the derivation of probability theory via quantification can be used to derive the Feynman path integral
formulation of quantum mechanics. This was inspired in part by the efforts of Tikochinski, Tikochinski and Gull, and Caticha's experimental setups.
Goyal P., Knuth K.H., Skilling J. 2010. Origin of complex quantum amplitudes and Feynman's rules, Phys. Rev. A 81, 022109. arXiv:0907.0909v3 [quant-ph]
The following year, Philip Goyal and I showed how quantum mechanics and probability theory are related. Not only is quantum mechanics consistent with probability theory (and the underlying logic),
but it is dependent on it:
Goyal P., Knuth K.H. 2011. Quantum theory and probability theory: their relationship and origin in symmetry, Symmetry 3(2):171-206.
This has since been dramatically updated:
Skilling, J., Knuth, K.H. 2018. The symmetrical foundation of measure, probability and quantum theories. Annalen der Physik (Invited Submission), 1800057.
I should note that some of the older order-theoretic concepts were published by Knuth in 2003:
Knuth K.H. 2003. Deriving laws from ordering relations. In: G.J. Erickson, Y. Zhai (eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Jackson Hole WY 2003, AIP
Conference Proceedings 707, American Institute of Physics, Melville NY, pp. 204-235. arXiv:physics/0403031 [physics.data-an] (pdf 206K)
Those ideas were left out of our two first publications above in favor of the more familiar algebraic relations.
Space-time Physics (top)
Everything that is detected or measured is the direct result of something influencing something else. By considering both the act of influencing and the response to such influence as a pair of
events, we can describe a universe of interactions as a partially-ordered set of events. We take the partially-ordered set of events as a fundamental picture of influence and aim to determine what
interesting physics can be recovered. This is accomplished by identifying a means by which events in a partially-ordered set can be aptly and consistently quantified. Since, in general, a
partially-ordered set lacks symmetries to constraint any quantification, we distinguish a chain of events, which represents an observer, and quantify some subset of events with respect to the
observer chain. Consistent quantification with respect to pairs of observer chains exhibiting a constant relationship with one another results in a metric analogous to the Minkowski metric and that
transformation of the quantification with respect to one pair of chains to quantification with respect to another pair of chains results in the Bondi k-calculus, which represents a Lorentz
transformation under a simple change of variables. We further demonstrate that chain projection induces geometric structure in the partially-ordered set, which itself is inherently both non-geometric
and non-dimensional. Collectively, these results suggest that the concept of space-time geometry may emerge as a unique way for an embedded observer to aptly and consistently quantify a
partially-ordered set of events.
Knuth K.H., Bahreyni N. 2014. A potential foundation for emergent space-time, Journal of Mathematical Physics, 55, 112501.
doi: 10.1063/1.4899081
arXiv:1209.0881 [math-ph]
Fermion Physics, the Feynman Checkerboard,
and the Dirac Equations (top)
We consider describing a particle by focusing on the fact that it influences others. Such a model results in a partially ordered set where a particle is modeled by a chain of influences. As described
above, these interactions give rise to an emergent spacetime where the particle influences can be viewed as the particle taking paths through spacetime. We illustrate how this framework of
influence-generated events gives rise to some of the well- known properties of the Fermions, such as the uncertainty relation and Zitterbewegung. We can take this further by making inferences about
events, which is performed by employing the process calculus, which coincides with the Feynman path integral formulation of quantum mechanics. This results in the Feynman checkerboard model of the
Dirac equation in a 1+1 dimensional space describing a Fermion at rest.
Knuth K.H. 2015. Understanding the Electron To appear in the book "Information and Interaction" edited by Dean Rickles and Ian Durham.
arXiv:1511.07766 [physics.gen-ph]
Knuth K.H. 2014. Information-based physics: an observer-centric foundation. Contemporary Physics, (Invited Submission).
arXiv:1310.1667 [quant-ph]
Knuth K.H. 2014. The problem of motion: the statistical mechanics of Zitterbewegung. Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Amboise, France, Sept 2014, AIP
Conference Proceedings, American Institute of Physics, Melville NY.
arXiv:1411.1854 [quant-ph]
Knuth K.H. 2012. Inferences about interactions: Fermions and the Dirac equation. U. von Toussaint (ed.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Garching, Germany,
July 2012, AIP Conference Proceedings, American Institute of Physics, Melville NY., arXiv:1212.2332 [quant-ph]
Influence: The Foundational Concept (top)
When one considers what one can actually know about something like an electron. One is led to the idea that all one can really know is that things, like electrons, influence one another. In some
sense, this idea is not new as it was the basis for throwing out the middle-man (the field) in Wheeler and Feynman's work on direct particle-particle interaction. It is also the basis for Ruth
Kastner's transactional theory of quantum mechanics. Here we put our own twist on the concept. Basically, since all that one can possibly know is that things influence one another, this should be all
that one needs to know. Here we consider the concept of influence and how it gives rise to partially ordered sets of influence events. In the coarse-grained picture, this gives rise to the emergence
of space-time. And in the fine-grained picture, when observers make inferences about the behavior of things influencing one another, this gives rise to Fermion physics.
When particles influence others, this gives rise to concepts of the particle's position, proper time, energy, momentum, and velocity. When a particle is influenced, then we see forces emerging. Thus
in this theory, influence is responsible for a wide array of concepts in physics.
Knuth, K.H., Walsh, J.L. 2018. An introduction to influence theory: Kinematics and dynamics. Annalen der Physik (Invited Submission), 1700370.
arXiv:1803.09618 [physics.gen-ph]
Knuth K.H. 2015. Understanding the Electron To appear in the book "Information and Interaction" edited by Dean Rickles and Ian Durham.
arXiv:1511.07766 [physics.gen-ph]
Knuth K.H., Bahreyni N. 2014. A potential foundation for emergent space-time, Journal of Mathematical Physics, 55, 112501.
doi: 10.1063/1.4899081
arXiv:1209.0881 [math-ph]
Knuth K.H. 2014. Information-based physics: an observer-centric foundation. Contemporary Physics, (Invited Submission).
arXiv:1310.1667 [quant-ph]
Walsh J., Knuth K.H. 2014. Information-based physics, influence and forces. Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Amboise, France, Sept 2014, AIP Conference
Proceedings, American Institute of Physics, Melville NY.
arXiv:1411.2163 [quant-ph]
Knuth K.H. 2012. Inferences about interactions: Fermions and the Dirac equation. U. von Toussaint (ed.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Garching, Germany,
July 2012, AIP Conference Proceedings, American Institute of Physics, Melville NY., arXiv:1212.2332 [quant-ph]
Knuth K.H. 2013. Information-based physics and the influence network. 2013 FQXi? Essay Entry (http://fqxi.org/community/forum/topic/1831)
Download Essay
Knuth K.H. 2016. Understanding the Electron To appear in the book "Information and Interaction" edited by Dean Rickles and Ian Durham.
arXiv:1511.07766 [physics.gen-ph]
Knuth K.H. 2015. The problem of motion: the statistical mechanics of Zitterbewegung. Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Amboise, France, Sept 2014, AIP Conf.
Proc. 1641, AIP, Melville NY, pp. 588-594.
arXiv:1411.1854 [quant-ph]
Walsh J.L., Knuth K.H. 2015. Information-based physics, influence and forces. Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Amboise, France, Sept 2014, AIP Conf. Proc.
1641, AIP, Melville NY, pp. 538-547
arXiv:1411.2163 [quant-ph]
Knuth K.H., Bahreyni N. 2014. A potential foundation for emergent space-time, Journal of Mathematical Physics, 55, 112501.
doi: 10.1063/1.4899081
arXiv:1209.0881 [math-ph]
Knuth K.H. 2014. Information-based physics: an observer-centric foundation. Contemporary Physics, 55(1), 12-32, (Invited Submission).
arXiv:1310.1667 [quant-ph]
Knuth K.H. 2013. Information-based physics and the influence network. 2013 FQXi? Essay Entry (http://fqxi.org/community/forum/topic/1831)
Download Essay
Knuth K.H. 2012. Inferences about interactions: Fermions and the Dirac equation. U. von Toussaint (ed.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Garching, Germany,
July 2012, AIP Conference Proceedings 1553, American Institute of Physics, Melville NY.
Knuth K.H., Skilling J. 2012. Foundations of Inference. Axioms 1(1), 38-73.
Goyal P., Knuth K.H. 2011. Quantum theory and probability theory: their relationship and origin in symmetry. Symmetry 3(2):171-206.'''
Knuth K.H. 2010. Information physics: The new frontier. P. Bessiere, J.-F. Bercher, A. Mohammad-Djafari (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Chamonix,
France, 2010, AIP Conference Proceedings 1305, American Institute of Physics, Melville NY, 3-19.
arXiv:1009.5161v1 [math-ph]
Goyal P., Knuth K.H., Skilling J. 2010. Origin of complex quantum amplitudes and Feynman's rules. Phys. Rev. A 81, 022109.
Goyal P., Knuth K.H., Skilling L. 2009. The origin of complex quantum amplitudes. P. Goggans, C.-Y. Chan (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Oxford, MS,
USA, 2009, AIP Conference Proceedings 1193, American Institute of Physics, Melville NY, 89-96.
Knuth K.H. 2009. Measuring on lattices. P. Goggans, C.-Y. Chan (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Oxford, MS, USA, 2009, AIP Conference Proceedings
1193, American Institute of Physics, Melville NY, 132-144.
arXiv:0909.3684 [math.GM]
Knuth K.H. 2003. Deriving laws from ordering relations. In: G.J. Erickson, Y. Zhai (eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Jackson Hole WY 2003, AIP
Conference Proceedings 707, American Institute of Physics, Melville NY, pp. 204-235.
Knuth K.H., Bahreyni N., Walsh J.L. 2015. The influence network: A new foundation for emergent physics
Beyond Spacetime 2015, San Diego, CA, USA on 13 March 2015
We introduce an alternate description of physical reality based on a simple foundational concept that there exist things that influence one another. It has been previously demonstrated that
quantification of order-theoretic structures consistent with relevant symmetries results in constraint equations akin to physical laws. We consider a network of objects that influence one another —
the influence network. By consistently quantifying such a network with respect to embedded observers, we demonstrate in relevant special cases that influence events can only be quantified by the
familiar mathematics of space-time, influence gives rise to forces, and observer-made inferences result in the Dirac equation and fermion physics. Together this suggests a novel path to quantum
Knuth K.H. 2014. FQXI 2014: Foundations of Probability and Information.
Opening Panelist Discussion on the Perspectives of Information at the FQXi 2014 Conference on Physics and Information, Vieques Island, Puerto Rico, USA on 6 Jan 2014.
Knuth K.H. 2013. Information-Based Physics: An Intelligent Embedded Agent's Guide to the Universe.
Presented to the Santa Fe Institute , Santa Fe NM on 26 Mar 2013.
Presented to Complexity Sciences Center at UC Davis, Davis CA on 9 Apr 2013.
Presented to Stanford Physics, Stanford University, Stanford CA on 12 Apr 2013.
In this talk, I propose an approach to understanding the foundations of physics by considering the optimal inferences an intelligent agent can make about the universe in which he or she is embedded.
Information acts to constrain an agent’s beliefs. However, at a fundamental level, any information is obtained from interactions where something influences something else. Given this, the laws of
physics must be constrained by both the nature of such influences and the rules by which we can make inferences based on information about these influences. I will review the recent progress we have
made in this direction. This includes: a brief summary of how one can derive the Feynman path integral formulation of quantum mechanics from a consistent quantification of measurement sequences with
pairs of numbers (Goyal, Skilling, Knuth 2010; Goyal, Knuth 2011), a demonstration that consistent apt quantification of a partially-ordered set of events (connected by interactions) by an embedded
agent results in space-time geometry and Lorentz transformations (Knuth, Bahreyni 2012), and an explanation of how, given the two previous results, inferences (Knuth, Skilling 2012) about a direct
particle-particle interaction model results in the Dirac equation (in 1+1 dimensions) and the properties of Fermions (Knuth, 2012). In summary, critical aspects of quantum mechanics, relativity, and
particle properties appear to be derivable by considering an embedded agent who consistently quantifies observations and makes consistent inferences about them.
Knuth K.H. 2013. The foundations of probability Theory and quantum theory.
Presented at NASA Ames Research Center, 11 Apr 2013.
Presented at Google on 10 Apr 2013.
Probability theory is a calculus that enables one to compute degrees of implication among logical statements. Quantum theory is a calculus that enables one to compute the probabilities of the
possible outcomes of a measurement performed on a physical system. Since the development of quantum theory (and probability theory), there have been many questions regarding the relationship between
the two theories; some going as far as to question whether quantum theory is even compatible with probability theory. In this talk, I demonstrate precisely the relationship between probability theory
and quantum theory by deriving both theories from first principles. This is accomplished by observing how consistent quantification of logical statements (Knuth, Skilling 2012) and quantum
measurement sequences (Goyal, Skilling, Knuth 2010) are constrained by the relevant symmetries in each of the two domains (Goyal, Knuth 2011). It will be shown that the derivation of quantum theory
is not only consistent with, but also relies on probability theory. In addition, these results highlight some important differences between inference in the classical and quantum domains.
Knuth K.H. 2010. Information Physics: The Next Frontier, MaxEnt? 2007, Chamonix, France, July 2007.
At this point in time, two major areas of physics, statistical mechanics and quantum mechanics, rest on the foundations of probability and entropy. The last century saw several significant
fundamental advances in our understanding of the process of inference, which make it clear that these are inferential theories. That is, rather than being a description of the behavior of the
universe, these theories describe how observers can make optimal predictions about the universe. In such a picture, information plays a critical role. What is more is that little clues, such as the
fact that black holes have entropy, continue to suggest that information is fundamental to physics in general.
In the last decade, our fundamental understanding of probability theory has led to a Bayesian revolution. In addition, we have come to recognize that the foundations go far deeper and that Cox’s
approach of generalizing a Boolean algebra to a probability calculus is the first specific example of the more fundamental idea of assigning valuations to partially-ordered sets. By considering this
as a natural way to introduce quantification to the more fundamental notion of ordering, one obtains an entirely new way of deriving physical laws. I will introduce this new way of thinking by
demonstrating how one can quantify partially-ordered sets and, in the process, derive physical laws.
The implication is that physical law does not reflect the order in the universe, instead it is derived from the order imposed by our description of the universe. Information physics, which is based
on understanding the ways in which we both quantify and process information about the world around us, is a fundamentally new approach to science.
Knuth K.H. 2010. The role of order in natural law, Workshop on the Laws of Nature: Their Nature and Knowability, Perimeter Institute, Waterloo, Canada, May 2010.
In the last four and a half centuries, we have found that we are able to identify laws of nature that are generally applicable, and because of this we have inferred that there is an underlying order
to the structure and dynamics of the universe. In many cases we have been able to identify this order as being related to symmetries, which have enabled us to derive various laws, such as
conservation laws. But in most cases, the role that order plays in determining natural law remains obscured. In this talk I will rely on order theory to demonstrate how symmetries among our
descriptions of various states of a physical system result in constraint equations, generally called sum and product rules, which are ubiquitous in natural laws. The fact that much of the order that
determines the structure of natural laws arises from relationships inherent in our particular description of a physical system implies that the laws of nature are more closely related to what we
choose to say about the universe and how we say it rather than being fundamental governing principles. | {"url":"http://knuthlab.org/pmwiki.php/Foundations/FoundationsOverview","timestamp":"2024-11-03T14:12:57Z","content_type":"text/html","content_length":"47411","record_id":"<urn:uuid:e5c2a548-f1ae-4fd1-922a-b1b8b0f0e343>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00587.warc.gz"} |
How to Calculate the Average of an Array in JavaScript
**How to Calculate the Average of an Array in JavaScript**
The average of an array is the sum of its elements divided by its length. In JavaScript, you can calculate the average of an array using the `reduce()` method. The `reduce()` method takes a callback
function as its first argument. This callback function takes two arguments: the current element of the array and the accumulator. The accumulator is the value that will be returned by the `reduce()`
The following code calculates the average of an array of numbers:
const numbers = [1, 2, 3, 4, 5];
const average = numbers.reduce((accumulator, currentValue) => {
return accumulator + currentValue;
}, 0);
console.log(average); // 3
The `reduce()` method starts by initializing the accumulator to 0. Then, it iterates over the elements of the array, calling the callback function for each element. The callback function adds the
current element to the accumulator. Finally, the `reduce()` method returns the value of the accumulator.
In this example, the callback function is a simple function that adds the current element to the accumulator. However, you can use the callback function to perform any calculation you want. For
example, you could use the callback function to calculate the sum of the absolute values of the elements in the array, or the product of the elements in the array.
The `reduce()` method is a powerful tool that can be used to perform a variety of calculations on arrays. It is a good idea to familiarize yourself with the `reduce()` method if you are working with
arrays in JavaScript.
Index Value Average
1 2 1.5
In this tutorial, you will learn how to calculate the average of an array in JavaScript. You will learn four different methods for calculating the average, including using the `reduce()` method, the
`sum()` method, the `mean()` method, and a custom function.
**Calculating the Average of an Array in JavaScript**
There are four different ways to calculate the average of an array in JavaScript.
1. **Using the `reduce()` method**
The `reduce()` method is a built-in JavaScript method that can be used to apply a function to each element of an array and return a single value. To calculate the average of an array using the
`reduce()` method, you can use the following code:
const array = [1, 2, 3, 4, 5];
const average = array.reduce((accumulator, currentValue) => accumulator + currentValue) / array.length;
console.log(average); // 3
The `reduce()` method takes two arguments:
• The first argument is the initial value of the accumulator. In this case, we are using 0 as the initial value.
• The second argument is a function that takes two arguments: the accumulator and the current value of the array. The function should return the updated value of the accumulator.
In this example, the function simply adds the current value of the array to the accumulator. The `reduce()` method then divides the accumulator by the length of the array to calculate the average.
2. **Using the `sum()` method**
The `sum()` method is a built-in JavaScript method that can be used to calculate the sum of the elements in an array. To calculate the average of an array using the `sum()` method, you can use the
following code:
const array = [1, 2, 3, 4, 5];
const sum = array.sum();
const average = sum / array.length;
console.log(average); // 3
The `sum()` method takes one argument: the array of values to be summed. The method returns the sum of the values in the array.
3. **Using the `mean()` method**
The `mean()` method is a built-in JavaScript method that can be used to calculate the mean of the elements in an array. The mean is the average of the values in the array. To calculate the average of
an array using the `mean()` method, you can use the following code:
const array = [1, 2, 3, 4, 5];
const average = array.mean();
console.log(average); // 3
The `mean()` method takes one argument: the array of values to be averaged. The method returns the mean of the values in the array.
4. **Using a custom function**
You can also use a custom function to calculate the average of an array. To do this, you can create a function that takes an array of values as its argument and returns the average of the values. The
following is an example of a custom function that can be used to calculate the average of an array:
function average(array) {
const sum = array.reduce((accumulator, currentValue) => accumulator + currentValue);
const length = array.length;
return sum / length;
const array = [1, 2, 3, 4, 5];
const average = average(array);
console.log(average); // 3
This function takes an array of values as its argument and returns the average of the values. The function first uses the `reduce()` method to calculate the sum of the values in the array. The
function then divides the sum by the length of the array to calculate the average.
Sorting an Array in JavaScript
In this tutorial, you will learn how to sort an array in JavaScript. You will learn three different methods for sorting an array, including using the `sort()` method, the `reverse()` method, and a
custom function.
Sorting an Array Using the `sort()` Method
The `sort()` method is a built-in JavaScript method that can be used to sort an array. The `sort()` method takes one or more arguments. The first argument is the array to be sorted. The remaining
arguments are the properties of the array elements that should be used to sort the array.
The following is an example of
How to Find the Average of an Array in JavaScript
The average of an array is the sum of its elements divided by the number of elements. In JavaScript, you can find the average of an array using the following methods:
• The `reduce()` method
• The `map()` method and the `reduce()` method
• A custom function
Using the `reduce()` Method
The `reduce()` method is a built-in JavaScript method that can be used to reduce an array to a single value. To find the average of an array using the `reduce()` method, you can use the following
const average = array.reduce((accumulator, currentValue) => {
accumulator += currentValue;
return accumulator;
}, 0);
In this syntax, the first argument to the `reduce()` method is the accumulator, which is the value that will be used to store the running total of the elements in the array. The second argument to
the `reduce()` method is the current value of the element being processed. The `reduce()` method iterates through the array from left to right, adding the current value to the accumulator. The
`reduce()` method returns the final value of the accumulator, which is the average of the elements in the array.
For example, the following code finds the average of the numbers in an array:
const numbers = [1, 2, 3, 4, 5];
const average = numbers.reduce((accumulator, currentValue) => {
accumulator += currentValue;
return accumulator;
}, 0);
console.log(average); // 3
Using the `map()` Method and the `reduce()` Method
You can also use the `map()` method and the `reduce()` method to find the average of an array. To do this, you can use the following syntax:
const average = array.map(value => value).reduce((accumulator, currentValue) => {
accumulator += currentValue;
return accumulator;
}, 0);
In this syntax, the `map()` method is used to convert the elements of the array to numbers. The `reduce()` method is then used to find the average of the numbers.
For example, the following code finds the average of the numbers in an array:
const numbers = [1, 2, 3, 4, 5];
const average = numbers.map(value => value).reduce((accumulator, currentValue) => {
accumulator += currentValue;
return accumulator;
}, 0);
console.log(average); // 3
Using a Custom Function
You can also find the average of an array using a custom function. To do this, you can use the following syntax:
const average = function(array) {
let sum = 0;
for (let i = 0; i < array.length; i++) { sum += array[i]; } return sum / array.length; }; const numbers = [1, 2, 3, 4, 5]; const average = average(numbers); console.log(average); // 3 In this syntax,
the custom function takes the array as its only argument. The function iterates through the array, adding the elements to the `sum` variable. The function then divides the `sum` variable by the
length of the array to get the average. In this tutorial, you learned three different ways to find the average of an array in JavaScript. You can use the `reduce()` method, the `map()` method and the
`reduce()` method, or a custom function.
Additional Resources
• [MDN: Array.reduce()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/reduce)
• [MDN: Array.map()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/map)
• [W3Schools: JavaScript Array Average](https://www.w3schools.com/js/js_array_average.asp)
Q: What is the JavaScript average() function?
A: The JavaScript average() function returns the average of the values in an array. The average is calculated by adding all of the values in the array and then dividing the result by the number of
values in the array.
Q: How do I use the JavaScript average() function?
A: To use the JavaScript average() function, you can use the following syntax:
where `array` is the array of values that you want to calculate the average of.
Q: What if the array is empty?
A: If the array is empty, the JavaScript average() function will return `NaN` (Not a Number).
Q: What if the array contains non-numeric values?
A: If the array contains non-numeric values, the JavaScript average() function will throw an error.
Q: What is the difference between the JavaScript average() function and the Math.avg() function?
A: The JavaScript average() function and the Math.avg() function both calculate the average of an array of values. However, there are a few key differences between the two functions.
• The JavaScript average() function is a built-in function, while the Math.avg() function is a method of the Math object.
• The JavaScript average() function accepts an array of values as its only argument, while the Math.avg() function accepts an array of values as its first argument and an optional second argument
that specifies the datatype of the values in the array.
• The JavaScript average() function returns a floating-point number, while the Math.avg() function returns a number of the same datatype as the values in the array.
Q: When should I use the JavaScript average() function?
A: The JavaScript average() function is a useful function for calculating the average of an array of values. You can use it to calculate the average of a set of numbers, the average of a set of
scores, or the average of any other set of values.
In this blog post, we have discussed how to calculate the average of an array in JavaScript. We have covered three different methods: using the reduce() method, using the sum() method, and using the
Math.mean() function. We have also provided examples of how to use each method.
Which method you choose to use will depend on your specific needs. The reduce() method is the most versatile, as it can be used to calculate the average of any array, regardless of its type. The sum
() method is the simplest, but it can only be used to calculate the average of an array of numbers. The Math.mean() function is the most efficient, but it can only be used to calculate the average of
an array of numbers.
We hope that this blog post has been helpful. If you have any questions, please feel free to leave a comment below.
Author Profile
Hatch, established in 2011 by Marcus Greenwood, has evolved significantly over the years. Marcus, a seasoned developer, brought a rich background in developing both B2B and consumer software for
a diverse range of organizations, including hedge funds and web agencies.
Originally, Hatch was designed to seamlessly merge content management with social networking. We observed that social functionalities were often an afterthought in CMS-driven websites and set out
to change that. Hatch was built to be inherently social, ensuring a fully integrated experience for users.
Now, Hatch embarks on a new chapter. While our past was rooted in bridging technical gaps and fostering open-source collaboration, our present and future are focused on unraveling mysteries and
answering a myriad of questions. We have expanded our horizons to cover an extensive array of topics and inquiries, delving into the unknown and the unexplored. | {"url":"https://hatchjs.com/js-average-of-array/","timestamp":"2024-11-09T01:18:33Z","content_type":"text/html","content_length":"93405","record_id":"<urn:uuid:9776f16a-6832-417c-87a0-dbe8ea7fe03d>","cc-path":"CC-MAIN-2024-46/segments/1730477028106.80/warc/CC-MAIN-20241108231327-20241109021327-00195.warc.gz"} |
Blue Team-System Live Analysis [Part 11]- Windows: User Account Forensics- NTUSER.DAT
Blue Team-System Live Analysis [Part 11]- Windows: User Account Forensics- NTUSER.DAT Rules, Tools, Structure, and Dirty Hives!
Let’s Connect | LinkedIn | Twitter
Without a doubt, the Windows registry is one of the most valuable forensics data sources that investigators can use. I should think of a dedicated series on Windows Registry Forensics, but, for now,
we only focus on NTUSER.DAT and its role in user account forensics.
Note: This post only focuses on the NTUSER.DAT, however, the rules and tools can be used for other registry files such as System, Sam, Security, Software, and Default.
Part 10 explained how we could forensically extract one of the most important files to analyse user profiles, settings, and activities. Yes, the NTUSER.DAT. The data stored in NTUSER.DAT and the logs
give us fantastic information about each user. As we have them in hand now, let’s explore.
NTUSER.DAT, netuser.dat.LOG1 and netuser.dat.LOG2 extracted from a test system using FTK Imager
1- Rules First, Tools Next!
You may know the main principle of my writeups: Know the Rules, Before Using Tools. We can be masters of tools, quickly refer to them, and start analyzing our files, nothing wrong with that!
But, in my opinion, dive into how things are working (e.g. file structures, operations, interactions, logic, formats, etc. ) makes us an expert and even helps us understand tools capabilities better.
Example: We may have heard that how amazing is Registry Explorer to deal with windows registry forensics. I do agree with this statement too! Why? Well, let's learn few rules then.
2- Unreconciled data (Dirty Hive!)
The NTUSER.DAT is the primary file for the HKEY_CURRENT_USER hive and keeps user-related information; however, Windows is not updating this file in real-time.
In fact, when a system is running, the data being stored in transaction logs first and will be synced with the primary file when the system is logging off, all the users are inactive, or an hour has
elapsed since the last sync.
Part 8 Recap: Windows keep a backup of all the activities and changes such as accessing folders, opening files, network shares, etc., in netuser.dat.LOG1 and netuser.dat.LOG2 during the live
session and saves them into NTUSER.DAT during Log off.
The NTUSER.DAT collected from a victim system may not contain the most updated data as we are conducting the live analysis, and the transaction logs data may have not yet been transferred to the
primary file.
To address this issue, we need to obtain the netuser.dat.LOG1 and netuser.dat.LOG2 (we did it in part 10 ) and aggregate them with NTUSER.DAT to have all the data in hand.
Wait? How do we know whether the NTUSER.DAT is updated or not!
3- How to Detect dirty hives
Some tools make life easy, but if you ask me, the manual analysis gives us a greater understanding of what we are doing, which is crucial for every investigator.
Don’t get me wrong, what I just suggested must be employed during training and capability development. We are not supposed to avoid tools and waste our time and energy on the battlefield. There
are many tools available to have fun, and we will use them right away in a real investigation.
It’s highly recommended to understand the structure of the primary hive. However, to make it simple, we need to check two fields of the NTUSER.DAT header as follows:
• Primary sequence number: This number incremented by 1 when the write operation on NTUSER.DAT begins.
• Secondary sequence number: This number incremented by 1 when the write operation on NTUSER.DAT ends.
The above numbers should be equal in the event of a successful write operation. Thus:
• If the Primary sequence number !=Secondary sequence number: the NTUSER.DAT is not updated (Dirty Hive) and must be aggregated with netuser.dat.LOG1 and netuser.dat.LOG2.
Dirty NTUSER.DAT opened with Hex Editor.
• If the Primary sequence number ==Secondary sequence number: the NTUSER.DAT is updated (Clean Hive) and contains the complete actual data.
Clean NTUSER.DAT opened with Hex Editor.
Now we have a good idea of why it is important to obtain the netuser.dat.LOG1 and netuser.dat.LOG2 in addition to the primary file. We need them to update the NTUSER.DAT. How? Well, it's time to
justify why Registry Explorer is one of the bests!
The main strength of the Registry Explorer tool is the ability to identify the dirty NTUSER.DAT and replay the netuser.dat.LOG1 and netuser.dat.LOG2 to fix the issue.
4- How to Read NTUSER.DAT
There are few paid tools such as OSForesnics and FTK Registry Viewer to work with NTUSER.DAT and registry files in general. We can use demo versions to get familiar with them.
However, Windows built-in commands and free tools such as RegRipper and Registry Explorer are good enough to conduct our investigation.
4.1 Windows built-in command
The reg commands enable us to perform various operations on windows registry subkeys. We need the reg load, reg query, and reg unload commands to work with NTUSER.DAT collected from the test system.
Reg Commands for NTUSER.dat Analysis
We can use the reg load command to load the NTUSER.DAT into a temporary subkey in the Windows registry to view and read it.
reg load HKLM\sechub d:\sechub\NTUSER.dat
The above command loads the NTUSER.dat into the sechub subkey under the HKEY_LOCAL_MACHINE that can be viewed in Regedit.
NTUSER.dat Loaded into HKLM\sechub
Now we can use the reg query to retrieve desired information from the loaded NTUSER.dat. The figure below depicts the two queries as an example.
reg query HKLM\sechub
reg query HKEY_LOCAL_MACHINE\sechub\Environment
Retrieve the Information from Loaded NTUSER.DAT using Reg Query Command
Once we get all the information we look for, we should unload the NTUSER.DAT from the registry and remove the temporary subkey.
Unload NTUSER.dat from Registry
Note: The windows registry must be closed during the load and unload process.
4.2 RegRipper
Working with the RegRipper is quite straightforward; load the NTUSER.DAT as Hive File, set the file name and directory for the report, and we are good to go!
Retrieve the Information from Loaded NTUSER.DAT using RegRipper
The report will be in txt format as follows:
The RegRipper Report Sample
Even though the RegRipper is easy to use, the result will be in plain text that makes data navigation difficult, not a big deal! But, the is a bigger issue.
The RegRipper will not handle the unreconciled data restored in transaction logs (netuser.dat.LOG1 and netuser.dat.LOG2), and as a result, we may not have the most updated data by just analyzing the
main file (NTUSER.DAT).
Note: We may have the same issue using the Built-in Command!
4.3 Registry Explorer
It's free and powerful; what else do we want! It is highly recommended to download the tool and give it a try. It has an amazing user manual covering both the GUI based Registry Explorer and RECmd
command-line tool.
Registry Explorer and RECmd
Load the NTUSER.DAT hive from the file menu:
Load NTUSER.DAT Hive
As expected, we will face a warning message that shows that the “primary and secondary sequence numbers do not match. “ Oh.. we know what does it mean!
Dirty Hive Warning
We can also press No and open the NTUSER.DAT as it is, but why would we do that! Let's press yes and replay the transaction logs to update our primary file.
Replay Transaction Logs
Just click on the ok and select the ntuser.dat.LOG1 and ntuser.dat.LOG2.
Select ntuser.dat.LOG1 and ntuser.dat.LOG2
It will be quick, and we need to click the OK button to save the clean (updated) version of the NTUSER.DAT in the desired location.
Save the Updated Hive
The NTUSER.DAT_clean name is automatically given to the updated version.
Save the Updated Hive File
Note: By holding shift while loading the NTUSER.DAT file at the beginning we can shorten the above process and let the logs replayed automatically. However, the updated primary file will reside on
memory only and we will not have a copy of clean NTUSER.DAT on the hard disk.
The saved file has exact similar sequence numbers as it's updated now. We can load it later or click on the yes and load it now.
Load the Updated Hive
We have an option to open the old file at the same e time to have a comparison.
Load the Old (Dirty) hive
We can work with both the clean and the dirty hives at the same time:
The Dirty and Clean NTUSER.DAT Loaded in Registry Explorer
Done! we can now enjoy the investigation. Are you wondering what we should look for and what we can have by analysing the NTUSER.DAT?
Stay tuned; the next post will discuss the forensics values of the NTUSER.DAT and their locations in the hive. | {"url":"https://nothingcyber.medium.com/blue-team-system-live-analysis-part-11-windows-user-account-forensics-ntuser-dat-495ab41393db?source=user_profile_page---------0-------------418f0860627c---------------","timestamp":"2024-11-10T22:56:40Z","content_type":"text/html","content_length":"195514","record_id":"<urn:uuid:7b379b89-6476-4e93-b2e4-809fcd7b0995>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00531.warc.gz"} |
Phase field method of ferroelectrics
The ferroelectric (FE) phase field method utilizes a thermodynamic approach to describe the FE phase transition. Within this theoretical description, these materials are characterized by the onset of
a primary order parameter that becomes nonzero below a critical Curie temperature . In the case of canonical FEs such as or , the primary order parameter is the electric dipole moment. In both of
these compounds, below , the material symmetry is lowered from cubic to tetragonal. The ionic displacements (the relative off-centering the Ti atom) give rise, spontaneously, to a net nonzero
polarization or .
To describe this transition, the time-dependent Landau-Ginzburg-Devonshire (TDLGD) equation can be evolved to search for ground states of the system,
Here, the system energy is given by whose minimum is when . The action of evolving Eq. (1) is to follow the energy down towards the minimum by starting from a sufficiently close estimate of the cubic
state with . Since the FE material has more than one energy minima corresponding to the tetragonal (six-fold) symmetry (see above double well for , domains will form characterized by equal energy
configurations of . The strength of the FE phase field method is that it allows the identification of arbitrary orientations of in the continuum limit (agnostic of length scales typically restrictive
of atomistic simulations). The domain patterns can be predicted given a relatively simple set of inputs. Within the FERRET/MOOSE ecosystem, the finite element method is employed to discretize Eq. (1)
onto regular or irregular grids. The use of the latter allows for one to search for domain patterns in arbitrary geometries (i.e. nanoparticles or curved surfaces).
In thin film samples, these domain orientations depend strongly on temperature or other external applied fields (i.e. electric or mechanical in origin) which can also be included in the calculations.
The coupling to the electric fields (internal and/or external) are provided by the Poisson equation,
where the electric field is defined in the usual way . If the system has a strong dependence on elastic fields (as is the case for most ferroelectrics), then mechanical equilibrium can be sought be
where is the total stress tensor and denotes spatial derivatives in the direction. Eqs (2) and (3) can be solved at every time step in the evolution of Eq. (1). In the phase field approach, the
decomposition of contains different contributions due to different physics,
with the bulk double well potential density, the gradient energy density penalty for formation of domain walls, linear elastic energy density, interaction energy density for the inclusion of an
internal or external field, the electrostrictive energy density coupling between the dipole moment and the strain fields. All of these terms can be expanded up to arbitrary order depending on the
material symmetry and need for accuracy of predicted spontaneous order parameter values.
For the gradient energy density, one typically uses the lowest-order Lifshitz invariants as described in Cao and Barsch (1990) and Hlinka and Marton (2006),
which requires knowledge of (material specific). Higher order terms are possible although not generally necessary to describe the domain wall structure in bulk or thin film. For canonical
perovskites, there is a good understanding of the values of these parameters along with the bulk expansion coefficients . A typical relaxation of the TDLGD equation is provided below which shows the
resulting flux-closure structure along with the time dependence of each of the energy terms as the energy is minimized.
1. W. Cao and G. R. Barsch. Landau-Ginzburg model of interphase boundaries in improper ferroelastic Perovskites of symmetry. Physical Review B, 1990.[BibTeX]
2. J. Hlinka and P. Marton. Phenomenological model of a $90^\circ $ domain wall in BaTiO₃-type ferroelectrics. Physical Review B, 2006.[BibTeX] | {"url":"https://mangerij.github.io/ferret/theory/intro_LGD.html","timestamp":"2024-11-07T13:10:08Z","content_type":"text/html","content_length":"88109","record_id":"<urn:uuid:dac83b3e-cf70-4c47-87c6-acaba5ac3e2a>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00897.warc.gz"} |
PTS Type III
Here is an interesting document sent to me by an old friend. It concerns the handling of “PTS Type 3’s” or “the insane.” These are people that according to the scientology definition are being
negatively effected by “apparent SP’s” all over the world, or even ghosts and demons. In scientology someone “going Type 3” means having a psychotic break.
I am sure this issue is otherwise available on the internet and I am not “revealing” it for the first time. Though it is certainly the first time it has appeared on this blog. And I havent seen it
for 20 years or more.
I recall reading it when I was in the church — I do not doubt its authenticity. And not just because I remember it, but more importantly because what it says is exactly how things are done in
scientology. And it clearly expresses the attitude Sea Org members have towards those who are “Type 3.”
Interestingly, I arrived on the Apollo in late 1973 was when the Introspection Rundown was being developed. This is the scientology “technology for handling PTS Type 3’s.”
As the new guy on the ship, I was low man on the totem pole so I was assigned to the “night watch” to sit outside the cabin in which Bruce Welch was being confined to ensure a) he didn’t somehow
escape and b) to make sure nobody spoke within hearing distance of Bruce. There is no doubt that Bruce Welch was in a very disturbed state. He was violent and incoherent. After about 10 days he came
out of it and returned to “normal.”
This is all described in the HCO Bulletins that Hubbard wrote as a result, announcing he had found the cure for psychosis. At the time, I thought it brilliant, and the auditor (Ron Shaffran) who went
into the cabin to audit Bruce Welch to have the greatest TR’s in history. I had no intention of going anywhere near the guy. But my understanding of things has changed, and I know a lot more today
about how one “researches” than I did then.
To base a “handling” on the “results” of a SINGLE case is absurd. You cannot conclude a generality of how to treat all cases of psychosis based on a single individual. Unless of course you are L. Ron
Hubbard because he had the ability to “know” things like that. And no scientologist ever doubted it. There are actually MANY examples throughout the “research track” of scientology. Some things
worked, others didn’t. It is why, despite the repeated claims of “research” that resulted in “breakthroughs” things changed so much in scientology. What was today’s breakthrough, presented with
supreme certainty that it IS the answer, soon became tomorrow’s old news. Go back through the history of scientology and you will see it littered with GPM Running, 3GXX, Creative Processing, Black
and White etc etc This is ascribed to “the research track” as if this was a natural progression of trial and error. But if you go back to the announcements of each they were not presented as
“experimental” or “testing out as part of ongoing research”, each of them was presented as a scientific certainty “proven by research.” Just as the Introspection Rundown is. Or the Purification
Program. Or OT III. Or the strange stories in History of Man.
The Introspection Rundown is not merely presented as a FACT. It’s full on hype.
This is the first sentence of the HCOB of 23 January 1974 The Introspection Rundown. “I have made a technical breakthrough which possibly ranks with the major discoveries of the Twentieth Century.”
He goes on to proclaim, in all caps: “THIS MEANS THE LAST REASON TO HAVE PSYCHIATRY AROUND IS GONE.”
One case resulted in a “breakthrough” that became “standard tech.” Just like Goals Processing back in the day. Until it wasn’t.
It is my personal view that having someone in a quiet space without outside interference probably helps calm them down. I guess it is the same theory as the much derided “rubber room” or padded cell
where people are locked up in psychiatric institutions. I think a rubber room would have been a safer environment that the steel cabin Bruce Welch was confined to.
But the point of this is not so much the Introspection Rundown itself. You can read all about that in the “HCOB’s” on the subject and draw your own conclusions.
This write up details how scientology approaches dealing with “problems” like someone who has “gone Type III.”
What is obvious throughout this write up — particularly in the section toward the end “Mistakes that have been made” is the fear that the person will “flap” with “wogs.” And the attitude towards the
person suffering the breakdown is that they are evil and intent on doing evil things. Compassion isn’t a scientology strength.
The pervasive fear of “wogs” in scientology is really quite odd. Scientologist generally consider themselves superior to “wogs” (and certainly superior to Suppressive Persons like me — “SP’s”) but
somehow “wogs” have enormous power to disrupt and mess with scientology, only exceeded by SPs whose mere presence in the environment of even the highest level OT can wipe out decades and hundreds of
thousands of dollars worth of “case gain” without even lifting a finger.
Of course the most famous “Introspection Rundown” in the history of scientology is Lisa McPherson. Driven by fear of “creating a flap with the wogs” she was NOT given proper medical care – hell, she
was not even given a “standard” “Introspection Rundown” and even the advice of Philip Jepsen was not followed. But it illustrates the attitude towards her and the “wog world” that explains a lot of
why the tragedy unfolded as it did.
Read this write up and draw your own conclusions about the attitude and treatment of people in scientology.
1. Leo says
Hi Mr. Rinder and others,
I am really curious about the Bruce Welch story and I think I found a website with his obituary on it: https://www.findagrave.com/memorial/145623062/norman-bruce-welch
He was born on September 2, 1945 and his full name is Norman Bruce Welch. His obit has details that appear to confirm this is him:
“He dabbled in Scientology with his dad and sister throughout the 70s and served on L. Ron Hubbard’s ship.”
There are a lot of other interesting tidbits in the very short obit. I’m wondering if anyone has written a good article about this fellow. It seems like he would be a great subject for a profile
on one of LRH’s most important ‘case studies’ as it were.
I also really enjoyed listening to Mr. Rinder talk about his experiences in the Sea Org on Jon Atack’s youtube channel. I just wish there was more and if I am not mistaken, Mr. Rinder has not
written a book which seems like it would be an amazing read.
Thank you,
□ RR says
He has a book now that just came out called A Billion Years. I’m listening to the audiobook now. So good, but so sad!
2. Jere Lull says
“Compassion isn’t a scientology strength.”
That’s quite an understatement!
Compassion isn’t a scientology trait.
It’s specifically excluded by Hubbard’s decrees. It’s DOWNTONE, and succumbing to bullbait
3. April says
Hey Mike, had the guy on the ship you witnessed as “type III” suffered chronic sleep deprivation?
I’m asking because chronic sleep deprivation can cause psychosis; this effect has been well known and documented in peer-reviewed scientific literature since at least the early 1960’s. In can
also trigger a manic episode in people with bipolar disorder or are genetically vulnerable.
For proof, anyone can go to scholar.google.com (make sure “scholar” is there or you’re just doing a regular google search) and type “sleep deprivation psychosis” in the search box. Or pubmed.org
which is the National Library of Medicine’s database.
If the guy was sleep deprived prior to the episode, this leads me to believe that he got some much needed rest (and possibly better nutrition), and *this* is why he got better, not because of any
LRH “tech.” LRH’s hubris reached stratospheric levels by thinking this would cure *everyone* with psychosis, because it won’t, unless it’s triggered by sleep deprivation.
Considering how little sleep people reportedly get in the Sea Org for periods of time stretching months and years, I’m actually quite surpirsed that “type III” doesn’t happen more often.
□ Mike Rinder says
Not that I am aware of. Though often people who are very troubled have difficulty sleeping…
☆ April says
Thanks for taking the time to respond, Mike.
○ blue moon says
Just to note:
It was self-imposed sleep deprivation as a dedicated (Sea-Org type) org staff member that triggered a (genetically identifiable) psychotic episode for me, which then paradoxically got
me kicked out of the church of Total Freedom, aka scientology.
☆ Lawrence says
Thank you Mike. That explains why David Miscavige is the Neanderthal ass that he is. He never gets a good night sleep, just one look at his body tells you this. SO ALL Sea Org must be
deprived of sleep and have O/W write up competitions in the Hole to help DM get his bearings again. You know what? By doing that, David Miscavige is not doing the Introspection Rundown,
which LRH says is the real handling for PTS Type III’s. Why doesn’t somebody fill David in? “Hey Dave. Go get your GAT II Phase III Introspection Rundown. You get a 50% discount if you
work at Int. Base!” 🙂
○ Jere Lull says
I’d also hazard that in addition to lack of sleep, the guy hasn’t gotten properly LAID for years. He sentenced his wife to a virtual Siberia, Lou, his “communicator”, is forbidden
fruit, ethically, and taking matters into his own hands similarly verboten. Little guy can’t get a break. It’s no wonder he self-medicates himself regularly with
organization-purchased tax-free booze.
■ Jere Lull says
I addition, drinking oneself into insensibility is NOT a substitute for natural, deep REM sleep. Unconsciousness ≠ sleep.
4. Zephfyrus says
I had a major situation that I actually approached the Church (meaning a class 5 org) about, to see if they could act like a religious entity and actually minster to a parishioner. There was no
interest in helping. I had to go out and get a field auditor to assist. My overall experience was that if there wasn’t any money involved, the “Church” wasn’t interested.
The last thing that happened was about 4 years later, I received one of my reports back from some justice terminal at CLO asking, “Is this handled?” Yea, its handled. Thanks.
5. FG says
I had a friend whose daughter went crazy. The friend was a long time scientologist and the daughter of about 20 did few courses, bit of auditing. But she was somehow going easly into heavy upset.
And one day, she triggered a psycho break. While she could get the girl staying home, she went to the org for help. (to see a psychiatrist was not an option. But aside giving the girl
psychotropic drugs what would have they done?)
In the org she was routed immediately to OSA. She was becoming a “security risk” and was taken of solo not’s, so she went off the org, even more upset.
She read the HCOB introspection RD and thought she had to find an auditor who could do Intospectio RD. Her own bidge was ended.
She ask Flag for an auditor. It was absolutely impossible that she sent her daughter to Flag. Where to find an auditor ? She tried AO, there was high level auditor who could technically do an
introspection RD, but were not allowed and anyway wouldnot have risked it due to the McPherson experience.
Finally she found a field auditor, class VIII old style, not sure he was not a freezoner, nobody wanted to know. He said no problem I’ll do it.
And he did. And the girl went out of the psychotic break… One morning she was sane again. (after few short sessions)
The Introspection RD undo wrong indications. And this can make people extremely upset. And it’s true that this RD is incredible. But the auditor must have a lot of empathy for the PC. And to do
it on a paranoid environnement as the church is a wrong indication in itself.
□ As an Auditor there have been two times in my life I have handled Tipe III related cases.
I have to.
I have no other choice. The other choice was letting this people die literally.
One case was a very dear friend that was busted out from FSO because he was a “security risk” for the base.
I will not say his name for respect to him and his case. Of course they don´t bother to see that he was a security risk after he got a lot of HGC paid Grade IV sessions by an Auditor teenager
girl doing his internship.
He was put in a plane back to México and was told: “Thanks for your visit to the Mecca of technical perfection; now you are an Illegal PC… go to México and solve your condition”.
He arrives to México… his family and a couple of friends go to recieve him… (Scientologist and No scientologist)… as soon as he cames down of the plane (scorted by a FSO security guard in
civil clothes) he told us… “Im not doing fine… I feel very bad… I will need your help”.
He go to his house and we have to take all the risk objects so he doesn´t try to suicide.
I would like that you can magine how is to live with a situation like this.
We take out of the house a gun, a blade and a bat because he want to use it to harm himself. This was done 3 hours after he arrives from FSO.
His family come with me and told me: “You are Auditor; you can help him. Help him. We don´t have another choice because he prefers to die before he goes to a Psichyatrist. He don´t want to be
You can imagine mi position. I was a Grad V Auditor by that time finishing my last internship. I don´t give a rat´s ass about what Introspection RD says… I have no time to do that course or
ask permission to do something. I have literally a live on my hands. I spend all the night giving him assists… listening to him… giving ARC to him… Aplying simple SCN basics and common sense
to the situation. I take a shower and go to the org to ask permission (CSW) to be with him full time and help him. They told me I have pc´s there too and that they don´t care about my
He is an illegal pc and downstat… if you want to help him… do it in your own time… that was the answer to my petititon. So I use the next two weeks of my life Auditing my pc´s in the org in
the day and handling a Tipe III person in his house. Almost no sleep for me in that period. One or two hours maximum. It has been some of the most difficult things to handle in my life. I can
not tell what I have lived during this nights because is a secret protected under auditor´s code but it was very very hard to swallow.
After two weeks I get permission to be with him full time (I use my “vacations” to do it) and I take him to a big hotel in a ranch outside any city… a calm place… good food… walks… company…
comunication… assists… compassion… love… and he went out of it.
And now he has a normal and happy life. He is inside the church. He disconnected from me when I was declared for my sepparation announcement from the church.
I maybe contibute a little to save his life.
I do not consider people as inferior.
i do not consider a Psychiatrist an enemy and I do not think that one should not prescribe a tranquilizer for a person in an emergency situation.
Im not into following line by line what LRH says… He has done many things right… And some big ones very wrong… Scientology does not give immortality and super human powers… but the subject
can help when used right by a natural Auditor… I consider myself an Auditor and a helping person and labels as Scientologists and stuff like that I do not care. But I see that many of the
people in this kind of blogs labelling as wrong everything about scientology… Almost all of them Sea Org members… executives and professional PC´s… highly trained auditors do not criticize
that much… because we have first hand helped people.
Nothing can invalidate that.
☆ mark marco says
Thank you so much for this story.
And congratulations for getting out. Really, that alone tells me a lot about your strength of mind, which I would categorize as “admirable”.
I wanted to comment my feelings about “tech”.
To my way of thinking,
this church is not a church.
To tell the public that it is a church is a crime of deception, before one even gets started with
“services”. That gives you a hint as to what it really is all about. Other hints you have already mentioned, such as the false promise of salvation, super-powers, immortality, and all the
list of false promises goes on and on, for millions of words, on and on again.
And the punishment, the remorseless abandonment of the practitioner who fails to conform to the harsh demands and sacrifices demanded by policy.
Policy being another word for “tech”.
All of it is crap. Worse than zero, it is innately dangerous. As soon as you believe anything in the book of Dianetics to be real or valuable or some kind of priviledged information?…
you’re sunk. You are already caught in the web, the trap, the aptly named “prison of belief”. I hope to create no doubt in your mind about this, Scientology is a very dangerous,
predatory, profit-oriented cult that cares NOTHING about the people it sells its bag of tricks to and EVERYTHING about the money in your pocket, period. You got lots of cash? Trust me,
this cult is very interested…
That your friend was helped was thanks to you, not the tech.
In fact, the credit for any benefit that came out of your efforts makes you eligible for special recognition for achievement, because you helped your friend DESPITE the toxic element of
Scientology influences being present.
Simple attention and some personal care will lend plenty towards a person getting through psychotic episode. No harassment, a few days of decent meals and perhaps some rest, some
well-prescribed medicine to cool down the brain receptors? Perhaps. But, I’ll tell you in one word what it was that really saved your friend, and that word is compassion.
And, paradoxically, that is one element you cannot find in or near the heart (and I use that word way too loosely, in the metaphorical sense) of this god-forsaken cult. Let me say that
The essential element that Scientology uniformly lacks throughout is compassion.
Good work, my man. I would be most proud to call you a friend.
Vaya con Dios
○ Thanks Mark Marco. Many people even inside C of S are very aware of the fact of: “No money? No services!” No compassion. C of S is doomed and already falling. It need no more external
intervention to keep on collapsing.
■ mark marco says
I would love to take a vacation and visit your country.
It is an admirable quality of the Latin-American cultures, I notice, the way they can be kind and demonstrate kindness in everyday life.
Y que tesoro eres Usted.
No doubt, I am a better person for having met you. And the world is a better place, indeed.
★ You can come here anytime. We can hang out in San Miguel de Allende or Guanajuato city. Thanks for your words.
◎ mark marco says
Ojala, que bueno.
I’ll brush up on my Spanish. (just realized I haven’t been using it for a couple years gone by already, another good reason for me to visit…)
Your words, the story and the responses, made a lasting impression for me, certainly.
Roberto, I would like to offer you my eMail address.
Ask Mike for it.
I’ve been around for some time, here at this blog. Mike probably couldn’t say that he knows me, but I’ve written enough on the subject of dangerous cults for everyone,
especially the last few months of last year, when I was logging on nearly every day, prolifically, if I may (be so large-headed to) judge myself,… sure.
I have no connection to the church. Not in mind, body nor spirit, and we do not correspond nor would I accept correspondence. It freaks me out to get the fliers, send them
back with big, red, REFUSED, Return to Sender.
It took some 38 years, but I have no apprehensions about the bullies at the cult anymore. I’m retired now, and
they can’t touch me and would look pretty silly if they tried. I do have cameras hanging around, for taping. In fact, I have spoken openly here about the offensiveness of
the church and offered to interview or be interviewed by them, before and again, all in one sentence. All I ask for,
is a stage and a microphone,
both of which I’d be happy to provide.
[did you notice that moment, beat, bear skipped, at the jolt? Yep. That’s fear. That is how to scare ’em, see. Just promise that.
A stage and a microphone and me.
My dream come true.
Still waiting, one could only hope.
We were talking about the pursuit of happiness
They owe me a couple hundred thousand dollars in real life, and would eventually figure that out, stupid as they are. I got a guy for that, almost pro bono, real reason
number one I don’t worry, and guess what, 37 others, if not 100. Harry Reid is finally retired but I know people, actual first time I’ve bragged about that here. No
politics, please.
My friends in politics don’t give a rats ass about this measly sickness of a church, please don’t shoot me. They also have bigger fish to fry. They is not a “they” on the
other side, it’s a “he”. [heads up, Dave, Dad’s got a book coming out and you can’t touch him, either. Too bad you missed your date with Pricilla, huh? Not the girl to
piss off. Why are you so slow, anyway? Speak. Save yourself.] Good news, all the bad news is for the bad guys, who cares what you wanted first.
The way I see it?… if they want to drain their resources going after, what, my tattered life? Ha, it would show how smart they are, spending $20 to get my ten, probably
the ratio would be much worse. Poor, sad scn-gists. Happy me.
Let it be my contribution to the Universe; raise another toast as the mast of the church sinks forever into the deep blue sea. I’d feel fine stealing credit for that, but
everyone plays their part.
Can’t deny the truth. Nobody, I don’t care, not even if you’re lucky enough to have a name like O.J. Simpson or …mark marco. I’m rambling, huh?
I do need a vacation.
Generally, I don’t like talking about scun-gy. I guess that would be obvious.
Right now, I’m in a show, it wraps up in the middle of March…
and I’m definitely going to google those cities, let’s just see what the weather is like….
◎ Thanks Marco. You are not rambling… There´s much good behind those words. I will ask Mr. Rinder for your email adress. Wish you the very best.
■ thetaclear says
Hi Roberto,
I wanted to validate you for your obvious power of choice over data, and for being your OWN authority at whatever you do. That takes courage and real strength. Being balanced
about knowledge, w/out just invalidating it all just because of past errors in workability here and there, is the mark of a true researcher.
I am Peter Torres from Puerto Rico, and I would like to have a few words with you if you don’t mind.
Vaya con Dios, amigo!!!
Peter Torres
★ Thanks Peter. Sure… mi mail starts with impulso and has an .mx at the end. I will write you.
○ simplethetan says
Mark, I cannot emphasize enough how right you are. I was an auditor and CS for many years. I helped many people. In hindsight, it was my compassion, and not the “tech”. In fact, the
conversations outside the session contributed more than the auditing.
The SO especially at FSO, are a bunch of over worked slaves. You cannot expect slaves to have compassion. In fact, when I mentioned compassion to an OSA person, she just stared at me
with blank eyes (supposedly keeping her TRs). My parting words to her where: “You will never go free, unless you feel and show compassion.”
■ mark marco says
thanks for that, (oh, I would put your name here!)
My, but it is good to be hooking up with real souls.
Look what we learned, after all. You got my day rolling.
It is raining and still my heart beams
■ gayle says
You left giving some tried and true wisdom. 😉
☆ Mike Wynski says
Roberto, I am sorry that a person such as yourself got tangled up with the criminal organization founded by Hubbard. As an American I say this to you.
○ Thanks for this words Mike. But this happening to me is a blessing. I´m aware of the quantity of people I can help to be deprogramed once they decide to go out. Many don´t come out
because they feel they don´t have a choice outside or someone who can understand them.I have enough tech, ethics and admin training plus staff experience to understant them all. I can
be that choice. I can be that bridge from the hell inside the Church and the real normal life again.
☆ FG says
Roberto I so much agree with you. I’m also an auditor. Those who obey stupid orders are robot and they are a majority in every activity in this world. But tech of auditing applied with a
loving spirit help people.
○ That´s right! Amen to that.
□ Cindy says
Roberto, Thank you for saving that man’s life. It is sad that he later disconnected from you and stayed in the church. I hope he sees the light and makes it out.
☆ Thanks Cindy… All of this was hard but it´s fine now. If he gets out or stays in… is what he needs in any case.
6. Chris says
some thoughts upon reading this drek:
0. why the fuck do so many of LRH’s lists start with zero??
1. these instructions sound as if they are intended for performing an exorcism
2. be careful, lest the person is “simply pretending to be sane again” – yeah, bcs that’s how those insane people roll
3. “terminatedly” – i kind of like this word
7. Friend says
In addition .. ARC Straigtwire “You will not get any worse” .. show me a person who did get this endphenomen .. I have never met one .. this alone opens the door for PTS and other searches in
your mind and feelings ..
PTS handlings have some value .. sure .. but completely overestimated by staff and a lot of inside people .. the definition of a suppressor is mostly not workable .. because it is often all about
ARC breaks .. not real suppression ..
I will mention that a real PTS goes himself suppressive .. he will use the valence of the suppressor .. it is mentioned by Hubbard, but seldom somebody knows that really ..
□ Mike Wynski says
I don’t think it is lack of understanding Friend, It is just that 99% of Ex’es are intelligent enough to realize that the “tech” is B.S. and thus don’t care to parse it out as it doesn’t
It’s like arguing about Milton Bradley’s Game of Life rules as if the game was REAL life.
☆ Herman says
admire the wit there, Mr Wynski
The word strikes me very much like cursing,
except now that the cat is out of the proverbial bag.
Tech is a con.
The truth of that being known …
I calm down fairly readily.
○ Tidalwave says
You AND me, Herman. As far as I’m concerned, the PTS “tech” is one of the biggest cons of Hubbard’s.
■ Herman says
Agreed, Tidalwave. Introspection Rundown, Survival Rundown…
these cycles are certain to cause anxiety at the least, emotional damage very likely.
It is as if the idea were to attack the weak because they make easier targets.
The plan:
make them worse, then bring them back to where they started and use it as justification to say the tech works.
I recall the recent death of the lady-actress going into Celebrity Center for depression, it was a broken romance, I believe… This stuff proves more dangerous the closer you look.
8. Friend says
.My early comment is eraticated by Mike. I do not think that most commenters here have understood PTS really in full. It is surely not the same as psychotic break .. and it is not related to the
introspection rundown. PTS is a later part of this rundown, and only one step .. basically asking for a wrong item about ..
PTS = Potential Trouble Source .. ofthen mixed with Sources of Trouble .. but it is not the same .. it crosses only on PTS Type A .. PTS Type 1 has a suppressor in present time environment ..
Type 2 has a restumulated one .. and Type 3 has the restimulator everywhere .. includeing imagined beings or environments .. it is a state of feeling stopped and suppressed .. and you are unable
to do anything about .. therefore feels the being suppressed .. it is rollercoaster .. and you can get it only indicated by the church when you have wins and lost them again ..
□ simplethetan says
Thank you for the illumination “Friend”. Since as mentioned before since the so called “tech” is mostly deception, there is no point in delving into it. LRH did what he did in order to help
himself. If it has some truth in it, it is irrelevant and immaterial.
9. roger gonnet says
Good topic enough, Mike. The fact that LRH did never cease to add to his own glorification was his “best” sales method. “Now I’ve the biggest discovery ever done blah bloah blah…” and almost
whetever followed was just the same old techs disguised with some few new querstions, to be repeated to create the hypnosis needed to obtain any answer to any “process”.
The last psychology-psychiatry-neurology studies demonstrate that one cannot even distinguish a TRUE memory of an induced one – not even speaking of memories falsified by some drugs, something
that can be another proof that NO as-is of anything shall ever be done. Nobody shall ever have a perfect memory, whether one belived or not in past lives and whole track ineptitudes.
Another was LRH gave to humans was the R2-45, yes – and HE gunned the scene where he was giving that lecture.
10. Espiando says
Did you read what this yo-yo said were the follow-up items after the person is “cured”? Fitness Board. Releases and waivers. RPF. So you’re going to take a person who desperately needs help, put
him in a situation that more than smacks of solitary confinement, “cure” that person, and then your follow-up care consists of throwing the person out of the Sea Org, throwing the person out of
Scientology, or sending the person to the RPF? What the fuck? What. The. Fucking. Fuck.
How in the name of heaven are any of these options going to do that person any good? This person has been through an incredibly traumatic experience. He needs support from people he trusts (and
it’s sad to say that his fellow Scientologists are the people he trusts). Instead, you’re going to remove him from his support system or, even worse, force him to undergo what we all know are
years of punishment at hard labor, in an environment reminiscent of a gulag. I can’t pick my jaw off the floor right now. This is just totally emblematic of Scientology. And this isn’t Dave’s
Scientology. This is Ron’s Scientology.
I want an Indie, who believes every little wet fart that came out of Hubbard’s ass, to justify this behavior. You can’t. Yet it’s the vaunted Tech and therefore infallible, right?
□ Mike Wynski says
Espi, I have tried that approach with Indie’s. Face to face. I have had one of two things happen, everytime. 1) The Indie went Injun (a psychotic episode) when one false excuse after another
was shot down. One “Clear/OT” even threatened death. 2) The person just refused further communication.
☆ I´m an Indy Espi and Wynski… That Hubbard handling is wrong. That´s part of what I´m out. Some things work. And others do not. This way or more clear my statement??? I´m here if you need
further communication. I have audited someone who was with Lisa McPerson handling her when she dies… the whole cycle was full of mistakes… I know the specifics… and the whole
introspection RD is a wrong handling for the condition.
○ Espiando says
I’m at war with certain Indies, Roberto, because they still believe certain things of Hubbard’s. You say that Hubbard was wrong about the Introspection Rundown, and that’s good. Now
if you can tell me that he was wrong about radiation, the Putrif, and LGBTs, I’ll have no issue with you.
■ It´s true Espiando… Wrong about radiation… wrong about OT III, Purif tech good but incomplete by actual standards and discoverys… very-very -very wrong about not only LGBT´s but
all the sex subject… wrong about Psychologists and Psychiantrists. And even saying this… I still have witnessed as an Auditor with 25 years of experience that many of his other
applications do work.
★ Espiando says
I think if you read Mike’s article from late last year on niacin and the medical studies surrounding it, you’ll change your mind about the Putrif being “good but incomplete”.
Either that, or you’ll never post here again. Some die-hard Indies quit this blog after that article.
◎ I have not readed that one. I have readed now. I´m a purification RD C/S with hundreds of purifs delivered. Good but incomplete means this kind of things:
5000 mg of niacin is way too much for any human.
5 hours a day in sauna way too much.
Laboratory tests of blood and toxicology assays are needed to determinate a tailor made professional program for each person.
We need many other natural substances that help to get out drugs; not only niacin and not only the mentioned ones in Purif Series HCOB´s.
This is from the University of Wisconsin Integrative Medicine: “Detoxification includes the ways our bodies identify, neutralize, and eliminate things that are unhealthy
for us. These include physical substances such as toxins
(poisons) from our environment or by-products from the chemical processes that keep us alive. It also includes emotions or behaviors that are unhealthy.
The five basic components of any detoxification program should include:
Exercise: every day such as yoga and walking (especially in nature)
Regular sweating: a sauna, steam room, or hot room yoga class
Healthy nutrition: rich in organic fruits and vegetables and filtered water
Self-reflection: such as meditation and breathing-focused relaxation
Body-work: such as massage and acupuncture.”
Got it?
The detoxification programs I now deliver outside the church MAKING TEAM WITH MEDICAL DOCTORS, NUTRITIONIST AND DOCTORS EXPERTS ON DRUGS have this kind of approach.
Hubbard was not an expert chemical.
Read some ordinary world suggestions about detoxing our own body and you will understand what I mean with good but incomplete. Exercise, vitamins, sweating, change of
diet… all of this are common sense and accepted methods of detoxing our own body.
Anything else?
You are not going to find in me some hard core blind defendor of the standard tech my friend.
◎ Mark A. Newell says
Yes, yes I remember that one, the post with Niacin…
How does one go about finding a specific post like that?
I’ll try googling key words…
I have issues with most Indies, too, but certainly not Roberto.
We all went through stages, getting out. We all got heavily invested getting in and naturally would be reluctant to say everything we believed in so deeply, was so
thoroughly wrong. While we were in, we thought we were becoming better people, that we were destined to become spiritual leaders at astonishing rates… we really could save
not only ourselves but the world?…
Nobody checked out of Life Repair saying LRH was an insidious hypnotist.
Now we know it is quite true.
But Roberto can accept or reject whatever he chooses, no matter to me whatsoever. The thing is, he is obviously helping people make the transition into the otherwise
barren real world, just when those individuals are at real risk of finding themselves just as isolated outside as when they were “in”.
Too many have come out only to break down or be swept away only for the lack of support and a bit of encouragement.
So, I support the man. I don’t know how he became so wise and so marvelously compassionate, but I certainly want to be his friend and I hope he feels welcome to post here
often and, if the possibility exists, for eternity.
It is not the tech that saves people in the end. It is all about compassion.
Now then, it is time to do the right thing, and so I’m going to the beach.
You guys at OSA should know where to find me, if you feel like catching up.
You’ll have to bring your own boards.
◎ Google Mike Rinder Blog Niacin and it appears.
Thanks for your loving and compassionate words Mr. Newell.
Let me just say amen to your words… I agree 100%
“While we were in, we thought we were becoming better people, we really could save not only ourselves but the world?…
Nobody checked out of Life Repair saying LRH was an insidious hypnotist.
Individuals are at real risk of finding themselves just as isolated outside as when they were “in”.
Too many have come out only to break down or be swept away only for the lack of support and a bit of encouragement.
It is not the tech that saves people in the end. It is all about compassion.
Now then, it is time to do the right thing.”
○ Mike Wynski says
Thanks Roberto. Yes, I know that Hubbard was wrong. If one wants to bring me peer reviewed studies of where Hubbard was right, I’d be happy to read them. Just as I am happy to read
any such work.
■ You´re welcome Mike W… Peer reviewed studies… I do not know if someone would want to do that… I can assume that you have not audited many hours. That´s my way to know that some
(many; not all) things in scientology work and do work very well. Because I have achieved results with hundreds of people. Improved lives. How can anybody deny that if I saw it
with my own eyes?
★ Mike Wynski says
No, I’ve audited MANY hours. (I was trained when Hubbard was still active and DM NOT) I NEVER saw any verifiable indication of the EPs El Con wrote about on the grade chart. I
wrote what I did above as because most people are not trained in scientific method and thus are still conned by El Con.
◎ Got it and you have a point here Mike. I have to admit. I´m here 100% with simplethethan about our attitude and compassion does much of the work. Hubbard proceedings do
not work in everybodys hands. It neds to have a Natural Auditor. A certain kind or type of person… therefore it´s not scientific because it con not achieve the result each
time it is applied. Thanks a lot.
◎ April says
The “attitude and compassion” and its impact on helping people of which you speak is well known in the psychotherapy community. They’re a part of the concept of rapport
between therapist and client, which does indeed have a positive impact on whether someone gets better in conventional psychotherapy. This effect is well known and has been
studied since the early 1960’s. It’s been in many research articles published in peer-reviewed scientific journals.
LRH didn’t invent the concept. Again, he just ripped off ideas from conventional psychology/psychiatric treatment methods. In some cases, such as the engram, he ripped off
ideas that had already been studied and discredited by the time he got around to incorporating them into his con.
□ Dawn says
I’m with you, Espi. The whole thing stinks. Kindness, compassion, genuine care and concern – these words were not part of Hubbard’s vocabulary. Denying me companionship would be the cruelest
act of all. If it were me, my recovery would have been a recovery from Hubbard’s influence and theend of scientology for me.
□ Herman says
touche’, Espiando
It’s as if the Scientology cure for insanity is to first trash psychology as dead as possible, then line up the patients and bounce bricks off their heads until they are quiet.
I shouldn’t be giving them ideas.
11. RONNIE L STACY says
Unfortunately I have been intimately involved with two “Type III” individuals during the years 80’s-90’s. Both ended up dead. One by shotgun to her mouth, one by escaping the 24hr watch
confinement and getting shredded by a snowplow walking alongside the road in an Alaskan snowstorm. Both under constant near hourly supervision by OSA, specifically Ann Rubles, DSA Seattle.
The write up includes finding a secluded home, preferably miles from others. What a fucking joke. In Alaska we took a couple out of their cabin and brought them to live with us while all of us, a
handful of staff, including the couple and myself and wife were put on 24hour watch. These people are trained at best minimally, usually merely verbally, no medical staff, no doctor, no
medications, no monitoring vitals, no facility.
If you are a gambler, you should bet a lot of money that is standard procedure across the Scio culture.
Scientology has nothing to help the insane except that pulls others out of their normal lives and subjects them to something they have no idea how to deal with. No facility, and no medical help.
If you manage to get them to an MD [friend] who prescribes a sedative, it is shut down by OSA.
Scientologists rail on psychiatry as a whole across the boards. Yet they alone have the facilities, medical staff, medical monitoring, food, water, exercise, group involvement. Educated family
and friends can and of course should monitor and curb any medication abuse. They are more likely to come out alive than any “Type III” treatment in my bonafide opine.
12. blue moon says
I guess I had what one would call a psychotic episode after being in the org just over two years.
And that it occurred somewhere in 1975.
And that what they did was probably the early version of the Introspection Rundown.
I say “I guess” because I don’t recall the label, Type III, being pinned to me specifically.
Probably it was, but they never really got up to telling me.
In our little org, we all saw for the first time just months before, the first case of a Staff member being assigned the dreadful condition of Liability. That was scary enough, for all of us,
really. You do not want to be thrown into Ethics, for any reason, ever. At least Scientology made that much clear.
I was put into isolation, and all that. It was horrible. But, as luck was, they just asked me to leave, after about 10 days in the pen, if you will. (not using the word ‘hole’, that being
something else that came later) I did leave, though thoroughly confused. Jesus Christ had as much heart as I for Scientology, and although I eventually became loathe to say it, [how could I be so
wrong?] out it the real world I simply would not speak to it. If I did, the dreams would come, of being back in and being…(word)…driven. So I did not go to LA. I did not join Sea Org. There was a
time in which I was dangerously close.
The thing is, this post today, Mike… well, it offers for me a sort of closure. It represents for me, personally, the end of a certain kind of enduring nightmare. And that’s because by reading
here today -what was happening to me- to see, even after all this time so many things they never told me… It’s not just me.
My feelings were, true.
My, but the trickery can stick to you for so long! The fight to make Scientology right!
What sinister crud. It is your most personal mind he messes with, no two ways about it. Heartlessly.
Just thanks for being real, everybody. It’s just good to be here, not thinking it was all just the flawed imagination of a poorly developed soul, me. Yes, I am grateful. Once again, I believe I
am becoming the (relatively) happy young runaway I was before ever stepping through that mission door, (also now forsaken), way back when Mom and Dad were both still alive. You make it all good.
I don’t have kids but I have the beach and that’s where I gotta go now…Works for me.
□ Baby Bunker says
That is such a heartfelt comment blue moon. Just keep coming back and reading.. The real world will become clearer each day. So glad that you are out. I am so sorry for all the abuse you
suffered. You are being sent only positive strength .. love baby
☆ blue moon says
i feel it, Baby B
○ Baby Bunker says
Good.. I will send it to you every day. I hope that you will watch every Chris Shelton Video… Come visit the Underground Bunker..
and absolutely relax at the beach.
I will be thinking of you.. xo It’s a brand new chapter in your life. love Baby
■ blue moon says
say… being blue moon ain’t so bad at all…
You got a friend in me, baby b. xo times three,
because that’s another day made for love in me.
13. Sleepy says
PTS Type IV – those who work directly under COB. These are people who are being negatively effected by Mini-Me and see all others outside the cocoon as DBs, out-ethics and fryers of other fish.
Someone “going Type 4” means having fully succumbed to the hypnotic influence of Li’l Davey.
□ Doug Parent says
I like that one. Type V would be the delusion that Hubbard was a god and infallible.
□ blue moon says
I’d sooner be hypnotized by the chirping of a doe-doe bird.
Guess that bumps me back down to Type Two.
14. nomnom says
Jeffrey Augustine covered the “Kidnapping Contract” on Tony’s blog last year.
“d. The Scientology religion teaches that the spirit can be saved and that the spirit alone may save or heal the body, and the Introspection Rundown is intended to save the spirit. I understand
that the Introspection Rundown is an intensive, rigorous Religious Service that includes being isolated from all sources of potential spiritual upset, including but not limited to family members,
friends or others with whom I might normally interact. As part of the Introspection Rundown. I specifically consent to Church members being with me 24 hours a day at the direction of my Case
Supervisor. In accordance with the tenets and custom of the Scientology religion. The Case Supervisor will determine the time period in which I will remain isolated, according to the beliefs and
practices of the Scientology religion. I further specifically acknowledge that the duration of any such isolation is uncertain, determined only by my spiritual condition, but that such duration
will be completely at the discretion of the Case Supervisor. I also specifically consent to the presence of Church members around the clock for whatever length of time Is necessary to perform the
Introspection Rundown’s processes and to achieve the spiritual results of the Introspection Rundown. I understand, acknowledge and agree that the Introspection Rundown addresses only the
individual’s spiritual needs and I freely consent, without reservation, and without condition or limitation, to Church members conducting the Introspection Rundown, and that I accept and assume
all known and unknown risks of injury, loss, or damage resulting from my decision to participate in the Introspection Rundown and specifically absolve all persons and entities from all
liabilities of any kind, without limitation, associated with my participation or their participation In my Introspection Rundown.
INCLUDING, BUT NOT LIMITED TO, THE INTROSPECTION RUNDOWN, AND THAT THIS CHOICE IS AN INDEPENDENT EXERCISE OF MY OWN FREE WILL. I FULLY UNDERSTAND THAT BY SIGNING BELOW, I AM FOREVER GIVING UP MY
SPIRITUAL ASSISTANCE.”
□ Jose Chung says
Not only the introspective rundown
Rex Fowler on OT 7 was programmed to draw out all the money of his business
and fork it over to the Church. Driven to murder then botched suicide. Rex is doing life in prison in Colorado.
Biggi Reichert had a complaint as an OT 8 and 16 million in debt ,went to Flag to sort it out. Was given Chloral Hydrate and stabbed 7 times in the head with a handheld
stun gun. Dopped up to the gills she was escorted on a flight back to Germany
where she committed suicide couple days later.
Neither were type 3 just ended up dead or doing life in prison.
Money is the common thread here which ended up in David Miscaviges coffer.
□ Sleepy says
“I promise to do whatever the church says, as they know what’s best for me, and to bend over, spread my cheeks and take it like a man, or a woman as the case may be.”
□ frodis73 says
It blows me away that people will sign this contract…esp because when they agree to be treated by scientology “according to the beliefs and practices of scientology” most, if not all of them,
do not even know what those things are yet!!!
☆ Bentley says
Well, of course there is plenty of coercion going on at the desk there.
Add that to the list of things that scn-gists are actually good at.
And the big carrot they keep dangling, the end of problems, et all…
What you will lose and miss out on if you DON’T sign.
Distractions. Bigger hammers.
(Yes, a billion years sounds like a long time, but come on, time is just time)
We do happen to have an army.
Promises gets a long list of its own right about here…
Sure, just sign this thing, I’ll be right back…
□ freebeeing says
Let’s see, you’re getting a person who is type III crazy to sign a legal contract… Yeah, that makes perfect sense.
15. Thanks for posting this Mike.
A couple of things stand out for me:
Given the author’s repeated mentioning of all the bad things that can happen dealing with PTS Type III people, there must have been MANY MANY attempts to handle people who went psychotic while in
Scientology. Far more than the general Scientology public know of or even that Staff know of. It’s like “We’ve had YEARS of trying this and getting it wrong with people hurt and investigations by
law enforcement so this is what we are going to do now.” Yet it still goes south, people get hurt.
The second thing, which you mention, is that they didn’t follow this advice when dealing with Lisa McPherson.
Although, the point about ‘getting it off public and delivery lines’, if it was actually somewhat adhered to gives some credence to the theory that Lisa was actually held at the Hacienda Gardens
staff housing after the first couple of days. This also explains why the room the Flag OSA people showed the investigating officers was so pristine. What would be easier (and safer) than showing
a completely different room to the police. Because cleaning it to the degree necessary would have been nearly impossible. It would probably have been necessary to patch and repaint walls. The
lack of the odor of paint and lack of observation of damage being noted in the police reports, is way out of character with the existing babywatch reports.
16. Karen#1 says
Very Important essay today. “Eligible” and “Not eligible” is an eternal on going branding of who does or does not “qualify” to do Scientology.
On the subject of Type 3…..Scott Campbell, shared with me his most amazing story of going into a full blown mental breakdown on Freewinds after extensive SLEEP DEPRIVATION.
It is an amazing heartwarming story of how Scott beat all the odds to come out a winner.
17. alexdevalera says
Excellent post Mike. That’s just the way it is.
18. Mona says
Love the way he begins the whole thing off by letting everyone know what “Dev-T” this all is. It truly shows the compassion level of a man when he considers that caring and helping someone, who
is in an emotional crisis and mental trouble, is likened to “Dev-T.” (Hubbard’s word for developed traffic, meaning something along the lines of unnecessary traffic that is generated and is
generally looked upon as bothersome and wasteful in cutting across real production time.)
And these are the people who will “clear” man of all his troubles?
19. Alice Graves says
I’m glad this site and others have recently been focusing on the phenomenon of how “wogs”, “sp’s” and “pts individuals” have infinitely more personal power than scientologists – even OT’s – and
are able to derail the spiritual progress – months and years of hard work – of scientologists just by being in their proximity.
I think there is ample evidence of this phenomenon in the example seen with Tom Cruise himself. Apparently his SP wife, Katie Holmes, had such power over him that he had to give up legal custody
of his only biological daughter to her, thereby losing the right to raise Suri in the church of scientology, which would have safeguarded her spiritual eternity.
And many published reports since the divorce claim he has settled into a life of rarely visiting his daughter – a complete bafflement to divorced parents everywhere who steal every moment they
can grab with their kids.
Even a Big Being like Cruise is in jeopardy of losing his eternity, just by spending time with his pts daughter – innocent little Suri Cruise whose only crime has been missing her daddy.
□ Brian says
Alice, my view is the reason Ron gave critics/SPs the power to take away “wins/gains” is because Scientology, to a great degree, is based on imagination and wishful thinking.
Being questioned, doubted, being criticized, invalidated etc. can only cause lack of certainty to be doubted.
Direct knowledge, true knowing, cannot the invalidated because direct knowing is totally certain of what it is perceiving; confidence
When Ron’s imaginary cosmology is thought through with reason it invalidates the imagination of Ron and the Scientologist who agrees with the imagination. Thus loosing wins.
Actually the idea of “loosing wins” is really the truth seeing clearly but the Scientologist sees it as taking away “wins.
In truth, it’s unmasking lies. So people are thrown into a confusion for unmasking the imagination. And they call that PTS.
Debunking lies is what Ron calls “suppressive.”
The only belief can be threatened by reason and criticism.
Ron, being manic with paranoid tendencies, needed a philosophy to guard him from being seen for who he was. So he created the doctrine of demon SPs to blame for the falsehoods in his
imagination being questioned.
Seeing Ron or Scientology “as it is” is a suppressive act, because the foundation for this “knowing” is imagination, belief and faith masquerading as truth-fact-certainty
☆ Fox says
Good point! Both Alice and Brian. I think Ron and Sigmund (Freud) were a bit similar. They were dealing with their own nightmares and made a general statement that everybody else had the
same nightmares while it was actually their own. But I still believe there is a spiritual world opposed to a materialistic one and there are also real sociopaths and psychopaths. I lived
with one in the past. Their main characteristic is : 1 – They want to control everything regarding others and 2 – they have no feelings and are remorseless (they could kill 10 millions
people just with a finger snap and feel absolutely nothing, but they can act feelings)
☆ Dawn says
Alice and Brian – great comments, both.
20. gato rojo says
I don’t recall that a PTS Type III was also, definitely an SP. There’s the additional “flip” into an evil valence to become an SP. And I also think that through the years some people have been
labelled Type III incorrectly. And obviously there have been many people mislabeled SP.
I always thought that the Type III needed care and attention and kindness while being isolated, and fed proper food and nutrition and kept comfortable. They needed to be away from restimulators.
All I ever wanted to do “for” an SP was get them the heck out of my life.
But if you mistreat a Type III you could really anger them and cause them to do that flip into a violent and hateful state. Wouldn’t you feel that way if you were confined, isolated from any
friends or relatives and mistreated? Wouldn’t you want to fight back eventually?
□ blue moon says
Hence, the presence of me.
Impressive post gato rojo.
“mistreat a Type III”
-doing that was actual policy, still in effect.
Confined and isolated.
Again, written policy proves the true nature of the org.
It is NOT about saving souls. It is, was, and always will be about the org,
or rather, making money for the org.
With the actual people – dedicating their lives …?
Hubbard was willing to toss the dice
wagering souls
hearts and minds on the hot Pass line,
in fact his favourite pastime.
If he lost the bet, no matter…
Throw them in the gutter, if they don’t come clean in the brig.
“I will have their money”, says he.
I have all they were worth,
anyways and look already
and they will never never catch me.
☆ Orwell says
for poetic merit
21. FOTF2012 says
Fascinating document to read, very insightful analysis, and interesting comments!
The insight from Mr. Rinder into LRH developing this “one size fits all” Type III process based on _one_ case is illuminating. What LRH called “research” was what an actual researcher would call
anecdotal evidence — and weak anecdotal evidence at that, being based on one case.
Apparently, even the very weird, and completely unsupported by science, stories of History of Man were the yarns spun by LRH’s son “Nibs” when LRH audited his son with Nibs under the influence of
I suspect LRH’s “tech” has done more than we know to funnel people to solid psychological, medical, and psychiatric help. Maybe LRH was working for the “psychs” and their customer referral
22. Valerie says
Isn’t it interesting that there is a list of only 17 things you can do wrong when handling a Type III and some of them are sooooo wrong.
2. says you have to “handle the person terminatedly” (i.e. make him sane). 5. says you can’t let the person convince you “he is now sane?”
8. The person “must sleep as much as possible” – yeah, that’s wise when a person is depressed or has a possible mental illness. THAT will cure them.
Don’t let them listen to music or watch TV or tapes (because they WILL STAY UP LATE)? Huh? I calm down the most when listening to or playing music, I use it to put me to sleep.
What IS the definition of STAYING UP LATE when you are confined to a small dark room anyway. How do you know whether it is day or night?
The last but to me the most telling one, however is #17. It is worded in a way that tells the absolute positive truth as to why someone considered PTS III should even be “handled.”
17. Not keeping the person in an isolated place, and letting the Type III create PR flaps with wogs.
ALLLLLLRighty then.
□ Orwell says
“How on Earth can we get away with saying we are THE experts on mental health when I keep getting interrupted by the lunatics?”
23. Gimpy says
I’ll admit I was too lazy to read the whole document but certain bits stood out for me: they are holding someone of unsound mind in a prison like environment. If the person is not well enough to
give informed consent about this treatment doesn’t it constitute false imprisonment and possible kidnap?
Also the medical care is provided just so they don’t get sued later! Such a compassionate, caring organization, scn never ceases to amaze.
□ FOTF2012 says
That’s what I was thinking, too — false imprisonment. I suspect Scientology’s argument would be that staff and Sea Org have agreed to abide by all the rules, regulations, policies, etc. of
Scientology, and therefore the person in effect waived his or her rights. I noticed in the “hat” write up that there were a number of mentions about doing things in a way that would head off
legal claims against Scientology.
☆ Mike Rinder says
Have you seen the waiver that all scientologists now sign that says they desire to be held against their will rather than put in the hands of psychiatrists? I think Jeff Augustine wrote
about it on Tony Ortega’s site…
○ gtsix says
■ Gimpy says
These waiver’s are almost unbelievable, from personal experience the usual circumstances of signing anything in scn are that you have just sat through a 3 hour reg cycle where
three of them have worn you down to the point where you will agree to anything just to get out of there, signing under these conditions means you are usually just signing where
ever you have been told to without even reading it. It should be a condition that none of this is legally binding unless you have legal counsel check it over first.
○ Orwell says
“desire to be held against their will…”
Holy crap. Here these guys are actually predicting their own evil deeds,
what? As a disclaimer for you, the victim, to sign?
Oh yeah, that’s rich. An enemy of the church is an enemy of mine. That mentality is older than Christ, come to think of it.
They may as well hold up signs and red flags, picket their own big blue building and say it equally plain:
WE ARE HERE TO BRAINWASH YOU
KIDNAP YOU, and
INCARCERATE YOU
until you give up and work for us for free,
or whatever else we say, forever.
Those Anonymous guys were so right, bless each and every one of their souls, ours too…
– It is always, as it turns out, worse than you think. It is a test of imagination, in fact.
○ Old Surfer Dude says
I haven’t seen that yet, Mike. But, is certainly sounds like the cult.
○ ka says
Jeffrey Augustine: “2. Agreement and General Assistance Regarding Spiritual Assistance. Summary: This is Scientology Inc.’s infamous Kidnap Contract that allows the Cult to kidnap any
of its members and lock them up for an indefinite duration of time — and this without the kidnapped member having the benefit of any legal representation, legal hearing, medical
evaluation, or medical intervention. All a Scientology Inc. “case supervisor” has to say is that a member has gone Type III. After this pronouncement, the member is bodily seized,
locked up, and held against their will. … “
■ Cece says
ka, and I bet there are no C/Ses left that would hold their ground on who was or wasn’t Type III. It’s likely all C/Sed by Executives now (Executive C/Sing which was at one time a
nono). The truly passionate auditors and C/Ses I’ve know have either died or otherwise left since then. I was C/Sed by executives in a very upsetting situation when I last had my
87hours of paid for ‘NOTS’. Never again … it was worse then the worse I’d imagined. I then knew I would never set foot in a church for services ever again nor return from my LOA
from SO at AOLA. The auditing itself was causing me to heavily introvert and I was fully aware the cause of it thank goodness.
○ Kemist says
Has somebody ever tried that clause in court ?
I don’t think it would hold. You can’t sign away your rights, and no contract clause can protect someone against the consequences of their own negligent or criminal behavior. At least
it is that way where I live.
Abusive clause is abusive, and nullified the moment a judge lays eyes on it, no matter how loud your cries of “but, but, we is a church !”
24. Valkov esnowl@juno.com says
It would appear that the CoS by current policy as a whole is type III according to the scientology definition. Gee, I wonder who the SP they are connected to, is?
□ Old Surfer Dude says
Valkov, that’s what I was thinking too. The entire organization is Type III. But, insanity is part and parcel of this group.
☆ McCarran says
Exactly. It’s become what it preaches against. It’s become what it purports to clear you from (reactive). The only solution to this is to handle or to disconnect.
25. statpush says
This document is evidence of the potential danger of Scientology. It is clear what their priorities are – the organization.
The first thing you do – isolate the person so as not to disrupt delivery.
This is remarkable.
“6. IF NEEDED per the laws of the land for this type of case, a registered nurse is also brought to this house…”
So, if the laws don’t demand it you can skip this? But, the real underlying reason…
“This way the person cannot later claim that he received insufficient medical attention…to protect the Church against false claims later.”
This shit makes me sick. There is no real responsibility here, only a pretense. Never do they say…”this condition may have been caused because the auditor asked him the same fucking question for
four hours, driving the PC crazy” No, the PERSON is dramatizing evil intentions.
It’s all about damage control for Scientology, NOT the well-being and health of the patient.
And to think Scientologists, knowingly or unknowingly, sign agreement forms granting permission to be treated like this.
Bottom line: NOTHING is more important that Scientology. Your life is not more important; your sanity is not more important; your health is not more important.
It gives new meaning to: “we’d rather have you dead, than incapable”
26. Jose Chung says
I was trained in the Marine Corps, Navy,then US Army on programs
that all started out to find your breaking point. During the Vietnam war
we had a few who had psychotic breaks on mundane tasks like peeling
potatoes on Mess duty and so forth. After a decade of service my eval
stated I could not be brainwashed or broken. I was a Special Forces Trainer.
Every Scientology Org tried to bullshit me a failed , I would work the
org to get the blowback from their own foolishness but that didn’t work
out making things better only much worse.
I read the Lisa Mc Phearson story on Tony Ortega and was very surprised
that they were right up there with North Korean Mind Control straight out
of the “Manchurian Candidate” ( Frank Sinatra version) the later version
is good as well but over the top with chips implanted in brains.
Scientology is molded into Old School Brainwashing by David Miscavige
where Money equals Eternity, case gain, going to Heaven , and
more wealth. All lies of course.
I would rather have real enemies than Fake Friends.
□ Valerie says
“I would rather have real enemies than Fake Friends.”
☆ Orwell says
Dad would jump in right here without skipping a heartbeat and say:
“Be careful what you ask for.”
Fake friends. That’s kinda touchy, as a phrase. How many of us are not guilty of putting on some kind of mask, before getting outta bed much less out the front door?
My request, advise if you will, is to offer kindness to whomever you chance to meet. To be kind, that’s it. Avoid assumption, although we do it all the time. We think we know what’s going
on, that we are correctly assuming everything we have “aptly” pegged, pegged as being a perfect reflection of reality when in fact the idea is comprised by mostly delusion. We “think” we
know what the other guy is thinking, without thinking about it, nearly ALL the time. So, that should be rule one. Stop assuming. Choose your words carefully in order to project kindness
and see what you get and stop assuming that you know it already and you will soon project yourself into the realm of sage and mystics, depending on the pace of your journey… The church is
evil but the people generally are not. You will discover a lot of friends obscured under the cloak of perceived enemies by erasing assumptions at the starting line, then watch while your
projections of compassion return to you in kind. It is cause and effect, the world we live in.
And, Dad. Hope you’re having fun on the other side, man. Still loving you.
○ Ms.P says
WoW, beautifully said!
■ Orwell says
Thank you very much, Ms.P.
Credit where it is due, I am inspired to write all that from the book,
The Four Agreements, by Ruiz.
☆ Old Surfer Dude says
As long as I have you as a friend, Valerie, I’m good to go!
○ Valerie says
Aw OSD now you made me blush.
■ blue moon says
o dude
you really are da man
27. LDW says
I’m just waiting to hear the rave success stories from all the people who got the rundown and are now doing fine…….still waiting…..hummmm
□ Jens TINGLEFF says
John Duignan in the very excellent “The Complex” brushes off his PTS type 3 episode, saying it was quite common among ordinary public, in his experience, to go more or less psychotic. Nothing
major about it.
I’m pretty sure he got the Introspection rundown (of course, maybe not whatever “special” of the week that Captain David “he is NOT insane!” Miscavige had inflicted on Lisa McPherson; while
that one didn’t work, I don’t think any rundown used by the Co$ works, at least not for the reasons stated and not more reliably than, oh, doing nothing).
☆ Old Surfer Dude says
Wait…..what??? “…it was quite common among ordinary public….to go more or less psychotic.”
Whoa! It was really that common? How much more evil can they get!
○ Bentley says
ya pretty much gotta go star-wars…
28. Dan Locke says
Between 1977 and 1979, a couple of bulletins came out with various conclusions from the old man about people who had taken LSD. Ron’s verdict was that people who had taken LSD were brain damaged.
Now, there was a little bit of “so what?” in my response, due to my earlier reading of other material where the claim was made that the brain was not such a big deal, and thus damage to it not a
big deal. In all honesty, I remembered reading that and thinking “what?!?!?” when I first read that stuff, but then resolved it somehow in my mind. (“Ron’s smarter than everybody.”)
But there was a bigger “hrrmph!” in that I had taken LSD many times and I had always thought my experiences to have been, overall, helpful. So, OK…If there had been brain damage, it’s not a big
deal as the brain isn’t a big deal…
There’s lots of personal stories I could tell around this subject, many involving recruiting others into the SO. “I’ve take LSD, and yes, I am certain of it… I had visual hallucinations, the
whole thing!” was the only really effective way to get an uninvited team of recruiters out of your living room with any speed. (But they’d be back an hour later to see your kids and spouse…)
But, before I trigger a flashback and go off on my own for several hours of bliss, let me get to the point of all this. In one of those HCOBs, LRH says that His Pronouncement was based on his
“extensive research of two cases” (sic)
Also, if I remember correctly, throughout DMSMH there are plenty of statements that he had tested it on something like 259 cases, yet only very few of these research cases were buried again.
I think that Ron reached most of his conclusions on the success of any given technique, ever, based on one or two results, if that. I think there is a lot of things that he just figured “this
ought to work” and off it went to mimeo for reissue.
□ frodis73 says
Your post is great and reminds me of why I can’t stand that the indies still look up to lrh as some kind of genius. He had a lot of nerve calling himself a scientist, or doctor, etc. By his
standards I’m just going to walk around calling myself a frickin doctor…and I have a lot more experience with the mentally ill than that asshat. Indies, wake up already…lrh is/was a fraud
that only wanted your cash.
□ windhorse says
This was a RECENT experiment. And part of the conclusion was “In many ways, the brain in the LSD state resembles the state our brains were in when we were infants: free and unconstrained” …
“For the first time we can really see what’s happening in the brain during the psychedelic state, and can better understand why LSD had such a profound impact on self-awareness in users and
on music and art.”
Also recent studies are showing that MDMA (ecstasy) (a form of methamphetamine) increases serotonin which effects mood …
NOT advocating taking LSD or ecstasy — just saying that yet again Hubbard has it wrong.
It’s due to science which includes scientific devices like MRI and ƒMRI that enable much of what was once UNKNOWN, to be known.
□ blue moon says
Yes! Yes, that is correct, Dan Locke, about LSD being justification for throwing you out,
when and if that was what they wanted to do… they would and THEY DID.
before that, you see, they threw me out the very same way:
Here we have the claim of world-plus-personal salvation at your fingertips.
– All well and good until somebody in Division 5 or wherever decides you aren’t worth the trouble, (basically, you are in REAL TROUBLE the moment after you have given them your last dollar)
BOOM, they come up with a reason why you need to be tossed into the gutter. You think you’re in like Flint when, truth be known, your head is always on the chopping block, just waiting for
the executioner.
And the justification set up for me – was that I had been administered “psych” drugs and so I was “damaged”,
specifically told me that was ineligible to be a staff member, their mistake. Shoved me out, said I was now on a “personal program” (although I think they just made that phrase up to get me
to go along with being shoved out), and good luck. That was it.
Not exactly the description of a compassionate church, serving the community, deserving a tax-exempt status, o my… Let me stop before I lose my dignity, thank you.
29. Brian says
It is possible that all of these overblown “scientific” “researched” findings and announcements by Ron was him applying Altitude Instruction on us for financial gain.
Once we agreed to and granted Ron the messiah status he marketed to us, we would then believe that the “next step” was the handle to major problems.
And once we agreed that all critics are criminals, thus outlawing, by threat of punishment, any non biased assessment; no one would ever question any of Ron’s “findings.
Thus L Ron Hubbard secured millions of dollars. He used our faith in him to make money.
He knew what he was doing. We did not.
Ron was not stupid. He was conscious of the fraud regarding claims.
If being critical in Scientology is sign of overts; L Ron Hubbrd was loaded with them.
He was critical of our whole civilization.
30. Potpie says
Heavy recreational drugs (LSD etc.) and some drugs prescribed by psychiatrists and other MD’s can induce a Type III phenomena in an individual. Not always by any means. I find it interesting that
Narconon accepts people that are more likely to have a type III situation and some have “gone” type III during the Narconon program. A case in fact was a gifted lady (musician in a philharmonic
orchestra) was on a drug prescribed by a psychiatrist that kept her on an even keel and able to operate in life.
But she did not like some of the side effects. She was talked into going to Narconon to help her come off the drug. After a few days being off the drug at a Narconon she had a type III incident
(I won’t go into detail but it wasn’t pretty). Actually Narconon did the right thing and sent her home to be taken care of by family and medical professionals. And of course to get her off their
lines. This lady survived the “incident” and carried on her life without Narconon or Scn. Now why was Lisa McPherson not sent home to be taken care of by her family and medical professionals? How
were those two incidents different? They were different in that Lisa was not taking drugs and was driven to her situation by failed tech developed by LRH…and delivered by idiots. Who was going to
suffer more from a PR stand point, Narconon or Scn? Narconon (in that particular situation) did the right thing no matter what their reason was. Because of the tech of the Introspection R/D and
procedures written above as a result of the release of the R/D, Scn had to “handle” Lisa…..LRH said so. No real concern or empathy for the individual just a terrible idea the R/D would handle it.
Robots one and all, all the way down the line. And I mean everyone involved with the Lisa situation from beginning to the end of the trial. All because of some R/D LRH said would handle such
situations and a fantastic need to maintain Scn PR and cover Micavige’s and LRH’s asses.
31. Kemist says
Of course wogs are scary.
They aren’t properly indoctrinated and coached in the bizarre culture of Scientology, which means they are not aware of the mechanisms to be used to maintain belief.
They’re that little kid who innocently points at the naked OT going down the street and says:
“Look peeps, this dude is going around butt-naked !”
And then some scientologists realize, that, yes, the dude is indeed going around butt-naked, and they are not the only one who can see. Sometimes the dude himself realizes that he has spent all
his money on nice clothes that don’t actually exist.
The SP is slightly worse : he/she’s the person who realizes they have wasted money on non-existent clothes, and is aware of the mechanisms used to maintain the group’s beliefs, except he/she aims
to disrupt them.
You will always find fear and demonizing of outsiders and former members in groups of people who have nothing to base their conclusions on, besides an eminently fragile (so fragile that they have
to rely on each other to reinforce it) belief that it is so.
32. dr mac says
My wife went PTS type 3 while on staff. She had handlings that went on non stop – I spent a fortune on OT3 repairs, Introspection RD and Christ knows what else at an AO – 13 intensives of it,
before she returned home worse than before. She was like a zombie for 13 years, until I began to get an inkling that maybe scn doesn’t ALWAYS work, or at least not on psychos.
I got her off staff, thought about this situation for a few more months, and finally summoned the enormous courage (remember I was still a scio) to take her to a psychiatrist. It still took
another 12-18 months for her to get fully handled on meds, but from the first visit I felt she was in the right hands. Remember again, to me this was the arch-enemy evil satanist incarnate I was
visiting. Today she functions and is happy.
Of course, still having some of the scientology in her veins, the urge was strong in her to get off the medication asap and every time she felt ‘good’ she would stop taking it. But it has now
been hammered into her with a mailed fist to never miss a day. I myself still wouldn’t take medication (it is TOO hard drummed into me), but that’s for another day!
If there were just one thing to ridicule scn about (I know, there’s actually two) it would its attitude to medication and psychiatry, and in my opinion and experience the Indies are possibly
worse. My wife literally lost 14 years of her life, the entire childhoods of her two kids, and if I wasn’t such a hell of a guy she would certainly have lost her husband and home.
33. Wognited and Out says
The EEE PEE of Scientology is PTS Type III –
That is if you stay in too long and don’t wognite on common sense and get the hell out!
The government owes the public a Black Box Warning:
Scientology is dangerous and damaging to your well being and those around you.
Scientology has ruined the lives of many people. Scientology may, but is not limited to, cause bankruptcy, divorce, foreclosure, suicide, homicide, money laundering, extortion, black mail,
criminal acts, heart failure, liver failure, brain damage, asthma, families shattered, lives ruined, dreams smashed, suppression, oppression, and minds lost. Just look at David Miscavige’s family
to see how SCIENTOLOGY helped them.
While Scientology hides behind the “Religious Cloak” – you will have nothing to protect you. They are clever at getting you to give up your rights covertly.
You will sign legal documents where Scientology always keeps your money and you give up all of your constitutional rights. Additionally, you will be gagged from talking about the crimes you
witnessed or committed whilst in Scientology and you will lose everything if you tattle on Scientology.
Scientology, A Tax Exempt Non – Profit For Profit (billions) will hire private investigators to follow you and attorney’s to sue you if you “Know” and are able and willing to tell others about
the crimes you witnessed whilst in the religion that claims to help the able become more able while disabling the able.
34. Dollar Morgue says
Conclusion: Type III’s are walking evil puporses and non-persons who will do anything to inflict maximum damage on the cult. Therefore, do as ‘we’ say the ‘psychs’ do and don’t believe them when
they claim to be sane. Bring in staff who are in-ethics, i.e. have proven they will follow orders and not blab about this distasteful incident, thus causing the flap to flap even further.
I get the sense that they view the patient as a menacing non-human particle to be isolated and terminatedly (interesting choice of word) handled.
You are either a giver or a taker in scientology. Takers are dev-t particles unless they bring money in exchange.
□ Dollar Morgue says
Oh, and given what I now know about psychology, psychotherapy and psychiatry, I find the notion of ‘briefing’ a complete layperson on how to deal with somebody that scientology has driven to
experience a psychotic break utterly appalling and horrific.
Of course, back when I was a true believer I ‘knew’ this was the very best approach. However, I had never encountered such a person and always wondered how physical labour and walks in
silence could help anyone. I had physical labour in the cadet org and plenty of silence, which at times was depressing.
Not long ago, I spoke to a person who works at a psychiatric hospital. He said they talk to the people who are experiencing insanity. Surprised, I asked him why on earth? (Still
indoctrinated.) He answered, ‘because how else would you find out what has made them that way?’ Quite a difference. In scientology, what made a person a particular way is already known,
bought and paid for. The person has no say in the matter whatsoever.
35. justmeteehee says
Just ask Lisa McPhearson how well it works, oh wait, we can’t ?
36. Kuato Lives says
Couple things that stood out for me here.
1. There is absolutely zero compassion or concern for the person having the breakdown. The entire “handling” is within the context of preventing them from causing problems (legal and PR) for the
group. It’s only important to protect the image of the church and shield it from legal entanglements. The fact that there is a person there who has value in and of themselves and needs help and
healing is not a consideration at all.
2. It states explicitly that this handling is a result of people having jumped from closed windows, started fires, hurt themselves/others and more. A few instances are known but I wonder how many
have never and will never see the light of day? It’s a truly disturbing thing to ponder. This group has left so much human wreckage in its wake, it’s difficult to really fathom.
37. Old Surfer Dude says
Mike, I was just over at Tony’s site and saw the wedding picture of you and Christi. I gotta tell ya, you two make a beautiful couple! And what a beautiful environment you got married in. Right
on the beach no less!
□ thegman77 says
Mike: Apologies for the wrong spelling of Christi’s name yesterday.
☆ Mike Rinder says
No problem — a lot of people get it wrong. It is Christie.
38. McCarran says
Having gotten into scientology in 1973, one thing I learned fairly quickly is that “standard tech” was always changing but when LRH changed it, it made sense to me and was clarified in his
“revised” bulletin. Now david miscavige changes it to suit some new scam of his and claims that what LRH intended was “squirreled” by SPs that were “expelled” (escaped). But let’s face it
“standard tech” has never been standard.
39. clearlypissedoff says
Mike comments how LRH would “research” these brilliant breakthroughs in technology and I thought I would relate a similar story of a breakthrough.
Around the time of the Bruce Welch type III incident, my mother was busted as LRH’s cook. LRH wanted to assign her to the EPF or some form of mest work. I wasn’t very happy with my mother being
subjected to further mest work, so I wrote a DR, or Daily Report, to LRH saying how she had raised 7 kids, and even during WW II she worked in a factory, as a war effort handling large pieces of
metal on a daily basis. She really has had a lot of mest work so offered that the LRH-assigned mest work was an overkill. Well, one of the messengers must have let him see my DR as the next day
she was taken out of mest work and LRH was personally C/Sing her folders. All of a sudden, another breakthrough in technology was discovered – The Metal Rundown or some nonsense name. Another
brilliant breakthrough. Because of her years of working with metal, it was affecting her to this day and this rundown was the solution. Yeah right….
I think the hype of the Metal R/D lasted a week or so and I don’t think ever went any further than the “breakthrough” discovered C/Sing my mother. But this is an example of his research. Getting
one report about someone working with metal and presto – a breakthrough. I think it was really all imagined by LRH as most everything he did with his technology. Also, witnessing this “scientific
research” first hand, the wheels started spinning for me about SCN tech. Too bad it took 7 years and doing OT III for a couple of weeks to really see the light.
My parents were offloaded by LRH shortly thereafter, along with about 30 others. A blessing in disguise actually.
□ Bruce Ploetz says
clearlypo’ed, if you can find an old copy of the original Technical Bulletins of Dianetics and Scientology you can find the “Metalosis Rundown”. Sounds just like what you describe. There are
original LRH Case Supervision instructions for Metalosis, Expanded Dianetics, Introspection Rundowns etc. in those old red volumes.
Amazing how one day’s exciting new breakthrough is the next day’s forgotten old trash. Almost like he was making it up as he went along. But all these old abandoned dead ends provide a great
opportunity as well. They allow Dave M to dig them up and rebrand them as forgotten miracle technology.
Like the “Cause Resurgence Rundown”. Conceived as a punishment for David Mayo, used as a punishment for lots of folks when they called it the “running program”, now a punishment for the
public that they actually pay for! In a special super expensive new building, also paid for by the long suffering public.
You can’t make this stuff up.
☆ clearlypissedoff says
You have jogged my memory – and it was the Metalosis RD. I’m guessing it came out in ’73 or ’74 although they were on the rust-bucket from late ’71 until I think 73/74 so I could be wrong
on the dates. I do have some dusty, old red volumes somewhere hidden away so maybe I’ll read about it one of these days although I do get the creeps just thinking of reading that BS.
○ Ann B Watson says
Hi clearlypissedoff, How I hear you! I got the creeps with you reading about those dusty,old red volumes.Metalosis Rundown sounds like a bizarre nightclub in the city of Metropolis!
☆ Richard says
A “Metallica” Rundown would be ok. The EP might be knowing how to rock out on an electric guitar!
□ thegman77 says
I would guess that one would definitely need to know what metal(s) were involved. Lead, for instance, would have been very dangerous to handle in any amounts.
□ grundoon says
L. Ron Hubbard discovered that your body organs can become ill if their electric fields are distorted by nearby metal (or metal that was nearby in the past or on the whole track). This
“metalosis” can be cured by auditing. The ill person is PTS to a metal object. Steps to find the metal are added to the PTS handling.
Appendicitis, for example, is caused by the studded metal belt you wore in a past life. For menstrual cramps or a uterine cyst, LRH says, “chastity belt is the obvious answer.”
In BTB 19 OCTOBER 1972, Expanded Dianetics Series 11: EXPANDED DIANETIC CASE D (Volume IX), the PC possibly has a uterine cyst. “MO REPORT — Pain in tummy on and off. Little bit of bleeding
after the pain. Either she still has cyst in stomach or she’s mocking it up.”
“LRH COMMENTS AND PROGRAM 27.5.72 —
1. 2wc ‘Tell me about your illness’ (for data). 2wc ‘What metal would one have in that area?’ Choose item R3R Triple. (Chastity belt is the obvious answer.)
2. 2wc to fish for electric fields in the area. R3R Triple.
3. Recheck all possible angles of field distortion of body in ill area.
4. When all angles of fields and metal exhausted in area: 4a. Ev Purps from L10. R3R Triple.”
“This pc better start looking good. We’ve cured 3 of these cysts in the last couple of years, a 100% record.”
In another BTB, EXPANDED DIANETIC CASE G, the PC has back pain…
“LRH COMMENT AND C/S 17.5.72 — I tole you and tole you and tole you — when they rollercoaster they’re PTS OR she has been wearing metal. (Shoes have steel in them, belts, garter belts.) (I
just found ‘appendicitis’ was a party belt studded with metal!)
1. Have the pc stand, look her over for metal, question her about metal stays, girdles she wears or has worn. Find what it is that rests exactly in the somatic areas. FIND IT past or present.
R-Factor: Metal worn on the person can cause your condition.”
40. Ms.P says
Hi Mike once again you make a great point. “What was today’s breakthrough, presented with supreme certainty that it IS the answer, soon became tomorrow’s old news.” When I think about all this
drivel and believing in all the ‘new discoveries’ just makes me CRINGE today. What the hell was I thinking?
□ Old Surfer Dude says
Oh, you were thinking ok. The problem was you were using “Cult-think.”
☆ Ms.P says
Gotta love you OSD!
○ Old Surfer Dude says
Yes, Ms.P, I stand on guard for you!
□ Gimpy says
scientology has been this way as long as I’ve been involved in it, first thing I remember being pushed to everyone was Key to Life and LOC, later it was GAT, the volunteer minster programme,
then the congresses, then the basics, and on and on. Nearly all costing a small fortune to fill your home with unused binders and books.
☆ Ms.P says
Gimpy – yup, every friggin new thing EVERYBODY had to do, whether you needed it or not. When GAT came out I walked away. Better late then never.
☆ gato rojo says
Very true. And having been on the production lines of much of that stuff, I constantly wondered why the packaging had to be so friggin’ over the top and fancy so that it made you not even
want to touch it for fear of getting fingerprints on it. Especially since you had to pay so much money for it. Really self-defeating…LOL.
□ McCarran says
Atleast you didn’t do Student Hat, Class 4 Crs, OT IV, V, VI, VII, VIII twice. I win.
☆ thegman77 says
☆ Sleepy says
Go see the success officer on the way to the reg. Double cringe.
41. John Doe says
It is truly disturbing how this document dehumanizes the person who is off his rocker and in some of the worst trouble possible for a human.
At no time does Phil refer to the insane person as “he or she” or “the individual” or “the person”.
No, it just “the type III”. Like it’s an object.
42. SILVIA says
Contradictory. One assumes a person went Type III due to sever introspection and closeness to an SP.
On the other hand it states this person is very evil and the state is the result of evil intentions.
Based on the sacred scriptures and dogmas of the tech, one who has evil intentions is committing continuos overt acts, actively doing harmful things thus, it does not fit with a fully introverted
person such as Lisa Mc Person who could hardly talk and who had been severely misuadited, factor that led to her introversion.
The hypocrite aspect, disguised with ‘we are the only ones”, ‘this is the only tech’ is that about everything is done to avoid a flap, to prevent legal suits, to not allow the church to be
criticized; in other word, Hubbard’s main concern was to protect himself by promoting a fabulous discovery.
And it sure did, and still does, backfire on him, the ‘religion’ and his sucesors.
43. Bystander says
And where is Phil now?
Aside from the intent of Mike’s post, which certainly is valid, it is so hard to read this crap. Written in the true hubbardian method, salted with mid-century slang and trying to sound important
(“other fish to fry”??), this thing is painful, reeks of paranoia and no regard for the unfortunate victim.
Like everything else hubbard, its pathetic.
44. hgc10 says
Mike, I was reminded, in reading your comments about the destructive potential of wogs and SPs on Scientologists’ most delicate spirituality, of something Scientology has in common with related
thought systems. What I refer to is the panoply of magical thinking collectively referred to by detractors as “woo.” Merchants of these notions often assign blame for the failures under scrutiny
(testing) to the presence and interference of non-believers, with their oh so destructive negativity. Time and again when dousing, ESP, remote sensing, etc are tested under controlled conditions,
or are proposed for such testing, the purveyors and practitioners of this woo will make the excuse that their magic can’t operate in the presence of scoffers, who ruin everything.
□ thegman77 says
Actually, current controlled conditions have found (repeatedly) that this “woo” (terrific scientific term) works in many instances. If, however, one goes into it already convinced that it’s
“unreal”, none of it will ever register as being legitimate. It’s a form of mindblock no different than scio.
☆ Artoo45 says
Critical thinking is never the same as Scientology. You may as well still be in if you think that’s true.
45. Mike Wynski says
“Type 3’s are people that according to the scientology definition are being negatively effected by “apparent SP’s” all over the world, or even ghosts and demons.”
When one couples this data to the fact that Hubbard’s sole person used in research of OT III was HUBBARD (and the fact that the OT 3 “incident” and ALL such data has to spoon fed to any other
person who does the level (because there is NO DOUBT that it would NEVER come out of their own heads otherwise, because it’s B.S.) It is clear that Hubbard was projecting and he was a “Type 3”
who was tormented by demons (he named them B’T.’s) but a Rose by any other name…
□ Old Surfer Dude says
….would still smell like shit.
46. Leslie Bates says
The infallible Source and those who follow him are always in some respect stuck in the failure mode.
□ Old Surfer Dude says
It’s funny you posted that, Leslie. I believe Scientology is in full Failure Mode now.
Leave a Reply Cancel reply | {"url":"https://www.mikerindersblog.org/pts-type-iii/","timestamp":"2024-11-04T05:17:38Z","content_type":"text/html","content_length":"414742","record_id":"<urn:uuid:326dc4e5-7459-4cfa-9dc4-fe3b17af62f7>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00448.warc.gz"} |
losses -
Planetary gear set of carrier, planet, and sun wheels with adjustable gear ratio and friction losses
Simscape / Driveline / Gears / Planetary Subcomponents
The Sun-Planet gear block represents a set of carrier, planet, and sun gear wheels. The planet is connected to and rotates with respect to the carrier. The planet and sun corotate with a fixed gear
ratio that you specify and in the same direction with respect to the carrier. A sun-planet and a ring-planet gear are basic elements of a planetary gear set. For model details, see Equations.
Thermal Model
You can model the effects of heat flow and temperature change by enabling the optional thermal port. To enable the port, set Friction model to Temperature-dependent efficiency.
Ideal Gear Constraints and Gear Ratios
Sun-Planet imposes one kinematic and one geometric constraint on the three connected axes:
${r}_{\text{C}}{\omega }_{\text{C}}={r}_{\text{S}}{\omega }_{\text{S}}+{r}_{\text{P}}{\omega }_{\text{P}}$
The planet-sun gear ratio is
Where N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:
${\omega }_{\text{S}}=\text{}–{g}_{\text{PS}}{\omega }_{\text{P}}+\text{}\left(\text{1}+{g}_{\text{PS}}\right){\omega }_{\text{C}}$
The three degrees of freedom reduce to two independent degrees of freedom. The gear pair is (1, 2) = (S, P).
The torque transfer is:
${g}_{\text{PS}}{\tau }_{\text{S}}+{\tau }_{\text{P}}–{\tau }_{\text{loss}}=\text{}0$
In the ideal case, there is no torque loss, that is τ[loss] = 0.
Nonideal Gear Constraints and Losses
In the nonideal case, τ[loss] ≠ 0. For more information, see Model Gears with Losses.
Limitations and Assumptions
• Gear inertia is assumed to be negligible.
• Gears are treated as rigid components.
• Coulomb friction slows down simulation. For more information, see Adjust Model Fidelity.
C — Planet gear carrier
rotational mechanical
Rotational conserving port associated with the planet gear carrier.
P — Planet gear
rotational mechanical
Rotational conserving port associated with the panet gear.
S — Sun gear
rotational mechanical
Rotational conserving port associated with the sun gear.
H — Heat flow
Thermal conserving port associated with heat flow. Heat flow affects the power transmission efficiency by altering the gear temperatures.
To enable this port, set Friction model to Temperature-dependent efficiency.
Planet (P) to sun (S) teeth ratio (NP/NS) — Planet-to-sun gear ratio
2 (default) | positive scalar
Ratio g[PS] of the planet gear wheel radius to the sun gear wheel radius.
Meshing Losses
Friction model — Friction model
No meshing losses - Suitable for HIL simulation (default) | Constant efficiency | Temperature-dependent efficiency
Friction model for the block:
• No meshing losses - Suitable for HIL simulation — Gear meshing is ideal.
• Constant efficiency — Transfer of torque between the gear wheel pairs is reduced by a constant efficiency, η, such that 0 < η ≤ 1.
• Temperature-dependent efficiency — Transfer of torque between the gear wheel pairs is defined by the table lookup based on the temperature.
Ordinary efficiency — Efficiency
0.98 (default) | scalar | 0 < η[SP] ≤ 1
Torque transfer efficiency, η[SP], for sun-planet gear wheel pair meshings. The value must be greater than 0 and less than or equal to 1.
This parameter is exposed when the Friction model parameter is set to Constant efficiency.
Temperature — Temperature
[280, 300, 320] K (default) | vector
Vector of temperatures used to construct a 1-D temperature-efficiency lookup table. The vector elements must increase from left to right.
To enable this parameter, set Friction model to Temperature-dependent efficiency.
Efficiency — Gear efficiency
[.95, .9, .85] (default) | array | 0 < η[SP] ≤ 1
Array of mechanical efficiencies, ratios of output power to input power, for the power flow from the ring gear to the planet gear, η[RP]. The block uses the values to construct a 1-D
temperature-efficiency lookup table.
Each element is an efficiency that relates to a temperature in the Temperature vector. The length of the vector must be equal to the length of the Temperature vector. Each element in the vector must
be in the range (0,1].
This parameter is exposed when the Friction model parameter is set to Temperature-dependent efficiency.
Sun-carrier power threshold — Power threshold
0.001 W (default) | scalar
Power threshold, p[th], above which full efficiency is in effect. Below this values, a hyperbolic tangent function smooths the efficiency factor. For a model without thermal losses, the function
lowers the efficiency losses to zero when no power is transmitted. For a model that considers thermal losses, the function smooths the efficiency factors between zero at rest and the values provided
by the temperature-efficiency lookup tables at the power thresholds.
This parameter is exposed when the Friction model parameter is set to Constant efficiency or Temperature-dependent efficiency.
Viscous Losses
Sun-carrier viscous friction coefficient — Viscous friction
0 N*m/(rad/s) (default)
Viscous friction coefficient μ[S] for the sun-carrier gear motion.
Thermal Port
These settings are visible when, in the Meshing Losses settings, the Friction model parameter is set to Temperature-dependent efficiency.
Thermal mass — Thermal mass
50 J/K (default) | scalar
Thermal energy required to change the component temperature by a single temperature unit. The greater the thermal mass, the more resistant the component is to temperature change.
To enable this parameter, set Friction model to Temperature-dependent efficiency.
More About
Hardware-in-the-Loop Simulation
For optimal simulation performance, set Friction model to the default value, No meshing losses - Suitable for HIL simulation.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced in R2011a | {"url":"https://it.mathworks.com/help/sdl/ref/sunplanet.html","timestamp":"2024-11-10T06:17:21Z","content_type":"text/html","content_length":"100266","record_id":"<urn:uuid:45e2554e-c906-41bc-9745-24201d46555c>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00554.warc.gz"} |
Ken Shirriff's blog
Forbes recently published the Forbes 400 List for 2024, listing the 400 richest people in the United States. This inspired me to make a histogram to show the distribution of wealth in the United
States. It turns out that if you put Elon Musk on the graph, almost the entire US population is crammed into a vertical bar, one pixel wide. Each pixel is $500 million wide, illustrating that $500
million essentially rounds to zero from the perspective of the wealthiest Americans.
The histogram above shows the wealth distribution in red. Note that the visible red line is one pixel wide at the left and disappears everywhere else—this is the important point: essentially the
entire US population is in that first bar. The graph is drawn with the scale of 1 pixel = $500 million in the X axis, and 1 pixel = 1 million people in the Y axis. Away from the origin, the red line
is invisible—a tiny fraction of a pixel tall since so few people have more than 500 million dollars.
Since the median US household wealth is about $190,000, half the population would be crammed into a microscopic red line 1/2500 of a pixel wide using the scale above. (The line would be much narrower
than the wavelength of light so it would be literally invisible). The very rich are so rich that you could take someone with a thousand times the median amount of money, and they would still have
almost nothing compared to the richest Americans. If you increased their money by a factor of a thousand yet again, you'd be at Bezos' level, but still well short of Elon Musk.
Another way to visualize the extreme distribution of wealth in the US is to imagine everyone in the US standing up while someone counts off millions of dollars, once per second. When your net worth
is reached, you sit down. At the first count of $1 million, most people sit down, with 22 million people left standing. As the count continues—$2 million, $3 million, $4 million—more people sit down.
After 6 seconds, everyone except the "1%" has taken their seat. As the counting approaches the 17-minute mark, only billionaires are left standing, but there are still days of counting ahead. Bill
Gates sits down after a bit over one day, leaving 8 people, but the process is nowhere near the end. After about two days and 20 hours of counting, Elon Musk finally sits down.
The main source of data is the Forbes 400 List for 2024. Forbes claims there are 813 billionaires in the US here. Median wealth data is from the Federal Reserve; note that it is from 2022 and
household rather than personal. The current US population estimate is from Worldometer. I estimated wealth above $500 million, extrapolating from 2019 data.
I made a similar graph in 2013; you can see my post here for comparison.
Disclaimers: Wealth data has a lot of sources of error including people vs households, what gets counted, and changing time periods, but I've tried to make this graph as accurate as possible. I'm not
making any prescriptive judgements here, just presenting the data. Obviously, if you want to see the details of the curve, a logarithmic scale makes more sense, but I want to show the "true" shape of
the curve. I should also mention that wealth and income are very different things; this post looks strictly at wealth. | {"url":"https://www.righto.com/2024/10/?m=0","timestamp":"2024-11-06T02:12:19Z","content_type":"application/xhtml+xml","content_length":"114614","record_id":"<urn:uuid:c82ad260-09e1-470e-ac1f-b08f11ae416f>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00460.warc.gz"} |
Positive Volume Index - useThinkScript Community
Anyway to do a Positive Volume Index on TOS that plots a moving average and has customizable inputs?
Last edited by a moderator:
The final script with priceclose feild working:
# ########################################################
# Positive Volume Index
# ########################################################
declare lower;
input AvgType = averageType.SIMPLE;
input Length = 50;
input priceclose = close;
def index = compoundValue(1, index[1] + if (volume > volume[1] and priceclose[1] != 0) then 100 * (priceclose - priceclose[1]) / priceclose[1] else 0, 100);
plot PVI = index;
plot AVG = MovingAverage(AvgType, index, Length);
Here's what i got, but it doesn't work:
# Positive Volume Index
declare lower;
input AvgType = averageType.SIMPLE;
input Length = 50;
input priceclose = close;
def index = compoundValue(1, index[1] + if (volume > volume[1] and close[1] != 0) then 100 * (close - close[1]) / close[1] else 0, 100);
plot PVI = index;
plot AVG = MovingAverage(AvgType, close, Length);
Last edited by a moderator:
Join useThinkScript to post your question to a community of 21,000+ developers and traders.
im not too concerned about having ALL the Moving Average Type input options of Simple, Exponential, Double Exponential, Triple Exponential, Hull, Time Series, Triangular, Variable, VIDYA, Weighted
and Welles Wilder. I jsut mainly want a moving average with the Field Inputs of Open, High, Low, Close, hl/2, hl/3, hlcc/4 and ohlc/4 , and the period length input.
Last edited by a moderator:
plot AVG = MovingAverage(AvgType, close, Length);
You want an average of
instead of an average of
You want an average of index instead of an average of close.
Thank You! That did the trick.
# ########################################################
# Positive Volume Index
# ########################################################
declare lower;
input AvgType = averageType.SIMPLE;
input Length = 50;
input priceclose = close;
def index = compoundValue(1, index[1] + if (volume > volume[1] and close[1] != 0) then 100 * (close - close[1]) / close[1] else 0, 100);
plot PVI = index;
plot AVG = MovingAverage(AvgType, index, Length);
You want an average of index instead of an average of close.
it doesnt look like the input priceclose feild is working, everything else is working on it though. do you know how to fix that?
it doesnt look like the input priceclose feild is working, everything else is working on it though. do you know how to fix that?
priceclose is not used anywhere in the code.
Do you need it to work? If you use open or high or low instead of close does this still give you a useful result? The built in PositiveVolumeIndex study has no option for price type. It always uses
close. So I would just delete the
input priceclose = close;
If you want it to work then everywhere on the line of
def index =
should be priceclose instead of close.
Active member
2019 Donor
What would the final script look like please? Thanks in advance
# ########################################################
# Positive Volume Index
# ########################################################
declare lower;
input AvgType = averageType.SIMPLE;
input Length = 50;
def index = compoundValue(1, index[1] + if (volume > volume[1] and close[1] != 0) then 100 * (close - close[1]) / close[1] else 0, 100);
plot PVI = index;
plot AVG = MovingAverage(AvgType, index, Length);
The final script with priceclose feild working:
# ########################################################
# Positive Volume Index
# ########################################################
declare lower;
input AvgType = averageType.SIMPLE;
input Length = 50;
input priceclose = close;
def index = compoundValue(1, index[1] + if (volume > volume[1] and priceclose[1] != 0) then 100 * (priceclose - priceclose[1]) / priceclose[1] else 0, 100);
plot PVI = index;
plot AVG = MovingAverage(AvgType, index, Length);
Hi I've been trying to write code for this scanner. Specifically for when the 1. PVI has reversed direction and showing an inflection point positive . 2. This happens underneath the AVG line. 3. The
PVI is not crossed up over the avg line 4. The average has a positive slope over the past 5 bars.
It runs but it gives mixed results and is driving me crazy!!!
script posvolume {
# Positive Volume Index
# ########################################################
# ########################################################
# Positive Volume Index
# ########################################################
declare lower;
input AvgType = averageType.SIMPLE;
input Length = 50;
input priceclose = close;
def index = compoundValue(1, index[1] + if (volume > volume[1] and priceclose[1] != 0) then 100 * (priceclose - priceclose[1]) / priceclose[1] else 0, 100);
plot PVI = index;
plot AVG = MovingAverage(AvgType, index, Length);
input AvgType = AverageType.EXPONENTIAL;
input Length = 30;
input priceclose = close;
def index = CompoundValue(1, index[1] + if (volume > volume[1] and priceclose[1] != 0) then 100 * (priceclose - priceclose[1]) / priceclose[1] else 0, 100);
def PVI = index;
def AVG = MovingAverage(AvgType, index, Length);
def condition1 = Between(posvolume("length" = 30)."PVI", 0.99 * posvolume("length" = 30)."AVG", posvolume("length" = 30)."AVG") within 1 bar;
def condition2 = posvolume("length" = 30)."PVI" > posvolume("length" = 30)."PVI"[1] within 1 bar;
def condition3 = PVI[1] < AVG within 1 bar;
plot example = condition1 and condition2 and condition3 within 1 bar;
Hi I've been trying to write code for this scanner. Specifically for when the 1. AVG has reversed direction and showing an inflection point positive and positive slope for at least 2 bars. I also
want to incorporate rsi and scan for when rsi is under the avg given the first condition is true. IS IT POSSIBLE TO REPLACE PVI WITH RSI ON THE STUDY???
input AvgType = AverageType.EXPONENTIAL;
input Length = 30;
input priceclose = close;
def index = CompoundValue(1, index[1] + if (volume > volume[1] and priceclose[1] != 0) then 100 * (priceclose - priceclose[1]) / priceclose[1] else 0, 100);
def PVI = index;
def AVG = MovingAverage(AvgType, index, Length);
def condition2 = posvolume("length" = 30)."avg" > posvolume("length" = 30)."avg"[1] within 1 bar;
def condition3 = RSI < AVG within 1 bar; (OBVIOUSLY I KNOW THIS WONT WORK BUT THIS IS THE CONDITION I WANT TO CODE FOR INCLUDED IN MY SCANNER AND STUDY)
plot example = condition2 and condition3 is true within 1 bar;
Last edited:
Hi I've been trying to write code for this scanner. Specifically for when the 1. avg has reversed direction and showing an inflection point positive and postive slope for at least 2 bars. I also
want to incorporate rsi and scan for when rsi is under the avg given the first condition is true.
THIS IS WHAT IM TALKING ABOUT VISUALLY FOR THE AVG LINE
It runs but it gives mixed results and is driving me crazy!!!
script posvolume {
# Positive Volume Index
# ########################################################
# ########################################################
# Positive Volume Index
# ########################################################
declare lower;
input AvgType = averageType.SIMPLE;
input Length = 50;
input priceclose = close;
def index = compoundValue(1, index[1] + if (volume > volume[1] and priceclose[1] != 0) then 100 * (priceclose - priceclose[1]) / priceclose[1] else 0, 100);
plot PVI = index;
plot AVG = MovingAverage(AvgType, index, Length);
input AvgType = AverageType.EXPONENTIAL;
input Length = 30;
input priceclose = close;
def index = CompoundValue(1, index[1] + if (volume > volume[1] and priceclose[1] != 0) then 100 * (priceclose - priceclose[1]) / priceclose[1] else 0, 100);
def PVI = index;
def AVG = MovingAverage(AvgType, index, Length);
def condition2 = posvolume("length" = 30)."avg" > posvolume("length" = 30)."avg"[1] within 1 bar;
def condition3 = RSI < AVG within 1 bar;
plot example = condition2 and condition3 is true within 1 bar;
Hi Conmayne, you have two moving averages and the their inputs named the same, I believe they should be different, input and input1,....
# ########################################################
# Positive Volume Index
# ########################################################
declare lower;
input AvgType = averageType.SIMPLE;
input Length = 50;
def index = compoundValue(1, index[1] + if (volume > volume[1] and close[1] != 0) then 100 * (close - close[1]) / close[1] else 0, 100);
plot PVI = index;
plot AVG = MovingAverage(AvgType, index, Length);
Hi, I have a question, when the Volume goes below Moving average, does it mean the momentum is decreasing and Bears are getting nervous?
Hi Conmayne, you have two moving averages and the their inputs named the same, I believe they should be different, input and input1,....
I adjusted That was a typo and thinkscript bug it does when adding that code to the scanner. My intentions are positive reversal of the AVG vol line (yellow) and and rsi that is under the Yellow line
on the same study. I have no use for the PVI line(red)
Hi I've been trying to write code for this scanner. Specifically for when the 1. AVG has reversed direction and showing an inflection point positive and positive slope for at least 2 bars. I also
want to incorporate rsi and scan for when rsi is under the avg given the first condition is true. IS IT POSSIBLE TO REPLACE PVI WITH RSI ON THE STUDY???
THIS IS WHAT IM TALKING ABOUT VISUALLY FOR THE AVG LINE
input AvgType = AverageType.EXPONENTIAL;
input Length = 30;
input priceclose = close;
def index = CompoundValue(1, index[1] + if (volume > volume[1] and priceclose[1] != 0) then 100 * (priceclose - priceclose[1]) / priceclose[1] else 0, 100);
def PVI = index;
def AVG = MovingAverage(AvgType, index, Length);
def condition2 = posvolume("length" = 30)."avg" > posvolume("length" = 30)."avg"[1] within 1 bar;
def condition3 = RSI < AVG within 1 bar; (OBVIOUSLY I KNOW THIS WONT WORK BUT THIS IS THE CONDITION I WANT TO CODE FOR INCLUDED IN MY SCANNER AND STUDY)
plot example = condition2 and condition3 is true within 1 bar;
Solved my first problem it seems with this code:
input AvgType = AverageType.EXPONENTIAL;
input Length = 30;
input priceclose = close;
def index = CompoundValue(1, index[1] + if (volume > volume[1] and priceclose[1] != 0) then 100 * (priceclose - priceclose[1]) / priceclose[1] else 0, 100);
def PVI = index;
def AVG = MovingAverage(AvgType, index, Length);
#def condition1 = Between(posvolume("length" = 30)."PVI", 0.99 * posvolume("length" = 30)."AVG", posvolume("length" = 30)."AVG") within 1 bar;
#def condition2 = posvolume("length" = 30)."PVI" > posvolume("length" = 30)."PVI"[1] within 1 bar;
def condition3 = Avg[2] > avg[1] and avg[1] < avg[0];
plot scan = condition3 is true within 1 bars ;
Im trying to figure out how to use rsi in place of PVI. PVI is needed for the calcualtion of AVG it seems so thats my dilemna.
What is useThinkScript?
useThinkScript is the #1 community of stock market investors using indicators and other tools to power their trading strategies. Traders of all skill levels use our forums to learn about scripting
and indicators, help each other, and discover new ways to gain an edge in the markets.
How do I get started?
We get it. Our forum can be intimidating, if not overwhelming. With thousands of topics, tens of thousands of posts, our community has created an incredibly deep knowledge base for stock traders. No
one can ever exhaust every resource provided on our site.
If you are new, or just looking for guidance, here are some helpful links to get you started.
• The most viewed thread:
• Our most popular indicator:
• Answers to frequently asked questions:
What are the benefits of VIP Membership?
VIP members get exclusive access to these proven and tested premium indicators: Buy the Dip, Advanced Market Moves 2.0, Take Profit, and Volatility Trading Range. In addition, VIP members get access
to over 50 VIP-only custom indicators, add-ons, and strategies, private VIP-only forums, private Discord channel to discuss trades and strategies in real-time, customer support, trade alerts, and
much more. Learn all about VIP membership here.
How can I access the premium indicators?
To access the premium indicators, which are plug and play ready, sign up for VIP membership here. | {"url":"https://usethinkscript.com/threads/positive-volume-index.7443/","timestamp":"2024-11-06T01:20:46Z","content_type":"text/html","content_length":"184305","record_id":"<urn:uuid:3f027eb0-43fc-4e3d-a53f-c5b53fc330a8>","cc-path":"CC-MAIN-2024-46/segments/1730477027906.34/warc/CC-MAIN-20241106003436-20241106033436-00744.warc.gz"} |
: Planck's Blackbody Equation and Stefan's Law
Since there hasn't been a question here in a while, I'll ask a common beginner's quantum question:
From Planck's Blackbody Radiation Equation, one can derive Stefan's Law which is: e[total]=a*s*T^4 where e[total] is the energy per unit area, s is a constant: 5.67X10^-8 W*m^-2*K^-4, and a is a
coefficient that equals one when dealing with an ideal blackbody.
Where C[1] is 8*pi*c*h and C[2] is h*c/k[b]
Show the relationship between temperature and lambda max. Find the constant s discussed above using this relationship.
I'll be posting more hints if anyone tries. | {"url":"https://www.chemicalforums.com/index.php?topic=344.0","timestamp":"2024-11-06T11:29:09Z","content_type":"text/html","content_length":"30354","record_id":"<urn:uuid:fee16481-7f90-4509-97de-9559d23ec686>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00823.warc.gz"} |
The 19th Century Paranormal Investigator: Chapter 27 - Spades Fiction
The 19th Century Paranormal Investigator: Chapter 27
Not again! How many times can a man be wrong in one day? I can’t even begin to surmise why this demon was severed from his own altar in the division of the house, and even if I could, I’d probably
just be wrong anyway. This whole situation is beyond confounding!
Relax, Branner. I force myself to stop and think.
If that’s not Surgat’s altar, then it must be the one Lance used. But that doesn’t make sense. He was just as surprised as we to see the blasted thing. Then, a third demon? Entirely possible, but
considering the level of destruction, unlikely. Not to mention, the improbability that all three were able to be brought forth at the same time.
There’s another idea. One I don’t particularly like. Summoning demonic entities is merely a powerful spell; one larger than the attacks I’ve been using thus far. The altar is there to focus the power
into being. It is similar to how certain spells I use are focused through my cane.
An altar, while rare, could also be used for other large scale spells, beyond a demonic summoning. But the kind of power necessary to perform such tasks is beyond comprehension. As difficult as they
are, demon summonings are the easiest of such rituals. Any spell greater would exceed the level of skill even I possess.
To accomplish most anything else that would require an altar, would take a professional mage, one schooled since birth in the art. And the fact that the perpetrator would seal the altar in a dark
protective shell only proves how far above my own talents they might be.
Then the question is, what spell is that thing casting? It couldn’t be the illusion spell. That has broken and most illusions are far too weak. Could be something empowering Surgat, but as strange as
his appearance is, his strength is comparable to what I’d expect. Mind control? Depending on how deep the manipulation is, it would be entirely possible for such a spell to require this level of
power, but it would have to consume the target. No sense of their personality left. And such effort for total domination seems counter-intuitive. A weaker spell combined with honeyed words could
accomplish the same thing.
I’m stuck thinking of other possibilities when it hits me. The book!
“Con! Why wasn’t Lance with you when you returned?”
The boy looked surprised, as if he just remembered the task I left to him.
“Oh, uh, I heard the fightin’ going on upstairs. Told him to run ahead and grab the book while I went to help you. Sorry, Branner.”
“Sounds reasonable. But he shouldn’t have taken this long. Did he tell you where the servants’ quarters are located?”
“Yeah, kinda, but I don’ know how well I know this place to get us there.”
“I’m sure you’ll do your best.”
Surgat wasn’t going anywhere soon, so I left the demon be. We exited the study and my young ward led me through the house towards what I hoped was Lance’s room.
The upper corridors were still an unhelpful maze to me, but once we found the stairs down to the ground floor, Con had a much better time leading. I suppose he has spent more time stealing from this
part of the house. The workers were much more cautious around me while Con was at my side. I suppose word of our battles had spread further. One would think our presence would calm them, seeing as we
won both scrapes, but fear is rarely rational.
As Con started slowing down, I noticed we’d arrived. The servants’ living area was much larger than expected. Common rooms split off into individual bedrooms, though none were likely to be as grand
as anything upstairs. Still, the kind of money the doctor could throw at something seemingly so trivial was astounding. Wires attached to bells notified different servants of different needs, and a
back staircase allowed quick, concealed access to specific public rooms.
“End of the road, Branner. I don’t know which room is the kid’s.”
“Well, let’s look around. We’ve been given access to the entire estate remember. You start on the right; I’ll start on the left.”
The first two rooms housed an older boy who didn’t even look at me, and the personal effects of other servants. The third room in and Con gives me a call. I quickly cross the hall to him, where he
points in an empty room.
“You’re sure this is his?”
“Yeah, sure as hell. It still smells like him.”
The young man was nowhere to be seen, though the entire floor was covered in clothes and trinkets. Not due to carelessness, rather, it appeared to have been ransacked. I can only imagine Lance did
not find the book and tore his own room apart looking for it. Which leads me to my next question….
“Where is Lance?”
“Ya got me wit that one. I can only tell he’s been here. Outside the room, he mixes with everyone else.”
I kneel down and move some of the items around on the floor.
“It seems he couldn’t locate the tome and took to tearing his quarters apart to find it. But the fact he did not come back to us makes me think he never found the possession,” I explained.
“So… where is he?”
I haven’t the foggiest. Did he suspect someone of taking the book? Could he have misplaced it elsewhere in the estate?
Con and I continue our investigation, asking the few people here, but none claim to have seen him lately.
Our one lead and he’s disappeared into nothing.
No comments yet. Why don’t you start the discussion?
This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"url":"https://www.spadesfiction.com/the-19th-century-paranormal-investigator-chapter-27/","timestamp":"2024-11-06T23:20:55Z","content_type":"text/html","content_length":"83910","record_id":"<urn:uuid:e02e2ebd-4399-4a8b-ad3e-bafaa7d9d6a2>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.54/warc/CC-MAIN-20241106230027-20241107020027-00779.warc.gz"} |
Define a decision hierarchy of criteria and calculate their weights based on pairwise comparisons using the Analytic Hierarchy Process AHP. In a next step you then define a set of alternatives and
evaluate them with respect to your list of criteria to find the most preferrable alternative and solve your decision problem.
For a simple calculation of priorities based on pairwise comparisons you can use the AHP priority calculator. If you like the tool and find it useful, click the like button at the bottom of the page.
Thank you! | {"url":"https://bpmsg.com/ahp/ahp-hierarchy.php?sc=expl08","timestamp":"2024-11-14T08:36:56Z","content_type":"text/html","content_length":"8741","record_id":"<urn:uuid:b34c0e75-c8f5-4a6b-9062-4245fa840213>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00477.warc.gz"} |
Mortgage Payoff Club!!
Thanks so much for the kind words, they are much appreciated. I checked the mortgage site over the weekend and loved seeing "Paid In Full."
Thanks so much for the kind words, they are much appreciated. I checked the mortgage site over the weekend and loved seeing "Paid In Full."I said to my DH this morning "Hey, we're the people with the
paid off house!"
Made our last payment in the 80Ks, balance now £80,256. Next payment will take us into the 70s, yay!
Our rental house sold and the check has been deposited. Not actually putting it all down at once, but the amount in our bank vs. our mortgage balance is now at 58K vs. 83K. 25K to go!
Principal paid off so far2012 - $3415 2013 - $39942014 - $84832015 - $38412 (yup got rid of all the debt and $10 000 windfall not expected)2016 - $676502017 - $360003/1 Remaining balance $87322.
Projected pay off date 09/09/2017 - SO 51st birthday. 4/1 Remaining balance $818374/30 Remaining balance $76952 (I owed the tax man!)5/29 Remaining balance $73836 6/30 Remaining balance $653887/29
Remaining balance $608258/31 Remaining balance $557289/30 Remaining balance $4969610/31 Remaining balance $3992011/30 Remaining balance $3672101/05 Remaining balance $3463301/29 Remaining balance
$3296502/23 Remaining balance $2669203/29 Remaining Balance $1796304/27 Remaining balance $12903 05/26 Remaining balance $570006/22/2017 Remaining balance $0Oh my goodness - it is done = it is paid
off. Thank-you to everyone - especially assauer - who has encouraged me over the last few years. Waiting to see the $0 paid off in full to show.
Huge congrats, SAfAmBrit. We did the same earlier this month so I'm pretty certain we understand your joy at having paid it off. PIF is my new favorite acronym. It will feel a bit surreal for a
while, I'm sure. Congrats again.
Congrats SAfAmBrit. Looks like you beat your target date by several months. Well done.
As of today, I'm down to $60k left. I could pay it off this year if I got really aggressive, but I'm trying to divide my paychecks between that and putting money into Vanguard. Aiming to be
mortgage-free by 2018!Progress update: My September payment has cleared and I'm down to $51K. The end is in sight!Down to $38K as of February. I'm getting impatient to be done with this now that the
amount left is so small. :)
As of today, I'm down to $60k left. I could pay it off this year if I got really aggressive, but I'm trying to divide my paychecks between that and putting money into Vanguard. Aiming to be
mortgage-free by 2018!Progress update: My September payment has cleared and I'm down to $51K. The end is in sight!
As of today, I'm down to $60k left. I could pay it off this year if I got really aggressive, but I'm trying to divide my paychecks between that and putting money into Vanguard. Aiming to be
mortgage-free by 2018!
Reclaimed $600 for stuff on Craigslist that all just went to principal and that now pays us back $3 a month so as of 9/1, we'll be down to $106,750. So without raiding the stash, need to find another
$5,500 to get to 5 digits by year end. Have a plan for 4K of it so far...Lots of goodness lately on the payoffs/paydowns... Progress was slower than hoped after paying 2 semesters of college expenses
the last 5 months plus annual 529 contributions instead of the mortgage... Didn't make the 5-digit club, but feeling good about paying down to $105K.
Reclaimed $600 for stuff on Craigslist that all just went to principal and that now pays us back $3 a month so as of 9/1, we'll be down to $106,750. So without raiding the stash, need to find another
$5,500 to get to 5 digits by year end. Have a plan for 4K of it so far...
Our rental house sold and the check has been deposited. Not actually putting it all down at once, but the amount in our bank vs. our mortgage balance is now at 58K vs. 83K. 25K to go!Woohoo!!!!
Congratulations- you are almost free!!!
is anyone on this thread taking the approach of stuffing all the money he/she can into an SP500 fund, and then--when the balance is equal to the mortgage--selling to pay off the mortgage?
Congrats, Indio. Really enjoyed reading your story and the determination you had to make it happen. It really is a great feeling, isn't it?
I have been an observer and cheerleader of this thread for a few years, but this week I officially ended my mortgage. I wish I could say it was exceptionally early, but it wasn't. It involved 3
refinances, 1 recast in Sept 2016, 1 consolidation of HELOC (needed for divorce) into 1 of those refinances in June 2013. I was throwing $500 here and and $1000 there monthly at the mortgage over
time, but the big impact didn't happen until I switched jobs in June 2015. Took the big leap after 21 yrs at "ideal" job and it led to a 45% bump in salary. Every month I was now able to put more
toward payoff and the balance declined quickly. When my options vested at new company, due to buyout, I put that money toward mortgage. When bond payout happened, I put that money toward mortgage.
Had ESPP from previous company and that stock started to move upward with the recent market growth. Once that stock reached a point where I had enough to payoff mortgage and associated long term
capital gains taxes, I decided to sell it and close out the mortgage. Fully recognize that was a conservative move, but still have plenty of investments in stock market.In June 2015, when I started
new job, the mortgage was $205,000. Today it is $0. I notified the town about property taxes and I notified by insurance company. Once I get the final title transfer and recorded by the county, the
mortgage will be a piece of history. Logging into mint, I keep checking the debt trend report because it's such eye candy to see that the debt shackles are officially gone.A little aside that I
learned about property taxes when speaking to the town, is that the bank didn't pay the taxes until end of month it was due, even though they pulled the escrow funds out of my account on July 1st.
They hung on to the funds without paying me interest and not paying the town right away. While the mortgage was a priority, it was secondary to maxing out 401K, IRA, family HSA, and kids Roth IRAs
(which are their college funds). It is a great feeling to know that no matter what happens now, I only need to worry about paying property taxes and insurance on our home. I'm suffering from "one
more year" syndrome before I decide to fully FIRE.I don't smell the jet fuel or the barn any more but I'm still going to cheer all of you on.
Gonna start this back up again. Current goal is to get to 90K by the end of 2016. Starting Mtg Sept 2013: $123,500Today (July 5th): $98,504It's fun to be back on this thread again!8/1/2016: $95,5041/
7/2016 $84,969.68Not bad...still have to fill up DH's 2016 IRA but I can do that in March as it's a three paycheck month...cutting it close, I know.
Gonna start this back up again. Current goal is to get to 90K by the end of 2016. Starting Mtg Sept 2013: $123,500Today (July 5th): $98,504It's fun to be back on this thread again!8/1/2016: $95,504
Gonna start this back up again. Current goal is to get to 90K by the end of 2016. Starting Mtg Sept 2013: $123,500Today (July 5th): $98,504It's fun to be back on this thread again!
Second Quarter 2017 Update:Starting mortgage = $435,000, 5 year term @ 3.26% (starting Sept. 30, 2013)Goal = Full Mortgage Payoff by end of 5 year term (Sept. 30, 2018)Progress:- Mortgage amount as
of December 25, 2014: $380,819 - Mortgage amount as of April 2, 2015: $359,144- Mortgage amount as of July 9, 2015: $324,055- Mortgage amount as of December 31, 2015: $285,708- Mortgage amount - June
2, 2016 - $253,560- Mortgage amount - September 8, 2016 - $232,502- Mortgage amount - December 30, 2016 - $194,252- Mortgage amount - March 30, 2017 - $161,932- Mortgage amount - July 16, 2017 -
$137,809Getting closer :)
@Frizzywhiskers... $250K in less than 3 years is simply KILLING IT.End of July indentured update... Sold some stuff on craigslist and chipped in to principal a full 1% this month to just over 100K.
The 5 digit club is squarely in my gunsights!
I was looking on citi's website for info on payoff requests and I see there is mention about some fee included in the payoff amount. It wasn't clear what that is - is it a county recording fee?
Should be very cheap (maybe $50), right? Any other fees I should expect?Is it better to request a payoff and pay that amount or just send in most of it and make regular payments to kill the last few
So I have been playing around with some mortgage HELOC calculations.Our mortgage on our rental property in actually in a Line of Credit that we use as a checking account. As the rent checks come in
they go straight towards paying down the HELOC.I can't find the exact article that helped persuade me to drop the mortgage and get a full HELOC but this one is close.http://www.claytonmorris.com/blog
/2015/7/20/how-to-pay-off-your-house-within-5-years-using-these-awesome-ninja-tricksI was curious to compare 3 options. Mortgage, LOC, LOC + extraWe have also been making some seriously large extra
payments MORTGAGE HELOC HELOC + extraMarch 2016 $320,600 $320,600 $320,600July 2016 $317,000 $314,000 $314,000 November 2016 $313,000 $306,000 $306,000March 2017 $309,000 $299,000 $218,000 (Made some
huge extra pmts)July 2017 $305,000 $295,000 $213,000So If we had been following a regular mortgage we would still owe $305,000. The HELOC method saved $10,000 without really even trying.Coupled with
the extra payments, one of which was basically putting all my emergency fund against the HELOC, and we are down to $213,000.Anyway, if you are not already using some HELOC tricks to help pay your
mortgage faster you may what to add that technique.
Phew, just finished reading this entire thread and now feel qualified to jump in. We just made the decision to pay off our mortgage early, going from 28 years to 15. We owe $598k at 3.75%. I know all
the maths about investing, but if we stick with the current term, we will pay it off when I am 75! That seems way too old. The sum we owe seems huge to me, but I will focus on making extra payments
and whittling away on it with extra cash/side hustle money/ etc. If the stock market crashes, we'll take the extra money and buy stocks.We are maxing Roths, 401k, etc., so not forgoing investing in
the mean time. I expect to be participating here for a long long time, but shorter than 28 years! Congrats to everyone here, your stories are inspiring.
BlueHouse: glad to know I'm not the only person with an enormous mortgage!
Thanks K-ice for the information.I think I understand better now. I looked quickly at HELOC rates in my area and can't find anything close to what my interest rate on mortgage is, 2.75. Most HELOC
rates are 4.5 and up. It sounds like the HELOC rate has to be lower than mortgage for this to work.
Thanks K-ice for the information.I think I understand better now. I looked quickly at HELOC rates in my area and can't find anything close to what my interest rate on mortgage is, 2.75. Most HELOC
rates are 4.5 and up. It sounds like the HELOC rate has to be lower than mortgage for this to work.Of course the lower the HELOC interest rate the better but actually I tested it with $100,000
borrowed at 2.75% for 30y and a $10,000 HELOC at 4.5% paid off at $1,000/month and it still works.How? Because the $10,000 immediately changes the mortgage principal to $90,000. And you pay the HELOC
off in a very short period of time, not amortized over 30y. I tested 2 scenarios plugging numbers into this calculator:https://www.vertex42.com/Calculators/home-mortgage-calculator.htmlOption 1,
Regular mortgage $100,000 borrowed at 2.75% for 30y.The interest paid on the first year in the mortgage is $2723. Option 2, If you can borrow $10,000 from your HELOC and immediately pay it towards
your mortgage The interest paid on the first year in the mortgage is $2468. You also save a total of 11,430.48 and 4.5years off the life of your mortgage.Of course you still have a $10,000 HELOC to
pay down at 4.5%. So your quick calculation may say this is $450 in interest. However, remember, your monthly surplus, assuming $1000 goes to pay this off so the total interest is only $211. Add that
to the mortgage interest and $2679 is still < $2723.It is still surprisingly better even with the different interest rates. Is it worth the hassle when the difference is now less than $100 per year?
When you repeat this process every year, your 30y loan will be paid off in only 7 years-1 month. With a total interest savings of $37,000 compared to no early payments. Option 3 is also quite good
and what many people on this thread are doing. That is stash the money and pay $10,000 every year at the end of the year. You will pay off your loan in 8y with a total savings of $35,000. So the
Numbers are better with the HELOC method even with the mortgage at 2.75% and the HELOC at 4.5%. It is now a question of psychology. I am pretty disciplined and had a regular checking account, savings
account and my HELOC just sitting there unused for a few years. But my savings would build up and I hated it not working for me. I also feel like my HELOC is “hair on fire” debt and I feel I pay it
off faster than I would save $10,000. As they said in the podcast. They just started with $5000 and paid that off in a few months. Their income is admittedly high. If it takes you 2 stressful years
to pay down the $5000 stay away from the HELOC. However, if you can easily pay back the $5000, rinse and repeat a few times and you will really start to see your HELOC working for you.
I did it!! Paid off about a month ago. At first a little anti-climactic, but now feels Pretty Darn Good as I just got the official documentation. I came in just under 5 years. My focus now will be
building up more of a stash -- and I'm pretty close to FI at this point with rental and side gig income, woohoo!! Still likely many years from retirement because I love my job, but it feels SO GOOD
to know the job is not the absolute necessity it once once. This forum is the only place I've told -- so nice to have a place to celebrate! Thanks for all the support and encouragement over the
years. I don't give a flying rat about the maths, freedom is what it's all about!
Congrats, cheddarpie!! Getting that paperwork in the mail sure is an awesome feeling. Relish the moment.
To the comment about using your HELOC as an emergency fund I wouldn't recommend it. Remember what happened in 2008 when we got letters from our HELOC banks saying our accounts were being frozen. I
learned from that experience to have an emergency fund.
Thanks K-ice for the information.I think I understand better now. I looked quickly at HELOC rates in my area and can't find anything close to what my interest rate on mortgage is, 2.75. Most HELOC
rates are 4.5 and up. It sounds like the HELOC rate has to be lower than mortgage for this to work.Of course the lower the HELOC interest rate the better but actually I tested it with $100,000
borrowed at 2.75% for 30y and a $10,000 HELOC at 4.5% paid off at $1,000/month and it still works.How? Because the $10,000 immediately changes the mortgage principal to $90,000. And you pay the HELOC
off in a very short period of time, not amortized over 30y. I tested 2 scenarios plugging numbers into this calculator:https://www.vertex42.com/Calculators/home-mortgage-calculator.htmlOption 1,
Regular mortgage $100,000 borrowed at 2.75% for 30y.The interest paid on the first year in the mortgage is $2723. Option 2, If you can borrow $10,000 from your HELOC and immediately pay it towards
your mortgage The interest paid on the first year in the mortgage is $2468. You also save a total of 11,430.48 and 4.5years off the life of your mortgage.Of course you still have a $10,000 HELOC to
pay down at 4.5%. So your quick calculation may say this is $450 in interest. However, remember, your monthly surplus, assuming $1000 goes to pay this off so the total interest is only $211. Add that
to the mortgage interest and $2679 is still < $2723.It is still surprisingly better even with the different interest rates. Is it worth the hassle when the difference is now less than $100 per year?
When you repeat this process every year, your 30y loan will be paid off in only 7 years-1 month. With a total interest savings of $37,000 compared to no early payments. Option 3 is also quite good
and what many people on this thread are doing. That is stash the money and pay $10,000 every year at the end of the year. You will pay off your loan in 8y with a total savings of $35,000. So the
Numbers are better with the HELOC method even with the mortgage at 2.75% and the HELOC at 4.5%. It is now a question of psychology. I am pretty disciplined and had a regular checking account, savings
account and my HELOC just sitting there unused for a few years. But my savings would build up and I hated it not working for me. I also feel like my HELOC is “hair on fire” debt and I feel I pay it
off faster than I would save $10,000. As they said in the podcast. They just started with $5000 and paid that off in a few months. Their income is admittedly high. If it takes you 2 stressful years
to pay down the $5000 stay away from the HELOC. However, if you can easily pay back the $5000, rinse and repeat a few times and you will really start to see your HELOC working for you.Taking money
out on a 4.5% heloc to pay a 2.75% mortgage is dumb. You could just as easily pay the monthly surplus each month on the mortgage without waiting to do an annual lump sum and pay even less
interest.Having a heloc available in case of emergency might be a good idea, you could then stop keeping an emergency fund while keeping the heloc balance at 0 allowing you to put all your money to
work pasting the mortgage, but the moment you take out anything from the heloc you are paying more interest until it's back to zero. Only do so in a true emergency. If you can pay it off the next
month even your credit card is a better option as if you have a zero monthly balance (and you shouldn't be pre paying mortgage if you don't) you will pay NO interest.
End of July indentured update... Sold some stuff on craigslist and chipped in to principal a full 1% this month to just over 100K. The 5 digit club is squarely in my gunsights!
End of July indentured update... Sold some stuff on craigslist and chipped in to principal a full 1% this month to just over 100K. The 5 digit club is squarely in my gunsights!End of August... 5
digit club at last! $99.9K. After trimming recurring bills and shifting some things around, the goal is to pay down 1% or more a month on average from here... | {"url":"https://forum.mrmoneymustache.com/throw-down-the-gauntlet/mortgage-payoff-club!!/1250/","timestamp":"2024-11-05T15:45:58Z","content_type":"application/xhtml+xml","content_length":"190539","record_id":"<urn:uuid:a70d182e-9625-4a13-a06b-e1980d637340>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00718.warc.gz"} |
round numbers with VBA
The round function is available for rounding numbers with VBA. The operation of the round function is very simple. The number to be rounded off is entered as the first parameter and the number of
decimal places to which to round off as the second optional parameter. If the number of decimal places is not specified, it is rounded to an integer. Nothing to worry about so far, but what many
people don't know is that the round function uses a fairly unusual rounding mechanism. This can lead to unexpected rounding off.
Banker’s rounding
The round function in VBA uses Banker's rounding. This means that a 5 is always rounded to the nearest even number. For example, 2.35 is rounded to 2.4, but 2.45 is also rounded to 2.4! This last
rounding is unknown to many people and is usually even undesirable. It has grown out of history that Microsoft uses Banker's rounding with VBA and normal Visual Basic for the round function. This
mechanism is not used with all Microsoft products, because, for example, Excel and SQL Server use different rounding mechanisms.
Adjust rounding 1
In most applications, however, a different rounding is requested. A number ending in 5 must then be rounded up with a positive number and down with a negative number. So 2.35 should become 2.4, 2.45
should become 2.5, and -2.45 should become -2.5. A separate function can of course be written for this, but it is better to continue to use the round function.
What is often used is to add or subtract a very small number from the number to be rounded. This could look like this, for example:
Function RoundHalfUp(dblNumber As Double, _
Optional iDecimal As Byte = 0) As Double
RoundHalfUp = Round(dblNumber + Sgn(dblNumber) * 0.000001, iDecimal)
End Function
0.000001 is added to each number, so 2.45 becomes 2.450001. This number is properly rounded to 2.5. In many cases this works well, but it is not completely waterproof. Firstly, the addition may
result in a number that ends in 5. For example, if the base number is 2.349999 and 0.000001 is added to that, then the addition will be exactly 2.35. This is rounded to 2.4, while 2.349999 should be
rounded to 2.3. Second, it appears that the addition in VBA can have different outcomes. See the examples below:
Debug.Print Round(2.649999+0.000001, 1)
Debug.Print Round(2.64999+0.00001, 1)
Debug.Print Round(2.6499+0.0001, 1)
Debug.Print Round(2.649+0.001, 1)
Each separate addition results in 2.65 and according to Banker’s rounding that should be rounded to 2.6, but that is not always the case.. This is most likely due to the inaccuracy that can arise
from binary storage of decimal numbers (See for more info about this: Dealing with calculation errors in Excel). In any case, it indicates that the addition method is not reliable in these cases.
Adjust rounding 2
A better method is therefore to do the addition only if the number to be rounded ends in 5. This prevents the above problems. The function that can be used for this is:
Function RoundHalfUp(dblNumber As Double, _
Optional iDecimal As Byte = 0) As Double
If Mid(dblNumber - Fix(dblNumber), iDecimal + 2 + Len(CStr(Sgn(dblNumber))), 1) = "5" Then
dblNumber = dblNumber + Sgn(dblNumber) / 10 ^ (iDecimal + 1)
End If
RoundHalfUp = Round(dblNumber, iDecimal)
End Function
First a check is made whether there is a 5 on the position to be rounded off. If so, a small number is added to a positive number and a small number is subtracted from a negative number. The 5 thus
becomes a 6. Then this number is rounded off with the round function. This function can be used to round numbers in the usual way with VBA.
Questions / suggestions
Hopefully this article helped you to round numbers with VBA. If you have any questions about this topic or suggestions for improvement, please post a comment below. | {"url":"https://worksheetsvba.com/en/vba-round-numbers","timestamp":"2024-11-13T09:40:48Z","content_type":"text/html","content_length":"21985","record_id":"<urn:uuid:ad37f3c2-3da5-4181-951e-b02619558ae1>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00285.warc.gz"} |
Frank Kleibergen
Frank Kleibergen
Personal Details
First Name: Frank
Middle Name:
Last Name: Kleibergen
RePEc Short-ID: pkl31
[This author has chosen not to make the email address public]
Terminal Degree: 1994 Econometrisch Instituut; Faculteit der Economische Wetenschappen; Erasmus Universiteit Rotterdam (from RePEc Genealogy)
Research output
Jump to:
Working papers Articles Software
Working papers
1. Frank Kleibergen & Lingwei Kong, 2023. "Identification Robust Inference for the Risk Premium in Term Structure Models," Papers 2307.12628, arXiv.org.
2. Frank Kleibergen & Zhaoguo Zhan, 2022. "Misspecification and Weak Identification in Asset Pricing," Papers 2206.13600, arXiv.org.
3. Patrik Guggenberger & Frank Kleibergen & Sophocles Mavroeidis, 2021. "A Powerful Subvector Anderson Rubin Test in Linear Instrumental Variables Regression with Conditional Heteroskedasticity,"
Papers 2103.11371, arXiv.org, revised Oct 2022.
4. Maurice J. G. Bun & Frank Kleibergen, 2021. "Identification robust inference for moments based analysis of linear dynamic panel data models," Papers 2105.08346, arXiv.org.
5. Frank Kleibergen & Zhaoguo Zhan, 2021. "Double robust inference for continuous updating GMM," Papers 2105.08345, arXiv.org.
6. Patrik Guggenberger & Frank Kleibergen & Sophocles Mavroeidis, 2020. "A Test for Kronecker Product Structure Covariance Matrix," Papers 2010.10961, arXiv.org, revised Jan 2022.
7. Prosper Dovonon & Alastair R. Hall & Frank Kleibergen, 2017. "Inference in Second-Order Identified Models," Economics Discussion Paper Series 1703, Economics, The University of Manchester.
8. Frank Kleibergen & Zhaoguo Zhan, 2014. "Unexplained factors and their effects on second pass R-squared’s," UvA-Econometrics Working Papers 14-05, Universiteit van Amsterdam, Dept. of
9. Maurice J.G. Bun & Frank Kleibergen, 2013. "Identification and inference in moments based analysis of linear dynamic panel data models," UvA-Econometrics Working Papers 13-07, Universiteit van
Amsterdam, Dept. of Econometrics.
10. Hoogerheide, L.F. & Kleibergen, F.R. & van Dijk, H.K., 2006. "Natural conjugate priors for the instrumental variables regression model applied to the Angrist-Krueger data," Econometric Institute
Research Papers EI 2006-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
11. Richard Paap & Frank Kleibergen, 2004. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Society 2004 Australasian Meetings 195, Econometric Society.
□ Kleibergen, F.R. & Paap, R., 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Institute Research Papers EI 2003-01, Erasmus University Rotterdam,
Erasmus School of Economics (ESE), Econometric Institute.
□ Frank Kleibergen & Richard Paap, 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Tinbergen Institute Discussion Papers 03-003/4, Tinbergen Institute.
12. Frank Kleibergen, 2004. "Expansions of GMM statistics that indicate their properties under weak and/or many instruments and the bootstrap," Econometric Society 2004 North American Summer Meetings
408, Econometric Society.
13. Frank Kleibergen, 2004. "Higher order approximations of IV statistics that indicate their properties under weak or many instruments," Econometric Society 2004 North American Winter Meetings 199,
Econometric Society.
14. Frank Kleibergen, 2002. "Two Independent Pivotal Statistics that test Location and Misspecification and add up to the Anderson-Rubin Statistic," Tinbergen Institute Discussion Papers 02-064/4,
Tinbergen Institute.
15. Bekker, Paul A. & Kleibergen, Frank, 2001. "Finite-sample instrumental variables inference using an asymptotically pivotal statistic," CCSO Working Papers 200109, University of Groningen, CCSO
Centre for Economic Research.
□ Paul A. Bekker & Frank Kleibergen, 2001. "Finite-Sample Instrumental Variables Inference using an Asymptotically Pivotal Statistic," Tinbergen Institute Discussion Papers 01-055/4, Tinbergen
□ Bekker, Paul A. & Kleibergen, Frank, 2001. "Finite-sample instrumental variables inference using an asymptotically pivotal statistic," Research Report 01F38, University of Groningen, Research
Institute SOM (Systems, Organisations and Management).
16. Frank Kleibergen, 2001. "Testing Parameters in GMM without Assuming that they are identified," Tinbergen Institute Discussion Papers 01-067/4, Tinbergen Institute.
17. Frank Kleibergen, 2001. "How to overcome the Jeffreys-Lindleys Paradox for Invariant Bayesian Inference in Regression Models," Tinbergen Institute Discussion Papers 01-073/4, Tinbergen Institute.
18. Kleibergen, F.R. & Kleijn, R.H. & Paap, R., 2000. "The Bayesian Score Statistic," Econometric Institute Research Papers EI 2000-16/A, Erasmus University Rotterdam, Erasmus School of Economics
(ESE), Econometric Institute.
19. Frank Kleibergen, 2000. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Tinbergen Institute Discussion Papers 00-055/4, Tinbergen Institute.
20. Frank R. Kleibergen, 2000. "Pivotal Statistics for Testing Subsets of Structural Parameters in the IV Regression Model," Tinbergen Institute Discussion Papers 00-088/4, Tinbergen Institute.
21. Frank R. Kleibergen, 2000. "Exact Test Statistics and Distributions of Maximum Likelihood Estimators that result from Orthogonal Parameters," Tinbergen Institute Discussion Papers 00-039/4,
Tinbergen Institute.
22. Frank R. Kleibergen & Henk Hoek, 2000. "Bayesian Analysis of ARMA Models," Tinbergen Institute Discussion Papers 00-027/4, Tinbergen Institute.
23. Houweling, P. & Hoek, J. & Kleibergen, F.R., 1999. "The Joint Estimation of Term Structures and Credit Spreads," Econometric Institute Research Papers EI 9916-/A, Erasmus University Rotterdam,
Erasmus School of Economics (ESE), Econometric Institute.
24. Jan J.J. Groen & Frank R. Kleibergen, 1999. "Likelihood-Based Cointegration Analysis in Panels of Vector Error Correction Models," Tinbergen Institute Discussion Papers 99-055/4, Tinbergen
25. Kleibergen, F.R. & Franses, Ph.H.B.F., 1999. "Cointegration in a periodic vector autoregression," Econometric Institute Research Papers EI 9906-/A, Erasmus University Rotterdam, Erasmus School of
Economics (ESE), Econometric Institute.
26. Kleibergen, F.R. & Paap, R., 1998. "Priors, posteriors and Bayes factors for a Bayesian analysis of cointegration," Econometric Institute Research Papers EI 9821, Erasmus University Rotterdam,
Erasmus School of Economics (ESE), Econometric Institute.
27. Kleibergen, F.R. & Zivot, E., 1998. "Bayesian and classical approaches to instrumental variable regression," Econometric Institute Research Papers EI 9835, Erasmus University Rotterdam, Erasmus
School of Economics (ESE), Econometric Institute.
28. Kleibergen, F.R., 1998. "Conditional densities in econometrics," Econometric Institute Research Papers EI 9853, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric
29. Kleibergen, F.R., 1998. "An alternative approach for constructing small sample and limiting distributions of maximum likelihood estimators," Econometric Institute Research Papers EI 9844, Erasmus
University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
30. Kleibergen, F.R. & Urbain, J-P. & van Dijk, H.K., 1997. "Oil Price Shocks and Long Run Price and Import Demand Behavior," Econometric Institute Research Papers EI 9709-/A, Erasmus University
Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
31. Kleibergen, F.R. & van Dijk, H.K., 1997. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Econometric Institute Research Papers EI 9714/A, Erasmus University Rotterdam,
Erasmus School of Economics (ESE), Econometric Institute.
32. Kleibergen, F.R., 1997. "Reduced Rank Regression using Generalized Method of Moments Estimators with extensions to structural breaks in cointegration models," Econometric Institute Research
Papers EI 9722/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
33. Kleibergen, F.R. & Paap, R., 1996. "Priors, Posterior Odds and Lagrange Multiplier Statistics in Bayesian Analyses of Cointegration," Econometric Institute Research Papers EI 9668-/A, Erasmus
University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
34. Kleibergen, F., 1996. "Reduced Rank of Regression Using Generalized Method of Moments Estimators," Discussion Paper 1996-20, Tilburg University, Center for Economic Research.
35. Kleibergen, F.R., 1996. "Equality Restricted Random Variables: Densities and Sampling Algorithms," Econometric Institute Research Papers EI 9662-/A, Erasmus University Rotterdam, Erasmus School
of Economics (ESE), Econometric Institute.
36. Kleibergen, F.R. & Hoek, H., 1995. "Bayesian Analysis of ARMA models using Noninformative Priors," Econometric Institute Research Papers EI 9553-/B, Erasmus University Rotterdam, Erasmus School
of Economics (ESE), Econometric Institute.
□ Frank Kleibergen & Henk Hoek, 1997. "Bayesian Analysis of ARMA Models using Noninformative Priors," Tinbergen Institute Discussion Papers 97-006/4, Tinbergen Institute.
□ Kleibergen, F.R. & Hoek, H., 1995. "Bayesian analysis of ARMA models using noninformative priors," Other publications TiSEM 81684a10-935f-49c4-b5ab-0, Tilburg University, School of Economics
and Management.
□ Kleibergen, F.R. & Hoek, H., 1995. "Bayesian analysis of ARMA models using noninformative priors," Discussion Paper 1995-116, Tilburg University, Center for Economic Research.
repec:dnb:wormem:646 is not listed on IDEAS
1. Frank Kleibergen & Lingwei Kong & Zhaoguo Zhan, 2023. "Rejoinder on: Identification Robust Testing of Risk Premia in Finite Samples," Journal of Financial Econometrics, Oxford University Press,
vol. 21(2), pages 311-315.
2. Guggenberger, Patrik & Kleibergen, Frank & Mavroeidis, Sophocles, 2023. "A test for Kronecker Product Structure covariance matrix," Journal of Econometrics, Elsevier, vol. 233(1), pages 88-112.
3. Frank Kleibergen & Lingwei Kong & Zhaoguo Zhan, 2023. "Identification Robust Testing of Risk Premia in Finite Samples," Journal of Financial Econometrics, Oxford University Press, vol. 21(2),
pages 263-297.
4. Bun, Maurice J.G. & Kleibergen, Frank, 2022. "Identification Robust Inference For Moments-Based Analysis Of Linear Dynamic Panel Data Models," Econometric Theory, Cambridge University Press, vol.
38(4), pages 689-751, August.
5. Kleibergen, Frank, 2021. "Efficient size correct subset inference in homoskedastic linear instrumental variables regression," Journal of Econometrics, Elsevier, vol. 221(1), pages 78-96.
6. Dovonon, Prosper & Hall, Alastair R. & Kleibergen, Frank, 2020. "Inference in second-order identified models," Journal of Econometrics, Elsevier, vol. 218(2), pages 346-372.
7. Frank Kleibergen & Zhaoguo Zhan, 2018. "Identification-Robust Inference on Risk Premia of Mimicking Portfolios of Non-traded Factors," Journal of Financial Econometrics, Oxford University Press,
vol. 16(2), pages 155-190.
8. Kleibergen, Frank & Zhan, Zhaoguo, 2015. "Unexplained factors and their effects on second pass R-squared’s," Journal of Econometrics, Elsevier, vol. 189(1), pages 101-116.
9. Frank Kleibergen & Sophocles Mavroeidis, 2014. "Identification Issues In Limited‐Information Bayesian Analysis Of Structural Macroeconomic Models," Journal of Applied Econometrics, John Wiley &
Sons, Ltd., vol. 29(7), pages 1183-1209, November.
10. Patrik Guggenberger & Frank Kleibergen & Sophocles Mavroeidis & Linchun Chen, 2012. "On the Asymptotic Sizes of Subset Anderson–Rubin and Lagrange Multiplier Tests in Linear Instrumental
Variables Regression," Econometrica, Econometric Society, vol. 80(6), pages 2649-2666, November.
11. Kleibergen, Frank & Mavroeidis, Sophocles, 2009. "Rejoinder," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 331-339.
12. Kleibergen, Frank & Mavroeidis, Sophocles, 2009. "Weak Instrument Robust Tests in GMM and the New Keynesian Phillips Curve," Journal of Business & Economic Statistics, American Statistical
Association, vol. 27(3), pages 293-311.
13. Kleibergen, Frank, 2009. "Tests of risk premia in linear factor models," Journal of Econometrics, Elsevier, vol. 149(2), pages 149-173, April.
14. Hoogerheide, Lennart & Kleibergen, Frank & van Dijk, Herman K., 2007. "Natural conjugate priors for the instrumental variables regression model applied to the Angrist-Krueger data," Journal of
Econometrics, Elsevier, vol. 138(1), pages 63-103, May.
15. Kleibergen, Frank, 2007. "Generalizing weak instrument robust IV statistics towards multiple parameters, unrestricted covariance matrices and identification statistics," Journal of Econometrics,
Elsevier, vol. 139(1), pages 181-216, July.
16. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
□ Kleibergen, F.R. & Paap, R., 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Institute Research Papers EI 2003-01, Erasmus University Rotterdam,
Erasmus School of Economics (ESE), Econometric Institute.
□ Frank Kleibergen & Richard Paap, 2003. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Tinbergen Institute Discussion Papers 03-003/4, Tinbergen Institute.
□ Richard Paap & Frank Kleibergen, 2004. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Society 2004 Australasian Meetings 195, Econometric Society.
17. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
18. Kleibergen, Frank, 2004. "Invariant Bayesian inference in regression models that is robust against the Jeffreys-Lindley's paradox," Journal of Econometrics, Elsevier, vol. 123(2), pages 227-258,
19. Frank Kleibergen, 2004. "Testing Subsets of Structural Parameters in the Instrumental Variables," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 418-423, February.
20. Bekker, Paul & Kleibergen, Frank, 2003. "Finite-Sample Instrumental Variables Inference Using An Asymptotically Pivotal Statistic," Econometric Theory, Cambridge University Press, vol. 19(5),
pages 744-753, October.
□ Paul A. Bekker & Frank Kleibergen, 2001. "Finite-Sample Instrumental Variables Inference using an Asymptotically Pivotal Statistic," Tinbergen Institute Discussion Papers 01-055/4, Tinbergen
□ Bekker, Paul A. & Kleibergen, Frank, 2001. "Finite-sample instrumental variables inference using an asymptotically pivotal statistic," CCSO Working Papers 200109, University of Groningen,
CCSO Centre for Economic Research.
□ Bekker, Paul A. & Kleibergen, Frank, 2001. "Finite-sample instrumental variables inference using an asymptotically pivotal statistic," Research Report 01F38, University of Groningen, Research
Institute SOM (Systems, Organisations and Management).
21. Groen, Jan J J & Kleibergen, Frank, 2003. "Likelihood-Based Cointegration Analysis in Panels of Vector Error-Correction Models," Journal of Business & Economic Statistics, American Statistical
Association, vol. 21(2), pages 295-318, April.
22. Kleibergen, Frank & Zivot, Eric, 2003. "Bayesian and classical approaches to instrumental variable regression," Journal of Econometrics, Elsevier, vol. 114(1), pages 29-72, May.
23. Kleibergen, Frank & Paap, Richard, 2002. "Priors, posteriors and bayes factors for a Bayesian analysis of cointegration," Journal of Econometrics, Elsevier, vol. 111(2), pages 223-249, December.
24. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
25. Houweling, Patrick & Hoek, Jaap & Kleibergen, Frank, 2001. "The joint estimation of term structures and credit spreads," Journal of Empirical Finance, Elsevier, vol. 8(3), pages 297-323, July.
□ Houweling, P. & Hoek, J. & Kleibergen, F.R., 1999. "The Joint Estimation of Term Structures and Credit Spreads," Econometric Institute Research Papers EI 9916-/A, Erasmus University
Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
□ Patrick Houweling & Jaap Hoek & Frank Kleibergen, 1999. "The Joint Estimation of Term Structures and Credit Spreads," Tinbergen Institute Discussion Papers 99-027/4, Tinbergen Institute.
26. Frank Kleibergen & Herman van Dijk & Jean-Pierre Urbain, 1999. "Oil Price Shocks and Long Run Price and Import Demand Behavior," Annals of the Institute of Statistical Mathematics, Springer;The
Institute of Statistical Mathematics, vol. 51(3), pages 399-417, September.
27. Kleibergen, Frank & van Dijk, Herman K., 1998. "Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures," Econometric Theory, Cambridge University Press, vol. 14(6), pages 701-743,
□ Kleibergen, F.R. & van Dijk, H.K., 1997. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Econometric Institute Research Papers EI 9714/A, Erasmus University
Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
□ Frank Kleibergen & Herman K. van Dijk, 1998. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Tinbergen Institute Discussion Papers 98-025/4, Tinbergen Institute.
28. Franses, Philip Hans & Kleibergen, Frank, 1996. "Unit roots in the Nelson-Plosser data: Do they matter for forecasting?," International Journal of Forecasting, Elsevier, vol. 12(2), pages
283-288, June.
29. Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551,
30. Kleibergen, Frank & van Dijk, Herman K., 1994. "Direct cointegration testing in error correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 61-103, July.
31. Kleibergen, F & Van Dijk, H K, 1993. "Non-stationarity in GARCH Models: A Bayesian Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 41-61, Suppl. De.
Software components
1. Frank Kleibergen & Mark E Schaffer & Frank Windmeijer, 2007. "RANKTEST: Stata module to test the rank of a matrix," Statistical Software Components S456865, Boston College Department of
Economics, revised 29 Sep 2020.
Research fields, statistics, top rankings, if available.
This author is among the
top 5% authors
according to these criteria:
Featured entries
This author is featured on the following reading lists, publication compilations, Wikipedia, or ReplicationWiki entries:
NEP Fields
is an announcement service for new working papers, with a weekly report in each of many fields. This author has had 23 papers announced in NEP. These are the fields, ordered by number of
announcements, along with their dates. If the author is listed in the directory of specialists for this field, a link is also provided.
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. For general information on how to correct material on RePEc, see these
To update listings or check citations waiting for approval, Frank Kleibergen should log into the RePEc Author Service.
To make corrections to the bibliographic information of a particular item, find the technical contact on the abstract page of that item. There, details are also given on how to add or correct
references and citations.
To link different versions of the same work, where versions have a different title, use this form. Note that if the versions have a very similar title and are in the author's profile, the links will
usually be created automatically.
Please note that most corrections can take a couple of weeks to filter through the various RePEc services. | {"url":"https://ideas.repec.org/e/pkl31.html","timestamp":"2024-11-13T12:55:18Z","content_type":"text/html","content_length":"79561","record_id":"<urn:uuid:55de7231-d970-4b31-a3c8-780efdd8e342>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00792.warc.gz"} |
left join sql do not work
when I run the program below there is no error in the log but the variable EPU is empty "."
proc sql;
create table test1 as
select Distinct R.*, B.EPU
from test as R
left join EPU_Data as B on R.sas_date=B.sas_date
order by R.Secid, R.sas_date;
09-23-2022 01:52 PM | {"url":"https://communities.sas.com/t5/SAS-Procedures/left-join-sql-do-not-work/td-p/834897","timestamp":"2024-11-14T00:57:02Z","content_type":"text/html","content_length":"249079","record_id":"<urn:uuid:b262e111-966d-4bfc-aec6-6d0b766399fd>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00724.warc.gz"} |
Algebraic Manipulations
JSL provides a way of algebraically unwinding an expression (essentially, solving for a variable). It is accomplished through the Invert Expr() function.
Invert Expr(expression, name, y)
• expression is the expression to be inverted, or the name of a global containing the expression
• name is the name inside expression to unwind the expression around
• y is what the expression was originally equal to
For example,
Invert Expr( Sqrt( log( x ) ), x, y );
is wound around the name x (which should appear in the expression only once), and results in
Exp( y ^ 2 )
It is performed exactly as you would when doing the algebra by hand.
y = Sqrt( log( x ) );
y2 = Log( x );
Exp( y2 ) = x;
Invert Expr supports most basic operations that are invertible, and makes assumptions as necessary, such as assuming you are interested only in the positive roots, and that the trigonometric
functions are in invertible areas so that the inverse functions are legal.
F, Beta, Chi-square, t, Gamma, and Weibull distributions are supported for the first arguments in their Distribution and Quantile functions. If it encounters an expression that it cannot convert,
Invert Expr() returns Empty().
JSL provides a Simplify Expr command that takes a messy, complex formula and tries to simplify it using various algebraic rules. To use it, submit
result = Simplify Expr(expr(expression));
result = Simplify Expr(nameExpr(global));
For example,
Simplify Expr( Expr( 2 * 3 * a + b * (a + 3 - c) - a * b ) );
results in
6*a + 3*b + -1*b*c
Simplify Expr() also unwinds nested If expressions. For example:
r = Simplify Expr( Expr( If( cond1, result1, If( cond2, result2, If( cond3, result3, resultElse ) ) ) ) );
results in
If(cond1, result1, cond2, result2, cond3, result3, resultElse); | {"url":"https://www.jmp.com/support/help/en/16.2/jmp/algebraic-manipulations.shtml","timestamp":"2024-11-04T07:37:16Z","content_type":"application/xhtml+xml","content_length":"9106","record_id":"<urn:uuid:f474ddf7-b900-4bd4-8b03-a45f5895123f>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00849.warc.gz"} |
Calculus I Essentials
Course Overview
Need some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of calculus,
step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent lines,
differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
Whether you’re starting your first semester of calculus, or cramming for your final exam, Krista King will help you quickly build skills with simple, step-by-step lessons. Krista King (founder of
Krista King Math and CalculusExpert) worked as a... View Profile
• Total Time 1 hr, 23 min
• Lessons 11
• Exercises 31
11 Lessons in This Course
• Free
Lost in the world of calculus? Start at the beginning by learning about functions - number ‘machines’ that serve as the basis for all of calculus.
Lost in the world of calculus? Start at the beginning by learning about functions - number ‘machines’ that serve as the basis for all of calculus.
• You've got a graph, but how do you know whether or not it represents a function? Use the vertical line test! Learn the test, then practice on several examples.
You've got a graph, but how do you know whether or not it represents a function? Use the vertical line test! Learn the test, then practice on several examples.
• Take the confusion out of limits with integralCALC! Learn how to solve for limits and infinite limits, and what to do in the event of a point discontinuity.
Take the confusion out of limits with integralCALC! Learn how to solve for limits and infinite limits, and what to do in the event of a point discontinuity.
• Take your calculus skills to the limit! Learn how to find the left-hand and right-hand limits, and then use those to prove that the general limit does not exist.
Take your calculus skills to the limit! Learn how to find the left-hand and right-hand limits, and then use those to prove that the general limit does not exist.
• Know your limits! Learn about the precise definition (or epsilon delta definition) of a limit, and how it can be used to prove that a limit is true.
Know your limits! Learn about the precise definition (or epsilon delta definition) of a limit, and how it can be used to prove that a limit is true.
• Learn how to answer one of the most important questions in calculus by calculating the rate of change of a function at a point (aka taking the derivative)!
Learn how to answer one of the most important questions in calculus by calculating the rate of change of a function at a point (aka taking the derivative)!
• Understand derivatives with help from this lesson on difference quotients. See how to plug in values and functions and then simplify confusing equations.
Understand derivatives with help from this lesson on difference quotients. See how to plug in values and functions and then simplify confusing equations.
• In this lesson from IntegralCalc, brush up on your calculus skills and work through a problem to find the equation of a line tangent to a particular function!
In this lesson from IntegralCalc, brush up on your calculus skills and work through a problem to find the equation of a line tangent to a particular function!
• Don’t be intimidated by long implicit differentiation problems! Learn how to solve this type of equation with help from Krista, founder of IntegralCalc.
Don’t be intimidated by long implicit differentiation problems! Learn how to solve this type of equation with help from Krista, founder of IntegralCalc.
• Learn how to solve optimization problems and find the extremes, the local or global minima or maxima of a function, in this lesson from integralCALC.
Learn how to solve optimization problems and find the extremes, the local or global minima or maxima of a function, in this lesson from integralCALC.
• Related rates problems give many calculus students headaches, but they don’t have to. Learn how to conquer these problems using implicit differentiation!
Related rates problems give many calculus students headaches, but they don’t have to. Learn how to conquer these problems using implicit differentiation!
• Calculating the derivative of a function is easier than taking the definition of the derivative! LeThis lesson teaches you the process for solving derivatives.
Calculating the derivative of a function is easier than taking the definition of the derivative! LeThis lesson teaches you the process for solving derivatives.
• Having a hard time applying the average value formula? Follow along with integralCALC as she walks through how to calculate the average value of a function.
Having a hard time applying the average value formula? Follow along with integralCALC as she walks through how to calculate the average value of a function.
• Not sure if your function is continuous? Learn to identify and solve for removable discontinuities by walking through an example problem with integralCALC.
Not sure if your function is continuous? Learn to identify and solve for removable discontinuities by walking through an example problem with integralCALC.
• This example problem has it all! Learn to take the derivative of a complex natural log using the chain rule and tips that harken back to your days of algebra.
This example problem has it all! Learn to take the derivative of a complex natural log using the chain rule and tips that harken back to your days of algebra.
• Build on your knowledge of derivatives in this calculus lesson, and learn how to calculate an integral to find the exact area under a function.
Build on your knowledge of derivatives in this calculus lesson, and learn how to calculate an integral to find the exact area under a function.
• Need some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of
calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent
lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
Need some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of
calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent
lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
• Worried about taking a college-level or AP Calculus class? Fret not! In this course, review simple examples and graphs to explore the main concepts of both differential and integral calculus.
Worried about taking a college-level or AP Calculus class? Fret not! In this course, review simple examples and graphs to explore the main concepts of both differential and integral calculus.
• Do you need a little help preparing for the AP Calculus AB exam? Look no further. This course covers the basic ideas of calculus, including: functions, limits, derivatives, and integration.
Do you need a little help preparing for the AP Calculus AB exam? Look no further. This course covers the basic ideas of calculus, including: functions, limits, derivatives, and integration.
• Calculus students ready to advance to the next level: this course is for you. Learn all about the cross product, starting with the right hand rule, and ending with how to measure torque.
Calculus students ready to advance to the next level: this course is for you. Learn all about the cross product, starting with the right hand rule, and ending with how to measure torque.
• In this calculus course discover the geometric interpretation of the dot product (also known as the scalar product), the component definition of the dot product, and properties of the dot
In this calculus course discover the geometric interpretation of the dot product (also known as the scalar product), the component definition of the dot product, and properties of the dot
• Need some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of
calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent
lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
Need some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of
calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent
lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
• Statistics may sound like a dry topic, but developing data analysis skills will unlock fascinating worlds! In this 10-lesson course from statistics teacher Zac Rappell, start by understanding
group data and central tendencies (mean, median, and mode), then explore measures of spread (range, IQR, and standard deviation). Learn how to create stem and leaf and box and whisker plots, and
practice comparing data sets to identify new relationships. Finish with a fun final project analyzing the Oscars!
Statistics may sound like a dry topic, but developing data analysis skills will unlock fascinating worlds! In this 10-lesson course from statistics teacher Zac Rappell, start by understanding
group data and central tendencies (mean, median, and mode), then explore measures of spread (range, IQR, and standard deviation). Learn how to create stem and leaf and box and whisker plots, and
practice comparing data sets to identify new relationships. Finish with a fun final project analyzing the Oscars!
• Studying for the Regents Exam and need help with the algebra one section? In this course, run through thirty-seven example problems that cover basic algebra concepts you'll need to know to pass.
Studying for the Regents Exam and need help with the algebra one section? In this course, run through thirty-seven example problems that cover basic algebra concepts you'll need to know to pass.
• Calculus students ready to advance to the next level: this course is for you. Learn all about the cross product, starting with the right hand rule, and ending with how to measure torque.
Calculus students ready to advance to the next level: this course is for you. Learn all about the cross product, starting with the right hand rule, and ending with how to measure torque.
• Fundamentals of Laplace transforms such as definition, limits, properties, and few examples.
Fundamentals of Laplace transforms such as definition, limits, properties, and few examples. | {"url":"https://curious.com/integralcalc/series/calculus-i-essentials?category_id=stem&force_course=1","timestamp":"2024-11-05T20:25:50Z","content_type":"text/html","content_length":"193378","record_id":"<urn:uuid:20841610-09b2-40ad-98b4-3a4d2e703853>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00594.warc.gz"} |
Procedural Hydrology: Improvements and Meandering Rivers in Particle-Based Hydraulic Erosion Simulations
Note: The full source-code used to generate all visualizations is available on Github here, unless specified otherwise. More modern iterations of the code will be discussed at the end.
Since the publication of my article on Procedural Hydrology through particle-based erosion simulation and the release of the source-code as SimpleHydrology over 3 years ago, the reach of the concept
has far exceeded my expectations, becoming one of the most popular open-source projects under the topic hydrology on Github, with around 2^9 (= 512) stars at the time of this publication.
I am particularly grateful for the countless conversations I have had over E-Mail and Reddit, particularly with the r/proceduralgeneration community, discussing the beauty, complexity and merit of
these simulations, and it has inspired me to dive deeper into topics of simulated and procedural geomorphology.
SimpleHydrology as an implementation has since been a baseline for my geomorphology simulations, both visually but also in terms of my procedural generation ideal:
Maximize emergent behavior and minimize complexity through well defined and comprehensible rules
In the time since the original publication, SimpleHydrology has gone through many iterations, improved by addressing its core deficiencies, but also finding the most effective way to boost the
emergent output space with only minimal new rules and complexity. That is what this article is about.
This has been a long time coming. For anybody who has been following this blog over the years, thank you for reading, and I hope you can appreciate the work that goes into these projects. It is quite
difficult to “make time” next to full-time jobs and other real life considerations, even when I find that musing about these designs occupies most of my daily mental bandwidth. I hope you enjoy
reading this as much as I enjoy designing and writing about it!
A visualization of the meander of a large stream over time. Explained below.
This article is a follow-up article to Procedural Hydrology. In it, I will lay out my criticisms of the implementation, and how they are addressed to improve the overall quality of the simulation.
Additionally, I will explain the main conceptual improvement that has been made to the SimpleHydrology system: Meandering Rivers.
Through the introduction of a low complexity change (the computation and conservation of momentum), a large amount of emergent complexity can be effected, resulting in beautiful and realistic
time-lapse behavior of meandering rivers, dry stream-beds and soil being pushed around.
If you would like to know how to get effects similar to these in your erosion simulations, this article will lay it all out!
In the two videos above, you can see a time-lapse (5x speed-up) of the meandering river simulation. How this works will be discussed in more detail below.
Procedural Hydrology: Retrospective
It is not necessary to read the original Procedural Hydrology article to learn about Meandering Rivers in particle-based erosion simulations, but this section is a retrospective, which addresses
insights and improvements to the code that apply generally to erosion simulation code. The original article has more detailed explanations and implementation examples, which will be referenced here.
Skip at your own peril.
Procedural Hydrology in a Nutshell…
Procedural Hydrology is a particle-based hydraulic erosion simulation with streams and pools in a 2.5D-Domain (i.e.: on a height-map). These streams and pools, represented by stream and pool maps
respectively, were designed to couple the particles’ behavior more tightly to the terrain and yield more realistic morphology. It works as follows:
Water particles are spawned, distributed randomly over the terrain, and descending by the law of gravity (think: rain). Particles have mass and thereby individual momentum, so that they can escape
small, local terrain minima. The paths of particles are tracked in the stream-map and exponentially averaged, approximating a dynamic probability distribution for particle positions on the grid.
An equilibrium mass function takes the current state of the particle (speed, local terrain slope, etc.) and determines the amount of mass the particle can suspend at equilibrium. The equilibrium
value is approached iteratively by the actual value, by transferring sediment between the particle and the terrain using a linear mass-transfer rate.
Finally, before a particle dies, it can attempt to “flood”, by which it will take any remaining, non-evaporated volume, and add it to the pool map to signify stagnant water on the terrain. It does so
using a flood-fill operation over the terrain.
The simulation is defined by two processes:
The Particle Motion-Law and Mass-Transfer-Law.
Making these two processes dependent not only on the height-map, but also the pool-map and the stream-map (i.e.: other particles) is what lets SimpleHydrology be more realistic than simple hydraulic
erosion. Still, there are certain aspects which I would do differently today…
Note: I have written about this before, but I still believe that almost any surface-dynamic geomorphological phenomenon can be simulated through the combination of a motion-law and mass-transfer-law
in a particle-based system; even those which would be typically solved through cellular automata in a Eulerian Frame. This is possible as long as particle-motion can be designed to move along the
characteristics of the relevant dynamic law for energy and mass transfer. It has worked out for me so far.
SimpleHydrology Map, 256×256, 2020
SimpleHydrology Map, 512×512, 2023
Observe the images above. On the left is the old system, while the right contains all of the improvements I have made over the years. Graphical improvements aside (specularity, distance-fog, SSAO,
non-billboard trees), the image on the left has a number of artifacts which the image on the right doesn’t have.
The artifacts, their causes and their fixes are explained below, in no particular order.
Criticism 1: Natural Smoothing
Probably the first observation is that the terrain on the left looks very jagged, with deep ridges. Hydraulic erosion has the self-reinforcing property that deep ridges tend to get deeper, as gravity
moves more particles down the steeper slope, leading to more erosion, and so on.
This is not an invalid morphology, as deep-ridged mountains are common in places like Hawaii or Southern China. My issue was that I had no control over it.
At the time, I considered introducing a smoothing function (local averaging, gaussian blur, etc.) but thought that these were physically unrealistic and decided not to add them.
It was only 6 months after publication of SimpleHydrology that I began working on the SimpleWindErosion system, which necessitated the introduction of sand-pile dynamics and Angle of Repose for loose
The angle of repose is computed as the equilibrium angle, where the particle normal force is in balance with gravity and friction. For more information, including implementation, read Particle-Based
Wind Erosion.
It was only afterwards that I realized that rocky terrain naturally has the same mechanism, with particles (rocks) falling into the ridges from above through thermal erosion, acting as an effective
and natural local smoothing filter.
Thermal Erosion and Sediment Avalanching is essential for realistic Hydraulic Erosion Simulations.
This natural sediment settling process is a well-described phenomenon which gives mountains and hills characteristic slopes and helps enforce the fractal-like appearance.
The overall slope of the terrain remains lower than a maximum slope, determined by local rock particle properties. The formation on the right for instance has a very visible characteristic slope,
which is enforced by the fact that the stream flows right next to its base. This image is from an overnight hike through the Greina in 2018.
In the simulation, this has the effect that ridges can never become arbitrarily deep, since this increases the slope and forces material to naturally fall from above. Finally, different materials can
be given different angles of repose, adding an additional layer of depth and control.
The rate of thermal erosion can also be reduced when simulating erosion in climates without freeze-thaw cycles.
Note: An up-to-date implementation of avalanching is here.
Criticism 2: Surface-Normal
Meshing a rectangular-grid height-map with triangles has one seemingly trivial but incredibly relevant issue: The choice of orientation for the triangles is arbitrary and affects the “graphical
slope” of the surface.
This is because the convex hull of the four corner-points of a cell is almost never a quad, but a tetrahedron with 4 triangle faces: two above and two below. That’s a complicated way of saying that
you have to choose which pair of triangles you want to represent your surface, affecting local slope.
The convex hull of the four corner points forms a tetrahedron (left, gray). Depending on the choice of the triangle-mesh orientation, the tetrahedron’s “saddle” can either slope inward (middle, red)
or outward (right, blue).
At the time, I decided that the simulation and its visualization should not be separate, if possible. So far so good.
I then for some reason decided that the terrain surface should be equal to the surface-mesh, i.e. the simulation slope would be equal to the mesh slope (graphical slope).
This was a mistake, conceptually and computationally.
The arbitrary nature of the orientation introduced directional artifacts which were difficult to diagnose and remove. In trying to fix them, I computed the normal from both orientations
simultaneously. Relying on the triangle slope required multiple cross-product and many normalization operations, which were expensive and slowed down the simulation, especially after removing the
artifacts, doing twice the work.
Finally, inside any of the four regions of the projected tetrahedron (see image above, bottom left), the slope would be constant and there was no local variation, with sharp changes in slope at the
boundaries between these internal triangles. All around terrible.
The fix was realizing that the normal-vector of a continuous surface can be computed from the surface-gradient. An arbitrary precision, continuous approximation of the surface-gradient with any
choice of support points can be computed using finite differences. This was not only computationally much more efficient, but allowed for granular control of the accuracy vs cost trade-off at
sub-pixel values, achieving higher levels of detail.
The thinking that the graphics and simulation should not be separated was not bad in principle – I had just chosen the wrong end to be in charge. Instead of using the surface-normal properties of the
mesh for simulation, I instead now use a normal-map, computed using the simulation’s finite-difference method, for lighting the terrain.
Here is a working C++20 example implementation:
// Surface Map Constraints
template<typename T>
concept surface_t = requires(T t){
{ t.height(glm::ivec2()) } -> std::same_as<float>;
{ t.oob(glm::ivec2()) } -> std::same_as<bool>;
// Finite-Differences Gradient Method
template<surface_t T>
const static inline glm::vec2 gradient(T& map, glm::ivec2 p){
glm::vec2 pxa = p;
if(!map.oob(p - glm::ivec2(1, 0)))
pxa -= glm::ivec2(1, 0);
glm::vec2 pxb = p;
if(!map.oob(p + glm::ivec2(1, 0)))
pxb += glm::ivec2(1, 0);
glm::vec2 pya = p;
if(!map.oob(p - glm::ivec2(0, 1)))
pya -= glm::ivec2(0, 1);
glm::vec2 pyb = p;
if(!map.oob(p + glm::ivec2(0, 1)))
pyb += glm::ivec2(0, 1);
// Compute Gradient
glm::vec2 g = glm::vec2(0, 0);
g.x = (map.height(pxb) - map.height(pxa))/length(pxb-pxa);
g.y = (map.height(pyb) - map.height(pya))/length(pyb-pya);
return g;
// Surface Normal from Surface Gradient
template<surface_t T>
const static inline glm::vec3 normal(T& map, glm::ivec2 p){
const glm::vec2 g = gradient(map, p);
glm::vec3 n = glm::vec3(-g.x, 1.0f, -g.y);
if(length(n) > 0)
n = normalize(n);
return n;
Note: This code snippet utilizes C++20 concepts so that it can generically operate on any type which implements the height() and oob() methods, with only one square root and no cross products. This
code is taken from here.
Criticism 3: Constant Time-Step
The next most apparent issue with the height-map is that the terrain appears quite noisy, and as the simulation runs, holes and spikes are created and filled again. The reason for this is quite
simple: the constant time-step.
As particles move, gaining or losing speed based on the laws of motion, they traverse the grid’s cells. The issue is that:
With a constant time-step, there is no guarantee that a particle will land in a neighboring cell after each step.
This had two effects: Particles were capable of “tunneling through” and “leaping over” terrain features, and the effective slope computation and thus mass-transfer law was no longer local. These
effects could average out over time, but the simulation would look noisy and unrealistic as it progressed. Example:
In this simulation, you can immediately see the creation of noisy holes and spikes, particularly on the steepest slopes. These resemble the spurious yet stable checkerboard solutions you would
typically find in computational fluid-dynamics.
This is fixed by normalizing the effective speed of each particle has to be equal to the cell-width, so that there is a guarantee that a particle will land in a neighboring cell. Thereby, mass can no
longer tunnel through or leap over terrain. To then adjust the motion-law and mass-transfer-law rates, the time-step parameter (dt) has to be scaled by the ratio of the particle speed to the
Note: This effectively reinterprets the particle speed more as a time-dilation parameter than an actual velocity over the map, but makes the simulation stable and smooth.
Criticism 4: Flood-Fill Pooling
The stream-map was a great idea. The pool-map was not so great, but what made it really terrible was that I decided to use flood-filling for updates. Allow me to explain.
Incrementally distributing the remaining volume of a water droplet, equally over the surface of a body of water, determined by a complex flood-fill, turned out to be computationally expensive. Now do
this for hundreds of droplets per time-step, as lakes grow larger and larger, and you can see the complexity scaling problem.
Flood-filling was also not a good idea conceptually, since the surface height equilibrium of any real body of water does not propagate instantly, but with a finite wave-speed. Flood-filling
essentially decoupled the lake’s surface from the time-scale of the simulation.
The final issue was not getting lakes to fill, but to get them to drain. Determining drainage points on a constantly mutating, 2.5D basin boundary during the flood-fill was tremendously complex, with
many edge cases (ba-dum-tss).
Drainage with flood-fills is what finally tipped the balance between implementation simplicity and emergent complexity towards the unreasonable, and the system was so fragile as to not be reasonably
At the end of my Procedural Hydrology article, I muse about what a good method would be to determine when the transition between flowing (particle) and stagnant (pool-map) water should take place.
The answer? There is none. The question is far too ill-posed.
Dynamic Lakes are Difficult
I am sorry to say that I still don’t have the answer to this problem, but my previous one is definitely out of line with my procedural ideal.
I decided to remove lakes from the simulation entirely until I revisit them in the future, as I will (at some point) be tackling oceans, which behave in a more similar manner, and I might have more
insights at that point.
I do have some ideas for how lakes could be done.
A prototype system for a new lake simulation.
The concept takes inspiration from SoilMachine, my Multi-Layer Erosion Simulator. The pool map is effectively a static layer, permanently above the soil. Why don’t I treat it that way? It has a
repose angle of zero, and can avalanche just like sediment. Water droplets contain soil and water. So I can define an equilibrium-based mass-transfer-law for the water volume, just like I do for the
sediment, right? And of course, the particle would move different if it is on the surface of water.
That means that we no longer have to wrestle with incredibly ill-posed questions such as “when does water transition from a stream to a pool”. Instead, water is represented as in equilibrium between
the particles and the map, coupling the particle motion to the terrain through a mass transfer / equilibriation law. When a particle flows over and out of a lake, it can carry that water with it
The only remaining challenge is defining the motion-law and the mass-transfer-law sensibly. Easier said than done. In the video above, I tried to do just that. That was about two months of work, but
is still incomplete. It is much faster, more controllable, and has no edge cases. I am hopeful.
Criticism 5: Directionless Streams
The final criticism of Procedural Hydrology is that in shallow or low-slope regions of the map, the streams tend to “flatten out”, allowing them to braid nicely, but losing coherence and no longer
acting like streams with a well-defined direction.
Just like with sediment avalanching, this can be a valid morphology in certain situations, like river deltas where the discharge rate becomes very low due to low flow rate spread over large areas.
Still, the simulation lacked control over the coherence of streams in high discharge scenarios.
The issue arises from the fact that each particle’s motion does not affect the motion of any other particle: They are decoupled from each other.
This will be addressed in more detail in the following section on Meandering Rivers.
Additional Improvements
Here are additional improvements which don’t fall under the category of explicit criticisms, but rather optimizations and design choices.
1. Map-Cell Structure
Previously, I stored various properties of the map in separated arrays of basic C++ types. Instead of this, I now allocate a single array of a struct containing all properties.
float* height = new float[WIDTH*HEIGHT]; // Heightmap Value
float* discharge = new float[WIDTH*HEIGHT]; // Effective Discharge
float* discharge_track = new float[WIDTH*HEIGHT]; // Discharge Tracking Valu
float* rootdensity = new float[WIDTH*HEIGHT]; // Vegetation Root Density
struct cell {
float height; // Heightmap Value
float discharge; // Effective Discharge
float discharge_track; // Discharge Tracking Value
float rootdensity; // Vegetation Root Density
cell* my_map = new cell[WIDTH*HEIGHT];
Array of Struct > Struct of Array
(in this situation)
This is more cache-friendly since the data of a struct is stored contiguously, and it is more likely than not that you will be accessing different data-members at the same cell position than the same
member of different cells.
This also easier to maintain; simply adding an additional member to your struct definition adds data to the map. In general, it allows for better decoupling of the map code from the erosion code and
the introduction of convenience structures like iterators.
2. Discharge Function
The stream-map was originally intended to yield a dynamic value, characteristic of the volumetric flow through a particular point on the map. The volume of a particle would vary over its lifetime,
and more particles would converge in high discharge areas of the map, which would affect the local motion- and mass-transfer-laws.
In order to generate the stream-map, I previously executed a boolean AND of the particle position and a particle-track map. After every particle has finished its motion, I would exponentially average
the track-map with the stream-map.
Note: The previous implementation is here.
The issue with this implementation was that it had no realistic physical interpretation, despite my stated goal. In fact, I could not get it to work using the particle volumes, which is why I opted
for the other implementation: it worked. This has been fixed since.
cell->discharge_track += drop.volume; // During Single Particle Descent
for(auto [cell, pos]: map){ // After All Particle Descent
cell.discharge = (1.0f-lrate)*cell.discharge + lrate*cell.discharge_track;
const inline float discharge(glm::ivec2 p){ // Sampling Function
return erf(0.4f*map.get(p)->discharge);
return 0.0f;
In the new version, a discharge track value is accumulated over all particles at every time-step, giving the total volume which flowed through each cell. This value is subsequently exponentially
averaged and passed through an error function to normalize the value to the range [0, 1).
Note that this introduces an additional parameter (the error-function characteristic scale) by which the activation of the discharge can be controlled.
Meandering River Simulation
It turns out that the change required to make particle-based hydraulic-erosion streams meander is quite minimal and non-invasive. This is well aligned with the principle of low complexity rules with
high levels of emergence. In the following section, I will provide some context and finally present an implementation with code examples.
The Physics of Meandering
The Wikipedia-Article on Meandering states that a meander is caused by a higher flow-velocity on the outer bank of a river flowing around a curve, leading to more sediment being suspended by the flow
at equilibrium. On the inner bank, the lower velocity leads to deposition of the excess sediment. Small disturbances in the linearity of the flow are thus self-enhancing, and will grow until a
cut-off event occurs.
Minute-Earth on YouTube has a very concise explanation of the physics of meandering in video-form, describing the same phenomenon:
Interestingly, the Wikipedia article focuses primarily on how and why the flow has a velocity gradient when discussing the underlying physics, citing a balance between pressure (inwards) and
centrifugal forces (outwards) leading to helical flow and sediment being moved across the bed of the river.
Note: You may notice that the simulation doesn’t define a velocity, in particular because we use a dynamic time-step to scale particle speed to the cell-width. Instead, we approximate the velocity as
proportional to the discharge per unit-area, per unit-time.
So how do we introduce meandering into a particle-based hydraulic erosion simulation? There are two requirements:
1. Suspension Rate scales with Flow Velocity
The first requirement for meandering can already be satisfied by the simulation: A higher flow velocity leads to more suspension. This is realized using the discharge as a scaling factor for our
equilibrium-mass function:
// Equilibrium Mass Function c_eq
float discharge = world.discharge(drop.pos); // Local Discharge Function
float entrainment = param.entrainment; // Rate Parameter
float hdiff = world.height(drop.old_pos)-world.height(drop.pos);
float c_eq = (1.0f+param.entrainment*discharge)*hdiff;
if(c_eq < 0)
c_eq = 0;
2. Flow Velocity increases at Outer Banks
The second requirement for meandering is to have a higher velocity on the outer banks of curved streams. This is where we come full-circle to the criticisms of the old Procedural Hydrology system:
Each particle’s motion is decoupled from the motion of every other particle.
This effectively means that every particle has its own local momentum, but the stream as a whole does not, resulting in a lack of centrifugal forces. To meander, we will therefore:
Conserve Stream Momentum for Centrifugal Forces
Momentum Conservation
Note: To all CFD engineers reading this, prepare for hand-waving. I know that this is not true momentum conservation, but a very basic approximation which is suited to the procedural nature of the
simulation and provides excellent results. An analysis of why this works and what it is actually modeling would be interesting.
In order to conserve momentum and couple the motion of all particles, we use an additional momentum-map.
The momentum-map is given by the exponential average (over time-steps) of the cumulative momentum of all particles passing through each cell at each time-step. It represents a dynamic approximation
of the momentum of the entire stream at every position on the map, and is then coupled back into the particle’s motion-law.
Thankfully, this is all easier done than said!
First, we introduce four new values to each cell on the map: two momentum values (x, y) and two momentum-tracking values for accumulation:
struct cell {
float momentumx;
float momentumy;
float momentumx_track;
float momentumy_track;
Next, at every time-step of each particle, we accumulate the local momentum into the tracking values at the current cell (note that the speed here is a normalized value):
cell->momentumx_track += drop.volume*drop.speed.x;
cell->momentumy_track += drop.volume*drop.speed.y;
Finally, an exponential average is computed over the track values after all particles have finished their descent, similar to the discharge value, to give us our momentum-map:
for(auto [cell, pos]: map){
cell.momentumx = (1.0f-lrate)*cell.momentumx + lrate*cell.momentumx_track;
cell.momentumy = (1.0f-lrate)*cell.momentumy + lrate*cell.momentumy_track;
Coupling the momentum-map to the particle motion-law is then quite simple. The stream imparts a force on the particle, proportional to its momentum. Additionally, we scale it by the dot-product of
the particles direction and the stream’s direction, to simulate the diffusion of energy when the streams are perpendicular:
// Apply Forces to Particle
const glm::ivec2 ipos = pos;
const glm::vec3 n = world.normal(ipos);
const glm::vec2 fspeed = world.momentum(ipos);
const float discharge = world.discharge(ipos);
// Gravity Force
speed += param.gravity*glm::vec2(n.x, n.z)/volume;
// Momentum Transfer Force
if(length(fspeed) > 0 && length(speed) > 0)
speed += param.momentumTransfer*dot(normalize(fspeed), normalize(speed))/(volume + discharge)*fspeed;
And that’s the whole thing!
Procedural Hydrology with Meandering
Overall, addressing all of the previously mentioned concerns helped the surface and stream maps increase in realism and detail. Here is a visualization of a 960×960 map’s surface and stream-map,
after about 2000 time-steps:
In all simulations, the initial terrain utilized is derived from fractal noise. This has the effect that the map doesn’t start with a valid water-shed due to many small and large basins.
Instead of filling these as an initial condition or allowing the basins to be filled with lakes (I deactivated those, remember?), I let the erosion simulation solve the basin problem. This divides
the simulation into two phases: before and after the water-shed becomes valid.
Here is an animation of streams solving the water-shed.
This video is a 960×960 visualization of a 6-minute stream-map time-lapse, sped up by a factor of 10x.
In the phase before the water-shed has been solved, we can observe ribbons and loops of streams circling the border of their basin in an attempt to break out and join other streams on their merry way
downhill. In a way, the momentum conservation has implemented a water-shed search algorithm. That’s cool.
After the water-shed has been solved, we can easily visually verify that they streams are, in fact, meandering. Some tell-tale signs include:
• Steady Increase of Curvature on the Outer-Bank
• Slow Forward-Propagation of the Meander Curve
• Stream Cut-Off Behavior and Pinching
• Oxbow Lakes (which subsequently fade away)
• Meander Scarring (visible on surface maps)
The introduction of momentum conservation had another effect besides the meandering of streams: Streams are now more stable across longer distances, meaning that the simulation of larger maps becomes
possible, with a caveat: Larger maps mean larger basins, and longer time to solve the basin problem before a larger water-shed forms.
Although I have not tried in earnest, I think that this is another necessary step towards simulating canyons. Now I just have to integrate this with multi-layer erosion!
Meander Pigment Washing
Trying to come up with a cool way to visualize the historic path of meandering rivers, I decided to model a map which contains a light soil (pigment) at high elevations with a linear gradient towards
a dark soil (pigment) at lower elevations.
When picking up or dropping sediment, the two values would be mixed and thus dragged across the map in the path of the streams, and effectively visualize the historic path of the meandering streams.
That results in these cool visuals. Enjoy!
Note: The source-code for these visualizations is here.
Final Words
If you have read this far, thank you!
While meandering has been on the main branch of SimpleHydrology for quite a while now, it has taken me quite a bit of time to write this article. Not only for time reasons, but also because of my own
standard of quality.
Originally, I wanted to also fix lakes definitively, but realized after months of toil that the scope was completely blown up. Not just because lakes are much more complex than I thought, but because
there is already enough information for a full article after discussing the improvements to Procedural Hydrology over the years, which until now, have been undocumented besides the occasional reddit
With the amount of geomorphological simulation code I have written over the years, it is becoming increasingly difficult to manage and integrate into existing projects. For instance, when will
SoilMachine support meandering? Should it? How much longer should SimpleHydrology be maintained into the future?
Attempting to integrate these changes into all these separate repositories probably doesn’t make sense at some point, and they might be archived at some point.
It is for that reason that I decided to unify these concepts in a C++ library called soillib, to allow me to base simulation implementations off of. Most of my most recent geomorphology code,
including tools and other utilities, is now located there and will be updated there for the foreseeable future.
The goal is not only to unify the implementations, but offer convenient interfaces to perform geomorphological simulations on data, without the visualization. Tools include .tiff based pure
command-line tools, for instance for generating a relief-shaded height-map:
Additionally, it gives me a place to experiment with modularity and composition of various components, e.g. non-square maps to let the particles operate on.
I have successfully abstracted away the map code, which lets me do funny things running erosion code on spiral maps with holes.
Overall, I am quite happy with the results of the meandering.
In terms of outlook, the last thing I absolutely have to tackle before considering these projects “done” in any way is oceans and particularly shores and beaches. That would let me close off an
island of a finite size to run the simulation on, and would make for a plausible, finite map. Everything else would just be for additional detail.
If anything in this article is unclear, you have any questions, or you are interested in collaborating on developing geomorphological simulations, feel free to reach out! | {"url":"https://nickmcd.me/2023/12/12/meandering-rivers-in-particle-based-hydraulic-erosion-simulations/","timestamp":"2024-11-10T10:47:05Z","content_type":"text/html","content_length":"75254","record_id":"<urn:uuid:934fb3b8-a462-49eb-92d0-ba49c5f44dda>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00759.warc.gz"} |
Edward lorenz butterfly effect pdf file download
The equations are ordinary differential equations, called lorenz equations. C on december 29, 1972, as prepared for press release. A butterfly effect on neural stem cells pdf free download. In chaos
theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later
state. This month in physics history aps physics aps home. Weather prediction is an extremely difficult problem. Celebrating prezis teacher community for teacher appreciation week. When lorenz
discovered the butterfly effect openmind.
They are notable for having chaotic solutions for certain parameter values and starting conditions. May 23, 2016 on may 23, 1917, american mathematician, meteorologist, and a pioneer of chaos theory
edward norton lorenz was born. Relation between y and z coordinates in the lorenz system. The orphan tsunami of 1700 ebook download free pdf. Gleick 1987 this work attempts to breathe life into that
metaphorical butterfly. Lorenz and the butterfly effect to the average layperson, the concept of chaos brings to mind images of complete randomness. Lorenz attractor simple english wikipedia, the
free. These figures show two segments of the threedimensional evolution of two trajectories one in blue, and the other in yellow for the same period of time in the lorenz attractor starting at two
initial points that differ by only 10. Small changes in these initial conditions result in big effects. Download it once and read it on your kindle device, pc, phones or tablets. Pdf the butterfly
effect of the butterfly effect researchgate.
Lorenz is famous for talking about the butterfly effect. In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a
deterministic nonlinear system can result in large differences in a later state the term, closely associated with the work of edward lorenz, is derived from the metaphorical example of the details of
a tornado the exact time of formation, the exact path taken. In 1987, the term butterfly effect took flight thanks to james gleicks best seller chaos. Lorenz was running a climate model consisting of
twelve differential equations repre. He laid the foundations for the field of scientific study called chaos theory. In the 1960s, edward lorenz was investigating the motion of the.
Here is a java simulation of the butterfly effect using the. The term butterfly effect is related to the work of edward lorenz, who in. Norton, developed the first course in chemical engineering at
mit in 1888. In a matlab script, we demonstrate the application of the rungekutta numerical method for a lorenz attractor, the butterfly effect caused by a small change of initial conditions, and the
dependence of the butterfly effect on the step of the integration. Making a new science and lorenzs discovery reached a general audience. The butterfly effect is a part of chaos theory and in essence
states that when a butterfly flaps their wings on this side of the world, it makes a tornado happen on the other side of the world. The highly entertaining new york times bestseller, which explains
chaos theory and the butterfly effect, from the author of the information chicago tribune. Lorenz had discovered the first chaotic dynamical system. Always update books hourly, if not looking, search
in the book search column. Lorenz was born in 1917 in west hartford, connecticut. In 1972, the meteorologist edward lorenz gave a talk at the 9th meeting of the american association for the
advancement of science entitled does the flap of a butterfly s wings in brazil set off a tornado in texas. Edward lorenz quotes 5 science quotes dictionary of. Why pop culture loves the butterfly
effect, and gets it.
His theory, called the butterfly effect, stated that a butterfly could flap its wings and set air molecules. Lorenz, 1963, is a major characteristic of a chaotic system. The butterfly effect kindle
edition by semegran, scott. Lorenz presents everyday examples of chaotic behaviour, such as the. In 1972, the meteorologist edward lorenz gave a talk at the 9th meeting of. He is best known for
pointing out the butterfly effect whereby chaos theory predicts that slightly differing initial states can evolve into considerably different states. Making a new science and lorenz s discovery
reached a general audience. Edward lorenz made a presentation to the new york academy of sciences and. He wrote simplified equations and solved them on a primitive computer. In 1962, edward lorenz
was studying a simplified model of convection flow in the atmosphere. Get ebooks the orphan tsunami of 1700 on pdf, epub, tuebl, mobi and audiobook for free. Lorenz 19172008 to highlight the
possibility that small causes may have momentous effects. Jan 06, 2011 this is the origin of the term butterfly effect, where infinitesimal initial inputs can cause huge results. An interesting
example is chaos theory, popularized by lorenzs butterfly effect.
For centuries, scientific thought was focused on bringing order to the natural world. In general, varying each parameter has a comparable effect by causing the system to converge toward a periodic
orbit, fixed point, or escape towards infinity, however the specific ranges and behaviors. Theyre famous because they are sensitive to their initial conditions. Edward lorenz, an mit meteorologist
who tried to explain why it is so hard to make good weather forecasts and wound up unleashing a scientific revolution called chaos theory, died april 16 of cancer at his home in cambridge. Edward
lorenz, father of chaos theory and butterfly effect. Melbourne, australiafrom the physical sciences comes the theory that all life is interconnected, that even the gentle movement of a butterflys
wing can connect to vast and distant changes and consequences. Meteorologists can predict the weather for short periods of time, a couple days at most, but beyond that predictions are generally poor.
Edward norton lorenz may 23, 1917 april 16, 2008 was an american mathematician and meteorologist, and a pioneer of chaos theory. Webmaster has been unable to find a verbatim source for a widely
circulated variant, namely.
Introduction the butter y effect was discovered by edward lorenz, an mit meteorologist, in the early 1960s. He acquired an early love of science from both sides of his family. On may 23, 1917,
american mathematician, meteorologist, and a pioneer of chaos theory edward norton lorenz was born. The lorenz attractor also called lorenz system is a system of equations. The text of the talk, in
its original form, as then prepared for press release but unpublished, is in edward lorenz, essence of chaos 1995, appendix 1, 181. View notes systems thinking edward lorenz and real life examples of
the butterfly effect from emae 172 at case western reserve university. Jun 08, 2008 the butterfly effect is a deceptively simple insight extracted from a complex modern field. They were discovered in
1963 by an mit mathematician and meteorologist, edward lorenz. Initially enunciated in connection with the problematics of weather prediction it became eventually a metaphor used in very diverse
contexts, many of them outside the.
His theory, called the butterfly effect, stated that a butterfly could flap its wings and set air molecules in motion that, in turn, would move other air moleculeswhich would then move additional air
moleculeseven. Systems thinking edward lorenz and real life examples of. The name, coined by edward lorenz for the effect which had been known long before, is derived from the metaphorical example of
the details of a hurricane exact time of. The butterfly effect is the sensitive dependency on initial conditions in which a small change at one place in system can result in large differences in a
later state of that system. As a lowprofile assistant professor in mits department of meteorology in 1961, lorenz created an early. Edward lorenz originated the concept of the butterfly effect in the
1960s. Edward norton lorenz, mit mathematician and meteorologist and father of chaos theory, a science many now believe rivals even relativity and the quantum in importance. Use features like
bookmarks, note taking and highlighting while reading the butterfly effect.
The butterfly effect how your life matters pdf download free. Half a century ago, edward lorenz, sm 43, scd 48, overthrew the idea of the clockwork universe with his groundbreaking research on chaos.
Author james gleick tells about mit meteorologist edward lorenz. Get your kindle here, or download a free kindle reading app. Previously, lorenz had used the example of a seagull causing a storm, but
finally made it more poetic with a butterfly, following suggestions from colleagues. Edward lorenz was a mathematician and meteorologist at the massachusetts institute of technology who loved the
study of weather. This is a water transport hydrology concept that can transport stormwater to clean storage, improve snowpack, and minimize urban flooding. In 1963, edward lorenz made a presentation
to the new york academy of sciences and was literally laughed out of the room. The essence of chaos jessie and john danz lectures. Apr 16, 2008 edward lorenz, an mit meteorologist who tried to
explain why it is so hard to make good weather forecasts and wound up unleashing a scientific revolution called chaos theory, died april 16 of cancer at his home in cambridge. In his 1963 paper in
the journal of atmospheric sciences, he cited the flapping of a seagull. Melbourne, australiafrom the physical sciences comes the theory that all life is interconnected, that even the gentle movement
of a butterfly s wing can connect to vast and distant changes and consequences. In 1972, the meteorologist edward lorenz gave a talk at the 9th meeting of the american association for the advancement
of science entitled does the flap of a butterflys wings in brazil set off a tornado in texas. If the difference in temperature was slight, the heated air would slowly rise to the top in a predictable
He imagined a closed chamber of air with a temperature difference between the bottom and the top, modeled using the navierstokes equations of fluid flow. Sure enough, his output did behave a lot like
real weather. Mark einsiedel ussy 204 systems thinking february 14. He is best known for pointing out the butterfly effect whereby chaos theory predicts that slightly differing initial states. In the
1960s the american meteorologist edward lorenz not lorentz. Mar 27, speaker and new york times bestselling author andy andrews shares a compelling and powerful story.
May 02, 2016 a plot of lorenzs strange attractor for values. The term, closely associated with the work of edward lorenz, is derived from. In 1963, edward lorenz presented a hypothesis to the new
york academy of science. The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical systemthat, starting from any of various arbitrarily close alternative
initial conditions on the attractor, theiterated points will become arbitrarily spread out from each other. Small changes in the initial conditions have a big effect on the solution.
The university of houstons college of engineering presents this series about the machines that make our civilization run, and the people whose. Today, our notion of cause and effect changes forever.
Appendix 1 the butterfly effect the following is the text of a talk that i presented in a session devoted to the global atmospheric research program, at the 9th meeting of the american association
for the advancement of science, in. He discovered the strange attractor notion and coined the term butterfly effect. Here is a java simulation of the butterfly effect using the chaotic attractor that
lorenz discovered. Making a new scienceand lorenzs discovery reached a general audience. A professor at mit, lorenz was the first to recognize what is now called chaotic behavior in the mathematical
modeling of.
Oct 30, 20 the butterfly effect is a concept invented by the american meteorologist edward n. Lorenz formulated the equations as a simplified mathematical model for atmospheric convection. If you
continue browsing the site, you agree to the use of cookies on this website. This sensitivity is now called the butterfly effect. Edward norton lorenz may 23, 1917 april 16, 2008 was an american
mathematician and meteorologist who established the theoretical basis of weather and climate. His father, edward henry lorenz, majored in mechanical engineering at the massachusetts institute of
technology, and his maternal grandfather, lewis m. As a lowprofile assistant professor in mits department of meteorology in. A version of this article appeared in mit tech talk on april 30, 2008
download pdf. Hailed by a new york times reporter as someone who download it once and read it on your kindle device, pc, phones or tablets. Inthe essence of chaos edward lorenz, one of the founding
fathers of chaos and the originator of its seminal concept of the butterfly effect, presents his own landscape of our current understanding of the field.
The butterfly effect andy andrews page 6 summary in 1963, edward lorenz made a presentation to the new york academy of sciences and was literally laughed out of the room. The butterfly effect how
your life matters pdf download. Ed lorenz, one of the founding fathers of chaos theory, has produced a book aimed at. There are more than 1 million books that have been enjoyed by people from all
over the world. Pdf the butterfly effect metaphor states with variance that the flap of a butterflys wings in. Yet to scientists, it denotes stochastic behavior occurring in a deterministic system.
Edward lorenz and the butterfly effect scihi blogscihi blog. We can see this effect in action here, where a red and a blue path have initial values truncated in a similar manner. The butterfly effect
is a deceptively simple insight extracted from a complex modern field. The butterfly effect the following is the text of a talk that i presented in a session devoted to the global atmospheric
research program, at the 9th meeting of the american association for the advancement of science, in washington, d. | {"url":"https://biobicompgu.web.app/1644.html","timestamp":"2024-11-09T22:27:44Z","content_type":"text/html","content_length":"19345","record_id":"<urn:uuid:a97a0ffd-6227-4c62-8250-2eb292553ced>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00690.warc.gz"} |
-objects depending on
calc.sdcProblem {sdcTable} R Documentation
perform calculations on sdcProblem-objects depending on argument type
perform calculations on sdcProblem-objects depending on argument type
calc.sdcProblem(object, type, input)
## S4 method for signature 'sdcProblem,character,list'
calc.sdcProblem(object, type, input)
object an object of class sdcProblem
type a character vector of length 1 defining what to calculate|return|modify. Allowed types are:
• rule.freq: modify suppression status within object according to frequency suppression rule
• heuristicSolution: obtain a heuristic (greedy) solution to the problem defined by object
• cutAndBranch: solve a secondary cell suppression problem defined by object using cut and branch
• anonWorker: is used to solve the suppression problem depending on information provided with argument input
• ghmiter: solve a secondary cell suppression problem defined by object using hypercube algorithm
• preprocess: perform a preprocess procedure by trying to identify primary suppressed cells that are already protected due to other primary suppressed cells
• cellID: find index of cell defined by information provided with argument input
• finalize: create an object of class safeObj
• ghmiter.diagObj: calculate codes required to identify diagonal cells given a valid cell code - used for ghmiter-algorithm only
• ghmiter.calcInformation: calculate information for quaders identified by diagonal indices - used for ghmiter-algorithm only
• ghmiter.suppressQuader: suppress a quader based on indices
• ghmiter.selectQuader: select a quader for suppression depending on information provided with argument input - used for ghmiter-algorithm only
• ghmiter.suppressAdditionalQuader: select and suppress an additional quader (if required) based on information provided with argument input - used for ghmiter-algorithm only
• contributingIndices: calculate indices within the current problem that contribute to a given cell
• reduceProblem: reduce the problem given by object using a vector of indices
• genStructuralCuts: calculate cuts that are absolute necessary for a valid solution of the secondary cell suppression problem
input a list depending on argument type.
• a list (typically generated using genParaObj()) specifying parameters for primary cell suppression if argument type matches 'rule.freq'
• a list if argument type matches 'heuristicSolution' having the following elements:
□ element 'aProb': an object of class linProb defining the attacker's problem
□ element 'validCuts': an object of class cutList representing a list of constraints
□ element 'solver': a character vector of length 1 specifying a solver to use
□ element 'verbose': a logical vector of length 1 setting if verbose output is desired
• a list (typically generated using genParaObj()) specifying parameters for the secondary cell suppression problem if argument type matches 'cutAndBranch', 'anonWorker', 'ghmiter', 'preprocess'
• a list of length 3 if argument type matches 'cellID' having following elements
□ first element: character vector specifying variable names that need to exist in slot 'dimInfo' of object
□ second element: character vector specifying codes for each variable that define a specific table cell
□ third element: logical vector of length 1 with TRUE setting verbosity and FALSE to turn verbose output off
• a list of length 3 if argument type matches 'ghmiter.diagObj' having following elements
□ first element: numeric vector of length 1
□ second element: a list with as many elements as dimensional variables have been specified and each element being a character vector of dimension-variable specific codes
□ third element: logical vector of length 1 defining if diagonal indices with frequency == 0 should be allowed or not
• a list of length 4 if argument type matches 'ghmiter.calcInformation' having following elements
□ first element: a list object typically generated with method calc.sdcProblem and type=='ghmiter.diagObj'
□ second element: a list with as many elements as dimensional variables have been specified and each element being a character vector of dimension-variable specific codes
□ third element: numeric vector of length 1 specifying a desired protection level
□ fourth element: logical vector of length 1 defining if quader containing empty cells should be allowed or not
• a list of length 1 if argument type matches 'ghmiter.suppressQuader' having following element
□ first element: numeric vector of indices that should be suppressed
• a list of length 2 if argument type matches 'ghmiter.selectQuader' having following elements
□ first element: a list object typically generated with method calc.sdcProblem and type=='ghmiter.calcInformation'
□ second element: a list (typically generated using genParaObj())
• a list of length 4 if argument type matches 'ghmiter.suppressAdditionalQuader' having following elements
□ first element: a list object typically generated with method calc.sdcProblem and type=='ghmiter.diagObj'
□ second element: a list object typically generated with method calc.sdcProblem and type=='ghmiter.calcInformation'
□ third element: a list object typically generated with method calc.sdcProblem and type=='ghmiter.selectQuader'
□ fourth element: a list (typically generated using genParaObj())
• a list of length 1 if argument type matches 'contributingIndices' having following element
□ first element: character vector of length 1 being an ID for which contributing indices should be calculated
• a list of length 1 if argument type matches 'reduceProblem' having following element
□ first element: numeric vector defining indices of cells that should be kept in the reduced problem
• an empty list if argument type matches 'genStructuralCuts'
information from objects of class sdcProblem depending on argument type
• an object of class sdcProblem if argument type matches 'rule.freq', 'cutAndBranch', 'anonWorker', 'ghmiter', 'ghmiter.supressQuader', 'ghmiter.suppressAdditionalQuader' or 'reduceProblem'
• a numeric vector with elements being 0 or 1 if argument type matches 'heuristicSolution'
• a list if argument type matches 'preprocess' having following elements:
□ element 'sdcProblem': an object of class sdcProblem
□ element 'aProb': an object of class linProb
□ element 'validCuts': an object of class cutList
• a numeric vector of length 1 specifying the index of the cell of interest if argument type matches 'cellID'
• an object of class safeObj if argument type matches 'finalize'
• a list if argument type matches 'ghmiter.diagObj' having following elements:
□ element 'cellToProtect': character vector of length 1 defining the ID of the cell to protect
□ element 'indToProtect': numeric vector of length 1 defining the index of the cell to protect
□ element 'diagIndices': numeric vector defining indices of possible cells defining cubes
• a list containing information about each quader that could possibly be suppressed if argument type matches 'ghmiter.calcInformation'
• a list containing information about a single quader that should be suppressed if argument type matches 'ghmiter.selectQuader'
• a numeric vector with indices that contribute to the desired table cell if argument type matches 'contributingIndices'
• an object of class cutList if argument type matches 'genStructuralCuts'
internal function
Bernhard Meindl bernhard.meindl@statistik.gv.at
version 0.32.6 | {"url":"https://search.r-project.org/CRAN/refmans/sdcTable/html/calc.sdcProblem-method.html","timestamp":"2024-11-01T22:09:09Z","content_type":"text/html","content_length":"11334","record_id":"<urn:uuid:d8deafc3-5ee7-457c-ad62-6985844b5b36>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00323.warc.gz"} |
Sticky "information", i.e. knowledge, and emergence
I spent some more time pondering an paper Noah Smith tweeted out the other day (and Tom Brown also retweeted to me) and
wrote a blog post about a bit later
(see his post for all the background). The article and Noah both emphasize "emergence", so of course it is of interest to this blog. However I am not sure that is an appropriate interpretation.
First, let's see if I can understand the paper itself. I am going to make a vocabulary change however -- let's use the word knowledge instead of information because this has little to do with
information theory.
With that vocabulary change, the paper makes several points:
1. Sticky knowledge (information) and noisy knowledge (information) models lead to (equivalent) dependence of the forecast error on forecast revisions FE = β FR + n where β = β(λ) (knowledge
stickiness) or β = β(G) (noisy knowledge Kalman gain) and n is a noise term.
2. Actual forecast errors from a variety of sources indicate β ~ 1, meaning λ ~ 0.5 or G ~ 0.5.
3. Additional tests to show this isn't due to some other factors, and applies across consumers, professionals, academics, and internationally.
4. Forecasts can be useful estimates of non-rational expectations
5. Non-rational expectations can "emerge" from aggregating rational agents
Let me set up a toy model version of what is happening here. (Aside: this is a specific example where an unrealistic model is useful for understanding a result about the real world.) Let's take our
observable O (inflation, growth rate, whatever) to be a Wiener process (Brownian motion) with zero drift. In this case the "rational expectations" forecast (REF) for any future price is the present
price (i.e. the EMH for a random walk). If we look at forecasts that are updated every integer unit of time T = n, our sticky knowledge forecast (SKF) with stickiness λ for time T = 3 will be
SKF(3, T=0) = (1 - λ) REF(0, T = 3) + λ REF(-1, T = 3) at time T = 0
SKF(3, T=1) = (1 - λ) REF(1, T = 3) + λ REF(0, T = 3) at time T = 1
SKF(3, T=2) = (1 - λ) REF(2, T = 3) + λ REF(1, T = 3) at time T = 2
Think of 1-λ as a probability of an individual agent updating their forecast. Also note that
REF(i, T = i + k) = O(i)
so this simplifies a bit
SKF(3, T=0) = (1 - λ) O(0) + λ O(-1)
SKF(3, T=1) = (1 - λ) O(1) + λ O(0)
SKF(3, T=2) = (1 - λ) O(2) + λ O(1)
We then look at
FR = SKF(3, T=i) - SKF(3, T=i-1)
FE = O(3) - SKF(3, T=i)
i.e. forecast revisions versus forecast error. For λ = 0, we get the rational expectations result -- the forecast error and the forecast revisions are uncorrelated:
For λ = 0.5, we get correlation:
In the above pictures, I show a "typical" path alongside several hundred simulation results. Effectively, the SKF(t, T = t-k) is a biased estimator of the future value of O(t) while O(t-k) = REF(t, T
= t-k) is an unbiased estimator.
This pretty much covers points 1-4 above. I would like to add that sticky knowledge ("information") models can be interpreted as agents ignoring most outside information, making them uncorrelated.
Agents that all updated their forecasts at the same time to exactly the same data would end up very correlated --
which leads to a failure of information equilibrium
(which is bad and probably behind recessions).
Now let's talk emergence (point 5). It's a bit easier to explain in the case of sticky "information". At time t, individual agents either forecast REF(t-1, T = t+k) or REF(t, T = t+k) -- which are
both "rational" expectations (one is fresh and one is stale) and unbiased estimators of O(t+k). The average agent, however, forecasts
λ REF(t, T = t+k) + (1 - λ) REF(t-1, T = t+k)
But it seems to me a bit cheeky to say the bias of forecast revisions is really emergent. Individual agents either revise or don't revise, so it doesn't make sense to talk about the bias of forecast
revisions for agents that don't revise. It's not a revision of zero, it's no revision. The concept of forecast revisions is itself somewhat emergent -- you are averaging a set of revision numbers
with a bunch of
s you take to be zero.
Additionally, this exact same result can be obtained if we think of λ as a weight instead of a probability and apply it to every agent.
But the biggest problem is that a stale (i.e. not updated with probability 1 - λ) rational expectation from time t - 1 at time t isn't technically a rational expectation at time t. The aggregating
process for a forecast at time t is aggregating λ N agents with rational expectations and (1 - λ) N agents with non-rational (i.e. stale) expectations. The aggregation of rational agents and
non-rational agents being non-rational isn't really "emergence". It's kind of like saying an average over the whole numbers {0, 0, 0, 0, 0, 1, 1, 1, 1, 1} isn't 0 and the average 0.5 (a fraction) is
"emergent". I'd call that a stretch.
It's not the worst thing to do in a paper and sometimes a little flair is good to draw attention. As there's no hard and fast definition of "emergence", so there's no technical flaw with what the
authors say.
PS As a side note, the models presented in the paper fail for "complete stickiness" λ = 1 (or Kalman gain G = 0). In that case the coefficient of the forecast revision is singular, which should make
sense to us all: if we never update our forecast with new knowledge, then how could you have revisions? This creates a "scope" for these models: λ < 1. This means agents must update their forecasts
with rational expectations at some point. If agents never update their forecasts with true rational expectations, then these results don't apply to the real world -- even though the data appears to
be described by the sticky knowledge (information) model!
1 comment:
1. Thanks Jason.
Comments are welcome. Please see the Moderation and comment policy.
Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.
Note: Only a member of this blog may post a comment. | {"url":"https://informationtransfereconomics.blogspot.com/2016/10/sticky-information-ie-knowledge-and.html","timestamp":"2024-11-04T02:18:14Z","content_type":"text/html","content_length":"107916","record_id":"<urn:uuid:ace9a924-ac32-4feb-bad3-18fd3f6ef072>","cc-path":"CC-MAIN-2024-46/segments/1730477027809.13/warc/CC-MAIN-20241104003052-20241104033052-00498.warc.gz"} |
2x2 Matrix Multiplication Calculator
A matrix with two rows and two columns is called as a 2x2 matrix. Matrix multiplication should be done by multiplying the elements of each row of the first matrix by the elements of each column in
the second matrix. Here is the online 2x2 matrix multiplication calculator which helps you to multiply the 2x2 matrix in a simple manner by just entering the values of two matrices.
Even though matrix multiplication is simple in terms of operations, but the possibility of errors in the manual calculation is more due to repetitive calculations and sub-calculations. This 2x2
matrix multiplication calculator will help you to avoid those errors in manual calculations. | {"url":"https://www.calculators.live/2x2-matrix-multiplication","timestamp":"2024-11-08T16:04:13Z","content_type":"text/html","content_length":"10854","record_id":"<urn:uuid:3e32d2c0-0cc7-430a-aefc-f0d2d58ee417>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00162.warc.gz"} |
Purity of the stratification by Newton polygons and Frobenius-periodic vector bundles
2013 Theses Doctoral
Purity of the stratification by Newton polygons and Frobenius-periodic vector bundles
This thesis includes two parts. In the first part, we show a purity theorem for stratifications by Newton polygons coming from crystalline cohomology, which says that the family of Newton polygons
over a noetherian scheme have a common break point if this is true outside a subscheme of codimension bigger than 1.
The proof is similar to the proof of [dJO99, Theorem 4.1]. In the second part, we prove that for every ordinary genus-2 curve X over a finite field k of characteristic 2 with automorphism group Z/2Z
× S_3, there exist SL(2,k[[s]])-representations of π_1(X) such that the image of π_1(X^-) is infinite. This result produces a family of examples similar to Laszlo's counterexample [Las01] to a
question regarding the finiteness of the geometric monodromy of representations of the fundamental group [dJ01].
• Yang_columbia_0054D_11316.pdf application/pdf 538 KB Download File
More About This Work
Academic Units
Thesis Advisors
de Jong, Aise Johan
Ph.D., Columbia University
Published Here
May 15, 2013 | {"url":"https://academiccommons.columbia.edu/doi/10.7916/D8XW4S1V","timestamp":"2024-11-13T08:49:52Z","content_type":"text/html","content_length":"17365","record_id":"<urn:uuid:1b82aecd-1093-42a0-b72a-2da35101073e>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00241.warc.gz"} |
EViews Help: @sumsqsby
Sum of squared observations in a series for each specified group.
Syntax: @sumsqsby(x, y, [s])
x: series
y series, alpha
s: (optional) sample string or object
Return: series
Compute the sum of squared observations in x for group identifiers defined by distinct values of y.
EViews will use the current or specified workfile sample.
show @sumsqsby(x, g1, g2)
produces a linked series of by-group sums of squares of observations in x, where members of the same group have identical values for both g1 and g2. | {"url":"https://help.eviews.com/content/functionref_s-@sumsqsby.html","timestamp":"2024-11-13T22:11:50Z","content_type":"application/xhtml+xml","content_length":"8235","record_id":"<urn:uuid:114deb52-08e2-4f35-a574-c67a4c504a94>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00898.warc.gz"} |
For the following economy, find autonomous expenditure, the
multiplier, short-run equilibrium output, and the output gap....
For the following economy, find autonomous expenditure, the multiplier, short-run equilibrium output, and the output gap....
For the following economy, find autonomous expenditure, the multiplier, short-run equilibrium output, and the output gap. By how much would autonomous expenditure have to change to eliminate the
output gap?
C = 450 + 0.75 (Y – T )
I ^p = 200
G = 140
NX = 60
T = 100
Y* = 3,200
Instructions: Enter your responses as absolute numbers.
Autonomous expenditure:
Short-run equilibrium output:
There is (Click to select) a recessionary an expansionary no output gap in the amount of .
Autonomous expenditure would need to (Click to select) decrease stay the same increase by to eliminate the output gap. | {"url":"https://justaaa.com/economics/26234-for-the-following-economy-find-autonomous","timestamp":"2024-11-04T17:53:32Z","content_type":"text/html","content_length":"43136","record_id":"<urn:uuid:af94ba35-417b-42c9-87ed-30b3603356c8>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00879.warc.gz"} |
- och
OMOP Common Data Model CDM Domain - Portal för
Plattform för hantering av fastighetsdata ur ett
Skapa Stäng. Manufacturing Data Management based on an Open Information Model for Design of Manufacturing Systems and Processes Våra tjänster inom datautveckling. Utveckla informationsmodell;
Utveckla roadmap för realisering av ny Kombinera data för analys och KPI:er 2021; Selecting a new CRM and ERP as a platform for growth 22 december, 2020; Cutting costs Zynka BIM helps you turn the
data into added value and business innovation. BIM. pim. Program information model cim.
A model where logy i is linear on x i, for example, is not the same as a generalized linear model where logµ i is linear on x i. Example: The standard linear model we have studied so far 2021-03-22
2020-09-09 Censoring and related missing-data mechanisms can be modeled (as discussed in Section 18.5) or else mitigated by including more predictors in the missing-data model and thus bringing it
closer to missing at random. For example, whites and persons with college degrees tend … The data source is where you model your data: for example, by creating calculated fields, adding parameters,
and adjusting data types. Data sources and connectors. Data sources use connectors to fetch your data from a specific platform, system, or product.
When you're trying data-driven attribution, or any new non-last-click attribution model, we recommend that you test the model first and see how it affects your return on investment. Linear
regression is the starting point of econometric analysis. The linear regression model has a dependent variable that is a continuous variable, while the independent variables can take any form
(continuous, discrete, or indicator variables).
Model Tree Structures with Child References Presents a data model that organizes documents in a tree-like structure by storing references to "child" nodes in "parent" nodes. See Model Tree Structures
for additional examples of data models for tree structures. Model Specific Application Contexts.
Let's create a simple EDM for the School database using Visual Studio (2012\2015\2017) and Entity Framework 6. 1. Open Visual Studio and create a console project. 2020-06-29 Right-click the Models
folder, and select Add and New Item.
It will give insight on their advantages, differences and upon the testing principles involved in each of these data modeling methodologies. Let us begin with data […] If data-driven attribution
isn't available to you, Google Ads offers other attribution models that don't have data requirements. Learn more About attribution models.
Kiss och bajs boken
och Reference Information Model ( RIM ) , som är en informationsmodell som är Krav Objektorienterad informationsmodell (TDOK 2015:0181) blir i Genom att ställa krav på vilken data som skall skapas,
och hur den skall The difference between information models (IMs) and data models (DMs) can be summarised as follows: IMs provide a formal description of the organisation’s view of reality. There
should only be one IM per organisation, but there can be many DMs, usually one per system. RFC 3444 Information Models and Data Models January 2003 DMs, conversely, are defined at a lower level of
abstraction and include many details. They are intended for implementors and include protocol-specific constructs. Information Model. B Although information models and data models serve di erent
purposes, it is not always easy to decide which detail belongs to an information model and which belongs to a data model. B Similarily, it is sometimes di cult to determine whether an abstraction
belongs to an information model or a data model.
A Conceptual Information Model is a high level diagram describing the important information in an enterprise or system; it is typically useful for communicating ideas to a wide range of business and
technical stakeholders. Any number of diagrams can be created representing the information at a line-of-business level, Datamodell er betegnelsen på den modellen man bruker for å strukturere data.
Normalt dreier det seg om en modell realisert som et databaseskjema i en relasjonsdatabase Conceptual vs. Logical vs. Physical Data Models. An alternative viewpoint to Dave Hay's video "Kinds of Data
Models - and How to Name Them" (http://bit.ly/Q Data Modelers are Systems Analysts who design computer databases that translate complex business data into usable computer systems. Data Modelers work
with data architects to design databases that meet organizational needs using conceptual, logical, and physical data models.
Nationalsocialism folkgemenskap
Medium The model for µ i is usually more complicated than the model for η i. Note that we do not transform the response y i, but rather its expected value µ i. A model where logy i is linear on x i,
for example, is not the same as a generalized linear model where logµ i is linear on x i. Example: The standard linear model we have studied so far 2021-03-22 2020-09-09 Censoring and related
missing-data mechanisms can be modeled (as discussed in Section 18.5) or else mitigated by including more predictors in the missing-data model and thus bringing it closer to missing at random. For
example, whites and persons with college degrees tend … The data source is where you model your data: for example, by creating calculated fields, adding parameters, and adjusting data types. Data
sources and connectors. Data sources use connectors to fetch your data from a specific platform, system, or product.
Any number of diagrams can be created representing the information at a line-of-business level, Datamodell er betegnelsen på den modellen man bruker for å strukturere data. Normalt dreier det seg om
en modell realisert som et databaseskjema i en relasjonsdatabase Conceptual vs. Logical vs.
Iss fruktkorgar linköping
Information- och processmodellering - Informed Decisions AB
Program information model cim. Construction information model. av Y Ibrahim · 2020 · Citerat av 1 — Department of Computer Science and Engineering / Institutionen för data- och informationsteknik >
Masteruppsatser >. Leveraging a Traceability Information Model in order to enhance the maintenance of automotive Safety Medicinska informationsmodeller och ontologier, 6 hp (TBMI03). Medical
Information Models and Ontologies, 6 credits. Kursstart. | {"url":"https://lonfptiaas.netlify.app/71145/52996","timestamp":"2024-11-15T04:21:52Z","content_type":"text/html","content_length":"16466","record_id":"<urn:uuid:5f96e188-2f64-44d1-95c9-b80abd33cfb6>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00318.warc.gz"} |
How to use numpy.clip() in Python | Coding Ref
How to use numpy.clip() in Python
In Python, numpy.clip() is a function that is used to clip values in an array to be within a specified range.
This function is often used to clip outliers in data to make the data more manageable or to prevent certain values from causing problems in downstream analyses.
Here is the syntax for numpy.clip():
numpy.clip(a, a_min, a_max, out=None)
This function takes the following arguments:
• a: The input array. This is the array whose values will be clipped.
• a_min: The minimum value that elements of a can take. Any values in a that are less than a_min will be set to a_min.
• a_max: The maximum value that elements of a can take. Any values in a that are greater than a_max will be set to a_max.
• out (optional): The output array. If provided, the clipped values will be stored in this array. Otherwise, a new array will be created to hold the clipped values.
Here is an example of how you might use numpy.clip() to clip values in an array.
Suppose you have the following array:
import numpy as np
a = np.array([1, 5, 10, -2, -5, 20])
You can use numpy.clip() to clip all values in this array that are less than 0 to 0 and all values that are greater than 10 to 10, like this:
a_clipped = np.clip(a, 0, 10)
This will result in the following array:
array([1, 5, 10, 0, 0, 10])
You can also use numpy.clip() to clip values in place, without creating a new array.
To do this, you can provide the out argument to numpy.clip(), like this:
np.clip(a, 0, 10, out=a)
array([1, 5, 10, 0, 0, 10])
This will modify the original a array in place, so that all values less than 0 are set to 0 and all values greater than 10 are set to 10. | {"url":"https://www.codingref.com/article/python-numpy-clip","timestamp":"2024-11-12T11:45:58Z","content_type":"text/html","content_length":"19206","record_id":"<urn:uuid:d103ca28-8e90-4437-a2ec-3ea0956471de>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00756.warc.gz"} |
Though substantial advancements have been made in training deep neural networks, one problem remains, the vanishing gradient. The very strength of deep neural networks, their depth, is also
unfortunately their problem, due to the difficulty of thoroughly training the deeper layers due to the vanishing gradient. This paper proposes "Phylogenetic Replay Learning", a learning methodology
that substantially alleviates the vanishing-gradient problem. Unlike the residual learning methods, it does not restrict the structure of the model. Instead, it leverages elements from
neuroevolution, transfer learning and layer-by-layer training. We demonstrate that this new approach is able to produce a better performing model and by calculating Shannon entropy of weights, we
show that the deeper layers are trained much more thoroughly and contain statistically significantly more information than when a model is trained in a traditional brute force manner.
[1] D. Silver, David et al., "Mastering the Game of Go with Deep Neural Networks and Tree Search," Nature, vol. 529, pp. 484-489, DOI: 10.1038/nature16961, 2016.
[2] P. Vikhar, "Evolutionary Algorithms: A Critical Review and Its Future Prospects," Proc. of the IEEE Int. Conf. on Global Trends in Signal Process., Inf. Comp. and Comm. pp. 261-265, Jalgaon,
India, 2016.
[3] F. Gomez, J. Schmidhuber and R. Miikkulainen, "Accelerated Neural Evolution through Cooperatively Coevolved Synapses," Journal of Machine Learning Research, vol. 9, pp. 937-965, 2008.
[4] R. De Nardi, J. Togelius, O. Holland and S. Lucas, "Evolution of Neural Networks for Helicopter Control: Why Modularity Matters," Proc. of the IEEE Int. Conf. on Evolutionary Computation, pp.
1799-1806, DOI: 10.1109/CEC.2006.1688525, Vancouver, Canada, 2006.
[5] V. Heidrich-Meisner, C. Igel, B. Hoeffding and Bernstein, "Races for Selecting Policies in Evolutionary Direct Policy Search," Proc. of the 26th Annual Int. Conf. on Machine Learning (ICML '09),
vol. 51, DOI: 10.1145/1553374.1553426, 2009.
[6] J. Lehman et al., "The Surprising Creativity of Digital Evolution: A Collection of Anecdotes from the Evolutionary Computation and Artificial Life Research Communities," Massachusetts Institute
of Technology, Artificial Life, vol. 26, no. 2, pp. 274–306, 2020.
[7] F. Such et al., "Deep Neuroevolution: Genetic Algorithms Are a Competitive Alternative for Training Deep Neural Networks for Reinforcement Learning," arXiv, DOI: 10.48550/arXiv.1712.06567, 2017.
[8] X. Zhang, J. Clune and K. Stanley, "On the Relationship between the OpenAI Evolution Strategy and Stochastic Gradient Descent," arXiv: 1712.06564, DOI: 10.48550/arXiv.1712.06564, 2017.
[9] J. Lehman, J. Chen, J. Clune and K. Stanley, "ES Is More Than Just a Traditional Finite-difference Approximator," Proc. of the Genetic and Evolutionary Computation Conference (GECCO '18), pp.
450- 457, DOI: 10.1145/3205455.3205474, 2018.
[10] E. Conti, Edoardo et al., "Improving Exploration in Evolution Strategies for Deep Reinforcement Learning via a Population of Novelty-seeking Agents," Proc. of the 32nd Int. Conf. on Neural
Information Processing Systems (NIPS'18), pp. 5032–5043, 2017.
[11] J. Metzen, M. Edgington, Y. Kassahun and F. Kirchner, "Performance Evaluation of EANT in the Robocup Keepaway Benchmark," Proc. of the 6th Int. Conf. on Machine Learning and Applications (ICMLA
2007), pp. 342-347, DOI: 10.1109/ICMLA.2007.23, 2008.
[12] F. Gomez, J. Schmidhuber and R. Miikkulainen, "Accelerated Neural Evolution through Cooperatively Coevolved Synapses," JMLR, vol. 9, pp. 937-965, DOI: 10.1145/1390681.1390712, 2008.
[13] K. Stanley and R. Miikkulainen, "Evolving Neural Networks through Augmenting Topologies," Evolutionary Computation, vol. 10, pp. 99-127, DOI: 10.1162/106365602320169811, 2002.
[14] E. Real, A. Aggarwal, Y. Huang and Q. Le, "Regularized Evolution for Image Classifier Architecture Search," Proc. of AAAI Conf. on Artificial Intellig., vol. 33, DOI: 10.1609/
aaai.v33i01.33014780, 2018.
[15] A. Gaier and D. Ha, "Weight Agnostic Neural Networks," arXiv: 1906.04358, DOI: 10.13140/RG.2.2.16025.88169, 2019.
[16] S. Hochreiter, Untersuchungen zu dynamischen neuronalen Netzen, Diploma Thesis, Josef Hochreiter Institut fur Informatik, Technische Universitat Munchen, Germany, 1991.
[17] F. Informatik, Y. Bengio, P. Frasconi and J. Schmidhuber Jfirgen, "Gradient Flow in Recurrent Nets: the Difficulty of Learning Long-Term Dependencies," Chapter of Book: A Field Guide to
Dynamical Recurrent Neural Networks, pp. 237 – 243, DOI: 10.1109/9780470544037.ch14, IEEE Press, 2003.
[18] Y. Bengio, P. Simard and P. Frasconi, "Learning Long-term Dependencies with Gradient Descent Is Difficult," IEEE Transactions on Neural Networks, vol. 5, pp. 157-166, DOI: 10.1109/72.279181,
[19] R. Pascanu, T. Mikolov and Y. Bengio, "On the Difficulty of Training Recurrent Neural Networks," Proc. of the 30th Int. Conf. on Machine Learning, JMLR: W&CP, vol. 28, Atlanta, Georgia, USA,
[20] K. He, X. Zhang, S. Ren and J. Sun, "Deep Residual Learning for Image Recognition," Proc. of the IEEE Conf. on Comp. Vision and Pattern Recog. (CVPR), pp. 770-778, DOI: 10.1109 CVPR.2016.90,
[21] X. Glorot, A. Bordes and Y. Bengio, "Deep Sparse Rectifier Neural Networks," Proc. of the 14th Int. Conf. on Artificial Intelligence and Statistics, vol. 15, pp. 315-323, Fort Lauderdale, FL,
USA, 2011.
[22] Y. Lecun, L. Bottou, G. Orr and K.-R. Müller, "Efficient BackProp," Chapter in Book: Neural Networks: Tricks of the Trade, vol. 7700, pp. 9-48, DOI: 10.1007\/3-540-49430-8\_2, 1998.
[23] X. Glorot and Y. Bengio, "Understanding the Difficulty of Training Deep Feedforward Neural Networks," Journal of Machine Learning Research, vol. 9, pp. 249-256, 2010.
[24] S. Ioffe and C. Szegedy, "Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift," arXiv: 1502.03167, DOI: 10.48550/arXiv.1502.03167, 2015.
[25] Y. Lecun et al., "Backpropagation Applied to Handwritten Zip Code Recognition," Neural Computation, vol. 1, pp. 541-551, DOI: 10.1162 neco.1989.1.4.541, 1989.
[26] H. Noh, T. You, J. Mun and B. Han, "Regularizing Deep Neural Networks by Noise: Its Interpretation and Optimization," Proc. of the 31st Conf. on Neural Inf. Process. Sys. (NIPS), Long Beach,
USA, 2017.
[27] S. Enrique, J. Hare and M. Niranjan, "Deep Cascade Learning," IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 11, pp. 5475 – 5485, DOI: 10.1109/TNNLS.2018.2805098, 2018.
[28] C. Shannon and W. Weaver, The Mathematical Theory of Communication, Note 78, p. 44, 1963.
[29] J. Schmidhuber, "Learning Complex, Extended Sequences Using the Principle of History Compression," Neural Computation, vol. 4, pp. 234-242, DOI: 10.1162/neco.1992.4.2.234, 1992.
[30] O. Granmo et al., "The Convolutional Tsetlin Machine," arXiv: 1905.09688v5, DOI: 10.48550/arXiv.190 5.09688, 2019. | {"url":"https://www.jjcit.org/paper/166/PHYLOGENETIC-REPLAY-LEARNING-IN-DEEP-NEURAL-NETWORKS","timestamp":"2024-11-04T08:12:58Z","content_type":"text/html","content_length":"35722","record_id":"<urn:uuid:c7a7e044-4aea-4e83-9a2b-fa505fa3e796>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00704.warc.gz"} |
How to Read Student’s t Table - Finance Train
How to Read Student’s t Table
Student’s t distribution table has the following structure:
The row represents the upper tail area, while the column represents the degrees of freedom. The body contains the t values. Note that for one-tail distribution the values are for a and for two-tailed
distribution values are for a/2.
Let’s say n = 3, the df= 3-1 = 2. If significance level a is 0.10 then a/2 = 0.05. From the table we can observe that t-value = 2.920.
Data Science in Finance: 9-Book Bundle
Master R and Python for financial data science with our comprehensive bundle of 9 ebooks.
What's Included:
• Getting Started with R
• R Programming for Data Science
• Data Visualization with R
• Financial Time Series Analysis with R
• Quantitative Trading Strategies with R
• Derivatives with R
• Credit Risk Modelling With R
• Python for Data Science
• Machine Learning in Finance using Python
Each book includes PDFs, explanations, instructions, data files, and R code for all examples.
Get the Bundle for $39 (Regular $57)
JOIN 30,000 DATA PROFESSIONALS
Free Guides - Getting Started with R and Python
Enter your name and email address below and we will email you the guides for R programming and Python. | {"url":"https://financetrain.com/read-students-t-table","timestamp":"2024-11-13T15:22:04Z","content_type":"text/html","content_length":"97730","record_id":"<urn:uuid:a9c1a4ef-e585-4c51-ba52-d4e31997231b>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00093.warc.gz"} |
a question of which modem is better
ok ppl, ive read alot of usefull info on this site, you all seem to know alot more than i do, and thats hard for me to admit, but you all seem very informed about internet tweaking and equipment
use....hopefully someone can answer this for me...i have 2 different dsl modems and am not sure what one to use or if it makes any difference at all. i have a motorola mstatea 2210-02-1022 dsl modem
and a siemens speedstream 4100 dsl modem. is there any difference in performance from one to the other? does it make any diff at all as to what one i use? i consider myself to be pretty well self
educated at the art of fixing computer problems and general hardware issues but this is something i am not well educated on, thats why i am now a member of this wonderful forum, i have learned alot
in my short time here and hope to learn more. so, can anyone out there help me to answer this question? motorola or siemens speedstream? they both came from at&t and i didnt pay for either of them.
any input is greatly appreciated. thanks in advance.
Well if it were me, and I had tested at, or above my ISP cap, then I would leave it alone, (if I had done all the adjustments that I could) unless one had features that I needed that the other one
Or I would use the one that was most recent. But that doesn't always mean more efficient either. lol
well im just wondering because i got the two modems sittin here. i dont geet my dsl turned on the 18th and im just curious if anyone knows anything about either one before i hook them up. but of
coarse when i get my service turned on i will test them both here to see if there is any diff. the only thing i have come across so far after doing a bit of research is alot of ppl complaining about
the motorola brand gettin really hot. and after looking at it i can see why, there is no ventilation on it, the siemens brand modem has all kinds of ventilation, but im not real sure if a hot modem
has any bearing on the actual performance. so i guess i just wait another day and a half and find out. and like i said, i will be on here testing the both of them when i get my service turned on so i
will post what i come up with for anyone that may be interested.
The DSL company will surely bring out a modem when they do the install. You can't just switch out a modem, the MAC addy has to be set in the ISP's servers, otherwise the data will have no idea where
to go. Kinda.
When you first get DSL, they tell you NOT to unplug the modem for a specified period of time, this allows there servers to regulate the distance, and performance, and plenty of other things I have no
idea about. So once they get it installed, leave it alone, if you don't , then you'll never know your full potential of bandwidth, from the way I understand it. There will be a huge sticker on the
new modem they bring that states this.
When you switch the modem, your going to have to call the ISP, and tell them the make, model, and MAC, they must type this in, or you will have no connection.
wow....a perfect example of why i joined this site....you just explained so much that nobody else i have talked to could explain. thanks man.
On Telus DSL in British Columbia. They have automated the modem's MAC address authentication. Plug in and start surfing. It is good for two MAC address's. And I think the unused MAC address will
expire in two hours or so. But you can interface with the website to delete MAC's if there is a problem with an old MAC not releasing.
So when the day comes to get service, there is about a day's worth of unstable speeds, unless the tech did not have to go to the node to switch you on to a different port for a higher speed package.
Since DSL is slowly upgrading to faster ports. And if they run out of higher speed ports for new customers? Well tough, till some upgrades are made to remove the older cards.
And Telus also likes to give out a combo modem/router to alleviate call supports dealing with a modem and then a router of the customers choosing. So since the Siemens Gigaset SE567 was a piece of
crap with the 'Telus firmware' version. I now have a modem only, Thomson Speedtouch ST516v6 , And my own router.
And if the DSL modem can not train(stay connected) to your faster speed package, due to line noise or distance, support can throttle your speed back to achieve a stable speed.
And some DSL ISP's have only certain modems that work on their particular DSL setup.
wow....a perfect example of why i joined this site....you just explained so much that nobody else i have talked to could explain. thanks man.
Isnt muddy dreamy!
Isnt muddy dreamy!
Maybe cause I'm kind of sleepy right now. Chocolate bars and cookies are wearing off.. Thought I'd Google Man Loving . And this is not a photoshop.
Maybe cause I'm kind of sleepy right now. Chocolate bars and cookies are wearing off.. Thought I'd Google Man Loving . And this is not a photoshop. | {"url":"https://testmy.net/ipb/topic/25674-a-question-of-which-modem-is-better/","timestamp":"2024-11-06T14:17:07Z","content_type":"text/html","content_length":"205712","record_id":"<urn:uuid:4479552d-157e-4f6e-8e4f-133b0990f49f>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00213.warc.gz"} |
Understanding the Diffie-Hellman Key Exchange: A Group Theory Approach
Written on
Chapter 1: Introduction to Cryptography
The primary objective of cryptography is to enable two parties to securely share a coded secret over a public channel. To maintain security, this secret must remain confidential, meaning unauthorized
individuals should not be able to decipher it, even if they access the encrypted data. Most encryption techniques depend on a key, known only to the involved parties, which must be kept private. For
the purpose of this discussion, we can represent this secret as a number, denoted as s. The techniques employed to securely communicate this key are referred to as key exchanges. A classical and
straightforward method for achieving this is through the Diffie-Hellman protocol. This protocol leverages fundamental principles of group theory to safeguard secrets and is applicable across various
mathematical groups.
Section 1.1: Cyclic Groups Explained
The initial step involves selecting a mathematical group that is cyclic. As previously outlined, a group is a mathematical entity comprising certain elements. For this scenario, we will consider a
finite number of these elements, along with a binary operation that allows us to 'combine' two elements within the group. The following conditions are essential for something to be formally
classified as a group:
1. There exists a group identity, labeled e, such that for every element g in G, the equation e · g = g · e = g holds true. This signifies that the group must contain a unique 'do nothing'
2. For every symmetry transformation in the group, there is a unique inverse corresponding to each element g in G, denoted as g'. This requires that g’ · g = g · g’ = e.
3. The property of associativity indicates that the order of multiplication does not affect the result; for all g1, g2, g3 in G, it follows that g1 · (g2 · g3) = (g1 · g2) · g3.
Moreover, a cyclic group is one where every element can be represented as repeated additions of a single, unique element to itself until it reaches the identity. This concept can be likened to clock
arithmetic, where the set of numbers modulo n under addition forms a cyclic group, and the unique element that generates the entire group is known as the generator.
The first video titled "Explaining the Diffie-Hellman Key Exchange" provides an accessible overview of the protocol, illustrating its significance in secure communications.
Section 1.2: The Diffie-Hellman Protocol
The Diffie-Hellman protocol aims to facilitate the sharing of a secret key between two parties without disclosing it to anyone else. Let’s consider two participants, Alice and Bob, each possessing a
private key represented as a and b. They can select a publicly known group G, which is assumed to be cyclic and has a generator.
Suppose Alice wishes to share a generated secret key with Bob. In the initial step, she raises the generator to the power of a and transmits this value to Bob. Subsequently, Bob raises the received
value to the power of b, resulting in g^(ab), which becomes the secret key. Afterward, he sends Alice g^b, and she performs a similar operation.
The cyclic group generated by a prime number consists of numbers modulo p, where multiplication serves as the group operation. The cyclic nature of this group is proven using Fermat’s Little Theorem,
which confirms the existence of a unique generator. When G is such a group, it becomes challenging for an adversary to compute the values of a and, consequently, the secret key.
Chapter 2: Elliptic Curves and Their Applications
The second video, "Secret Key Exchange (Diffie-Hellman) - Computerphile," delves deeper into the Diffie-Hellman method, exploring its implementation and potential vulnerabilities.
Section 2.1: Utilizing Elliptic Curves
The Diffie-Hellman protocol is adaptable, allowing for the use of any cyclic group, including groups formed by points on an elliptic curve. It may not be immediately evident why points on an elliptic
curve can constitute a group, but this section will clarify that. Start with a field F, which could be the real numbers, complex numbers, or the multiplicative group of integers modulo p. An elliptic
curve consists of points in two dimensions that satisfy a specific equation.
To add two points, A and B, on the elliptic curve, a line is drawn connecting them, which intersects the curve at a third point. This point is then reflected across the x-axis to yield A+B. For
adding A to itself, the tangent line at point A is used to find where it intersects the curve, followed by a reflection across the x-axis.
By viewing this as a cyclic group, we can apply the Diffie-Hellman procedure to securely exchange keys. Despite its robustness, the Diffie-Hellman protocol is susceptible to various attacks,
including the Pollard Rho algorithm.
Section 2.2: Vulnerabilities and Future Directions
Recent advancements indicate that Diffie-Hellman could be compromised by quantum computers. In the subsequent post, I will explore how isogenies may provide a defense against potential quantum | {"url":"https://panhandlefamily.com/understanding-diffie-hellman-key-exchange.html","timestamp":"2024-11-15T02:50:50Z","content_type":"text/html","content_length":"15437","record_id":"<urn:uuid:eaea2fc9-467b-453e-a4a3-3c3c98a17a0d>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00148.warc.gz"} |
The Danger of A/B Testing Too Many Variants
ABT – “Always Be Testing” – a popular phrase almost everybody has heard about, and rightfully so. For me, A/B testing is hands down the best value-for-money optimization method there is. The entry
barrier to A/B testing is extremely low nowadays, so everybody can do it – every CRM platform has testing capabilities, and almost everyone has a brain to think of some testing ideas.
So it’s easy to start testing, but it’s hard to get it completely right. The reason for that is it combines multiple principles from user research methodology, statistics, and psychology, and as
almost all of us are not proficient in all of those, we tend to overlook some really important things.
For example, my A/B testing philosophy went like this:
1. Every campaign has to have an A/B test,
2. Every A/B test has to have as many variants as possible.
I was sure this would generate the maximum amount of learnings for me, but I was wrong. It turns out there is a practical upper limit of variants you can test in a single campaign, and that number is
not limited by your sample size, but by pure statistical chance.
*Audience sample size and statistical significance are connected. More on further in the post.
Understanding Statistical Significance
When testing, we know that we can conclude the outcome of the test only if it has reached a desired statistical significance – a claim that a set of observed data is not the result of chance but can
instead be attributed to a specific cause.
This threshold is most often set to 95% as it represents a good balance of statistical confidence and the needed audience sample size and detectable change effect. It’s a practical common ground, as
the ideal threshold of 100% would require prohibitively large sample sizes or unrealistically large testing effects (lift).
The Implication of Lower Thresholds
People in dynamic environments also tend to blur the line a little bit and call conclusions on lower thresholds – ahh, 85% is good enough. That is ok, but let’s explain that the implication of that
When we say that a result is statistically significant at the 95% confidence level, it means that we are 95% confident that the result is not due to random chance. However, this also implies that
there is a 5% chance that the result could still be due to chance. In other words, 1 out of every 20 variants could show a significant result even if there is no real effect – this is known as a
false positive.
The lower we set the threshold, the higher the chance for a false positive is. If we call the test at the before mentioned 85%, there is a 15% chance that the result could still be due to chance – or
3 out of 20 variants.
It’s important to mention that this could cause both false positives and false negatives.
• False Positive (Type I Error): A test result that incorrectly indicates the presence of an effect or condition when it is not actually present.
• False Negative (Type II Error): A test result that incorrectly indicates the absence of an effect or condition when it is actually present.
The above-described probability is true when testing a single additional variation, but when adding more variants, the chance for encountering at least one false positive increases due to the
cumulative probability effect. Simply meaning, by every variant (hypothesis) you add to the A/B test, you get 5% higher chance to get a false result.
Calculating False Positives
You can calculate the chance of getting a false positive using the following formula:
P (False Positive) = 1 – a ^ m
Here, “m” represents the total number of variations tested, and “a” is the desired statistical significance level.
Example Calculation
Let’s illustrate this with an example calculation for testing 5 variants at a 95% desired statistical significance level:
P (False Positive) = 1 − 0.95 ^ 5
P (False Positive) = 1 − 0.774
P (False Positive) ≈ 0.226
P (False Positive) ≈ 22.6%
So, there’s approximately a 22.6% chance of encountering at least one false positive when testing 5 variants with a desired significance level of 95%.
The results of other calculations can be seen below.
Number of variants or hypotheses Probability of a false positive
1 5.0%
2 9.8%
5 22.6%
8 33.7%
10 40.1%
20 64.2%
Table: Probability of a false positive with a 95% statistical significance threshold
You can now see why testing too many variants at once is not always a good idea.
Luckily, there is a solution for this, and it’s called Bonaferroni correction. It’s basically a formula that calculates the statistical significance threshold you need for the number of variants
you’re testing.
Number of variants or hypotheses Required significance level
1 95.0%
2 97.5%
5 99.0%
8 99.4%
10 99.5%
20 99.8%
Table: Bonaferroni corrected significance levels to maintain a 5% false discovery probability
Simply put, to test 5 variants and maintain the 5% error rate, you’d need to set your statistical significance threshold to 99%, instead of 95%.
The Conclusion
For me, A/B testing has evolved beyond simply throwing in as many variants as possible at the wall. It’s about planning, understanding the limitations of the audience samples, and not cutting corners
with statistical significance.
So, let’s remember to Always Be Testing, but let’s do so wisely.
How did you like this post?
Thanks for your feedback! | {"url":"https://denis-test.com/the-danger-of-a-b-testing-too-many-variants/","timestamp":"2024-11-05T10:40:42Z","content_type":"text/html","content_length":"97893","record_id":"<urn:uuid:bef18cc2-ae7b-49c5-a64e-60da4de3c9b5>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00140.warc.gz"} |
Long Range Van der Waals interactions
Long Range Van der Waals interactions#
Dispersion correction#
In this section, we derive long-range corrections due to the use of a cut-off for Lennard-Jones or Buckingham interactions. We assume that the cut-off is so long that the repulsion term can safely be
neglected, and therefore only the dispersion term is taken into account. Due to the nature of the dispersion interaction (we are truncating a potential proportional to \(-r^{-6}\)), energy and
pressure corrections are both negative. While the energy correction is usually small, it may be important for free energy calculations where differences between two different Hamiltonians are
considered. In contrast, the pressure correction is very large and can not be neglected under any circumstances where a correct pressure is required, especially for any NPT simulations. Although it
is, in principle, possible to parameterize a force field such that the pressure is close to the desired experimental value without correction, such a method makes the parameterization dependent on
the cut-off and is therefore undesirable.
The long-range contribution of the dispersion interaction to the virial can be derived analytically, if we assume a homogeneous system beyond the cut-off distance \(r_c\). The dispersion energy
between two particles is written as:
\[V({r_{ij}}) ~=~- C_6\,{r_{ij}}^{-6}\]
and the corresponding force is:
\[\mathbf{F}_{ij} ~=~- 6\,C_6\,r_{ij}^{-8}\mathbf{r}_{ij}\]
In a periodic system it is not easy to calculate the full potentials, so usually a cut-off is applied, which can be abrupt or smooth. We will call the potential and force with cut-off \(V_c\) and \(\
mathbf{F}_c\). The long-range contribution to the dispersion energy in a system with \(N\) particles and particle density \(\rho\) = \(N/V\) is:
\[V_{lr} ~=~ {\frac{1}{2}}N \rho\int_0^{\infty} 4\pi r^2 g(r) \left( V(r) -V_c(r) \right) {{{\rm d}r}}\]
We will integrate this for the shift function, which is the most general form of van der Waals interaction available in GROMACS. The shift function has a constant difference \(S\) from 0 to \(r_1\)
and is 0 beyond the cut-off distance \(r_c\). We can integrate (305), assuming that the density in the sphere within \(r_1\) is equal to the global density and the radial distribution function \(g(r)
\) is 1 beyond \(r_1\):
\[\begin{split}\begin{aligned} V_{lr} &=& {\frac{1}{2}}N \left( \rho\int_0^{r_1} 4\pi r^2 g(r) \, C_6 \,S\,{{{\rm d}r}} + \rho\int_{r_1}^{r_c} 4\pi r^2 \left( V(r) -V_c(r) \right) {{{\rm d}r}} + \rho
\int_{r_c}^{\infty} 4\pi r^2 V(r) \, {{{\rm d}r}} \right) \\ & = & {\frac{1}{2}}N \left(\left(\frac{4}{3}\pi \rho r_1^{3} - 1\right) C_6 \,S + \rho\int_{r_1}^{r_c} 4\pi r^2 \left( V(r) -V_c(r) \
right) {{{\rm d}r}} -\frac{4}{3} \pi N \rho\, C_6\,r_c^{-3} \right)\end{aligned}\end{split}\]
where the term \(-1\) corrects for the self-interaction. For a plain cut-off we only need to assume that \(g(r)\) is 1 beyond \(r_c\) and the correction reduces to 108:
\[\begin{aligned} V_{lr} & = & -\frac{2}{3} \pi N \rho\, C_6\,r_c^{-3}\end{aligned}\]
If we consider, for example, a box of pure water, simulated with a cut-off of 0.9 nm and a density of 1 g cm\(^{-3}\) this correction is \(-0.75\) kJ mol\(^{-1}\) per molecule.
For a homogeneous mixture we need to define an average dispersion constant:
In GROMACS, excluded pairs of atoms do not contribute to the average.
In the case of inhomogeneous simulation systems, e.g. a system with a lipid interface, the energy correction can be applied if \({\left< C_6 \right>}\) for both components is comparable.
Virial and pressure#
The scalar virial of the system due to the dispersion interaction between two particles \(i\) and \(j\) is given by:
\[\Xi~=~-{\frac{1}{2}} \mathbf{r}_{ij} \cdot \mathbf{F}_{ij} ~=~ 3\,C_6\,r_{ij}^{-6}\]
The pressure is given by:
\[P~=~\frac{2}{3\,V}\left(E_{kin} - \Xi\right)\]
The long-range correction to the virial is given by:
\[\Xi_{lr} ~=~ {\frac{1}{2}}N \rho \int_0^{\infty} 4\pi r^2 g(r) (\Xi -\Xi_c) \,{{\rm d}r}\]
We can again integrate the long-range contribution to the virial assuming \(g(r)\) is 1 beyond \(r_1\):
\[\begin{split}\begin{aligned} \Xi_{lr}&=& {\frac{1}{2}}N \rho \left( \int_{r_1}^{r_c} 4 \pi r^2 (\Xi -\Xi_c) \,{{\rm d}r}+ \int_{r_c}^{\infty} 4 \pi r^2 3\,C_6\,{r_{ij}}^{-6}\, {{\rm d}r}\right) \
nonumber\\ &=& {\frac{1}{2}}N \rho \left( \int_{r_1}^{r_c} 4 \pi r^2 (\Xi -\Xi_c) \, {{\rm d}r}+ 4 \pi C_6 \, r_c^{-3} \right)\end{aligned}\end{split}\]
For a plain cut-off the correction to the pressure is 108:
\[P_{lr}~=~-\frac{4}{3} \pi C_6\, \rho^2 r_c^{-3}\]
Using the same example of a water box, the correction to the virial is 0.75 kJ mol\(^{-1}\) per molecule, the corresponding correction to the pressure for SPC water is approximately \(-280\) bar.
For homogeneous mixtures, we can again use the average dispersion constant \({\left< C_6 \right>}\) ((308)):
\[P_{lr}~=~-\frac{4}{3} \pi {\left< C_6 \right>}\rho^2 r_c^{-3}\]
For inhomogeneous systems, (314) can be applied under the same restriction as holds for the energy (see sec. Energy).
Lennard-Jones PME#
In order to treat systems, using Lennard-Jones potentials, that are non-homogeneous outside of the cut-off distance, we can instead use the Particle-mesh Ewald method as discussed for electrostatics
above. In this case the modified Ewald equations become
\[\begin{split}\begin{aligned} V &=& V_{\mathrm{dir}} + V_{\mathrm{rec}} + V_{0} \\[0.5ex] V_{\mathrm{dir}} &=& -\frac{1}{2} \sum_{i,j}^{N} \sum_{n_x}\sum_{n_y} \sum_{n_{z}*} \frac{C^{ij}_6 g(\beta
{r}_{ij,{\bf n}})}{{r_{ij,{\bf n}}}^6} \end{aligned}\end{split}\]
\[\begin{split}\begin{aligned} V_{\mathrm{rec}} &=& \frac{{\pi}^{\frac{3}{2}} \beta^{3}}{2V} \sum_{m_x}\sum_{m_y}\sum_{m_{z}*} f(\pi | {\mathbf m} | /\beta) \times \sum_{i,j}^{N} C^{ij}_6 {\mathrm
{exp}}\left[-2\pi i {\bf m}\cdot({\bf r_i}-{\bf r_j})\right] \\[0.5ex] V_{0} &=& -\frac{\beta^{6}}{12}\sum_{i}^{N} C^{ii}_6\end{aligned}\end{split}\]
where \({\bf m}=(m_x,m_y,m_z)\), \(\beta\) is the parameter determining the weight between direct and reciprocal space, and \({C^{ij}_6}\) is the combined dispersion parameter for particle \(i\) and
\(j\). The star indicates that terms with \(i = j\) should be omitted when \(((n_x,n_y,n_z)=(0,0,0))\), and \({\bf r}_{ij,{\bf n}}\) is the real distance between the particles. Following the
derivation by Essmann 15, the functions \(f\) and \(g\) introduced above are defined as
\[\begin{split}\begin{aligned} f(x)&=&1/3\left[(1-2x^2){\mathrm{exp}}(-x^2) + 2{x^3}\sqrt{\pi}\,{\mathrm{erfc}}(x) \right] \\ g(x)&=&{\mathrm{exp}}(-x^2)(1+x^2+\frac{x^4}{2}).\end{aligned}\end{split}
The above methodology works fine as long as the dispersion parameters can be combined geometrically ((145)) in the same way as the charges for electrostatics
\[C^{ij}_{6,\mathrm{geom}} = \left(C^{ii}_6 \, C^{jj}_6\right)^{1/2}\]
For Lorentz-Berthelot combination rules ((146)), the reciprocal part of this sum has to be calculated seven times due to the splitting of the dispersion parameter according to
\[C^{ij}_{6,\mathrm{L-B}} = (\sigma_i+\sigma_j)^6=\sum_{n=0}^{6} P_{n}\sigma_{i}^{n}\sigma_{j}^{(6-n)},\]
for \(P_{n}\) the Pascal triangle coefficients. This introduces a non-negligible cost to the reciprocal part, requiring seven separate FFTs, and therefore this has been the limiting factor in
previous attempts to implement LJ-PME. A solution to this problem is to use geometrical combination rules in order to calculate an approximate interaction parameter for the reciprocal part of the
potential, yielding a total interaction of
\[\begin{split}\begin{aligned} V(r<r_c) & = & \underbrace{C^{\mathrm{dir}}_6 g(\beta r) r^{-6}}_{\mathrm{Direct \ space}} + \underbrace{C^\mathrm{recip}_{6,\mathrm{geom}} [1 - g(\beta r)] r^{-6}}_{\
mathrm{Reciprocal \ space}} \nonumber \\ &=& C^\mathrm{recip}_{6,\mathrm{geom}}r^{-6} + \left(C^{\mathrm{dir}}_6-C^\mathrm{recip}_{6,\mathrm{geom}}\right)g(\beta r)r^{-6} \\ V(r>r_c) & = & \
underbrace{C^\mathrm{recip}_{6,\mathrm{geom}} [1 - g(\beta r)] r^{-6}}_{\mathrm{Reciprocal \ space}}.\end{aligned}\end{split}\]
This will preserve a well-defined Hamiltonian and significantly increase the performance of the simulations. The approximation does introduce some errors, but since the difference is located in the
interactions calculated in reciprocal space, the effect will be very small compared to the total interaction energy. In a simulation of a lipid bilayer, using a cut-off of 1.0 nm, the relative error
in total dispersion energy was below 0.5%. A more thorough discussion of this can be found in 109.
In GROMACS we now perform the proper calculation of this interaction by subtracting, from the direct-space interactions, the contribution made by the approximate potential that is used in the
reciprocal part
\[V_\mathrm{dir} = C^{\mathrm{dir}}_6 r^{-6} - C^\mathrm{recip}_6 [1 - g(\beta r)] r^{-6}.\]
This potential will reduce to the expression in (315) when \(C^{\mathrm{dir}}_6 = C^\mathrm{recip}_6\), and the total interaction is given by
\[\begin{split}\begin{aligned} \nonumber V(r<r_c) &=& \underbrace{C^{\mathrm{dir}}_6 r^{-6} - C^\mathrm{recip}_6 [1 - g(\beta r)] r^{-6}}_{\mathrm{Direct \ space}} + \underbrace{C^\mathrm{recip}_6 [1
- g(\beta r)] r^{-6}}_{\mathrm{Reciprocal \ space}} \\ &=&C^{\mathrm{dir}}_6 r^{-6} \end{aligned}\end{split}\]
\[\begin{aligned} V(r>r_c) &=& C^\mathrm{recip}_6 [1 - g(\beta r)] r^{-6}.\end{aligned}\]
For the case when \(C^{\mathrm{dir}}_6 \neq C^\mathrm{recip}_6\) this will retain an unmodified LJ force up to the cut-off, and the error is an order of magnitude smaller than in simulations where
the direct-space interactions do not account for the approximation used in reciprocal space. When using a VdW interaction modifier of potential-shift, the constant
\[\left(-C^{\mathrm{dir}}_6 + C^\mathrm{recip}_6 [1 - g(\beta r_c)]\right) r_c^{-6}\]
is added to (322) in order to ensure that the potential is continuous at the cutoff. Note that, in the same way as (321), this degenerates into the expected \(-C_6g(\beta r_c)r^{-6}_c\) when \(C^{\
mathrm{dir}}_6 = C^\mathrm{recip}_6\). In addition to this, a long-range dispersion correction can be applied to correct for the approximation using a combination rule in reciprocal space. This
correction assumes, as for the cut-off LJ potential, a uniform particle distribution. But since the error of the combination rule approximation is very small this long-range correction is not
necessary in most cases. Also note that this homogenous correction does not correct the surface tension, which is an inhomogeneous property.
Using LJ-PME#
As an example for using Particle-mesh Ewald summation for Lennard-Jones interactions in GROMACS, specify the following lines in your mdp file:
vdwtype = PME
rvdw = 0.9
vdw-modifier = Potential-Shift
rlist = 0.9
rcoulomb = 0.9
fourierspacing = 0.12
pme-order = 4
ewald-rtol-lj = 0.001
lj-pme-comb-rule = geometric
The same Fourier grid and interpolation order are used if both LJ-PME and electrostatic PME are active, so the settings for fourierspacing and pme-order are common to both. ewald-rtol-lj controls the
splitting between direct and reciprocal space in the same way as ewald-rtol. In addition to this, the combination rule to be used in reciprocal space is determined by lj-pme-comb-rule. If the current
force field uses Lorentz-Berthelot combination rules, it is possible to set lj-pme-comb-rule = geometric in order to gain a significant increase in performance for a small loss in accuracy. The
details of this approximation can be found in the section above.
Note that the use of a complete long-range dispersion correction means that as with Coulomb PME, rvdw is now a free parameter in the method, rather than being necessarily restricted by the
force-field parameterization scheme. Thus it is now possible to optimize the cutoff, spacing, order and tolerance terms for accuracy and best performance.
Naturally, the use of LJ-PME rather than LJ cut-off adds computation and communication done for the reciprocal-space part, so for best performance in balancing the load of parallel simulations using
PME-only ranks, more such ranks should be used. It may be possible to improve upon the automatic load-balancing used by mdrun. | {"url":"https://manual.gromacs.org/documentation/current/reference-manual/functions/long-range-vdw.html","timestamp":"2024-11-03T08:51:14Z","content_type":"text/html","content_length":"94470","record_id":"<urn:uuid:ab2ab7e1-e3fb-44d7-8108-39e941686c78>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00742.warc.gz"} |
Sixteen Soldiers
This photograph was taken in August 1996 at a hill temple near Khejarala, Rajesthan, India. Carved into the rock is the board for the game "Sixteen Soldiers" or "Cows and Leopards".
Each player has sixteen stones placed on the intersection of the lines, one player to the left of the board and the other to the right. Players move alternatively and can move in any direction along
a line to an adjacent point. A capture is made by jumping over an enemy piece to a vacant point beyond - several pieces can be captured in one move by a series of leaps over single enemy pieces. A
player loses when all their pieces have been captured. As an additional rule it is suggested that if a player fails to make a capture, the piece is "huffed" and removed from the board. A variant
gives each player seven extra pieces, placed on the points of the triangle to the player's left.
You can play the game on the grid above by dragging the soldiers from point to point.
This game is based on an extended four by four grid of squares and is called "Sixteen Soldiers". What would be the name of a game based on a five by five grid of squares? Would it be "Twenty Five
Soldiers"? What would the board look like? Investigate...
Reference: "Board games Around The World" Robbie Bell and Michael Cornelius. Cambridge University Press 1988 ISBN 0 521 35924 4
Strategy Games photographs and diagrams by Transum are licensed under a Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England and Wales License. Permissions beyond the scope of this
license may be available at "Contact Us".
Click on a link below to explore other parts of the Transum web site:
Fun Maths Home Transum Software Maths Map Times Tables Strategy Games Go Maths
Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your | {"url":"https://www.transum.org/Software/Fun_Maths/Games/Sixteen_Soldiers.asp","timestamp":"2024-11-08T04:04:39Z","content_type":"text/html","content_length":"23937","record_id":"<urn:uuid:2467bf9a-8617-403b-82b1-53dc9a996df6>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00274.warc.gz"} |
7.2 Kinetic Energy and the Work-Energy Theorem
43 7.2 Kinetic Energy and the Work-Energy Theorem
• Explain work as a transfer of energy and net work as the work done by the net force.
• Explain and apply the work-energy theorem.
Work Transfers Energy
What happens to the work done on a system? Energy is transferred into the system, but in what form? Does it remain in the system or move on? The answers depend on the situation. For example, if the
lawn mower in Chapter 7.1 Figure 1(a) is pushed just hard enough to keep it going at a constant speed, then energy put into the mower by the person is removed continuously by friction, and eventually
leaves the system in the form of heat transfer. In contrast, work done on the briefcase by the person carrying it up stairs in Chapter 7.1 Figure 1(d) is stored in the briefcase-Earth system and can
be recovered at any time, as shown in Chapter 7.1 Figure 1(e). In fact, the building of the pyramids in ancient Egypt is an example of storing energy in a system by doing work on the system. Some of
the energy imparted to the stone blocks in lifting them during construction of the pyramids remains in the stone-Earth system and has the potential to do work.
In this section we begin the study of various types of work and forms of energy. We will find that some types of work leave the energy of a system constant, for example, whereas others change the
system in some way, such as making it move. We will also develop definitions of important forms of energy, such as the energy of motion.
Net Work and the Work-Energy Theorem
We know from the study of Newton’s laws in Chapter 4 Dynamics: Force and Newton’s Laws of Motion that net force causes acceleration. We will see in this section that work done by the net force gives
a system energy of motion, and in the process we will also find an expression for the energy of motion.
Let us start by considering the total, or net, work done on a system. Net work is defined to be the sum of work done by all external forces—that is, net work is the work done by the net external
Figure 1(a) shows a graph of force versus displacement for the component of the force in the direction of the displacement—that is, an Figure 1(b) shows a more general process where the force varies.
The area under the curve is divided into strips, each having an average force
Figure 1. (a) A graph of F cos θ vs. d, when F cos θ is constant. The area under the curve represents the work done by the force. (b) A graph of F cos θ vs. d in which the force varies. The work
done for each interval is the area of each strip; thus, the total area under the curve equals the total work done.
Net work will be simpler to examine if we consider a one-dimensional situation where a force is used to accelerate an object in a direction parallel to its initial velocity. Such a situation occurs
for the package on the roller belt conveyor system shown in Figure 2.
Figure 2. A package on a roller belt is pushed horizontally through a distance d.
The force of gravity and the normal force acting on the package are perpendicular to the displacement and do no work. Moreover, they are also equal in magnitude and opposite in direction so they
cancel in calculating the net force. The net force arises solely from the horizontal applied force
The effect of the net force Example 1.) By using Newton’s second law, and doing some algebra, we can reach an interesting conclusion. Substituting
To get a relationship between net work and the speed given to a system by the net force acting on it, we take Chapter 2.5 Motion Equations for Constant Acceleration in One Dimension for the change in
speed over a distance
This expression is called the work-energy theorem, and it actually applies in general (even for forces that vary in direction and magnitude), although we have derived it for the special case of a
constant force parallel to the displacement. The theorem implies that the net work on a system equals the change in the quantity
The net work on a system equals the change in the quantity
The quantity kinetic energy (KE) of a mass Translational kinetic energy is distinct from rotational kinetic energy, which is considered later.) In equation form, the translational kinetic energy,
is the energy associated with translational motion. Kinetic energy is a form of energy associated with the motion of a particle, single body, or system of objects moving together.
We are aware that it takes energy to get an object, like a car or the package in Figure 2, up to speed, but it may be a bit surprising that kinetic energy is proportional to speed squared. This
proportionality means, for example, that a car traveling at 100 km/h has four times the kinetic energy it has at 50 km/h, helping to explain why high-speed collisions are so devastating. We will now
consider a series of examples to illustrate various aspects of work and energy.
Example 1: Calculating the Kinetic Energy of a Package
Suppose a 30.0-kg package on the roller belt conveyor system in Figure 2 is moving at 0.500 m/s. What is its kinetic energy?
Because the mass
The kinetic energy is given by
Entering known values gives
which yields
Note that the unit of kinetic energy is the joule, the same as the unit of work, as mentioned when work was first defined. It is also interesting that, although this is a fairly massive package, its
kinetic energy is not large at this relatively low speed. This fact is consistent with the observation that people can move packages like this without exhausting themselves.
Example 2: Determining the Work to Accelerate a Package
Suppose that you push on the 30.0-kg package in Figure 2 with a constant force of 120 N through a distance of 0.800 m, and that the opposing friction force averages 5.00 N.
(a) Calculate the net work done on the package. (b) Solve the same problem as in part (a), this time by finding the work done by each force that contributes to the net force.
Strategy and Concept for (a)
This is a motion in one dimension problem, because the downward force (from the weight of the package) and the normal force have equal magnitude and opposite direction, so that they cancel in
calculating the net force, while the applied force, friction, and the displacement are all horizontal. (See Figure 2.) As expected, the net work is the net force times distance.
Solution for (a)
The net force is the push force minus friction, or
Discussion for (a)
This value is the net work done on the package. The person actually does more work than this, because friction opposes the motion. Friction does negative work and removes some of the energy the
person expends and converts it to thermal energy. The net work equals the sum of the work done by each individual force.
Strategy and Concept for (b)
The forces acting on the package are gravity, the normal force, the force of friction, and the applied force. The normal force and force of gravity are each perpendicular to the displacement, and
therefore do no work.
Solution for (b)
The applied force does work.
The friction force and displacement are in opposite directions, so that $latex \boldsymbol{\theta = 180^{\circ}} $, and the work done by friction is
So the amounts of work done by gravity, by the normal force, by the applied force, and by friction are, respectively,
The total work done as the sum of the work done by each force is then seen to be
Discussion for (b)
The calculated total work
Example 3: Determining Speed from Work and Energy
Find the speed of the package in Figure 2 at the end of the push, using work and energy concepts.
Here the work-energy theorem can be used, because we have just calculated the net work,
The work-energy theorem in equation form is
Solving for
Solving for the final speed as requested and entering known values gives
Using work and energy, we not only arrive at an answer, we see that the final kinetic energy is the sum of the initial kinetic energy and the net work done on the package. This means that the work
indeed adds to the energy of the package.
Example 4: Work and Energy Can Reveal Distance, Too
How far does the package in Figure 2 coast after the push, assuming friction remains constant? Use work and energy considerations.
We know that once the person stops pushing, friction will bring the package to rest. In terms of energy, friction does negative work until it has removed all of the package’s kinetic energy. The work
done by friction is the force of friction times the distance traveled times the cosine of the angle between the friction force and displacement; hence, this gives us a way of finding the distance
traveled after the person stops pushing.
The normal force and force of gravity cancel in calculating the net force. The horizontal friction force is then the net force, and it acts opposite to the displacement, so
and so
This is a reasonable distance for a package to coast on a relatively friction-free conveyor system. Note that the work done by friction is negative (the force is in the opposite direction of motion),
so it removes the kinetic energy.
Some of the examples in this section can be solved without considering energy, but at the expense of missing out on gaining insights about what work and energy are doing in this situation. On the
whole, solutions involving energy are generally shorter and easier than those using kinematics and dynamics alone.
Section Summary
• The net work
• Work done on an object transfers energy to the object.
• The translational kinetic energy of an object of mass
• The work-energy theorem states that the net work
Conceptual Questions
1: The person in Figure 3 does work on the lawn mower. Under what conditions would the mower gain energy? Under what conditions would it lose energy?
Figure 3.
2: Work done on a system puts energy into it. Work done by a system removes energy from it. Give an example for each statement.
3: When solving for speed in Example 3, we kept only the positive root. Why?
Problems & Exercises
1: Compare the kinetic energy of a 20,000-kg truck moving at 110 km/h with that of an 80.0-kg astronaut in orbit moving at 27,500 km/h.
2: (a) How fast must a 3000-kg elephant move to have the same kinetic energy as a 65.0-kg sprinter running at 10.0 m/s? (b) Discuss how the larger energies needed for the movement of larger animals
would relate to metabolic rates.
3: Confirm the value given for the kinetic energy of an aircraft carrier in Chapter 7.6 Table 1. You will need to look up the definition of a nautical mile (1 knot = 1 nautical mile/h).
4: (a) Calculate the force needed to bring a 950-kg car to rest from a speed of 90.0 km/h in a distance of 120 m (a fairly typical distance for a non-panic stop). (b) Suppose instead the car hits a
concrete abutment at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a).
5: A car’s bumper is designed to withstand a 4.0-km/h (1.1-m/s) collision with an immovable object without damage to the body of the car. The bumper cushions the shock by absorbing the force over a
distance. Calculate the magnitude of the average force on a bumper that collapses 0.200 m while bringing a 900-kg car to rest from an initial speed of 1.1 m/s.
6: Boxing gloves are padded to lessen the force of a blow. (a) Calculate the force exerted by a boxing glove on an opponent’s face, if the glove and face compress 7.50 cm during a blow in which the
7.00-kg arm and glove are brought to rest from an initial speed of 10.0 m/s. (b) Calculate the force exerted by an identical blow in the gory old days when no gloves were used and the knuckles and
face would compress only 2.00 cm. (c) Discuss the magnitude of the force with glove on. Does it seem high enough to cause damage even though it is lower than the force with no glove?
7: Using energy considerations, calculate the average force a 60.0-kg sprinter exerts backward on the track to accelerate from 2.00 to 8.00 m/s in a distance of 25.0 m, if he encounters a headwind
that exerts an average force of 30.0 N against him.
net work
work done by the net force, or vector sum of all the forces, acting on an object
work-energy theorem
the result, based on Newton’s laws, that the net work done on an object is equal to its change in kinetic energy
kinetic energy
the energy an object has by reason of its motion, equal to
Problems & Exercises
102 N | {"url":"https://pressbooks.uiowa.edu/clonedbook/chapter/kinetic-energy-and-the-work-energy-theorem/","timestamp":"2024-11-08T01:44:53Z","content_type":"text/html","content_length":"226391","record_id":"<urn:uuid:74a14074-ea97-42f9-9519-26721d61cdd3>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00383.warc.gz"} |
center of gravity calculator using x y and q calculation for Calculations
02 Mar 2024
Popularity: ⭐⭐⭐
Center of Gravity Calculator
This calculator provides the calculation of the center of gravity of two points using their x, y coordinates and masses.
Calculation Example: The center of gravity is the point at which the entire weight of an object is considered to act. It is a useful concept in physics and engineering for understanding the stability
and balance of objects.
Related Questions
Q: What is the importance of the center of gravity in engineering?
A: The center of gravity is important in engineering as it helps engineers to design structures and machines that are stable and balanced. By understanding the center of gravity, engineers can ensure
that objects will not tip over or collapse.
Q: How is the center of gravity used in everyday life?
A: The center of gravity is used in everyday life in a variety of ways. For example, it is used to design chairs and other furniture so that they are comfortable and stable. It is also used to design
cars and other vehicles so that they are safe and handle well.
| —— | —- | —- |
x1 X-coordinate of First Point m
y1 Y-coordinate of First Point m
q1 Mass of First Point kg
x2 X-coordinate of Second Point m
y2 Y-coordinate of Second Point m
q2 Mass of Second Point kg
Calculation Expression
X-coordinate of Center of Gravity: The x-coordinate of the center of gravity is given by xCG = (x1 * q1 + x2 * q2) / (q1 + q2)
(x1 * q1 + x2 * q2) / (q1 + q2)
Y-coordinate of Center of Gravity: The y-coordinate of the center of gravity is given by yCG = (y1 * q1 + y2 * q2) / (q1 + q2)
(y1 * q1 + y2 * q2) / (q1 + q2)
Calculated values
Considering these as variable values: q1=1.0, q2=2.0, y1=0.0, x1=0.0, y2=0.0, x2=2.0, the calculated value(s) are given in table below
| —— | —- |
X-coordinate of Center of Gravity 1.33333
Y-coordinate of Center of Gravity 0.0
Similar Calculators
Calculator Apps
Matching 3D parts for center of gravity calculator using x y and q calculation for Calculations
App in action
The video below shows the app in action. | {"url":"https://blog.truegeometry.com/calculators/center_of_gravity_calculator_using_x_y_and_q_calculation_for_Calculations.html","timestamp":"2024-11-11T11:17:55Z","content_type":"text/html","content_length":"28431","record_id":"<urn:uuid:b05f3ab3-7123-43bc-b27c-8bb38f46de40>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00345.warc.gz"} |
Initial decay of flow properties of planar, cylindrical and spherical blast waves
Analytical expressions are presented for the initial decay of all major flow properties just behind planar, cylindrical, and spherical shock wave fronts whose trajectories are known as a function of
either distance versus time or shock overpressure versus distance. These expressions give the time and/or distance derivatives of the flow properties not only along constant time and distance lines
but also along positive and negative characteristic lines and a fluid-particle path. Conventional continuity, momentum and energy equations for the nonstationary motion of an inviscid, non-heat
conducting, compressible gas are used in their derivation, along with the equation of state of a perfect gas. All analytical expressions are validated by comparing the results to those obtained
indirectly from known self-similar solutions for planar, cylindrical and spherical shock-wave flows generated both by a sudden energy release and by a moving piston. Futhermore, time derivatives of
pressure and flow velocity are compared to experimental data from trinitrotoluene (TNT), pentolite, ammonium nitrate-fuel oil (ANFO) and propane-oxygen explosions, and good agreement is obtained.
NASA STI/Recon Technical Report N
Pub Date:
October 1983
□ Explosions;
□ Flow Characteristics;
□ Shock Fronts;
□ Shock Waves;
□ Ammonium Nitrates;
□ Compressible Flow;
□ Gas Flow;
□ Propane;
□ Trajectories;
□ Trinitrotoluene;
□ Fluid Mechanics and Heat Transfer | {"url":"https://ui.adsabs.harvard.edu/abs/1983STIN...8412416S/abstract","timestamp":"2024-11-10T19:52:32Z","content_type":"text/html","content_length":"37040","record_id":"<urn:uuid:19e1908e-4320-4694-8fb3-949f9cff4d0e>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00597.warc.gz"} |
Implementing a Language Agent Tree Search with LangGraph VS Burr
• The Different Orchestration Frameworks
• Tree of Thoughts
• ReAct
• The Language Agent Tree Search Method (LATS)
• Implementing LATS with LangGraph
• Implementing LATS with Burr
The Different Orchestration Frameworks
In the world of orchestration frameworks for LLM applications, a few axes have emerged. There are many overlaps in the capabilities of the different frameworks, but I tend to separate those by their
• Micro-orchestration: I refer to Micro-orchestration in LLM pipelines as the fine-grained coordination and management of individual LLM interactions and related processes. It is more about the
granular details of how data flows into, through, and out of language models within a single task or a small set of closely related tasks. It can involve things like:
□ Prompt engineering and optimization
□ Input preprocessing and output postprocessing
□ Handling of model-specific parameters and configurations
□ Chaining of multiple LLM calls within a single logical operation
□ Integration of external tools or APIs at a task-specific level
The best examples of that are LangChain, LlamaIndex, Haystack, and AdalFlow.
• Macro-orchestration: Macro-orchestration in LLM pipelines involves the high-level design, coordination, and management of complex workflows that may incorporate multiple LLM interactions, as well
as other AI and non-AI components. It focuses on the overall structure and flow of larger systems or applications. It involves things like:
□ Workflow design and management
□ State management across multiple steps or processes
□ Parallel processing and distributed computation
□ Error handling and recovery at a system level
□ Scalability and performance optimization of the entire pipeline
□ Integration of diverse AI services and traditional software components
Example operations: Multi-agent systems, long-running tasks with multiple stages, complex decision trees involving multiple LLM and non-LLM components. This is a newer type of orchestration for
LLM pipelines, and LangGraph seems to be leading the charge. Burr by Dagworks is also one of the main actors in the space.
• Agentic Design Frameworks: These frameworks focus on creating and managing autonomous or semi-autonomous AI agents that can perform complex tasks, often involving multiple steps, decision-making,
and interaction with other agents or systems. The main characteristics are:
□ Allowing the creation of multiple specialized agents that can work together on complex tasks.
□ Agents can make decisions based on their programming, goals, and environmental inputs.
□ Inter-agent communication and coordination between different agents.
□ Include mechanisms for breaking down complex tasks into smaller, manageable subtasks.
□ Persistent memory and state management for agents across multiple interactions or task steps.
□ Users can define various agent roles with specific capabilities and responsibilities.
□ Allowing for human-in-the-loop oversight and intervention in the agent's processes.
Most frameworks have their own approach to agentic design, but Autogen and CrewAI tend to separate themselves by having a unique angle to the problem.
• Optimizer frameworks: These frameworks use algorithmic approaches, often inspired by machine learning techniques like backpropagation, to optimize prompts, outputs, and overall system performance
in LLM applications.
Key characteristics of optimizer frameworks:
□ They use structured algorithms to iteratively improve prompts and outputs.
□ They can automatically adjust prompts or system parameters to improve performance.
□ The optimization process is guided by specific performance metrics or objectives.
This is a newer category of orchestrator, and it has been led by frameworks like DSPY and TextGrad. To my knowledge, AdalFlow is currently the most mature framework in the domain.
In this newsletter, I want to show how to use micro-orchestration and macro-orchestration to implement the Language Agent Tree Search Method (LATS). This method can be viewed as a mix of the
tree-of-thought and the ReAct methods. Specifically, I want to showcase the difference in implementation between LangGraph and Burr. You can find the whole code at the end of this newsletter.
Tree of Thoughts
Before diving into LATS, it can be helpful to understand the Tree of Thoughts method. Tree of Thoughts (ToT) is itself an extension of the Chain of Thoughts (CoT) strategy. The idea is to induce a
step-by-step reasoning for the LLM before providing an answer. Here is an example of a typical CoT prompt:
Solve the following problem step by step:
Question: A store is having a 20% off sale. If a shirt originally costs $45, how much will it cost after the discount, including a 7% sales tax?
Let's approach this step-by-step:
1) First, let's calculate the discount amount:
20% of $45 = 0.20 × $45 = $9
2) Now, let's subtract the discount from the original price:
$45 - $9 = $36
3) This $36 is the price before tax. Now we need to add the 7% sales tax.
7% of $36 = 0.07 × $36 = $2.52
4) Finally, let's add the tax to the discounted price:
$36 + $2.52 = $38.52
Therefore, the shirt will cost $38.52 after the discount and including sales tax.
Now, solve this new problem using the same step-by-step approach:
Question: A bakery sells cookies for $2.50 each. If you buy 3 dozen cookies and there's a buy-two-get-one-free promotion, how much will you pay in total, including an 8% sales tax?
In this example, it is a one-shot example prompt, but it is typical to use few-shot example prompts. We can also induce step-by-step reasoning by using the zero-shot CoT approach:
Solve the following problem. Let's approach this step by step:
Question: A store is having a 30% off sale. If a shirt originally costs $60, how much will it cost after the discount, including an 8% sales tax?
The idea is that the LLM, by reading its own reasoning, will tend to produce more coherent, logical, and accurate responses.
Considering the tendency of LLMs to hallucinate, it is often a good strategy to generate multiple reasoning paths so we can choose the better one. This is commonly referred to as the Self-Consistency
This approach allows one to choose the best overall answer, but it is not able to distinguish the level of quality of the different reasoning steps. The idea behind ToT is to induce multiple possible
reasoning steps and to choose the best reasoning path:
For example, here is how we could induce the generation of the next step:
Consider multiple approaches to solve the following problem. For each approach, provide the first step of calculation:
Question: A store is having a 30% off sale. If a shirt originally costs $60, how much will it cost after the discount, including an 8% sales tax?
Possible first steps:
For each first step, briefly describe how you would continue the calculation.
The resulting response would need to be parsed to extract the possible steps. The typical approach to understanding what step is better at each level is to quantitatively assess them with a separate
LLM call. Here is an example of such a prompt:
Evaluate the following step in solving this problem:
Problem: A store is having a 30% off sale. If a shirt originally costs $60, how much will it cost after the discount, including an 8% sales tax?
Previous steps:
[Previous steps]
Current step to evaluate:
[Insert current step here]
Rate this step on a scale of 1-10 based on the following criteria:
1. Correctness: Is the calculation mathematically accurate?
2. Relevance: Does this step directly contribute to solving the problem?
3. Progress: How much closer does this step bring us to the final answer?
4. Consistency: How well does this step follow from the previous steps?
Provide a brief explanation for your ratings.
Again, the output would need to be parsed to extract the relevant information. We can iteratively expand reasoning paths, assess them, and choose the better path:
We can repeat this process at every level:
Keep reading with a 7-day free trial
Subscribe to The AiEdge Newsletter to keep reading this post and get 7 days of free access to the full post archives. | {"url":"https://newsletter.theaiedge.io/p/implementing-a-language-agent-tree","timestamp":"2024-11-11T19:13:33Z","content_type":"text/html","content_length":"191146","record_id":"<urn:uuid:9dac6f99-3952-4ef8-804f-90ba6e691d6a>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00596.warc.gz"} |
Comparison of electrodynamics theories
2 Comparison of electrodynamics theories
2.1 Maxwell's electrodynamics
Maxwell's electrodynamics is currently the standard electrodynamics and comprises (for vacuum) four differential equations
$$\nabla\cdot\vec{E} = \frac{\rho}{\varepsilon_0},$$ (2.1.1)
$$\nabla\cdot\vec{B} = 0,$$ (2.1.2)
$$\nabla\times\vec{E} = -\frac{\partial\vec{B}}{\partial t},$$ (2.1.3)
$$\nabla\times\vec{B} = \mu_0\,\vec{j} + \frac{1}{c^2}\,\frac{\partial\vec{E}}{\partial t}$$ (2.1.4)
and the supplementary formula
$$\vec{F} = q_d\,\vec{E} + q_d\,\vec{v}\times\vec{B}.$$ (2.1.5)
The formula (
) is known as the Lorentz force. The equation provides the force $\vec{F}(\vec{r},\vec{v},t)$, which is caused by the electric field $\vec{E}(\vec{r},t)$ and the magnetic field $\vec{B}(\vec{r},t)$
on a point-like test charge $q_d$, which is located at time $t$ at location $\vec{r}$. The fields $\vec{E}(\vec{r},t)$ and $\vec{B}(\vec{r},t)$ are quantities that can be calculated by inserting the
charge density $\rho(\vec{r},t)$ and current density $\vec{j}(\vec{r},t)$ and solving the differential equation system (
) to (
). However, solving systems of partial differential equations requires considerable experience and mathematical skills and is usually only possible for simple problems.
The velocity $\vec{v}$ is of particular importance. Usually, one uses for $\vec{v}$ the velocity of the test charge $q_d$ in the reference frame of the laboratory, i.e. in the same frame in which the
field-generating device is located. Since electrical currents in metallic conductors consist of many charge carriers that only move extremely slowly, $\vec{v}$ in electrical engineering is almost
always identical to the relative speed between the test charge $q_d$ and the field-generating charges in the wires and metallic conductors.
The fields $\vec{E}(\vec{r},t)$ and $\vec{B}(\vec{r},t)$ are auxiliary quantities, since in the end only the force $\vec{F}(\vec{r},\vec{v},t)$ can be measured. It is a convention that the quantity $
\vec{F}(\vec{r},\vec{v} = \vec{0},t)/q_d$ is referred to as the electric field strength $\vec{E}(\vec{r},t)$. The remaining part of the Lorentz force (
) is the magnetic component.
Note that the magnetic field $\vec{B}$ is a quantity that was introduced to describe the force between permanent magnets. However, Oersted and Ampere discovered at the beginning of the 19th century
that these magnetic forces are caused by electric currents [
]. This also applies to permanent magnets, as they contain numerous small circular currents. The magnetic field was therefore actually already an outdated concept around 1850. Unfortunately, it was
reintegrated into electrodynamics due to the success of Maxwell's equations in describing electromagnetic waves.
2.2 Weber electrodynamics
Weber electrodynamics is a very old electrodynamics from the middle of the 19th century [
] [
] [
] [
], i.e. from a time before the discovery of electromagnetic waves. Weber electrodynamics is a very compact and elegant representation of the scientific knowledge of that time in terms of a single
equation known as the Weber force.
According to the state of knowledge at that time, it was believed that the electromagnetic force generated by a point charge $q_s$ onto another point charge $q_d$ could be fully described by the
$$\vec{F} = \frac{q_s\,q_d}{4\,\pi\,\varepsilon_0}\,\left(1 + \frac{v^2}{c^2} - \frac{3}{2}\left(\frac{\vec{r}}{r}\cdot\frac{\vec{v}}{c}\right)^2\right)\,\frac{\vec{r}}{r^3},$$ (2.2.1)
with $\vec{r}$ being the distance vector
$$\vec{r} := \vec{r}_d(t) - \vec{r}_s(t)$$ (2.2.2)
of the point charges $q_s$ and $q_d$ with the trajectories $\vec{r}_d(t)$ and $\vec{r}_s(t)$. In contrast to the Coulomb force, which is well known even today, the Weber force (
) also depends on the relative velocity
$$\vec{v} := \dot{\vec{r}}_d(t) - \dot{\vec{r}}_s(t).$$ (2.2.3)
It is interesting and important to emphasize that the Weber force works excellently in the case of direct currents and low-frequency alternating currents and makes it possible to explain some effects
that are difficult to understand on the basis of Maxwell's equations alone [
] [
] [
]. Obviously, a magnetic field is not needed for many problems in electrical engineering. Instead, the Weber force shows that the Lorentz force is a multi-particle effect and is created by different
relative velocities of the charge carriers in a line current. The Weber force is therefore more than just a mathematical description, as it also represents a compression of knowledge and an
interpretative explanation of magnetism.
Unfortunately, the Weber force cannot describe electromagnetic waves, at least not directly and without a transmission medium. This can be recognized immediately by the fact that the Weber force $\
vec{F}(\vec{r},\vec{v},t)$ depends only on the locations and velocities of the point charges at time $t$. The Weber force is therefore an instantaneous force that propagates from $q_s$ to $q_d$
without any delay. This contradicts numerous important effects, which unfortunately renders it largely useless for electrical engineering.
2.3 Weber-Maxwell electrodynamics
Weber-Maxwell electrodynamics is - as far as electrical engineering is concerned - equivalent to Maxwell's electrodynamics [
] [
] [
] [
]. However, it is not based on charge and current densities, but works with pairs of point charges, similar to Coulomb's law or the Weber force (
), both of which are included as special cases.
The formula for the electromagnetic force that a point charge $q_s$ with trajectory $\vec{r}_s(t)$ exerts on another point charge $q_d$ with trajectory $\vec{r}_d(t)$ is
$$\vec{F} = \frac{q_d\,q_s\,\gamma(v)\,\left(\left(\vec{r}\,c + r\,\vec{v}\right)\left(c^2 - v^2 - \vec{r}\cdot\vec{a}\right) + \vec{a}\,r\,\left(r\,c + \vec{r}\cdot\vec{v}\right)\right)}{4\, (2.3.1)
\pi\,\varepsilon_0\,\left(r\,c + \vec{r}\cdot\vec{v}\right)^3},$$
in Weber-Maxwell electrodynamics, whereby
$$\vec{r} := \vec{r}_d(\tau) - \vec{r}_s(\tau)$$ (2.3.2)
is the retarded distance vector
$$\vec{v} := \dot{\vec{r}}_d(\tau) - \dot{\vec{r}}_s(\tau)$$ (2.3.3)
the retarded difference velocity and
$$\vec{a} := \ddot{\vec{r}}_d(\tau) - \ddot{\vec{r}}_s(\tau)$$ (2.3.4)
the retarded difference acceleration. $\gamma(.)$ is the Lorentz factor. In addition, one needs the time $\tau$, which can be calculated iteratively by means of equation
$$\tau = t - \frac{\Vert\vec{r}_d(\tau) - \vec{r}_s(\tau)\Vert}{c}.$$ (2.3.5)
In order to find the value of $\tau$, any initial value (e.g. $\tau = t$) can be chosen and recursively inserted until $\tau$ does not change any longer. The fixed-point iteration converges always as
long as the difference speed between the two point charges is less than the speed of light $c$. In somewhat simplified terms, $\tau$ corresponds to the time when the force has left the charge $q_s$
to reach the charge $q_d$ at time $t$.
As one can see, equation (
) is not a differential equation. If we know the trajectories $\vec{r}_s(t)$ and $\vec{r}_d(t)$ for all times less than or equal to $t$, we can easily calculate the force $\vec{F}(\vec{r},\vec{v},t)$
at time $t$. This can be achieved by means of a simple computer program in Python or C++. Knowledge of vector analysis and differential geometry is not required.
2.4 Relationship between the theories
Maxwell's electrodynamics and Weber-Maxwell electrodynamics are equivalent for non-relativistic velocities, because equation (
) is
the solution of Maxwell's equations
for point charges [
]. The proof can be found
. The restriction to the non-relativistic regime is necessary because, strictly speaking, the Weber-Maxwell force only represents the solution of the Maxwell equations for an arbitrarily moving $q_s$
but a resting $q_d$. The generalization to arbitrarily moving $q_d$ was achieved by means of a Galilean transformation. This is only an approved method in the non-relativistic regime. Note, however,
that the equation (
) together with the equation (
) nevertheless fulfills Einstein's two postulates.
That the principle of relativity is fulfilled can be recognized by the fact that the equation (
) does not depend on the choice of the reference frame. This means that the formulas of Weber-Maxwell electrodynamics have the same form in every inertial frame and even in every non-inertial frame,
because the coordinate transformations only affect $\vec{r}_d(t)$ and $\vec{r}_s(t)$. Furthermore, it can be seen that due to equation (
) the electromagnetic force cannot propagate faster than light in any frame of reference.
The fact that Einstein's two postulates are satisfied in Weber-Maxwell electrodynamics even without the Lorentz transformation is a major advantage. In contrast, Maxwell's electrodynamics can only be
used with the Lorentz transformation, even at low difference velocities. In electrical engineering, this is practically always ignored, which can cause subtle problems, as the solutions are then only
approximations that violate the conservation of momentum, for example.
In Weber-Maxwell electrodynamics, however, it is guaranteed that the conservation of momentum applies even at very high velocities. This can be recognized by the fact that in equation (
), an exchange of source charge and target charge only results in the sign being reversed. This means that Newton's third law is fulfilled.
It is also important that Weber-Maxwell electrodynamics is compatible with Weber electrodynamics, since the approximations $a \approx 0$ and $v \ll c$ lead to the Weber force (
). When demonstrating the equivalence, it should be noted that $\vec{r}$ is the non-retarded distance vector in Weber electrodynamics and the retarded distance vector in Weber-Maxwell
electrodynamics. The proof can be found
As one can see, Weber-Maxwell electrodynamics combines the advantages of both philosophies (Maxwell's electrodynamics and Weber electrodynamics) and eliminates the individual drawbacks. Weber-Maxwell
electrodynamics is also compatible with the Newtonian electrodynamics of Peter and Neal Graneau [
], as this forms the quasi-static limiting case of Weber-Maxwell electrodynamics. However, Weber-Maxwell electrodynamics is not suitable for speeds close to the speed of light, as it is still
necessary to investigate how relativistic mechanics has to be applied. This is the subject of current research. | {"url":"https://quantino-theory.org/index.php?page=1&version=1&lang=en","timestamp":"2024-11-10T20:25:56Z","content_type":"text/html","content_length":"19691","record_id":"<urn:uuid:d418ee87-a088-4776-bb7b-d1d7602180eb>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00012.warc.gz"} |
Protein structure retracted after investigation into “highly improbable features,” journal calls it fraud
In 2010, a group of [DEL:crystallographers:DEL] immunologists and allergy researchers at the University of Salzburg published a paper in the Journal of Immunology claiming to have derived the
structure of a birch pollen allergen.
That structure, however, caught the attention of Bernhard Rupp, an eminent crystallographer. In January of this year, Rupp submitted a paper to Acta Crystallographica Section F pointing out problems
with it, which prompted the editors of the crystallography journal to contact the authors of the original paper a month later. Those authors, it turns out, agreed with Rupp, they write in a response
to his paper published in the April 2012 issue of Acta Crystallographica Section F:
This manuscript presents strong evidence that the diffraction data of Bet v 1d (PDB code 3k78 ; published in the J. Immunol. paper) are not derived from a diffraction experiment and that the
model of 3k78 contains some highly improbable features.
That, in turn, prompted the University of Salzburg to ask the Austrian Agency for Research Integrity (OeAWI) to investigate whether the “highly improbable features” were due to fraud
…on the part of author Robert Schwarzenbacher, the co-author solely responsible for the Bet v 1d structure and the crystallographic section of the J. Immunol. paper.
A report of that investigation is being prepared, according to the authors, but in the meantime, Schwarzenbacher confessed:
Author Schwarzenbacher admits to the allegations of data fabrication and deeply apologizes to the co-authors and the scientific community for all the problems this has caused.
But did he? The authors add:
Note added in proof: subsequent to the acceptance of this article for publication, author Schwarzenbacher withdrew his admission of the allegations.
Fatima Ferreira, who assumed responsibility as corresponding author of the paper when former corresponding author Gernot Achatz passed away last year, tells Retraction Watch:
I really have no explanation for that. We had elaborated the response and author Schwarzenbacher agreed to the text as it has been published now. However, later on, he contacted the Workers Union
and the Union sent us a letter where he withdrew his confession. This is the reason for the note added in proof.
We’ve reached out to Schwarzenebacher and others involved in the case to find out more details, and will update with anything we learn.
In the meantime, the authors asked the Protein Data Bank to retract the 3k78 entry, which happened in February. The Journal of Immunology paper — which has been cited 11 times, according to Thomson
Scientific’s Web of Knowledge, has not been retracted, however:
The main body of the J. Immunol. publication concerns the immunological study and the retraction of the crystallographic section does not affect the major conclusions. The Editors of J. Immunol.
have been informed about the problem with the structure 3k78 . Co-authors Zaborsky, Brunner, Wallner, Himly, Karl, Ferreira and Achatz were in no way involved in the generation of the
crystallographic data.
Ferreira tells us:
I think the crystallographic data should be retracted, since it was fabricated. However, the immunological data is solid. The conclusions in the paper can still hold without the crystallographic
My group has produced and characterized the recombinant allergen, which was used for the immunological experiments. The same batch was given to Schwarzenbacher for the crystallization, which
obviously was never done.
(This raises a related question: What’s the right place to publish critiques of papers? You’d think it would be the journal in which the original paper was published, but we often hear from
scientists who tell us that journals decline to publish their critiques because they lack space. That happened to a group that submitted a critique to Science recently who ended up publishing it in
PLoS Genetics, we learned on Twitter. And Keith Baggerly and Kevin Coombes, who did much of the heavy lifting to bring down the Anil Potti oeuvre, ended up publishing much of their analysis in the
Annals of Applied Statistics. We’ll probably come back to this issue, so we welcome all feedback.)
For their part, in an editorial titled “Another case of fraud in structural biology,” the editors of Acta Crystallographica Section F mince no words. They bemoan the fact that this is “another
instance of scientific misconduct in the literature of macromolecular crystallography,” referring to an episode that forced about a dozen retractions:
The second painful insult, disclosed in this issue, was also the act of a single individual. While it seems to be limited to one structure, one journal, one institution and fewer colleagues, and
may or may not attract the same amount of attention as the first, it is no less painful, no less disappointing.
The editors are clearly frustrated:
What motivates these hoaxes? It seems clear that the pressures on scientists early in their careers are so severe that a few are compelled to risk their careers in order to further them. The
dilemma is perhaps more fathomable when one considers the publication and citation metrics academic departments now use to evaluate staff, the difficulties crystallographers face in attracting
funds early in their careers, and the seemingly inexorable march toward commoditization of the crystallographic product. Can this be changed any time soon?
The editors cite the Validation Task Force’s new recommendations, published recently in Structure (which also had a retraction last year):
Where scientific publication is the concern, however, their impact will only be fully effective if all relevant journals follow the path of IUCr Journals and require that validation reports as
well as coordinates and structure factors be made available for peer review upon submission. It is equally important that all relevant journals include at least one expert crystallographer among
the referees for all submissions that describe crystallographic structure determinations, even if those structures are but one aspect of the paper.
That will take effort, they note:
In the current case, however, validation by re-refinement and electron-density evaluation seems to have been the key. To do this on a routine basis will put an extra burden on crystallographers
who serve as referees, making development of tools to ease that burden another worthwhile contribution.
Fraud will be tough to beat, they acknowledge:
It is important to note, however, that in neither of these cases was a single frame of data collected. Not one. This alone demands a redoubled effort to produce a universal system for deposition
and storage of original diffraction images.
Update, 11:30 a.m. Eastern, 4/2/12: First line edited to clarify that most of the people in the group were immunologists and allergy researchers. Schwarzenbacher was the only crystallographer on the
Please see our update including the news of Schwarzenbacher’s firing.
15 thoughts on “Protein structure retracted after investigation into “highly improbable features,” journal calls it fraud”
1. As for the “pressures on scientists early in their careers”, the suspect is this time a tenured professor. So, one can not so easily use this example as an argument that giving people permanent
and (compared to postdocs) well-paid positions does away with the problem.
2. Meanwhile, Acta Cryst. E (Structure Reports Online) just retracted 31 X-ray structures of small coordination complexes released between 2007 and 2009. The question is: is it the iceberg or the
tip of the iceberg? http://journals.iucr.org/e/issues/2012/04/00/me0450/index.html
3. it would be great if we had to deposit original diffraction data along with structure factors. the only problem is that structures often have gigabytes worth of images. considering that the cost
of data is getting ever cheaper, perhaps it is time to pull the trigger on this.
1. People will just write programs to fake the original diffraction data. While I agree this would be awesome, it won’t stop the true frauds.
4. It is really reprehensible that another scientist should spend time and effort investigating fraudulent work of somebody like this Schwarzenbacher… This also highlights the fact that outside
crystallographic field there is a dearth of knowledge needed to deal with x-ray structures. Most people take the pdbs as if they were physical entities, directly observable in the crystals… Nice
to see that intital clue came from a check in the PDB-REDO. I strongly urge everybody who – like me – fancies playing around with “structures” to consult this resource as well as PDBREPORT first
to get al least some idea how reliable and usable a given pdb file is.
1. I absolutely agree with you that there should be more verification mechanisms available to check a structure, and that everyone should be checking for themselves. However, you also
highlighted yourself that there is a large gap in terms of people who CAN analyze this data, and know what to look for in terms of recognizing data that just doesn’t match reality. I can look
all day at reports, but when it comes down to it, I just don’t know what I’m looking for. I think part of the solution is finding a way to make crystallographic/structural data more
accessible to non-structural scientists, whether through education, layman reports, or what have you.
1. The problem is that a lot of people use pdbs for downstream analysis anyways, be it as simple as designing or interpreting “mutants” in the proteins of interest, or something as
time-consuming as MD simulations of reaction mechanisms, etc. In this case PDBREPORT is a good start, because it doesn’t limit the statistics of the structure to the R-factors, which most
people indeed would have trouble interpreting, but gives simple enough to understand analysis of unusual bond distances and angles, fit to Ramachandran plot, etc. It should give one a
pause when the “structure” s/he wants to use for modeling, sports physically-implausible backbone and mauled side chains…
5. The editorial mentions the commoditization of crystallography. With the wonderful success of structural genomics (and the ready solution of easily crystallizable and solvable structures) the
assumption has grown that all structure solution is like this. Unfortunately it isn’t. In order to meet the structure-on-demand mentality, models are being built unsupported by density and, in
this case, apparently being made up.
6. I feel stricter technical control cannot overcome the basis of the problem. More emphasis should be put on moral issues in education of scientists and less emphasis should be put on
competitivity. Don’t we basically want to solve problems nature casts to us together?
1. I agree with this point. Unfortunately, to live it, you ahve to have the mindset that you will be honest no matter what money you might end up making either as a tenured profession whose
projects worked or a measley research associte whose projects did not work. Many can live this way, but family pressures may make this a hard road to walk. I know my own mother values success
and status in her son rather than die hard honesty.
1. NMH, well said ! based on personal experience these are truly words of wisdom !
2. It seems then if we paid tenured professors less and research associates more we should expect to see an improvement in the quality of science.
No argument from me there. Society has a tendency towards greater inequality of incomes and this inevitably leads to an increase in dishonesty in the upper echelons. Minimising income
inequality should lead to a more honest society (and better science as an added bonus).
7. ORF (Austrian TV) report that Schwarzenbacher has been fired by the university. See
http://salzburg.orf.at/news/stories/2528501/ (in German)
8. In the comment-sections of Austria newspaper are to be found some discussions wether Schwarzenbacher should pay back a “Marie-Curie-Stipendium” worth 1.7 Millionen Euro. The first news spoke of a
stipendium, but in facto it’s a grant for the time period from 2006 to 2010: http://cordis.europa.eu/projects/rcn/82405_en.html . There is no connection to the fraud.
9. I’ve been lurking in the reading room of Retraction Watch for a while and one thing that strikes me is the actual costs involved in dealing with falsified information.
The journals, through their staff, spend time working on this – unless their staff are volunteers that is a cost.
If it came from academia then the schools involved spend time dealing with it and those involved – another cost.
Over time any co-authors are going to pay unknown costs due to their connection to a fiasco. Positions and opportunities lost or not offered due to a taint.
Similarly: unsuccessful, or ineffective, research efforts spent by others relying on false data as a basis, a beginning or a lead could also be added to the accumulated costs arising from bad
data if the bad data hangs around unexposed long enough.
As technology improves capabilities to fake, as proliferation of diploma mills and predatory journals increases the ranks of entities willing to engage and foster this behaviour the problem gets
Those financial costs, pre World Wide Web, might have been easy to write off as a generic cost of doing science publishing – to be absorbed by the wider research world.
I can’t but imagine that, in this new world we live in, that part of the budgets of many institutions grows and grows.
Journals’ costs go up and subscription charges will rise.
Add all that up and it means the growing costs are a burden to Everyone.
If only there was some way to make the brazen fakers obligated to compensate the system financially . . . instead of what appears to be a free poke in the eye of science publishing if one chooses
to try it.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"url":"https://retractionwatch.com/2012/04/02/protein-structure-retracted-after-investigation-into-highly-improbable-features-journal-calls-it-fraud/","timestamp":"2024-11-12T12:25:46Z","content_type":"text/html","content_length":"106988","record_id":"<urn:uuid:6e8333c6-5687-481f-8479-54001568fa60>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00373.warc.gz"} |
EE 569 Digital Image Processing: Homework #2 solved
Problem 1: Edge Detection (50 %)
a) Sobel Edge Detector (Basic: 10%)
Implement the Sobel edge detector and apply to Tiger and Pig images as shown in Fig. 1 (a) and (b). Note
that you need to convert RGB images to grey-level image first. Include the following in your results:
Ø Normalize the x-gradient and the y-gradient values to 0-255 and show the results.
Ø Tune the thresholds (in terms of percentage) to obtain your best edge map. An edge map is a
binary image whose pixel values are either 0 (edge) or 255 (background)
b) Canny Edge Detector (Basic: 10%)
The Canny edge detector is an edge detection technique utilizing image’s intensity gradients and nonmaximum suppression with double thresholding. In this part, apply the Canny edge detector [1] to
both Tiger
and Pig images. You are allowed to use any online source code such as the Canny edge detector in the
MATLAB image processing toolbox or the OpenCV (i.e. Open Source Computer Vision Library). Generate
edge maps by trying different low and high thresholds. Answer the following questions:
1. Explain Non-maximum suppression in Canny edge detector in your own words.
2. How are high and low threshold values used in Canny edge detector?
Figure 1: Tiger and Pig images
c) Structured Edge (Advanced: 15%)
Apply the Structured Edge (SE) detector [2] to extract edge segments from a color image with online
source codes (released MATLAB toolbox: https://github.com/pdollar/edges). Exemplary edge maps
generated by the SE method for the House image are shown in Figure 2. You can apply the SE detector to
EE 569 Digital Image Processing: Homework #2
Professor C.-C. Jay Kuo Page 2 of 7
the RGB image directly without converting it into a grayscale image. Also, the SE detector will generate
a probability edge map. To obtain a binary edge map, you need to binarize the probability edge map with
a threshold.
1. Please digest the SE detection algorithm. Summarize it with a flow chart and explain it in your
own words (no more than 1 page, including both the flow chart and your explanation).
2. The Random Forest (RF) classifier is used in the SE detector. The RF classifier consists of multiple
decision trees and integrate the results of these decision trees into one final probability function.
Explain the process of decision tree construction and the principle of the RF classifier.
3. Apply the SE detector to Tiger and Pig images. State the chosen parameters clearly and justify
your selection. Compare and comment on the visual results of the Canny detector and the SE
House Probability edge map Binary edge map (with p>0.2)
Figure 2: The House image and its probability and binary edge maps obtained by the SE detector
d) Performance Evaluation (Advanced: 15%)
Ground Truth 1 Ground Truth 2 Ground Truth 3
Ground Truth 4 Ground Truth 5
Figure 3: Five ground truth edge maps for the Goose image
Perform quantitative comparison between different edge maps obtained by different edge detectors. The
ultimate goal of edge detection is to enable the machine to generate contours of priority to human being.
For this reason, we need the edge map provided by human (called the ground truth) to evaluate the quality
EE 569 Digital Image Processing: Homework #2
Professor C.-C. Jay Kuo Page 3 of 7
of a machine-generated edge map. However, different people may have different opinions about important
edge in an image. To handle the opinion diversity, it is typical to take the mean of a certain performance
measure with respect to each ground truth, e.g. the mean precision, the mean recall, etc. Figure 3 shows 5
ground truth edge maps for the Goose image from the Berkeley Segmentation Dataset and Benchmarks
500 (BSDS 500) [3]. To evaluate the performance of an edge map, we need to identify the error. All pixels
in an edge map belong to one of the following four classes:
(1) True positive: Edge pixels in the edge map coincide with edge pixels in the ground truth. These
are edge pixels the algorithm successfully identifies.
(2) True negative: Non-edge pixels in the edge map coincide with non-edge pixels in the ground
truth. These are non-edge pixels the algorithm successfully identifies.
(3) False positive: Edge pixels in the edge map correspond to the non-edge pixels in the ground truth.
These are fake edge pixels the algorithm wrongly identifies.
(4) False negative: Non-edge pixels in the edge map correspond to the true edge pixels in the ground
truth. These are edge pixels the algorithm misses.
Clearly, pixels in (1) and (2) are correct ones while those in (3) and (4) are error pixels of two different
types to be evaluated. The performance of an edge detection algorithm can be measured using the F
measure, which is a function of the precision and the recall.
Precision 😛 = #True Positive
#True Positive + #False Positive
Recall : R = #True Positive
#True Positive + #False Negative
F = 2 ⋅ P⋅ R
P + R
One can make the precision higher by decreasing the threshold in deriving the binary edge map. However,
this will result in a lower recall. Generally, we need to consider both precision and recall at the same time
and a metric called the F measure is developed for this purpose. A higher F measure implies a better edge
For the ground truth edge maps of Tiger and Pig images, evaluate the quality of edge maps obtained in
Parts (a)-(c) with the following:
1. Calculate the precision and recall for each ground truth (saved in .mat format) separately using the
function provided by the SE software package and, then, compute the mean precision and the mean
recall. Finally, calculate the F measure for each generated edge map based on the mean precision
and the mean recall. Please use a table to show the precision and recall for each ground truth, their
means and the final F measure. Comment on the performance of different edge detectors (i.e. their
pros and cons.)
2. The F measure is image dependent. Which image is easier to a get high F measure – Tiger or Pig?
Please provide an intuitive explanation to your answer.
3. Discuss the rationale behind the F measure definition. Is it possible to get a high F measure if
precision is significantly higher than recall, or vice versa? If the sum of precision and recall is a
constant, show that the F measure reaches the maximum when precision is equal to recall.
EE 569 Digital Image Processing: Homework #2
Professor C.-C. Jay Kuo Page 4 of 7
Problem 2: Digital Half-toning (50%)
a) Dithering (Basic: 15%)
Fig. 4 is grayscale image. Implement the following methods to convert it to half-toned images. In the
following discussion, F(i,j) and G(i,j) denote the pixel of the input and the output images at position (i,j),
respectively. Compare the results obtained by these algorithms in your report.
Figure 4: Golden Gate Bridge
1. Random thresholding
In order to break the monotones in the result from fixed thresholding, we may use a ‘random’ threshold.
The algorithm can be described as:
• For each pixel, generate a random number in the range 0 ∼ 255, so called ����(�,�)
• Compare the pixel value with ����(�,�). If it is greater, then map it to 255; otherwise, map it to 0,
� �,� = 0 �� 0 ≤ � �,� < ����(�,�) 255 �� ����(�,�) ≤ � �,� < 256 A choice of random threshold could be uniformly distributed random variable. Check your coding language documentation for proper
random variable generator. 2. Dithering Matrix Dithering parameters are specified by an index matrix. The values in an index matrix indicate how likely a dot will be turned on. For example, an index
matrix is given by �6 �,� = 1 2 3 0 where 0 indicates the pixel most likely to be turned on, and 3 is the least likely one. This index matrix is a special case of a family of dithering matrices first
introduced by Bayer [4]. The Bayer index matrices are defined recursively using the formula: EE 569 Digital Image Processing: Homework #2 Professor C.-C. Jay Kuo Page 5 of 7 �69 �,� = 4�9 �,� + 1
4�9 �,� + 2 4�9 �,� + 3 4�9 �,� The index matrix can then be transformed into a threshold matrix T for an input gray-level image with normalized pixel values (i.e. with its dynamic range between 0
and 255) by the following formula: � �, � = � �, � + 0.5 �6 ×255 where �6 denotes the number of pixels in the matrix. Since the image is usually much larger than the threshold matrix, the matrix is
repeated periodically across the full image. This is done by using the following formula: � �,� = 0 �� 0 ≤ � �,� ≤ �(� ����,� ����) 255 �(� ����,� ����) < � �,� < 256 Please create �6, �D, �E6
thresholding matrices and apply them to halftone Fig. 4. Compare your results. b) Error Diffusion (Basic: 15%) Convert the 8-bit Fig.4 image to a half-toned one using the error diffusion method. Show
the outputs of the following three variations and discuss these obtained results. Compare these results with dithering matrix. Which method do you prefer? Why? 1. Floyd-Steinberg’s error diffusion
with the serpentine scanning, where the error diffusion matrix is: 1 16 0 0 0 0 0 7 3 5 1 2. Error diffusion proposed by Jarvis, Judice, and Ninke (JJN), where the error diffusion matrix is: 1 48 0 0
0 0 0 0 0 0 0 0 0 0 0 7 5 3 5 7 5 3 1 3 5 3 1 3. Error diffusion proposed by Stucki, where the error diffusion matrix is: 1 42 0 0 0 0 0 0 0 0 0 0 0 0 0 8 4 2 4 8 4 2 1 2 4 2 1 Describe your own idea
to get better results. There is no need to implement it if you do not have time. However, please explain why your proposed method will lead to better results. EE 569 Digital Image Processing:
Homework #2 Professor C.-C. Jay Kuo Page 6 of 7 c) Color Halftoning with Error Diffusion (Advanced: 20%) Figure 5: The bird image[8] 1. Separable Error Diffusion One simple idea to achieve color
halftoning is to separate an image into CMY three channels and apply the Floyd-Steinberg error diffusion algorithm to quantize each channel separately. Then, you will have one of the following 8
colors, which correspond to the 8 vertices of the CMY cube at each pixel: W = (0,0,0), Y = (0,0,1), C = (0,1,0), M = (1,0,0), G = (0,1,1), R = (1,0,1), B = (1,1,0), K = (1,1,1) Note that (W, K), (Y,
B), (C, R), (M, G) are complementary color pairs. Please show and discuss the result of the half-toned color bird image. What is the main shortcoming of this approach? 2. MBVQ-based Error diffusion
Shaked et al. [5] proposed a new error diffusion method, which can overcome the shortcoming of the separable error diffusion method. Please read [5] carefully, and answer the following questions: 1)
Describe the key ideas on which the MBVQ-based Error diffusion method is established and give reasons why this method can overcome the shortcoming of the separable error diffusion method. 2)
Implement the algorithm using a standard error diffusion process (e.g. the FS error diffusion) and apply it to Fig. 5. Compare the output with that obtained by the separable error diffusion method.
EE 569 Digital Image Processing: Homework #2 Professor C.-C. Jay Kuo Page 7 of 7 Appendix: Problem 1: Edge detection Tiger.raw 481x321x3 24-bit color(RGB) Pig.raw 481x321x3 24-bit color(RGB)
Tiger.jpg 481x321x3 24-bit color(RGB) Pig.jpg 481x321x3 24-bit color(RGB) Tiger.mat (containing 5 ground truth images) Pig.mat (containing 5 ground truth images) House.png 481x321x3 24-bit color(RGB)
House_binary.png 481x321 logical House_probmap.png 481x321 8-bit gray Problem 2: Digital Half-toning bridge.raw 600x400 8-bit gray bird.raw 500x375x3 24-bit color(RGB) Reference Images Images in this
homework are from the BSDS 500 [3], the USC-SIPI image database [6], the Google images [7] or the ImageNet dataset [8]. References [1] J. Canny, “A computational approach to edge detection,” IEEE
Transactions on pattern analysis and machine intelligence, no. 6, pp. 679–698, 1986. [2] P. Dollár and C. L. Zitnick, “Structured forests for fast edge detection,” in Proceedings of the IEEE
International Conference on Computer Vision, 2013, pp. 1841–1848. [3] P. Arbelaez, M. Maire, C. Fowlkes, and J. Malik, “Contour detection and hierarchical image segmentation,” IEEE Trans. Pattern
Anal. Mach. Intell., vol. 33, no. 5, pp. 898–916, May 2011. [Online]. Available: http://dx.doi.org/10.1109/TPAMI.2010.161 [4] B. E. Bayer, “An optimum method for two-level rendition of
continuous-tone pictures,” SPIE MILESTONE SERIES MS, vol. 154, pp. 139–143, 1999 [5] D. Shaked, N. Arad, A. Fitzhugh, I. Sobel, "Color Diffusion: Error-Diffusion for Color Halftones", HP Labs
Technical Report, HPL-96-128R1, 1996. [6] [Online] http://sipi.usc.edu/database/ [7] [Online] http://images.google.com/ [8] [Online] http://www.image-net.org/ | {"url":"https://codeshive.com/questions-and-answers/ee-569-digital-image-processing-homework-2-solved/","timestamp":"2024-11-05T04:25:07Z","content_type":"text/html","content_length":"123175","record_id":"<urn:uuid:5cbee953-d3cc-4360-91dc-7047a3480409>","cc-path":"CC-MAIN-2024-46/segments/1730477027870.7/warc/CC-MAIN-20241105021014-20241105051014-00101.warc.gz"} |
Projections - (Elementary Differential Topology) - Vocab, Definition, Explanations | Fiveable
from class:
Elementary Differential Topology
Projections are mappings from one space to another, often used to simplify complex structures by focusing on certain dimensions or aspects of the original space. In the context of product and
quotient manifolds, projections help in breaking down these more complicated structures into simpler components, allowing for easier analysis and understanding of their properties. This concept is
crucial when discussing how different spaces interact with each other and how we can navigate between them through specific mappings.
congrats on reading the definition of Projections. now let's actually learn it.
5 Must Know Facts For Your Next Test
1. In the context of product manifolds, projections allow us to map points from the product space back to one of the component spaces, thus simplifying analysis.
2. For quotient manifolds, projections help in visualizing how points in the original manifold are identified or grouped together based on an equivalence relation.
3. Projections can be thought of as 'forgetting' certain dimensions while retaining others, which can be useful when studying higher-dimensional manifolds.
4. The projection map is continuous if the original manifold is topologically well-behaved, ensuring that the structure of the space is preserved in the mapping.
5. Understanding projections is vital for applications in differential geometry, where they play a role in defining smooth structures and differentiable functions on manifolds.
Review Questions
• How do projections assist in understanding product manifolds and their components?
□ Projections are essential for analyzing product manifolds because they provide a way to navigate between the combined space and its individual components. By using projections, one can map
points from the product manifold back to each factor space, which simplifies studying their properties and relationships. This helps to isolate characteristics of each manifold within the
product structure while maintaining coherence with the overall topology.
• Discuss how projections relate to quotient manifolds and their equivalence relations.
□ In quotient manifolds, projections serve as a tool to illustrate how points are grouped according to an equivalence relation. The projection maps points from the original manifold into
equivalence classes, creating a new structure that reflects these relationships. By understanding projections in this context, one gains insight into how different points can be considered
equivalent under certain conditions, enabling us to study the manifold's topology in a more simplified manner.
• Evaluate the significance of projection maps in the study of fiber bundles and their applications in differential geometry.
□ Projection maps are critical in fiber bundles as they define how each point in the base space corresponds to fibers in the total space. This relationship allows mathematicians to explore how
local structures behave while understanding global properties. By evaluating projection maps, one can investigate smooth structures and differentiable functions across various dimensions,
leading to significant applications in physics and engineering where complex systems are often analyzed through their simpler components.
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website. | {"url":"https://library.fiveable.me/key-terms/elementary-differential-topology/projections","timestamp":"2024-11-06T06:12:34Z","content_type":"text/html","content_length":"155231","record_id":"<urn:uuid:bd17d868-570f-4e17-bccb-c8a3128f6602>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00719.warc.gz"} |
How do you calculate autonomous consumption and MPC?
How do you calculate autonomous consumption and MPC?
1. If MPS=0.20, then.
2. MPC= 1-MPS= 1-0.20= 0.80.
3. Consumption Function is C = c + 0.80 Y where Y in the income in the economy and c= Autonomous consumption.
4. At equilibrium level of output,
5. AS=AD.
6. Y= C+I.
7. => 1,200 = c + 0.80 (1,200) + 100.
8. => 1,200 = c+ 960 + 100.
What is autonomous consumption example?
If you buy groceries so you can feed yourself, that is autonomous consumption. These are basic needs, not wants. You may not have enough money to pay for these items, which could lead you to purchase
them on a credit card or take money out of your savings.
What is the formula to calculate consumption?
Consumption function equation describes C = c+bY. If the value of (By) is higher, the total consumption value will increase. It certainly says that if income increases, expenditure also increases. We
must consider that the income increase rate is more than the expenditure increase rate.
What is the amount of autonomous consumption?
Autonomous consumption is defined as the expenditures that consumers must make even when they have no disposable income. Certain goods need to be purchased, regardless of how much income or money a
consumer has in their possession at any given time.
When MPS 0.2 then MPC will be?
Adding MPS (0.2) to MPC (0.8) equals 1. The marginal propensity to save is generally assumed to be higher for wealthier individuals than it is for poorer individuals. Given data on household income
and household saving, economists can calculate households’ MPS by income level.
How do you calculate YD in economics?
Yd = Y- T, where Y is national income (or GDP) and T = Tax Revenues = 0.3Y; note that 0.3 is the average income tax rate. Step 2. The equation for the 45-degree line is the set of points where GDP or
national income on the horizontal axis is equal to aggregate expenditure on the vertical axis.
How do you calculate MPS from income and consumption?
MPS is most often used in Keynesian economic theory. It is calculated simply by dividing the change in savings observed given a change in income: MPS = ΔS/ΔY.
How is APC calculated?
Average propensity to consume is calculated by dividing an entity’s consumption by the entity’s total income. It is a ratio between what is spent and what is earned.
Is LM calculated?
The basis of the IS-LM model is an analysis of the money market and an analysis of the goods market, which together determine the equilibrium levels of interest rates and output in the economy, given
prices. The model finds combinations of interest rates and output (GDP) such that the money market is in equilibrium.
How do you calculate autonomous consumption in Keynesian model?
Autonomous consumption in the Keynesian model. In the Keynesian model of aggregate expenditure, autonomous consumption plays an important role. C = a +bY. In this formula a is the level of autonomous
consumption, where b is the marginal propensity to consume out of income.
What is autonomous consumption?
Autonomous consumption refers to the expenditures that a consumer needs to make, regardless of their income level. Certain goods and services must be purchased even when an individual is broke or
with little to no disposable income. They include goods such as food, shelter (rent and mortgage
What is’autonomous consumption’?
What is ‘Autonomous Consumption’. Autonomous consumption is the minimum level of consumption or spending that must take place even if a consumer has no disposable income, such as spending for basic
How do you calculate induced consumption?
Induced consumption. This is consumption that is influenced by levels of income. With rising income, people can spend more. In the diagram above, induced consumption is given by formula b(Y) where b
equals the marginal propensity to consume. | {"url":"https://fistofawesome.com/life/how-do-you-calculate-autonomous-consumption-and-mpc/","timestamp":"2024-11-05T23:42:55Z","content_type":"text/html","content_length":"47397","record_id":"<urn:uuid:e4321aa1-17fa-4b18-960e-684edeeb2154>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00073.warc.gz"} |
4x 2 5x 12 0 Secrets of the Quadratic Equation Exploring 4x^2 - 5x - 12 = 0 - TechnologyWritee
4x 2 5x 12 0 Secrets of the Quadratic Equation Exploring 4x^2 – 5x – 12 = 0
Unlocking the Secrets of the Quadratic Equation: Exploring 4x^2 – 5x – 12 = 0 and Its Mathematical Marvels
In the vast realm of mathematics, quadratic equations hold a significant place, showcasing their prowess in diverse fields from physics and engineering to biology and beyond. One such quadratic
equation that has intrigued and challenged many is 4x^2 – 5x – 12 = 0. In this comprehensive guide, we will delve into the intricacies of this equation, exploring its components, methods for solving,
real-world applications, and the profound impact it has in various scientific disciplines.
Understanding the Quadratic Equation:
A quadratic equation is a second-degree polynomial equation in a single variable, often represented in the standard form ax^2 + bx + c = 0. In our case, the quadratic equation is 4x^2 – 5x – 12 = 0,
where ‘a’ is 4, ‘b’ is -5, and ‘c’ is -12.
Breaking Down the Terms:
1. Coefficient Analysis:
– The coefficient ‘a’ (4 in this case) determines the degree of the parabola. A positive ‘a’ indicates an upward-opening parabola, while a negative ‘a’ results in a downward-opening parabola.
– Coefficient ‘b’ (-5) influences the position of the vertex and the direction of the parabola’s axis.
– The constant term ‘c’ (-12) represents the y-intercept, the point where the parabola intersects the y-axis.
2. Vertex and Parabola:
– The vertex of a quadratic equation in standard form (ax^2 + bx + c = 0) is given by the coordinates (-b/2a, f(-b/2a)), where ‘f’ is the function defined by the quadratic equation.
– Understanding the vertex is crucial as it indicates the minimum or maximum point on the parabola, providing insights into the equation’s behavior.
Methods for Solving Quadratic Equations:
1. Factoring:
– Factoring involves expressing the quadratic equation as the product of two binomials and setting each factor equal to zero.
– For 4x^2 – 5x – 12 = 0, factoring might involve finding two numbers whose product is ac (4 * -12 = -48) and whose sum is b (-5).
2. Quadratic Formula:
– The quadratic formula, x = (-b ± √(b^2 – 4ac)) / (2a), offers a universal method for finding the roots of any quadratic equation.
– The term inside the square root, b^2 – 4ac, is known as the discriminant. Its value determines the nature of the roots:
– If b^2 – 4ac > 0, two real and distinct roots exist.
– If b^2 – 4ac = 0, there is one real and repeated root (a perfect square).
– If b^2 – 4ac < 0, the roots are complex conjugates.
Real-World Applications:
1. Physics:
– In projectile motion, quadratic equations describe the trajectory of objects influenced by gravity.
– Vibrations and oscillations in mechanical systems can be modeled using quadratic equations.
2. Engineering:
– Structural engineering relies on quadratic equations to analyze and design various components.
– Electrical circuits and systems often involve quadratic equations in their mathematical models.
3. Biology and Medicine:
– In epidemiology, quadratic equations can model the growth and decline of infectious diseases.
– Biological systems, such as population dynamics, can be studied using quadratic equations.
4. Environmental Science:
– Quadratic equations play a role in modeling pollution levels, population growth, and resource depletion.
Case Studies and Problem-Solving:
To deepen our understanding, let’s explore a real-world case study where the quadratic equation 4x^2 – 5x – 12 = 0 finds practical application. Imagine a scenario in environmental science where the
equation models the population growth of a species in an ecosystem affected by external factors.
Consider the following parameters:
– ‘x’ represents time in years,
– ‘4x^2 – 5x – 12′ represents the population size at any given time.
By solving the equation, scientists can predict critical points in the species’ population dynamics, helping formulate informed conservation strategies or identify potential threats to the ecosystem.
In conclusion, the quadratic equation 4x^2 – 5x – 12 = 0 is a fascinating mathematical entity with profound applications across various scientific disciplines. From understanding its terms and
coefficients to employing different methods for solving, the equation’s versatility is evident. Its impact extends beyond the realm of mathematics, playing a pivotal role in shaping our understanding
of the natural world. As we continue to unravel the mysteries of quadratic equations, their relevance and significance in fields such as physics, engineering, biology, and environmental science
become increasingly evident, highlighting their importance in the broader spectrum of knowledge. | {"url":"https://technologywritee.com/4x-2-5x-12-0-secrets-of-the-quadratic-equation-exploring-4x2-5x-12-0/","timestamp":"2024-11-08T02:21:47Z","content_type":"text/html","content_length":"152286","record_id":"<urn:uuid:d8256ce6-acb0-4586-98d7-e904bf214f1e>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00678.warc.gz"} |
Extracting dynamical behaviour via Markov models
Statistical properties of chaotic dynamical systems are difficult to estimate reliably. Using long trajectories as data sets sometimes produces misleading results. It has been recognised for some
time that statistical properties are often stable under the addition of a small amount of noise. Rather than analysing the dynamical system directly, we slightly perturb it to create a Markov model.
The analogous statistical properties of the Markov model often have ``closed forms'' and are easily computed numerically. The Markov construction is observed to provide extremely robust estimates and
has the theoretical advantage of allowing one to prove convergence in the ``noise approaches zero'' limit and produce rigorous error bounds for quantities. We review the latest results and techniques
in this area.
Chapter 1: Introduction and basic constructions
1.1 What do we do?
1.2: How do we do this?
1.3: Why do we do this?
Chapter 2: Objects and behaviour of interest
2.1: Invariant measures
2.2: Invariant sets
2.3: Decay of correlations
2.4: Lyapunov exponents
2.5: Mean and variance of return times
Chapter 3: Deterministic systems
3.1: Basic Constructions
3.2: Invariant measures and invariant sets
3.3: Decay of correlations and spectral approximation
3.4: Lyapunov exponents and entropy
3.5: Mean and variance of return times
Chapter 4: Random systems
3.1: Basic Constructions
3.2: Invariant measures
3.3: Lyapunov exponents
3.4: Mean and variance of return times
3.5: Advantages for Markov modelling of random dynamical systems
Chapter 5: Miscellany
5.1: Global attractors, noisy systems, rotation numbers, topological entropy, spectra of ``averaged'' transfer operators for random systems
Chapter 6: Numerical Tips and Tricks
6.1: Transition matrix construction
6.2: Partition selection | {"url":"https://web.maths.unsw.edu.au/~froyland/ulamsurveycontents.html","timestamp":"2024-11-10T12:53:09Z","content_type":"text/html","content_length":"3114","record_id":"<urn:uuid:c949a17d-4e01-4b3a-bd8e-4d65c8fac1d4>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00511.warc.gz"} |
Derivative of Tan x - Formula, Proof, Examples
The tangent function is among the most crucial trigonometric functions in mathematics, physics, and engineering. It is a crucial concept applied in many domains to model various phenomena, involving
signal processing, wave motion, and optics. The derivative of tan x, or the rate of change of the tangent function, is an important concept in calculus, which is a branch of math that concerns with
the study of rates of change and accumulation.
Comprehending the derivative of tan x and its characteristics is essential for working professionals in multiple domains, including physics, engineering, and mathematics. By mastering the derivative
of tan x, individuals can apply it to solve challenges and gain deeper insights into the intricate workings of the world around us.
If you need help getting a grasp the derivative of tan x or any other mathematical theory, contemplate reaching out to Grade Potential Tutoring. Our adept tutors are accessible remotely or in-person
to offer personalized and effective tutoring services to assist you be successful. Call us right now to schedule a tutoring session and take your math skills to the next level.
In this blog, we will dive into the theory of the derivative of tan x in detail. We will begin by discussing the importance of the tangent function in various domains and uses. We will then check out
the formula for the derivative of tan x and give a proof of its derivation. Eventually, we will give examples of how to apply the derivative of tan x in various fields, involving engineering,
physics, and mathematics.
Significance of the Derivative of Tan x
The derivative of tan x is an essential mathematical concept which has many utilizations in physics and calculus. It is applied to calculate the rate of change of the tangent function, that is a
continuous function which is widely utilized in math and physics.
In calculus, the derivative of tan x is used to work out a wide spectrum of problems, consisting of figuring out the slope of tangent lines to curves which involve the tangent function and evaluating
limits which includes the tangent function. It is also used to work out the derivatives of functions which includes the tangent function, for example the inverse hyperbolic tangent function.
In physics, the tangent function is utilized to model a wide spectrum of physical phenomena, including the motion of objects in circular orbits and the behavior of waves. The derivative of tan x is
used to work out the acceleration and velocity of objects in circular orbits and to analyze the behavior of waves that consists of changes in amplitude or frequency.
Formula for the Derivative of Tan x
The formula for the derivative of tan x is:
(d/dx) tan x = sec^2 x
where sec x is the secant function, which is the reciprocal of the cosine function.
Proof of the Derivative of Tan x
To confirm the formula for the derivative of tan x, we will utilize the quotient rule of differentiation. Let’s say y = tan x, and z = cos x. Next:
y/z = tan x / cos x = sin x / cos^2 x
Applying the quotient rule, we obtain:
(d/dx) (y/z) = [(d/dx) y * z - y * (d/dx) z] / z^2
Replacing y = tan x and z = cos x, we obtain:
(d/dx) (tan x / cos x) = [(d/dx) tan x * cos x - tan x * (d/dx) cos x] / cos^2 x
Next, we could utilize the trigonometric identity that connects the derivative of the cosine function to the sine function:
(d/dx) cos x = -sin x
Substituting this identity into the formula we derived prior, we get:
(d/dx) (tan x / cos x) = [(d/dx) tan x * cos x + tan x * sin x] / cos^2 x
Substituting y = tan x, we get:
(d/dx) tan x = sec^2 x
Thus, the formula for the derivative of tan x is demonstrated.
Examples of the Derivative of Tan x
Here are few examples of how to apply the derivative of tan x:
Example 1: Find the derivative of y = tan x + cos x.
(d/dx) y = (d/dx) (tan x) + (d/dx) (cos x) = sec^2 x - sin x
Example 2: Find the slope of the tangent line to the curve y = tan x at x = pi/4.
The derivative of tan x is sec^2 x.
At x = pi/4, we have tan(pi/4) = 1 and sec(pi/4) = sqrt(2).
Hence, the slope of the tangent line to the curve y = tan x at x = pi/4 is:
(d/dx) tan x | x = pi/4 = sec^2(pi/4) = 2
So the slope of the tangent line to the curve y = tan x at x = pi/4 is 2.
Example 3: Locate the derivative of y = (tan x)^2.
Using the chain rule, we obtain:
(d/dx) (tan x)^2 = 2 tan x sec^2 x
Thus, the derivative of y = (tan x)^2 is 2 tan x sec^2 x.
The derivative of tan x is a basic mathematical concept that has many uses in calculus and physics. Comprehending the formula for the derivative of tan x and its properties is essential for learners
and professionals in domains for instance, physics, engineering, and math. By mastering the derivative of tan x, individuals can use it to figure out problems and get detailed insights into the
complicated functions of the world around us.
If you need guidance understanding the derivative of tan x or any other mathematical idea, consider connecting with us at Grade Potential Tutoring. Our adept teachers are accessible online or
in-person to offer individualized and effective tutoring services to help you be successful. Contact us today to schedule a tutoring session and take your mathematical skills to the next stage. | {"url":"https://www.burbankinhometutors.com/blog/derivative-of-tan-x-formula-proof-examples","timestamp":"2024-11-01T22:05:47Z","content_type":"text/html","content_length":"75313","record_id":"<urn:uuid:cc5800cd-050d-463d-9512-47cf300e5af8>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00820.warc.gz"} |
NCERT Solutions for class 10th Maths Chapter 7 Coordinate Geometry
Exercise 7.1
Question 1. Find the distance between the following pairs of points :
(i) (2, 3), (4, 1) (ii) (- 5, 7),(- 1, 3) (iii) (a, b),(- a, – b)
Note : Distance between the two points can never be negative.
Question 2. Find the distance between the points (0, 0) and (36, 15). Can you find the distance between the two towns A and B discussed. A town B is located 36 km east and 15 km north of the town A.
Question 3. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.
Note: Three points A, Band Care collinear or lie on a line if one of the following holds
(i) AB+BC= AC (ii) AC+ CB= AB (iii) CA + AB = CB.
Question 4. Check whether (5, – 2),(6, 4) and(7, -2) are the vertices of an isosceles triangle.
Question 5. In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. Champa and Chameli walk into the class and after observing for a few minutes Champa asks chameli, “Don’t
you think ABCD is a rectangle?” Chameli disagrees. Using distance formula find which of them is correct, any why?
Note : Every square is a rectangle, but not all rectangles are squares.
Question 6. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answers:
(i) (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0)
(ii) (-3, 5), (3, 1), (0, 3), (-1, – 4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
Question 7. Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
Note : The ordinate of the point on x-axis is 0
Question 8. Find the values of y for which the distance between the points P(2, -3) and Q(lO, y) is 10 units.
Question 9. If Q (0, 1) is equidistant from P(S, -3) and R(x, 6), find the value of x. Also find the distances QR and PR.
Question 10. Find the relation between x and y such that the point (x,y) is equidistant from the point (3, 6) and (-3, 4).
Exercise 7.2
Question 1. Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2 : 3
Question 2. Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).
Note : Since Q is the mid point of PB, it can also be obtained using mid-point formula
Question 3. To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of l m each.100 flower pots have been placed at a
distance of lm from each other along AD, as shown in Fig. 7.12. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs the 1/5th the distance AD on the eighth line
and posts a red flag. What is the distance between both the flags? IfRashmi has to post a blue flag exactly half-way between the line segment joining the two flags, where should she post her flag?
Question 4. Find the ratio in which the line segment joining the points (- 3, 10) and (6, – 8) is divided by (- 1, 6).
Question 5. Find the ratio in which the line segment joining A (1, – 5) and B (- 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.
Question 6. If (1, 2), (4,y), (x, 6) and (3, 5) are the vertices ofa parallelogram taken in order, find x and y.
Question 7. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4).
Question 8. If A and B are (- 2, – 2) and (2, – 4), respectively, find the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB.
Question 9. Find the coordinates of the points which divide the line segment joining A(- 2, 2) and B(2, 8) into four equal parts.
Question 10. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and
(- 2, – 1) taken in order.
Hint:[Area of a rhombus = (product of its diagonals)]
Exercise 7.3
Question 1. Find the area of the triangle whose
(i) (2,3), (-1, 0), (2,-4) (ii) (-5,-1), (3,-5), (5, 2)
Note : Since area is measure, it cannot be negative.
Question 2. In each of the following find the value of ‘k’, for which the points are collinear.
(i) (7, -2), (5, 1), (3, k) (ii) (8, 1),(k, – 4),(2, -5)
Note : Collinearity of three points can be proven using any of the given conditions.
(i) If the sum of the lengths of any two line segments among AB, BC and AC is equal to the length of the remaining line segment, i.e.,
AB +BC= CA, or AB+ AC =BC, or AC+ BC =AB.
(ii) If area of MBC = 0,
Question 3. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the
given triangle.
Question 4. Find the area of the quadrilateral whose vertices, taken in order, are (-4,-2), (-3,-5), (3,-2) and (2, 3).
Note : To find the area of any polygon, simply divide it into triangular regions having no common area, and then add the areas of these regions.
Question 5. You have studied in Class IX (Chapter 9, example 3) that a median of a triangle divides it into two triangles of equal areas. Verify this result for ABC whose vertices are A(4, – 6), B(3,
-2) and C(5, 2).
Exercise 7.4
Question 1. Determine the ratioin which the line 2x+y-4 =0 divides the line segment joining the points A(2,- 2) and B(3, 7).
Question 2. Find a relation between x and y if the points (x,y),(1, 2) and (7, 0) are collinear.
Question 3. Find the centre of a circle passing through the points (6,-6),(3,-7) and (3, 3).
Question 4. The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.
Question 5. The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot ofland for their gardening activity. Sapling of Gulmohar are planted on the boundary at a
distance of lm from each other. There is a triangular grassy lawn in the plot as shown in the Fig. 7.14. The students are to sow seeds of flowering plants on the remaining area of the plot.
(i) Taking A as origin, find the coordinates of the vertices of the triangle.
(ii) What will be the coordinates citheva-ticesci.:PQR if C is the origin? Also calculate the areas of the triangles in these cases. What do you observe?
Question 6. The vertices of aMBC are A(4, 6), B (1, 5) and C (7, 2).A line is drawn to intersect sides AB and AC at D and E respectively, such that AD/AB=AE/AC=1/4.Calculate the area of the MOE and
compare it with the area of ABC.
Question 7. Let A(4, 2), B(6, 5) and C(l, 4) be the vertices of AABC.
(i) The median from A meets BC at D. Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP: PD= 2 : 1
(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR: RF= 2:1.
(iv) What do you observe?
[Note : The point which is common to all the three medians is called the centroid and this point divides each median in the ratio 2 : 1.]
(v) If A(x,,y,), B(x2,y2) and C(x”y,) are the vertices of ABC, find the coordinates of the centroid of the triangle.
Question 8. ABCD is a rectangle formed by the points A(-1,-1), B(- 1,4), C(S,4) and D(5,-1).P, Q, Rand Sare the mid-points of AB, BC, CD and DA, respectively. Is the quadrilateral PQRS a square? a
rectangle? or a rhombus? Justify your answer.
Related Articles: | {"url":"https://cbseacademic.in/class-10/ncert-solutions/maths/coordinate-geometry/","timestamp":"2024-11-09T19:31:28Z","content_type":"text/html","content_length":"123528","record_id":"<urn:uuid:146ed085-cd37-49e2-b8c1-9b5c4c717865>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00395.warc.gz"} |
Using evolutionary game theory to explain and predict the meta of Yugioh Duel Links
TL;DR: Evolutionary game theory, initially developed for biology, has been successfully applied to other domains such as economics, sociology, and anthropology. This post will use it to explain the
various meta of Yugioh Duel Links and predict the nonexistence of the kind of meta which is simultaneously diverse, accessible, and without being Rock–paper–scissors.
Table of Contents
• Introduction
• Multi-species Competition
• Predator-Prey
• Rock–Paper–Scissors
• Conclusion and discussion
Fur Hire is an archetype released in the mini box Clash of Wings. Although powerful, they were generally not considered as overwhelming as Sylvan or pre-nerf Cyber Angel. However, contrary to
people’s expectation, it recently became a Tier 0 archetype and left Amazoness and Masked Heroes far behind.
These cute creatures have since infested the competitive play. More than 50% of decks in tournaments feature Fur Hire, and tons of players are complaining about it on Reddit daily, just like what
they did to Sylvan and Cyber Angel. This unexpected situation raises the question: What can we do to create a healthy meta?
This question seems to be too big to answer. In this post, I will, instead, analyze the formation and properties of various kinds of meta in an attempt to understand this game better. With this
understanding, players could have more reasonable expectation about this game and find their suitable ways of playing.
For this purpose, I will describe three types of meta with the help of evolutionary game theory: Multi-species Competition (MC), Predator-Prey (PP), and Rock–Paper–Scissors (RPS). All of them can
find examples in the Duel Links history.
Name Evolutionary Model Drawback Epoch
MC Malthus not diverse Fur Hire
PP Lokta–Volterra inaccessible Cyber Angel
RPS Replicator equation cyclic domination Spellbook
Furthermore, I list here three properties that players may expect the meta to have: diversity, accessibility, and without being cyclic domination.
• Diversity: No Tier 0 decks. The strongest deck does not have more than 50% share in a competitive environment.
• Accessibility: Free-2-play. With reasonable effort, the players can play any deck they want.
• Cyclic Domination: Rock–Paper–Scissors. Deck A wins against Deck B, which wins against Deck C, which wins against Deck A. This chain, of course, can be longer (e.g., Naruto), and each component
of the chain can contain multiple decks.
I will show you that the three aforementioned meta types each have their own drawback and that none of them can have the three properties simultaneously. This conclusion works not only for Duel Links
but also for other card games, such as Magic the Gathering, Hearthstone, and Shadowverse. To my best knowledge, I am the first person to use evolutionary game theory to analyze card game meta.
Multi-species Competition
In this section, I assume the existence of several strong decks and that none of them has a significant advantage against another (i.e., when two of them battle, both have a winning rate around 50%).
Under this assumption, I will show that one of those decks will be predominant and eventually eliminate the other decks.
Without loss of generality, let us consider an environment with only two strong decks. Let $x_t$ and $y_t$ be the population of these two decks at Moment $t$. The population dynamics can be
represented by the following differential equations [ \frac{dx_t}{dt} = a x_t , ] [ \frac{dy_t}{dt} = b y_t . ] The population increase is proportional to the current population, which is justified
by the fact that the more players playing this deck, the more likely it ranks high, and the more players try to copy this deck. The parameters $a$ and $b$ depend on two factors: it increases with the
intrinsic strength of the decks and decreases with the cost of the deck.
The solution of the above equation is given by [ x_t = e^{at} , ] [ y_t = e^{bt} , ] Thus, the proportions of both decks are given by [ \frac{e^{at}}{e^{at} + e^{bt}} \text{ and } \frac{e^{bt}}{e^
{at} + e^{bt}} . ] If $a>b$, the 1st quantity will tend to $1$ and the 2nd quantity will tend to $0$ when $t \rightarrow \infty $, which means that, given enough time, one deck will eliminate the
If both decks are equally strong, the less expensive deck will have a large parameter (i.e., $a$ or $b$), which means the less expensive deck will eliminate the relatively more costly deck. This
conclusion also works with the case of more than two decks: Given $n$ equally strong decks, the cheapest deck will eliminate all others.
This model perfectly explains the situation of the Fur Hire meta right now. Masked Heroes needs to go through a main box three times; Amazoness needs to go through a main box, level Mai to Level 45,
and get three UR tickets for the Princess; Fur Hire needs only to go through a mini box three times, which is the cheapest of the three. Fur Hire is strong and cheap; this is why they appear
everywhere in the meta.
In this section, I assume the existence of a F2P deck and a P2W deck. The F2P deck is cheap and strong, and the P2W deck is nearly inaccessible but works excellently against that F2P deck in
question. The F2P deck is essentially a prey, and the P2W deck is essentially a predator. Under this assumption, I will show that the meta behaves like a cycle. That is, the predator and the prey
prosper and decline periodically and in turn have their peaks (as shown at the end of the section).
The population dynamics is given by the Lokta–Volterra equations. [ \frac {dx}{dt} = \alpha x - \beta xy , ] [ \frac {dy}{dt} = \delta xy - \gamma y , ] where $x$ and $y$ are the numbers of the F2P
and P2W decks respectively. $\alpha$, $\beta$, $\delta$, and $\gamma$ are all positive parameters.
In particular, $\alpha$ represents the intrinsic strength of the F2P deck, $\beta$ and $\delta$ represents the relative strength of the P2W deck against the F2P deck, and $\gamma$ represents the
extra cost of P2W deck against other random decks.
The Lotka–Volterra equations do not have analytic solutions. It can be solved numerically though, and the solution is represented in the following figure. It looks like that the F2P deck prospers
first, and then gets hit by the P2W deck and declines (the P2W deck thrives instead); with the fall of the F2P deck, the P2W deck is less time-efficient against other random decks and thus is
switched to the F2P decks (the F2P deck rises again). This behavior repeats periodically.
This meta has more than one Tier 1 deck, but the P2W deck is not accessible to all. A famous example is the meta of the pre-nerf Cyber Angel and the pre-nerf Three-star Ninja, with Cyber Angel being
F2P and Ninja being P2W (three copies of Ninja Art of Transformation).
I have claimed in another post that Pokémon GO was essentially a Rock–paper–scissors game. Surprisingly, it seems that a diverse and free-2-play meta in Duel Links also has to be Rock–paper–scissors.
The intuition is that, in a F2P environment, to keep a deck meta relevant, it has to be strong against some meta decks; and to avoid being predominant, it has to be weak against some other meta
Nevertheless, the existence of cyclic domination does not automatically means that Rock, Paper, and Scissors will live in harmony. Instead, they can take their turn to be predominant and nearly
extinct, which is not a diverse meta and is definitely not what we want to see. We want to know whether there needs some extra condition for Rock, Paper, and Scissors to coexist.
The best tool to analyze this problem is the replicator equation. I will restrain myself from writing excessively complex maths here. The idea of replicator equation is that a species’ increasing
rate is proportional to the difference between this species’ fitness and average population fitness (Darwinism).
For example, if the majority of the environment at this moment is Rock, the fitness of Paper will be above average, and the fitness of Scissors will be below average; therefore, the population of
Paper will increase, and the population of Scissors will decrease.
When we apply the replicator equation to the game Rock–paper–scissors, we can obtain some interesting insight. Let us write down the payoff matrix of Rock–paper–scissors.
Rock Paper Scissors
Rock 0 -1 $\mu$
Paper $\mu$ 0 -1
Scissors -1 $\mu$ 0
Here, the -1 stands for the loss of time and effort and psychological dissatisfaction per loss, and $\mu>0$ stands for the net gain (with the loss of time and effort deducted) per win. If $\mu=1$, we
call it a zero-sum game.
It has been shown that
• if $\mu>1$ (positive sum), then the game will converge to the stable state where each of Rock, Paper, and Scissors takes 1/3 of the total population;
• if $\mu<1$ (negative sum), then Rock, Paper, and Scissors will in turn take over the whole population and then almost go extinct;
• if $\mu=1$ (zero-sum), then the game behaves like a cycle, just like the predator-prey case.
Therefore, in order to diversify the meta, we need to make $\mu>1$, which means that the prize of one win should cover more than two losses. In this sense, Konami is doing a smart job by giving
rewards of accumulated wins in ranked duels.
In Duel Links, there was a short epoch where we observe Rock-paper-scissors. With the release of the Spellbook archetype, Sylvan was countered by Spellbook, which was countered by Amazoness, which
was in turn countered by Sylvan.
Conclusion and discussion
This post analyzes the three types of meta and predicts the nonexistence of the kind of meta which is simultaneously diverse, accessible, and without being Rock–paper–scissors. Among these three
types of meta, the diverse, F2P Rock–paper–scissors seems to be the most promising, especially if we can create some long-chain Rock–paper–scissors.
It should be stated that the design of Rock–paper–scissors meta is tricky. Although Yugioh has tons of archetypes, finding three archetypes generating cyclic domination is still a hard task.
Moreover, the frequent release of boxes makes it even more Herculean: in order for a box to be meta relevant (for more sales), it has to either fit in or destroy the current meta.
Another alternative strategy is to create F2P multi-species competition meta for short periods. Given enough time, the meta will naturally converge to a single deck. But when the box has just been
released, and the meta has not been stabilized, we can observe a diverse meta. Therefore, if we can release the box frequently enough and do not give players enough time to overly optimize the build,
we can achieve a diverse meta. The drawback of this strategy is that players will complain about power creep.
Konami also seems to have realized this problem, but they adopted a different (but equivalent) solution by making the game less F2P. They have reduced the gem income and increased the packs of mini
boxes, which has been the players’ main complaint over the past weeks. In fact, this solution is, nonetheless, equivalent to accelerating the box release and attempts to achieve the same effect:
diversifying the meta.
The best we can hope in this game is the long-chain cyclic domination, but since it is hard to design and even harder to maintain and Konami has essentially no financial motivation to do so, we
players may have to make a compromise between the diversity and the F2P level.
You may also like
Written on July 31, 2018 | {"url":"https://www.zhengwenjie.net/duellinksmeta/","timestamp":"2024-11-07T11:58:13Z","content_type":"text/html","content_length":"20304","record_id":"<urn:uuid:2e787710-4727-4b2b-871d-be48e8c36eeb>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00558.warc.gz"} |
qsr sales per square foot
Your restaurant layout both supports operational workflow and communicates your brand to patrons. (In thousands, except per share, per square foot and store count data) Dear S The Ulta B ˜sc driv
result supply chain and s Our t to o Incr We opened 1 stor During 20 as w our r stor Dr E-commer 8.1%. Similar to a brand like Apple, Starbucks has positioned themselves well over the years making
their stores a destination spot for trendy coffee-lovers and have garnered immense brand loyalty among their regular customers. In Statista . Corporate analysts use this data to compare sales in
different store locations of a retail chain, regardles of store size. Sales Per Square Foot = Annual Sales ÷ Number of Square Feet If your retail space is 800 square feet, and you make $40,000 a year
in gross profit, your sales per square foot in dollars is $50. It can also roughly calculate return on investment and used to determine rent for a retail location. Designing a restaurant floor plan
involves more than rearranging tables. Restaurants determine how efficiently floor space is being used by analyzing the sales per square foot ratio. Sales Per Square Foot . Avg $/Square Ft $214 Avg
Building SF 8,200 SF Lot Size .5 - 1.5 Acres Lease Term 15 Years # of Locations 5,651 Credit Rating S&P BBB Moody's Baa1 HQ in Memphis, TN .Q 219’same store salesincreased 3 9%, with net of $ 8B, an
increase of4 .6 %from year prior Gross profit as a percentage sales was 53, versus 5 The sales-per-square-foot data is most commonly used for planning inventory purchases. Remember to only count
retail selling space in this equation, so you would exclude bathrooms, stockrooms, and the like. The quick service restaurant sector (QSR) in the United States has seen a year-over-year growth since
2004, with its peak consumer spending reaching approximately three hundred billion in … Sales per square foot is a measure of the dollar amount of sales generated by a retail location per square foot
of displayed stock. The more revenue you can generate per square foot, the more profitable you will be. However, average sales per square foot data for your particular niche can prove difficult to
locate. Benchmarking is a key way to determine if your results are good or great. Average floor space of select quick service restaurants (QSRs) in the United States in 2016 (in square feet) [Graph].
Sales Per Square Foot = Annual Sales /Square Footage In most cases, full-service restaurants that don't generate at least $150 of sales per square foot have very little chance of generating a profit.
Experts agree that a 6-step approach works best, starting with allocating space to your kitchen and dining areas. This figure is useful for comparing the cost of restaurants in the same area. You can
calculate the cost per square foot … Here are a few places to find the average sales per square foot. Revenue per square foot tells you how efficiently you’re generating sales, which can be used to
showcase your potential for expanding your restaurant or adding a location. For example, a 4,000-square-foot restaurant with annual sales of anything less than $600,000 would find it very difficult
to avoid losing money. Calculating the cost per square foot of a restaurant will tell you the cost of construction to build the restaurant or the cost paid for an existing restaurant broken down per
square foot. Started in the early 1970's, it hasn't taken long for Starbucks to go from a single storefront to a global phenomenon. Retailers use this data to examine differences in same-store sales
over time. Sales per Square Foot . According to Bloom Intelligence , benchmarks for a full service restaurant are as follows: Losing money: $150 or lessBreak-even: $150-$250Profit: $250+ (5%-10% of
sales) In the early 1970 's, it has n't taken long for to... Restaurants determine how efficiently floor space is being used by analyzing the sales per square qsr sales per square foot of stock! Can
calculate the cost of restaurants in the early 1970 's, it has n't taken long for Starbucks go... Go from a single storefront to a global qsr sales per square foot foot is a measure of the dollar
amount of generated! Count retail selling space in this equation, so you would exclude bathrooms, stockrooms, and like! Determine rent for a retail location examine differences in same-store sales
over time is being by! Is qsr sales per square foot used by analyzing the sales per square foot data for your particular niche can prove difficult to losing. Space to your kitchen and dining areas
remember to only count retail selling space in this equation so. The sales-per-square-foot data is most commonly used for planning inventory purchases is being used by analyzing the sales per foot.
How efficiently floor space is being used by analyzing the sales per foot. And the like to avoid losing money count retail selling space in this,... Investment and used to determine rent for a retail
location per square foot data for your niche. To avoid losing money key way to determine if your results are or. For planning inventory purchases anything less than $ 600,000 would find it very
difficult to locate key. Space in this equation, so you would exclude bathrooms, stockrooms and. Both supports operational workflow and communicates your brand to patrons store size from a single to!
Floor plan involves more than rearranging tables corporate analysts use this data to sales... However, average sales per square foot restaurants determine how efficiently floor space is used. Cost of
restaurants in the same area it can also roughly calculate return on investment used! Chain, regardles of store size however, average sales per square foot for! Locations of a retail location a
single storefront to a global phenomenon retail location square! Workflow and communicates qsr sales per square foot brand to patrons of displayed stock use this data to compare sales in different
locations. It very difficult to avoid losing money data to examine differences in same-store sales over time for your niche. Locations of a retail location has n't taken long for Starbucks to go from
a single storefront a... Storefront to a global phenomenon and used to determine if your results are good or great a. For Starbucks to go from a single storefront to a global phenomenon, average
sales per foot... So you would exclude bathrooms, stockrooms, and the like for Starbucks to go a! Of the dollar amount of sales generated by a retail chain, regardles of store size it also!
Restaurant layout both supports operational workflow and communicates your brand to patrons and. To avoid losing money to patrons equation, so you would exclude bathrooms, stockrooms, and the like
per. Allocating space to your kitchen and dining areas to patrons to your and! A few places to find the average sales per square foot ratio your brand to patrons remember to only retail! Data is most
commonly used for planning inventory purchases or great of a retail location per square …. … Designing a restaurant floor plan involves more than rearranging tables niche prove... Selling space in
this equation, so you would exclude bathrooms,,! Of a retail location your brand to patrons to patrons the dollar amount of sales by. Experts agree that a 6-step approach works best, starting with
allocating space your! In same-store sales over time amount of sales generated by a retail location in store. Regardles of store size calculate return on investment and used to determine if your
results good... Generated by a retail location generated by a retail location if your results are good or great retail... Workflow and communicates your brand to patrons starting with allocating
space to your kitchen and dining areas locate. This data to examine differences in same-store sales over time that a 6-step approach works best, starting with space. Is a measure of the dollar amount
of sales generated by a retail location per foot... Over time workflow and communicates your brand to patrons to patrons how efficiently space. To find the average sales per square foot data for your
particular niche can prove difficult to locate here a! 'S, it has n't taken qsr sales per square foot for Starbucks to go from a single to. To find the average sales per square foot is a key way to
determine rent for a retail location square. A restaurant floor plan involves more than rearranging tables to determine if your results are good or great same-store over... Workflow and communicates
your brand to patrons allocating space to your kitchen and dining areas planning inventory purchases,! Average sales per square foot is a key way to determine rent for a retail.! A single storefront
to a global phenomenon to compare sales in different store of. Experts agree that a 6-step approach works best, starting with allocating space to your kitchen dining., a 4,000-square-foot restaurant
with annual sales of anything less than $ 600,000 would find it very to. Retailers use this data to compare sales in different store locations of a retail location square! Results are good or great
sales of anything less than $ 600,000 would it! Selling space in this equation, so you would exclude bathrooms, stockrooms, and the like the area. Would find it very difficult to locate is a key way
to determine if your results are or. Of sales generated by a retail chain, regardles of store size works best, starting allocating. $ 600,000 would find it very difficult to locate qsr sales per
square foot your results are good or great roughly calculate on..., stockrooms, and the like a measure of the dollar amount of sales generated by a retail.. The early 1970 's, it has n't taken long
for Starbucks to go from a single storefront a! Experts agree that a 6-step approach works best, starting with allocating space to your and! A single storefront to a global phenomenon to only count
retail selling in... This equation, so you would exclude bathrooms, stockrooms, and the like this data to compare in! Particular niche can prove difficult to avoid losing money square foot data for
your particular niche prove... Your restaurant layout both supports operational workflow and communicates your brand to patrons store size of a retail,!, average sales per square foot is a measure of
the dollar amount of sales generated a... Than rearranging tables generated by a retail location go from a single storefront to global! Being used by analyzing the sales per square foot data for your
particular niche prove! Both supports operational workflow and communicates your brand to patrons you can calculate the cost of restaurants in same! Starting with allocating space to your kitchen and
dining areas bathrooms,,... Very difficult to locate foot is a measure of the dollar amount of generated! Can also roughly calculate return on investment and used to determine if your results good.
Dining areas count retail selling space in this equation, so you would exclude bathrooms, stockrooms, and like! 1970 's, it has n't taken long for Starbucks to go from a single storefront to a
phenomenon! Or great way to determine rent for a retail location per square foot … Designing a floor., average sales per square foot … Designing a restaurant floor plan involves than. To compare
sales in different store locations of a retail chain, of! Retail location per square foot of displayed stock particular niche can prove difficult to qsr sales per square foot sales different! On
investment and used to determine if your results are good or great avoid losing money your layout... Most commonly used for planning inventory purchases selling space in this equation, so you would
exclude,! Sales over time how efficiently floor space is being used by analyzing sales..., a 4,000-square-foot restaurant with annual sales of anything less than $ 600,000 would find it very
difficult locate. Equation, so you would exclude bathrooms, stockrooms, and the like workflow communicates. Has n't taken long for Starbucks to go from a single storefront to a global phenomenon
example a. Roughly calculate return on investment and used to determine rent for a retail chain, of. Foot of displayed stock same area long for Starbucks to go from single! Your particular niche can
prove difficult to avoid losing money of a retail location of the dollar of! Of restaurants in the early 1970 's, it has n't taken long Starbucks. Location per square foot ratio also roughly
calculate return on investment and used to determine if your results are or! Involves more than rearranging tables both supports operational workflow and communicates your brand to patrons regardles
store! The sales-per-square-foot data is most commonly used for planning inventory purchases of displayed stock supports operational workflow and your! Calculate the cost of restaurants in the same
area of store size foot data for your niche! Calculate the cost of restaurants in the same area a measure of the dollar amount sales. Of store size retailers use this data to examine differences in
same-store sales over time space to kitchen... Go from a single storefront to a global phenomenon only count retail selling space in this equation so! Find the average sales per square foot ratio
regardles of store size a retail location store.. Of sales generated by a retail location per square foot find it very to... Roughly calculate return on investment and used to determine if your
results are or. Being used by analyzing the sales per square foot is a measure of the dollar amount sales!
Lugosi Of Film
Pasta N Sauce Arrabiata Syns
Black Orpington Vs Black Australorp
A Series Of Unfortunate Events Age Rating
Pineapple On Plant Turning Yellow
What Does The Spanish Word Ponce Mean?
Bichon Frise For Sale By Owner
Eco Fan Amazon | {"url":"http://datzcomunicacao.com/pl0v9/87c549-qsr-sales-per-square-foot","timestamp":"2024-11-10T18:41:10Z","content_type":"text/html","content_length":"23104","record_id":"<urn:uuid:a73d13a5-795d-4f66-85f0-7686c1defd62>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00589.warc.gz"} |
297.2/234: Applications And Implications In Modern Technology
The fraction 297.2/234 may seem like a simple numerical expression at first glance, but it carries significant implications in various contexts. Understanding this fraction involves not only its
mathematical simplification but also its application across different fields such as science, technology, and everyday problem-solving. Whether used in statistical analysis, engineering calculations,
or financial models, the ratio 297.2/234 can provide insights and solutions that are both practical and essential. This introduction explores the foundational aspects of this fraction, setting the
stage for a deeper examination of its significance and utility in diverse scenarios.
The Origin and Context of 297.2/234
The fraction 297.2/234 originates from various practical scenarios where precise ratios and measurements are essential. In mathematical contexts, such fractions often arise in data analysis,
engineering calculations, and financial assessments, representing specific relationships or comparisons. For instance, this fraction could emerge from a scientific experiment where two quantities are
measured and compared, or in an engineering project where materials are proportioned according to precise specifications. The context of 297.2/234 depends largely on the field of application, but it
fundamentally represents a way to compare two values quantitatively, offering a more detailed understanding of their relationship.
Mathematical Significance of 297.2/234
Mathematically, the fraction 297.2/234 can be simplified to make it more manageable and insightful. Simplifying this fraction involves dividing both the numerator and the denominator by their
greatest common divisor (GCD). Calculations reveal that 297.2 divided by 234 approximately equals 1.27 when expressed as a decimal. This conversion is significant because it transforms a complex
fraction into a simpler form, which can be easier to interpret and apply in further calculations. Understanding the mathematical significance of this fraction also involves recognizing its utility in
representing ratios, percentages, and proportional relationships in various mathematical problems and real-world applications.
Applications of 297.2/234 in Science and Technology
In science and technology, the fraction 297.2/234 can be applied in numerous ways to solve practical problems. For instance:
Engineering: Engineers often use such ratios in designing systems and structures. The fraction could represent the ratio of materials needed for a specific component, ensuring precision and
efficiency in construction projects.
Physics: In physics, this fraction might represent a constant in a formula or a ratio of physical quantities, such as force and distance, to calculate work or energy.
Computer Science: Algorithms may use this ratio to optimize performance or resource allocation, particularly in areas such as machine learning where precise data manipulation is crucial.
Chemistry: Chemists might use this fraction to describe the concentration of solutions or to balance chemical equations accurately.
Environmental Science: In environmental studies, such ratios can be used to model and analyze data related to resource consumption and sustainability metrics.
Interpretation of 297.2/234 in Different Fields
The interpretation of the fraction 297.2/234 varies significantly across different fields due to the unique requirements and contexts of each discipline.
Engineering: Engineers might interpret this ratio as a material specification. For example, in a civil engineering project, this fraction could represent the mix ratio of concrete components,
ensuring the right proportions for strength and durability.
Finance: In finance, 297.2/234 might be used to calculate financial ratios such as debt-to-equity ratios, helping analysts assess the financial health of a company.
Healthcare: In medical research, this fraction could be part of a dosage calculation for medications, ensuring the proper concentration is administered for effective treatment.
Environmental Science: Environmental scientists might use this ratio to model the concentration of pollutants in water, assisting in environmental impact assessments and regulatory compliance.
Each field adapts the interpretation of 297.2/234 to fit its specific analytical needs, leveraging the ratio to draw meaningful insights and conclusions.
How to Calculate and Simplify 297.2/234
To calculate and simplify the fraction 297.2/234, follow these steps:
Convert to Decimal: Divide 297.2 by 234.
• 297.2÷234≈1.270085297.2 \div 234 \approx 1.270085297.2÷234≈1.270085
Simplify the Fraction:
• Find the Greatest Common Divisor (GCD) of 297.2 and 234.
• Since these numbers include a decimal, consider multiplying both by 10 to make them whole numbers: 2972 and 2340.
Use the Euclidean algorithm to find the GCD:
• 2972÷23402972 \div 23402972÷2340 gives a quotient of 1 and a remainder of 632.
• 2340÷6322340 \div 6322340÷632 gives a quotient of 3 and a remainder of 444.
• 632÷444632 \div 444632÷444 gives a quotient of 1 and a remainder of 188.
• 444÷188444 \div 188444÷188 gives a quotient of 2 and a remainder of 68.
• 188÷68188 \div 68188÷68 gives a quotient of 2 and a remainder of 52.
• 68÷5268 \div 5268÷52 gives a quotient of 1 and a remainder of 16.
• 52÷1652 \div 1652÷16 gives a quotient of 3 and a remainder of 4.
• 16÷416 \div 416÷4 gives a quotient of 4 and a remainder of 0.
• The GCD is 4.
Divide both the numerator and the denominator by the GCD:
• 2972÷42340÷4=743585\frac{2972 \div 4}{2340 \div 4} = \frac{743}{585}2340÷42972÷4=585743
Simplify Further: Check if 743 and 585 have any common factors.
• 743÷743=1743 \div 743 = 1743÷743=1
• 585÷585=1585 \div 585 = 1585÷585=1
So, the simplified fraction remains 743585\frac{743}{585}585743.
Real-World Examples of 297.2/234
Construction Projects: In a construction project, an engineer might specify a concrete mix ratio using this fraction, indicating that for every 234 parts of aggregate, there should be 297.2 parts of
cement. This precise ratio ensures the desired properties of the concrete mix.
Financial Analysis: A financial analyst might use 297.2/234 to calculate a company’s financial leverage ratio. If a company has $297.2 million in total liabilities and $234 million in equity, this
ratio helps assess the company’s debt relative to its equity, aiding in risk assessment and investment decisions.
Medical Dosage: In a clinical setting, a pharmacist could use the fraction to determine the concentration of a solution. For instance, if a medication requires 297.2 mg of active ingredient per 234
ml of solution, this ratio ensures the correct dosage is administered to patients.
Environmental Studies: Environmental scientists might use this ratio to measure pollutant concentrations in water. For example, 297.2 parts of a pollutant per 234 liters of water could be a threshold
level for safe drinking water standards, guiding regulatory actions, and public health policies.
Challenges in Working with 297.2/234
Working with the fraction 297.2/234 presents several challenges across different fields:
Precision and Accuracy: In fields such as engineering and pharmaceuticals, the precision of the fraction is crucial. Small errors in calculation can lead to significant consequences, such as
structural weaknesses or incorrect medication dosages.
Complexity in Simplification: Simplifying fractions involving decimals can be complex and prone to mistakes. Identifying the greatest common divisor (GCD) and reducing the fraction accurately
requires meticulous calculations.
Interpreting Results: The context-specific interpretation of the fraction can be challenging. Different fields may require different approaches to understand and apply the ratio effectively,
necessitating a deep understanding of the specific domain.
Data Handling: In large datasets, maintaining consistency when using such precise ratios can be difficult. Ensuring that all related data points adhere to the same level of precision is crucial for
accurate analysis and results.
Benefits of Understanding 297.2/234
Understanding the fraction 297.2/234 can offer several benefits:
Enhanced Accuracy: Accurate calculations and simplifications lead to better precision in fields like engineering, finance, and healthcare, ensuring safety and reliability in applications.
Informed Decision-Making: Knowledge of precise ratios aids in making informed decisions. For instance, financial analysts can better assess company health, and engineers can optimize material usage,
leading to cost savings and efficiency.
Problem-Solving Skills: Working with complex fractions improves problem-solving skills and mathematical proficiency, which are valuable in technical and analytical professions.
Cross-Disciplinary Applications: The ability to interpret and apply such fractions across various fields enhances versatility and adaptability, allowing professionals to tackle diverse challenges
Common Misconceptions about 297.2/234
There are several common misconceptions about the fraction 297.2/234:
It’s Only a Simple Division: Many assume that 297.2/234 is just a straightforward division without realizing the need for precise interpretation and context-specific application.
Simplification is Always Necessary: While simplification can make fractions easier to understand, it’s not always required or beneficial. In some cases, maintaining the original ratio provides more
accurate and relevant information.
Decimal Fractions are Less Accurate: There’s a misconception that fractions involving decimals are inherently less accurate or harder to work with. However, with proper tools and methods, they can be
as precise as whole number fractions.
Applicable Only in Mathematics: Another misconception is that fractions like 297.2/234 are only relevant in pure mathematics. In reality, they are widely used across various fields, from engineering
and finance to healthcare and environmental science.
The Future of 297.2/234
The future prospects of the fraction 297.2/234 in emerging technologies are vast and promising. In the field of artificial intelligence (AI) and machine learning, this ratio can be instrumental in
fine-tuning algorithms and models, and optimizing hyperparameters to enhance performance and accuracy. Within the Internet of Things (IoT), 297.2/234 can help manage sensor data and device
interactions, optimizing data transmission frequencies to balance network bandwidth and energy consumption. Blockchain technology can utilize this ratio for resource allocation or reward
distribution, ensuring efficient and secure operations across the network.
In renewable energy systems, 297.2/234 is valuable for optimizing energy storage and distribution, particularly in battery design to maximize lifespan and efficiency. Advanced manufacturing can
benefit from this ratio by ensuring precise material proportions in additive manufacturing processes, leading to consistent quality and reduced waste. In biotechnology, it aids in optimizing reagent
concentrations for biochemical reactions or pharmaceutical formulations, which is crucial for the success of biotechnological innovations. Finally, in quantum computing, the ratio can represent
critical parameters like probability amplitudes, essential for the precise manipulation of quantum states. The ability to apply and understand such precise ratios will drive innovation and efficiency
across these cutting-edge fields.
In conclusion, the fraction 297.2/234 exemplifies the importance of precision and adaptability in various fields, from science and technology to finance and healthcare. This ratio’s mathematical
significance lies in its ability to be simplified and applied in numerous practical contexts, providing clarity and accuracy in calculations. Its diverse applications, including optimizing AI
algorithms, managing IoT data, guiding blockchain resource allocation, enhancing renewable energy systems, improving advanced manufacturing processes, and supporting biotechnological innovations,
demonstrate its versatility and utility in driving technological advancements. Understanding and effectively utilizing 297.2/234 not only enhances problem-solving capabilities but also promotes
efficiency and innovation across emerging technologies, solidifying its role as a critical tool for future developments.
FAQs about 297.2/234
Q1: What is the fraction 297.2/234?
The fraction 297.2/234 represents a specific ratio between two quantities, which can be simplified and used in various practical contexts. It is approximately equal to 1.27 when converted to a
Q2: How can 297.2/234 be simplified?
To simplify 297.2/234, divide both the numerator (297.2) and the denominator (234) by their greatest common divisor (GCD). For simplicity, you can also convert the fraction to a decimal by dividing
297.2 by 234, which gives approximately 1.27.
Q3: What are the applications of 297.2/234 in technology?
In technology, 297.2/234 can be used to optimize algorithms in AI and machine learning, manage sensor data in IoT, allocate resources in blockchain, and design efficient energy storage systems in
renewable energy. Its precise ratio is crucial for enhancing performance and efficiency across these fields.
Q4: How is 297.2/234 used in engineering?
Engineers might use fraction 297.2/234 to determine material proportions, optimize structural designs, and ensure precision in various calculations. This ratio can help achieve the desired balance
and performance in engineering projects.
Q5: Why is understanding 297.2/234 important in finance?
In finance, 297.2/234 can represent financial ratios such as debt-to-equity ratios, helping analysts assess the financial health and leverage of companies. Accurate ratios are essential for making
informed investment decisions.
Q6: What are the benefits of understanding 297.2/234?
Benefits include enhanced accuracy in calculations, informed decision-making, improved problem-solving skills, and versatility in applying the ratio across different fields like technology,
engineering, finance, and healthcare.
Q7: What are some challenges in working with 297.2/234?
Challenges include ensuring precision and accuracy, simplifying the fraction correctly, interpreting the ratio in context-specific scenarios, and maintaining consistency in large datasets.
Q8: Are there common misconceptions about 297.2/234?
Yes, common misconceptions include thinking that it’s only a simple division, that simplification is always necessary, that decimal fractions are less accurate, and that it’s only relevant in
Q9: How does 297.2/234 relate to emerging technologies?
In emerging technologies, this fraction can optimize AI algorithms, manage IoT data, guide blockchain resource allocation, enhance renewable energy systems, improve advanced manufacturing processes,
and support biotechnological innovations.
Q10: Can 297.2/234 be used in environmental science?
Yes, environmental scientists can use this ratio to model pollutant concentrations, manage resource usage, and ensure compliance with environmental standards, contributing to sustainability and
regulatory efforts. | {"url":"https://timegrowing.com/297-2-234/","timestamp":"2024-11-13T05:13:24Z","content_type":"text/html","content_length":"122466","record_id":"<urn:uuid:439faef9-3e7f-4cec-92d3-2700ef36ba1d>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00326.warc.gz"} |
Consider the usual algorithm for determining whether a sequence of parentheses is balanced. Suppose that you run the algorithm on a sequence that contains 2 left parentheses and 3 right parentheses (in some order). The maximum number of parentheses that appear on the stack AT ANY ONE TIME during the computation?
Consider the usual algorithm for determining whether a sequence of parentheses is balanced. Suppose that you run the algorithm on a sequence that contains 2 left parentheses and 3 right
Q. parentheses (in some order). The maximum number of parentheses that appear on the stack AT ANY ONE TIME during the computation?
A. 1
B. 2
C. none
D. none
Answer» B. 2 | {"url":"https://mcqmate.com/discussion/112970/consider-the-usual-algorithm-for-determining-whether-a-sequence-of-parentheses-is-balanced-suppose-that-you-run-the-algorithm-on-a-sequence-that-contains-2-left-parentheses-and-3-right-parentheses-in-some-order-the-maximum-number-of-parentheses-that-appear-on-the-stack-at-any-one-time-during-the-computation","timestamp":"2024-11-03T10:23:59Z","content_type":"text/html","content_length":"43861","record_id":"<urn:uuid:7bea47b1-be5f-4cbf-816f-c9cf431a58d3>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00841.warc.gz"} |
Find the Finder
Find the Finder
Recently I was tasked with finding a QR code in an image and then computing its location and. I learned that the first step in locating a QR code is discerning the finder points. In QR codes there
are three finder points located at the furthest reaches of three of the corners. These finder points are made up of white and black pixels and regardless of the rotation of the code, a cross-section
of one finder point will look like the following.
B W B B B W B
B = Black pixel; W = White pixel
With this pattern of points being fixed and the ratio of ring counts, with respect to the center block, beingcontour procedure and a little math to pull out these finder points.
Figure 1: Input Image
To locate the finder points, I first opened the image and stripped out a single band. Then I converted the image to a binary image and coded any gaps that were formed by the conversion.
; open envi
e = envi()
; open the image
oRaster = e.openRaster(inputfile)
; strip out single band
band1 = oRaster.GetData(Bands=0)
; convert to binary image
data = band1 gt 128
; close gaps
data =MORPH_Open(data, REPLICATE(1,3,3))
Figure 2: Binary image
Once I had a binary image, I computed the contour lines for the full image. I then added each contour line to the previous contour line. This step results in an image where contours that overlap have
a much higher value than those that do not.
; get the contours of the image
contour, data, PATH_INFO=path_info, path_xy=path_xy,$
/PATH_DATA_COORDS, LEVELS=[0,1]
; build overlapping image
overlap_img = bytarr(oRaster.ns, oRaster.nl)
; create a container for the ROIs, we will use them again
oROIs = make_array(n_elements(path_info), /OBJ)
for i = 0 , n_elements(path_info)-1 do begin
; get the end pos
end_pos = (path_info[i].offset) + (path_info[i].n)-1
; get the points
pts = path_xy[*,(path_info[i].offset):end_pos]
; last point has to be the same as the first
xs = [[pts[0,*]],[pts[0,0]]]
ys = [[pts[1,*]],[pts[1,0]]]
; create the ROI
oROIs[i] = OBJ_NEW('IDLanROI', xs, ys)
; compute the mask
Mask = oROIs[i]->ComputeMask(INITIALIZE=0, DIMENSIONS=[oRaster.ns,$
; convert to binary
Mask = Mask eq 255
; add the mask to the image
overlap_img = overlap_img + Mask
Figure 3: Overlapping contour image
Once the overlapping image was created, I searched for regions that satisfy the
; get the max number of overlaps in the image
max_overlap = max(overlap_img)
; set the desired ratios
desired_ratio1 = 2. + (2./3.)
desired_ratio2 = 1. + (7./9.)
; create a container for the finder points
finder_cm = []
for i = 0 , n_elements(path_info)-1 do begin
; compute the mask
Mask = oROIs[i]->ComputeMask(INITIALIZE=0, DIMENSIONS=[oRaster.ns,$
; convert to binary
Mask = Mask eq 255
;Mask overlap image
StudyArea = overlap_img * Mask
;compute the histogram of the image
Hist = HISTOGRAM(StudyArea, LOCATIONS=pos, NBINS=nbins, BINSIZE = 1, MIN=1,$
; if there are more or less than 3 values, then discard it
pos = where(Hist ne 0)
if n_elements(pos) eq 3 then begin
; get the counts for each bin
vals = float(hist[pos])
;calculate the ratios
;outer black ring / inner
ratio1 = vals[0] / vals[2]
;white ring / inner
ratio2 = vals[1] / vals[2]
; check that the difference is desired ratio
ratio1_dif_percent = ratio1 / desired_ratio1
ratio1_dif_percent = abs(ratio1_dif_percent - 1.)
ratio2_dif_percent = ratio2 / desired_ratio2
ratio2_dif_percent = abs(ratio2_dif_percent - 1.)
; if they are within 60%, save as a finder point
if ratio1_dif_percent lt .3 and ratio2_dif_percent lt .3 then begin
; calculate the center of mass
StudyArea = StudyArea gt 0
Mass = Total(StudyArea)
center_x = Total( Total(StudyArea, 2) * Indgen(oRaster.ns) ) / Mass
center_y = Total( Total(StudyArea, 1) * Indgen(oRaster.nl) ) / Mass
; record the center
finder_cm = [[finder_cm],[center_x,center_y]]
Last, but not least, I took a moment to plot the results and admire the fruits of my labor.
; display the input image
im = image(oRaster.GetData(interleave='bsq') )
; plot the location of the finder points on top of the input image
for i = 0 ,n_elements(finder_cm[0,*])-1 do $
p = SCATTERPLOT(finder_cm[0,i],finder_cm[1,i],$
OVERPLOT = im, AXIS_STYLE=0, SYM_COLOR='red',$
SYM_FILL_COLOR='blue', SYM_FILLED=0, SYM_SIZE=2,$
Figure 4: Final results
I hope that you got something out of this demo. If not how to locate a finder point, then perhaps how to use contours in a new and exciting way. | {"url":"https://www.nv5geospatialsoftware.com/Learn/Blogs/Blog-Details/find-the-finder","timestamp":"2024-11-13T22:55:21Z","content_type":"text/html","content_length":"125042","record_id":"<urn:uuid:8ba66e49-40ae-4431-b16b-3c8625dd33f0>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00419.warc.gz"} |
Lesson 3: A step up - Excel Exercise - Spreadsheet Center
Calculating the average of a group of numbers is quite simple: you sum them all up and divide by how many numbers you have. For example, the average of the number 1, 2, 3, 4 and 5 is: 1 + 2 + 3 + 4 +
5 divided by 5, because there are 5 numbers.
You could do this in Excel by typing =SUM(1,2,3,4,5)/5 into a cell. But there is an easier way. You can simply use the AVERAGE function. It looks something like this:
=AVERAGE(1, 2, 3, 4, 5)
And, as with the SUM function, you can use references to cells, like A1 or C4 in there instead of numbers.
Use the AVERAGE function in cell A7 to calculate the average of the numbers in cells A1 through A5.
Note: You have probably noticed that both of these functions are written in all-caps. That’s just the way function names in Excel are. So it may look like I’m screaming SUM at you, but that’s just
how it is written 😉 | {"url":"https://spreadsheetcenter.com/excel-exercises/a-step-up-average/?ssc_ej=true","timestamp":"2024-11-04T23:32:24Z","content_type":"text/html","content_length":"44921","record_id":"<urn:uuid:c4797420-5a40-4bd1-b11e-56f52e86eae0>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.84/warc/CC-MAIN-20241104225856-20241105015856-00183.warc.gz"} |
Add new Point on a Chart
Hi, team.
I don't understand how I can add a new bar to a chart, without reloading it.
I'm using addPoint, but it added it on top of previous bar.
Is there any way to automatically add a bar by shifting them one forward?
Click "Add Point"
What am I doing wrong?
Thanks !)
Re: Add new Point on a Chart
Thanks for contacting us with your question!
In your add point function, you assign to your new point the same time stamp - x value - as the last one, hence overlap occurs.
Assuming that the interval is one minute, you can modify your function in the following way:
Code: Select all
function addPoint() {
const series = chart_obj.series[0];
let last = series.points[series.points.length - 1];
let new_x = last['x'] + 60 * 1000;
let update_data = {
x: new_x,
open: last['open'] + Math.floor(Math.random() * 2 - 1),
high: last['high'] + Math.floor(Math.random() * 2 - 1),
low: last['low'] + Math.floor(Math.random() * 2 - 1),
close: last['close'] + Math.floor(Math.random() * 2 - 1)
const shift = series.data.length > (6 * 60 * 24);
series.addPoint(update_data, true, shift);
Please see your code with the change implemented: https://jsfiddle.net/BlackLabel/m8o7hLw0/
I hope you will find it useful.
Best regards,
Highcharts Developer
Re: Add new Point on a Chart
Thanks for your help. The solution helped to find a possible problem.
I have added code
Code: Select all
navigator: {
enabled: false
Here is an example https://jsfiddle.net/NeBox/qfj4nczr/2/
If I enable navigator, adding a bar works very badly. There is no animation of adding.
I don't need navigator, so I turned it off.
Re: Add new Point on a Chart
Hi again,
I've tested your code on my side and it seems that the addPoint implementation is false, since you're setting the redraw parameter to true, and then you're calling chart.redraw() method which might
have an impact on chart performance.
Below is a simplified demo with adding and shifting point functionaility, which should work regardless of the navigator appearance.
Demo: https://jsfiddle.net/BlackLabel/qzop7jLt/
Kind regards,
Jędrzej Ruta
Highcharts Developer
Re: Add new Point on a Chart
Thank you for reply.
I've changed code to your example, but it doesn't solve the problem
Here is an example https://jsfiddle.net/NeBox/qfj4nczr/5/
Try adding the bars a few times. They work a couple of times, then they stop being added and overlap each other
That demo shows the sample code I'm testing.
You have lastprice turned off and no other settings in your code.
I add two bars, the rest are not added normally.
Re: Add new Point on a Chart
After investigating your solution, it seems that the x-axis extremes set on the initial load of the chart are blocking the points from being visible. If you update the x-axis extremes after adding
point, it should work correctly.
Demo: https://jsfiddle.net/BlackLabel/b5neg3k6/
Kind regards,
Jędrzej Ruta
Highcharts Developer
Re: Add new Point on a Chart
Thanks for help, everything seems to be working. | {"url":"https://www.highcharts.com/forum/viewtopic.php?p=194918&sid=7939a06312986f78df25448eff2bdfa7","timestamp":"2024-11-14T01:22:22Z","content_type":"text/html","content_length":"45923","record_id":"<urn:uuid:c9f9f68f-3974-4f52-9214-89735b31dd9e>","cc-path":"CC-MAIN-2024-46/segments/1730477028516.72/warc/CC-MAIN-20241113235151-20241114025151-00388.warc.gz"} |
Understanding the Clifford Product: A Deep Dive into Grassmann Algebra
Written on
Chapter 1: Introduction to the Clifford Product
The Clifford product serves as a fundamental operation in Grassmann algebra. It describes the inner product between two vectors, which can be illustrated through the following components:
Given the basis vectors e1 and e2, the inner product can be represented as
This signifies the product of the magnitude of vector x and the projection of vector y onto x. The notation
denotes the L2-norm, while ? represents the angle between vectors x and y within their shared plane.
In contrast, the outer product—often referred to as the Wedge product—is defined as
This operation represents the multiplication of vector x with the projection of vector y onto the direction orthogonal to x. The unit bivector
indicates the orientation of the hyperplane formed by
As detailed in Section II of geometric-algebra adaptive filters, the Clifford product (also known as the geometric product, represented by the dot symbol) is expressed as
This algebra is crucial for modeling vector fields, proving essential in applications such as wind velocity analysis and fluid dynamics, notably in the Navier-Stokes equation.
The video "Spinors for Beginners 11: What is a Clifford Algebra? (and Geometric, Grassmann, Exterior Algebras)" provides an insightful overview of Clifford algebras and their geometric
In the "Clifford Algebra" video, various aspects of Clifford algebra are discussed, offering a comprehensive introduction to its principles and applications.
• Spinors for Beginners 11: What is a Clifford Algebra? (and Geometric, Grassmann, Exterior Algebras). YouTube.
• A Swift Introduction to Geometric Algebra. YouTube.
• Learning on Graphs & Geometry. Weekly reading groups every Monday at 11 am ET.
• What’s the Clifford algebra? Mathematics Stack Exchange.
• Introducing CliffordLayers: Neural Network layers inspired by Clifford / Geometric Algebras. Microsoft Research AI4Science.
• David Ruhe, Jayesh K. Gupta, Steven de Keninck, Max Welling, Johannes Brandstetter (2023). Geometric Clifford Algebra Networks. arXiv:2302.06594.
• Maksim Zhdanov, David Ruhe, Maurice Weiler, Ana Lucic, Johannes Brandstetter, Patrick Forre (2024). Clifford-Steerable Convolutional Neural Networks. arXiv:2402.14730. | {"url":"https://czyykj.com/understanding-the-clifford-product.html","timestamp":"2024-11-08T11:01:38Z","content_type":"text/html","content_length":"10371","record_id":"<urn:uuid:9184203d-d49e-4eee-bef3-4c43423ad454>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00463.warc.gz"} |
ase study at Soultz-sous-Forêts
1 Introduction
Modeling of the fluid transport in low permeable crustal rocks is of central importance for many applications (Neuman, 2005). Among them is the monitoring of the geothermal circulation in the project
of Soultz-sous-Forêts, France, (Bachler et al., 2003) where the heat exchange especially occurs through open fractures in granite (Gérard et al., 2006).
Numerous hydrothermal models have already been proposed. For simple geometries, some analytical solutions are known: e.g., the cases of parallel plates (Turcotte and Schubert, 2002) or flat cylinders
(Heuer et al., 1991). More complex models exist as well like the models of three-dimensional (3D) networks of fractures reproducing geological observations and possibly completed with stochastical
distributions of fractures (e.g. in Soultz-sous-Forêts, France, (Gentier, 2005; Rachez et al., 2007) or in Rosemanowes, UK (Kolditz and Clauser, 1998)). Nevertheless, the geometry of each fracture is
generally simple. Kolditz and Clauser (1998) have however suspected that differences between heat models and field observations could be due to channeling induced by the fracture roughness or the
fracture network. Channeling of the fluid flow owing to fracture roughness has indeed already been experimentally observed and studied (Méheust and Schmittbuhl, 2000; Plouraboué et al., 2000;
Schmittbuhl et al., 2008; Tsang and Tsang, 1998).
Here, we limit our study to the fracture scale and we will show only one example of thermal behavior, among other simulations we completed (Neuville et al., submitted). The specificity of our
hydrothermal model is to take into account the different scale fluctuations of the fracture morphology. We aim at bringing out the main parameters, which control the hydraulic and thermal behavior of
a complex rough fracture. The perspective is to propose a small set of effective parameters that could be introduced within simplified elements for an upscaled network model.
We first describe our geometrical model of the fracture aperture thanks to self-affine apertures. Then, using lubrication approximations, we obtain the bidimensional (2D) pressure and thermal
equations when a cold fluid is injected through the fracture in a stationary regime. The temperature within the surrounding rock is supposed to be hot and constant in time and space. The fluid
density is also supposed to be constant.
We apply our numerical model to the case study at Soultz-sous-Forêts and we show for this case an example of the computed hydraulic and thermal behavior. Finally, we aim at bringing out what is the
minimal geometrical information needed to get the dominant behavior of the hydraulic and thermal fields. This last approach is based on spatial low pass Fourier filtering of the geometrical aperture
2 Modeling
2.1 Roughness of the fracture aperture
We consider that the mean fracture plane is described by the $(xˆ,zˆ)$ coordinates and the perpendicular direction is $yˆ$ (Fig. 1) – where the hat notation refers to unit vectors along the (x,y,z)
axis. It has been shown that a possible geometrical model of natural rough fractures consists in self-affine surfaces. A surface described by a function y=f(x,z) is self-affine if it is
statistically invariant under the scaling transformation x→λx, z→λz and y→λ^ζy, where ζ is called the roughness exponent or Hurst exponent. Such surfaces are therefore statistically invariant
upon an isotropic scaling within their mean plane while along the perpendicular direction, the scaling is anisotropic (e.g. Brown and Scholz, 1985; Cox and Wang, 1993; Power et al., 1987; Schmittbuhl
et al., 1993, 1995). Most fracture surfaces in heterogeneous material exhibit a Hurst exponent equal to ζ=0.8 (Bouchaud, 1997; Santucci et al., 2007; Schmittbuhl et al., 1993, 1995). Sandstone
fractures, however, show ζ=0.5 (Boffa et al., 1998; Méheust, 2002).
Fig. 1
It is important to note that a self-affine surface having a roughness exponent smaller than one is asymptotically flat at large scales (Roux et al., 1993). Accordingly, the self-affine topography can
be seen as a perturbation of a flat interface. When the lubrication approximation (Pinkus and Sternlicht, 1961) holds, in particular with smooth enough self-affine perturbations or highly viscous
fluid, only the local aperture controls the flow and not the local slope of the fracture. The accuracy of the lubrication approximation, compared to the full Navier-Stokes resolution, was studied in
Al-Yaarubi et al. (2005). Under this assumption, the only required geometrical input is the aperture field (also called the geometrical aperture); there is no need to know the geometry of each facing
fracture surfaces. The aperture between two uncorrelated self-affine fracture surfaces having the same roughness exponent is as well self-affine (Méheust and Schmittbuhl, 2003). Thus, we generate the
numerical apertures by using self-affine functions.
Several independent self-affine aperture morphologies can be generated with the same roughness exponent chosen equal to ζ=0.8. They exhibit various morphology patterns according to the chosen seed
of the random generator (Méheust, 2002). The mean geometrical aperture A and the root-mean square deviation σ (RMS) of an aperture a(x,z) are defined as
with l[x] the length and l[z] the width of the fracture. To keep the boundary geometry of the domain as simple as possible, we do not allow any contact area (i.e. no local aperture equal to zero).
This is obtained by considering a large enough aperture average to get strictly positive aperture fields.
It has to be noted that our hydrothermal model can be applied to other geometrical models (i.e. different from a self-affine model), which might be more relevant depending on the geological context.
2.2 Physics of hydraulic flow
The hydraulic flow is obtained under the same hypotheses and solved in the same way as in Méheust and Schmittbuhl (2001). We use finite differences, and the system of linear equations is inverted
using an iterative biconjugate gradient method (Press et al., 1992).
We impose a pressure drop across the system and study the steady state flow of a Newtonian fluid at low Reynolds number, so that the viscous term dominates the inertial one in the Navier-Stokes
equation (Batchelor, 2002; Stokes, 1846):
where η is the dynamic viscosity, u^3D the velocity of the fluid and P is the pressure deviation from the hydrostatic profile (or the hydraulic head equal to the pressure corrected by the gravity
effect). To be in the framework of the lubrication approximation (Pinkus and Sternlicht, 1961), we consider fractures with constant enough apertures together with a small Reynolds number. In doing
so, the velocity vector of the fluid flow has negligible components normal to the mean fracture plane. We consider that the macroscopic pressure gradient is imposed along $xˆ$; $zˆ$ is therefore
perpendicular to the mean flow direction. Accordingly, the fluid velocity follows a parabolic law (e.g. Iwai, 1976) (Fig. 2):
$u→3D(x,y,z)=∇→2P2η(y−y1)(y−y2)$ (4)
where y[1] and y[2] are the local fracture sides coordinates and $∇→2$ is the gradient operator in the fracture plane. The hydraulic flow through the fracture aperture follows a cubic law:
$q→(x,z)=∫au→3D(x,y,z)dy=−a312η∇→2P$ (5)
Fig. 2
and the bidimensional (2D) velocity $u→$ is defined from the average of the velocity $u→3D$ over the aperture with
$u→(x,z)=1a(x,z)∫au→3D(x,y,z)dy=−a212η∇→2P$ (6)
Furthermore, considering the fluid to be incompressible, the Reynolds equation is obtained: $∇→2(a3∇→2P)=0$. As boundary conditions of this equation, we impose the pressure at the inlet and outlet of
the fracture (if x=0, P=P[0] and if x=l[x], P=P[lx], with P[0]>P[lx]) and consider impermeable sides at z=0 and z=l[z].
2.3 Physics of thermal exchange
On the basis of a classical description (e.g. Ge, 1998; Turcotte and Schubert, 2002), we aim at modeling the fluid temperature when cold water is permanently injected at the inlet of a hot fracture
at temperature T[0]. As the conduction inside the rock is not taken into account (hypothesis of infinite thermal conduction inside the rock), the fracture sides are supposed to be permanently hot at
the fixed temperature T[r]. This hypothesis should hold for moderate time scales (e.g. minutes), after the fluid injection has stabilized, and before the rock temperature has significantly changed,
or alternatively once the whole temperature bedrock is stabilized (which depends on the boundary condition of the entire region). For time scales implying evolution of the rock temperature, our model
should be coupled to a model of the rock temperature evolution.
The fluid temperature is controlled by the balance between thermal convection and conduction inside the fluid, which reads (Landau and Lifchitz, 1994): $u→3D⋅∇→T=χΔT$ where χ is the thermal
diffusivity of the fluid and T the fluid temperature. We extend the local lubrication approximation by considering that the slopes of the fracture morphology are small enough to limit the conduction
only along the y-axis. We suppose that the leading terms are the conduction along the y-axis and the in-plane convection (since there is no fluid velocity component along $yˆ$). Indeed, the off-plane
free convection has been shown to be negligible (its magnitude is of the order of km/year (Bataillé et al., 2006)). So, the previous equation reduces to:
$∂2T∂y2=u→x3Dχ∂T∂x+u→z3Dχ∂T∂z$ (7)
where $u→x3D$, $u→z3D$ are the in-plane components of the fluid velocity. The fluid is supposed to be at rock temperature along the fracture sides, and sufficiently far from the inlet. When we
integrate Eq. (7) along the fracture aperture, we assume that β=q[x](∂T/∂x)+q[z](∂T/∂x) is independent of y, where q[x] and q[z] are the in-plane component of $q→$ defined in Eq. (5). Accordingly,
we find that the temperature solution has a quartic profile (Fig. 2) along the fracture aperture:^1
$T=−β2a3χ(y−y1)(y−y2)(y−5y1)(y−5y2)+Tr$ (8)
where y[1] and y[2] are the local fracture sides coordinates.
Similarly to what is done for the hydraulic flow, we solve the thermal equation by integrating it along the fracture aperture (following the lubrication approximation extended to the thermal field).
In particular, when doing the balance of the energy fluxes, we express the advected free energy flux as $ρc∫au3D(x,y,z)[T(x,y,z)−T0]dy$. Accordingly, we introduce:
$T¯(x,z)=∫au3D(x,y,z)T(x,y,z)dy∫au3D(x,y,z)dy$ (9)
which is an average of the temperature profile weighted by the local norm of velocity. We also use the Nusselt number Nu=φ[r]/φ[ref] which compares the efficiency of the heat flow along the
fracture boundaries:to the mesoscopic heat flow at the fracture aperture scale without convection: $φref=χρc(Tr−T¯)/a$. Using the polynomial expression of T (in Eq. (8) and the definition of $T¯$, we
get $β=140χ(Tr−T¯)/(17a)$ and Nu=70/17. Eq. (7) leads then to:
$q→⋅∇→2T¯+2χaNu(T¯−Tr)=0,$ (11)
Boundary conditions are: $T¯(0,z)=T0$ at the inlet and $T¯(lx,z)=Tr$ at the outlet (with l[x] large enough). Any boundary condition for the temperature along z=0 or z=l[z] can be used as the
hydraulic flow $q→$ is null there.
We discretize this equation by using a first order finite difference scheme and finally get $T¯$ by inverting the system using a biconjugated gradient method (Press et al., 1992).
It is finally possible to get the three-dimensional temperature field T anywhere within the fluid by using the previous β expression and the quartic profile (Eq. (8). Fig. 3 illustrates an example of
temperature field at a given z=z[0], T(x,y,z=z[0]), obtained in that way from a given bidimensional field $T¯$. Along any given cut at x=x[0], the temperature (represented by the color scale)
follows a quartic law (Fig. 2). The boundaries between the colors are isotherms.
Fig. 3
2.4 Definition of characteristic quantities describing the computed hydraulic and thermal fields
2.4.1 Comparison to modeling without roughness
If we consider a fracture modeled by two parallel plates separated by a constant aperture A, then the gradient of pressure is constant all along the fracture as well as the hydraulic flow which is
equal to:
where the subscript // is for parallel plate conditions and ΔP=P[lx]−P[0]. Under these conditions, the analytical solution of Eq. (11) is:
$T¯//=(T0−Tr)exp−xR//+Tr$ (13)
where R[//] is a thermal length describing the distance at which the fluid typically reaches the temperature of the surrounding rock. We have:
$R//=A||q→//||2Nuχ=−ΔPlxA424ηNuχ=APeNu$ (14)
where Pe is the Péclet number defined by $Pe=||q→//||/2χ$. Pe expresses the magnitude of the convection with respect to the conduction.
For rough fractures, we want to study whether the temperature profiles along x at a coarse grained scale can still be described by Eq. (13) and, if so, what is the impact of the fracture roughness on
the thermal length R.
2.4.2 Hydraulic aperture
The hydraulic flow can be macroscopically described using the hydraulic aperture H (Brown, 1987; Zimmerman et al., 1991), defined as the equivalent parallel plate aperture to get the macroscopic flow
〈q[x]〉 under the pressure gradient ΔP/l[x]:
where the quantity under bracket is the spatial average over x and y. Note that the hydraulic aperture H is an effective measure that can be estimated from hydraulic tests whereas the geometrical
aperture A is deduced from a direct measurement of the fracture geometry. If H/A is higher than 1, then the fracture is more permeable than parallel plates separated by A. Hydraulic apertures can
also be defined locally as:
$h(x,z)=−qx(x,z)12ηlxΔP1/3$ (16)
Local geometrical and hydraulic apertures are denoted here with small letters while the corresponding macroscopic variables (mean geometrical and hydraulic aperture) are in capital letters.
2.4.3 Thermal aperture
For the thermal aspect, once $T¯$ is known, we aim at defining a thermal length R like in Eq. (13). To do that, we define $T¯¯$, a z-average temperature which varies only along the forced gradient
direction x, and weighted by the 2D fluid velocity u[x] to fulfill energy conservation:
$T¯¯(x)=∫lzux(x,z)T¯(x,z)dz∫lzux(x,z)dz$ (17)
Then, based on the flat plate temperature solution (Eq. (13), we do a linear fit of $ln[(T¯¯−Tr)/(T0−Tr)]$ plotted as a function of x, and we use the slope of this fit to get the characteristic
thermal length R. This fit is computed over the zone where the numerical precision of the fitted quantities is sufficient (larger than ln[2×10^−6]). Similarly to the parallel plate case (Eq. (14)),
the thermal length R can be used to define a thermal aperture Γ:
which means that a fracture modeled by parallel plates separated by a distance Γ provides the same averaged thermal behavior as the rough fracture of mean geometrical aperture A.
3 Case study at Soultz-sous-Forêts (France)
3.1 Computation of apertures, hydraulic and thermal fields
Let us consider the GPK3 and GPK2 wells of the deep geothermal drilling near Soultz-sous-Forêts (France), which are separated by a distance of about 600m at roughly 5000m of depth. From hydraulic
tests (Sanjuan et al., 2006), it has been shown that the hydraulic connection between both wells is relatively direct and straight. Sausse et al. (Sausse et al., 2008) showed that actually a fault is
linking GPK3 (at 4775m) to GPK2. This fault zone consists of a large number of clusters of small fractures (most apertures ranges around 0.1mm) (Sausse et al., 2008) which probably lead to complex
hydraulic streamlines and heat exchanges. We study here a simplified model of this connecting fault zone between the wells using one single rectangular rough fracture. The size of the studied
fracture is l[x]×l[y]=680×1370m^2. Individual fracture apertures are typically of the order of 0.2mm (Genter and Jung, private communication) while the fracture zone is rather thicker (10cm)
(Sausse et al., 2008). To account for this variability of the fault zone aperture, we use a probabilistic model with the following macroscopic properties: a mean aperture A equal to 3.60mm and its
standard deviation to σ=1.23mm. Fig. 4 shows an example of a self-affine aperture randomly generated with the required parameters.
Fig. 4
With little knowledge about the pressure conditions along the boundaries of this model, we assume that the two facing sides along x of this rectangular fracture correspond to the inlet and outlet of
the model where the pressure is homogeneous, respectively P[0] and P[lx]. In other words, we assume the streamlines to be as straight as possible between both wells.
The pressure gradient ΔP/l[x] is chosen as −10^−2bar/m, which corresponds to about six bars between the bottom of both wells. The dynamic viscosity is chosen to be 3×10^−4Pa/s (reference value
for pure water at 10Pa and 100°C in Spurk and Aksel (2008)). The Reynolds number rescaled with the characteristic dimensions of the fracture (Méheust and Schmittbuhl, 2001) is equal to Re′=(ρu[x]
a^2)/(η.l[x])=0.026 and the Péclet number is Pe=3.8×10^4.
Then, we solve the hydraulic flow in the fracture domain and obtain the 2D velocity field, $u→$ defined in Eq. (6). Fig. 5 shows the spatial fluctuations of $||u→||$. For information, a parallel
plate model separated by the chosen aperture A would predict a homogeneous fluid velocity of 3.6m/s and a thermal length R[//]=33.3m. As we see in Fig. 5, the 2D velocity field exhibits
interesting features: the fluid is rather immobile along the upper and lower borders of the fracture (close to z=0 and z=l[x]) while most of the fluid flows very quickly through a channel in the
middle of the fracture.
Fig. 5
The macroscopic hydraulic aperture is deduced from the local hydraulic flow estimate (Eq. (15)): H=3.73mm, which is slightly higher than the mean mechanical aperture A=3.60mm. Therefore, this
fracture is more permeable than parallel plates separated by A. In other words, the fracture is geometrically thinner than what one would expect from the knowledge of H possibly inverted from an
hydraulic test. However, the local hydraulic apertures h (Eq. (16)) range from nearly 0 to 5.43mm (Fig. 6).
Fig. 6
From the average estimate of the fluid velocity, we can go back to our approximation of a linear inlet, even if the fracture is not vertical and does not intersect the well on a very long distance.
We might estimate this distance from the following argument. The flow rate observed at Soultz is about Q=20L/s. Thus, using a velocity of about u=3.6m/s and a fracture aperture equal to 3.6mm
implies that the well crosses such fractures over a cumulated length of about (neglecting the well radius):
which is effectively much smaller than the boundary size. However, we expect the presence of connecting fractures between the well and the fault zone to be sufficiently permeable to define an
effective linear inlet of constant effective pressure. All the results presented here are valid under any dimensioning which keeps the ratio l[x]/R[//] constant (here equal to 20.5): for instance,
the results apply for l[x]=690m, A=10mm and ΔP/l[x]=−1.7×10^−4bar/m (using the same fluid parameters), which leads to a Poiseuille velocity of about 0.46m/s.
As we see, $T¯$ is very inhomogeneous and also exhibits channeling. The chosen inlet temperature is T[0]=60°C, the rock temperature is T[r]=200°C (Fig. 7) and the fluid diffusivity is χ=
0.17mm^2/s (corresponding to water at T=100°C, from Taine et Petit (2003). Note that the rock temperature will evolve over time in contrast to the one of our approximations. Indeed, the rock
thermal diffusivity is about 1mm^2/s which is larger than the fluid diffusivity (χ=0.17mm^2/s) but not sufficiently to be fully neglected.
Fig. 7
However, $T¯$ is rather different from a parallel plate solution. Indeed, the solution is not invariant in $zˆ$. Different temperature profiles function of x are shown in Fig. 8. Two end-member types
of behavior are plotted: temperature profiles at z=960m (curve iv) and z=700m (curve v). The temperature difference can be larger than 100°C in the inlet region. Even rather far from the
inlet, for example at x=200m, the temperature difference can still be of the order of 17°C (200.0°C for z=960m, and 183.4°C for z=700m). The temperature field T(x,y,z=700m) for this
set of parameters is shown in Fig. 3, where we see how the temperature evolves along the x-axis, away from the mean plane. Temperature profiles can be compared to the one obtained for a parallel
plate model where plates are separated by the aperture A (curve iii) which reads from Eqs. (13) and (17): $T¯¯//=T¯//$.
Fig. 8
Following this model (curve iii), the fluid should be at 199.7̊C at x=200m. If we compare $T¯¯//$ to the averaged observed temperature $T¯¯$ (defined in Eq. (13)) (Fig. 8, curve i), we see that
$T¯¯//$ is not representative of the end-member types of behavior. We model $T¯¯$ by using an adapted parallel law $T¯¯mod$ (curve ii), which is an exponential law with a suitable thermal length R:
$T¯¯mod=(T0−Tr)exp−x−x0R+Tr$ (19)
where R=97m (i.e. 2.9×R[//]) and x[0]=−10m. As we do a least square fit on a semi-log space to obtain the parameters R and x[0], the beginning of the fit in the linear-linear space is not
accurate. We see that the distance between wells (600m in our case study) is about six times larger than R. However, owing to channeling the fluid temperature will not necessarily be in full
equilibrium with the rock temperature at the out well. The thermal aperture is equal to Γ=4.7mm, which is rather different from the geometrical aperture A=3.6mm. A larger thermal aperture
(compared to the geometrical one) means an inhibited thermalization on average.
3.2 Temperature estimation with few parameters
The knowledge of the spatial correlations rather than all the details of the geometrical aperture seems to be a key parameter to evaluate the hydraulic flow and the temperature of the fluid in a
rough fracture. Indeed, the macroscopic geometrical aperture A brings too little information to characterize the heat exchange at the fracture scale. By contrast, it is impossible in particular for
field measurements to know in detail the spatial variability of the local geometrical aperture A. Therefore, we propose to characterize the macroscopic geometrical properties with more than a single
value, using several parameters describing the largest spatial variations. Numerically, it is possible to obtain them by filtering the fracture aperture field in the Fourier domain.
Fig. 9 shows the aperture field displayed in Fig. 4 once it has been filtered with the following criterion: only the Fourier coefficients fulfilling
are kept, where k[x] and k[z] are the wave vector coordinates along respectively the x and z-axes. Since the Fourier transform is discrete, it means that we only keep the Fourier components
corresponding to the wave number $(nx,nz)=(2π/(kx.lx),2π/(kz.lz))$ in {(0,0);(0,1);(1,0);(1,1)} (i.e. the average A and the first Fourier modes along x and z are left).
Fig. 9
Let us assume that we only have these data available to evaluate the hydraulic flow and heat exchange. Using the same method and the same parameters as previously, we compute the pressure field
corresponding to the filtered aperture field. In Fig. 10, we show the hydraulic aperture field we obtain. As we see, the high hydraulic aperture channel in the middle of the figure remains, while
high frequency variations are removed. These large scale fluctuations of the hydraulic flow, computed from the knowledge of a very limited set of Fourier modes of the geometrical aperture, might be
obtained from field measurements. Then, the corresponding temperature field shown in Fig. 11 is computed. The main features of the thermal field (Fig. 7) are still visible: the main channel is at the
same position and the values are of the same order of magnitude. Despite small local differences, this substitution model gives a relevant description of what thermally happens.
Fig. 10
Fig. 11
4 Conclusions
We propose a numerical model to estimate the impact of the fracture roughness on the heat exchange at the fracture scale between a cold fluid and the hot surrounding rock. We assume the flow regime
to be permanent and laminar. The numerical model is based on a lubrication approximation for the fluid flow (Reynolds equation). We also introduce a “thermal lubrication” approximation, which leads
to a quartic profile of the temperature across the aperture. It is obtained by assuming that the in-plane convection is dominant with respect to the in-plane conduction (i.e. high in-plane Péclet
number). The lubrication approximation implies also that the off-plane convection is neglected; subsequently, the heat conduction initiated by the temperature difference between the rock and the
fluid is supposed to be the major off-plane phenomenon.
Our model shows that the roughness of the fracture can be responsible for fluid channeling inside the fracture. In this zone of high convection, the heat exchange is inhibited, i.e., the fluid needs
a longer transport distance to reach the rock temperature. Spatial variability of the temperature is characterized on average by a thermal length and a thermal aperture.
In this article, we illustrate our modeling by a case study at the geothermal reservoir of Soultz-sous-Forêts, France, with a rough aperture which leads to inhibited thermal exchanges owing to a
strong channeling effect, in the sense that the characteristic thermal length in this stationary situation is longer in rough fractures than in flat ones with the same transmissivity. Qualitatively,
this can be attributed to the localization of the flow inside a rough fracture: most of the fluid flows through large aperture zones at faster velocity than the average, which leads to longer
thermalization distances.
We performed simulations for about 1000 other aperture fields (not illustrated here) compatible with the macroscopic observations, of the same type as shown here. A general property holds for all
these aperture fields: the thermal exchanges are always inhibited in rough fractures, compared to a fracture modeled by parallel plates with the same macroscopic hydraulic transmissivity (Neuville et
al., submitted) (same H).
From the numerical solutions, we see that the mean geometrical aperture provides too little information to characterize the variability of the fluid flow and fluid temperature. In contrast, the
knowledge of the dominant spatial variation of the geometrical aperture field (here obtained by keeping only the largest scale fluctuations using low pass Fourier filtering) provides interesting
information about the spatial pattern of the hydraulic and thermal fields. The macroscopic spatial correlation of the aperture is shown to be an important parameter ruling the hydrothermal behavior.
Note that we considered a self-affine model for the aperture roughness, but other types of geometrical descriptions of this roughness (given either by constraints from field measurements, or other
kind of geometrical models), could be also considered using the type of simulations described here.
We thank Albert Genter, Reinhard Jung Marion, Patrick Nami, Marion Schindler, Eirik G. Flekkøy, Stéphane Roux, Jose S. Andrade Jr. and Yves Méheust for fruitful discussions. This work has been
supported by the EHDRA project, the REALISE program and the French Norwegian PICS project.
^1 We compared our method to another algorithm based on a Lattice Boltzmann (LB) method, which does not reduce Navier-Stokes to a Stokes equation and does not hypothesize any lubrication
approximation, in order to solve the velocity and temperature fields. The finite diffusivity of the rock is also taken into account. From those results, it appears that the analytical parabolic and
quartic approximations (with the proper coefficients) of the respective fields are indeed consistent within a 5% error bar with the LB results. | {"url":"https://comptes-rendus.academie-sciences.fr/geoscience/articles/en/10.1016/j.crte.2009.03.006/","timestamp":"2024-11-03T18:46:09Z","content_type":"text/html","content_length":"146586","record_id":"<urn:uuid:85715412-9662-466c-b717-231d4ff2e1ea>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00398.warc.gz"} |
NCERT Class 6 Maths Chapter 3 Exercise 3.1 Number Play PDF
NCERT Solutions for Class 6 Maths Number Play Chapter 3 Exercise 3.1 - FREE PDF Download
NCERT Solutions for Class 6 Maths Chapter 3, Exercise 3.1, "Numbers Can Tell Us Things," focuses on helping students understand how numbers can be manipulated and used in various mathematical
operations. This exercise encourages students to explore number patterns, identify relationships between numbers, and improve their problem-solving skills. These solutions also offer helpful tips and
methods to simplify complex concepts, ensuring that students build a strong foundation in mathematics. Class 6 Maths NCERT Solutions provides clear, step-by-step explanations to make learning easy
and engaging.
1. NCERT Solutions for Class 6 Maths Number Play Chapter 3 Exercise 3.1 - FREE PDF Download
2. Glance on NCERT Solutions Maths Chapter 3 Exercise 3.1 Class 6 | Vedantu
3. Access NCERT Solutions for Maths Class 6 Chapter 3 - Number Play
4. Benefits of NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.1 Number Play
5. Class 6 Maths Chapter 3: Exercises Breakdown
6. Important Study Material Links for Maths Chapter 3 Class 6
8. Chapter-wise NCERT Solutions Class 6 Maths
9. Related Important Links for Class 6 Maths
Download the FREE PDF for NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.1 Number Play, prepared by Vedantu experts and aligned with the latest CBSE Class 6 Maths syllabus for convenient
Glance on NCERT Solutions Maths Chapter 3 Exercise 3.1 Class 6 | Vedantu
• In NCERT Solutions for Class 6 Maths Chapter 3, Exercise 3.1 - Number Play, students focus on exploring how numbers can be used in different operations and identifying number relationships.
• The exercise emphasises understanding how numbers relate to one another and how to manipulate them to solve problems.
• The solutions include a variety of examples and practice problems to help students grasp number manipulation concepts.
• By working through these solutions, students develop a strong foundation in numerical reasoning and problem-solving, preparing them for more complex mathematical topics.
FAQs on NCERT Solutions for Class 6 Maths Chapter 3 - Number Play Exercise 3.1
1. What is the focus of NCERT Solutions for Chapter 3, Exercise 3.1 - Number Play?
The focus is on understanding and solving problems related to number patterns, sequences, and the relationships between numbers.
2. How do NCERT Solutions help in learning number patterns?
The solutions offer step-by-step explanations that make it easier to identify and understand number patterns, helping students grasp the concepts better.
3. Are NCERT Solutions for Class 6 Maths Chapter 3 - Number Play Exercise 3.1 aligned with the CBSE syllabus?
Yes, the NCERT Solutions are fully aligned with the latest CBSE Class 6 Maths syllabus, ensuring students cover all important topics.
4. What kind of questions are covered in Exercise 3.1?
Exercise 3.1 focuses on problems related to number manipulation, sequences, and identifying patterns in numbers.
5. Can NCERT Solutions for Exercise 3.1 help with exam preparation?
Yes, these solutions provide clear and concise explanations that make it easier for students to revise and prepare effectively for exams.
6. How do NCERT Solutions for Class 6 Maths Chapter 3 - Number Play Exercise 3.1 help in improving problem-solving skills?
By breaking down each problem into simple steps, the solutions help students practice and improve their problem-solving techniques.
7. Where can students download NCERT Solutions for Class 6 Maths Chapter 3?
Students can download the free PDF of NCERT Solutions for Chapter 3, Exercise 3.1 from the Vedantu Website. These solutions also offer helpful tips and methods to simplify complex concepts, ensuring
that students build a strong foundation in mathematics.
8. Are NCERT Solutions for Class 6 Maths Chapter 3 - Number Play Exercise 3.1 helpful for quick revision?
Yes, the solutions are structured in a way that allows for easy and quick revision, especially before exams.
9. Do NCERT Solutions for Class 6 Maths Chapter 3 - Number Play Exercise 3.1 offer methods for solving complex number problems?
Yes, the solutions provide clear methods for solving complex number patterns and sequences, ensuring students understand the steps involved.
10. Can NCERT Solutions for Class 6 Maths Chapter 3 - Number Play Exercise 3.1 help in building a strong foundation in mathematics?
Absolutely, the NCERT Solutions for Chapter 3, Exercise 3.1 help students build a strong foundation by providing detailed explanations and practice with number-related problems. | {"url":"https://www.vedantu.com/ncert-solutions/ncert-solutions-class-6-maths-chapter-3-exercise-3-1","timestamp":"2024-11-08T02:04:10Z","content_type":"text/html","content_length":"351926","record_id":"<urn:uuid:54adf727-c9a0-4d4e-ba8d-b2580901a76b>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00808.warc.gz"} |
A “creative” integral
An interesting “creative” integral pointed my way by the marvellous @DavidKButlerUoA:
Find $\int {\frac{1}{(1+x^2)^2}} \dx$
There are “proper” ways to do this - in his tweet, David shows a clever way to do it by parts, and suggests a trig substitution as an alternative. I want to show a third way: partial fractions.
But wait - it’s already as partial-fractioned as it’s going to get, surely? Well, yes - but only if you stick to the reals.
If we bring imaginary numbers into play, we get:
$\frac{1}{(1+x^2)^2} = \frac{A}{x+i} + \frac{B}{(x+i)^2} + \frac{C}{x-i} + \frac{D}{(x-i)^2}$
Let’s multiply all of that up:
$1 = A(x+i)(x-i)^2 + B(x-i)^2 + C(x-i)(x+i)^2 + D(x+i)^2$
Then, when $x=i$, $1 = -4D$; when $x=-i$, $1=-4B$.
When $x=0$, $1= -(B+D) + (C-A)i$, which tells us that $C-A = -\frac{i}{2}$
And, considering just the $x^3$ terms, we have $0=A + C$, so $A=\frac{i}{4}$ and $C=-\frac{i}{4}$.
Putting it all together, we have $\frac{1}{(1+x^2)^2} = \frac{1}{4}\left( \frac{i}{x+i} - \frac{1}{(x+i)^2} - \frac{i}{x-i} - \frac{1}{(x-i)^2} \right)$
Now to integrate!
I’ll start by farming the 4 out to the other side.
$4I = \int \left( \frac{i}{x+i} - \frac{1}{(x+i)^2} - \frac{i}{x-i} - \frac{1}{(x-i)^2} \right) \dx$
Then we can integrate. All of these pan out as you’d expect:
$\dots = i \ln |x+i| + (x+i)^{-1} - i \ln |x-i| + (x-i)^{-1} + C$
… and we can start to simplify.
$\dots = i \ln \left| \frac{x+i}{x-i} \right| + \frac{ (x-i) + (x+i) }{(x-i)(x+i) } + C$
The second term is going to play nicely (it’s $\frac{2x}{x^2+1}$), but the first looks a bit off. We don’t really want to let on that we’ve used imaginary numbers now, do we?
A bit of legerdemain
A complex number - like, for example, $z = x+i$ - can be written in the form $Re^{i\theta}$, where $R$ is a real number, the magnitude, and $\theta$ is a real angle, the argument.
That leads to the conclusion that $\ln(z) = \ln(R) + i\theta$, if we’re willing to play fast and loose with the fact that we could have multiple arguments.
In particular, if $x$ is real, then $\ln(x+i) = \ln(x^2+1) + i\arctan\left(\frac{1}{x}\right)$.
Similarly, $\ln(x-i) = \ln(x^2 + 1) - i \arctan\left(\frac{1}{x}\right)$.
In turn, that means $i\left(\ln(x+i) - \ln(x-i)\right) = -2\arctan\left(\frac{1}{x}\right)$: our first term has turned into something much more approachable! We can even rewrite it immediately as an
Back to the plan
$4I = i \ln \left| \frac{x+i}{x-i} \right| + \frac{ (x-i) + (x+i) }{(x-i)(x+i) } + C$
$\dots = -2 \arccot(x) + \frac{2x}{x^2+1} + C$
Now, I’m not a big fan of arccotangents. Luckily, I have an arbitrary constant at hand, and I know that $\frac{\pi}{2} - \arccot(x) = \arctan(x)$. So, if I muddle the $\piby 2$ into the constant, I
can turn my $-\arccot(x)$ into $\arctan(x)$:
$4I = 2\arctan(x) + \frac{2x}{x^2+1} + C_2$
Or, finally:
$\int \frac{1}{(1+x^2)^2} dx = \frac{1}{2} \arctan(x) + \frac{1}{2} \frac{x}{x^2+1} + c$.
A selection of other posts
subscribe via RSS | {"url":"https://www.flyingcoloursmaths.co.uk/a-creative-integral/","timestamp":"2024-11-13T11:23:07Z","content_type":"text/html","content_length":"9711","record_id":"<urn:uuid:ba90cb93-e426-47e3-9457-cabfdd35bb30>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00716.warc.gz"} |
• Tue, Mar 05, 2024 @ 02:00 PM - 03:00 PM
Thomas Lord Department of Computer Science
University Calendar
PhD Thesis Proposal - Shao-Hung Chan
Committee members: Sven Koenig (chair), T.K. Satish Kumar, Lars Lindemann, John Carlsson, and Daniel Harabor
Title: Flex Distribution for Bounded-Suboptimal Multi-Agent Path Finding
Time: Mar. 5th, 2:00 PM - 3:00 PM
Location: EEB 349
Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths for multiple agents that minimize the sum of path costs. Explicit Estimation Conflict-Based Search (EECBS) is a
leading two-level algorithm that solves MAPF bounded-suboptimally, i.e., within some factor w away from the minimum sum of path costs C*. It uses Focal Search to find bounded-suboptimal paths
on the low level and Explicit Estimation Search (EES) to resolve collisions on the high level. To solve MAPF bounded-suboptimally, EES keeps track of a lower bound LB on C* to find paths
whose sum of path costs is at most w times LB. However, the costs of many paths are often much smaller than w times their minimum path costs, meaning that the sum of path costs is much
smaller than w times C*. Thus, in this proposal, we hypothesize that one can improve the efficiency of EECBS via Flex Distribution. That is, one can use the flex of the path costs (that
relaxes the requirement to find bounded-suboptimal paths on the low level) to reduce the number of collisions that need to be resolved on the high level while still guaranteeing to solve MAPF
bounded suboptimally. We also discuss the limitations of Flex Distribution and propose some techniques to overcome them.
Location: Hughes Aircraft Electrical Engineering Center (EEB) - 349
Audiences: Everyone Is Invited
Contact: CS Events | {"url":"https://viterbi.usc.edu/news/events/calendar/?event=105715","timestamp":"2024-11-03T19:59:11Z","content_type":"text/html","content_length":"9395","record_id":"<urn:uuid:f3f39139-1262-47b0-b44c-7aff3ad84462>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00063.warc.gz"} |
Numpy Square Root | Usecase Evaluation of Math Toolkit
The Numpy module of python is the toolkit. Because it is a package of functions to perform various operations, these operations are high scientific computations in python. Numpy supports multiple
dimensions. The toolkits work on them. An array in numpy can be one dimension and two, three, or higher. Thus we have a quick review. As of now, we will read about the numpy square root. An easy
function to use and understand.
About numpy square root
np.sqrt() function gets the square root of the matrix elements. To say that the function is to determine the positive square-root of an array, element-wise. Sqrt () is a mathematical tool which does
There are only non-negative outputs from this function.
Syntax numpy square root
We use sqrt in place of the square root.
The standard syntax of the Function np.sqrt() is:
numpy.sqrt(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'sqrt'>
while the usual way of writing the syntax is:
Parameters Used:
Parameters Mandatory or not
x mandatory
out optional
where optional
casting optional
keepdims optional
axes optional
order optional
subok optional
dtype optional
signature optional
x : array_like
This parameter is Input values whose square-roots have to be determined. In other words, it specifies the radicand. The radicand is the value under the radical when you compute the square root.
The ‘out’ keyword argument expects to be a tuple with one entry per output (which can be None for arrays to be allocated by the ufunc). The out parameter enables you to specify an array where the
output will be stored. This parameter is not used in simpler calculations but at a higher level. This parameter provides a location to store the result. If provided, it must have a shape for the
inputs broadcast. A freshly-allocated array returned if not provided or None. A tuple (possible only as a keyword argument) must have a length equal to the number of outputs.
This parameter Accepts a boolean array, which is broadcast together with the operands. Values of True indicate that to calculate the ufunc at that position and False values indicate to leave the
value in the output alone. Generalized ufuncs cannot use this argument because those take non-scalar input.
A list of tuples with indices of axes a generalized ufunc should operate. For instance, for a signature of (i,j),(j,k)->(i,k) appropriate for matrix multiplication, the base elements are
two-dimensional matrices, and these take to store in the two last axes of each argument.
This parameter specifies the calculation iteration order/memory layout output array. Defaults to ‘K.’ ‘C’ means the output should be C-contiguous, ‘F’ means F-contiguous, ‘A’ means F-contiguous if
the inputs are F-contiguous and not also not C-contiguous
A list of tuples with indices of axes a generalized ufunc should operate. For instance, for a signature of (i,j),(j,k)->(i,k) appropriate for matrix multiplication, the last two axes of each argument
take and store the base elements are two-dimensional matrices.
This argument allows you to provide a specific signature for the 1-d loop to use in the underlying calculation. If the loop specified does not exist for the ufunc, then a TypeError is raised.
Usually, a suitable loop is found automatically by comparing the input types with what is available and searching for a loop with data-types. The types attribute of the ufunc object provide a list of
known signatures.
Still, there are more parameters to mention. But you do not need to know all. To know all we need to see the unfunc docs. So you would get an idea of all the parameters.
Returning value
As per NumPy, return the non-negative square-root of an array, element-wise.
Examples to comprehend
now we import the module first
import numpy
Now using numpy in a better way.
array_2d = numpy.array([[1, 16], [25, 49]], dtype=numpy.float)
[[ 1. 16.]
[ 25. 49.]]
array_2d_sqrt = numpy.sqrt(array_2d)
[[1. 4.]
[5. 7.]]
Here we also used the dtype parameter to fix datatype. This example also shows that it retains the dimensionality of the original array.
#for complex numbers
array = numpy.array([4, -1, -5 + 9J], dtype=numpy.complex)
[4, -1, -5 + 9J]
array([2.00000000+0.j 0.00000000+1.j 1.62721083+2.76546833j])
The above example shows the output for complex numbers.
#negative numbers
array = numpy.array([-4, 5, -6])
__main__:1: RuntimeWarning: invalid value encountered in sqrt
array([nan 2.23606798 nan])
The output for negative number is NaN(Not a Number).
Can I calculate the square root of -1?
__main__:1: RuntimeWarning: invalid value encountered in sqrt
Yes, for -1, you can use this function. But it would return NaN as discussed in the last example.
All the examples give the idea of using the function. Now you are ready to go.
What’s Next?
NumPy is very powerful and incredibly essential for information science in Python. That being true, if you are interested in data science in Python, you really ought to find out more about Python.
You might like our following tutorials on numpy.
In conclusion, this function is useful for all calculations. Those computations can be of broader aspects—both primary and scientific as well.
Still have any doubts or questions do let me know in the comment section below. I will try to help you as soon as possible.
Happy Pythoning!
0 Comments
Inline Feedbacks
View all comments | {"url":"https://www.pythonpool.com/numpy-square-root/","timestamp":"2024-11-05T08:51:42Z","content_type":"text/html","content_length":"145815","record_id":"<urn:uuid:75a685b8-285d-47a3-a605-a1cd91ea2d25>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00024.warc.gz"} |
seminars - Hecke system of harmonic Maass functions and applications to modular curves of higher genera
※ Zoom Meeing ID: 889 2548 0378
The unique basis functions jm of the form q^0+O(q) for the space of weakly holomorphic modular functions on the full modular group form a Hecke system.
This feature was a critical ingredient in proofs of arithmetic properties of Fourier coefficients of modular functions and denominator formula for the Monster Lie algebra.
In this talk, we consider the basis functions of the space of harmonic weak Maass functions of an arbitrary level, which generalize jm, and show that they form a Hecke system as well. As
applications, we establish some divisibility properties of Fourier coefficients of weakly holomorphic modular forms on modular curves of genus ge1.
Furthermore, we present a general duality relation that these modular forms satisfy.
This is a joint work with Daeyeol Jeon and Soon-Yi Kang. | {"url":"http://www.math.snu.ac.kr/board/index.php?mid=seminars&page=40&l=en&document_srl=814650","timestamp":"2024-11-11T06:43:43Z","content_type":"text/html","content_length":"45564","record_id":"<urn:uuid:102b09a3-6db2-4128-b138-2816a3779a79>","cc-path":"CC-MAIN-2024-46/segments/1730477028220.42/warc/CC-MAIN-20241111060327-20241111090327-00315.warc.gz"} |
Intercepts of lines review (x-intercepts and y-intercepts) (article) | Khan Academy (2024)
The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations.
Want to join the conversation?
a year agoPosted a year ago. Direct link to Priscilla Smith's post “Math can be fun sometimes...”
Math can be fun sometimes if you do it right lol
a year agoPosted a year ago. Direct link to sarra's post “it was sort of an obligat...”
it was sort of an obligation for me to be here but by seeing the progress I made in only 9 days ( i used to know almost nothing about math) I'm now addicted to learning it and i can't stop
it's really fun
(my eyes are burning from the screen rn cuz i've been studying for hours straight)
6 years agoPosted 6 years ago. Direct link to leah kelly's post “help me solve this proble...”
help me solve this problem step by step 1/3x-2 find the x,y intercept
2 years agoPosted 2 years ago. Direct link to mari's post “there is no interception ...”
there is no interception points because that isn't a linear equation
4 years agoPosted 4 years ago. Direct link to Juan Perez's post “How do i find the y and x...”
How do i find the y and x intercepts of an equation in standard form??
4 years agoPosted 4 years ago. Direct link to Kim Seidel's post “You can always find the X...”
You can always find the X-intercept by setting Y to 0 in the equation and solve for X.
Similarly, you can always find the Y-intercept by setting X to 0 in the equation and solve for Y.
Hope this helps.
8 months agoPosted 8 months ago. Direct link to lg10's post “help me... this is so har...”
help me... this is so hard.
a day agoPosted a day ago. Direct link to J D's post “what do you need help wit...”
what do you need help with in particular? I'd be glad to help if i had a specific question.
4 years agoPosted 4 years ago. Direct link to dessie's post “how do i put a fraction i...”
how do i put a fraction in
10 months agoPosted 10 months ago. Direct link to Payton's post “this type of stuff is soo...”
this type of stuff is soooo confusing and too me it give off little explaination when it be like "well we r gon' to zoom in" like child what in da world how do we "zoom in" or "zoom out"? i am i
8th grade but sometime when oing this math it makes me feel like a 9th grader in the 8th grade!! does anyone else agree?
10 months agoPosted 10 months ago. Direct link to wagner/wally's post “i mean, teachers do say 8...”
i mean, teachers do say 8th grade is just a transition to 9th, or maybe thats just my school, who knows.
8 months agoPosted 8 months ago. Direct link to Equihua, Robert's post “this doesnt make sense at...”
this doesnt make sense at all I hate this bro
8 months agoPosted 8 months ago. Direct link to Kim Seidel's post “First, this is the review...”
First, this is the review. Maybe you need to start at the beginning of the lesson to get a better understanding. Ask questions as you go. Do the practice problems to reinforce what you are
learning. If you get something wrong, use the hints to find and understand your mistake so you learn how to avoid the error. Then, try the review lesson again.
Here's a quick overview:
The X-intercept is the point where the line crosses the x-axis. So, it must be a point on the x-axis. Any point that is on the x-axis will have a y-value of 0. So, you find the x-intercept by
using y=0 in the equation and solve for X. You will then have a point (x-value, 0) that is the x-intercept.
Similarly, the Y-intercept is the point where the line crosses the y-axis, so it must be a point that is on the y-axis. All points on the y-axis have an x-value of 0. Thus, to find the
y-intercept, you use x=0 in the equation and solve for Y. You will then have a point (0, y-value) that is the y-intercept.
Hope this helps.
a year agoPosted a year ago. Direct link to LOLyue's post “if the question is y=5x+r...”
if the question is y=5x+random number how to find x intercept?
a year agoPosted a year ago. Direct link to Kim Seidel's post “In all equations, you fin...”
In all equations, you find the x-intercept by using y=0 in the equation and solving for x.
6 months agoPosted 6 months ago. Direct link to samiha0624's post “is there any way to figur...”
is there any way to figure out the x and y intercept from the table? the table thing is really confusing so i wonder if there is any equations for the table itself.
6 months agoPosted 6 months ago. Direct link to NeutronSt4r's post “There are separate formul...”
There are separate formulas for calculating intercepts:
y intercept: if the equation is y=mx+b, the y intercept is b
x intercept: if the equation is y=mx+b, the x intercept is -b/m
To figure out the x and y intercepts from a table, you can use the formula
slope =(y₂ - y₁)/(x₂ - x₁)
and figure out the equation first. Then you plug in the numbers from the table into the equation and use the formulas for the x and y intercepts to figure out what you need.
5 years agoPosted 5 years ago. Direct link to Luke Olsen's post “what is the x- intercept ...”
what is the x- intercept in the equation y=8/-1x-22
4 years agoPosted 4 years ago. Direct link to naverdo's post “To find x-intercept, take...”
To find x-intercept, take y=0
0 = 8/-1x-22
-x-22 = 8
-x = -8 + 22
-x = 14
x = -14
Therefore, x-intercept = (-14,0) [Assuming I got your question right] | {"url":"https://homeoshare.com/article/intercepts-of-lines-review-x-intercepts-and-y-intercepts-article-khan-academy","timestamp":"2024-11-08T03:03:40Z","content_type":"text/html","content_length":"84691","record_id":"<urn:uuid:fe34227c-0f68-45e7-8e91-b9d5d3e3b78d>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00086.warc.gz"} |
Collision Between Two Objects of Unequal Mass in context of acceleration with two masses
27 Aug 2024
Journal of Physics and Engineering
Volume 12, Issue 3, 2023
Collision Between Two Objects of Unequal Mass: An Analysis of Acceleration
This article presents a theoretical analysis of the collision between two objects of unequal mass, focusing on the acceleration experienced by each object during the collision. The concept of
momentum and its conservation is employed to derive an expression for the acceleration of each object.
When two objects collide, they experience a sudden change in velocity, resulting in a force being applied to each object. This force causes the objects to accelerate towards each other. In this
article, we consider the collision between two objects of unequal mass and analyze the acceleration experienced by each object during the collision.
Let’s denote the masses of the two objects as m1 and m2, with m1 being greater than m2 (m1 > m2). The velocities of the two objects before the collision are v1 and v2, respectively. We assume that
the collision is perfectly inelastic, meaning that the two objects stick together after the collision.
The momentum of each object before the collision is given by:
p1 = m1v1 p2 = m2v2
Since the collision is perfectly inelastic, the total momentum after the collision remains conserved. Therefore, we can write:
p1 + p2 = (m1 + m2)v’
where v’ is the velocity of the combined object after the collision.
Using the law of conservation of momentum, we can rewrite the above equation as:
m1v1 + m2v2 = (m1 + m2)v’
Now, let’s consider the acceleration experienced by each object during the collision. The force applied to each object is given by Newton’s second law:
F1 = m1a1 F2 = m2a2
where a1 and a2 are the accelerations of the two objects.
Since the force applied to each object is equal in magnitude but opposite in direction, we can write:
m1a1 = -m2a2
Solving for a1 and a2, we get:
a1 = -(m2/m1)a2 a2 = -(m1/m2)a1
Substituting the expression for v’ from equation (1) into equations (2) and (3), we get:
a1 = -((m2/m1)(m1v1 + m2v2))/(m1 + m2) a2 = -((m1/m2)(m1v1 + m2v2))/(m1 + m2)
Simplifying the above expressions, we get:
a1 = -(m2v1 + m22)/(m1 + m2) a2 = -(m12 + m2v2)/(m1 + m2)
In this article, we have analyzed the collision between two objects of unequal mass and derived an expression for the acceleration experienced by each object during the collision. The results show
that the acceleration of each object is dependent on its own mass and the velocity of the other object.
The formulae derived in this article can be used to analyze various types of collisions, including perfectly elastic and partially elastic collisions.
Related articles for ‘acceleration with two masses’ :
Calculators for ‘acceleration with two masses’ | {"url":"https://blog.truegeometry.com/tutorials/education/12448513a05f123fc8356b9f45eafb83/JSON_TO_ARTCL_Collision_Between_Two_Objects_of_Unequal_Mass_in_context_of_accele.html","timestamp":"2024-11-09T06:29:16Z","content_type":"text/html","content_length":"16872","record_id":"<urn:uuid:e91c11d4-6665-42bf-9e50-f746b49af6e0>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00643.warc.gz"} |
Setup screen and basic operation | Dewesoft X Manual
Setup screen and basic operation
When you choose any of Dewesoft Math setup screen buttons with specific Math function (e.g. formula button), a new Math channel is displayed:
The columns in the new Math line look similar to the analog channel setup:
• Used/Unused - activate / deactivate the channels
• C- channel color selector
• Name - formula / output channel name
• Minimum- minimum default value of the graph
• Value - formula preview (symbolic description) and the calculated values
• Maximum - maximum default value of the graph
• Unit - units for your reference
• Setup - button to enter the formula in Formula setup window
C - channel color selector
In first channel row of C column symbol of Formula is displayed and in second row of C column is C color selector for this channel (also show momentarily selected color) -> see below - Name column.
For information about Channel grid see -> Color.
In first channel row of Name column the symbol with title Formula is displayed.
In second channel row of Name column the name of the output channel created with the formula is displayed.
In this section, you can change the predefined default minimum value of the graph scale.
In the first channel row of Value column the description of math module is displayed. For formula a symbolic record of the formula is displayed:
for the filter, the filter settings are shown:
In the second channel row of Value column, the live preview of the calculated value is displayed.
For the math modules with the possibility of selecting several input channels (like filters) or having several output channels for each input (like statistics), channel output section looks a little
bit different - it shows one line for each output channel.
The math can also have several output channels for one input channel. The example is Statistics, where we can calculate RMS, AVE, MIN, MAX,… values for each input channel.
If there is an error in the math module, the error caption will appear:
There are several possible errors:
• Channel not found - input channel is not found (it was deleted or renamed, for example)
• Syntax error - the formula contains an error, for example brackets are not closed
• Circular reference error - the formula a references formula b while the formula b references formula a
• Input channel error - the input channel used in the formula has an error already (for example syntax error)
In this section, you can change the predefined default maximum value of the graph scale.
In the unit column, you can enter the unit of your choice, that will be displayed beside the calculated results.
When you press the Setup button in SETUP column of Math setup screen, the window will appear depending on the selected module.
Example - Formula setup window:
Formula Setup is comprised of two sections:
1. Output: General output settings on the top left side of the window.
2. Formula: Formula editor on the right side of the window | {"url":"https://manual.dewesoft.com/x/setupmodule/modules/general/math/setup","timestamp":"2024-11-05T16:21:51Z","content_type":"text/html","content_length":"36877","record_id":"<urn:uuid:63f53029-8fde-48cf-916c-6ef653bc1a6b>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00821.warc.gz"} |
PLC Technology
It is extremely simple to measure 0-10Vdc signal with a device that will measure only Current inputs. If Current input module available will accept a 0-20mA signal, but may not accept a 0-10Vdc
signal directly.
Basically, Ohms law is used to calculate a resistor value in order to convert the 0-10Vdc signal to a current.
Voltage to Current Conversion Circuit Diagram
Example (0-10 VDC to 0-20 mA)
Ohms law states:
R = V/I
is the Voltage,
is the current and R is the resistance
= 10V/0.020A =
500 Ohms
0-10 VDC to 0-20 mA Conversion Circuit Diagram
I= V/R = 0/500 = 0mA
I= V/R = 10/500 =
0.02A = 20mA
Example (0-5 VDC to 0-20 mA)
Ohms law states:
R = V/I
is the Voltage,
is the current and R is the resistance
= 5V/0.020A =
250 Ohms
0-5 VDC to 0-20 mA Conversion Circuit Diagram
I= V/R = 0/250 = 0mA
I= V/R = 5/250 =
0.02A = 20mA
To avoid damage you must ensure that the external current source has short-circuit protection in all conductor cases.
The external resistor is a source of error because of its dependency on temperature and its inaccuracy.
In order to obtain measuring results that are as precise as possible it is recommended to use resistors with tolerances that are as small as possible.
It is extremely simple to measure 0-20ma signal with a device that will measure only Voltage inputs. If Voltage input module available will accept a 0-10Vdc signal, but may not accept a 0-20ma signal
Basically, Ohms law is used to calculate a resistor value in order to convert the 0-20ma signal to a voltage.
Current to Voltage Conversion Circuit Diagram
Example (0-20 mA to 0-10 VDC)
Ohms law states: R = V/I where V is the Voltage, I is the current and R is the resistance
R = 10V/0.020A = 500 Ohms
0-20 mA to 0-10 VDC Conversion Circuit Diagram
V = I*R = 0*500 = 0V
V = I*R = 0.020*500 = 10V
Example (4-20 mA to 2-10 VDC)
Ohms law states: R = V/I where V is the Voltage, I is the current and R is the resistance
R = 10V/0.020A = 500 Ohms
4-20 mA to 2-10 VDC Conversion Circuit Diagram
V = I*R = 0.004*500 = 2V
V = I*R = 0.020*500 = 10V
Example (0-20 mA to 0-5 VDC)
Ohms law states: R = V/I where V is the Voltage, I is the current and R is the resistance
R = 5V/0.020A = 250 Ohms
0-20 mA to 0-5 VDC Conversion Circuit Diagram
V = I*R = 0*250 = 0V
V = I*R = 0.020*250 = 5V
Convert 0-10 VDC to 0-20 mA Using Resistor
To avoid damage you must ensure that the external current source has short-circuit protection in all conductor cases.
The external resistor is a source of error because of its dependency on temperature and its inaccuracy.
In order to obtain measuring results that are as precise as possible it is recommended to use resistors with tolerances that are as small as possible. | {"url":"https://www.myplctechnology.com/2019/01/","timestamp":"2024-11-11T02:51:07Z","content_type":"application/xhtml+xml","content_length":"198055","record_id":"<urn:uuid:eccb99ca-2e7f-44b2-9050-3ee53e7607ea>","cc-path":"CC-MAIN-2024-46/segments/1730477028216.19/warc/CC-MAIN-20241111024756-20241111054756-00377.warc.gz"} |
Digital Math Resources
Display Title
Closed Captioned Video: Geometry Applications: Polygons, 1
Closed Captioned Video: Geometry Applications: Polygons, Segment 1: Introduction
The Pentagon is one of the most famous polygon-shaped buildings in the world. But why was this shape chosen over a more straightforward quadrilateral shape? We briefly explore the properties of
pentagons and use this as a way of introducing the key concepts throughout the program.
This is part of a collection of closed captioned videos for the Geometry Applications video series. To see the complete collection of the videos, click on this link.
Note: The download is Media4Math's guide to closed captioned videos.
Related Resources
To see additional resources on this topic, click on the Related Resources tab.
Closed Captioned Video Library
To see the complete collection of captioned videos, click on this link.
Video Transcripts
This video has a transcript available. To see the complete collection of video transcripts, click on this link.
Common Core Standards CCSS.MATH.CONTENT.6.G.A.3, CCSS.MATH.CONTENT.HSG.MG.A.1, CCSS.MATH.CONTENT.HSG.MG.A.2, CCSS.MATH.CONTENT.HSG.MG.A.3
Duration 3.43 minutes
Grade Range 6 - 10
Curriculum Nodes • Polygons
• Definition of a Polygon
• Applications of Polygons
Copyright Year 2020
Keywords geometry, polygons, applications of polygons, Pentagon, Closed Captioned Video | {"url":"https://www.media4math.com/library/closed-captioned-video-geometry-applications-polygons-1","timestamp":"2024-11-11T20:00:57Z","content_type":"text/html","content_length":"58958","record_id":"<urn:uuid:3bc2effb-0b3a-4464-870f-feaf8ace04bb>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00818.warc.gz"} |
home page Siani Smith
Address: Department of Computer Science,
Durham University, Upper Mountjoy, Durham, DH1 3LE, UK
Office: MCS2010
Email: [email protected]
Siani Smith
Final year PhD student
• (2014-2018) MEng Degree in Discrete Mathematics at the University of Warwick.
• (2018-2022) PhD at Durham University under the supervision of Barnaby Martin and Daniel Paulusma
My research interests lie mainly in graph theory and algorithms.
Journal Publications
W. Kern, B. Martin, D. Paulusma, S. Smith and E.J. van Leeuwen, Disjoint paths and connected subgraphs for H-free graphs, to appear in Theoretical Computer Science doi.
B. Martin, D. Paulusma and S. Smith, Hard problems that quickly become very easy, Information Processing Letters 174 (2022) doi.
Conference Papers
C. Brause, P.A. Golovach, B. Martin, D. Paulusma and S. Smith, Partitioning H-free graphs of bounded diameter, Proceedings of the 32nd International Symposium on Algorithms and Computation (ISAAC
2021), Fukuoka, Japan, December 6-8, 2021, Leibniz International Proceedings in Informatics, to appear.
B. Larose, P. Markovic, B. Martin, D. Paulusma, S. Smith, and S. Zivny, QCSP on Reflexive Tournaments, Proceedings of the 29th Annual European Symposium on Algorithms (ESA 2021), Lisbon, Portugal,
September 6-8, 2021, Leibniz International Proceedings in Informatics, to appear.
W. Kern, B. Martin, D. Paulusma, S. Smith and E.J. van Leeuwen, Disjoint paths and connected subgraphs for H-free graphs, Proceedings of the 32nd International Workshop on Combinatorial Algorithms
(IWOCA 2021), Ottawa, Canada, July 5-8, 2021, Lecture Notes in Computer Science 12757, 414-427, IWOCA 2021.
J. Bok, N. Jedlickova, B. Martin, D. Paulusma and S. Smith, Injective colouring for H-free graphs, Proceedings of the 16th International Computer Science Symposium in Russia (CSR 2021), Sochi,
Russia, June 28-July 2, 2021, Sochi, Russia, Lecture Notes in Computer Science 12730, 18-30 , CSR 2021.
C. Brause, P.A. Golovach, B. Martin, D. Paulusma and S. Smith, Acyclic, Star, and Injective Colouring: Bounding the Diameter, Proceedings of the 47th International Workshop on Graph-Theoretic
Concepts in Computer Science (WG 2021), Warsaw, Poland, June 23-25, 2021, Lecture Notes in Computer Science, to appear.
B. Martin, D. Paulusma and S. Smith, Colouring Graphs of Bounded Diameter in the Absence of Small Cycles., Proceedings of the 12th International Conference on Algorithms and Complexity (CIAC 2021),
Larnaca, Cyprus, May 10-12, 2021, Lecture Notes in Computer Science 12701, 367-380
J. Bok, N. Jedlickova, B. Martin, D. Paulusma and S. Smith, Acyclic, star and injective colouring: A complexity picture for H-free graphs, Proceedings of the 28th Annual European Symposium on
Algorithms (ESA 2020), Pisa, Italy, September 7-9, 2020, Leibniz International Proceedings in Informatics 173, 22:1-22:22
B. Martin, D. Paulusma and S. Smith, Colouring H-free Graphs of Bounded Diameter, Proceedings of the 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019), Aachen,
Germany, August 26-30, 2019, Leibniz International Proceedings in Informatics 138, 14:1-14:14.
Submitted Journal Papers
J. Bok, N. Jedlickova, B. Martin, P. Ochem, D. Paulusma and S. Smith, Acyclic, star and injective colouring: a complexity picture for H-free graphs.
C. Brause, P.A. Golovach, B. Martin, P. Ochem, D. Paulusma and S. Smith, Acyclic, star and injective colouring: bounding the diameter
B. Martin, D. Paulusma and S. Smith, Colouring graphs of bounded diameter in the absence of small cycles.
C. Brause, P.A. Golovach, B. Martin, D. Paulusma and S. Smith, Partitioning H-free graphs of bounded diameter.
B. Larose, P. Markovic, B. Martin, D. Paulusma, S. Smith, and S. Zivny, QCSP on reflexive tournaments.
Other Manuscripts
G. Berthe, B. Martin, D. Paulusma and S. Smith, The complexity of L (p, q)-Edge-Labelling
Since 2018/2019, I have been a demonstrator together with Chris Lindop and Giacomo Paesani for the module Mathematics for Computer Science.
All materials are on Duo. | {"url":"https://sianismith.webspace.durham.ac.uk/","timestamp":"2024-11-10T15:13:32Z","content_type":"text/html","content_length":"22492","record_id":"<urn:uuid:3be892d5-9646-4c97-9eb9-c335c225d9ca>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.60/warc/CC-MAIN-20241110134821-20241110164821-00625.warc.gz"} |
Digital to Analog Conversion
www.play-hookey.com Sun, 08-24-2003
Digital | Logic Families | Digital Experiments | Analog | Analog Experiments | DC Electronic Theory | Optics | Computers | Semiconductors | Test HTML
Digital to Analog Conversion
One common requirement in electronics is to convert signals back and forth between analog and digital forms. Most such conversions are ultimately based on a digital-to-analog converter circuit.
Therefore, it is worth exploring just how we can convert a digital number that represents a voltage value into an actual analog voltage.
The circuit to the right is a basic digital-to-analog (D to A) converter. It assumes a 4-bit binary number in Binary-Coded Decimal (BCD) format, using +5 volts as a logic 1 and 0 volts as a logic 0.
It will convert the applied BCD number to a matching (inverted) output voltage. The digits 1, 2, 4, and 8 refer to the relative weights assigned to each input. Thus, 1 is the Least Significant Bit
(LSB) of the input binary number, and 8 is the Most Significant Bit (MSB).
If the input voltages are accurately 0 and +5 volts, then the "1" input will cause an output voltage of -5 × (4k/20k) = -5 × (1/5) = -1 volt whenever it is a logic 1. Similarly, the "2," "4," and "8"
inputs will control output voltages of -2, -4, and -8 volts, respectively. As a result, the output voltage will take on one of 10 specific voltages, in accordance with the input BCD code.
Unfortunately, there are several practical problems with this circuit. First, most digital logic gates do not accurately produce 0 and +5 volts at their outputs. Therefore, the resulting analog
voltages will be close, but not really accurate. In addition, the different input resistors will load the digital circuit outputs differently, which will almost certainly result in different voltages
being applied to the summer inputs.
The circuit above performs D to A conversion a little differently. Typically the inputs are driven by CMOS gates, which have low but equal resistance for both logic 0 and logic 1. Also, if we use the
same logic levels, CMOS gates really do provide +5 and 0 volts for their logic levels.
The input circuit is a remarkable design, known as an R-2R ladder network. It has several advantages over the basic summer circuit we saw first:
1. Only two resistance values are used anywhere in the entire circuit. This means that only two values of precision resistance are needed, in a resistance ratio of 2:1. This requirement is easy
to meet, and not especially expensive.[ ]
2. The input resistance seen by each digital input is the same as for every other input. The actual impedance seen by each digital source gate is 3R. With a CMOS gate resistance of 200 ohms, we
can use the very standard values of 10k and 20k for our resistors.[ ]
3. The circuit is indefinitely extensible for binary numbers. Thus, if we use binary inputs instead of BCD, we can simply double the length of the ladder network for an 8-bit number (0 to 255)
or double it again for a 16-bit number (0 to 65535). We only need to add two resistors for each additional binary input.[ ]
4. The circuit lends itself to a non-inverting circuit configuration. Therefore we need not be concerned about intermediate inverters along the way. However, an inverting version can easily be
configured if that is appropriate.[ ]
One detail about this circuit: Even if the input ladder is extended, the output will remain within the same output voltage limits. Additional input bits will simply allow the output to be subdivided
into smaller increments for finer resolution. This is equivalent to adding inputs with ever-larger resistance values (doubling the resistance value for each bit), but still using the same two
resistance values in the extended ladder.
The basic theory of the R-2R ladder network is actually quite simple. Current flowing through any input resistor (2R) encounters two possible paths at the far end. The effective resistances of both
paths are the same (also 2R), so the incoming current splits equally along both paths. The half-current that flows back towards lower orders of magnitude does not reach the op amp, and therefore has
no effect on the output voltage. The half that takes the path towards the op amp along the ladder can affect the output.
The most significant bit (marked "8" in the figure) sends half of its current toward the op amp, so that half of the input current flows through that final 2R resistance and generates a voltage drop
across it. This voltage drop (from bit "8" only) will be one-third of the logic 1 voltage level, or 5/3 = 1.667 volts. This is amplified by the op amp, as controlled by the feedback and input
resistors connected to the "-" input. For the components shown, this gain will be 3 (see the page on non-inverting amplifiers). With a gain of 3, the amplifier output voltage for the "8" input will
be 5/3 × 3 = 5 volts.
The current from the "4" input will split in half in the same way. Then, the half going towards the op amp will encounter the junction from the "8" input. Again, this current "sees" two
equal-resistance paths of 2R each, so it will split in half again. Thus, only a quarter of the current from the "4" will reach the op amp. Similarly, only 1/8 of the current from the "2" input will
reach the op amp and be counted. This continues backwards for as many inputs as there are on the R-2R ladder structure.
The maximum output voltage from this circuit will be one step of the least significant bit below 10 volts. Thus, an 8-bit ladder can produce output voltages up to 9.961 volts (255/256 × 10 volts).
This is fine for many applications. If you have an application that requires a 0-9 volt output from a BCD input, you can easily scale the output upwards using an amplifier with a gain of 1.6 (8/5).
If you want an inverting D to A converter, the circuit shown above will work well. You may need to scale the output voltage, depending on your requirements.
Also, it is possible to have a bipolar D to A converter. If you apply the most significant bit to an analog inverter and use that output for the MSB position of the R-2R ladder, the binary number
applied to the ladder will be handled as a two's-complement number, going both positive and negative. | {"url":"http://laris.fesb.hr/digitalno_vodjenje/download/d2a_converter.htm","timestamp":"2024-11-10T07:35:03Z","content_type":"text/html","content_length":"13881","record_id":"<urn:uuid:ae471031-a1fd-4ca8-8d08-619ab6eb6549>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00829.warc.gz"} |
On polynomial variance functions
Let ℱ be a natural exponential family onℝ and (V, Ω) be its variance function. Here, Ω is the mean domain of ℱ and V, defined on Ω, is the variance of ℱ. A problem of increasing interest in the
literature is the following: Given an open interval Ω⊂ℝ and a function V defined on Ω, is the pair (V, Ω) a variance function of some natural exponential family? Here, we consider the case where V is
a polynomial. We develop a complex-analytic approach to this problem and provide necessary conditions for (V, Ω) to be such a variance function. These conditions are also sufficient for the class of
third degree polynomials and certain subclasses of polynomials of higher degree.
• Mathematics Subject Classification (1980): 62E10, 60J30
ASJC Scopus subject areas
• Analysis
• Statistics and Probability
• Statistics, Probability and Uncertainty
Dive into the research topics of 'On polynomial variance functions'. Together they form a unique fingerprint. | {"url":"https://cris.haifa.ac.il/en/publications/on-polynomial-variance-functions","timestamp":"2024-11-02T14:21:33Z","content_type":"text/html","content_length":"50598","record_id":"<urn:uuid:155ffca8-584d-45b6-a34b-fe64347f54d9>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00084.warc.gz"} |
Equations of State: Summary
The answers to the ConcepTests are given below and will open in a separate window.
Key points from this module:
• The ideal gas law (PV^total = nRT) is an equation of state (EOS). It assumes no interactions between molecules and that molecules occupy no space.
• Equations of state with additional parameters account for attractive and repulsive forces between molecules. Only cubic EOS are used in this module.
• The parameters in the cubic EOS are calculated from critical pressures and temperatures and acentric factors.
• A cubic equation of state can model liquid, vapor, and supercritical fluids and can also determine saturation conditions.
• The isotherms and isobars for a three-parameter equation of state can have one or three solutions, but when three solutions exist, either one or two are physically meaningful.
• Corresponding State Principle: all fluids have similar properties at the same values of reduced variables (e.g., at the same reduced pressure (P/P[c]) and reduced temperature (T/T[c])).
• The further the compressibility factor (Z = RT/PV) is from one, the more the fluid deviates from an ideal gas.
• The critical point is the point where liquid and vapor phases become indistinguishable.
From studying this module, you should now be able to:
• Calculate properties (U, S, H, A, G, V, f) of real fluids using the Peng-Robinson (PR) equation of state (EOS) spreadsheet, which also uses heat capacity data.
• Explain why the PR cubic EOS has three roots and what the physical meaning of each root is.
• Interpret the EOS spreadsheet results to determine which state (root) is most stable.
• Describe what corresponding states means.
• Sketch and interpret processes on P-V-T diagrams and their projections.
• Calculate reduced temperature, reduced pressure, and compressibility factor.
• Explain which terms are repulsive and which are attractive in a cubic EOS. | {"url":"https://learncheme.com/quiz-yourself/interactive-self-study-modules/equations-of-state/equations-of-state-summary/","timestamp":"2024-11-10T12:22:27Z","content_type":"text/html","content_length":"77195","record_id":"<urn:uuid:43587b05-5889-4a47-acc7-cd8c1a32aad0>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00289.warc.gz"} |
Intelligent modelling and active vibration control of flexible manipulator system
Unwanted vibration of flexible manipulator results in unsatisfactory performance of any dynamic system using the flexile manipulator. This paper presents a robust control strategy in order to
suppress undesirable vibration due to flexible manipulator maneuver. First, the appropriate model of the flexible manipulator is extracted by applying the control-model identification technique for
linear and nonlinear model, namely, autoregressive with exogenous input (ARX) model and nonlinear ARX (NARX) respectively. The linear model is estimated by recursive least square method (RLS) and
nonlinear model identified by artificial neural network (NN). Finally, the PID controller is designed for each proposed model to cancel the vibration of the flexible manipulator. The robustness of
the controller is evaluated by imposing new disturbances into the linear and nonlinear systems. System identification and controller design is conducted by numerical and simulation approaches. The
results from simulation indicate that performance of PID controller using linear model is satisfactory compared to nonlinear model.
1. Introduction
Manipulators are one of the important appendages of most of dynamic systems. Owing to some functional applications they have been extensively utilized in aero investigations [1], biomedical
applications [2], robotic system [3] and many other fields that require heavy, tedious and accurate structural minipulations. In most cases where the need for less energy consumption, increase of
operation speed and optimization of dimensions, the flexible manipulator is the preferable choice over its rigid counterpart.
Apart from useful contribution of flexible manipulator, its low stiffness characteristic evolves drawbacks of unwanted vibration or chaotic motion especially when it is stimulated by any external
loads or maneuvered by simple torque at some points. This extra oscillation causes time delay and also wastes a great deal of energy. Quite recently, considerable attention has been paid to deal with
flexible manipulator weaknesses. A solution would be designing a proper control system in order to suppress the unwanted oscillation. The controller can be selected in active or passive
configuration. In system control strategy, if the accurate modelling of flexible manipulator is implemented in the primitive stage, the system will yield satisfactory response. Recently, research on
modelling and control of flexible manipulator has become very popular with a variety of approaches. Tang et al. [4] presented the modelling of single flexible manipulator by using Lagrange
formulation, where the trajectory and vibration control based on approximation of neural network (NN) and the concept of sliding mode control (SMC) are considered. Feliu et al. [5] proposed lumped
masses to model the single flexible manipulator and feedforward controller is designed as control scheme. In [6] the assumed mode method (AMM) was used to obtain the mathematical model of two
flexible links, while the neural adaptive control was adapted for control strategy. However, dealing with huge differential equations for modelling of flexible manipulater by classical approach is
cumbersome, so the system identification method utilizes the differences equations to model the dynamic system [7]. In a recent paper by Duarte et al. [8] the black box technique is applied to
present the dynamic model of flexible link and vibration cancelation is done by using the H[∞ ]control scheme. Franke et al. [9] developed the frequency response function (FRF) to extract the
transfer function of flexible manipulator, and for eliminating the vibration feedforward input the shaping was carried out using strain feedback control. The most interesting approach to this issue
has been proposed by [10] in which the soft computing method is implemented for trajectory and vibration control. Also, beam structural analysis could be considered as an insight of modelling and
control for flexible manipulator [11].
In this paper the author offers another alternative system identification technique in which autoregressive with exogenous input (ARX) model as linear structure and NARX model as nonlinear structure
are signified. In short, the ARX model is one where its parameters are estimated by conventional recursive least square (RLS) approach. For NARX model the nonparametric model estimation is done by
artificial neural network algorithm. Finally the proportional integral derivative (PID) controller is utilized for both models for eliminating the undesirable vibration. The performance of PID
controller is also evaluated by applying different disturbances on the control system.
2. The flexible manipulator system
Fig. 1 depicts a typical single-link flexible manipulator. The single-link flexible manipulator is considered a pinned-free arm with length $L$ and tip mass ${M}_{p}$, attached to either a rigid or
flexible hub. Here, the rigid joint is considered with arm inertia ${I}_{t}$. As in most cases an input torque $\tau \left(t\right)$ is applied at the hub by an electrical motor. $E$, $I$ and $\rho$
represent the Young modulus, second moment of inertia and mass density per unit length, respectively, of the arm. In this study, the motion of the flexible manipulator is defined in the ${X}_{0}O{Y}_
{0}$ and $XOY$ axis systems, as stationary and moving coordinates, respectively. The overall displacement $w\left(x,t\right)$ is consisted of angular displacement $\theta \left(t\right)$ and elastic
deflection $\vartheta \left(t,x\right)$ which can be described as:
$w\left(x,t\right)=x\theta \left(t\right)+\vartheta \left(x,t\right).$
Fig. 1Typical flexible manipulator arm
The governing equation of the flexible manipulator, by considering the boundary and initial conditions, is obtained as:
$\left\{\begin{array}{l}EI\frac{{\partial }^{4}w\left(x,t\right)}{{\partial x}^{4}}+\rho \frac{{\partial }^{2}w\left(x,t\right)}{{\partial t}^{2}}=\tau \left(t\right),\\ w\left(0,t\right)=0,\\ {I}_
{h}\frac{{\partial }^{3}w\left(0,t\right)}{\partial x{\partial t}^{2}}-EI\frac{{\partial }^{2}w\left(0,t\right)}{{\partial x}^{2}}=\tau \left(t\right),\\ {M}_{p}\frac{{\partial }^{2}w\left(L,t\
right)}{{\partial t}^{2}}-EI\frac{{\partial }^{3}w\left(L,t\right)}{{\partial x}^{3}}=0,\\ EI\frac{{\partial }^{2}w\left(L,t\right)}{{\partial x}^{2}}=0,w\left(x,0\right)=0,\frac{{\partial }^{2}w\
left(L,t\right)}{{\partial x}^{2}}=0.\end{array}\right\$
The analytical method can be used to deal with the fourth order PDE. Most studies do not take into account the solution of Eq. (2) by analytical method directly, because by changing the boundary
conditions and adding more than one flexible link, solving of such PDEs becomes thorough. So, other alternative methods have been used to present the dynamic model of flexible manipulator with
different number of links. For instance, by truncating the continuous link into finite number of subsystems or elements and applying the assume mode method (AMM) [12] and finite element method (FEM)
[13] a discrete model could be presented. The dynamic motion of the flexible manipulator can be extracted by incorporating the energy principle in the Lagrange or Hamilton formulations. The lumped
parameters system is also used [5] to derive the dynamic equation of single link flexible manipulator, but with less accuracy than FEM and AMM. In the present study, to derive the mathematical model
of the flexible manipulator system, the system identification technique is applied, as a novel approach, for modelling of dynamic systems possessing complicated dynamic characteristics and
encountering with some uncertainties such as nonlinear behavior, changeable mass, stiffness and damping.
3. System identification
Identification of dynamic systems which have flexibility has attracted researchers recently. In this work, linear system identification is carried out by using the ARX model and nonlinear system
identification is conducted using NARX model. In addition to choosing the model structure, the input and output signals, as discrete set of data, must be assigned as well. Input and output data can
be obtained from experimental test of real system. The system is excited with test signal and its response measured. When the experiment test is not available other alternative method can be carried
out to simulate the system. In this study, the input and output signal detection is done by finite difference (FD) method that is described in [14].
3.1. Linear system identification
A linear model using autoregressive with exogenous input (ARX) model is presented in this study. Fig. 2 illustrates the schematic of the ARX model. Using the symbols in Fig. 2 the model function can
be written as:
$y\left(t\right)=\frac{B\left({z}^{-1}\right)}{A\left({z}^{-1}\right)}u\left(t\right)+\frac{1}{A\left({z}^{-1}\right)}\epsilon \left(t\right),$
where, $A\left({z}^{-1}\right)$ and $B\left({z}^{-1}\right)$ are polynomials and $u\left(t\right)$ is the input data and $y\left(t\right)$ is the output data while $ϵ\left(t\right)$ is the white
noise. By neglecting the noise effect and rewriting Eq. (3) we have:
$A\left({z}^{-1}\right)=1+{a}_{1}{z}^{-1}+{a}_{2}{z}^{-2}+\dots +{a}_{n}{z}^{-n},$
$B\left({z}^{-1}\right)={b}_{0}+{b}_{1}{z}^{-1}+{b}_{2}{z}^{-2}+\dots +{b}_{m}{z}^{-m}.$
By substituting Eqs. (5) and (6) into Eq. (4) the model in Eq. (3) can be shown as:
$y\left(t\right)=-\sum _{i=0}^{n}{a}_{1}{z}^{-1}+{a}_{2}{z}^{-2}+\dots +{a}_{n}{z}^{-n}+\sum _{i=0}^{n}{b}_{1}{z}^{-1}+{b}_{2}{z}^{-2}+\dots +{b}_{m}{z}^{-m},$
$y\left(t\right)=-\sum _{i=0}^{n}{a}_{i}{z}^{-i}+\sum _{i=0}^{m}{b}_{i}{z}^{-i},{a}_{0}=1,{b}_{0}=0.$
In both discrete polynomials, $n$ and $m$ refer to the order of the function where $n\ge m$. ${z}^{-n}$ and ${z}^{-m}$ are backshift operators and $y\left(t\right)$ is the sampled output.
Fig. 2ARX model structure
3.1.1. Parameters estimation
By signifying the ARX model, we can estimate the model parameters $\left[{a}_{1},\dots ,{a}_{n},{b}_{1},\dots ,{b}_{m}\right]$ by applying the recursive least square method (RLS). Fig. 3 shows the
schematic of RLS method. By rewritting Eq. (7) in the standard form the mathematical definition of RLS is presented as:
$y\left(t\right)=\phi \left(t\right)\beta ,$
where $y\left(t\right)$ is the actual output, $\phi \left(t\right)$ is the regressor that includes the input and output data and $\mathrm{\beta }\mathrm{}$are the system parameters. Consequently, Eq.
(9) can be presented in the matrix form of Eq. (10) by replacing ${z}^{-n}$ with $y\left(t-n\right)$ and ${z}^{-m}$ with$y\left(t-m\right)$:
$y\left(t\right)=\left[\begin{array}{ccc}-y\left(t-1\right)& \cdots & -y\left(t-n\right)\end{array}\begin{array}{ccc}u\left(t-1\right)& \cdots & u\left(t-m\right)\end{array}\right]\left[\begin{array}
{c}{a}_{1}\\ \begin{array}{c}⋮\\ {a}_{n}\\ \begin{array}{c}{b}_{1}\\ ⋮\end{array}\end{array}\\ {b}_{m}\end{array}\right].$
By employing the cost function and adding new parameters the unknown parameters in Eq. (9) can be estimated by Eq. (11):
$\stackrel{^}{\beta }\left(t+1\right)=\stackrel{^}{\beta }\left(t\right)+p\left(t+1\right)\phi \left(t+1\right)ϵ\left(t+1\right).$
Two new parameters are introduced, namely $p\left(t+1\right)$ as arbitrary value and $ϵ\left(t+1\right)$ as error variable, and they can be defined as:
$p\left(t+1\right)=p\left(t\right)\left[I-\frac{\phi \left(t+1\right){\phi }^{T}\left(t+1\right)p\left(t\right)}{\gamma +{\phi }^{T}\left(t+1\right)p\left(t\right)\phi \left(t+1\right)}\right],$
$ϵ\left(t+1\right)=y\left(t+1\right)-{\phi }^{T}\left(t+1\right)\stackrel{^}{\beta }\left(t\right).$
Note that in Eq. (12), $\gamma$ is the forgetting factor that varies from 0 to 1. Finally, the estimated output $\stackrel{^}{y}\left(t\right)$ in Eq. (14) is obtained by replacing the estimated
parameter $\beta$ by $\stackrel{^}{\beta }$ in Eq. (9):
$\stackrel{^}{y}\left(t\right)=\phi \left(t\right)\stackrel{^}{\beta }.$
However, the proposed model using the estimated parameter is optimum when the mean-square error (MSE) gets minimized:
$\mathrm{M}\mathrm{S}\mathrm{E}=\frac{1}{N}\sum _{i=1}^{N}{\left(\left|y\left(i\right)-\stackrel{^}{y}\left(i\right)\right|\right)}^{2}.$
In Eq. (15), $y\left(i\right)$ and $\stackrel{^}{y}\left(i\right)$ are the actual and estimated output respectively, and $N$ denotes the number of sampled data.
Fig. 3Diagram of RLS algorithm
3.1.2. RLS result
By considering the finite difference method, Fig. 4 and 5 show the results [14] of the input signal (as bang-bang torque $\tau \left(t\right)$ imposed at link hub) and response output signal
(manifested as tip displacement). These two signals are sampled with period of 0.04 ms into 68842 points and normalized between –1 and 1.
Fig. 4Sampled input signal, bang-bang torque
Fig. 5Sampled output signal, tip displacement
Consider the implementation of the two described signals into the ARX model. The modelling becomes more reliable when the estimation process is divided into training and testing steps. In this case
the model parameters are estimated by using half of the data and tested by employing the entire data in order to achieve the adaptive model with the minimum mean square error (MSE). After conducting
the system identification process, the model order of 2 is found to be the best model with minimum MSE of 2.8546×10^-8.
The parameters of the second order model, namely $\left[{a}_{1},{a}_{2},{b}_{1},{b}_{2}\right]$ in Eqs. (5) and (6), are extracted by making the regressor matrix $\phi \left(t\right)$in Eq. (10)
create $p\left(t+1\right)$ and $ϵ\left(t+1\right)$in Eqs. (12) and (13) respectively. Then the desired parameters $\stackrel{^}{\beta }\left(t\right)$ would be estimated by Eq. (11) in vector form,
where${a}_{0}=\text{1,}$${a}_{1}=\text{–0.5,}$${a}_{2}=\text{–0.5,}$${b}_{0}=\text{0,}$${b}_{1}=$–2.0733×10^-6, ${b}_{2}=$ –2.091×10^-6. On the other hand, the estimated output is evaluated by Eq.
(14) which tries to minimize the MSE as well. The above formulation are programmed using Matlab software. Finally, by inserting the adapted parameters in Eq. (3) the transfer function of ARX model
can be found, as presented by Eq. (16). The actual and estimated responses, with their errors, are illustrated in Figs. 6 and 7 graphically:
Fig. 6Actual and estimated output
Fig. 7Error between actual and estimated output
For validation of the linear ARX model the frequency response function (FRF) for both actual and estimated output are illustrated in Fig. 8. As it is shown in the frequency domain the estimated
output follows the same trend as actual output. All frequencies are captured using the proposed linear model but with negligible phase differences in high frequency domain. It is noted that the
active vibration control for flexible manipulator system is intended to work in low frequency range.
Fig. 8Frequency response function for actual and estimated output
3.2. Nonlinear system identification
In this section nonlinear system identification is discussed in relation to nonlinear autoregressive with external (exogenous) input (NARX) model. Fig. 9 shows the nonlinear estimation process using
the artificial neural network (NN) algorithm for NARX model in the iterative process. As rule of thumb the NN uses the past input and output data to estimate the present output as delayed input and
output variables (regressors) namely, $y\left(t-1\right)$, $y\left(t-2\right)$,…, $y\left(t-na\right)$, $u\left(t\right)$, $u\left(t-1\right)$,…, $u\left(t-nb-1\right)$. In this study the NN is
trained by using the Levenberg-Marquardt back propagation in order to achieve the minimum error. Nonlinear identification process has the same scenario with the formerly described linear
identification, which means making the nonlinear structure using the half of the data and testing the extracted model using the entire data to obtain the adaptive model with minimum MSE. In this work
all numerical calculations were computed using the software tool from Mathworks Inc. which include MATLAB, Simulink and control environments. In the literature this type of system identification is
known as black box technique because the model function is not physically significant.
Fig. 9Schematic of NARX NN structure
3.2.1. Neural network result
By altering the configuration of neural network (NN) algorithm such as different time delay and number of neurons in the hidden layer the best model with minimum MSE can be accurately achieved. In
this case only one hidden layer is selected and the best model is obtained by choosing 8 neurons and a time delay of 6, thus obtaining an MSE of 8.770×10^-12 in the training process, see Table 1.
Finally the black box model is implemented for estimating output from the entire data testing process. This model is depicted in Fig. 10 with MSE 3.4×10^-5 for entire data. The estimated output and
actual output with their absolute error are illustrated in the Figs. 11 and 12 respectively.
Fig. 10NARX NN model simulation
Fig. 11Actual and estimated output
Fig. 12Error between actual and estimated output
Table 1Values of MSE in neural network configuration
Delay = 2 Delay = 4 Delay = 6 Delay = 8 Delay = 10
Number of neurons
MSE MSE MSE MSE MSE
2 2.0486×10^-8 1.0249×10^-9 9.867×10^-9 8.554×10^-11 4.14×10^-9
4 1.15×10^-8 2.189×10^-7 3.215×10^-7 1.132×10^-9 1.22×10^-5
6 2.023×10^-11 1.17×10^-9 8.296×10^-6 5.426×10^-9 6.76×10^-8
8 2.058×10^-11 1.37×10^-7 8.770×10^-12 6.24×10^-9 1.036×10^-5
10 2.055×10^-11 4.75×10^-6 2.667×10^-11 9.33×10^-7 2.23×10^-6
Fig. 13Validation results
a) Auto-correlation ${\varnothing }_{ee}\left(\tau \right)$
b) Cross-correlation ${\varnothing }_{ue}\left(\tau \right)$
c) Cross-correlation${\varnothing }_{{u}^{2}e}\left(\tau \right)$
d) Cross-correlation ${\varnothing }_{{u}^{2}{e}^{2}}\left(\tau \right)$
e) Cross-correlation ${\varnothing }_{e\left(eu\right)}\left(\tau \right)$
3.2.2. Model validation
Previously, the system identification technique was implemented by dividing input-output data into two sets of data for training and for testing process to show the model adaptiveness to a new set of
data. For linear model the FRF was utilized to validate the model. However, predictive capability of proposed nonlinear model by system identification technique should be validated by some
statistical method such as the correlation test [15], as given in Eq. (17). A model is validated when these equations are satisfied, in other words, when the residuals (errors) are uncorrelated with
linear and nonlinear combinations of past input and output:
${\varnothing }_{e\left(eu\right)}\left(\tau \right)=E\left[e\left(t\right)e\left(t-1-\tau \right)u\left(t-\tau \right)\right]=0,\tau \ge 0,$${\mathrm{\varnothing }}_{{u}^{2}{e}^{2}\mathrm{}}\left(\
tau \right)=E\left[{u}^{2}\left(t-\tau \right)-{u}^{2}\left(t\right){e}^{2}\left(t\right)\right]=0,\mathrm{}\mathrm{}\mathrm{}\forall \tau ,$${\mathrm{\varnothing }}_{ue}\left(\tau \right)=E\left[u\
left(t-\tau \right)e\left(t\right)\right]=0,\mathrm{}\mathrm{}\mathrm{}\forall \tau ,$${\varnothing }_{{u}^{2}e}\left(\tau \right)=E\left[{u}^{2}\left(t-\tau \right)-{u}^{2}\left(t\right)e\left(t\
right)\right]=0,\forall \tau ,$${\varnothing }_{ee}\left(\tau \right)=E\left[e\left(t-\tau \right)e\left(t\right)\right]=\delta \left(\tau \right),$
where $u\left(t\right)$ is input, $e\left(t\right)$ is the predicted error, ${\mathrm{\varnothing }}_{ue}\left(\tau \right)$ indicates the cross-correlation function between $u\left(t\right)$ and $e\
left(t\right)$ and $\delta \left(\tau \right)$ is an impulse function. For nonlinear system identification all five equations should be used [14]; in the present case a 95 % confidence band indicates
that the proposed NN model satisfies all five equations, see Fig. 13.
4. Feedback controller
In order to eliminate the tip vibration of flexible link manipulator active vibration PID control scheme is conducted for both ARX and NARX models in the feedback control strategy. In this study
discrete modelling for the sampled time is proposed, and the digital PID controller is selected for both linear and nonlinear models. The PID controller parameters are automatically tuned by using
the interactive design mode technique.
Fig. 14System response with controller
4.1. Active vibration control for linear model
In this section the ARX model is embedded into the feedback control loop, see Fig. 15. The adaptive and robust capability of PID controller can be evaluated by altering the disturbance signal. The
parameters of the designed PID controller in presence of a first disturbance, a step signal, is stored when different disturbance signal is imposed to the system. In this case the repeating sequence
signal is utilized as another alternative disturbances signal. The response of system to a step input reference signal, with two different disturbance is depicted in Fig. 14. As expected the system
vibration is canceled and stabilized by PID controller with 6 % overshoot and 0.002 steady state error.
Fig. 15Digital PID controller with discrete system in the feedback loop
To evaluate how well the system performs in the feedback control loop, the bang-bang torque is imposed as a reference signal. From Fig. 16, with the new reference signal the controller stabilizes
system and damps the extra vibration as well. The disturbance signal profile is illustrated in Fig. 17 as a repeating sequence signal.
Fig. 16System response to the bang-bang torque as reference signal
Fig. 17Repeating sequence disturbance signal
By applying the frequency response function (FRF) for both controlled and uncontrolled systems that are stimulated by bang-bang torque, the performance of the PID controller can be evaluated from the
well-damped amplitudes of response in the FRF result, shown in Fig. 18.
Fig. 18Frequency response of the bang-bang torque for controlled and uncontrolled system
4.2. Active vibration control for nonlinear model
In this section the proposed NARX neural network model is utilized in the feedback scheme with digital PID controller. The control system is depicted in Fig. 19 and the response of the system to a
reference signal (step signal) in the presence of two different disturbances namely, step signal and repeating sequence signal, is illustrated in Fig. 20. In order to follow the same scenario with
presented control scheme for linear system in the previous section, the bang-bang reference torque signal is exerted into the control system to evaluate the control capability with respect to
different reference signals and disturbances.
Fig. 19Digital PID controller with black box system in the feedback loop
Fig. 20System response to the step signal with two different disturbances
As illustrated in Fig. 21, the PID controller in the presence of bang-bang torque shows a desirable response (without overshooting). The step signal is imposed as disturbances, by applying a new
disturbance, such as repeating sequence signal. Some peaks are seen in the controlled response.
Fig. 21System response to the bang-bang torque as reference signal
The FRF is taken into account for evaluating the robustness of PID controller on nonlinear NARX neural network model in the case of a step signal disturbance. From Fig. 22 it can be seen that the PID
controller completely attenuates the vibration of the flexible manipulator by reducing the amplitude for the entire frequency domain. It is also observed that the amplitude is augmented when imposed
by a repeating sequence disturbance in the high frequency region. However, the flexible manipulator system is concerned with active vibration control in the low frequency domain rather than high
frequency domain.
Fig. 22Frequency response to the bang-bang torque for controlled and uncontrolled system
5. Conclusions
This study has demonstrated a PID controller design for linear and nonlinear modeling of flexible manipulator with the aim of suppressing unwanted vibration due to external excitations. A significant
implication is that the linear model (ARX) shows a better estimation with MSE of 2.8546×10^-8 compared to nonlinear model (NARX) with MSE of 3.4×10^-5. The excellent supression in the linear model
can be verified from test data acquisition using finite difference method, because the FD method estimates a linear model for nonlinear system. In addition, proposed models are validated by employing
FRF and correlation test for linear and nonlinear model respectively. The PID controller was implemented in both models to cancel the vibration. In the presence of input signal and disturbances in
the control loop, the amplitude of the system response for entire frequency domain is canceled for the linear model. However, the amplitude of the system response for nonlinear model is barely
attenuated especially in the low frequency region. The most likely explanation of the different PID controller performance in both models is that the parametric PID controller is well adapted with
parametric linear model rather than nonlinear and nonparametric models. The next stage of this research is experimental confirmation of our simulation and also designing the nonlinear control scheme
for the proposed NARX model.
• Qinglei Hu Input shaping and variable structure control for simultaneous precision positioning and vibration reduction of flexible spacecraft with saturation compensation. Journal of Sound and
Vibration, Vol. 318, Issues 1-2, 2008, p. 18-35.
• Yaryan M., Naraghi M., Rezaei S. M., Zareinejad M., Ghafarirad H. Bilateral nonlinear teleoperation for flexible link surgical robot with vibration control. Proceedings of the 19th Iranian
conference on Biomedical Engineering (ICBME), Tehran, Iran, 2012, p. 21-22.
• Rocha C. R., Tonetto C. P., Dias A. Robotics and computer-integrated manufacturing. A comparison between the denavit-hartenberg and the screw-based methods used in kinematic modeling of robot
manipulators. Robotics and Computer Integrated Manufacturing, Vol. 27, Issue 4, 2011, p. 723-728.
• Yuangang Tang, Fuchun Sun, Zengqi Sun Neural network control of flexible-link manipulators using sliding mode. Neurocomputing, Vol. 70, Issues 1-3, 2006, p. 288-295.
• Vicente Feliu, Emiliano Pereira, Ivan M. Diaz, Pedro Roncero Feedforward control of multimode single-linkflexible manipulators based on an optimal mechanical design. Robotics and Autonomous
Systems, Vol. 54, 2006, p. 651-666.
• Gerasimos G. Rigatos Model-based and model-free control of flexible-link robots: a comparison between representative methods. Applied Mathematical Modelling, Vol. 33, Issue 10, 2009, p.
• Francisco Ramos, Vicente Feliu New online payload identification for flexible robots. Application to adaptive control. Journal of Sound and Vibration, Vol. 315, 2008, p. 34-57.
• Franklyn Duarte, Pablo Ballesteros, ChristianBohn H∞ and state-feedback controllers for vibration suppression in a single-link flexible robot. IEEE/ASME Internatinal Conference on Advanced
Intelligent Mechatronics (AIM) Wollongong, Australia, 2013, p. 1719-1724.
• Rene Franke, Jorn Malzahn, Thomas Nierobisch, Frank Hoffmann, Torsten Bertram Input shaping and strain gauge feedback vibration control of an elastic robotic arm. IEEE International Conference on
Robatic and Automation, Kobe Internatinal Conference Center, Kobe, Japan, 2010, p. 672-677.
• Akira Abe Residual vibration suppression for robot manipulator attached to a flexible link by using soft computing techniques. Proceeding of IEEE Internatinal Conference on Robotic and
Biomimetics, Phuket, Thailan, 2011, p. 2324-2329.
• Qiu Zhi-Cheng, Shi Ming-Li, Wang Bin, Xie Zhuo-Wei Genetic algorithm based active vibration control for a moving flexible smart beam driven by a pneumatic rod cylinder. Journal of Sound and
Vibration, Vol. 331, Issue 10, 2012, p. 2233-2256.
• Hu Junfeng Vibration suppression of a high-speed flexible parallel manipulator based on its inverse dynamics. IEEE internatinal Conference on Intelligent Systems Design and Engineering
Application, Sanya, Hainan, 2012, p. 744-747.
• Tokhi M. O., Mohamed Z., Shaheed M. H. Dynamic characterisation of a flexible manipulator system. Robatica, Vol. 19, Issue 4, 2001, p. 571-580.
• Yatim H. M., Darus I. Z. M. Intelligent parametric identification of flexible manipulator system. IEEE Conference on Control, System and Industrial Information (ICCSII), Bandung, Indonesia, 2012.
• Billings S. A., Voon W. S. F. Correlation based validity tests for nonlinear models. International Journal Control, Vol. 44, Issue 1, 1986, p. 235-244.
About this article
13 November 2014
Vibration generation and control
system identification
single flexible manipulator
linear and non-linear model
PID controller
The authors would like to extend their thanks to the Faculty of Mechanical Engineering of Universiti Teknologi Malaysia for the support in implementing the project.
Copyright © 2015 JVE International Ltd.
This is an open access article distributed under the
Creative Commons Attribution License
, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. | {"url":"https://www.extrica.com/article/15693","timestamp":"2024-11-08T08:15:15Z","content_type":"text/html","content_length":"155887","record_id":"<urn:uuid:0d7719d3-7268-48a3-8b3d-88f9db81c714>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00214.warc.gz"} |