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Automatically add columns and formulae then fill-down in Excel
Some simple VBA code to add columns in Excel, insert specific formulae at the top then fill-down to the bottom of the sheet.
For those who work with log files, it may be necessary to routinely insert columns at a specific position, insert a formula and then fill-down to derive certain values. This can be automated in Excel
using Visual Basic using four simple scripts.
Inserting Columns
To insert columns at a specific position in a worksheet, use the following VBA script.
Sub AddColumns()
'Inserts Two Columns at B and C
End Sub
In this example, two columns are inserted where Column B is located. Adjust the range as required.
Adding headers
If the new columns require headers in Row 1, then the following script can do that.
For instance, let’s say that we want the header in B1 to be called “Value 1” and the header in C1 to be called “Value 2”. The following script will do this:
Sub AddHeader()
Worksheets(1).Range("B1").Formula = "Value 1"
Worksheets(1).Range("C1").Formula = "Value 2"
End Sub
Adding formulae
After adding columns, you may want to insert a formula to perform a calculation based on data elsewhere in the sheet. Since cells B1 and C1 contain headers, we’ll add them to cells B2 and C2:
Sub AddFormula()
'Inserts specific formulae to cells B2 and C2
Dim Formulas(1 To 2) As Variant
With ThisWorkbook.Worksheets("Transposed Data")
Formulas(1) = "=SUM(E2+G2)"
Formulas(2) = "=SUM($E$2+2)"
.Range("B2:C2").Formula = Formulas
'Changes number format in Columns B and C to general
.Range("B:C").NumberFormat = "General"
End With
End Sub
This code adds the formula =SUM(E2+G2) to B2 and =SUM($E$2+2) to C2. These should be changed to suit your circumstances. As many formulae can be added to the code as desired, so long as Dim Formulas
(1 To 2) As Variant, Formulas( ) and .Range is expanded to accommodate them.
In addition, this code will change the NumberFormat to “General”. Again, this can be changed to whatever type is required. The number type really only becomes an issue of the contents of the cells on
the left of the new columns have a different number format. For instance, if Column A had a series of dates and was therefore in Date format, Columns B and C would have been created in Date format
Once the automated formulae have been added to the top of the column, you may want them to automatically fill down.
The following code will identify how many rows contain data in the worksheet and then fill-down from B2 to the last data-containing row in Column B.
Sub FillColumn()
'Fills column to last row of data from Cell B2
Dim LastRow As Long
LastRow = Cells.Find(What:="*", SearchOrder:=xlByRows, SearchDirection:=xlPrevious).Row
Range("B2:B" & LastRow).FillDown
End Sub
The range can be adjusted to accommodate more columns. In our previous example, we added formulae to the first rows in Columns B and C, so we need to change the code from Range("B2:B" &
LastRow).FillDown to Range("B2:C" & LastRow).FillDown.
By using this series of scripts, your worksheet should now automatically:
1. Insert columns
2. Add column headers
3. Add formulae to the first row
4. Fill down to the last row
Don’t forget that the easiest way to manage this is to link all of the scripts together:
Sub DoEverything()
End Sub
5 responses to “Automatically add columns and formulae then fill-down in Excel”
Is it possible to modify this to insert a column after the last column containing data, then add a formula?
Many thanks for this simple yet efficient code !
Hi, May i ask that how to automatically fill all the above for formula without adding header(s) and actually i want all my files have additional column and formula as well?
Can you pls write the code to sum below Coloumn ‘B’ value with respect to coloumn ‘A’ or Coloumn ‘C’.
Name Amount site Purpose Date
qwe 123 sss opi 01-01-2015
qwe 345 sss qas 01-01-2015
asd 345 kkk zxc 02-02-2015
zxc 789 sss mnb 03-03-2015
& so on…….
Have Your Say | {"url":"https://code.adonline.id.au/automatically-add-columns-and-formulae-then-fill-down-in-excel/","timestamp":"2024-11-11T04:54:21Z","content_type":"text/html","content_length":"49709","record_id":"<urn:uuid:d8d75099-473d-495d-8ea2-2e60674279cd>","cc-path":"CC-MAIN-2024-46/segments/1730477028216.19/warc/CC-MAIN-20241111024756-20241111054756-00790.warc.gz"} |
Mathematics of Natural Choices
As a sub-discipline of the social sciences, the collective choice theory was based on very good mathematics at the end of the 18th century and evolved from the work of Nicolas de Caritat, marquis de
Condorcet, a prominent French scientist. He put forward an example, later called the Condorcet paradox, where he showed that if the number of alternatives (for instance, candidates in an election)
and the number of voters are more than two, then the simple majority rule may not result in any decisions. Condorcet's model accounted for both the most preferable options and the whole order of
The Condorcet paradox made a huge impression on his contemporaries and fascinated scientists of the 19th and early 20th centuries. Since the Classical Period, people had believed that the majority
was always right and that its opinion reflected the will of higher forces. There was even a wonderful Roman proverb ‘Vox populi—Vox dei’, which means ‘The voice of the people is the voice of God’.
Condorcet demonstrated that sometimes the vox populi may lead to contradictory results.
Throughout the 19th century and the first half of the 20th century, scientists tried to propose rules that would help avoid the "Condorcet paradox". However, it continued to manifest itself in one
way or another.
At the same time as Condorcet, another great French scientist, Jean-Charles de Borda, proposed another decision-making rule, where alternatives were ranked, their ranks were summed up, and the
alternative with the maximum rank was selected. This was essentially a direct generalization of the plurality voting rule that we apply today.
A century and a half later in 1951, Kenneth Arrow—one of the five greatest economists of all time—developed a different approach to rules formation. He was the first to introduce a system of axioms,
external constraints that any reasonable rule should satisfy, and as a result, shaped up a corresponding rule from these axioms.
For example, it included the Pareto condition: if all participants of the voting procedure believe that alternative x is better than alternative y, then the collective choice should be the same. The
axioms included neutrality—the rule should be applied to the same extent to all alternatives (candidates), and anonymity—the same condition, but with regard to voters.
Apart from the theories above, Arrow introduced another fundamental axiom that he called independence of irrelevant alternatives. This condition seems to be absolutely crucial in the Arrow model. It
states that when making decisions on the mutual ordering of alternatives x and y, we do not need to consider the mutual relations between x and other alternatives, as well as between y and other
In other words, collective preference between alternatives x and y depends exclusively on individual preferences between x and y. Moreover, if x is more preferable to y from the range {x, y}, then
the introduction of the third option z and expansion of the range up to {x, y, z} should not make y more preferable to x. This means that the preference for x or y should not change with the
introduction of z.
We called this axiom a locality condition in our works. I remember telling this for the first time to Professor Arrow of whom I still cherish the fondest memories. He thought a little and said:
"Indeed, this is a locality. I have never even thought of it".
The result of Arrow's work, called "Arrow Theorem" or "Arrow Paradox", was unfavourable in the sense that the only procedure that meets the conditions above is completely non-democratic—a
dictatorship. In other words, one member is assigned, and the collective choice inevitably coincides with his individual decision.
Two decades later, back in 1977, the young scientist Eric Maskin proposed considering such correspondences of group choice that allow representing the collective decision in the form of Nash
equilibria in a specific formation. Later, Maskin successfully solved this fundamental problem, for which he was awarded the Nobel Prize in Economics in 2007 (which he shared with Leonid Hurwicz and
Roger Myerson).
With this problem, the locality condition is formed in the following way: we consider the relations between x and y so that the elements under the x variant (i.e., the elements that are worse than x)
would be the same, but their order is irrelevant.
We also obtained fundamental results in this field. One of my works describes an axiomatic substantiation of the so-called collective choice correspondences, which, in particular, meets Maskin's
monotonicity condition (if the alternative (candidate) x improves his or her position compared to y, then his or her position in the collective decision should also improve).
Just recently, Professor Maskin has received some new results. He proposed evaluating the relationship between the alternatives x and y, and if the positions of the elements between x and y remains
unchanged, the relationship between x and y in the collective decision does not change either. If there are other well-known constraints—neutrality, anonymity and monotony—the Borda count turns out
to be the solution that satisfies this system of axioms.
In my opinion, this is an outstanding achievement in the study of non-local procedures for collective decision making, which will trigger a significant amount of work afterwards. This is the first
axiomatics ever that generalizes the Arrow axiomatics and leads to one of the well-known positional rules—the Borda rule. A fundamental breakthrough has been made in a field that is more than 200
years old, and I am very pleased to know that the author of this breakthrough is a friend of mine and an employee of our Centre and HSE, Professor Eric Maskin. | {"url":"https://iq.hse.ru/en/news/385619516.html","timestamp":"2024-11-13T18:14:32Z","content_type":"text/html","content_length":"41014","record_id":"<urn:uuid:b14399ce-dbe0-4858-be96-d837909893a0>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00353.warc.gz"} |
Impact of the Regularization Parameter in the Mean Free Path Reconstruction Method: Nanoscale Heat Transport and Beyond
Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and The Barcelona Institute of Science and Technology (BIST), Campus UAB, 08193 Bellaterra, Barcelona, Spain
Instituto de Química, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile
ICREA-Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
Author to whom correspondence should be addressed.
Submission received: 18 February 2019 / Revised: 6 March 2019 / Accepted: 6 March 2019 / Published: 11 March 2019
The understanding of the mean free path (MFP) distribution of the energy carriers in materials (e.g., electrons, phonons, magnons, etc.) provides a key physical insight into their transport
properties. In this context, MFP spectroscopy has become an important tool to describe the contribution of carriers with different MFP to the total transport phenomenon. In this work, we revise the
MFP reconstruction technique and present a study on the impact of the regularization parameter on the MFP distribution of the energy carriers. By using the L-curve criterion, we calculate the optimal
mathematical value of the regularization parameter. The effect of the change from the optimal value in the MFP distribution is analyzed in three case studies of heat transport by phonons. These
results demonstrate that the choice of the regularization parameter has a large impact on the physical information obtained from the reconstructed accumulation function, and thus cannot be chosen
arbitrarily. The approach can be applied to various transport phenomena at the nanoscale involving carriers of different physical nature and behavior.
1. Introduction
In solid-state materials there is a variety of scattering mechanisms for energy carriers involved in different transport phenomena, such as impurities, boundaries, and collisions with other particles
/quasi-particles. The average distance that a moving particle (photon, electron, etc.) or quasi particle (phonon, magnon, etc.) travels before being absorbed, attenuated, or scattered is defined as
the mean free path (MFP). It is well known that energy carriers that propagate over different distances in a material, having different MFP contribute differently to the energy transport. Thus, the
use of a single-averaged MFP may be inaccurate to describe the system [
It is possible to quantitatively describe how energy carriers with a specific MFP contribute to the total transport property by an MFP spectral function or MFP distribution [
], which contains the information of the specific transport property associated with the energy carriers with a certain MFP. By normalizing and integrating this spectral function we obtain the
accumulation function, which describes the contribution of carriers with different MFPs below a certain MFP cut off to the total transport property, being very intuitive to identify which MFPs are
the most relevant to the transport phenomenon under study by plotting this function.
When studying transport at the nanoscale, boundary scattering becomes important as the characteristic size of the nanostructure approaches the MFP of the carriers involved. From the bulk MFP
distribution, it is possible to predict how size reduction will affect a transport property in this material given that we know which MFPs are contributing the most. Inversely, it is possible to
obtain the bulk MFP distribution from size-dependent experiments, where the critical size of each measurement acts as an MFP cut off due to boundary scattering.
This relation between the transport property at the nanoscale and the bulk MFP distribution is given by an integral transform. A suppression function (SF), which accounts for the specific geometry of
the experiment and depends upon the characteristic size of the structures and the MFP of the carriers, connects the bulk MFP distribution and the experimental measurements; acting in the kernel of
the integral transformation. Using this integral relation, it is possible to recover the MFP distribution from experimental data. This is known as the MFP reconstruction method [
This mathematical procedure however is an ill-posed problem with, in principle, infinite solutions. To obtain a physically meaningful result from it, some restrictions must be imposed. These
constraints are mainly related to the shape of the mean free path distribution. The distribution is a cumulative distribution function and it is subjected to some restrictions, e.g., the MFP
distribution is unlikely to have abrupt steps because it is spread over such a wide range of MFPs. The distribution therefore must obey some type of smoothness restriction [
]. Now, the problem becomes a minimization problem, where the solution lies in the best balance between the smoothness of the reconstructed function (solution norm) and its proximity to the
experimental data (residual norm). This balance is controlled by the choice of the regularization parameter. The role of this parameter has been widely overlooked in the literature, where the choice
of its value has been poorly justified and, on some occasions, it remains unmentioned. In this work, we present a method to obtain the optimal value of this parameter using the L-curve criterion [
]. We apply this criterion to the thermal conductivity and the phonon-MFP distribution and we present a study of the impact that the choice of its value has in the reconstructed accumulation. We
demonstrate that this methodology can be extended to several transport properties involving carriers of different physical nature and behavior.
2. Materials and Methods
To perform the reconstruction of the MFP distribution of the energy carriers, the only input needed is a characteristic SF and a well distributed set of experimental data, i.e., a large amount the
experimental measurements spread over the different characteristic sizes of the system. The suppression function strongly depends on the specific geometry of the sample and the experimental
configuration. It relates the transport property of the nanostructure
and that of the bulk
. The suppression has been derived for different experimental geometries from the Boltzmann transport equation [
The relation between the transport coefficient
) and the suppression function was originally derived for thermal conductivity [
], and more recently has been used to determine the MFP of magnons and the spin diffusion length distribution [
]. This relation can be expressed by means of a cumulative MFP distribution as
$α = α n a n o ( d ) α b u l k = − ∫ 0 ∞ F a c c ( Λ b u l k ) d S ( χ ) d χ d χ d Λ b u l k d Λ b u l k$
) is the suppression function,
is the Knudsen number
= Λ
, Λ
is the bulk MFP and
the characteristic length of the sample and
is the accumulation function given by
$F a c c = 1 α b u l k ∫ 0 Λ c α Λ ( Λ b u l k ) d Λ b u l k$
Λ is the contribution to the total transport property of carriers with a mean free path Λ. This function represents the contribution of carriers with MFPs up to an upper limit, Λ
, to the total transport property, and is the object that will be recovered by applying the MFP reconstruction technique. From this definition it is easy to see that the accumulated function is
subject to some physical restrictions: it cannot take values lower than zero for Λ
= 0 or higher than one for Λ
→ ∞, and it must be monotonous [
]. We can recognize that Equation (2) is a Fredholm integral equation of the first kind that transforms the accumulation function
) into
$K = d S ( χ ) d χ d χ d Λ b u l k$
acting as a kernel. As the inverse problem of reconstructing the accumulation function
is an ill-posed problem with infinite solutions [
]. Minnich demonstrated some restriction can be imposed on
to obtain a unique solution [
]. Furthermore, it is reasonable to require the smoothness conditions mentioned before on
, since it is unlikely to have abrupt behavior in all its domain. These requirements can be applied through the Tikhonov regularization method, where the criterion to obtain the best solution
is to find the following minimum:
$min { ∥ A · F a c c − α i ∥ 2 2 + μ 2 ∥ Δ 2 F a c c ∥ 2 2 }$
is the normalized
-th measurement,
$A = K ( χ i , j ) × β i , j$
is an
matrix, where
is the number of measurements and
is the number of discretization points,
$K i , j$
is the value of the kernel at
$χ i , j = Λ i , j / d i$
, and
$β i , j$
the weight of this point for the quadrature. The operators
$∥ ∥ 2$
$Δ 2$
are the 2-norm and the (n − 2) × n trigonal Toeplitz matrix which represent a second order derivative operator, respectively. The first term of Equation (3) is related to how well our result fits to
experimental data (residual norm), while the second term represents the smoothness of the accumulation function (solution norm). The balance between both is controlled by the regularization parameter
. In other words,
sets the equilibrium between how good the experimental data is fitted and how smooth is the fitting function. The choice of
will thus have a huge impact on the final result of the accumulation function, and a criterion to obtain the optimal value must be established. The selection of the most adequate
is still an open question in mathematics. Several heuristic methods are frequently used, such as the Morozov’s discrepancy principle, the Quasi-Optimally criterion, the generalized cross validation,
L-curve criterion, the Gfrerer/Raun method, to name a few [
]. Among these methods, the L-curve criterion is one of the most popular methods due to its robustness, convergence speed and efficiency. This method establishes a balance between the size of the
discrepancy of the fitting function and the experimental data (residual norm) with the size of the regularized solution (solution norm) for different values of
. The curve has an L-like shape composed by a steep part where the solutions are dominated by perturbation errors and a flat part where the solution is dominated by regularization errors. The corner
represents a compromise between a good fit of the experimental data and the smoothness of the solution. It has been found that the corresponding point lies in the corner of the L-curve in the
residual norm-solution norm plane, which can be defined as the point of maximum curvature. The optimal value of
can be found by locating the peak position of the curvature as a function of
The method employed is depicted in
Figure 1
, and is common to all cases presented here. The experimental data in the case studies shown in this work was reproduced from the digitalization of the images and the corresponding uncertainties. A
specific suppression function is selected for each case, depending on the particular geometry and experimental configuration. As explained above, the integral in Equation (2) is discretized, and an
adequate integration interval depending on the span of experimental data is chosen. At this point, instead of introducing an arbitrary value of the regularization parameter, we determine the optimal
value via the L-curve criterion. We have observed that the distribution of the curvature depending on log
follows a Gaussian distribution, thus allowing us to obtain the peak, i.e., the highest curvature (corresponding to the corner of the
-curve), using a Gaussian fitting with a reduced number of computational points. With this optimal value of the regularization parameter we can proceed to apply the Tikhonov regularization method and
impose the conditions on
using a convex optimization package for MATLAB called CVX [
3. Results and Discussions
The MFP reconstruction method, as well as the method here presented for the selection of μ, does not require a priory any physical assumption about the carrier, such as band structure or velocity. In
this section, we apply the method to heat transport by phonons in three examples cases where the characteristic size is given by (a) the thickness of the nanostructure in a layered system, (b) a
length scale of the measurement technique and (c) a combination of the former two. The extension of the method to magnon-mediated transport phenomena, namely, the spin Seebeck effect and spin-Hall
torque coefficient, is further examined in the supporting information.
3.1. Phonons in Out-of-Plane Thermal Transport in Graphite from Molecular Dynamic Simulations
Firstly, we will study the MFP reconstruction of phonons in cross-plane thermal transport along the c-axis of graphite. The thermal conductivities (κ) were obtained from a set of simulations
performed by Wei et al. [
] From this numerical experiment, we have recovered the MFP distribution in bulk graphite along the
-axis by using the L-curve criterion based MFP reconstruction method. This will illustrate the different steps and details which apply to all of the cases that we present here.
As shown in
Figure 1
after obtaining the “experimental data” the only input needed is the SF. As the thermal transport occurs in the c-direction, i.e., in the cross-plane direction, we will employ the cross-plane
Fuchs-Sondheimer SF, described by [
$S ( χ ) = 1 − 3 χ ( 1 4 − ∫ 0 1 y 3 e − 1 / ( χ y ) d y )$
Equation (4) describes the modification of the phonon transport along the perpendicular direction of a thin film due to the finite size effect. Once the SF is fixed, the next step is to find the
-parameter by minimizing Equation (3) for different
-values. The dependence of both the residual and the solution norms on
can be visualized as a 3-D curve (see
Figure 2
a), and its projection on
-plane is the
-curve, named after its characteristic shape. The curve was generated using the simulated cross-plane
of graphite as function of thickness at T = 300 K [
Figure 2
b shows the curvature distribution of
$∥ A · F a c c − α i ∥ 2$
$∥ Δ 2 F a c c ∥ 2$
expressed in heat-like colour map representing the maximum (yellow) and minimum (black) values of the curvature. We can observe that the maximum of the curvature is found right at the corner of the
-curve for
≈ 0.95, which is extracted from the Gaussian distribution of the curvature. In this corner the balance between a smooth function and a good fitting of the experimental data can be found.
Figure 3
a shows the
as a function of the MFP for different
-values. For this particular example, we can observe that depending on the
-values, the span of MFP can fluctuate from a very wide (5 nm–6.88 μm for
= 10) to very narrow (60–100 nm for
= 0.1) distribution. It is also important to notice that
-values between 0.1–4.0 lead to quite good agreement between the simulated κ (“experimental data”) and
product (see
Figure 3
b), although these values yield to a completely different span of the MFP. The MFP distribution varies from very narrow (low
-values) to very wide (high
-values). This difference in the MFP distribution is a direct consequence of the weight given to each component in the Equation (3). The low
-values give a large weight to the residual norm and, as a consequence, it leads to an overfitting of the reconstructed function. At the same time, large
-values give higher importance to the solution norm, leading to and over smoothing of the reconstructed function.
Figure 3
a also shows the MFP reconstruction generated by Zhang et al. [
] (cyan solid line) and by Wei et al. (grey dotted line). The first reconstruction was carried out using the measured κ of graphite as function of the thickness and the suppression function given by
Equation (4). We can see that for the optimal value of
= 0.95, the MFP of the carriers spans 36 nm < Λ < 270 nm, in similar range compared with the reconstructed values obtained by Zhang et al. 40 nm < Λ < 210 nm [
]. The second reconstruction was calculated using the simulated κ and a quasi-ballistic model to describe the suppression function (Equations (3) and (4) of ref. [
]). If the drastic change of the MFP-distribution is due to the reconstruction method being an ill-posed problem, then, a drastic change of SF can have a strong impact on its distribution. The
will be strongly affected by the “shape” of the selected SF. Therefore the choice of a different SF will lead to a different MFP distribution [
3.2. In-Plane Thermal Transport in 400 nm Thick Si Membrane
The second case of study is the in-plane thermal transport in a 400 nm Si membrane at room temperature probed by the Thermal Transient Grating (TTG) technique, obtained from Johnson et al. [
]. In the previous example, the characteristic length of the system was the thickness of the graphite sheets. Here the Si membrane has fixed thickness
= 400 nm and the variable length scale is the period of the thermal grating
. Since the measurement of in-plane thermal conductivity in the membrane will correspond to phonons with MFPs lower than L in each measurement, the grating period becomes the equivalent of the
maximum MFP.
In this case we have to consider two different effects: (i) the impact of the finite size of the membrane and the boundary scattering of the effective in-plane MFP and (ii) the crossover from
non-diffusive to diffusive phonon transport given by the period of the thermal grating. Then, a combination of two suppression functions have to be introduced that takes both effects into account [
In the first place, we define an effective MFP (Λ’) to take into account the effect of the boundary scattering due to thickness of the membrane as follow:
where Λ is the bulk MFP, d is the thickness of the membrane and S
is Fuchs-Sondheimer SF for in-plane thermal transport given by [
$S 2 ( d / Λ ) = 1 − 3 8 d Λ + 3 2 d Λ ∫ 1 ∞ ( y − 3 − y − 5 ) e − y Λ / d d y$
With this effective MFP we proceed to perform the reconstruction using the suppression function for the specific geometry of the experiment given by [
$S 1 ( q Λ ′ ) = 3 q 2 Λ ′ 2 ( 1 − arctan ( q Λ ′ ) q Λ ′ )$
where q = 2Λ/
is the grating wavevector. If we define
= qΛ’, the kernel for the reconstruction is given by
$d S ( ζ ) d ζ d ζ d Λ ′ d Λ d Λ ′ = 2 π L 3 ζ 3 ( 3 arctan ( ζ ) ζ − 3 + 2 ζ 2 1 + ζ 2 ) ( 1 + 3 2 ∫ 1 ∞ d t ( t − 3 − t − 5 ) e − t Λ d ( 1 − t ) )$
function is unity in the limit qΛ’ << 1, in the diffusive limit, and goes like (qΛ’)
for qΛ’ >> 1, in the ballistic regime, thus describing the transition between both regimes necessary to adequately interpret the measured quantities in the experiment [
Similarly to the previous case, we apply a Gaussian fitting procedure to obtain a value
= 1.05 at room temperature. In
Figure 4
we can observe the effect of the different values of
. Note that, in this case, the reduction of
affects mainly the smoothness of the reconstructed function with large changes on the concavity and convexity of the accumulation function. However, there was not a significant change on the
product for small
-values. The oscillations observed for low
-values are a direct consequence of the overfitting of the reconstructed function, due to the large weight imposed to the minimization problem. The increase of the regularization parameter beyond the
optimal value results in an increase of the span of the MFP of the carriers, as shown in
Figure 4
a, and a poor agreement with the experimental data, as can be seen in
Figure 4
3.3. In-Plane Thermal Transport in Si: Reconstruction by Changing the Thickness of the Membrane
The dependence of the reconstructed accumulation function on the regularization parameter relies on the L-curve and the dependence of the residual norm $∥ A · F a c c − α i ∥ 2$ and solution norm $∥
Δ 2 F a c c ∥ 2$ on μ. The following case illustrates an example of how the particular shapes of these different curves can strongly affect the reconstruction.
For this example, we used the thickness dependence of the in-plane κ measured by Cuffe et al. [
]. The experiment consisted in the measurement of the κ of free standing Si membranes ranging from 15–1518 nm using the transient thermal grating technique in the diffusive regime. As the thermal
transport occurs along the films, the Fuchs-Sondheimer for in-plane thermal transport (see Equation (6)) was selected as SF.
As we can see in
Figure 5
, the three-dimensional (3D) visualization of the minimization problem is manifestly different to that presented for graphite in
Figure 2
a. For graphite, we observed very smooth behavior of each of the projections (
planes) in the 3D curve. This leads a continuous variation of MFP from a narrow to a wide distribution as
increases. On the other hand,
Figure 5
shows singularities and abrupt jumps of the different projections. For the case of low
-values, this leads to large oscillations in the MFP distribution function, as is shown in the blue solid line in
Figure 6
a. However for large
-values, we observe a linear distribution of the reconstructed curve as a function of the logarithm of MFP (see red solid line in
Figure 6
a). For intermediate
-values (0.8–3), we can observe no major differences either in the smoothness or in the MFP span of the accumulated function. Similarly, we did not observe huge changes in the fitted function as it
is displayed in
Figure 6
Figure 6
a also shows the MFP reconstruction generated by Cuffe et al. [
]. This reconstruction was carried out using the same procedure than that shown in this section, including the same suppression function and the minimization procedure. However, no information is
given regarding the regularization parameter or the procedure to estimate it. Despite this, we can observe that the MFP distribution estimated for the optimal value of
= 0.8 and the one obtained by Cuffe et al. spans in similar range with MFP ranging from 20 nm < Λ < 100 μm. Slight deviations can be observed for MFP around Λ = 1 μm, which are expected from small
differences in the regularization parameter and the numerical calculation of the minimization problem. For comparison, the calculated and measured MFP distribution of bulk Si are also included. The
good agreement between our reconstruction distribution and the molecular dynamics simulations by Henry et al. [
] and the measurements performed by Regner et al. [
] is remarkable. In the latter case, it is important to keep in mind that the experiment is completely different from the one presented here.
The L-curve criterion is efficient for obtaining the most adequate regularization parameter, but in this case the reconstructed accumulation function is very robust against changes in
due to the particular flatness of the residual and solution norm depending on the values of
. It is also important to remark that the estimation of the optimum
-value has to be carried out for each set of measurements. As we showed in the supporting information, for the case of temperature dependence measurements of the Spin Seebeck coefficient, the optimal
-value varies among the measurements (See
Figure S2
). This effect comes from the differences in the spread of the experimental data in each temperature regime and the importance of carriers with longer MFPs as the temperature decreases [
4. Conclusions
We have demonstrated that the choice of the regularization parameter μ has a large impact on the physical information obtained from the reconstructed accumulation function, and thus cannot be chosen
arbitrarily. On one hand, small μ-values lead to a very narrow MFP distribution but also very good agreement between the fitting function and the experimental data. However, they also introduce
artefacts (oscillations) to the reconstructed MFP distributions. These oscillations are the consequence of an overfitting of the reconstructed function due to the low weight given to the solution
norm. On the other hand, large μ-values lead to a wider MFP distribution but worse agreement between the fitting function and the experimental data. This is a direct consequence of the larger weight
to the solution norm and, as consequence, an over smoothing of the fitted function. It is also important to notice that the estimation of the optimum μ-value has to be carried out for each set of
measurements. It cannot be assumed the same value for temperature dependence measurements will occur, as we show in the supporting information.
The method presented here is not limited only to phonon transport and it can be applied to many different cases. The only input needed to reconstruct the mean free path distribution of the carriers
is a well-known suppression function and a well distributed set of experimental data points. Regardless of the carrier physical behavior or the span of MFP, we have proven the method to be
applicable, and we have seen that the robustness of the reconstruction against deviations from the estimated value of μ will depend on the particular variation of the solution norm and reduced norm
with μ.
Supplementary Materials
The following are available online at
, Figure S1: (a) Magnon mean free path distribution of the accumulation function for spin Seebeck effect experiments. (b) Normalized Longitudinal Spin-Seebeck coefficient for different thickness of
the YIG. Figure S2: Optimal values of
for the Magnon-MFP reconstruction. Figure S3: (a) Spin diffusion length distribution of the accumulation function reconstructed for spin-Hall torque experiments. The blue and red lines are the result
obtained using a low and high value of
, respectively. The green line represent the MFP distribution reconstructed using
. (b) Normalized Longitudinal spin-Hall torque coefficient for different thickness of the Pt filmvalues of μ for the Magnon-MFP reconstruction at different temperatures for LSSE experiments.
Author Contributions
M.-Á.S.-M., F.A., E.C.-A. wrote the article. M.-Á.S.-M., J.O. and E.C.-A. designed the different numerical programs. C.M.S.T. and F.A. supervised the work and discussed the results. All authors
discussed the results and commented on the manuscript.
This research was funded by the EU FP7 project QUANTIHEAT (Grant No 604668) and the Spanish MINECO-Feder project PHENTOM (FIS2015-70862-P). M.-Á.S.-M. acknowledges support from SO-FPI fellowship BES
2015-075920. ICN2 acknowledges support from Severo Ochoa Program (MINECO, Grant SEV-2017-0706) and funding from the CERCA Programme/Generalitat de Catalunya.
We thank G. Whitworth for a critical reading of the manuscript.
Conflicts of Interest
The authors declare no conflict of interest.
Figure 1. Flow-chart of the reconstruction method used to obtain the accumulation function from experimental data.
Figure 2. (a) Three-dimensional visualization of the relation between the L-Curve (blue) and the different values of μ for a cross-plane Fuchs-Sondheimer suppression function at T = 300 K for
graphite simulations. (b) L-curve or xz projection of 3D curve, the maximum curvature is displayed as heat-like color bar.
Figure 3.
) Phonon mean free path distribution of the accumulation function reconstructed for different values of
(0.1–10) using the FS cross-plane suppression function and the simulated κ made by Wei et al. [
]. The black-dashed and black-dotted lines represent reconstructions obtained by using an optimum (0.95) and large (4.0)
-value, respectively. The cyan solid and grey dotted line represent the MFP reconstruction obtained by Zhang et al. [
] and Wei et al. [
] (
) Thermal conductivity normalized to the bulk value and/or
product as function of graphite thickness. The open dots represent the simulated thermal conductivity (“experimental data”). Heat-like lines correspond to different
-values in a range of 0.1 <
< 10.
Figure 4.
) Phonon mean free path distribution of the accumulation function for a 400 nm Si film reconstructed for
(green line). The blue and red lines are the result obtained using a low and high value of
, respectively. (
) Thermal conductivity of 400 nm Si film corresponding to the different accumulation functions (red, green, and blue lines) for different transient grating periods in the experimental technique [
Figure 5. Three-dimensional visualization of the relation between the L-Curve (blue) and the different values of μ for an in-plane Fuchs-Sondheimer suppression function at T = 300 K for silicon
Figure 6.
) Phonon mean free path distribution of bulk Silicon reconstructed from the thickness dependence of thermal conductivity. The dark green, red, dotted grey and dotted dark cyan lines represent
reconstructions for different
-values. The black stared and blue dotted lines represent the MFP reconstruction and molecular dynamic calculation performed by Cuffe et al. [
] and Henry et al. [
], respectively. The orange-solid dots represent the experimental phonon-MFP distribution of bulk silicon measured by Regner et al. [
]. (
) Thermal conductivity corresponding to the different accumulation functions for different samples with different thickness [
© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http:/
Share and Cite
MDPI and ACS Style
Sanchez-Martinez, M.-Á.; Alzina, F.; Oyarzo, J.; Sotomayor Torres, C.M.; Chavez-Angel, E. Impact of the Regularization Parameter in the Mean Free Path Reconstruction Method: Nanoscale Heat Transport
and Beyond. Nanomaterials 2019, 9, 414. https://doi.org/10.3390/nano9030414
AMA Style
Sanchez-Martinez M-Á, Alzina F, Oyarzo J, Sotomayor Torres CM, Chavez-Angel E. Impact of the Regularization Parameter in the Mean Free Path Reconstruction Method: Nanoscale Heat Transport and Beyond.
Nanomaterials. 2019; 9(3):414. https://doi.org/10.3390/nano9030414
Chicago/Turabian Style
Sanchez-Martinez, Miguel-Ángel, Francesc Alzina, Juan Oyarzo, Clivia M. Sotomayor Torres, and Emigdio Chavez-Angel. 2019. "Impact of the Regularization Parameter in the Mean Free Path Reconstruction
Method: Nanoscale Heat Transport and Beyond" Nanomaterials 9, no. 3: 414. https://doi.org/10.3390/nano9030414
Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details
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Weight Calculator Angle - Calculatorey
Weight Calculator Angle
Are you looking for a simple way to calculate the weight of an object based on its angle? Then you’ve come to the right place. Our weight calculator angle tool is designed to help you easily
determine the weight of an object by simply inputting the angle at which it is being held. Whether you’re a fitness enthusiast looking to track your progress or a construction worker needing to
ensure proper weight distribution, our tool is perfect for all your weight calculation needs.
Understanding Weight and Angle
Before we dive into how to use our weight calculator angle tool, it’s important to understand the concepts of weight and angle. Weight is the force exerted by an object due to gravity, and it is
typically measured in pounds or kilograms. On the other hand, an angle is the measure of rotation between two lines or planes, and it is usually measured in degrees. By combining these two concepts,
we can determine the weight of an object based on the angle at which it is being held.
How to Use the Weight Calculator Angle Tool
Using our weight calculator angle tool is quick and easy. Simply input the angle at which the object is being held, and the tool will automatically calculate the weight of the object for you. This
tool is perfect for a wide range of applications, from weightlifting to engineering, and everything in between. Whether you’re looking to track your progress in the gym or ensure proper weight
distribution in a construction project, our tool has got you covered.
Benefits of Using a Weight Calculator Angle Tool
There are several benefits to using a weight calculator angle tool. Firstly, it allows for quick and accurate weight calculations without the need for complex formulas or equations. This can save you
time and effort, especially when working with multiple objects or angles. Additionally, using a weight calculator angle tool can help prevent potential injuries or accidents by ensuring that weight
is distributed properly. This is essential in industries such as construction or manufacturing where safety is paramount.
Applications of Weight Calculator Angle Tool
Our weight calculator angle tool can be used in a variety of applications. For fitness enthusiasts, it can help track progress and set goals for weightlifting or other exercises. In the construction
industry, it can ensure proper weight distribution in building projects to prevent structural issues. Engineers can also benefit from using this tool to calculate the weight of materials or equipment
in various projects. The possibilities are endless with our versatile weight calculator angle tool.
In conclusion, our weight calculator angle tool is a valuable resource for anyone looking to easily calculate the weight of an object based on its angle. Whether you’re a fitness enthusiast,
construction worker, or engineer, our tool can help you make quick and accurate weight calculations. By understanding the concepts of weight and angle and using our tool effectively, you can ensure
proper weight distribution and safety in your projects. Try out our weight calculator angle tool today and see the difference it can make! | {"url":"https://calculatorey.com/weight-calculator-angle/","timestamp":"2024-11-08T04:36:38Z","content_type":"text/html","content_length":"77654","record_id":"<urn:uuid:dd9cb6b9-4dba-4fa9-baf1-f754b28d670b>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00876.warc.gz"} |
NCERT Solutions for Chapter 9 Some Applications of Trigonometry Class 10 Maths
NCERT Solution for Class 10 Mathematics Chapter 9 Some Applications of Trigonometry
│Chapter Name │NCERT Solution for Class 10 Maths Chapter 9 Some Applications of Trigonometry │
│Topics Covered│ • Short Revision for the Chapter │
│ │ • NCERT Exercise Solution │
│ │ • NCERT Solution for Class 10 Maths │
│ │ • NCERT Revision Notes for Class 10 Maths │
│Related Study │ • Important Questions for Class 10 Maths │
│ │ • MCQ for Class 10 Maths │
│ │ • NCERT Exemplar Questions For Class 10 Maths │
Short Revision for Some Applications of Trigonometry
1. The height of an object and the distance between two distinct objects can be determined by using the trigonometric ratios.
2. The line of sight is the line drawn from the eye of an observer to the point in the object.
3. The angle of elevation is the angle formed by the line of sight with the horizontal when the object is above the horizontal level.
4. The angle of depression is the angle formed by the line of sight with the horizontal when the object is below the horizontal level.
NCERT Exercise Solutions
Exercise 9.1
1. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the
ground level is 30°. (see fig. 9.11)
Let height of the pole AB = x m
Length of the rope AC = 20 m
In △ABC, ∠ACB = 30°
∴ sin 30° = AB/AC ⇒ 1/2 = x/20 ⇒ x = 10 m
∴ Height of the pole = 10 m.
2. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the
top touches the ground is 8 m. Find the height of the tree.
Let the height of tree before storm be AB. Due to storm it breaks from C such that its top A touches the ground at D and makes an angle of 30° .
3. A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is
inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of
the slide in each case?
4. The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
Let AB be the tower and C be a point on the ground such that BC = 30 m. Also let AB = x m.
The angle of elevation of the top A from C is 30° .
So, in right - angled △ABC,
5. A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the
length of the string, assuming that there is no slack in the string.
6. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building.
Find the distance he walked towards the building.
Let a 1.5 m tall boy DP finds the angle of elevation to the top A of the building A.
Let DCB be the horizontal eye sight. When that boy walks towards the building finds increased angle of 60° at C.
7. From a point on the ground, the angles of elevation of the bottom and the top of a
transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
8. A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top
of the pedestal is 45°. Find the height of the pedestal.
9. The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m
high, find the height of the building.
10. Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles
are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.
11. A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away
from this point on the line joing this point to the foot of the tower, the angle of elevation of the top of the tower is 30° (see Fig. 9.12). Find the height of the tower and the width of the canal.
12. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
In the figure, AB represents a 7 m high building and PQ represents a cable tower. Angle of elevation to the top P from A is 60° and angle of depression to the bottom Q from same point A is 45°.
13. As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the
lighthouse, find the distance between the two ships.
In the figure, AB represents a 75 m high lighthouse, C and D are the positions of two ships where angles of depression from top of the tower are 45° and 30° respectively.
Let BC = x m and BD = y m.
We have to find the distance between the to ships,
i.e., CD = BD - BC = y - x
14. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant
is 60°. After some time, the angle of elevation reduces to 30° (see Fig. 9.13). Find the distance travelled by the balloon during the interval.
When the horizontally moving balloon is at P, a girl AB (say) finds ∠PAC is 60° and at the position R, ∠RAD is 30° .
We have to find the distance travelled in horizontal line, i.e., PR of CD.
Consider PC = PQ - CQ = (88.2 - 1.2)m = 87 m = RD
15. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform
speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.
Let AB be the tower on the top of which a man is standing and finds angle of depression to the position D of the running car as 30° .
After 6 seconds, angle is found 60° at C.
Let AB = h m, DC = x m and BC = y m.
16. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the
height of the tower is 6 m.
In the drawn figure, AB represents a tower, C and D are two points distant 4 m and 9 m away from the base B.
Let angle of elevation to the top A from C is α and from D is 90° - α . | {"url":"https://www.icserankers.com/2021/11/ncert-solutions-for-chapter9-some-applications-of-trigonometry-class10-maths.html","timestamp":"2024-11-07T20:16:59Z","content_type":"application/xhtml+xml","content_length":"311592","record_id":"<urn:uuid:c46a73f6-1707-4b36-9cb2-1a3284156df4>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00434.warc.gz"} |
Class 11 Maths Chapter 2 Relations and Functions MCQ - Sanfoundry
Class 11 Maths MCQ – Relations and Functions
This set of Class 11 Maths Chapter 2 Multiple Choice Questions & Answers (MCQs) focuses on “Relations and Functions”. These MCQs are created based on the latest CBSE syllabus and the NCERT
curriculum, offering valuable assistance for exam preparation.
1. A relation is a subset of cartesian products.
a) True
b) False
View Answer
Answer: a
Explanation: A relation from a non-empty set A to a non-empty set B is a subset of cartesian product A X B. First element is called the preimage of second and second element is called image of first.
2. Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find the domain.
a) {1,2,3,4,5}
b) {2,3,4,5}
c) {1,2,3,4}
d) {1,2,3,4,5,6}
View Answer
Answer: a
Explanation: We know, domain of a relation is the set from which relation is defined i.e. set A.
So, domain = {1,2,3,4,5}.
3. Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find the codomain.
a) {1,2,3,4,5}
b) {2,3,4,5}
c) {1,2,3,4}
d) {1,2,3,4,5,6}
View Answer
Answer: a
Explanation: We know, codomain of a relation is the set to which relation is defined i.e. set A.
So, codomain = {1,2,3,4,5}.
4. Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find the range.
a) {1,2,3,4,5}
b) {2,3,4,5}
c) {1,2,3,4}
d) {1,2,3,4,5,6}
View Answer
Answer: b
Explanation: Range is the set of elements of codomain which have their preimage in domain.
Relation R = {(1,2), (2,3), (3,4), (4,5)}.
Range = {2,3,4,5}.
5. If set A has 2 elements and set B has 4 elements then how many relations are possible?
a) 32
b) 128
c) 256
d) 64
View Answer
Answer: c
Explanation: We know, A X B has 2*4 i.e. 8 elements. Number of subsets of A X B is 2^8 i.e. 256.
A relation is a subset of cartesian product so, number of possible relations are 256.
6. Is relation from set A to set B is always equal to relation from set B to set A.
a) True
b) False
View Answer
Answer: b
Explanation: A relation from a non-empty set A to a non-empty set B is a subset of cartesian product A X B. A relation from a non-empty set B to a non-empty set A is a subset of cartesian product B X
Since A X B ≠ B X A so, both relations are not equal.
7. If A={1,4,8,9} and B={1, 2, -1, -2, -3, 3,5} and R is a relation from set A to set B {(x, y): x=y^2}. Find domain of the relation.
a) {1,4,9}
b) {-1,1, -2,2, -3,3}
c) {1,4,8,9}
d) {-1,1, -2,2, -3,3,5}
View Answer
Answer: c
Explanation: We know, domain of a relation is the set from which relation is defined i.e. set A.
So, domain = {1,4,8,9}.
8. If A={1,4,8,9} and B={1, 2, -1, -2, -3, 3,5} and R is a relation from set A to set B {(x, y): x=y^2}. Find codomain of the relation.
a) {1,4,9}
b) {-1,1, -2,2, -3,3}
c) {1,4,8,9}
d) {-1,1, -2,2, -3,3,5}
View Answer
Answer: d
Explanation: We know, codomain of a relation is the set to which relation is defined i.e. set B.
So, codomain = {-1,1, -2,2, -3,3,5}.
9. If A={1,4,8,9} and B={1, 2, -1, -2, -3, 3,5} and R is a relation from set A to set B {(x, y): x=y^2}. Find range of the relation.
a) {1,4,9}
b) {-1,1, -2,2, -3,3}
c) {1,4,8,9}
d) {-1,1, -2,2, -3,3,5}
View Answer
Answer: b
Explanation: Range is the set of elements of codomain which have their preimage in domain.
Relation R = {(1,1), (1, -1), (4,2), (4, -2), (9,3), (9, -3)}.
Range = {-1,1, -2,2, -3,3}.
10. Let A={1,2} and B={3,4}. Which of the following cannot be relation from set A to set B?
a) {(1,1), (1,2), (1,3), (1,4)}
b) {(1,3), (1,4)}
c) {(2,3), (2,4)}
d) {(1,3), (1,4), (2,3), (2,4)}
View Answer
Answer: a
Explanation: A relation from set A to set B is a subset of cartesian product of A X B. In ordered pair, first element should belong to set A and second element should belongs to set B.
In {(1,1), (1,2), (1,3), (1,4)}, 1 and 2 should also be in the set B which is not so as given in question.
Hence, {(1,1), (1,2), (1,3), (1,4)} is not a relation from set A to set B.
More MCQs on Class 11 Maths Chapter 2:
To practice all chapters and topics of class 11 Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers. | {"url":"https://www.sanfoundry.com/mathematics-questions-answers-relations/","timestamp":"2024-11-14T12:34:40Z","content_type":"text/html","content_length":"147466","record_id":"<urn:uuid:a1f0d85b-821d-4b56-8cfc-abbbe7cfe03f>","cc-path":"CC-MAIN-2024-46/segments/1730477028558.0/warc/CC-MAIN-20241114094851-20241114124851-00055.warc.gz"} |
Implementation of a simplified approach to radiative transfer in general relativity
We describe in detail the implementation of a simplified approach to radiative transfer in general relativity by means of the well-known neutrino leakage scheme (NLS). In particular, we carry out an
extensive investigation of the properties and limitations of the NLS for isolated relativistic stars to a level of detail that has not been discussed before in a general-relativistic context.
Although the numerous tests considered here are rather idealized, they provide a well-controlled environment in which to understand the relationship between the matter dynamics and the neutrino
emission, which is important in order to model the neutrino signals from more complicated scenarios, such as binary neutron-star mergers. When considering nonrotating hot neutron stars we confirm
earlier results of one-dimensional simulations, but also present novel results about the equilibrium properties and on how the cooling affects the stability of these configurations. In our idealized
but controlled setup, we can then show that deviations from the thermal and weak-interaction equilibrium affect the stability of these models to radial perturbations, leading models that are stable
in the absence of radiative losses, to a gravitational collapse to a black hole when neutrinos are instead radiated.
Physical Review D
Pub Date:
September 2013
□ 04.25.D-;
□ 95.30.Jx;
□ 97.60.Jd;
□ 26.60.-c;
□ Numerical relativity;
□ Radiative transfer;
□ scattering;
□ Neutron stars;
□ Nuclear matter aspects of neutron stars;
□ General Relativity and Quantum Cosmology;
□ Astrophysics - High Energy Astrophysical Phenomena
32 pages, 16 figures, updated to version published on PRD. Corrected an error in table II | {"url":"https://ui.adsabs.harvard.edu/abs/2013PhRvD..88f4009G/abstract","timestamp":"2024-11-10T15:19:53Z","content_type":"text/html","content_length":"41941","record_id":"<urn:uuid:714a4493-951f-4713-91fa-abff9a20a68f>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.60/warc/CC-MAIN-20241110134821-20241110164821-00225.warc.gz"} |
MACD in T-SQL - Tomas Lind
MACD in T-SQL
The MACD (Moving Average Converenge Divergence) is a calculation in technical analysis used as a indicator of strength in a trend, or momentum in a stocks closing prices. The calculation uses
different lengths of EMA (I covered the calculation of EMA in an earlier blog post here).
The MACD calculation uses the difference between a long EMA and a short EMA to create a oscillator (usually EMA12 – EMA26). The term Moving Average Converenge Divergence comes from the converging and
divergence of these two moving averages. When the two moves towards each other there is convergence, and when they move away from each other, there is divergence. A divergence is commonly interpreted
as a sign that the current trend is ending.
The MACD also moves around a zero line and when the MACD is above the zero line, that is used as a indicator of upward momentum (higher closing prices) since the short term EMA is above the long term
EMA. And of course, if MACD is below the zero line this is an indicator of downward momentum.
Image by Kevin Ryde. Green line is MACD, red line is EMA9 of MACD.
White histogram is the difference between the two.
Further, a EMA9 is calculated for the MACD. This line is called the “Signal line”. The signal line is used in a trigger for buy and sell signals. More specifically, traders look for crossovers of the
two lines. When the MACD moves over the MACD:EMA9, this is a buy signal since it indicates a upward momentum (a bullish market) of the closing prices. And when the MACD crosses under the MACD:EMA9,
this is a sell signal since this is a indicator of downward momentum (bearish market).
This blog post will show how to calculate MACD in T-SQL. It works on all versions of SQL Server.
The examples use the database TAdb. A script to create TAdb can be found here.
Using a extended version of the EMA calculation, the T-SQL below calculates EMA12, EMA26 and MACD:
IF OBJECT_ID('tempdb..#TBL_EMA_LOOP') IS NOT NULL BEGIN
DROP TABLE #TBL_EMA_LOOP
SELECT *, CAST(NULL AS FLOAT) AS EMA12, CAST(NULL AS FLOAT) AS EMA26 INTO #TBL_EMA_LOOP FROM dbo.Quotes
CREATE UNIQUE CLUSTERED INDEX EMA_IDX ON #TBL_EMA_LOOP (StockId, QuoteId)
DECLARE @StockId INT = 1, @QuoteId INT, @QuoteIdMax INT, @StartAvgEMA12 FLOAT, @StartAvgEMA26 FLOAT, @C_EMA12 FLOAT = 2.0 / (1 + 12), @C_EMA26 FLOAT = 2.0 / (1 + 26), @EMA12 FLOAT, @EMA26 FLOAT
WHILE @StockId <= 2 BEGIN
SELECT @QuoteId = 1, @QuoteIdMax = MAX(QuoteId) FROM dbo.Quotes WHERE StockId = @StockId
SELECT @StartAvgEMA12 = AVG(QuoteClose) FROM dbo.Quotes WHERE StockId = @StockId AND QuoteId <= 12
SELECT @StartAvgEMA26 = AVG(QuoteClose) FROM dbo.Quotes WHERE StockId = @StockId AND QuoteId <= 26
WHILE @QuoteId <= @QuoteIdMax BEGIN
EMA12 =
WHEN @QuoteId = 12 THEN @StartAvgEMA12
WHEN @QuoteId > 12 THEN (T0.QuoteClose * @C_EMA12) + T1.EMA12 * (1.0 - @C_EMA12)
,EMA26 =
WHEN @QuoteId = 26 THEN @StartAvgEMA26
WHEN @QuoteId > 26 THEN (T0.QuoteClose * @C_EMA26) + T1.EMA26 * (1.0 - @C_EMA26)
#TBL_EMA_LOOP T0
#TBL_EMA_LOOP T1
T0.StockId = T1.StockId
T0.QuoteId - 1 = T1.QuoteId
T0.StockId = @StockId
T0.QuoteId = @QuoteId
SELECT @QuoteId = @QuoteId + 1
SELECT @StockId = @StockId + 1
,CAST(EMA12 AS NUMERIC(10,2)) AS EMA12
,CAST(EMA26 AS NUMERIC(10,2)) AS EMA26
,CAST(EMA12 - EMA26 AS NUMERIC(10,2)) AS MACD
A sample of the results look like this:
MACD Results
In this example, following the theory stated above, the stock is in a negative momentum (bearish market) up until 2010-03-03 when a crossover occurs and the stock enters a positive momentum (bullish
market). And indeed, the stock price rises between 2010-03-03 and 2010-03-29. (If you do the query yourself you will see that the positive momentum lasts up until 2010-05-20 ending at a closing price
of 31.78.)
[blue_box]This blog post is part of a serie about technical analysis, TA, in SQL Server. See the other posts here.[/blue_box]
This Post Has 11 Comments
1. At the moment I can only complemeny you and you work. Genius!!!
I tested your calculation….it’s perfect. Your amazing. I’ve been searching for 3 days now. I must repeat. GENIUS.
1. Thanks, glad to hear it is working!
3. Hey – just wanted to say thank you for keeping this up and up to date with sql server 2012 — personally i am working on 2008 so i REALY appreciate the nod at older RDBMS’
using this and a few others I can figure out how to implement the other technical indicators I need to write.
Thank you and please keep this archive alive
1. Thanks, Felix!
4. Hi ..
i’m trying to find stochastic(%K,%D) script
can you help me ?
Thanks in advance
1. Hi, I haven’t done that calculation in T-SQL. Can’t remember seeing it anywhere either…
2. Hi Shahram, this seems to work for calculating a 14 day Stochastic with 3 day and 5 day moving averages:
Calculate Stochastic Oscillator
%K = (Current Close – Lowest Low)/(Highest High – Lowest Low) * 100
%D = 3-day SMA of %K
Lowest Low = lowest low for the look-back period
Highest High = highest high for the look-back period
%K is multiplied by 100 to move the decimal point two places
Fast Stochastic Oscillator:
– Fast %K = %K basic calculation
– Fast %D = 3-period SMA of Fast %K
Slow Stochastic Oscillator:
– Slow %K = Fast %K smoothed with 3-period SMA
– Slow %D = 3-period SMA of Slow %K
USE StockMarket
IF OBJECT_ID(‘StockMarket.dbo.usp_CalculateStochastic’) IS NOT NULL BEGIN
DROP PROCEDURE dbo.usp_CalculateStochastic
CREATE PROCEDURE dbo.usp_CalculateStochastic
SET NOCOUNT ON
SET ANSI_WARNINGS OFF
IF OBJECT_ID(‘tempdb..#Stoch’) IS NOT NULL BEGIN
DROP TABLE #Stoch
/* Create Temp Table */
SELECT *,
CAST(NULL AS FLOAT) AS HighestHigh14,
CAST(NULL AS FLOAT) AS LowestLow14,
CAST(NULL AS FLOAT) AS StochFast14,
CAST(NULL AS FLOAT) AS SMAFast3,
CAST(NULL AS FLOAT) AS SMAFast5,
CAST(NULL AS FLOAT) AS StochSlow14,
CAST(NULL AS FLOAT) AS SMASlow3,
CAST(NULL AS FLOAT) AS SMASlow5
INTO #Stoch
FROM StockMarket.dbo.HistoricalStockPrices
WHERE MarketDate >= ( GetDate() – 380 )
CREATE UNIQUE CLUSTERED INDEX Stoch_IDX ON #Stoch (Ticker, MarketDate)
DECLARE @Ticker VARCHAR(5),
@MarketDate DateTime,
@MarketDateMin DateTime,
@MarketDateMax DateTime,
@HighestHigh14 FLOAT,
@LowestLow14 FLOAT
/* Set first ticker */
SELECT @Ticker = ( SELECT TOP 1 Ticker
FROM #Stoch h
ORDER BY h.Ticker )
WHILE @Ticker <= 'ZX'
SELECT @MarketDate = MIN(MarketDate),
@MarketDateMin = MIN(MarketDate),
@MarketDateMax = MAX(MarketDate)
FROM #Stoch
WHERE Ticker = @Ticker
WHILE @MarketDate <= @MarketDateMax
/* Get Highest Highs and Lowest Lows */
SELECT @HighestHigh14 = Max(HighPrice),
@LowestLow14 = MIN(LowPrice)
FROM ( SELECT TOP 14
FROM #Stoch
WHERE Ticker = @Ticker
AND MarketDate <= @MarketDate
ORDER BY MarketDate DESC ) vt
/* Need to update Stoch Fast 14 first as other other calculations are dependend upon it */
UPDATE s
SET HighestHigh14 = @HighestHigh14,
LowestLow14 = @LowestLow14,
/* (Current Close – Lowest Low)/(Highest High – Lowest Low) * 100 */
StochFast14 = CASE WHEN ( @HighestHigh14 – @LowestLow14 ) = 0
THEN ( ( s.ClosePrice – @LowestLow14 ) / ( .01 ) ) * 100 /* Setting to .01 cent to avoid divide by zero error */
ELSE ( ( s.ClosePrice – @LowestLow14 ) / ( @HighestHigh14 – @LowestLow14 ) ) * 100 END
FROM #Stoch s
WHERE s.Ticker = @Ticker
AND s.MarketDate = @MarketDate
/* Update values based on Stoch Fast 14 */
UPDATE s
SET /* 3-period SMA of Fast Stoch */
SMAFast3 = (SELECT Avg(StochFast14)
FROM ( SELECT TOP 3
FROM #Stoch
WHERE Ticker = @Ticker
AND MarketDate <= @MarketDate
ORDER BY MarketDate DESC ) vt ),
/* 5-period SMA of Fast Stoch */
SMAFast5 = (SELECT Avg(StochFast14)
FROM ( SELECT TOP 5
FROM #Stoch
WHERE Ticker = @Ticker
AND MarketDate <= @MarketDate
ORDER BY MarketDate DESC ) vt ),
/* Fast Stoch smoothed with 3-period SMA */
StochSlow14 = ( SELECT Avg(StochFast14)
FROM ( SELECT TOP 3
FROM #Stoch
WHERE Ticker = @Ticker
AND MarketDate <= @MarketDate
ORDER BY MarketDate DESC ) vt )
FROM #Stoch s
WHERE s.Ticker = @Ticker
AND s.MarketDate = @MarketDate
/* Update values based on Stoch Slow 14 */
UPDATE s
SET /* 3-period SMA of Slow Stoch */
SMASlow3 = (SELECT Avg(StochSlow14)
FROM ( SELECT TOP 3
FROM #Stoch
WHERE Ticker = @Ticker
AND MarketDate <= @MarketDate
ORDER BY MarketDate DESC ) vt ),
/* 5-period SMA of Slow Stoch */
SMASlow5 = (SELECT Avg(StochSlow14)
FROM ( SELECT TOP 5
FROM #Stoch
WHERE Ticker = @Ticker
AND MarketDate @MarketDate
ORDER BY h.MarketDate )
SELECT @Ticker = ( SELECT TOP 1 Ticker
FROM #Stoch h
WHERE h.Ticker > @Ticker
ORDER BY h.Ticker )
/* Truncate Stochastic Table */
TRUNCATE TABLE StockMarket.dbo.Stochastic
/* Populate Stochastic Table */
INSERT INTO StockMarket.dbo.Stochastic
SELECT Ticker
,CAST(HighestHigh14 AS NUMERIC(10,2)) AS HighestHigh14
,CAST(LowestLow14 AS NUMERIC(10,2)) AS LowestLow14
,CAST(StochFast14 AS NUMERIC(10,2)) AS StochFast14
,CAST(SMAFast3 AS NUMERIC(10,2)) AS SMAFast3
,CAST(SMAFast5 AS NUMERIC(10,2)) AS SMAFast5
,CAST(StochSlow14 AS NUMERIC(10,2)) AS StochSlow14
,CAST(SMASlow3 AS NUMERIC(10,2)) AS SMASlow3
,CAST(SMASlow5 AS NUMERIC(10,2)) AS SMASlow5
FROM #Stoch
ORDER BY Ticker, MarketDate
5. These scripts are great, thank you for your efforts! Have you ever implemented one for SAR?
6. Thanks you are amazing, Is it possible to find divergence in MACD ?
7. Hello
i want to calculate MACD FOR ALL SYMBOL
CAN U HELP ME
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Design elements - Logic gate diagram | Design elements - Logical network diagram | Computer Network Diagrams | Element Of Logic Symbol Diagram
The vector stencils library "Logic gate diagram" contains 17 element symbols for drawing the logic gate diagrams.
"To build a functionally complete logic system, relays, valves (vacuum tubes), or transistors can be used. The simplest family of logic gates using bipolar transistors is called resistor-transistor
logic (RTL). Unlike simple diode logic gates (which do not have a gain element), RTL gates can be cascaded indefinitely to produce more complex logic functions. RTL gates were used in early
integrated circuits. For higher speed and better density, the resistors used in RTL were replaced by diodes resulting in diode-transistor logic (DTL). Transistor-transistor logic (TTL) then
supplanted DTL. As integrated circuits became more complex, bipolar transistors were replaced with smaller field-effect transistors (MOSFETs); see PMOS and NMOS. To reduce power consumption still
further, most contemporary chip implementations of digital systems now use CMOS logic. CMOS uses complementary (both n-channel and p-channel) MOSFET devices to achieve a high speed with low power
dissipation." [Logic gate. Wikipedia]
The symbols example "Design elements - Logic gate diagram" was drawn using the ConceptDraw PRO diagramming and vector drawing software extended with the Electrical Engineering solution from the
Engineering area of ConceptDraw Solution Park.
The vector stencils library "Logical network diagram" contains 16 icon symbols.
Use these shapes for drawing logical computer network topology diagrams using the ConceptDraw PRO diagramming and vector drawing software.
The clipart example "Design elements - Logical network diagram" is included in the Computer and Networks solution from the Computer and Networks area of ConceptDraw Solution Park. | {"url":"https://www.conceptdraw.com/examples/element-of-logic-symbol-diagram","timestamp":"2024-11-09T03:09:09Z","content_type":"text/html","content_length":"34645","record_id":"<urn:uuid:779747db-a325-4e9a-bb16-4ec3452177d2>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00323.warc.gz"} |
Starting This Early Can Make You Filthy RichStarting This Early Can Make You Filthy Rich
Starting This Early Can Make You Filthy Rich
|Last Updated on November 18, 2019
“If you could only give one piece of financial advice to a person, what advice would you give them?”
I get asked this question a lot, and it’s a pretty easy answer for me. I always say, spend less than you earn. Ask that exact question to any personal finance expert and I bet that 9 times out of 10,
they answer the same way.
However, I always want to talk about the second best piece of advice too because I feel that it goes hand and hand with the advice I just mentioned. That advice would be to learn about compound
If you learn about compound interest, I can guarantee that it will encourage you to stockpile that money you are saving from living on less than you earn.
The Basics
Essentially, there are two types of interest: simple interest and compound interest.
With simple interest, you will only earn interest on your initial principal deposit. For example, if you deposit $1,000 in the bank and it earns 5%, you will earn $50 in the first year. In the second
year, you are still only earning interest on the initial deposit of $1,000. So, assuming that the interest rate is still 5%, you will earn another $50. If you kept the same $1,000 deposit in the
account for 10 years, you would have a total of $1,500 in the bank (10 years of $50 interest payments + the initial $1,000 deposit).
Compound interest is another beast all together. With compound interest, you will not only earn interest on your initial principal deposit but also on any interest that is credited to the account.
Using the same example above, if you deposit $1,000 in the bank and it earns 5%, you will earn $50 in interest, in the first year. However in the second year, not only will you earn interest on the
principal, you will also begin earning interest on the interest in the account. So, in year 2 the 5% interest will be credited against the full $1,050 you have in the account and your total interest
for year 2 would be $52.50. Pretty sweet!
If you kept the same $1,000 deposit in the account for 10 years, you would have a total of $1,628.89. That is an increase in $128.89 from the simple interest calculation. You may be saying to
yourself, “so what Adam, it’s a measly $128.89 over 10 years”. Well you’re right, it is. However, when you look at compound interest over 20 or 30 years and with more money, it becomes apparent that
it’s a miraculous thing.
Timing Is Everything
As I mentioned above, the longer you are able to let compound interest work in your favor, the better. Since the definition of compound interest is the ability to “earn interest on interest”, the
additional interest adds up immensely over time.
Once again, let’s explore the example used previously. Let’s say that you are wise enough to deposit $1,000 in the bank on your 18th birthday and you miraculously earn an average of 5% annually on
the account (I know what is pretty high in these times, but humor me). Let’s also say that over the years, you do not add any additional money to the account and just let it sit. We could even say
you forgot about it. By the time you reach age 65, the account will have $7,761.59 in it! The next years interest will be $388.08. That’s a hefty increase from the original $50 in interest you
received in the first year. And to think, you didn’t even add another penny to the account! Like I said above, the longer you let compound interest work in your favor, the better. I have created this
graph to illustrate that phenomenon.
As you can see from the graph, as the interest begins to accrue in the later years, the account value increases faster every year (hence the sharper incline in the later years). What I’m essentially
trying to say is, if you save early on in your life, you won’t have to save as much later.
Saving Early = Saving Less
So, you now have a pretty good idea of how compound interest works. So, I would like to show you how essential it is to save early on in your life.
In this example, I want to introduce you to Responsible Rachel and Procrastinating Pete. They are two completely different people financially and are both 22. Responsible Rachel understands the
concept of compound interest and really wants to take advantage of it. She lives on less than she earns and saves the rest. Procrastinating Pete, on the other hand, really wants to enjoy his new
income out of college. He spends everything that he makes (and then some). He doesn’t save a penny.
Since Responsible Rachel is so well, responsible, she is able to put $5,000 per year into a Roth IRA (we’ll talk about these is a future post). Let’s also assume that she invests it into a growth
mutual fund that averages about an 8% annual return. She does this every year until she reaches 32 when she just decides to stop. In those 10 years, she will contribute a total of $50,000.
After 10 years of messing around, Procrastinating Pete realizes that Social Security isn’t going to be there when he retires. He decides to start contributing to a Roth IRA as well. He too
contributes $5,000 a year and invests in the same mutual fund that averages 8% per year. However, he feels that since he got a late start, he would continue to contribute the $5,000 per year until he
retires at age 65. Here is a visual of our two savers at age 31 (Rachel’s last contribution and the year before Pete’s first):
As you can see, Responsible Rachel already has approximately $78,227.44 in the account before Procrastinating Pete even puts in a dime. However, in the back of your mind you are more than likely
thinking that even though Procrastinating Pete got a late start, Responsible Rachel stopped contributing all together, and there is no way that she will have more at age 65 than Procrastinating Pete
because he is still socking away $5,000 a year.
Well, if you are thinking that, you’re wrong. Check out this chart to see what I mean:
At age 65, Responsible Rachel will have a whooping $1,070,944.07 in her account while Procrastinating Pete will only have $856,584.02. That’s a difference of $214,360.05!
You also have to take into account the fact that Procrastinating Pete contributed $120,000 MORE (of principal) into his account than Responsible Rachel did into hers. So, he has $214,360.05 less in
his account while contributing $120,000 more. Crazy!
The main thing that I want to hammer home is that the sooner you get started, the more opportunity you have for compound interest to work in your favor.
Be more like Responsible Rachel, and not like Procrastinating Pete. | {"url":"https://adamhagerman.com/compound-interest-calculation/","timestamp":"2024-11-08T17:15:05Z","content_type":"text/html","content_length":"70773","record_id":"<urn:uuid:97b69999-6a28-4694-9b79-6f6f22586d7c>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00029.warc.gz"} |
Maths Shortcut Tricks for Competitive Exam PDF - SSC STUDY
Maths Shortcut Tricks for Competitive Exam PDF
Maths Shortcut Tricks PDF for Competitive Exam for free download. Quick Maths Tricks in English (Maths Fundas) useful for SSC CGL, CHSL, CPO, IBPS Bank, RRB, UPSSSC PET and Govt jobs examinations.
Why Maths Shortcut Tricks are required ?
In all competitive exams, the candidate has to attempt question with in specified time limit. In most of the exam questions are MCQ type and correct answer from the given option to be selected. To
attempt and solve the questions with speed and accuracy, Quick Math Funda and short tricks are required. One have to master the tricks to crack the competitive exam.
Contents of Maths Shortcut Tricks PDF
The Shortcut tricks of following Maths topics are given in PDF Book.
Laws of Indices
Last digit of a”
HCF and LCM
Factor Theory
Divisibility Rules
Algebraic Formula
Remainder / Modular Arithmetic
Profit & Loss
Mixtures & Allegation
Ratio & Proportion
Time Speed & Distance
Raced & Clocks
Time & Work
Quadratic and Other Equations
Lines and Angles
Solid Figures
Co-ordinate Geometry
Set Fundamentals
Binomial Theorem
Permutation & Combination
Sequence, Series & Progression
Maths Shortcut Tricks
1. Multiplying by 11: To multiply a two-digit number by 11, add the two digits together and place the result in the middle. For example, 11 x 13 = 143.
2. Squaring Numbers Ending in 5: To square a number ending in 5, take the number before 5, multiply it by the next consecutive number, and append 25 to the result. For example, 35^2 = (3 * 4) + 25 =
3. Percentage Calculations: To find 10% of a number, move the decimal point one place to the left. To find 1% of a number, move the decimal point two places to the left. For example, 10% of 250 = 25,
and 1% of 250 = 2.5.
4. Finding Fractions of Numbers: To find a fraction of a number, multiply the number by the numerator and then divide by the denominator. For example, 3/4 of 80 = (3 * 80) / 4 = 60.
5. Divisibility Rules: Learn divisibility rules for numbers like 2, 3, 4, 5, 6, 9, and 10. These rules can help you quickly determine if a number is divisible by another.
6. Multiplying by 9: To multiply a number by 9, multiply it by 10 and then subtract the original number. For example, 9 x 7 = (10 x 7) – 7 = 63.
7. Finding the Square of Any Number: To square any number, use the formula (a + b)^2 = a^2 + 2ab + b^2, where a is the tens digit and b is the units digit. For example, to square 47, use (40 + 7)^2 =
1600 + 560 + 49 = 2209.
8. Cross-Multiplication for Proportions: When solving proportions, you can use cross-multiplication to find the missing value. For example, if a/b = c/d, then ad = bc.
9. Finding Percent Increase or Decrease: To find the percentage increase or decrease between two numbers, use the formula ((New Value – Old Value) / Old Value) * 100%.
10. Prime Factorization: Break down numbers into their prime factors to simplify calculations involving factors and multiples.
Download Maths Shortcut Tricks PDF for Competitive Exam
Name : Math Fundas for Competitive Exams
Medium : English
Number of Pages : 64
Thanks for free download Maths Shortcut Tricks for Competitive Exams.
Disclaimer : We are not the owner of tis Math Tricks PDF. We share the google drive link of Maths Funds for the self study of students preparing for competitive exams.
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Maths Worksheets For Class 8 Rational Numbers Pdf
Maths Worksheets For Class 8 Rational Numbers Pdf work as fundamental devices in the realm of mathematics, supplying an organized yet versatile platform for learners to explore and master
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Unveiling the Essence of Maths Worksheets For Class 8 Rational Numbers Pdf
Maths Worksheets For Class 8 Rational Numbers Pdf
Maths Worksheets For Class 8 Rational Numbers Pdf -
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CBSE Class 8 Mathematics Worksheet Rational Numbers PDF
CBSE Class 8 Mathematics Worksheet Rational Numbers PDF
Grade 8 Rational Numbers Worksheets November 10 2020 by worksheetsbuddy do87uk Grade 8 Maths Rational Number Multiple Choice Questions MCQs 1 Associative property is not followed in a whole numbers b
integers c natural numbers d none of these 2 is the identity for the
Number line representation of rational numbers Comparison of rational numbers Operation like addition subtraction multiplication and division Now in class 8 we will study the recap of all operation
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From Theory to Real-World Application
NCERT Solutions Class 8 Maths Chapter 1 Rational Numbers Download Free PDFs
NCERT Solutions Class 8 Maths Chapter 1 Rational Numbers Download Free PDFs
Class Vill SUBJECT r MATHEMATICS WORKSHEET Rational Numbers SESSION 201 1 10 Q 2 Find three rational numbers between a 6 and and 25 26 QB If the product of two rational numbers is find the other and
one of them is 0 4 What number should be added to 42 to get 11
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RD Sharma Class 8 Solutions Chapter 1 Rational Numbers Ex 1 1 Exercise 1 1 Free PDF
CBSE Class 8 Mental Maths Rational Numbers Worksheet
Check more of Maths Worksheets For Class 8 Rational Numbers Pdf below
CBSE Class 8 Mathematics Rational Numbers Worksheet Set C
Grade 8 Rational Numbers Worksheets
Rational Numbers Class 8 Worksheet Class 8 Maths Rational Numbers Worksheet
Galaxy Coaching Classes Worksheet Class 8 Ch 1 Rational Numbers 8th Grade Math Worksheets
35 Rational Numbers Worksheet Grade 8 Support Worksheet
8th Grade Rational Numbers Class 8 Worksheet Kidsworksheetfun
Rational Numbers Class 8 Worksheet Free PDF Download
Mathematics Rational Numbers Worksheets for Class 8 We have provided chapter wise worksheets for class 8 Mathematics Rational Numbers which the students can download in Pdf format for free This is
the best collection of Mathematics Rational Numbers standard 8th worksheets with important questions and answers for
Rational Numbers Worksheet For Class 8 Byju s
Rational Numbers Worksheet for Class 8 1 Simplify 7 26 16 39 2 Subtract from 3 The sum of two rational numbers is if one of the numbers is 9 20 Find the other 4 What number should be subtracted from
3 7 to get 5 4 5 Find ten rational numbers between and 6 Multiply 7 11 by 5 4 7 Zero has reciprocal 8
Mathematics Rational Numbers Worksheets for Class 8 We have provided chapter wise worksheets for class 8 Mathematics Rational Numbers which the students can download in Pdf format for free This is
the best collection of Mathematics Rational Numbers standard 8th worksheets with important questions and answers for
Rational Numbers Worksheet for Class 8 1 Simplify 7 26 16 39 2 Subtract from 3 The sum of two rational numbers is if one of the numbers is 9 20 Find the other 4 What number should be subtracted from
3 7 to get 5 4 5 Find ten rational numbers between and 6 Multiply 7 11 by 5 4 7 Zero has reciprocal 8
Galaxy Coaching Classes Worksheet Class 8 Ch 1 Rational Numbers 8th Grade Math Worksheets
Grade 8 Rational Numbers Worksheets
35 Rational Numbers Worksheet Grade 8 Support Worksheet
8th Grade Rational Numbers Class 8 Worksheet Kidsworksheetfun
NCERT Solutions For Class 8 Maths Ch 1 Rational Numbers Download
Grade 8 Math Worksheets And Problems Rational Numbers Rational Numbers Number Worksheets
Grade 8 Math Worksheets And Problems Rational Numbers Rational Numbers Number Worksheets
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1.6: The Measurement of Matter
Last updated
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• Express quantities properly, using a number and a unit.
• State the different measurement systems used in chemistry.
• Express a large number or a small number in scientific notation.
• Learn how to use SI prefixes.
• Perform unit conversions using conversion factors.
A coffee maker’s instructions tell you to fill the coffeepot with 4 cups of water and use 3 scoops of coffee. When you follow these instructions, you are measuring. When you visit a doctor’s office,
a nurse checks your temperature, height, weight, and perhaps blood pressure (Figure \(\PageIndex{1}\)); the nurse is also measuring.
Figure \(\PageIndex{1}\): A nurse or a doctor measuring a patient’s blood pressure is taking a measurement. Figure used with permission (GFDL; Pia von Lützau).
Chemists measure the properties of matter and express these measurements as quantities. A quantity is an amount of something, and consists of a number and a unit. The number tells us how many (or how
much), and the unit tells us what the scale of measurement is. For example, when a distance is reported as “5 kilometers,” we know that the quantity has been expressed in units of kilometers and that
the number of kilometers is 5. If you ask a friend how far he or she walks from home to school, and the friend answers “12” without specifying a unit, you do not know whether your friend walks 12
miles, 12 kilometers, 12 furlongs, or 12 yards...etc. Both a number and a unit must be included to express a quantity properly.
To understand chemistry, we need a clear understanding of the units chemists work with and the rules they follow for expressing numbers. The next two sections examine the rules for expressing
All measurements depend on the use of units that are well known and understood. The English system of measurement units (inches, feet, ounces, etc.) are not used in science because of the difficulty
in converting from one unit to another. The metric system is used because all metric units are based on multiples of 10, making conversions very simple. The metric system was originally established
in France in 1795. The International System of Units is a system of measurement based on the metric system. The acronym SI is commonly used to refer to this system and stands for the French term, Le
Système International d'Unités. The SI was adopted by international agreement in 1960 and is composed of the seven base units shown in Table \(\PageIndex{1}\).
Table \(\PageIndex{1}\) SI Base Units of
Quantity SI Base Unit Symbol
Length meter \(\text{m}\)
Mass kilogram \(\text{kg}\)
Temperature kelvin \(\text{K}\)
Time second \(\text{s}\)
Amount of a Substance mole \(\text{mol}\)
Electric Current ampere \(\text{A}\)
Luminous Intensity candela \(\text{cd}\)
The first units are frequently encountered in chemistry. All other measurement quantities, such as volume, force, and energy, can be derived from these seven base units.
Exponential Numbers: Powers of Ten
Chemists often work with numbers that are exceedingly large or small. For example, entering the mass in grams of a hydrogen atom into a calculator would require a display with at least 24 decimal
places. A system called scientific notation avoids much of the tedium and awkwardness of manipulating numbers with large or small magnitudes. Furthermore, use of prefixes is another way to express
measurements involving large and small numbers.
Scientific Notation
In scientific notation, numbers are expressed in the form
\[ N \times 10^n \nonumber \]
where N is greater than or equal to 1 and less than 10 (1 ≤ N < 10), and n is a positive or negative integer (10^0 = 1). The number 10 is called the base because it is this number that is raised to
the power \(n\). Although a base number may have values other than 10, the base number in scientific notation is always 10.
A simple way to convert numbers to scientific notation is to move the decimal point as many places to the left or right as needed to give a number from 1 to 10 (N). The magnitude of n is then
determined as follows:
• If the decimal point is moved to the left n places, n is positive.
• If the decimal point is moved to the right n places, n is negative.
Another way to remember this is to recognize that as the number N decreases in magnitude, the exponent increases and vice versa. The application of this rule is illustrated in Example \(\PageIndex{1}
Convert each number to scientific notation.
1. 637.8
2. 0.0479
3. 12,378
4. 0.00032
Example \(\PageIndex{1}\) Solution and Explanation
Explanation Answer
To convert 637.8 to a number from 1 to 10, we move the decimal point two places to the left: 637.8
a \(6.378 \times 10^2\)
Because the decimal point was moved two places to the left, n = 2.
To convert 0.0479 to a number from 1 to 10, we move the decimal point two places to the right: 0.0479
b \(4.79 \times 10^{−2}\)
Because the decimal point was moved two places to the right, n = −2.
c Because the decimal point was moved four places to the left, n = 4. \(1.2378 \times 10^4\)
d Because the decimal point was moved four places to the right, n = −4. \(3.2 \times 10^{−4}\)
Convert each ordinary number to scientific notation, or vice versa.
1. 67,000,000,000
2. 1,689
3. 12.6
Answer a
6.7 × 10^10
Answer b
1.689 × 10^3
Answer c
1.26 × 10^1
Convert each ordinary number to scientific notation, or vice versa.
1. 0.000006567
2. 6.22 × 10^−2
3. 9.9 × 10^−9
Answer a
6.567 × 10^−6
Answer b
Answer c
Metric Prefixes
Conversions between metric system units are straightforward because the system is based on powers of ten. For example, meters, centimeters, and millimeters are all metric units of length. There are
10 millimeters in 1 centimeter and 100 centimeters in 1 meter. Metric prefixes are used to distinguish between units of different size. These prefixes all derive from either Latin or Greek terms. For
example, mega comes from the Greek word \(\mu \varepsilon \gamma \alpha \varsigma\), meaning "great". Table \(\PageIndex{2}\) lists the most common metric prefixes and their relationship to the
central unit that has no prefix. Length is used as an example to demonstrate the relative size of each prefixed unit.
Table \(\PageIndex{2}\) SI Prefixes
Prefix Unit Abbreviation Meaning Example
giga \(\text{G}\) 1,000,000,000 1 gigameter \(\left( \text{Gm} \right)=10^9 \: \text{m}\)
mega \(\text{M}\) 1,000,000 1 megameter \(\left( \text{Mm} \right)=10^6 \: \text{m}\)
kilo \(\text{k}\) 1,000 1 kilometer \(\left( \text{km} \right)=1,000 \: \text{m}\)
hecto \(\text{h}\) 100 1 hectometer \(\left( \text{hm} \right)=100 \: \text{m}\)
deka \(\text{da}\) 10 1 dekameter \(\left( \text{dam} \right)=10 \: \text{m}\)
1 1 meter \(\left( \text{m} \right)\)
deci \(\text{d}\) 1/10 1 decimeter \(\left( \text{dm} \right)=0.1 \: \text{m}\)
centi \(\text{c}\) 1/100 1 centimeter \(\left( \text{cm} \right)=0.01 \: \text{m}\)
milli \(\text{m}\) 1/1,000 1 millimeter \(\left( \text{mm} \right)=0.001 \: \text{m}\)
micro \(\mu\) 1/1,000,000 1 micrometer \(\left( \mu \text{m} \right)=10^{-6} \: \text{m}\)
nano \(\text{n}\) 1/1,000,000,000 1 nanometer \(\left( \text{nm} \right)=10^{-9} \: \text{m}\)
pico \(\text{p}\) 1/1,000,000,000,000 1 picometer \(\left( \text{pm} \right)=10^{-12} \: \text{m}\)
There are a couple of odd little practices with the use of metric abbreviations. Most abbreviations are lowercase. We use "\(\text{m}\)" for meter and not "\(\text{M}\)". However, when it comes to
volume, the base unit "liter" is abbreviated as "\(\text{L}\)" and not "\(\text{l}\)". So, 3.5 milliliters is written as \(3.5 \: \text{mL}\).
As a practical matter, whenever possible, you should express the units in a small and manageable number. If you are measuring the weight of a material that weighs \(6.5 \: \text{kg}\), this is easier
than saying it weighs \(6500 \: \text{g}\) or \(0.65 \: \text{dag}\). All three are correct, but the \(\text{kg}\) units in this case make for a small and easily managed number. However, if a
specific problem needs grams instead of kilograms, go with the grams for consistency.
Give the abbreviation for each unit and define the abbreviation in terms of the base unit.
1. kiloliter
2. microsecond
3. decimeter
4. nanogram
Example \(\PageIndex{2}\) Solution and Explanation
Explanation Answer
a The prefix kilo means “1,000 ×,” so 1 kL equals 1,000 L kL
b The prefix micro implies 1/1,000,000th of a unit, so 1 µs equals 0.000001 s. µs
c The prefix deci means 1/10th, so 1 dm equals 0.1 m. dm
d The prefix nano means 1/1000000000, so a nanogram is equal to 0.000000001 g ng
Give the abbreviation for each unit and define the abbreviation in terms of the base unit.
1. kilometer
2. milligram
3. nanosecond
4. centiliter
Answer a:
Answer b:
Answer c:
Answer d:
Mass and Weight
Mass is a measure of the amount of matter that an object contains. The mass of an object is made in comparison to the standard mass of 1 kilogram. The kilogram was originally defined as the mass of \
(1 \: \text{L}\) of liquid water at \(4^\text{o} \text{C}\) (volume of a liquid changes slightly with temperature). In the laboratory, mass is measured with a balance (see below), which must be
calibrated with a standard mass so that its measurements are accurate.
Figure \(\PageIndex{2}\) (From left to right:) Triple beam balance (source(opens in new window)), digital top-loading balance (source(opens in new window)), and an analytical balance (source).
Other common units of mass are the gram and the milligram. A gram is 1/1000th of a kilogram, meaning that there are \(1000 \: \text{g}\) in \(1 \: \text{kg}\). A milligram is 1/1000th of a gram, so
there are \(1000 \: \text{mg}\) in \(1 \: \text{g}\).
Mass is often confused with the term weight. Weight is a measure of force that is equal to the gravitational pull on an object. The weight of an object is dependent on its location. On the moon, the
force due to gravity is about one sixth that of the gravitational force on Earth. Therefore, a given object will weigh six times more on Earth than it does on the moon. Since mass is dependent only
on the amount of matter present in an object, mass does not change with location. Weight measurements are often made with a spring scale, by reading the distance that a certain object pulls down and
stretches a spring.
Length and Volume
Length is the measurement of the extent of something along its greatest dimension. The SI basic unit of length, or linear measure, is the meter \(\left( \text{m} \right)\). All measurements of length
may be made in meters, though the prefixes listed in various tables will often be more convenient. The width of a room may be expressed as about 5 meters \(\left( \text{m} \right)\), whereas a large
distance, such as the distance between New York City and Chicago, is better expressed as 1150 kilometers \(\left( \text{km} \right)\). Very small distances can be expressed in units such as the
millimeter or the micrometer. The width of a typical human hair is about 10 micrometers \(\left( \mu \text{m} \right)\).
Figure \(\PageIndex{3}\): Metric and English measuring devices. (CC BY-SA 4.0; Ejay)
Volume is the amount of space occupied by a sample of matter. The volume of a regular object can be calculated by multiplying its length by its width and its height. Since each of those is a linear
measurement, we say that units of volume are derived from units of length. The SI unit of volume is the cubic meter \(\left( \text{m}^3 \right)\), which is the volume occupied by a cube that measures
\(1 \: \text{m}\) on each side. This very large volume is not very convenient for typical use in a chemistry laboratory. A liter \(\left( \text{L} \right)\) is the volume of a cube that measures \(10
\: \text{cm}\) \(\left( 1 \: \text{dm} \right)\) on each side. A liter is thus equal to both \(1000 \: \text{cm}^3\) \(\left( 10 \: \text{cm} \times 10 \: \text{cm} \times 10 \: \text{cm} \right)\)
and to \(1 \: \text{dm}^3\).
1L = \(1000 \: \text{cm}^3\) \(\left( 10 \: \text{cm} \times 10 \: \text{cm} \times 10 \: \text{cm} \right)\) = \(1 \: \text{dm}^3\)
A smaller unit of volume that is commonly used is the milliliter (\(\text{mL}\)). A milliliter is the volume of a cube that measures \(1 \: \text{cm}\) on each side. Therefore, a milliliter is equal
to a cubic centimeter \(\left( \text{cm}^3 \right)\).
1 mL \(\left( \text{cm}^3 \right)\)
There are \(1000 \: \text{mL}\) in \(1 \: \text{L}\), which is the same as saying that there are \(1000 \: \text{cm}^3\) in \(1 \: \text{dm}^3\).
Figure \(\PageIndex{4}\) A typical water bottle is 1 liter in volume.
Figure \(\PageIndex{5}\) This Rubik's cube is \(5.7 \: \text{cm}\) on each side and has a volume of \(185.2 \: \text{cm}^3\) or \(185.2 \: \text{mL}\).
Figure \(\PageIndex{6}\): Buret & graduated cylinder: graduated glassware is used to deliver variable volumes of liquid. Pipette & volumetric flask: volumetric glassware is used to deliver (pipette)
or contain (volumetric flask) a single volume accurately when filled to the mark. (CC BY-SA-NC; anonymous).
During your studies of chemistry (and physics also), you will note that mathematical equations are used in many different applications. Many of these equations have a number of different variables
with which you will need to work. You should also note that these equations will often require you to use measurements with their units. Algebra skills become very important here!
Converting Between Units with Conversion Factors
A conversion factor is a factor used to convert one unit of measurement into another. A simple conversion factor can be used to convert meters into centimeters, or a more complex one can be used to
convert miles per hour into meters per second. Since most calculations require measurements to be in certain units, you will find many uses for conversion factors. Always remember that a conversion
factor has to represent a fact; this fact can either be simple or much more complex. For instance, you already know that 12 eggs equal one dozen. A more complex fact is that the speed of light is \
(1.86 \times 10^5\) miles/sec. Either one of these can be used as a conversion factor, depending on what type of calculation you might be working with (Table \(\PageIndex{1}\)).
Table \(\PageIndex{3}\) Conversion Factors from SI
units to English Units
English Units Metric Units Quantity
1 ounce (oz) 28.35 grams (g) *mass
1 fluid once (oz) 2.96 mL volume
2.205 pounds (lb) 1 kilogram (kg) *mass
1 inch (in) 2.54 centimeters (cm) length
0.6214 miles (mi) 1 kilometer (km) length
1 quarter (qt) 0.95 liters (L) volume
*Pounds and ounces are technically units of force, not mass, but this fact is often ignored by the non-scientific community.
Of course, there are other ratios which are not listed in Table \(\PageIndex{1}\). They may include:
• Ratios embedded in the text of the problem (using words such as per or in each, or using symbols such as / or %).
• Conversions in the metric system, as covered earlier in this chapter.
• Common knowledge ratios (such as 60 seconds \(=\) 1 minute).
If you learned the SI units and prefixes described, then you know that 1 cm is 1/100th of a meter.
\[ 1\; \rm{cm} = \dfrac{1}{100} \; \rm{m} = 10^{-2}\rm{m} \nonumber \]
\[100\; \rm{cm} = 1\; \rm{m} \nonumber \]
Suppose we divide both sides of the equation by \(1 \text{m}\) (both the number and the unit):
\[\mathrm{\dfrac{100\:cm}{1\:m}=\dfrac{1\:m}{1\:m}} \nonumber \]
As long as we perform the same operation on both sides of the equals sign, the expression remains an equality. Look at the right side of the equation; it now has the same quantity in the numerator
(the top) as it has in the denominator (the bottom). Any fraction that has the same quantity in the numerator and the denominator has a value of 1:
\[ \dfrac{ \text{100 cm}}{\text{1 m}} = \dfrac{ \text{1000 mm}}{\text{1 m}}= \dfrac{ 1\times 10^6 \mu \text{m}}{\text{1 m}}= 1 \nonumber \]
We know that 100 cm is 1 m, so we have the same quantity on the top and the bottom of our fraction, although it is expressed in different units.
Performing Dimensional Analysis
Dimensional analysis is amongst the most valuable tools used by physical scientists. Simply put, it is the conversion between an amount in one unit to the corresponding amount in a desired unit,
using various conversion factors. This is valuable because certain measurements are more accurate or easier to find than others. The use of units in a calculation to ensure that we obtain the final
proper units is called dimensional analysis.
Here is a simple example: How many centimeters are there in 3.55 m? Perhaps you can determine the answer in your head. If there are 100 cm in every meter, then 3.55 m equals 355 cm. To solve the
problem more formally with a conversion factor, we first write the quantity we are given, 3.55 m. Then we multiply this quantity by a conversion factor, which is the same as multiplying it by 1. We
can write 1 as \(\mathrm{\frac{100\:cm}{1\:m}}\) and multiply:
\[ 3.55 \; \rm{m} \times \dfrac{100 \; \rm{cm}}{1\; \rm{m}} \nonumber \]
The 3.55 m can be thought of as a fraction with a 1 in the denominator. Because m, the abbreviation for meters, occurs in both the numerator and the denominator of our expression, they cancel out:
\[\dfrac{3.55 \; \cancel{\rm{m}}}{ 1} \times \dfrac{100 \; \rm{cm}}{1 \; \cancel{\rm{m}}} \nonumber \]
The final step is to perform the calculation that remains once the units have been canceled:
\[ \dfrac{3.55}{1} \times \dfrac{100 \; \rm{cm}}{1} = 355 \; \rm{cm} \nonumber \]
In the final answer, we omit the 1 in the denominator. Thus, by a more formal procedure, we find that 3.55 m equals 355 cm. A generalized description of this process is as follows:
quantity (in old units) × conversion factor = quantity (in new units)
You may be wondering why we use a seemingly complicated procedure for a straightforward conversion. In later studies, the conversion problems you will encounter will not always be so simple. If you
can master the technique of applying conversion factors, you will be able to solve a large variety of problems.
In the previous example, we used the fraction \(\frac{100 \; \rm{cm}}{1 \; \rm{m}}\) as a conversion factor. Does the conversion factor \(\frac{1 \; \rm m}{100 \; \rm{cm}}\) also equal 1? Yes, it
does; it has the same quantity in the numerator as in the denominator (except that they are expressed in different units). Why did we not use that conversion factor? If we had used the second
conversion factor, the original unit would not have canceled, and the result would have been meaningless. Here is what we would have gotten:
\[ 3.55 \; \rm{m} \times \dfrac{1\; \rm{m}}{100 \; \rm{cm}} = 0.0355 \dfrac{\rm{m}^2}{\rm{cm}} \nonumber \]
For the answer to be meaningful, we have to construct the conversion factor in a form that causes the original unit to cancel out. Figure \(\PageIndex{1}\) shows a concept map for constructing a
proper conversion.
Figure \(\PageIndex{7}\): A Concept Map for Conversions. This is how you construct a conversion factor to convert from one unit to another.
1. Identify the "given" information in the problem. Look for a number with units to start this problem with.
2. What is the problem asking you to "find"? In other words, what unit will your answer have?
3. Use ratios and conversion factors to cancel out the units that aren't part of your answer, and leave you with units that are part of your answer.
4. When your units cancel out correctly, you are ready to do the math. You are multiplying fractions, so you multiply the top numbers and divide by the bottom numbers in the fractions.
Steps for Performing Dimensional Analysis and Examples
Example \(\PageIndex{2}\) Example \(\PageIndex{3}\)
Steps for Problem Solving The average volume of blood in an adult male is 4.7 L. What is this A hummingbird can flap its wings once in 18 ms. How many seconds are in
volume in gallons? 18 ms?
Identify the "given" information and what the problem is Given: 4.7 L Given: 18 ms
asking you to "find." Find: gal Find: s
List other known quantities. \(1\, L = 3.785 gal \) \(1 \,ms = 10^{-3} s \)
Prepare a concept map and use the proper conversion
\( 18 \; \cancel{\rm{ms}} \times \dfrac{10^{-3}\; \rm{s}}{1 \; \cancel{\
rm{ms}}} = 0.018\; \rm{s}\)
Cancel units and calculate. \( 4.7 \cancel{\rm{L}} \times \dfrac{1 \; \rm{gal}}{3.785\; \cancel{\ or
rm{L}}} = 1.2\; \rm{gal}\)
\( 18 \; \cancel{\rm{ms}} \times \dfrac{1\; \rm{s}}{1,000 \; \cancel{\rm
{ms}}} = 0.018\; \rm{s}\)
Think about your result. The amount in gal should be slightly less than 4 times smaller than The amount in s should be 1/1000 the given amount in ms.
the given amount in L.
Perform each conversion.
1. 101,000 ns to seconds
2. 32.08 kg to grams
3. 1.53 grams to cg
Answer a:
\(1.01000 x 10^{-4} s \)
Answer b:
\(3.208 x 10^{4} g \)
Answer c:
\(1.53 x 10^{2} g \)
Multiple Conversions
Sometimes you will have to perform more than one conversion to obtain the desired unit. For example, suppose you want to convert 54.7 km into millimeters. We will set up a series of conversion
factors so that each conversion factor produces the next unit in the sequence. We first convert the given amount in km to the base unit, which is meters. We know that 1,000 m =1 km. Then we convert
meters to mm, remembering that \(1\; \rm{mm}\) = \( 10^{-3}\; \rm{m}\).
Concept Map
Convert kilometers to meters to millimeters: use conversion factors 1000 meters per 1 kilometer and 1 millimeter per 0.001 meter
\[ 54.7 \; \cancel{\rm{km}} \times \dfrac{1,000 \; \cancel{\rm{m}}}{1\; \cancel{\rm{km}}} \times \dfrac{1\; \cancel{\rm{mm}}}{\cancel{10^{-3} \rm{m}}} & = 54,700,000 \; \rm{mm} \\ &= 5.47 \times 10^7
\; \rm{mm} \nonumber \]
In each step, the previous unit is canceled and the next unit in the sequence is produced; each successive unit cancels out, until only the unit needed in the answer is left.
Convert 58.2 ms to megaseconds in one multi-step calculation.
Example \(\PageIndex{4}\) Steps for Problem Solving Unit Conversion
Steps for Problem Solving Unit Conversion
Given: 58.2 ms
Identify the "given" information and what the
problem is asking you to "find." Find: Ms
\(1 ms = 10^{-3} s \)
List other known quantities.
\(1 Ms = 10^6s \)
Prepare a concept map. Convert milliseconds to seconds to microseconds: use conversion factors 0.001 second per millisecond and 1 microsecond per 1 million seconds
\[ 58.2 \; \cancel{\rm{ms}} \times \dfrac{10^{-3} \cancel{\rm{s}}}{1\; \cancel{\rm{ms}}} \times \dfrac{1\; \rm{Ms}}{1,000,000\; \cancel{ \rm{s}}} & =
0.0000000582\; \rm{Ms} \nonumber\\ &= 5.82 \times 10^{-8}\; \rm{Ms}\nonumber \nonumber \]
Neither conversion factor affects the number of significant figures in the final answer.
How many seconds are in a day?
Example \(\PageIndex{5}\): Steps for Problem Solving Unit Conversions
Steps for Problem Solving Unit Conversion
Given: 1 day
Identify the "given" information and what the problem is
asking you to "find." Find: s
1 day = 24 hours
List other known quantities. 1 hour = 60 minutes
1 minute = 60 seconds
Prepare a concept map. Convert day to hour to minute to second: use conversion factors 24 hours per day, 60 minutes per hour, and 60 seconds per minute
Calculate. \[1 \: \text{d} \times \frac{24 \: \text{hr}}{1 \: \text{d}}\times \frac{60 \: \text{min}}{1 \: \text{hr}} \times \frac{60 \: \text{s}}{1
\: \text{min}} = 86,400 \: \text{s} \nonumber \]
Perform each conversion in one multistep calculation.
1. 43.007 ng to kg
2. 1005 in to ft
3. 12 mi to km
Answer a:
\(4.3007 x 10^{-14} kg \)
Answer b:
83.75 ft
Answer c:
19 km
• Metric prefixes derive from Latin or Greek terms. The prefixes are used to make the units manageable.
• The SI system is based on multiples of ten. There are seven basic units in the SI system. Five of these units are commonly used in chemistry.
• Mass is a measure of the amount of matter that an object contains.
• Weight is a measure of force that is equal to the gravitational pull on an object.
• Mass is independent of location, while weight depends on location.
• Length is the measurement of the extent of something along its greatest dimension.
• Volume is the amount of space occupied by a sample of matter.
• Volume can be determined by knowing the length of each side of the item.
• Conversion factors are used to convert one unit of measurement into another.
• Dimensional analysis (unit conversions) involves the use of conversion factors that will cancel unwanted units and produce desired units.
Contributors and Attributions
• Henry Agnew (UC Davis)
• Hayden Cox (Furman University) | {"url":"https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Chemistry_for_Changing_Times_(Hill_and_McCreary)/01%3A_Chemistry/1.06%3A_The_Measurement_of_Matter","timestamp":"2024-11-06T13:54:23Z","content_type":"text/html","content_length":"193681","record_id":"<urn:uuid:9dda753b-295a-40c9-b008-7f332b4c5791>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00223.warc.gz"} |
Ratios 1
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1. Question 1 of 4
Express the following as ratios:
`(i)` A fluid with `7` parts water to `1` part oil
`(ii)` A mixture with `5` parts water to `3` parts flour
Write your answers as “a:b”
[Back] [Check] [Next]
Well Done!
A ratio compares quantities of the same type given in the same units.
`(i)` Find the ratio of a fluid with `7` parts water to `1` part oil.
This indicates that the ratio of the fluid would be `7` parts of water for every `1` part of oil.
`(ii)` Find the ratio of a mixture with `5` parts water to `3` parts flour
This indicates that the ratio of the mixture would be `5` parts of water for every `3` parts of flour.
2. Question 2 of 4
[Back] [Hint] [Check] [Next]
Nice Job!
A ratio compares quantities of the same type given in the same units.
Divide both sides by their highest common factor
`15` `:` `12`
`15``divide3` `:` `12``divide3` `3` is the highest common factor
`5` `:` `4`
3. Question 3 of 4
[Back] [Hint] [Check] [Next]
A ratio compares quantities of the same type given in the same units.
Divide both sides by their highest common factor
`6` `:` `24`
`6``divide6` `:` `24``divide6` `6` is the highest common factor
`1` `:` `4`
4. Question 4 of 4
[Back] [Hint] [Check] [Next]
A ratio compares quantities of the same type given in the same units.
Divide both sides by their highest common factor
`16` `:` `64`
`16``divide4` `:` `64``divide4` `4` is the highest common factor
`1` `:` `4` | {"url":"https://vividmath.com/practice/ratios-1/","timestamp":"2024-11-07T03:47:48Z","content_type":"text/html","content_length":"99370","record_id":"<urn:uuid:205d02aa-e601-4edf-8c98-98086ee5f436>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00481.warc.gz"} |
Variance Reduction via Antithetic Markov Chains
Variance Reduction via Antithetic Markov Chains
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:708-716, 2015.
We present a Monte Carlo integration method, antithetic Markov chain sampling (AMCS), that incorporates local Markov transitions in an underlying importance sampler. Like sequential Monte Carlo
sampling, the proposed method uses a sequence of Markov transitions to adapt the sampling to favour more influential regions of the integrand (modes). However, AMCS differs in the type of transitions
that may be used, the number of Markov chains, and the method of chain termination. In particular, from each point sampled from an initial proposal, AMCS collects a sequence of points by simulating
two independent, but antithetic, Markov chains, each terminated by a sample-dependent stopping rule. This approach provides greater flexibility for targeting influential areas while eliminating the
need to fix the length of the Markov chain a priori. We show that the resulting estimator is unbiased and can reduce variance on peaked multi-modal integrands that challenge existing methods.
Cite this Paper
Related Material | {"url":"https://proceedings.mlr.press/v38/neufeld15.html","timestamp":"2024-11-07T09:46:37Z","content_type":"text/html","content_length":"17621","record_id":"<urn:uuid:cd114912-a1c1-491f-9fc0-eff54ad200c2>","cc-path":"CC-MAIN-2024-46/segments/1730477027987.79/warc/CC-MAIN-20241107083707-20241107113707-00178.warc.gz"} |
NCERT Solution For Class 6, Maths, Chapter 4, Basic Geometrical Ideas - Solutions For Class
NCERT Solution For Class 6, Maths, Chapter 4, Basic Geometrical Ideas involves knowledge of basic shapes and geometry. Students can through the each exercise for practicing questions present in
chapter 4, Basic Geometrical Ideas. Class 6 maths, ch.4 contains total six exercises given below.
the solutons of NCERT class 6 maths chapter 4, Basic Geometrical Ideas involves ex.4.1, ex.4.2,ex.4.3, ex.4.5 and ex.4.6.
NCERT Solution For Class 6, Maths, Chapter 4, Basic Geometrical Ideas
Key points
Point: A point determines a location and i is usually denoted by a capital letters in given figure.
Line segment: A line segment corresponds to the shortest distance between two points. The line segment joining points A and B is denoted by $\overline{AB}$ .
Intersecting lines: Two distinct lines meeting at a point are called intersecting lines.
Parallel lines: if the two lines do not meet in a plane, they are said to be parrel lines.
Ray: it is a portion of line starting at a point and going in one direction endlessly.
Curve: Any drawing (straight or non-straight) done continuously without lifting the pencil may be called a curve.
Closed and open curve: A curve is said to be closed if its ends are joined. Otherwise, it is said to be open.
Polygon: it is a simple closed curve made up of line segments.
Triangle: A triangle is a three-sided polygon.
Quadrilateral : it is a four-sided polygon.
Circle: A circle is the path of a point moving at the same distance (the radius) from a fixed point (the centre). Here, the fixed point is the centre, the fixed distance is the radius.
Diameter: it goes straight across the circle, through the centre of circle. The diameter of a circle divides it into two semi-circles.
Circumference: the distance once around the circle is the circumference.
Chapter 4, Basic Geometrical Ideas | {"url":"https://solutionsforclass.com/ncert-solution-class-6-maths/ncert-solution-for-class-6-maths-chapter-4-basic-geometrical-ideas/","timestamp":"2024-11-09T06:30:08Z","content_type":"text/html","content_length":"136742","record_id":"<urn:uuid:f23cd98e-b7b2-4bec-a563-b36a3cf6502a>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00577.warc.gz"} |
Bayes' Theorem
Bayes can do magic!
Ever wondered how computers learn about people?
An internet search for "movie automatic shoe laces" brings up "Back to the future"
Has the search engine watched the movie? No, but it knows from lots of other searches what people are probably looking for.
And it calculates that probability using Bayes' Theorem.
Bayes' Theorem is a way of finding a probability when we know certain other probabilities.
The formula is:
P(A|B) = P(A) P(B|A)P(B)
Which tells us: how often A happens given that B happens, written P(A|B),
When we know: how often B happens given that A happens, written P(B|A)
and how likely A is on its own, written P(A)
and how likely B is on its own, written P(B)
Let us say P(Fire) means how often there is fire, and P(Smoke) means how often we see smoke, then:
P(Fire|Smoke) means how often there is fire when we can see smoke
P(Smoke|Fire) means how often we can see smoke when there is fire
So the formula kind of tells us "forwards" P(Fire|Smoke) when we know "backwards" P(Smoke|Fire)
• dangerous fires are rare (1%)
• but smoke is fairly common (10%) due to barbecues,
• and 90% of dangerous fires make smoke
We can then discover the probability of dangerous Fire when there is Smoke:
P(Fire|Smoke) =P(Fire) P(Smoke|Fire)P(Smoke)
=1% x 90%10%
So it is still worth checking out any smoke to be sure.
Example: Picnic Day
You are planning a picnic today, but the morning is cloudy
• Oh no! 50% of all rainy days start off cloudy!
• But cloudy mornings are common (about 40% of days start cloudy)
• And this is usually a dry month (only 3 of 30 days tend to be rainy, or 10%)
What is the chance of rain during the day?
We will use Rain to mean rain during the day, and Cloud to mean cloudy morning.
The chance of Rain given Cloud is written P(Rain|Cloud)
So let's put that in the formula:
P(Rain|Cloud) = P(Rain) P(Cloud|Rain)P(Cloud)
• P(Rain) is Probability of Rain = 10%
• P(Cloud|Rain) is Probability of Cloud, given that Rain happens = 50%
• P(Cloud) is Probability of Cloud = 40%
P(Rain|Cloud) = 0.1 x 0.50.4 = .125
Or a 12.5% chance of rain. Not too bad, let's have a picnic!
Just 4 Numbers
Imagine 100 people at a party, and you tally how many wear pink or not, and if a man or not, and get these numbers:
Bayes' Theorem is based off just those 4 numbers!
Let us do some totals:
And calculate some probabilities:
• the probability of being a man is P(Man) = 40100 = 0.4
• the probability of wearing pink is P(Pink) = 25100 = 0.25
• the probability that a man wears pink is P(Pink|Man) = 540 = 0.125
• the probability that a person wearing pink is a man P(Man|Pink) = ...
And then the puppy arrives! Such a cute puppy.
But all your data is ripped up! Only 3 values survive:
• P(Man) = 0.4,
• P(Pink) = 0.25 and
• P(Pink|Man) = 0.125
Can you discover P(Man|Pink) ?
Imagine a pink-wearing guest leaves money behind ... was it a man? We can answer this question using Bayes' Theorem:
P(Man|Pink) = P(Man) P(Pink|Man)P(Pink)
P(Man|Pink) = 0.4 × 0.1250.25 = 0.2
Note: if we still had the raw data we could calculate directly 525 = 0.2
Being General
Why does it work?
Let us replace the numbers with letters:
Now let us look at probabilities. So we take some ratios:
• the overall probability of "A" is P(A) = s+ts+t+u+v
• the probability of "B given A" is P(B|A) = ss+t
And then multiply them together like this:
Now let us do that again but use P(B) and P(A|B):
Both ways get the same result of ss+t+u+v
So we can see that:
P(B) P(A|B) = P(A) P(B|A)
Nice and symmetrical isn't it?
It actually has to be symmetrical as we can swap rows and columns and get the same top-left corner.
And it is also Bayes Formula ... just divide both sides by P(B):
First think "AB AB AB" then remember to group it like: "AB = A BA / B"
P(A|B) = P(A) P(B|A)P(B)
Cat Allergy?
One of the famous uses for Bayes Theorem is False Positives and False Negatives.
For those we have two possible cases for "A", such as Pass/Fail (or Yes/No etc)
Example: Allergy or Not?
Hunter says she is itchy. There is a test for Allergy to Cats, but this test is not always right:
• For people that really do have the allergy, the test says "Yes" 80% of the time
• For people that do not have the allergy, the test says "Yes" 10% of the time ("false positive")
If 1% of the population have the allergy, and Hunter's test says "Yes", what are the chances that Hunter really has the allergy?
We want to know the chance of having the allergy when test says "Yes", written P(Allergy|Yes)
Let's get our formula:
P(Allergy|Yes) = P(Allergy) P(Yes|Allergy)P(Yes)
• P(Allergy) is Probability of Allergy = 1%
• P(Yes|Allergy) is Probability of test saying "Yes" for people with allergy = 80%
• P(Yes) is Probability of test saying "Yes" (to anyone) = ??%
Oh no! We don't know what the general chance of the test saying "Yes" is ...
... but we can calculate it by adding up those with, and those without the allergy:
• 1% have the allergy, and the test says "Yes" to 80% of them
• 99% do not have the allergy and the test says "Yes" to 10% of them
Let's add that up:
P(Yes) = 1% × 80% + 99% × 10% = 10.7%
Which means that about 10.7% of the population will get a "Yes" result.
So now we can complete our formula:
P(Allergy|Yes) = 1% × 80%10.7% = 7.48%
P(Allergy|Yes) = about 7%
This is the same result we got on False Positives and False Negatives.
In fact we can write a special version of the Bayes' formula just for things like this:
P(A|B) = P(A)P(B|A) P(A)P(B|A) + P(not A)P(B|not A)
"A" With Three (or more) Cases
We just saw "A" with two cases (A and not A), which we took care of in the bottom line.
When "A" has 3 or more cases we include them all in the bottom line:
P(A1|B) = P(A1)P(B|A1) P(A1)P(B|A1) + P(A2)P(B|A2) + P(A3)P(B|A3) + ...etc
Example: The Art Competition has entries from three painters: Pam, Pia and Pablo
• Pam put in 15 paintings, 4% of her works have won First Prize.
• Pia put in 5 paintings, 6% of her works have won First Prize.
• Pablo put in 10 paintings, 3% of his works have won First Prize.
What is the chance that Pam will win First Prize?
P(Pam|First) = P(Pam)P(First|Pam) P(Pam)P(First|Pam) + P(Pia)P(First|Pia) + P(Pablo)P(First|Pablo)
Put in the values:
P(Pam|First) =(15/30) × 4% (15/30) × 4% + (5/30) × 6% + (10/30) × 3%
Multiply all by 30 (makes calculation easier):
P(Pam|First) =15 × 4% 15 × 4% + 5 × 6% + 10 × 3%
=0.60.6 + 0.3 + 0.3
A good chance!
Pam isn't the most successful artist, but she did put in lots of entries.
Now, back to Search Engines.
Search Engines take this idea and scale it up a lot (plus some other tricks).
It makes them look like they can read your mind!
It can also be used for mail filters, music recommendation services and more. | {"url":"http://wegotthenumbers.org/bayes-theorem.html","timestamp":"2024-11-08T12:16:42Z","content_type":"text/html","content_length":"16134","record_id":"<urn:uuid:8f9eb597-bb74-40a3-9479-8eaa0365c672>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00417.warc.gz"} |
🔥 Unleash the Data Structure Dynamo: Mastering Binary Search Trees
[Data Structures 1] Search Binary Tree
🧩Problem 💡: The search algorithm determines the node that contains the key from the binary search tree.
public static nodetype search(nodetype tree, keytype keyin){
boolean found;
nodetype p;
p = tree;
found = false;
while (!found){
if (p.key == keyin){
found = true;
} else if (keyin < p.key){
p = p.left; // search the left child
} else {
p = p.right; // search the right child
return p;
Search time is the number of comparisons made to locate a key. The search function determines a tree structure to minimize the average search time.
💡What are the binary search tree characteristics?
During each iteration, comparisons between the search value and the current node key determine whether the target is found or to move left or right. During each comparison, the search will eliminate
half of the remaining nodes from the search space, which contributes to a time complexity:
N represents the number of nodes in the tree.
An example is determining the depth of the node "Ursula", a node in the second tree level, and its search time is calculated as:
🌲An optimal binary search tree
🧩Problem: Determine an optimal binary search tree using a set of keys as input.
💡Dynamic programming is a solution for calculating the cumulative probabilities.
def compute_prefix_sums(p):
n = len(p) - 1
P = [0] * (n + 1)
for j in range(1, n + 1):
P[j] = P[j - 1] + p[j]
return P
The algorithm has a time complexity of O(n) to iterate through the loop where each computation of P takes O(1).
A prefix sum array is an alternative to calculate the optimal sum of probabilities within a range in O(1) time complexity. If the index is j, the sum is P[j]. Compute a sum for a scope using the
equation: "P[j] - P[i - 1]".
1. Initialization:
Create a prefix sum array P of size n+1, where n is the number of keys.
Initialize P[0] to 0. This extra element is for easier indexing.
2. Prefix Sum Calculation:
For i=1 to n:
3. Using the Prefix Sum Array:
To compute
The sum is simply P[j].
To compute a sum for a range, say:
The sum is P[j]-P[i-1].
The example allows us to calculate probability sum across any range in a constant time complexity. | {"url":"https://haochengcodedev.hashnode.dev/data-structures-1-search-binary-tree","timestamp":"2024-11-04T22:04:54Z","content_type":"text/html","content_length":"110271","record_id":"<urn:uuid:e9c13c06-405c-43e4-87f5-ae955dbf3ff4>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00846.warc.gz"} |
Through-Wall Crowd Counting with WiFi
Through-Wall Crowd Counting with WiFi, Without Relying On Personal Devices
Crowd Counting Through Walls With WiFi
In the News (2018): Tech Crunch, Digit, New Atlas, The Register, Science Daily, UCSB Current, and other outlets
WiFi signals are everywhere these days. Can they do more than communication? For instance, can they count the total number of people in an area from behind the walls? Can this be done with only
WiFi power measurements and without relying on people to carry a device? In this project, we have shown that this is indeed possible and have enabled the first demonstration of crowd counting
through walls. See the video and the paper for more details and results.
Project Information
Related Publication
• S. Depatla and Y. Mostofi, "Crowd Counting Through Walls Using WiFi," in the proceedings of the IEEE International Conference on Pervasive Computing and Communications (PerCom), 2018.[pdf]
Summary of Our Approach
We have proposed a new approach that has enabled the first demonstration of crowd counting through walls with only WiFi received power measurements, and without relying on people to carry a device.
As an example, consider the room in Fig. 1 below with a WiFi transmitter and receiver outside, behind the walls, as marked. A number of people are present in this room. The transmitter transmits a
wireless signal whose received signal strength (RSSI) is measured by the receiver for a brief period of time. Can we count the total number of people from behind the walls, based on only such
received power measurements? This a considerably challenging problem as the walls will severely attenuate the signal. In this project, we have proposed a new methodology that has enabled the first
demonstration of crowd counting through walls.
Here are some key features of our proposed approach:
• Only uses WiFi received power measurements
• Does not rely on people to carry a device
• Minimal prior calibration that does not have to be in the same area
• Preserves privacy
Figure 1. A WiFi transmitter and receiver are inserted outside of a classroom, behind the walls. We are interested in counting the total number of people in the room, from outside, based on only the
received signal power measurements of this link, and without relying on people to carry a device.
Consider the discrete event sequence that corresponds to the significant signal drops, and the corresponding inter-event times, as shown in Fig. 2 below. We have observed that while the amplitude of
the signal can be severely attenuated through walls, the inter-event times are more robust to wall attenuations. Thus, we propose to exploit them for crowd counting through walls and fundamentally
characterize how much information they carry on occupancy.
Figure 2. A demonstration of the discrete-event sequence corresponding to the events of significant signal drops (S[1],S[2], ...), as well as the corresponding inter-event times (T[1], T[2], ...).
More specifically, we propose to model the discrete-event sequence corresponding to the movements of one person as a renewal-type process. Then, the discrete event sequence corresponding to the
movements of N people is the superposition of N renewal-type processes. A renewal process is an extension of the Poisson process, where the inter-event times can have any distribution. Such a process
has found applications in areas such as reliability and risk analysis. We then utilize mathematical tools from the renewal process literature to fundamentally understand the amount of information the
received signal carries on occupancy in our problem of interest.
After a long derivation and analysis, we have developed a new mathematical model that explicitly relates the statistics of the inter-event times to the total number of occupants in the area, as
summarized in the following theorem:
It is noteworthy that in our past work JSAC 2015, we had shown crowd counting with WiFi signals, but with the transmitter and receiver in the same area as people. Enabling through-wall crowd
counting, however, is considerably more challenging due to the high level of attenuation by the walls, necessitating a new approach, which is the main motivation for the proposed methodology of this
Sample Experimental Results
We have tested our proposed approach extensively in several through-wall scenarios. Here, we show sample experimental results where a pair of WiFi cards are used for counting people through walls.
Figure 3. A WiFi transmitter and receiver are inserted outside of this room where the walls are made of concrete. The table shows the performance of our proposed approach when different number of
people walk in the area.
Figure 4. A WiFi transmitter and receiver are inserted outside of this room where the walls are made of concrete. The table shows the performance of our proposed approach when different number of
people walk in the area.
Figure 5. A WiFi transmitter and receiver are inserted outside of this room where the walls are made of wood. The table shows the performance of our proposed approach when different number of people
walk in the area.
Figure 6. A WiFi transmitter and receiver are inserted outside of this room where the walls are made of a mixture of concrete and plaster. 20 people were present in this room and our proposed
approach counted them as 19.
Overall, we ran 44 experiments in different locations, with different wall properties, and several different number of people, and achieved an estimation error of 2 people or less, 100% of the time.
This is estimation through highly-attenuating walls such as concrete that can attenuate the signal 20 dB per 10 cm. It is noteworthy that our approach does not need prior calibration in the area of
Potential Applications:
There are several potential applications that can benefit from an estimation of how crowded an area is, especially through walls. Smart energy management in buildings (e.g., heating/cooling, or
lighting), retail business planning, and security/search and rescue are a few sample applications. More specifically, lighting or heating/cooling of a building can be better optimized based on
learning the concentration of people over the building. Stores can benefit from counting the number of shoppers for better business planning. Emergency evacuation can also benefit from an estimation
of the level of occupancy.
• All the students who walked in our experiments. | {"url":"https://web.ece.ucsb.edu/~ymostofi/ThroughWallCrowdCounting.html","timestamp":"2024-11-11T12:54:14Z","content_type":"text/html","content_length":"11267","record_id":"<urn:uuid:efa565ae-549a-4f98-a7b5-54558775948b>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00540.warc.gz"} |
Trading Up to One | U.S. Mint for Kids
Trading Up to One
Students will use various coin denominations to explore the concept of fractions.
Students will demonstrate an understanding of the fractions 1/2 (50 cents), 1/4 (25 cents), 10ths (10 cents) and 20ths (5 cents) by using fraction circle pieces to create whole units (1 dollar).
Subject Area
Class Time
• Total Time: 0-45 Minutes minutes
• Fraction circles: whole circle, half, quarters, tenths and twentieths
• Coin pictures (half dollar, quarter, dime, and nickel)
• Fraction and coin dice (or spinner)
Lesson Steps
1. Divide the students into pairs. Give each student a complete set of fraction circles (whole, half, quarters, tenths, twentieths). The object of the activity is to see who can create a whole unit
(or $1.00) first.
2. Have the students place their whole circle in front of them and take turns rolling the fraction or money dice or spinning the spinner. They then place the corresponding fraction piece onto their
whole piece if they can. As they go, the players should trade down their fraction parts (2 dimes and a nickel for a quarter, 2 quarters for a half dollar, and so on).
3. Let the play continue until someone wins by creating a whole unit or exactly $1.00.
Use observation to see which student pairs understand the fraction concepts, and which pairs are having difficulty. After everyone is comfortable with the rules and the fractions, the students should
be able to finish a whole unit (1 dollar).
Common Core Standards
Discipline: Math
Domain: 2.OA Operations and Algebraic Thinking
Grade(s): Grade 2
Cluster: Add and subtract within 20
• 2.OA.2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, eg, by using objects, drawings, and equations with a symbol for the unknown number
to represent the problem.
Discipline: Math
Domain: 3.NF Number and Operations: Fractions
Grade(s): Grade 2
Cluster: Develop understanding of fractions as numbers
• 3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
• 3.NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
□ Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the
endpoint of the part based at 0 locates the number 1/b on the number line.
□ Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the
number line.
• 3.NF.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
□ Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
□ Recognize and generate simple equivalent fractions, eg, 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, eg, by using a visual fraction model
□ Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same
point of a number line diagram.
□ Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole.
Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, eg, by using a visual fraction model
National Standards
Discipline: Mathematics
Domain: 3-5 Number and Operations
Cluster: Compute fluently and make reasonable estimates.
Grade(s): Grades 3–5
In grades 3–5 all students should
• develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 × 50;
• develop fluency in adding, subtracting, multiplying, and dividing whole numbers;
• develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results;
• develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience;
• use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals; and
• select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the
computation and use the selected method or tools.
Discipline: Mathematics
Domain: 3-5 Number and Operations
Cluster: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
Grade(s): Grades 3–5
In grades 3–5 all students should
• understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals;
• recognize equivalent representations for the same number and generate them by decomposing and composing numbers;
• develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers;
• use models, benchmarks, and equivalent forms to judge the size of fractions;
• recognize and generate equivalent forms of commonly used fractions, decimals, and percents;
• explore numbers less than 0 by extending the number line and through familiar applications; and
• describe classes of numbers according to characteristics such as the nature of their factors.
Discipline: Mathematics
Domain: All Problem Solving
Cluster: Instructional programs from kindergarten through grade 12 should enable all students to
Grade(s): Grades 3–5
• Build new mathematical knowledge through problem solving
• Solve problems that arise in mathematics and in other contexts
• Apply and adapt a variety of appropriate strategies to solve problems
• Monitor and reflect on the process of mathematical problem solving
Discipline: Mathematics
Domain: All Communication
Cluster: Instructional programs from kindergarten through grade 12 should enable all students to
Grade(s): Grades 3–5
• organize and consolidate their mathematical thinking through communication
• communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
• analyze and evaluate the mathematical thinking and strategies of others; and
• use the language of mathematics to express mathematical ideas precisely. | {"url":"https://kids.usmint.gov/learn/kids/resources/lesson-plans/trading-up-to-one","timestamp":"2024-11-13T02:14:15Z","content_type":"text/html","content_length":"54045","record_id":"<urn:uuid:4b117948-a6b6-4f31-821c-3f18e295f1c0>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00131.warc.gz"} |
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On structure of one dimensional basic sets of endomorphisms of surfaces
V. Z. Grines^1, E. D. Kurenkov.^2
This paper deals with the study of the dynamics in the neighborhood of one-dimensional basic sets of $C^k$, $k \geq 1$, endomorphism satisfying axiom of $A$ and given on surfaces. It is
established that if one-dimensional basic set of endomorphism $f$ has the type $ (1, 1)$ and is a one-dimensional submanifold without boundary, then it is an attractor smoothly embedded in
Annotation ambient surface. Moreover, there is a $ k \geq 1$ such that the restriction of the endomorphism $f^k$ to any connected component of the attractor is expanding endomorphism. It is also
established that if the basic set of endomorphism $f$ has the type $ (2, 0)$ and is a one-dimensional submanifold without boundary then it is a repeller and there is a $ k \geq 1 $ such
that the restriction of the endomorphism $f^k$ to any connected component of the basic set is expanding endomorphism.
Keywords axiom $A$, endomorphism, basic set
^1Professor of Department of fundamental mathematics, Higher School of Economics, Nizhny Novgorod; vgrines@hse.ru
^2Laboratory TAPRADESS, National Research University Higher School of Economics; ekurenkov@hse.ru
Citation: V. Z. Grines, E. D. Kurenkov., "[On structure of one dimensional basic sets of endomorphisms of surfaces]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:2 (2016) 16–24 (In | {"url":"https://journal.svmo.ru/en/archive/article?id=1415","timestamp":"2024-11-07T19:20:00Z","content_type":"text/html","content_length":"15646","record_id":"<urn:uuid:97b3798e-29dd-4b8d-9e2e-d695567925f1>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00823.warc.gz"} |
Re: [tlaplus] Parse error was expecting "==== or more module body"
concerning the syntax errors:
1. Your _expression_ "CHOOSE k \in Nat : P(k)" appears where TLA+ expects a definition, an axiom / assumption or a theorem. Since m and k are declared as constants, I believe what you really mean is
ASSUME k \in Nat /\ (k > (1+(1+4/m)^0.5) / 2) /\ (k < (2+(1+4/m)^0.5) / 2)
Alternatively, you could remove the constant parameter k and write the definition
k == CHOOSE k \in Nat : ( (k > (1+(1+4/m)^0.5) / 2) /\ (k < (2+(1+4/m)^0.5) / 2) )
but presumably you'd like to check your spec for all possible values of k rather than a fixed one.
2. The final conjunct of your next-state relation is incomplete because the ELSE branch is missing. Perhaps you meant to write
c' >= k => E' >= r' * c'
in order to restrict transitions to those that satisfy this implication, but perhaps you rather meant to assert the invariant
c >= k => E >= r * c
and verify that this implication is true for every state along every run of the system? In that case, you should write a definition like
Inv == c >= k => E >= r * c
and use the TLA+ tools to verify that it holds (but see below).
3. [][Next] is not a well-formed formula of TLA+, you should write
Spec == Init /\ [][Next]_<<c,E,r>>
4. Although not an error, it is a bit strange that your definitions of the initial predicate and the next-state relation are written as disjunctions with a single disjunct. You may want to remove the
leading "\/" (but perhaps this is a simplified version and you have other disjuncts in mind).
More fundamentally, while TLA+ has a standard module representing the real numbers, the currently available TLA+ tools (the model checkers TLC and Apalache as well as the interactive proof system
TLAPS) do not support real numbers. I am therefore afraid that TLA+ is not the most appropriate formalism for what you are trying to do.
Best regards, | {"url":"https://discuss.tlapl.us/msg04715.html","timestamp":"2024-11-04T07:44:00Z","content_type":"text/html","content_length":"11610","record_id":"<urn:uuid:7d67accd-e28c-42ec-80a5-a74ac71fbaec>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00397.warc.gz"} |
Yanjun LIU | Associate Professor | PhD | Jiangxi Normal University | College of mathematics and information sience | Research profile
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In this paper we complete the proof of Brauer’s height zero conjecture for two primes proposed by G. Malle and G. Navarro.
Let p,q be different primes and suppose that the principal p- and the principal q-block of a finite group have only one irreducible complex character in common, namely the trivial one. We conjecture
that this condition implies the existence of a nilpotent Hall {p,q}-subgroup and prove that a minimal counter-example must be an almost simple group wh...
In this paper we first state a conjecture on the lower bound of the maximal height of characters in a p-block of a finite group. Then we show that our conjecture holds for all blocks of covering
groups of a sporadic simple group, for all blocks of a quasi-simple group G with G/Z(G) isomorphic to A6,A7 or a simple group of Lie type with an exception...
Geoffrey Robinson conjectured in 1996 that the $p$ -part of character degrees in a $p$ -block of a finite group can be bounded in terms of the center of a defect group of the block. We prove this
conjecture for all primes $p\neq 2$ for all finite groups. Our argument relies on a reduction by Murai to the case of quasi-simple groups which are then s...
In this note we prove that the Eaton-Moretó conjecture holds for all blocks of finite general linear and unitary groups for all primes. Also, we show that no block of a finite quasi-simple group of
classical Lie type provides a minimal counterexample to the conjecture, and so for ℓ > 5 no ℓ-block of any quasi-simple group can be a minimal counterex...
The Hilbert divisor pa(φ) of an irreducible p-Brauer character φ of a finite group G carries deep information about φ, respectively the module affording φ. In [8] we conjectured that φ belongs to a
p-block of defect 0 if and only if its Hilbert divisor is 1. In this note we continue our investigations.
Robinson’s conjecture states that the height of any irreducible ordinary character in a block of a finite group is bounded by the size of the central quotient of a defect group. This conjecture had
been reduced to quasi-simple groups by Murai. The case of odd primes was settled completely in our predecessor paper. Here we investigate the 2-blocks o...
We study p-Brauer characters of a finite group G which are restrictions of generalized characters vanishing on p-singular elements for a fixed prime p dividing the order of G. Such Brauer characters
are called quasi-projective. We show that for each irreducible Brauer character φ there exists a minimal p-power, say pa(φ), such that pa(φ)φ is quasi-...
This paper studies intersections of principal blocks of a finite group with respect to different primes. We first define the block graph of a finite group G, whose vertices are the prime divisors of
|G| and there is an edge between two vertices p \ne q if and only if the principal p- and q-blocks of G have a nontrivial common complex irreducible ch...
Let $G$ be a finite group, and write ${\rm cd}(G)$ for the degree set of the complex irreducible characters of $G$. The group $G$ is said to satisfy the {\it two-prime hypothesis} if, for any
distinct degrees $a, b \in {\rm cd}(G)$, the total number of (not necessarily different) primes of the greatest common divisor ${\rm gcd}(a, b)$ is at most $2...
Let G be a finite group, and write cd(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \
usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{cd}(G)$$\end{document} for the degree set of the complex irreducible cha...
Let G be a finite group and p be a prime. In this note, we show that if Op(G) = 1 and all subgroups of G of order p are conjugate, then either G has a p-block of defect zero, or p = 2 and G is a
direct product of a simple group S {M22,A7} and an odd order group. This improves one of our previous works.
In this note, it is shown that a finite group G is solvable if for each odd prime divisor p of , , where is the set of complex irreducible characters of the principal p-block of G. Also, the
structure of such groups is investigated. Examples show that the bound 2 is best possible.
In this note, we characterize finite nonsolvable groups whose principal p-blocks consist of ordinary irreducible characters of prime power degrees for every prime p. In addition, we give an upper
bound of the nilpotent length for the solvable situation.
The main purpose of this note is to show that there is a one-to-one correspondence between minimal non-nilpotent (resp., locally nilpotent) saturated fusion systems and finite p′-core-free
p-constrained minimal non-nilpotent (resp., locally p-nilpotent) groups. © 2016 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzh...
Let G be a finite group, and write (Formula presented.) for the degree set of the complex irreducible characters of G. The group G is said to satisfy the two-prime hypothesis if, for any distinct
degrees (Formula presented.), the total number of (not necessarily different) primes of the greatest common divisor (Formula presented.) is at most 2. In...
Recently, Isaacs, Moretó, Navarro, and Tiep investigated finite groups with just one irreducible character degree divisible by a given prime p, and showed that their Sylow p-subgroups are almost
normal and almost abelian. In this paper, we consider the corresponding situation for Brauer characters. In particular, we show that if a finite group G ha...
A finite simple group of Lie type in defining characteristic p has exactly two p-blocks, the principal block and a block of defect zero consisting of the Steinberg character whose degree is the
p-part of the order of the group. In this paper we characterize finite groups G which have exactly the principal p-block and a p-block of defect zero consis...
In this paper we characterize finite quasi-simple groups of
Let $p$ be an odd prime. In this note, we show that a finite group $G$ is solvable if all degrees of irreducible complex characters of $G$ not divisible by $p$ are either 1 or a prime.
Let p be a prime. The Sylow p-number of a finite group G, which is the number of Sylow p-subgroups of G, is called solvable if its ℓ-part is congruent to 1 modulo p for any prime ℓ. P. Hall showed
that solvable groups only have solvable Sylow numbers, and M. Hall showed that the Sylow p-number of a finite group is the product of two kinds of factor...
Motivated by Isaacs and Passman’s characterization of finite groups all of whose nonlinear complex irreducible characters have prime degrees, we investigate finite groups [Formula: see text] with
exactly one character degree that is not a prime. We show that either [Formula: see text] is solvable with [Formula: see text] or [Formula: see text] for...
In this note, we show that if a finite group G has only one conjugacy class of subgroups of an odd prime order p, then G has a p-block of defect zero if and only if O p (G) = 1. Generally, this
result is not true for p even. However, we show that it is true if G does not have quotient groups isomorphic to M 22 or A 7.
Let $G$ be a finite group and $\mathrm{bcl}(G)$ the largest conjugacy class length of $G$ . In this note we slightly improve He and Shi’s lower bound for $\mathrm{bcl}(G)$ , showing that $|\mathrm
{bcl}(G)|\ge p^{\frac{1}{p}}(|G:O_{p}(G)|_{p})^{\frac{p-1}{p}}$ .
Let G be a finite group with the degree set cd(G)cd(G) of its complex irreducible characters. We call that G satisfies the prime-power hypothesis if, for distinct degrees χ(1),ψ(1)∈cd(G)χ(1),ψ(1)∈cd
(G), the greatest common divisor gcd(χ(1),ψ(1))gcd(χ(1),ψ(1)) is a prime power. In this paper, we show that |cd(G)|⩽18|cd(G)|⩽18 if G is a nonsolvable g...
The main purpose is to investigate almost simple DD-groups. It proves that the almost simple group G is not a DD-group unless G is one of the following groups: 1) M22, J2, Co1, Fi'24, McL, Th, B, and
the automorphism group of M12 or J2; 2) A5, A6, A7, A9, A10, A16, S5, Aut(A6), S8, S10, or An (62≤n≤205); 3) L3(2), Aut(L3(3)), or L2(q) for q=4, 5, 7...
Let G be a finite classical group of characteristic p. In this paper, we give an arithmetic criterion of the primes r ≠ p, for which the Steinberg character lies in the principal r-block of G. The
arithmetic criterion is obtained from some combinatorial objects (the so-called partition and symbol).
Our main purpose of this paper is to give π-block forms of Brauer’s k(B)−conjecture and Olsson’s conjecture for finite π−separable groups. Keywords π-blocks–Olsson’s conjecture– π-separable groups
In this paper, we show that the alternating group A5 is the only nonsolvable group whose character graph has no triangles.
In this note, we first investigate the degrees of irreducible π-Brauer characters of a finite π-separable group G. Then we relate degrees of irreducible π-Brauer characters to class lengths of
π-regular elements of G. | {"url":"https://www.researchgate.net/profile/Yanjun-Liu-19","timestamp":"2024-11-04T18:00:38Z","content_type":"text/html","content_length":"503589","record_id":"<urn:uuid:476e3633-a0b0-4110-857d-21730c338a62>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00064.warc.gz"} |
In an article on his minimum viable homepage
Keunwoo Lee argues against the simulation argument
. In short, "future superintelligences" would be too busy with other things and "once you have the resources to simulate many beings of a given type with high fidelity, doing so becomes
I do not disagree with this argument, but I disagree that "superintelligence" is required to simulate us.
Every simulation or simulation program would be equivalent to a long string of 0s and 1s; in other words it would be equivalent to a very large natural number. It can indeed require intelligence to
calculate a specific large number, e.g. a large prime number or a particular simulation.
But it does not require "superintelligence" to calculate
numbers, it only requires a counter with vast resources, i.e. a simple Turing machine.
One could argue that the simulation programs need to be somehow 'executed', but again a simple process with vast resources could do that:
If Sij stands for the i-th program step of the j-th simulation, then we can arrange S11, S12, S13, ... S21, S22, ... in an infinite square and use a variant of
the proof that rational numbers are countable
to show that i) a simple Turing machine can generate all possible simulations and ii) another simple machine can actually 'execute' all possible simulations. The combination of i) + ii) would
basically be a giant clock, no "superintelligence" would be necessary, just a (quasi)infinite amount of resources.
However, we do not know what resources are available in the "really real world" and therefore we cannot estimate how likely it is that we are the result of such a process.
But we could be the result of a giant clock counting time ... tik, tok ...
1 comment:
Francis W said...
Greaat post thankyou | {"url":"https://wbmh.blogspot.com/2022/06/simulations.html?showComment=1725624271371","timestamp":"2024-11-13T19:27:53Z","content_type":"application/xhtml+xml","content_length":"48782","record_id":"<urn:uuid:4a3856fa-5b73-4c99-aa5e-3673b406b3b5>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00663.warc.gz"} |
This is a generic function, with methods in base R for classes "aov", "glm" and "lm" as well as for "negbin" (package MASS) and "coxph" and "survreg" (package survival).
The criterion used is $$AIC = - 2\log L + k \times \mbox{edf},$$ where \(L\) is the likelihood and edf the equivalent degrees of freedom (i.e., the number of free parameters for usual parametric
models) of fit.
For linear models with unknown scale (i.e., for lm and aov), \(-2\log L\) is computed from the deviance and uses a different additive constant to logLik and hence AIC. If \(RSS\) denotes the
(weighted) residual sum of squares then extractAIC uses for \(- 2\log L\) the formulae \(RSS/s - n\) (corresponding to Mallows' \(C_p\)) in the case of known scale \(s\) and \(n \log (RSS/n)\) for
unknown scale. AIC only handles unknown scale and uses the formula \(n \log (RSS/n) + n + n \log 2\pi - \sum \log w\) where \(w\) are the weights. Further AIC counts the scale estimation as a
parameter in the edf and extractAIC does not.
For glm fits the family's aic() function is used to compute the AIC: see the note under logLik about the assumptions this makes.
k = 2 corresponds to the traditional AIC, using k = log(n) provides the BIC (Bayesian IC) instead.
Note that the methods for this function may differ in their assumptions from those of methods for AIC (usually via a method for logLik). We have already mentioned the case of "lm" models with
estimated scale, and there are similar issues in the "glm" and "negbin" methods where the dispersion parameter may or may not be taken as ‘free’. This is immaterial as extractAIC is only used to
compare models of the same class (where only differences in AIC values are considered). | {"url":"https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/extractAIC","timestamp":"2024-11-09T13:20:55Z","content_type":"text/html","content_length":"71412","record_id":"<urn:uuid:8cbdcbe3-d9ef-4ef4-9325-fc01d29b6935>","cc-path":"CC-MAIN-2024-46/segments/1730477028118.93/warc/CC-MAIN-20241109120425-20241109150425-00457.warc.gz"} |
Expressions and Conversions | Blitz Basic Language Reference
The following operators are supported, listed in order of precedence:
Unary operators take one operand, while Binary operators take two.
Arithmetic operators produce a result of the same type as the operands. For example, adding two integers produces an integer result.
If the operands of a binary arithmetic or comparison operator are not of the same type, one of the operands is converted using the following rules:
If one operand is a custom-type object, the other must be an object of the same type, or Null.
Else if one operand is a string, the other is converted to a string.
Else if one operand is floating point, the other is converted to floating point.
Else both operands must be integers.
When floating point values are converted to integer, the value is rounded to the nearest integer. When integers and floating point values are converted to strings, an ascii representation of the
value is produced.
When strings are converted to integer or floating point values, the string is assumed to contain an ascii representation of a numeric value and converted accordingly. Conversion stops at the first
non-numeric character in the string, or at the end of the string.
The only arithmetic operation allowed on string is +, which simply concatenates the two operands.
Int, Float, and Str can be used to convert values. They may be optionally followed by the appropriate type tag - ie: Int%, Str$ and Float#.
Comparison operators always produce an integer result: 1 for true, 0 for false.
If one of the operators is a custom-type object, the other must be an object of the same type, or Null, and the only comparisons allowed are => and <>.
Bitwise and logical operators always convert their operands to integers and produce an integer result.
The Not operator returns 0 for a non-zero operand, otherwise 1. When an expression is used to conditionally execute code - for example, in an If statement - the result is converted to an integer
value. A non-zero result means true, a zero result means false. | {"url":"https://gitbook.ziyuesinicization.site/blitz-basic-language-reference/expressions-and-conversions","timestamp":"2024-11-12T15:08:39Z","content_type":"text/html","content_length":"228994","record_id":"<urn:uuid:dd82c851-2441-4f1f-ae48-d48443f5c40a>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00162.warc.gz"} |
Mathematical Proof: Detective Work for Kids
Did you know that the proof of the Pythagorean Theorem was a mystery for 2,000 years? It was thought to be unsolvable until two students, Calcea Johnson and Ne’Kiya Jackson, proved it in 2023. Their
discovery at an American Mathematical Society conference showed how fun and skillful math could be. It opened a new world for young math enthusiasts.
This article will show how math proofs can be both fun and educational. We will mix reading, solving problems, and telling exciting stories. By doing this, kids get to explore proofs like real-life
detectives and improve their thinking skills. It’s a way to help them love and understand the power of numbers.
Key Takeaways
• Discover how to make mathematical proof accessible and engaging for children through hands-on activities and real-life scenarios.
• Learn strategies for fostering a growth mindset in mathematics and building a strong foundation for future mathematical learning.
• Explore the importance of visual aids, collaborative learning, and conceptual understanding in teaching mathematical proof to kids.
• Understand the role of simplifying complex concepts and relating math to everyday life in nurturing a love for numbers in young learners.
• Gain insights into the inspiring stories of barrier-breaking students who have achieved remarkable feats in mathematics.
Making Math Mysteries Engaging
Getting kids to like math is tough but rewarding. The “Math Detective®” series makes math fun and easy to understand. It mixes reading with problem-solving using topics from national math standards.
This way, it gets students ready for more advanced math.
Combining Reading and Problem-Solving
Students start by reading short, fun stories. These stories use charts and graphs. Then, they have to answer questions that need deep thinking. This helps improve their math understanding and
problem-solving skills. The questions are like those they’ll find in important math tests. But, they ask for more critical thinking.
Age-Relevant, High-Interest Stories
The “Math Detective®” stories are just right for the students’ age. They are also very interesting. It shows kids how math is used in everyday life. This makes math more real and exciting for them.
Fostering Critical Thinking Skills
The questions in the “Math Detective®” series push students hard. They have to explain their answers. This helps a lot. It not only makes math concepts clearer. It also builds up their critical
thinking. These skills are key for doing well in tough math classes and tests.
How to explain mathematical proof to a child
Explaining the complexities of mathematical proof to a young mind can be tough. But with smart methods, educators can simplify and make these concepts interesting. They use visual aids and activities
to connect mathematical proof with real life. This helps children understand and value mathematical reasoning more.
Visual Aids and Hands-On Activities
Visual aids and interactive resources are key in making math proofs easier for kids to grasp. They show the steps clearly, making it simpler to understand. Adding hands-on activities, like using
objects or solving problems, can improve their understanding too.
Relating Math to Real-Life Scenarios
Showing kids how math proof applies to real life is crucial. Using examples from their daily life helps them see its importance. It makes learning math proofs fun and highlights its role in
understanding the world around us.
Teachers who use these strategies help children enjoy learning about math proofs. Lessons become an exciting journey of discovery and understanding.
Building Math Intuition
It’s key for kids to understand math and its proofs by developing a math intuition. This starts with number sense and making tough ideas simpler. Teachers aim to give deep knowledge. It helps kids
feel sure when dealing with math problems.
Developing Number Sense
Kids in the U.S.A. at age 6 often figure out simple math without writing. They see that adding 3 and taking away 3 leave nothing. This way of building number sense is different from just learning the
steps. It helps kids get a good start in math.
Simplifying Complex Concepts
At age 9, kids might use a long way to solve simple math if they’re taught that method. But they can mess up simple multiplication. By simplifying math concepts and showing real examples, teachers
can make math feel natural. This helps kids really understand math’s basic rules.
Child-Friendly Explanations
Offering child-friendly math explanations is crucial. It helps third graders, especially eight- and nine-year-old girls, understand proof in math. Using language suitable for their age, relatable
stories, and fun examples, teachers make complex math easy to grasp. They do this for topics like the Euler characteristic for connected graphs.
When teaching about Euler’s discovery that the Euler characteristic always equals two, teachers get creative. They encourage students to make their own graphs. Then, students test ideas in fun ways.
This hands-on approach and simplifying math concepts for kids make learning exciting. Students love finding out why the characteristic is always two.
Teachers can also add a step with algebra to make geometry proofs less daunting. This step helps kids feel more ready to tackle proof writing. It bridges the gap between simple and complex math
Explaining the difference between equality and congruence is also essential. Along with guided notes and clear steps, digital tools can help a lot. They make the learning process more interactive and
interesting. This way, kids get to understand math proofs better.
In the end, the secret to teaching math well is using relatable examples, simple language, and hands-on activities. With these methods, third graders can build a strong math foundation. They also
learn to love numbers for life.
Nurturing Math Skills
Math starts with building a solid base in children. We can make math fun by motivating them and cheering their successes, no matter how small. This helps them feel good about numbers and learn more
about proving math theories.
Encouraging Persistence
Many find math tough, but we can change this. Teaching kids to have a growth mindset is vital for boosting their math abilities. It’s all about showing them that hard work leads to improvement and
that making mistakes is part of the learning process. This makes them more likely to face math challenges with a positive spirit.
Celebrating Small Victories
It’s important to cheer for kids when they do well in math, even in small ways. This keeps them eager and active in learning. By praising their steps forward, creative problem solving, and improved
math sense, we create a support system. This encourages them to keep going and trying their best in math.
Teaching Math to Kids
Teaching mathematics to kids well means knowing how they learn. Every child learns differently. It’s vital to match the lesson to each student’s way of learning. This ensures all students can do
well, even those who find math tough.
Assessing Learning Styles
It’s key to figure out how each child learns best. For example, some love to see things visually, others need hands-on work, and some learn best by listening. Teachers mix different ways of teaching
to meet everyone’s needs. This helps students understand even the hardest parts of math.
Adapting to Individual Needs
Customizing math lessons for each student is very important. Some might need a few extra steps to understand, while others might grasp concepts quickly. By providing extra help for some and extra
challenges for others, every student gets what they need to succeed. This personalized approach helps everyone gain a deeper understanding of math.
Engaging Math Lessons
Math lessons with games and puzzles are a fun way for kids to learn about proof. Play makes learning exciting. It sparks curiosity and helps kids understand math better. With games, students also get
to work together. This teamwork helps them grasp proof techniques more deeply.
Incorporating Games and Puzzles
Math games and puzzles are great for teaching proof. They make learning fun and challenge students. Logic puzzles, for instance, help students think in a structured way. This is key for creating and
analyzing proofs.
Collaborative Learning Experiences
Working on math challenges together is very effective. It helps students understand proofs better. By discussing, sharing ideas, and solving problems together, they gain a stronger concept of math
proofs. This teamwork also improves their critical thinking, communication, and teamwork skills for future success.
Simplifying Proofs
Simplifying mathematical proofs is key for children to understand. By turning complex steps into smaller, relatable parts, educators can make learning easier. They use stories and real-life examples
to engage children in the process.
Breaking Down Complex Steps
Some students find it hard to move from solving algebra to proving theorems. An approach using the transitive property and substitution can make it clearer for them. Dividing these steps into smaller
ones boosts children’s confidence and deepens their understanding.
Using Analogies and Examples
Real-world examples help students get geometry before they write proofs. By linking maths to everyday life with stories and analogies familiar to kids, educators can simplify hard ideas. This
strengthens the ability to write proofs through intuitive learning.
Making Math Relatable
It’s vital to show kids how math can be used in their daily lives. This helps them really get into the subject. When we link math to real-life situations, we spark their interest and make them
curious. So, finding connections between math and life can turn math into something they love.
Connecting to Everyday Life
Many think math stays in the classroom, but it doesn’t have to be that way. We can show how math relates to their own experiences. For example, they can learn math from the shapes of shadows or the
patterns in nature. This helps them realize how math is everywhere.
Sparking Curiosity and Wonder
Exploring math through everyday examples is a great start. But we can do more to get them excited. For instance, we can share beautiful and simple math proofs. These proofs show the beauty of math.
They include Euclid’s work on prime numbers and the proof that square root of 2 is irrational.
We can also talk about books like Hans Magnus Enzensberger’s “The Number Devil”. It’s a fun way to learn about math. Discussing topics like infinity and whether math is made up or found is
interesting too. This makes students really think about math in new ways.
To make math interesting, we tie it with real life. Plus, we make it exciting by showing its wonders. Educators play a big role in helping kids love math. They do this by showing them the beauty of
math and its real-world applications.
Visual Aids for Math
The use of visual aids, like diagrams and illustrations, can boost math learning for kids. These tools help students understand hard ideas, see how to solve problems, and get more excited about math.
Diagrams and Illustrations
Diagrams and illustrations make math proofs easier and more fun for kids. They show abstract ideas in a clear way, helping students see how math concepts are connected. For instance, number lines
make addition and subtraction easier to understand. Strip diagrams are great for fractions and ratios.
Interactive Digital Resources
Interactive digital resources bring math proofs to life in a unique way. Apps and virtual tools let students learn math by doing, which helps them truly get the concepts. Using tech like interactive
whiteboards in class makes learning proofs exciting and gets students to take part more.
Fostering Math Understanding
Nurturing a deep understanding of mathematical proof in children involves more than just teaching formulas and procedures. It requires fostering an environment that encourages questions and
discussions. This allows students to explore ideas and gain a solid grasp of the underlying principles.
Creating a space where students feel comfortable asking questions and having open talks is key. Educators can help build a stronger foundation in mathematics this way. This foundation will support
students in their future academic and personal paths.
Emphasizing conceptual learning is essential for understanding mathematical proof. Instead of just memorizing and solving problems, the focus should be on grasping the concepts. This approach also
prepares students for complex mathematical challenges. It helps develop their critical thinking and problem-solving skills.
A mix of open discussions, teamwork, and mastering concepts can empower students. It makes them confident, adaptable, and eager to learn about math. This complete teaching method prepares students
for success and grows their love for mathematics.
In conclusion, turning math proofs into detective games can help children a lot. It boosts their intuition, grows their love for numbers, and enhances their critical thinking. With the help of cool
stories, hands-on stuff, and easy-to-understand math, teachers can make kids enjoy math more. This method ensures they get the hang of tough math ideas and lay a strong base for their math knowledge.
Since Paul Halmos introduced the “conclusion of maximal concision” in 1950, math proof has come a long way. Key moments include Ngô Bảu Châu’s proof of the “Fundamental Lemma” and Paul Erdos’s idea
of “The Book.” Erdos thought God kept the best proofs in it. This idea inspired others like Martin Aigner and Gunter M. Ziegler to create a similar “Book.”
By making math proofs fun, teachers help create future math lovers and thinkers. They encourage children to solve problems by making math exciting and easy to understand. This approach unlocks
students’ abilities and sparks their interest in math for life.
How can combining reading and problem-solving help make mathematical proof more engaging for kids?
The “Math Detective®” series mixes fun stories with math problems and charts. Students solve mysteries by answering questions. This way, math becomes an adventure and not just homework.
What are some ways to make math lessons more age-relevant and high-interest for children?
Using stories and scenarios that connect with kids’ lives can make math meaningful. This approach shows them how math matters outside the classroom. It turns learning into a fun and interesting
How can visual aids and hands-on activities help explain mathematical proof to children?
Pictures and interactive tools help kids see the math behind the words. Activities that let them touch and try the math make learning fun. Both tools make math clearer and more enjoyable.
What strategies can help children develop a strong math intuition and grasp the underlying principles of mathematical proof?
Getting a feel for numbers, making math simple, and linking it to life works. These steps help kids grasp math more deeply. Understanding the basics sets them up for harder math later on.
Why is it important to provide child-friendly explanations of mathematical proof?
Using words and examples that kids get is key. It builds a base for future math skills. This early understanding builds their confidence and liking for math.
How can educators nurture math skills and a growth mindset in children when teaching mathematical proof?
Cheering them on and focusing on learning’s wins is crucial. Teaching kids to face challenges positively helps them grow. This turns stumbles into steps toward learning more.
What considerations should teachers keep in mind when teaching mathematical proof to children with diverse learning styles?
Teachers should look at how each student learns best. Tweaking lessons for everyone’s style is vital. It ensures every child can understand the math being taught.
How can engaging math lessons that incorporate games, puzzles, and collaborative learning experiences help children learn mathematical proof?
Turning math into a social and playful experience is smart. It lures kids into problem-solving and understanding math better. Games and working together make the learning enjoyable.
What strategies can be used to simplify the process of mathematical proof for children?
Making steps simple, using stories and real-life examples, and focusing on big ideas is effective. It makes learning about math proofs clear and fun for kids. This method creates a strong base for
future math.
How can educators help children see the relevance and importance of mathematical proof in their everyday lives?
Linking math to real life and feeding their natural curiosity is key. This strategy shows the value of math and grows a love for it. It helps kids see math as something useful and exciting.
In what ways can visual aids, such as diagrams and interactive digital resources, enhance the learning of mathematical proof for children?
Images and interactive tools make math easy to see and engage with. They make learning fun and clear. These aids help kids understand complex math, making it more fun.
How can educators foster a deep understanding of mathematical proof by encouraging questions, discussions, and a focus on conceptual learning?
Creating a space for questions and deep talks helps kids learn math’s core ideas. This makes them confident and curious about math. It builds a strong love and understanding of the subject.
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Imagine Sarah, a young researcher, intrigued by patterns in nature. She finds a link between math and the tangled...
Knot Theory: Untangling the Loops in Mathematics | {"url":"https://www.littleexplainers.com/how-to-explain-mathematical-proof-to-a-child/","timestamp":"2024-11-12T22:42:34Z","content_type":"text/html","content_length":"274853","record_id":"<urn:uuid:988a1e3c-8b80-4b59-9500-c3543d6de1ed>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00558.warc.gz"} |
Transformations of Exponential graphs | Stage 5 Maths | HK Secondary S4-S5 Compulsory
A general exponential curve
The exponential curve given by $y=A\times b^{mx+c}+k$y=A×bmx+c+k represents a transformation of the basic curve $y=b^x$y=bx. Introducing constants enables the model to become a powerful tool in the
investigation of certain types of growth and decay phenomena. Modelling with theoretical functions in this way provides a great example of why the study of mathematics is so crucial to our
understanding of nature.
The functions $y=2^{5x+3}$y=25x+3 and $y=120\times2^{-x}$y=120×2−x are examples of the general exponential function given by $y=A\times b^{mx+c}+k$y=A×bmx+c+k, with both $A$A and $m$m non-zero. The
number $b$b is known as the base of the function, and it is strictly defined as a positive number not equal to 1.
For $y=2^{5x+3}$y=25x+3, we would say that $A=1$A=1, $b=2$b=2, $m=5$m=5, $c=3$c=3 and $k=0$k=0. For $y=120\times2^{-x}$y=120×2−x, we would say that $A=120$A=120, $b=2$b=2, $m=-1$m=−1, $c=0$c=0 and $k
The function $y=4-2\times\left(0.5\right)^{-x}$y=4−2×(0.5)−x has $A=-2$A=−2, $b=0.5$b=0.5, $m=-1$m=−1, $c=0$c=0 and $k=4$k=4. Each constant has a particular effect on the overall graph.
The constant $m$m is often called the growth constant (or decay constant if $m$m is negative). It can take on a range of non-zero values designed to suit particular real life growth or decay rates.
However, for our immediate purposes, we will restrict $m$m to non-zero integer values only.
We introduce all of these constants in order to accurately model real world phenomena. This is the power of a generalised model. We can adjust the constants to fit reality and in so doing learn more
about the way nature works.
A few key points
Whilst the general form is a comprehensive tool for sketching exponential curves, there are a few simpler observations to keep in mind. We can summarise them using examples as shown in this table:
Specific Example Observation
$y=-3^x$y=−3x Reflect $y=3^x$y=3x across the $x$x-axis
$y=3^{x-5}$y=3x−5 Translate $y=3^x$y=3x horizontally to the right by $5$5 units
$y=3^x-5$y=3x−5 Translate $y=3^x$y=3x vertically downward by $5$5 units
$y=2\times3^x$y=2×3x Double every $y$y value of $y=3^x$y=3x
$y=8-3^x$y=8−3x Reflect $y=3^x$y=3x across the $x$x axis then translate $8$8 units upward
More complex forms of the exponential require more thought. For example, the function $y=3^{2x-5}$y=32x−5 is quite interesting to think about. The applet below can produce the graph as a plot of
points, but we can think about what the curve might look like without it.
For example, we can rewrite the function as follows:
Hence, the function could be thought of as the function $y=9^x$y=9x translated to the right by $2\frac{1}{2}$212 units.
The applet
The applet below is extremely versatile, but we need to keep in mind that it is a learning tool exploring the effects of the different constants involved. As a guide, it might be helpful to use the
applet to create the four graphs shown in this table.
Verify the $y$y-intercepts of each graph, the limiting value of $y$y (this is the value that the function gets close to without actually ever reaching) and whether or not the graph is rising or
Function $y$y-intercept limiting value rising/falling
$y=2^x$y=2x $y=1$y=1 $y=0$y=0 rising
$y=3^{-x+1}$y=3−x+1 $y=1$y=1 $y=0$y=0 falling
$y=3\times4^x-2$y=3×4x−2 $y=1$y=1 $y=-2$y=−2 rising
$y=\left(0.5\right)^x$y=(0.5)x $y=1$y=1 $y=0$y=0 falling
After experimenting with these, try other combinations of constants. What can you learn?
BASES BETWEEN 0 AND 1
One final point that should be noted is that a curve like $y=\left(0.5\right)^x$y=(0.5)x is none other than $y=2^{-x}$y=2−x in disguise. Thus:
In a similar way we can say that $y=\left(\frac{1}{b}\right)^x=b^{-x}$y=(1b)x=b−x, and so every exponential curve of the form $y=b^x$y=bx, with a base $b$b in the interval $00<b<1, can be
re-expressed as $y=\left(\frac{1}{b}\right)^{-x}$y=(1b)−x. Since $b$b is a positive number, this means that exponential functions of the form $y=b^x$y=bx where $00<b<1 are in fact decreasing | {"url":"https://mathspace.co/textbooks/syllabuses/Syllabus-99/topics/Topic-4548/subtopics/Subtopic-58870/","timestamp":"2024-11-11T19:56:27Z","content_type":"text/html","content_length":"672019","record_id":"<urn:uuid:ef38aa08-f8ae-4947-b308-6e4654a31f79>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00781.warc.gz"} |
Improving Search Within Large C++ Functions - VimNotes
Improving Search Within Large C++ Functions
Searching within large C++ functions can be a daunting task, especially when dealing with extensive data sets and complex algorithms. However, understanding the intricacies of the C++ Standard
Library search functions and optimizing algorithms can lead to significant improvements in performance. This article delves into various strategies to enhance search efficiency, compares different
search algorithms, addresses common issues encountered in C++, and explores advanced techniques to refine your searching skills.
Key Takeaways
• Understanding the C++ Standard Library search functions like binary_search, lower_bound, and upper_bound is crucial for efficient searching.
• Optimizing search algorithms, such as binary search, and utilizing data structures like unordered sets and maps can greatly improve performance.
• Comparing search algorithms, including linear, binary, and interpolation search, helps in selecting the most appropriate method for a given problem.
• Solving common search-related problems in C++ involves debugging issues with custom data structures and resolving anomalies in constructor calls.
• Advanced search techniques, such as implementing sentinel linear search and optimizing custom data structures, can further enhance search capabilities.
Understanding C++ Standard Library Search Functions
Overview of binary_search, lower_bound, and upper_bound
The C++ Standard Library provides several search functions that are essential for efficient data retrieval in sorted collections. The binary_search, lower_bound, and upper_bound functions are
particularly useful for this purpose. Each function serves a unique role in searching: binary_search checks for the existence of a value, lower_bound finds the first element not less than the target,
and upper_bound locates the first element greater than the target.
When using these functions, it’s important to remember that they require the data to be sorted prior to the search. This precondition is crucial for the algorithms to function correctly and to ensure
optimal performance. Here’s a quick guide to their usage:
• binary_search: Determine if a value is present in a sorted range.
• lower_bound: Find the position to insert a value in a sorted range without violating the order.
• upper_bound: Identify the end of a range of equivalent values in a sorted sequence.
The correct application of these functions can significantly reduce the complexity of search operations, transforming a potentially linear time-consuming process into a logarithmic one.
Implementing Binary Search in C++
Binary Search is a fundamental algorithm in computer science, used to quickly locate an item in a sorted array. The process involves repeatedly dividing the search interval in half, a method that is
both efficient and effective for large datasets. The essence of binary search lies in its divide-and-conquer approach, which significantly reduces the time complexity compared to linear search
To implement binary search in C++, one must follow a series of steps:
1. Ensure the array is sorted.
2. Initialize two pointers, low and high, to the start and end of the array.
3. While low <= high, calculate the middle index mid.
4. Compare the middle element with the target value.
5. If they match, return the mid index.
6. If the middle element is greater, adjust high to mid - 1.
7. If the middle element is less, adjust low to mid + 1.
8. If the search ends with low > high, the target is not in the array.
It’s crucial to handle the calculation of mid carefully to avoid integer overflow. A robust choice is mid = low + (high – low) / 2.
While the concept of binary search is straightforward, its implementation can be nuanced, especially when dealing with edge cases or large data structures. Properly handling these cases is key to
ensuring the reliability and efficiency of the search.
Common Mistakes and Errors with STL Search Functions
When utilizing the C++ Standard Library’s search functions, such as binary_search, lower_bound, and upper_bound, developers often encounter a variety of errors. One of the most prevalent issues is
the misuse of comparison functions, leading to undefined behavior or incorrect results. Properly defining comparison functions is crucial for these algorithms to work as expected.
Another common pitfall is the incorrect usage of iterators. For instance, passing the wrong iterator range to these functions can cause them to search in unintended portions of the container or even
result in runtime errors. It’s essential to ensure that the iterators define a valid range within the container.
Here are some typical errors encountered with STL search functions:
• Compilation error related to map and unordered_map: "attempting to reference a deleted function"
• C++ error: no match for 'operator[]' when using custom data structures
• Move constructor called twice for std::function from a lambda with by-value captures
• Using an object reference as a key in std::unordered_map
Misunderstandings about the behavior of search functions in subarrays or with custom data structures can lead to subtle bugs. It’s important to review the documentation and understand the nuances of
each function.
Optimizing Search Algorithms in Large C++ Functions
Improving Binary Search Efficiency
Binary search is a powerful algorithm that can be used to solve a wide range of problems. To ensure its efficiency, especially within large functions, certain practices must be adhered to. Ensuring
the array is sorted is the first critical step, as binary search relies on the division of a sorted dataset to find an element.
The process involves setting two pointers, low and high, to the beginning and end of the search space, and iteratively adjusting them based on the comparison with the middle element. Here’s a concise
guide to the process:
1. Start with a sorted array or list.
2. Initialize low = 0 and high = length of the array – 1.
3. Calculate the middle index: mid = (low + high) / 2.
4. Compare the middle element with the target value.
5. Adjust the low and high pointers based on the comparison.
6. Repeat steps 3 to 5 until the element is found or the search space is exhausted.
By optimizing the calculation of the middle index to avoid potential overflow, such as using mid = low + (high – low) / 2, we can improve the robustness of binary search in large datasets.
Understanding the nuances of binary search, such as when to use lower_bound and upper_bound functions from the C++ Standard Library, can also lead to performance gains. These functions can handle
edge cases more gracefully and can be more efficient than a hand-rolled binary search in certain scenarios.
Utilizing Unordered Sets and Maps
When optimizing search algorithms within large C++ functions, unordered sets and maps play a crucial role due to their average constant-time complexity for search, insert, and delete operations.
Unlike ordered maps, unordered maps use a hash table where elements are organized based on their hash values rather than their order. This makes them particularly efficient for scenarios where the
order of elements is not important.
To insert a std::pair into an std::unordered_map, the [std::unordered_map::insert()](https://www.geeksforgeeks.org/how-to-insert-pair-into-unordered-map-in-cpp/) method is commonly used. This method
ensures that the pair is added to the map without affecting the order of other elements. For example, to insert a pair with a string key and an integer value, one would do the following:
std::unordered_map<std::string, int> map;
map.insert(std::make_pair("key", 42));
When dealing with large objects as keys, such as those encapsulating a large vector, it’s important to consider the impact on performance. Using pointers or smart pointers like std::shared_ptr can
avoid the costly copying of keys during insertion.
In cases where trivial keys are used, the choice between map and unordered_map may come down to specific use cases and performance requirements. It’s essential to profile and understand the
trade-offs involved in each scenario.
Handling Subarrays and Partial Searches
When dealing with large C++ functions, searching within subarrays or performing partial searches can be critical for maintaining performance. Efficiently handling subarrays often involves identifying
the segment of interest and applying a tailored search algorithm. For instance, the Largest Sum Contiguous Subarray problem, commonly solved using Kadane’s Algorithm, focuses on finding the maximum
sum contiguous subarray within a one-dimensional array of numbers. This is a classic example where a specialized approach outperforms a generic search.
In the context of partial searches, it’s important to define the boundaries of the search space accurately. A common technique is to use iterators or pointers to delineate the start and end of the
subarray. Here’s a simple strategy:
• Determine the subarray’s boundaries.
• Choose the appropriate search algorithm based on the subarray’s characteristics.
• Apply the algorithm within the defined boundaries to locate the desired element or pattern.
By carefully selecting the search region and algorithm, we can significantly reduce the computational complexity and improve the efficiency of our search operations within large functions.
When optimizing these searches, consider the data structure’s properties and the nature of the search problem. For example, if the subarray is sorted, binary search can be highly effective. However,
for unsorted data, a linear search might be necessary, albeit with optimizations like early termination when a match is found.
Comparative Analysis of Search Algorithms
Linear Search vs Binary Search: A Performance Showdown
When comparing linear search to binary search, the differences in performance are not just theoretical but can be significant in practice. Linear search, which performs equality comparisons, is
straightforward and does not require the data to be sorted. On the other hand, binary search, which performs ordering comparisons, necessitates a sorted array but offers a much faster search time for
large datasets.
The choice between linear and binary search can greatly affect the efficiency of an application, especially when dealing with large amounts of data.
Here’s a quick comparison of the two search methods:
• Linear search works on both multidimensional and single dimensional arrays, while binary search is typically used on single dimensional arrays.
• Binary search has a logarithmic time complexity (O(log n)), making it vastly superior for large datasets.
• Linear search has a linear time complexity (O(n)), which becomes impractical as the dataset size increases.
Interpolation Search vs Binary Search: When to Use Which
Interpolation search and binary search are both efficient algorithms for finding elements in sorted lists, but they differ significantly in their approach to locating the target element.
Interpolation search estimates the position of the target value by considering the values at the endpoints of the search range, which can lead to faster results if the elements are uniformly
distributed. Binary search, on the other hand, consistently divides the search space in half, making it a robust choice for any sorted list.
When deciding between interpolation search and binary search, consider the following points:
• Use interpolation search when dealing with large, uniformly distributed datasets where the target value’s approximate location can be easily predicted.
• Opt for binary search when the dataset’s distribution is unknown, non-uniform, or when working with smaller datasets where the overhead of calculation in interpolation search may not provide
significant benefits.
While binary search is a universally applicable method, interpolation search shines in scenarios where the distribution of values is known and can be leveraged to reduce search times.
Here’s a comparative analysis of the two algorithms:
Algorithm Best Case Average Case Worst Case
Binary Search O(1) O(log n) O(log n)
Interpolation Search O(1) O(log log n) O(n)
In conclusion, the choice between interpolation search and binary search should be guided by the dataset characteristics and the specific requirements of the search operation.
Binary vs Ternary Search: Understanding the Differences
When it comes to search algorithms, Binary Search is a well-known technique for its efficiency in sorted arrays. However, Ternary Search offers an alternative approach by dividing the search space
into three parts, using two splitting points, which can be advantageous in certain scenarios. Binary Search is typically used for Monotonic Functions, where the values are either strictly increasing
or decreasing. In contrast, Ternary Search is more suited for Unimodal Functions, where the objective is to find the maximum or minimum of a concave or convex function.
Ternary Search can be particularly useful in competitive programming, where finding the optimal solution quickly is crucial.
Here’s a comparison of key aspects of both search methods:
• Binary Search: Divides the search space into two parts; efficient for monotonic functions.
• Ternary Search: Divides the search space into three parts; ideal for unimodal functions.
While Binary Search is often the go-to choice due to its simplicity and effectiveness, Ternary Search can outperform it in specific cases, especially when dealing with complex search spaces that have
a single peak or trough.
Solving Common Search-Related Problems in C++
Debugging ‘operator[]’ Issues in Custom Data Structures
When working with custom data structures in C++, developers often encounter the dreaded ‘operator[]’ error. This error typically arises when attempting to access elements in a custom container that
does not properly support this operator, especially when the container is marked as const. A common scenario involves using std::unordered_map with a custom class as the key. To resolve this, ensure
that your class has a well-defined copy constructor and hash function, and that the operator== is properly overridden.
Here are some steps to debug ‘operator[]’ issues:
• Verify that the operator[] is correctly implemented for non-const and const instances.
• Check if the custom key class in unordered_map has a valid hash function and equality operator.
• Review the copy and move constructors to prevent unnecessary or erroneous calls.
Remember, the efficiency of your custom data structures directly impacts the performance of search operations. Inefficient copying or hashing can lead to significant slowdowns, particularly with
large objects or datasets.
Resolving Move Constructor Call Anomalies
When dealing with large C++ functions, particularly those involving containers like std::unordered_map, developers may encounter unexpected move constructor calls. Understanding the conditions under
which move constructors are invoked is crucial for optimizing performance and avoiding unnecessary object copies. For instance, when an object is used as a key in a map and does not have an efficient
move constructor, or when the move constructor is inadvertently deleted or not accessible, performance can degrade significantly.
To address these issues, consider the following steps:
• Ensure that your class is movable and that the move constructor is correctly implemented and accessible.
• If the class must have a special destructor, explicitly delete the copy/move constructors/operators if they are not needed.
• Avoid using large objects as keys in maps; consider using pointers or smaller proxy objects instead.
By carefully managing move semantics, developers can prevent the common pitfall of excessive move constructor calls, which can be particularly costly in large-scale data manipulations.
Remember that the choice of key in an unordered_map can have significant implications on performance. A move constructor call anomaly might indicate a deeper design issue that requires reevaluation
of the data structures in use.
Effective Use of Unordered Maps and Sets
In C++, unordered_map and unordered_set are powerful data structures designed for efficient access and manipulation of elements using hash tables. Optimizing these structures is crucial for achieving
O(1) operations and can significantly improve the performance of your program, especially when dealing with large datasets.
When choosing between std::map and unordered_map, it’s important to consider the nature of the keys. For trivial keys, unordered_map often provides a performance advantage due to its hash-based
implementation. However, when using custom class types as keys, ensure that your class is hashable and that the hash function is efficient to avoid performance bottlenecks.
Remember, the choice of data structure should align with your program’s requirements. Using pointers or making your class movable can mitigate the cost of copying large objects as keys.
Here are some common operations and their typical complexities in an unordered_map:
• Insertion: O(1) average, O(n) worst case
• Deletion: O(1) average, O(n) worst case
• Search: O(1) average, O(n) worst case
Understanding and utilizing these complexities can lead to more effective and optimized code.
Advanced Search Techniques in C++
Implementing Sentinel Linear Search
Sentinel Linear Search is an optimization of the traditional linear search algorithm. By placing the target element, known as the sentinel, at the end of the array, we can eliminate the need for a
boundary check on each iteration. This small change can lead to a significant reduction in the number of comparisons required, especially in large datasets.
The key to sentinel search lies in its simplicity; it cleverly reduces the overhead of checking array bounds, which can be particularly beneficial in tight loops.
To implement Sentinel Linear Search, follow these steps:
1. Append the target element to the end of the array.
2. Iterate through the array from the beginning.
3. If the current element matches the target, check if the index is within the original array bounds.
4. If within bounds, the element is found; otherwise, it’s not present in the original array.
While Sentinel Linear Search may not always be the best choice, it serves as a useful technique in scenarios where performance is critical and the overhead of traditional checks is a bottleneck.
Search Optimization in Custom Data Structures
Optimizing search within custom data structures is a pivotal step towards enhancing the performance of C++ applications. By tailoring search algorithms to the specific needs of the data structure,
significant gains in efficiency can be realized. This is particularly true for structures that are not well-served by generic algorithms.
For instance, a custom tree structure may benefit from a search algorithm that takes advantage of its unique branching patterns. Similarly, a graph data structure might require an algorithm that can
handle its complex connectivity. The key is to identify the characteristics of the data structure and design a search method that leverages those traits.
A case study will show that by optimizing data structures and algorithms, considerable performance improvements can be achieved.
It’s also crucial to consider the cost of operations like insertion, deletion, and updates, as these can affect the overall search performance. Below is a list of considerations for optimizing search
in custom data structures:
• Analyze the data structure’s properties and tailor the search algorithm accordingly.
• Evaluate the impact of other operations on search efficiency.
• Experiment with different search strategies to find the most effective one.
• Continuously profile and optimize the code to ensure peak performance.
Leveraging Medium Difficulty Search Problems to Improve Skills
Tackling medium difficulty search problems can significantly enhance a programmer’s problem-solving abilities in C++. These problems often strike a balance between the straightforwardness of easy
problems and the complexity of hard ones, providing a fertile ground for learning and improvement. For instance, problems like finding the median of two sorted arrays or searching in an almost sorted
array require a deeper understanding of algorithmic concepts and data structure manipulation.
• Median of two sorted arrays
• Search in an almost sorted array
• Find position in a sorted array of infinite numbers
• Pair with a given sum in a rotated sorted array
By consistently practicing medium difficulty problems, developers can build a robust foundation in search algorithms, which is crucial for tackling more complex challenges.
It’s important to approach these problems methodically, breaking them down into smaller, manageable components. This not only makes the problem less intimidating but also allows for a more structured
solution process. As you progress, you’ll find that the skills acquired from these exercises are transferable to a wide range of real-world applications.
Throughout this article, we’ve explored various strategies and techniques to enhance search functionality within large C++ functions. From leveraging the power of C++ Standard Library’s searching
algorithms to understanding the nuances of different searching approaches, we’ve covered a broad spectrum of topics. We delved into the intricacies of binary search, compared linear and binary search
methods, and even touched upon medium complexity problems that challenge our understanding of search algorithms. It’s clear that efficient search is crucial in optimizing the performance of C++
applications, and by applying the insights from this article, developers can significantly improve their code’s search capabilities. Remember, the key to mastering search within large functions lies
in choosing the right algorithm for the task at hand and implementing it with precision and care.
Frequently Asked Questions
What are the main binary search functions provided by the C++ Standard Library?
The C++ Standard Library provides binary_search, lower_bound, and upper_bound as the main binary search functions.
How does binary_search differ from lower_bound and upper_bound?
binary_search checks for existence of a value, while lower_bound and upper_bound return iterators to the lower and upper bounds of a range that includes the value.
Can binary search be used on subarrays in C++?
Yes, binary search can be adapted to work on subarrays by providing the appropriate range of iterators.
What are some common mistakes when using STL search functions?
Common mistakes include not ensuring the range is sorted, using incorrect iterators, and misunderstanding the return values of these functions.
How can unordered sets and maps improve search efficiency?
Unordered sets and maps use hash tables, offering average constant time complexity for search operations, which is faster than binary search for large datasets.
What is Sentinel Linear Search and how does it differ from regular linear search?
Sentinel Linear Search places the target element at the end of the array, eliminating the need for bound checking during iteration. It can be more efficient than regular linear search. | {"url":"https://vimnotes.com/improving-search-within-large-c-functions/","timestamp":"2024-11-12T08:22:25Z","content_type":"text/html","content_length":"128349","record_id":"<urn:uuid:7f698e46-fef2-4fe1-bacb-a33aa3c5a877>","cc-path":"CC-MAIN-2024-46/segments/1730477028249.89/warc/CC-MAIN-20241112081532-20241112111532-00514.warc.gz"} |
Hello and a warm welcome to everyone! We're excited to have you in the Cody Discussion Channel. To ensure the best possible experience for everyone, it's important to understand the types of content
that are most suitable for this channel.
Content that belongs in the Cody Discussion Channel:
• Tips & tricks: Discuss strategies for solving Cody problems that you've found effective.
• Ideas or suggestions for improvement: Have thoughts on how to make Cody better? We'd love to hear them.
• Issues: Encountering difficulties or bugs with Cody? Let us know so we can address them.
• Requests for guidance: Stuck on a Cody problem? Ask for advice or hints, but make sure to show your efforts in attempting to solve the problem first.
• General discussions: Anything else related to Cody that doesn't fit into the above categories.
Content that does not belong in the Cody Discussion Channel:
• Comments on specific Cody problems: Examples include unclear problem descriptions or incorrect testing suites.
• Comments on specific Cody solutions: For example, you find a solution creative or helpful.
Please direct such comments to the Comments section on the problem or solution page itself.
We hope the Cody discussion channel becomes a vibrant space for sharing expertise, learning new skills, and connecting with others.
I was browsing the MathWorks website and decided to check the Cody leaderboard. To my surprise, William has now solved 5,000 problems. At the moment, there are 5,227 problems on Cody, so William has
solved over 95%. The next competitor is over 500 problems behind. His score is also clearly the highest, approaching 60,000.
Please take a moment to congratulate @William.
I've been working on some matrix problems recently(Problem 55225)
and this is my code
It turns out that "Undefined function 'corr' for input arguments of type 'double'." However, should't the input argument of "corr" be column vectors with single/double values? What's even going on
I am trying to earn my Intro to MATLAB badge in Cody, but I cannot click the Roll the Dice! problem. It simply is not letting me click it, therefore I cannot earn my badge. Does anyone know who I
should contact or what to do?
function ans = your_fcn_name(n)
The Ans Hack is a dubious way to shave a few points off your solution score. Instead of a standard answer like this
function y = times_two(x)
y = 2*x;
you would do this
function ans = times_two(x)
The ans variable is automatically created when there is no left-hand side to an evaluated expression. But it makes for an ugly function. I don't think anyone actually defends it as a good practice.
The question I would ask is: is it so offensive that it should be specifically disallowed by the rules? Or is it just one of many little hacks that you see in Cody, inelegant but tolerable in the
context of the surrounding game?
Incidentally, I wrote about the Ans Hack long ago on the Community Blog. Dealing with user-unfriendly code is also one of the reasons we created the Head-to-Head voting feature. Some techniques are
good for your score, and some are good for your code readability. You get to decide with you care about.
Twitch built an entire business around letting you watch over someone's shoulder while they play video games. I feel like we should be able to make at least a few videos where we get to watch over
someone's shoulder while they solve Cody problems. I would pay good money for a front-row seat to watch some of my favorite solvers at work. Like, I want to know, did Alfonso Nieto-Castonon just sit
down and bang out some of those answers, or did he have to think about it for a while? What was he thinking about while he solved it? What resources was he drawing on? There's nothing like watching a
master craftsman at work.
I can imagine a whole category of Cody videos called "How I Solved It". I tried making one of these myself a while back, but as far as I could tell, nobody else made one.
I hereby challenge you to make a "How I Solved It" video and post it here. If you make one, I'll make another one.
There are a host of problems on Cody that require manipulation of the digits of a number. Examples include summing the digits of a number, separating the number into its powers, and adding very large
numbers together.
If you haven't come across this trick yet, you might want to write it down (or save it electronically):
digits = num2str(4207) - '0'
That code results in the following:
Now, summing the digits of the number is easy:
I'm having problem in its test 6 ... passing 5/6 what would be the real issue..
am wring Transformation matrix correct.. as question said SSW should be 202.5 degree...
so what is the issue..
I'm trying to solve one problem in Cody, but a function 'fmincon' is not recognized by the online compiler. Is there any way to use functions in optimization toolbox in Cody?
That's the question:
The file cars.mat contains a table named cars with variables Model, MPG, Horsepower, Weight, and Acceleration for several classic cars.
Load the MAT-file. Given an integer N, calculate the output variable mpg.
Output mpg should contain the MPG of the top N lightest cars (by Weight) in a column vector.
I wrote this code and the resulting column vector has the right values but it doesn't pass the tests. What's wrong?
function mpg = sort_cars(N)
Thats the task:
Given a square cell array:
x = {'01', '56'; '234', '789'};
return a single character array:
I wrote a code that passes Test 1 and 2 and one that passes Test 3 but I'm searching a condition so that the code for Test 3 runs when the cell array only contains letters and the one for Test 1 and
2 in every other case. Can somebody help me?
This is my code:
That's the question: Given four different positive numbers, a, b, c and d, provided in increasing order: a < b < c < d, find if any three of them comprise sides of a right-angled triangle. Return
true if they do, otherwise return false .
I wrote this code but it doesn't pass test 7. I don't really understand why it isn't working. Can somebody help me?
function flag = isTherePythagoreanTriple(a, b, c, d)
Hi, I'm trying to solve this problem but I'm getting an error so far.
Given a vector a, find the number(s) that is/are repeated consecutively most often. For example, if you have
a = [1 2 2 2 1 3 2 1 4 5 1]
The answer would be 2, because it shows up three consecutive times
What I've written so far (not done):
a = [1 2 2 2 1 3 2 1 4 5 1];
[x,y] = size(a);
counter = zeros(1,10);
if x == 1
for i=1:1:y
if a(i) == a(i+1)
counter(a(i)) = counter(a(i))+1
for i=1:1:x
if a(i) == a(i+1)
counter(a(i)) = counter(a(i))+1
But it says "error" in the line of "if a(i) == a(i+1)". I noticed that it creates a variable called "i" which value is 11, but it should create a vector from 1 to 11. What's wrong here?
I know my solution might not be in the right direction or something, but please don't tell me anything!
Thanks in advance
If a large number of fair N-sided dice are rolled, the average of the simulated rolls is likely to be close to the mean of 1,2,...N i.e. the expected value of one die. For example, the expected value
of a 6-sided die is 3.5.
Given N, simulate 1e8 N-sided dice rolls by creating a vector of 1e8 uniformly distributed random integers. Return the difference between the mean of this vector and the mean of integers from 1 to N.
function dice_diff = loln(N)
dice_diff =abs(M-m);
Here is my code, but it can't work out as it needs too long time to creat A.
I recently have found that I am no longer able to give my difficulty rating for questions on Cody after sucessfully completing a question. This is obviously not a big deal, I was just wondering if
this was an issue on my end or if there was some change that I was not aware of.
The option to rate does not pop up after solving a problem, and the rating in general does not even show up anymore when answering questions (though it is visible from problem groups).
When solving problems over on Cody, I can almost always view all solutions to a problem after submitting a correct solution of my own. Very rarely, however, this is not the case, and I instead get
the following message:
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
You may solve another problem from Community group to unlock all the solutions to this problem.
If this happens, then again, I can almost always rectify this by submitting a (correct) solution to a different problem (I take it that the Community group is the implicit group of all problems on
Cody --- is it?). But sometimes that, too, fails.
So my question is, why? What are the criteria that determine when all solutions are, in fact, unlocked?
(There is a related question here, but I feel the posted answer does not answer the question.)
I have submitted a problem in cody some days back. Now it is not showing in my profile. Initially it was accepted and some people submitted the solutions also, however It has been removed after that,
are there some guidelines which I am not following?
Simple question: I noticed there's a Modeling & Simulation Challenge Master badge over on Cody, but I can't find the corresponding group. So: where is it? Does it still exist at all?
I created a problem in Cody that approximates e. To test the user's solution, I compare their solution to e. What I want to do instead is compare the user's solution to my reference solution. The
question is how do I call the reference solution in the test suite?
This is currently my test suite.
y_correct = playgame(); | {"url":"https://it.mathworks.com/matlabcentral/discussions/cody/?view=full","timestamp":"2024-11-03T23:09:04Z","content_type":"text/html","content_length":"212342","record_id":"<urn:uuid:98cc8612-5e18-4e7b-aaf8-b200070aa051>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00898.warc.gz"} |
Stabilization distance bounds from link Floer homology
We consider the set of connected surfaces in the 4-ball with boundary a fixed knot in the 3-sphere. We define the stabilization distance between two surfaces as the minimal (Formula presented.) such
that we can get from one to the other using stabilizations and destabilizations through surfaces of genus at most (Formula presented.). Similarly, we consider a double-point distance between two
surfaces of the same genus that is the minimum over all regular homotopies connecting the two surfaces of the maximal number of double points appearing in the homotopy. To many of the concordance
invariants defined using Heegaard Floer homology, we construct an analogous invariant for a pair of surfaces. We show that these give lower bounds on the stabilization distance and the double-point
distance. We compute our invariants for some pairs of deform-spun slice disks by proving a trace formula on the full infinity knot Floer complex, and by determining the action on knot Floer homology
of an automorphism of the connected sum of a knot with itself that swaps the two summands. We use our invariants to find pairs of slice disks with arbitrarily large distance with respect to many of
the metrics we consider in this paper. We also answer a slice-disk analog of Problem 1.105 (B) from Kirby's problem list by showing the existence of non-0-cobordant slice disks.
All Science Journal Classification (ASJC) codes
Dive into the research topics of 'Stabilization distance bounds from link Floer homology'. Together they form a unique fingerprint. | {"url":"https://collaborate.princeton.edu/en/publications/stabilization-distance-bounds-from-link-floer-homology","timestamp":"2024-11-02T05:42:45Z","content_type":"text/html","content_length":"50137","record_id":"<urn:uuid:740c7889-5900-4450-b85e-d4abe6bde9e5>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00198.warc.gz"} |
Find the Largest Cube formed by deleting minimum number of digits from a number
Open-Source Internship opportunity by OpenGenus for programmers. Apply now.
Reading time: 20 minutes | Coding time: 5 minutes
Given a number N, our task is to find the largest perfect cube that can be formed by deleting minimum digits (possibly 0) from the number. Any digit can be removed from the given number to reach the
X is called a perfect cube if X = Y^3 for some integer Y.
If the number cannot be perfect cube print -1.
let N = 1205;
if we remove 0 from the above number we will get 125 as remaning number, which is cube root of 5(5 * 5 * 5 = 125).
let N = 876
if we remove 7 and 6 then we will have 8 which is cube root of 2 (2 * 2 * 2 = 8)
We explored two approaches:
• A brute force approach O(2^N)
• A greedy approach O(N^(1/3)log(N)log(N))
Naive Solution O(2^N)
Check for every subsequence of the number check the number is cube or not and then compare it with the maximum cube among them.
To generate all substring we remove last character so that next permutation can be generated.
We have a number num = "123"
we add each element to curr string which will give us:
after this the recuression will return back with "12", then '2' is removed and the next iteration will be called which will give subsequence "13". This will complete the resuresion for '1', the
subsequence will start from '2' which will give "2" and "23" after that "3".
This will give all the subsequence of the given number 123
#include <bits/stdc++.h>
using namespace std;
#define ll long long
ll mx = INT_MIN;
bool is_Cube(ll x)
int found = 0;
for (int i = 2; i <= (x / 2); i++)
if (x % i == 0)
if ((i * i * i) == x)
found = 1;
if (found == 1)
return true;
return false;
void printSubSeqRec(string str, int n, int index = -1, string curr = "")
if (index == n)
if (curr != "")
ll temp = stoi(curr);
if (is_Cube(temp))
mx = max(mx, temp);
for (int i = index + 1; i < n; i++)
curr += str[i];
printSubSeqRec(str, n, i, curr);
curr = curr.erase(curr.size() - 1);
int main()
int nums = 102050;
string str = to_string(nums);
printSubSeqRec(str, str.size());
if (mx != INT_MIN)
cout << mx;
cout << "NOT FOUND ANY CUBE";
return 0;
The Time complexity of the above code is more than 2^n, where n is the number of digit the given number.
Greedy Algorithm O(N^(1/3)log(N)log(N))
Now, we know that the largest cube will be smaller the number its self, so we can generate perfect cubes of all numbers from 1 to N, and keep them in an array, after that starting from the largest
cube we check if the cube is a subsequence of the given number if yes then we got the desired number otherwise no such number exists.
Given Number is N = 102050
we generate all the perfect cube from 1 to N.
Now we check from the largest number weather its a subsequence of the given N number.
like here 1000 is the subsequence of 102050, so 1000 is the Largest Cube formed by Deleting minimum Digits from a number.
To check if a number is a subsequence of the given number, we iterate over the number and check if the each digit is present in the the number or not.
Eg: we have a number nums = 1025, and we have a perfect cube pc = 125, we iterate over the nums, check if nums[0] is equal to pc[index], then we move to check nums[1] is equal to pc[1], then nums[2]
with pc[1], next nums[3] with pc[2], if we reach the end of the pc then pc is a subsequence of the nums, other wise not.
#include <bits/stdc++.h>
using namespace std;
// Returns vector of Pre Processed perfect cubes
vector<string> calPerfectCube(long long int n)
vector<string> perfectCubes;
for (int i = 1; i * i * i <= n; i++) {
long long int iThCube = i * i * i;
// convert the cube to string and push into
// perfectCubes vector
string cubeString = to_string(iThCube);
return perfectCubes;
//Returns the Largest cube number that can be formed
string CheckSubSequence(string num, vector<string> perfectCubes)
// reverse the calPerfectCubeed cubes so that we
// have the largest cube in the beginning
// of the vector
reverse(perfectCubes.begin(), perfectCubes.end());
int totalCubes = perfectCubes.size();
// iterate over all cubes
for (int i = 0; i < totalCubes; i++) {
string currCube = perfectCubes[i];
int digitsInCube = currCube.length();
int index = 0;
int digitsInNumber = num.length();
for (int j = 0; j < digitsInNumber; j++) {
// check if the current digit of the cube
// matches with that of the number num
if (num[j] == currCube[index])
if (digitsInCube == index)
return currCube;
// if control reaches here, the its
// not possible to form a perfect cube
return "Not Possible";
void FLC(long long int n)
// pre process perfect cubes
vector<string> perfectCubes = calPerfectCube(n);
// convert number n to string
string num = to_string(n);
string ans = CheckSubSequence(num, perfectCubes);
cout << "Largest Cube is " << ans << endl;
// Driver Code
int main()
long long int n;
n = 105200;
return 0;
Largest Cube is 1000
• Worst case time complexity:O(N^(1/3)log(N)log(N)
• Space complexity: O(N^(1/3)) | {"url":"https://iq.opengenus.org/find-the-largest-cube-formed-by-deleting-minimum-digits-from-a-number/","timestamp":"2024-11-07T23:11:24Z","content_type":"text/html","content_length":"64081","record_id":"<urn:uuid:99c959d0-9b96-4060-953a-3b28bf6b5100>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00200.warc.gz"} |
NA Digest
NA Digest Monday, October 28, 2013 Volume 13 : Issue 36
Today's Editor:
Daniel M. Dunlavy
Sandia National Labs
Today's Topics:
• Subscribe, unsubscribe, change address, or for na-digest archives:
Submissions for NA Digest:
From: Joseph Grcar jfgrcar@gmail.com
Date: October 22, 2013
Subject: Edinburgh Mathematical Laboratory 100th Anniversary
This month is the 100th anniversary of what was likely the earliest
academic program in Computational Science and Engineering, the
Edinburgh Mathematical Laboratory (EML).
EML was established when Edmund Whittaker took the mathematics chair
at Edinburgh in 1913. As the former royal astronomer of Ireland,
Whittaker's appointment illustrates the dominance of astronomy in
mathematics though the turn of the 20th century. Whittaker's interest
in astronomy, and the need for calculation in astronomy, fit well with
a faculty who had recently lost both Peter Guthrie Tait, the
collaborator of William Thomson (the two were known as T and T'), and
also Edward Sang, a calculator of mathematical tables (to 26 places,
The mathematics laboratory was inaugurated in October, 1913 at a
colloquium of the Edinburgh Mathematical Society. Whittaker
demonstrated a calculation for astronomy in the laboratory's large
classroom, which seated eighty people at special computing desks. The
next colloquium in 1914 coincided with the tercentenary of the
invention of logarithms by arguably Edinburgh's most famous son, John
Napier. His logarithms are the oldest modern mathematics, and note,
they are computational mathematics. The exhibition catalog describes a
huge collection of computing paraphernalia with some items from the
EML that suggest what else may have been in the computing classroom:
books of tables, calculating machines (Brunsviga, Millionaire, etc.),
computing forms for harmonic analysis, models of curves and surfaces,
and a pantograph.
Edinburgh University made an effort to promote the EML. A curriculum
emphasizing calculations in astronomy was announced in at least one
foreign (German) journal. The laboratory invited researchers,
solicited students, and offered degrees up to the D.Sc. Six EML books
including four texts for courses were published in 1915 to positive
reviews. There is no further mention of the EML, which may have been
an indirect casualty of the first World War. A course entitled
"mathematical laboratory" was taught at Edinburgh from about 1920
until 1960 when the name was changed to "numerical analysis".
From: Antonella Zanna anto@math.uib.no
Date: October 24, 2013
Subject: Call for Nominations, Stephen Smale Prize
The second Stephen Smale Prize will be awarded in the meeting
Foundations of Computational Mathematics (FoCM) in Montevideo in
December 2014, http://www.fing.edu.uy/~jana/www2/focm_2014.html
Nominations should be sent to FoCM secretary Antonella Zanna at:
Deadline: 24:00 (GMT), March 10, 2014
Full announcement of prize here:
http://focm-society.org/smale_prize.php .
The Society for the Foundations of Computational Mathematics was
created in the summer of 1995, following the month-long meeting in
Park City, Utah, which was principally organized by Steve Smale. The
Park City meeting aimed, in Smale's words from the preliminary
announcement, “to strengthen the unity of mathematics and numerical
analysis, and to narrow the gap between pure and applied mathematics."
Smale's vision has been the Society's inspiration for all these
years. The journal Foundations of Computational Mathematics was
created, several colloquia and research semesters were organized and
international conferences are held every three years. After fifteen
years of existence, with an established and recognized position in the
scientific community, the Society has created the "Stephen Smale
Prize" whose objective is to recognize the work of a young
mathematician in the areas at the heart of the society's interests and
to help to promote his or her integration among the leaders of the
scientific community. The first Stephen Smale Prize was awarded at the
Budapest meeting in 2011 to Snorre H. Christiansen.
From: Patrick Farrell patrick.farrell@maths.ox.ac.uk
Date: October 25, 2013
Subject: 14th European AD Workshop, UK, Dec 2013
The 14th European AD Workshop
Mathematical Institute, University of Oxford, UK
December 9--10, 2013
This two day workshop is the fourteenth in the series of the EuroAD
Automatic Differentiation workshops, which take place twice a year.
These workshops provide a forum for the presentation of theoretical
developments in and applications of Automatic Differentiation (AD) and
adjoint methods. The workshop is informal and presentations on
subjects such as work in progress, problem areas for AD, or possible
application areas, as well as completed work are welcome. We
particularly encourage PhD students and those new to the field to
attend and present their work. The workshop is hosted by the
Mathematical Institute of the University of Oxford.
Registration: If you are willing to present or participate, please
register on
If you would like to give a 25-minute talk, please send a title and
abstract to patrick.farrell@maths.ox.ac.uk by November 25th, 2013.
From: Bert de Jong wadejong@lbl.gov
Date: October 25, 2013
Subject: Bay Area Scientific Computing Day, USA, Dec 2013
We are pleased to announce that the Bay Area Scientific Computing Day
(BASCD) will be hosted by LBNL on December 11, 2013.
BASCD is an annual one-day meeting focused on fostering interactions
and collaborations between researchers in the fields of scientific
computing and computational science and engineering from the San
Francisco Bay Area. The event provides junior researchers a venue to
present their work to the local community, and for the Bay Area
scientific and computational science and engineering communities at
large to interchange views on today’s multidisciplinary computational
challenges and state-of-the-art developments.
The speakers at this year’s meeting are Kevin Carlberg (Sandia), Erin
Carson (UC Berkeley), Lixin Ge (SLAC), Jeff Irion (UC Davis), Lex
Kemper (LBNL), Christian Linder (Stanford University), Ding Lu (UC
Davis), Ali Mani (Stanford University), François-Henry Rouet (LBNL),
Cindy Rubio-Gonzalez (UC Berkeley), Khachik Sargsyan (Sandia) and
Samuel Skillman (SLAC).
This year we will have a combined lunch and poster session. If you are
interested in presenting a poster, please indicate this during
registration.The schedule, registration, and the title and abstract of
the speakers are available on the BASCD website:
Please distribute this announcement to others who may be
interested. Looking forward to seeing you all at the 2013 Bay Area
Scientific Computing Day on December 11, 2013 at LBNL.
From: David Gleich dgleich@purdue.edu
Date: October 27, 2013
Subject: Stanford SVG70 Meeting, USA, Jan 2014
The SVG70 Meeting, Stanford University
January 25, 2014 - All day.
Registration is now open for the SVG70 Meeting, which will celebrate
the birthdays and accomplishments of Michael Saunders, Jim Varah, and
Alan George. The one-day workshop on numerical linear algebra and
optimization will be followed by a banquet dinner.
Space is limited and registration closes on December 15th.
For registration and other details, see
Confirmed invited speakers:
Iain Duff (Rutherford Appleton Laboratory)
John Gilbert (UC Santa Barbara)
Philip Gill (UC San Diego)
Joseph Grcar
Anne Greenbaum (University of Washington)
Scott MachLachlan (Tufts University)
Dominique Orban (Ecole Polytechnique de Montreal)
Michael Overton (New York University)
Chris Paige (McGill University)
From: Travis Austin austint73@gmail.com
Date: October 25, 2013
Subject: Engineer Position, HPC Scientist, MSC Software
MSC Software, based in Newport Beach, CA, has an opening for a
Development Engineer 3 and/or 4 - HPC Scientist. The HPC Scientist
will create innovative parallel methods and implementations providing
an overall speedup to company-wide products. We are particularly
interested in job candidates with experience in solving large complex
eigenvalue problems.
This role is part of a distributed and highly collaborative team of
motivated HPC Scientists driven to create the fastest HPC solutions
possible. The successful candidate will be involved in reviewing
parallel method proposals from fellow group members for merit and
estimating time for development. Initial focus will be on the
development of innovative eigenvalue solvers with additional focus on
assisting in accelerating existing sparse direct and iterative
solution methods.
Please go to http://www.mscsoftware.com/careers/job-listings and
refer to Job ID 1652.
From: JIE SHEN shen7@purdue.edu
Date: October 22, 2013
Subject: Professor Position, Applied Mathematics, Purdue
The Department of Mathematics at Purdue University invites
applications for an appointment at the rank of tenured full professor
to fill the newly endowed Andris A. Zoltners Professorship in
Mathematics. A Ph.D. (or its equivalent) in mathematics or a closely
related field is required. The target area is applied mathematics. We
are expecting applications from candidates with an outstanding record
of research accomplishment, internationally recognized stature,
credentials suitable for immediate nomination as a Distinguished
Professor, and great potential for future work.
Direct all inquiries to goeke@math.purdue.edu. Review of applications
will begin immediately, and applications will be considered on a
continuing basis until the position is filled.
From: Kyle Rader kwrader@asu.edu
Date: October 22, 2013
Subject: Professor Position, Statistics, Arizona State Univ
Associate or full Professor (JOB# 10571)
School of Mathematical and Statistical Sciences
Arizona State University
The School of Mathematical and Statistical Sciences (SoMSS) at
Arizona State University invites applications for a tenured or
tenure-track position as associate or full professor in statistics
or applied statistics beginning in fall 2014. Rank and tenure will
be commensurate with experience.
The successful candidate must have a Ph.D. in the mathematical or
statistical sciences with a research emphasis in statistics and/or
its applications to other disciplines and an outstanding record of
excellence in research and teaching at the graduate and
undergraduate levels.
Applications must be submitted online through
All applications must include the following:
1. Cover letter
2. Curriculum vitae
3. Personal statement addressing the candidate's research program
4. Statement of teaching and service/administrative experience
5. At least four names and e-mail addresses of experts who would be
willing to serve as referees on the candidate's research, teaching
and service (the referees will be contacted later for letters for
those candidates who pass through an initial screening).
The application deadline is December 10, 2013; if not filled, every
two weeks thereafter until the search is closed.
Informal inquiries may be sent to Al Boggess, Director of SoMSS
From: Boyce Griffith boyceg@unc.edu
Date: October 25, 2013
Subject: Faculty Position, Applied Mathematics, UNC-Chapel Hill
The Department of Mathematics of the University of North Carolina at
Chapel Hill invites applications for a tenure track position in
applied mathematics at the assistant professor level starting on July
1, 2014. Candidates are sought to enhance the interdisciplinary focus
of the applied mathematics research group. We specifically seek
applicants who will work to establish an externally funded research
program that actively collaborates with researchers in the biological,
computer, environmental, medical, physical, or social sciences. A
Ph.D. or equivalent degree is required, and some postdoctoral
experience, outstanding research promise, and dedication to excellent
teaching are expected.
To be considered for this position, applicants must apply online by
December 1, 2013 both at:
and also at:
Further information is available at http://www.math.unc.edu, and
specific questions can be referred to Roberto Camassa at
The University of North Carolina is an Equal Opportunity Employer.
From: Michael Smiley mwsmiley@iastate.edu
Date: October 23, 2013
Subject: Faculty Position, Mathematical Biology, Iowa State Univ
The Department of Mathematics at Iowa State University invites
applications for a position at the assistant or associate professor
level beginning August 16, 2014. The Department is seeking a
candidate with research expertise in the application of mathematics to
the biological sciences, and demonstrated excellence in teaching. For
more detailed information about the position and application
requirements, interested candidates should consult the
Department's web page:
From: Timo Betcke t.betcke@ucl.ac.uk
Date: October 22, 2013
Subject: Postdoc Fellowship, Univ College London
The Department of Mathematics at University College London invites
applications from outstanding postdoctoral researchers for the
Clifford Fellowship in Mathematics. This is a new 3-year developmental
research fellowship at UCL available from August 2014 for talented
mathematicians. Candidates should, allowing for career and other
breaks, have less than four years postdoctoral research experience in
an academic environment.
The successful candidate is expected to undertake high standard
research in pure or applied mathematics leading to conference
presentations and publications in leading journals, and to contribute
to the research environment of the department through interaction with
staff and students. A limited amount of teaching at undergraduate
level will be expected.
Application closing date is 1 December 2013. Interviews are planned
for January 2014.
Informal enquiries may be addressed to Professor Robb McDonald,
Head of Department tel. +44 (0)20-7679-2853, email:
n.r.mcdonald@ucl.ac.uk, Professor Valery Smyshlyaev, Head of
Applied Mathematics tel. +44 (0)20-7679-3854, email:
v.smyshylaev@ucl.ac.uk, or Professor Leonid Parnovski, Head of Pure
Mathematics tel. +44 (0)20-7679-2847, email: l.parnovski@ucl.ac.uk.
Further details are available at:
From: Colin Cotter colin.cotter@imperial.ac.uk
Date: October 28, 2013
Subject: Postdoc Position, Mathematics, Imperial College London
A three year postdoc position is available at the Department of
Mathematics, Imperial College London, under the supervision of Dr
Colin Cotter who has recently been appointed there. The position is
funded from a NERC-funded project on understanding how discretisation
error and model error around under-resolved fronts can effect the
prediction of the large scale circulation in numerical weather
prediction models. This project is in collaboration with Prof Mike
Cullen at the UK Met Office.
This project is at the interface between numerical analysis and
geophysical fluid dynamics and we are inviting candidates with
expertise in one or (preferably) both of these areas.
A link to the application form, together with a detailed job
description and person specification, for the position is given below:
From: Andreas Dedner a.s.dedner@warwick.ac.uk
Date: October 27, 2013
Subject: Postdoc Position, NA/Scientific Computing, Warwick, UK
Applications are invited for a Postdoctoral Research Associate in
Numerical Analyis/Modelling/Scientific Computing to work with Dr.
A. Dedner (University of Warwick, Mathematics), Prof S. Arridge (UCL
Centre for Medical Image Computing) and Dr T. Betcke (UCL Mathematics)
on schemes for coupling finite element and boundary element methods
(FEM+BEM) with applications to medical imaging. The aim is to combine
two existing packages (DUNE and BEM++), building a powerful software
platform for solving a wide range of problems involving
discretizations on surfaces and in bulk domains using HPC
facilities. This is part of a large interdisciplinary group,
researching finite element and boundary element methods, their
application and implementation. The group involves both experts in
FEM/BEM and in Electrical Impedance Tomography, Ultrasound and Optical
Tomography, including industrial collaboration.
Key Requirements:
The Research Associate will contribute to the development of the
methods and their implementation for large-scale problems on high
performance computing facilities. A strong background in mathematics,
scientific computing or related areas is required. In particular,
candidates should have experience with finite and/or boundary element
methods. Software development experience in C++ is essential.
Further Details:
From: Karl Meerbergen karl.Meerbergen@cs.kuleuven.be
Date: October 27, 2013
Subject: Postdoc Positions, HPC for Life Sciences
KU Leuven (Karl Meerbergen) and University of Antwerp (Wim Vanroose)
have three postdoctoral research positions for a joint research
project on high performance computing for Life Sciences. The project
is funded in part by Intel and Johnson&Johnson pharmaceuticals. The
topic of the research is the development of HPC algorithms for the
solution of ODEs/PDEs with stochastic parameters with the aim to
improve the efficiency of parameter estimation problems from the
pharmaceutical industry.
The successful candidate should be interested in high performance
computing, inverse problems, high dimensional numerical integration
and parametric model order reduction and is expected to have expertise
in at least one of these themes. In addition, the interested candidate
should be willing to develop code in C++. The researchers will work in
close collaboration with both teams from Leuven and Antwerp and
scientists from Johnson&Johnson and Intel. Part of the time will be
spent in the ExaScience lab in Leuven, an interdisciplinary lab on
software, bio-statistics, bio-informatics and hardware simulation. The
initial contract is for one year with a possible extension after
positive evaluation.
Candidates should send their CV with full list of publication to
Wim.Vanroose@ua.ac.be and Karl.Meerbergen@cs.kuleuven.be
From: Marcus Garvie mgarvie@uoguelph.ca
Date: October 24, 2013
Subject: PhD Position, Finite Element Simulation, Univ of Guelph, Canada
A PhD position is offered in the Department of Mathematics &
Statistics at the University of Guelph, Ontario Canada, see
The application area is mathematical ecology, in particular,
metapopulation dynamics, which will combine theoretical techniques
from Reaction Diffusion Equations (systems of Partial Differential
Equations (PDEs)), the Finite Element Method (a numerical method for
solving PDEs), and Scientific Computing. The project will involve the
modeling, simulation and analysis of fully spatially structured
metapopulation dynamics, with the ultimate goal of contributing to our
understanding of the conservation of species in fragmented habitats.
The PhD researcher will work in a department of applied mathematicians
with outstanding expertise in mathematical biology. The PhD position
offers excellent opportunity to gain expertise in computational
mathematics (e.g. the Finite Element Method), scientific computing
(e.g., MATLAB, commercial PDE solvers), Partial Differential
Equations, and Applied Mathematics in general.
The candidate must have an MSc degree in an appropriate area of
Applied Mathematics, or Computational Mathematics / Numerical
Analysis. The candidate should be a landed immigrant of Canada
(i.e. Permanant Resident) or be fully self funded, have excellent
writing skills, and be willing to learn some rigorous mathematics in
addition to applications. Good programming skills is an advantage.
Interested candidates will need to make a formal application via
https://www.uoguelph.ca/graduatestudies/apply . Further information
about the application procedure can be obtained from the graduate
secretary Susan McCormick (smccormi@uoguelph.ca).
The advisor is Prof. M.R. Garvie, see http://www.uoguelph.ca/~mgarvie/
from whom further details can be obtained concerning the research
Closing date: February 15, 2014. Please apply as soon as possible.
Starting date: Fall 2014 (early September).
From: Wim Michiels Wim.Michiels@cs.kuleuven.be
Date: October 26, 2013
Subject: PhD Positions, KU Leuven
PhD positions "Computational methods for nonlinear eigenvalue problems
and eigenvalue optimization, with applications in control and
structural dynamics"
Nonlinear eigenvalue problems of a high current interest,primarily in
numerical linear algebra and scientific computing (e.g. in the context
of solving partial differential equations). Important developments
have also taken place in engineering, in particular systems and
control, and in physics.
The Numerical Analysis and Applied Mathematics Section of KU Leuven
has recently gained key expertise on iterative methods for solving
eigenvalue problems that are nonlinear in the eigenvalue parameter.
The aim of the PhD research is to advance the state-of-the-art in two
complementary direction. The first one is on eigenvalue
optimization. The optimization problems stem from the analysis of
eigenvalue problems with uncertainty and from the synthesis of
controller or design parameters. Applications are mainly envisaged in
systems and control and in structural dynamics, in the framework of
the Optimization in Engineering Centre OPTEC. The second direction is
on computing and optimizing eigenvalues where the nonlinearity is not
only in the eigenvalue but also in the eigenvector. The eigenvector
nonlinearity can be inherent to the problem, as in quantum physics
problems, but may also arise in computational schemes for solving
matrix distance problems.
More information about the positions and application instructions can
be found at http://people.cs.kuleuven.be/wim.michiels/vacancy-eig.pdf
From: Piotr Matus matus@im.bas-net.by
Date: October 24, 2013
Subject: Contents, Computational Methods in Applied Mathematics, 13 (4)
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS Vol. 13 (2013), No. 4
The Contribution of Piotr Matus to Computational Mathematics,
Lemeshevsky, Sergey / Sherbaf, Almas / Vabishchevich, Petr; pp.
On 3D DDFV Discretization of Gradient and Divergence Operators:
Discrete Functional Analysis Tools and Applications to Degenerate
Parabolic Problems, Andreianov, Boris / Bendahmane, Mostafa / Hubert,
Florence; pp. 369-410
Rolf Dieter Grigorieff. Applications of Functional Analysis, Emmrich,
Etienne / Hoppe, Ronald H. W. / Kornhuber, Ralf; pp. 411- 414
Sparse Optimal Control of the Schlögl and FitzHugh–Nagumo Systems,
Casas, Eduardo / Ryll, Christopher / Tröltzsch, Fredi; pp. 415-442
Operator Differential-Algebraic Equations Arising in Fluid Dynamics,
Emmrich, Etienne / Mehrmann, Volker; pp. 443-470
A Second Order Approximation for Quasilinear Non-Fickian Diffusion
Models, Ferreira, José A. / Gudiño, Elias / de Oliveira, Paula;
pp. 471-494
A Short Theory of the Rayleigh–Ritz Method, Yserentant, Harry;
pp. 495-502
For more information, please, visit
http://www.degruyter.com/view/j/cmam .
All CMAM ahead of print papers can be viewed at
http://www.degruyter.com/printahead/j/cmam .
From: Joseph Traub traub@cs.columbia.edu
Date: October 25, 2013
Subject: Contents, Journal of Complexity, 30 (1)
Journal of Complexity
Volume 30, Issue 1, February 2014
- Christoph Aistleitner Wins the 2013 Information-Based Complexity
Young Researcher Award
- Nominations for 2014 Information-Based Complexity Young Researcher
Compressed sensing with sparse binary matrices: Instance optimal error
guarantees in near-optimal time, M. Iwen
A Lower Bound for the Discrepancy of a Random Point Set, B. Doerr
The Cost of Deterministic, Adaptive, Automatic Algorithms: Cones, Not
Balls, N. Clancy, Y. Ding, C. Hamilton, F. Hickernell, Y. Zhang
Level permutation method for constructing uniform designs under the
wrap-around L2 discrepancy 1, G. Xu, J. Zhang, Y. Tang
Quasi-Polynomial Tractability of Linear Problems in the Average Case
Setting, X. Guiqiao
Weighted discrepancy and numerical integration in function spaces,
H. Triebel
On lower bounds for integration of multivariate permutation-invariant
functions, M. Weimar
Construction of Uniform Designs Without Replications, B. Jiang, M. Ai
End of Digest | {"url":"https://www.netlib.org/na-digest-html/13/v13n36.html","timestamp":"2024-11-11T17:44:58Z","content_type":"text/html","content_length":"31178","record_id":"<urn:uuid:a4fdde49-0cd6-417a-8dda-34531feae7a8>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00486.warc.gz"} |
What is a Trisector of a triangle?
What is a Trisector of a triangle?
In plane geometry, Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley
triangle or simply the Morley triangle. The theorem was discovered in 1899 by Anglo-American mathematician Frank Morley.
What angles can be Trisected?
A 90° angle can be trisected by constructing a 30° angle on each of the two lines. In general, it turns out that an angle whose measure is 2π/N can be trisected if and only if N is not divisible by
What are the 4 types of triangle?
Triangle Types and Classifications: Isosceles, Equilateral, Obtuse, Acute and Scalene.
What are the 3 triangles?
There are three types of triangle based on the length of the sides: equilateral, isosceles, and scalene. The green lines mark the sides of equal (the same) length.
What is trisection of a line segment?
Trisection means dividing a line segment in three equal parts or dividing a line segment in the ratio 1:2 and 2:1.
Can 90 degrees be Trisected?
The angle is drawn for you on a piece of paper and you need to draw another line, coming from the vertex of the given angle, which trisects the given angle. There are some angles which can be
trisected. Indeed, as we shall see in a moment, a 90 degree angle can be trisected – as can a 45 degree angle.
When you Trisect an angle you cut?
Explanation: When you bisect an angle (cut it into two equal pieces), you use 1 ray. And so to cut an angle into three equal pieces, you use 2 rays.
What are the 7 triangles?
Different Types of Triangles
• Equilateral Triangle.
• Isosceles Triangle.
• Scalene Triangle.
• Right Triangle.
• Oblique Triangle.
What are the 12 types of triangles?
Terms in this set (6)
• Scalene Triangle. A triangle that has no congruent sides.
• Acute Triangle. A triangle that has all three angles with measures of less than 90 degrees.
• Obtuse Triangle. A triangle that has one angle with a measure of greater than 90 degrees.
• Isosceles Triangle.
• Equilateral Triangle.
• Right Triangle.
What does the Viking valknut mean?
Its name isn’t mentioned in any period sources; valknut is a modern Norwegian compound word that means “knot of those fallen in battle” and was introduced by Norwegians who lived long after the
Viking Age.
What is sector rotation?
The economy moves in reasonably predictable cycles. Various industries and the companies that dominate them thrive or languish depending on the cycle. That simple fact has spawned an investment
strategy that is based on sector rotation.
What is the definition of trisection?
Trisection means dividing a line segment in three equal parts or dividing a line segment� in the ratio 1:2 and 2:1 internally. Trisection means dividing a line segment in three equal parts or
dividing a line segment in the ratio 1:2 and 2:1 internally.
What is the difference between trisection and given coordinates?
Given coordinates are and Trisection means dividing a line segment in three equal parts or dividing a line segment in the ratio 1:2 and 2:1 internally.
How many trisector cells does the trisector have?
The Trisector solution comes to the market in a camouflaged version applicable to the concept of Smart Cities. A downlink transmission with only large scale fading is assumed using a 19 trisector
cell hexagonal layout. | {"url":"https://stylesubstancesoul.com/life/what-is-a-trisector-of-a-triangle/","timestamp":"2024-11-06T06:06:11Z","content_type":"text/html","content_length":"49469","record_id":"<urn:uuid:bd03ec84-a781-4f7c-9680-16dd13a29cc7>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00708.warc.gz"} |
Vestnik КRAUNC. Fiz.-Mat. Nauki. 2023. vol. 42. no. 1. P. 9-26. ISSN 2079-6641
Vestnik КRAUNC. Fiz.-Mat. Nauki. 2023. vol. 42. no. 1. P. 9-26. ISSN 2079-6641
Research Article
Full text in Russian
MSC 35K35
Solvability of a Nonlocal Inverse Problem for a Fourth-Order Equation
A. B. Bekiev^*
Karakalpak State University named after Berdakh, Uzbekistan, Republic of Karakalpakstan, 230112, Nukus, Ch. Abdirov St. 1.
Abstract. In this paper, we consider a nonlocal inverse problem of finding an unknown right-hand side with
one variable for a fourth-order partial differential equation in a rectangular domain. The eigenfunctions and
associated functions of the corresponding spectral problem and its biorthogonal functions are complete and
form a Riesz basis in the space L_2\left(0,1\right) . Criteria for the uniqueness and existence of a solution to the considered nonlocal inverse problem for a fourth-order equation are established.
The uniqueness of the solution of the nonlocal inverse problem follows from the completeness of the system of biorthogonal functions. The solution of the problem is constructed as the sum of a series
in terms of eigenfunctions and associated functions of the corresponding spectral problem. Sufficient conditions are established for the boundary functions that guarantee existence and stability
theorems for the solution of the problem under consideration. In a closed domain, absolute and uniform convergence of the found solution of the inverse problem is shown in the form of a series, as
well as series obtained by term-by-term differentiation with respect to t and x two and four times, respectively, depending on the smoothness of the function given the initial conditions. In this
case, small denominators arise, which hinder the convergence of these series. It is proved that, depending on the size of the domain, the set of non-zero solutions of the expression in the
denominator is not empty. And also, it is shown that if this denominator is equal to zero, then this problem will have a non-trivial solution under homogeneous conditions. It is also proved that the
solution of the inverse problem is stable in the norms of the spaces L_2, W^n_2 and C\left(\Omega\pm\right) with respect to changes in the input data.
Key words: fourth order equation, inverse nonlocal problem, uniqueness, existence, stability.
Received: 02.01.2023; Revised: 01.02.2023; Accepted: 08.04.2023; First online: 15.04.2023
For citation. Bekiev A. B. Solvability of a nonlocal inverse problem for a fourth-order equation. Vestnik KRAUNC. Fiz.-mat. nauki. 2023, 42: 1, 9-26. EDN: BJBNHI. https://doi.org/10.26117/
Funding. The study was carried out without financial support from foundations.
Competing interests. There are no conflicts of interest regarding authorship and publication.
Contribution and Responsibility. The author participated in the writing of the article and is fully responsible for submitting the final version of the article to print.
^* Correspondence: E-mail: ashir1976@mail.ru
The content is published under the terms of the Creative Commons Attribution 4.0 International License
© Bekiev A. B., 2023
© Institute of Cosmophysical Research and Radio Wave Propagation, 2023 (original layout, design, compilation)
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Information about the author
Bekiev Ashirmet Bekievich – Ph.D. (Phys.& Math.), Assistant professor, Department of Differensial Equation, Karakalpak State University, Nukus, Uzbekistan, | {"url":"https://krasec.ru/bekiev421023-eng/","timestamp":"2024-11-06T04:48:53Z","content_type":"text/html","content_length":"69957","record_id":"<urn:uuid:bd44f714-bddb-439c-a1a4-bd70251ed1d2>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00661.warc.gz"} |
Number and algebra: My thinkboard - WS2
Understanding / Problem-Solving / Reasoning
Year 1
Number and algebra: My thinkboard
Summary of task
The students were presented with a basket containing five skipping ropes. They were told that previously there was a basket full of skipping ropes and were asked to list three different solutions to
how many skipping ropes had gone missing. Students gave the strategy that was used for each solution.
At this year level understanding includes connecting names, numerals and quantities, and partitioning numbers in various ways.
At this year level problem-solving includes using materials to model authentic problems, giving and receiving directions to unfamiliar places, using familiar counting sequences to solve unfamiliar
problems and discussing the reasonableness of the answer.
At this year level reasoning includes explaining direct and indirect comparisons of length using uniform informal units, justifying representations of data and explaining patterns that have been
1 Understanding
Interprets the problem as a problem involving the subtraction of one number from another to obtain an answer of ‘5’ 2 Problem-Solving
Communicates a first solution to the problem effectively in two different ways by using a number sentence and a pictorial representation 3 Problem-Solving
Communicates three further solutions to the problem effectively in two different ways in each case, by using a number sentence and a number line 4 Reasoning
Identifies the strategies used from a given list to explain that the solutions were obtained by using ‘pictures’ and ‘counting back’ for ‘Answer 1’ and ‘counting back’ and ‘number lines’ for the
solutions obtained under ‘Answer 2’ and ‘Answer 3’
• Annotations
• 1
Interprets the problem as a problem involving the subtraction of one number from another to obtain an answer of ‘5’
• 2
Communicates a first solution to the problem effectively in two different ways by using a number sentence and a pictorial representation
• 3
Communicates three further solutions to the problem effectively in two different ways in each case, by using a number sentence and a number line
• 4
Identifies the strategies used from a given list to explain that the solutions were obtained by using ‘pictures’ and ‘counting back’ for ‘Answer 1’ and ‘counting back’ and ‘number lines’ for the
solutions obtained under ‘Answer 2’ and ‘Answer 3’ | {"url":"https://australiancurriculum.edu.au/resources/mathematics-proficiencies/samples/number-and-algebra-my-thinkboard-ws2/","timestamp":"2024-11-12T00:30:42Z","content_type":"text/html","content_length":"52147","record_id":"<urn:uuid:775eaa81-be0d-4a5d-843a-b95e4e846971>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00139.warc.gz"} |
Home Highlights of research
Improvements to the Sink Strength Theory Used in Multi-Scale Rate Equation Simulations of Defects in Solids,
Tommy Ahlgren and Kalle Heinola, Materials 13 (2020) 2621.
The application of kinetic Rate Equations (kRE) have proven to be a versatile method in simulating defect dynamics and temporal changes in the microstructure of materials.
The reliability and usefulness of the method, however, depends critically on the defect interaction parameters used.
• We show that the main interaction parameter for the kRE method, the sink strength, intrinsically depends on the detrapping, or the dissociation process itself
• The correct sink strength required for a detrapping defect, is considerably larger than the values commonly used
• Theory is presented how to determine the appropriate sink strengths
Hydrogen isotope exchange in tungsten during annealing in hydrogen atmosphere,
T. Ahlgren, P. Jalkanen, K. Mizohata, V. Tuboltsev, J. Raisanen, K. Heinola and P. Tikkanen,
Nuclear Fusion 59 (2019) 026016.
The radiological safety of the future thermonuclear fusion devices depends critically on the total tritium inventory in the plasma-facing components.
• We show that tritium removal from tungsten can be enhanced by the isotope exchange mechanism by doing the baking in H2 atmosphere
• The retained deuterium from 30 keV implantation drop almost to zero after 24h annealing at 250C in H2 atmosphere
• Annealing in vacuum requires temperatures above 400C for close to zero retention
Sink strength simulations using the Monte Carlo method: applied to spherical traps,
T. Ahlgren and L. Bukonte, Journal of Nuclear Materials, 496 (2017) 66.
• The reasons for the discrepancies between the sink strengths obtained with MC simulations and analytical studies are explained
• Equation to determine the sink strengths for multiple traps from Monte Carlo simulations is given
• The equation to estimate the statistical errors for Monte Carlo sink strengths is derived
• A new concept for much faster sink strength calculations with the Monte Carlo method is presented
Thermodynamics of impurity-enhanced vacancy formation in metals,
L. Bukonte, T. Ahlgren and Kalle Heinola, J. Appl. Phys. 121 (2017) 045102.
• The effect of vacancy formation energy, the hydrogen (or impurity) binding, and the divacancy binding energy on the total equilibrium vacancy concentration in metals is given
• The divacancies give the major contribution to the total vacancy fraction at high H fractions and cannot be neglected when studying superabundant vacancies
• At high hydrogen (impurity) fractions, superabundant vacancy formation takes place regardless of the binding energy between vacancies and hydrogen (impurity)
• The reason of superabundant vacancy formation mainly in the fcc phase (compared to bcc phase) is explained
• The results of this theory are compared and found to be in good agreement with experiments of H induced vacancy formation in fcc metals Pd, Ni, Co, and Fe
Modelling of monovacancy diffusion in W over wide temperature range,
L. Bukonte, T. Ahlgren and K. Heinola, J. Appl. Phys. 115 (2014) 123504.
• The diffusion of monovacancies in W is studied using molecular dynamics simulation (MD) and density functional theory (DFT)
• The diffusion pre-exponential factor for monovacancy diffusion is found to be two to three orders of magnitude higher than commonly used in computational studies,
resulting in an attempt frequency of the order 10^15 Hz
• Multiple nearest neighbour jumps of monovacancy are found to play an important role in the contribution to the total diffusion coefficient,
especially at temperatures above 2/3 of T[m], resulting in an upward curvature of the Arrhenius diagram
Simulation of irradiation induced deuterium trapping in tungsten,
T. Ahlgren, K. Heinola, K. Vörtler, and J. Keinonen, Journal of Nuclear Materials, 427 (2012) 152.
• The kinetic Rate Equation (kRE) computer program HIM (hydrogen in metals) is presented, which can take into account most of the dynamic processes, including defect annihilation, during
• The results show that H is mainly trapped in W monovacancies, and trapping in larger vacancy clusters increase with increasing H implantation energy
• The slow H desorption observed in experiments after irradiation, was found to be mainly due to detrapping of the weakly bound sixth hydrogen from monovacancies
• Impurity self-interstitial atom complexes could be the nucleation site for formation of large interstitial type dislocation loops observed experimentally
Plastic deformation of single nanometer-sized crystals,
L. Sun, A. V. Krasheninnikov, T. Ahlgren, K. Nordlund and F. Banhart, Phys. Rev. Lett. 101 (2008) 156101.
• in situ electron microscopy observations of the plastic deformation of individual nanometersized Au, Pt, W, and Mo crystals
• The correlation with atomistic simulations shows that the observed slow plastic deformation is due to dislocation activity
• We see evidence that the vacancy concentration in a nanoscale system can be smaller than in the bulk material, an effect which has not been studied experimentally before
Fast Monte Carlo simulation for elastic ion backscattering,
P. Pusa, T. Ahlgren and E. Rauhala, Nucl. Instr. And Meth. B, 219-220 (2004) 95.
• A very fast Monte Carlo method using ion packets is introduced
• The method presented is optimal for the low probability scattering simulations of multiple and plural backscattering effects
Concentration of interstitial and substitutional nitrogen in GaN[(x)]As[(1-x)],
T. Ahlgren, E. Vainonen-Ahlgren, J. Likonen, W. Li and M. Pessa, Appl. Phys. Lett. 80 (2002) 2314.
• The interstitial to substitutional nitrogen atoms in Ga(In)NAs is determined by nuclear reaction analysis (NRA) and ion channeling techniques
• The fraction of N atoms occupying substitutional sites was observed to increase linearly with increasing N amount, while the concentration of interstitial N was nearly constant
• Annealing at 750 C decreases the concentration of interstitial N
Origin of improved luminescence efficiency after annealing of Ga(In)NAs materials grown by molecular-beam epitaxy,
Wei Li, Markus Pessa, Tommy Ahlgren and James Dekker,
Appl. Phys. Lett. 79 (2001) 1094.
• Positron annihilation spectroscopy (PAS) and nuclear reaction analysis (NRA) in conjunction with ion channeling measurements show that
a high density of N interstitials and Ga vacancies are present in molecular beam epitaxy grown Ga(In)NAs
• These measured point defects are believed to be the reason for the low luminescence efficiency of as-grown Ga(In)NAs materials
• Annealing is shown reduce the Ga vacancies and N interstitials, which improves the luminescence efficiency
Identification of vacancy charge states in diffusion of arsenic in germanium,
E. Vainonen-Ahlgren, T. Ahlgren, J. Likonen, S. Lehto, J. Keinonen, W. Li and J. Haapamaa,
Appl. Phys. Lett. 77 (2000) 690.
• Concentration dependent As diffusion in p-type Ge is observed
• The concentration dependence is explained by a Fermi-level dependent diffusion model, where the As atoms diffuse through Ge vacancies with the charge state 2- and 0
• No presence of singly negatively charged Ge vacancy was observed, indicating that Ge vacancy is a negative U center
Suppression of carbon erosion by hydrogen shielding during high-flux hydrogen bombardment,
E. Salonen, K. Nordlund, J. Tarus, T. Ahlgren and J. Keinonen,
Phys. Rev. B (rapid communications), 60 (1999) 14005.
• The carbon erosion in fusion reactor divertor due to intensive hydrogen bombardment is studied by molecular dynamics simulations
• The sharp decrease of carbon erosion at very high H fluxes is found to be due to the buildup of a shielding H layer at the surface
Identification of Si interstitials in ion implanted GaAs,
T. Ahlgren, Phys. Rev. Lett. 81 (1998) 842.
• A diffusion model that takes into account silicon located on Ga and As sites, Si[Ga]^+-Si[As]^- pairs and interstitial Si is presented
• The charge state of the interstitial Si was found to be +1 in order to best fit the experiments
Concentration dependent and independent Si diffusion in ion implanted GaAs,
T. Ahlgren, J. Likonen, J. Slotte, J. Räisänen, M. Rajatora and J. Keinonen,
Phys. Rev. B, 56 (1997) 4597.
• A very fast numerical method to solve concentration dependent diffusion equation with solubility limit is presented
• Two silicon diffusion mechanisms in GaAs observed
1. Concentration independent diffusion: interstitial Si diffusion
2. Concentration dependent diffusion via vacancies in the Ga and As sublattices
• The solid solubility limit of Si in GaAs is determined | {"url":"https://www.mv.helsinki.fi/home/tahlgren/Own-pubs/highlights.html","timestamp":"2024-11-07T08:45:06Z","content_type":"text/html","content_length":"13508","record_id":"<urn:uuid:056c2cde-be96-4a16-9730-becb016c2fef>","cc-path":"CC-MAIN-2024-46/segments/1730477027987.79/warc/CC-MAIN-20241107083707-20241107113707-00589.warc.gz"} |
✓ Check Mark Symbol Text (Meaning, Type on Keyboard, Copy & Paste) - Symbol Hippo
✓ Check Mark Symbol Text (Meaning, Type on Keyboard, Copy & Paste)
This post will teach you a lot about the Check Mark Symbol.
First, we’ll look at its meaning, HTML, CSS, and Alt codes, Copy & Paste button, then the steps you may take to type this symbol text on your keyboard, and many more.
Without any further ado, let’s get started.
Copy Check Mark Symbol Text
The easiest way to get the Check Mark text symbol is to copy and paste it wherever you need it. The copy button above will save you some time in doing so.
After copying this symbol, you can paste it anywhere by pressing Ctrl and V on your keyboard.
Meaning of the CheckMark Symbol
A check mark is a symbol (√) often used to indicate the completion, correctness, or approval of a task, item, or action. It signifies that something has been verified, validated, or accomplished
successfully. The checkmark is commonly used to indicate a positive outcome or a positive status in various contexts, such as to mark off items on a to-do list, confirm the accuracy of the
information, or indicate that a step has been completed.
In Unicode, the Check Mark text symbol is the character at code point U+2713. Its HTML code is ✓ and you can type it on your keyboard by pressing Alt + 10003 (in MS Word Only).
Continue reading for more details on this symbol.
Check Mark Symbol Information Table
The table below depicts a bird’s-eye-view of the Check Mark Symbol.
It summarises to include all the essential and technical information about this symbol. We will keep updating it to include the latest facts.
SYMBOL ✓
NAME Check Mark Symbol
CATEGORY Other Symbol
ALT CODE 10003
SHORTCUT 1 (MS WORD) Alt + 10003
UNICODE U+2713
HTML CODE ✓
HEX CODE ✓
CSS CODE \2713
To the best of our ability, the above table presents some technical information about this Symbol, including the keyboard shortcut, Unicode, and HTML code.
Continue reading to better understand how to type this symbol using the keyboard and other methods.
How to Type the Check Mark Symbol
Although there is no dedicated key on the keyboard to type the Check Mark Symbol, you can still get it through the keyboard.
You can also insert this symbol in Word, Excel, PowerPoint, or Google Docs if you use one of the Microsoft Office or Google apps.
Below you’ll find several methods for accessing this symbol, including keyboard shortcuts and methods utilising MS Office and Google Docs’ built-in navigation systems.
The Check Mark Alt Code (Keyboard Shortcut)
The Check Mark Alt Code is Alt + 10003.
Note: This Alt Code shortcut works in Microsoft Word for Windows only.
This Alt code method can be used to type this symbol by holding down the Alt key while typing 10003 on the separate numeric keypad on the right side of the keyboard.
Below is a detailed step-by-step guide you may use to type the Symbol for the Check Mark with your keyboard.
• Open your Microsoft Word document where you need to type this symbol.
• Place your cursor in the document where you need to type this symbol.
• On the keyboard, press down the Alt key with one hand.
• As you hold down the Alt key, use your other hand to press the Check Mark Symbol Alt Code (10003).
• Now release the Alt key.
After you release the Alt key, the symbol (✓) will immediately appear precisely where you place the cursor.
Insert Check Mark Symbol in Word/Excel/PowerPoint
Using this simple mouse navigation, you can quickly insert the Check Mark Symbol into Microsoft Office applications such as Word, Excel, or PowerPoint.
The steps below will show you how to insert this symbol in Word, Excel, or PowerPoint.
• Open your Word or Excel, or PowerPoint document.
• Go to the Insert tab.
• On the far-right section, you’ll see the Symbols group. Select Symbol > More Symbols.
The Symbol window will appear.
• The symbol (✓) can be found in this window. To find it quickly, change the font to Segoe UI Symbol, then type 2713 in the Character code: box. The Check Mark sign will be selected as soon as you
type the code.
• Insert it into your Word document by clicking the Insert button.
• Close the Symbol dialog.
These are the steps for inserting the Check Mark Symbol (✓) and any other symbol in Microsoft Word or other Office apps on Windows and Mac OS.
Check Mark Symbol In Google Docs
Google Docs is another text editor with which users may struggle to type or insert the Check Mark sign.
Meanwhile, Google Docs provides the most straightforward method for inserting symbols not found on the keyboard.
Without further ado, let’s get into it.
To get this Symbol in Google Docs:
• Launch Google Docs and position your cursor where the symbol will be inserted.
• Go to Insert > Special Characters.
The Insert special characters window will appear., which includes a search bar and a drawing pad.
• Using the Search bar, search for Check Mark. Then, double-click on the text Symbol in the search results to insert it into Google Docs.
• You can also draw the Check Mark Symbol using the drawing pad below the search bar. If Google Docs recognizes the drawing, it will display the symbol and similar signs in the results box. Then
double-click the symbol to insert it.
These steps are to insert this and any other symbol into Google Docs.
Check Mark Symbol on The Character Map (Windows)
In Windows, the Character Map is a tool that can be used to view characters in any installed font, determine what keyboard input (or Alt code) is used to type those characters and copy characters to
the clipboard instead of typing them with your keyboard.
This section will demonstrate how to use the Character Map tools to easily copy and paste this Symbol.
Without further ado, let’s get into it.
• Search for Character Map in the Windows Start menu.
• You should see the character Map appear in the search results. Click on it to launch it.
• When it’s open, go to the bottom left corner of the window and click to expand the Advanced view options.
• To quickly locate this symbol on the Character Map, change the Font to Segoe UI Symbol and search for the symbol name (Check Mark) in the search box.
The symbol will be displayed for you to copy.
• To copy this symbol, double-click it, and it will be selected in the Characters to Copy box. Then, click the Copy button to copy it to your clipboard.
• Place your cursor where you want the symbol and press Ctrl + V to paste it.
And there you have it.
You can take these steps to copy and paste the Check Mark Symbol or other symbols on your Windows PC.
Adding Check Mark Symbol in HTML/CSS
The Check Mark Symbol can also be added in HTML and CSS using entities.
HTML and CSS entities are special codes used to represent characters that have special meanings or cannot be displayed as regular text in HTML and CSS.
Entities are used to display characters such as angle brackets, ampersands, and quotation marks, as well as special symbols such as copyright, trademark, and multiplication signs.
Using entity codes is important for ensuring that HTML and CSS code is valid and can be interpreted correctly by web browsers.
The HTML code for the Check Mark Symbol is ✓
The CSS code for the Check Mark Symbol is \2713
To add the Check Mark Symbol to an HTML page, you can use its entity name or number (decimal or hexadecimal reference), as shown in the example below:
// html example
<span> ✓ </span>
To display the Check Mark Symbol from CSS, you can use a CSS shortcode or CSS entity, as shown in the example below:
// css example
span {
content: "\2713";
Most people have difficulty typing or inserting this symbol. So, we’ve broken down the various methods and steps required to type or get it into your documents.
And as you can see above, we’ve attempted to cover as much information about the Check Mark text Symbol as possible.
Thank you for taking the time to go through this blog. | {"url":"https://symbolhippo.com/check-mark-symbol-text/","timestamp":"2024-11-08T14:49:29Z","content_type":"text/html","content_length":"118724","record_id":"<urn:uuid:33428c1e-0797-42ba-80f7-f719b2d91a3a>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00174.warc.gz"} |
367 research outputs found
A new Monte Carlo move for polymer simulations is presented. The ``wormhole'' move is build out of reptation steps and allows a polymer to reptate through a hole in space; it is able to completely
displace a polymer in time N^2 (with N the polymer length) even at high density. This move can be used in a similar way to configurational bias, in particular it allows grand canonical moves, it is
applicable to copolymers and can be extended to branched polymers. The main advantage is speed since it is exponentially faster in N than configurational bias, but is also easier to program.Comment:
8 pages, 6 figure
A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example,
we study the 2-dimensional +/-J Edwards-Anderson model. The new algorithm allows us to equilibrate systems of size 100^2 down to temperature T = 0.1. Our main result is that the correlation length
diverges as an exponential and not as a power law as T -> Tc = 0.Comment: 6 pages, 9 figures, section 2 completly rewritte
The problem of the survival of a spin glass phase in the presence of a field has been a challenging one for a long time. To date, all attempts using equilibrium Monte Carlo methods have been
unconclusive. In their comment to our paper, Marinari, Parisi and Zuliani use out-of-equilibrium measurements to test for an Almeida-Thouless line. In our view such a dynamic approach is not based on
very solid foundations in finite dimensional systems and so cannot be as compelling as equilibrium approaches. Nevertheless, the results of those authors suggests that there is a critical field near
B=0.4 at zero temperature. In view of this quite small value (compared to the mean field value), we have reanalyzed our data. We find that if finite size scaling is to distinguish between that small
field and a zero field, we would need to go to lattice sizes of about 20x20x20.Comment: reply to comment cond-mat/9812401 on ref. cond-mat/981141
A controversial issue in spin glass theory is whether mean field correctly describes 3-dimensional spin glasses. If it does, how can replica symmetry breaking arise in terms of spin clusters in
Euclidean space? Here we argue that there exist system-size low energy excitations that are sponge-like, generating multiple valleys separated by diverging energy barriers. The droplet model should
be valid for length scales smaller than the size of the system (theta > 0), but nevertheless there can be system-size excitations of constant energy without destroying the spin glass phase. The
picture we propose then combines droplet-like behavior at finite length scales with a potentially mean field behavior at the system-size scale.Comment: 7 pages; modified references, clarifications;
to appear in EP
We perform Monte Carlo simulations of large two-dimensional Gaussian Ising spin glasses down to very low temperatures $\beta=1/T=50$. Equilibration is ensured by using a cluster algorithm including
Monte Carlo moves consisting of flipping fundamental excitations. We study the thermodynamic behavior using the Binder cumulant, the spin-glass susceptibility, the distribution of overlaps, the
overlap with the ground state and the specific heat. We confirm that $T_c=0$. All results are compatible with an algebraic divergence of the correlation length with an exponent $u$. We find $-1/u=
-0.295(30)$, which is compatible with the value for the domain-wall and droplet exponent $\theta\approx-0.29$ found previously in ground-state studies. Hence the thermodynamic behavior of this model
seems to be governed by one single exponent.Comment: 7 pages, 11 figure
We present basic properties of Dipolar SLEs, a new version of stochastic Loewner evolutions (SLE) in which the critical interfaces end randomly on an interval of the boundary of a planar domain. We
present a general argument explaining why correlation functions of models of statistical mechanics are expected to be martingales and we give a relation between dipolar SLEs and CFTs. We compute SLE
excursion and/or visiting probabilities, including the probability for a point to be on the left/right of the SLE trace or that to be inside the SLE hull. These functions, which turn out to be
harmonic, have a simple CFT interpretation. We also present numerical simulations of the ferromagnetic Ising interface that confirm both the probabilistic approach and the CFT mapping.Comment: 22
pages, 4 figure
We numerically extract large-scale excitations above the ground state in the 3-dimensional Edwards-Anderson spin glass with Gaussian couplings. We find that associated energies are O(1), in agreement
with the mean field picture. Of further interest are the position-space properties of these excitations. First, our study of their topological properties show that the majority of the large-scale
excitations are sponge-like. Second, when probing their geometrical properties, we find that the excitations coarsen when the system size is increased. We conclude that either finite size effects are
very large even when the spin overlap q is close to zero, or the mean field picture of homogeneous excitations has to be modified.Comment: 11 pages, typos corrected, added reference
We probe the energy landscape of the 3D Edwards-Anderson spin glass in a magnetic field to test for a spin glass ordering. We find that the spin glass susceptibility is anomalously large on the
lattice sizes we can reach. Our data suggest that a transition from the spin glass to the paramagnetic phase takes place at B_c=0.65, though the possibility B_c=0 cannot be excluded. We also discuss
the question of the nature of the putative frozen phase.Comment: RevTex, 4 pages, 4 figures, clarifications and added reference
Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with
actual properties of finite dimensional systems. Our focus here is on minimum matching problems, because they are computationally tractable while both frustrated and disordered. We first study a mean
field model taking the link lengths between points to be independent random variables. For this model we find perfect agreement with the results of a replica calculation. Then we study the case where
the points to be matched are placed at random in a d-dimensional Euclidean space. Using the mean field model as an approximation to the Euclidean case, we show numerically that the mean field
predictions are very accurate even at low dimension, and that the error due to the approximation is O(1/d^2). Furthermore, it is possible to improve upon this approximation by including the effects
of Euclidean correlations among k link lengths. Using k=3 (3-link correlations such as the triangle inequality), the resulting errors in the energy density are already less than 0.5% at d>=2.
However, we argue that the Euclidean model's 1/d series expansion is beyond all orders in k of the expansion in k-link correlations.Comment: 11 pages, 1 figur
Excitations of three-dimensional spin glasses are computed numerically. We find that one can flip a finite fraction of an LxLxL lattice with an O(1) energy cost, confirming the mean field picture of
a non-trivial spin overlap distribution P(q). These low energy excitations are not domain-wall-like, rather they are topologically non-trivial and they reach out to the boundaries of the lattice.
Their surface to volume ratios decrease as L increases and may asymptotically go to zero. If so, link and window overlaps between the ground state and these excited states become ``trivial''.Comment:
Extra fits comparing TNT to mean field, summarized in a tabl | {"url":"https://core.ac.uk/search/?q=author%3A(Houdayer%2C%20J.)","timestamp":"2024-11-02T02:14:14Z","content_type":"text/html","content_length":"148781","record_id":"<urn:uuid:1e715e89-3aef-4d5a-be95-364f77b15764>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00017.warc.gz"} |
Merging sorted sequences
How to merge several iterable sequences and keep things ordered.
Python, 45 lines
1 def xmerge(*ln):
2 """ Iterator version of merge.
4 Assuming l1, l2, l3...ln sorted sequences, return an iterator that
5 yield all the items of l1, l2, l3...ln in ascending order.
6 Input values doesn't need to be lists: any iterable sequence can be used.
7 """
8 pqueue = []
9 for i in map(iter, ln):
10 try:
11 pqueue.append((i.next(), i.next))
12 except StopIteration:
13 pass
14 pqueue.sort()
15 pqueue.reverse()
16 X = max(0, len(pqueue) - 1)
17 while X:
18 d,f = pqueue.pop()
19 yield d
20 try:
21 # Insort in reverse order to avoid pop(0)
22 lo, hi, d = 0, X, f()
23 while lo < hi:
24 mid = (lo+hi)//2
25 if d > pqueue[mid][0]: hi = mid
26 else: lo = mid+1
27 pqueue.insert(lo, (d,f))
28 except StopIteration:
29 X-=1
30 if pqueue:
31 d,f = pqueue[0]
32 yield d
33 try:
34 while 1: yield f()
35 except StopIteration:pass
38 def merge(*ln):
39 """ Merge several sorted sequences into a sorted list.
41 Assuming l1, l2, l3...ln sorted sequences, return a list that contain
42 all the items of l1, l2, l3...ln in ascending order.
43 Input values doesn't need to be lists: any iterable sequence can be used.
44 """
45 return list(xmerge(*ln))
As said Guido, this not something you need very often, but I couldn't stay with 13 recipes anymore ;-)
Implementation use a priority queue to find the next shorter item. Iterators wich have no more items to provide are progressively removed from the queue. The size of this queue is the stop condition
of the loop. cf p178 'Algorithms'(Robert Sedgewick) 2d edition ISBN:0-201-06673-4
5 comments
In the future, no need to roll your own priority queue. Looking into the future, Py2.3 comes with a wonderfully efficient priority queue implementation in a module called heapq. Applying heapq
simplifies and speeds the above code considerably.
from heapq import heapify, heappop, heapreplace
def xmerge(*ln):
pqueue = []
for i in map(iter, ln):
pqueue.append((i.next(), i.next))
except StopIteration:
while pqueue:
val, it = pqueue[0]
yield val
heapreplace(pqueue, (it(), it))
except StopIteration:
Recursive is faster. In spite of number of comparisons on random ordered sequences:
def imerge ( *ordered ) :
"""Merge ordered iterables.
L = len(ordered)
if L == 0 : return ()
if L == 1 : return ordered[0]
if L == 2 : return imerge_two(ordered[0],ordered[1])
L /= 2
return imerge_two(imerge(*ordered[:L]),imerge(*ordered[L:]))
Where imerge_two - real merging iterator.
More readable. I was a bit stymied by the way iterators were used in the original code (frankly, I did not understand the code), I came up with one using heapq, but with easier to read, but producing
the same effect. I am not sure of performance hit on large sequences due to the multiple maps, but the number of lines are reduced, which was my goal .
def xmerge2(*ln):
""" Uses a simplified syntax """
heap = []
map(lambda l: map(heap.append, l), ln)
while heap:
yield heappop(heap)
Using itertools. Using itertools, simplifies it further.
def xmerge3(*ln):
from itertools import chain
heap = []
for i in chain(*ln):
while heap:
yield heappop(heap)
There's now a method in heapq that does exactly what you want:
import heapq
l = heapq.merge((x*6 for x in xrange(10)),(x*x for x in xrange(5)))
print list(l)
[0, 0, 1, 4, 6, 9, 12, 16, 18, 24, 30, 36, 42, 48, 54] | {"url":"https://code.activestate.com/recipes/141934-merging-sorted-sequences/?in=lang-python","timestamp":"2024-11-13T15:19:40Z","content_type":"text/html","content_length":"33208","record_id":"<urn:uuid:aa600327-83c5-4331-8815-3921a9ea89d0>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00394.warc.gz"} |
Solving a gamebook : can we solve five books at once? The 2022 update.
This post is part of the "Gamebook solver" serie:
The Lone Wolf series starts with a five books arc. I now believe it might be possible to solve all of them at once, and compute the ultimate walkthrough!
The reason why it might make sense to solve them all at once instead of in isolation is that there are elements that are kept between books, namely selected disciplines and items. This means that
some high-risk items might not be worth it in a book, but very much worth it in a subsequent book.
Since last time, the following items were improved:
• I finally implemented the healing discipline properly ... at least kind of properly. This changes everything with regards to balancing, which means that all previous statistics are to be
discarded :)
• I also implemented book 05. This book has several specific mechanisms. There is poisoning, disease, and equipment confiscation. The latter is especially costly with regards to performance, as a
copy of the inventory must be stored ...
• ... but now that I can't fit the state in 96 bits, there is more space for extra items :)
Notes on solving Book 05
Note that everything here is to be considered with suspicion, as there might be bugs lurking in the way I encoded the books (I just found one this morning where I forgot to encode a shop).
Book 05 has 400 chapters instead of 350, and is noticeably more complex than the others, which makes computation much more taxing. As a result, I decided to compute the stats only for hard mode Lone
Wolf, that is with a weak (10 skill, 20 endurance) character. This is offset by the fact that you wield the Sommerswerd, but well, it is still hard :)
The other consequence is that I had to buy an extra 64GB of RAM for some computations to eventually complete. Of course, I later optimized it and everything fits in 20GB, but at least I can run more
jobs in parallel :/
There is an interesting part in this book, where you can get imprisoned, and your equipment is seized. Later, there is the opportunity to retrieve it.
It turns out that it is never worth retrieving it!
• if you wield the Sommerswerd, it makes more sense to avoid this episode entirely, as the weapon is too valuable to be lost, and strong enough that you can withstand the harder route ;
• if you do not wield it, then the equipment you find is plenty sufficient, and it is not worth it trying to get your previous stuff back.
Contrast this with this walkthrough, where it recommends recovering the equipment! Also in this walkthrough it recommends items from previous books, but I did not find they made any difference :) I
still have to compute if having previously fought an Elix , or having received a Crystal Star Pendant makes a difference!
But perhaps for a stronger character, or a character with only 5 disciplines, it is very much worth it.
Notes on healing
Healing changed everything. In book 05, section 98, if you go to chapter 118, you have 1/10 chance of dying, and 9/10 chance of ending up at the same place you would be if you chose the other path.
It seems like it is strictly better to avoid this path, but my solver sometimes chose the "wrong" path anyways!
It turns out that there is a fight just after, and the "wrong" path, being longer, let you heal some more, which makes a difference for this fight!
Next time
Hopefully, next time I will have a solution for the whole five books :) I still have to model book 03 (book 04 is done but needs debugging), and to write a way to stitch them together. I am however
confident this is computable, so let's check it again next time!
click here for a solution visualization of the following starting state:
• Max endurance 20, skill 10
• Sommerswerd, 1 potion of Laumspur, shield, 2 meals | {"url":"https://hbtvl.banquise.net/posts/2022-01-15-GBS-newyearupdate.html","timestamp":"2024-11-12T19:53:20Z","content_type":"text/html","content_length":"8719","record_id":"<urn:uuid:62c2e333-4580-49c2-90ca-3271f486419e>","cc-path":"CC-MAIN-2024-46/segments/1730477028279.73/warc/CC-MAIN-20241112180608-20241112210608-00002.warc.gz"} |
Penrose Tiling Quilt
Diameter: approximately 60"
This updated photograph was taken November 13, 2005.
The quilt now hangs on the wall in Mark's computer room.
It's almost too big for the wall.
That's a bookshelf on the left, and a closet door on the right.
The top point almost touches the ceiling.
Hanging the quilt was tricky (details below).
Here's the original picture that was on this web page:
Photographed March 8, 1996 on a snow pile in our back yard.
The pattern is an area selected from a Penrose tiling.
Mark designed the quilt by computer and Serena made it.
This was before Serena knew about "paper piecing".
The 6 colors were chosen to produce a 3-D effect.
The Golden Ratio appears in the relative lengths of the triangle sides.
There are only two kinds of pieces: a 72-36-72 degree triangle and a 36-36-108 degree triangle.
Penrose Tiling:
Several aperiodic tilings discovered by the British mathematician/physicist Roger Penrose.
A way of precisely covering an infinite plane with a fixed set of shapes.
Non-repeating. There is no way you can rotate and/or shift the infinite pattern so that the rotated/shifted pattern is the same as the original pattern. (This is not apparent from the quilt
because the quilt is not the entire infinite pattern. In fact, we chose a particularly symmetrical part of the infinite pattern.)
Correction/clarification by Dave Green (August 1, 1998):
• The phrase "the infinite pattern" is misleading, since there are an infinite number of different infinite patterns.
• There are two Penrose tilings with five-fold rotational symmetry -- they can be created by radially extending the two implied Penrose tilings in your quilt around a single point (the center of
your quilt).
Hanging the Quilt:
This quilt spent many years in a dresser drawer because we didn't have a way to hang it.
Then Mark got industrious and found a source of hoops on the web.
These fiberglass hoops are made for use in fishing nets (I guess they hold the net open).
They're sturdy and very nearly circular.
The Penrose Tiling quilt required a 4-foot diameter hoop.
Here's the hoop in our doorway:
Here's a closeup:
It's splintery and will make your hand itch if you touch it.
So we wrapped the hoop in duct tape.
The quilt is attached to the hoop with loops of fabric.
For now, they're just pinned on.
Lengths of coat-hanger wire keep the topmost points from flopping.
Related Links:
<Dogfeathers Home Page> <Serena's Page> <Serena's Quilts> Email: Serena Mylchreest
This page URL: http://dogfeathers.com/quilt/penrose.html | {"url":"https://dogfeathers.com/quilt/penrose.html","timestamp":"2024-11-14T19:04:00Z","content_type":"text/html","content_length":"6257","record_id":"<urn:uuid:d9136281-2cbc-4ee0-a141-55bc633477ca>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00183.warc.gz"} |
Create a generator that will limit the size of a generated sequence
There are a lot of generators that return a sequence (list, vector, tuple, map, string, etc). Sometimes it us useful to set size limits, either min or max, on the generated sequence. It would be nice
to have a generator that would accept a sequence generator and ensure that the sequences are of a certain length. Three examples would be:
(of-length min max gen)
(of-max-length max gen) => (of-length 0 max gen)
(of-min-length min gen) => (of-length min nil gen)
of-length check the length of the generated sequence. If it is too small, use (take min (cycle s)) to extend the length of the sequence.
If it is too long, use (take max s) to return the max length
It will need to be careful to return the same type it received.
If it does not receive a sequence, treat it as though it was one element sequence.
If min is not 0, use such-that not nil to ensure a proper seq is generated.
Comment made by: m0smith
I completely missed those that take the :min and :max options
In particular I was looking at the string based generators as I need to populate database tables and so the strings have to match the column definition like not null and varchar (15). As I was
thinking about the problem it seemed like writing a composable generator to enforce length restraints might make more sense than trying to retro fit all the generators that produce sequence-like
A short check of generators.cljc shows list, hash-map and even the array based ones could use min and max options.
Comment made by: m0smith
If I try to update string from a def to a defn in an attempt to allow multiple arguments for sizes like
(defn string ([] (fmap clojure.string/join (vector char))) ([size] (fmap clojure.string/join (vector char size))) ([min max] (fmap clojure.string/join (vector char min max))))
Then (sample string) no longer works but (sample (string)) (sample (string 5)) (sample (string 3 7)) all work
Is there a trick to getting a just "string" to work? Or is there a better way to modify string to accept multiple arugments?
_Comment made by: gfredericks_
I don't think there's any clean approach to solving the problem you noted, which is one reason that I don't see an obvious solution here.
I faced this issue when creating the {{large-integer}} and {{double}} generators, and I decided to create two generators: {{large-integer}} is a generator with default behavior, and
{{large-integer*}} is a function that takes options and returns a generator.
In hindsight I don't know if this was the best choice, since it's confusing. I asked David MacIver about how he handles this in hypothesis (a similar python library) and he said he doesn't have *any*
raw generators, just functions that return generators (sometimes with 0 arguments). I like the uniformity of that approach, but it would obviously be a big breaking change for test.check (though
there are some hacky tricks that could preserve backwards compatibility).
That issue is a bit bigger than this ticket. With respect to the code you showed, I think I'd prefer an API closer to what {{gen/set}} has, with an options map rather than positional args.
Now that you've got me thinking about this, I'm starting to get fixated on the idea of a big breaking API change that uses hacks to preserve backwards compatibility for a few versions, for the sake
of cleaning up a lot of inconsistencies. But again, that's bigger than this ticket.
If we can't come up with a clean short-term approach, my standards for accepting things are much more relaxed at [test.chuck|https://github.com/gfredericks/test.chuck] ☺.
_Comment made by: m0smith_
My very thought for making this request. Do we really want to double the number of string generators? Not to mention other things like arrays etc.
Another thought would be to add a single new generator, to-string, that can take a different character generator and use it to make strings based on an element generator:
(defn to-string
([element-gen] (to-string element-gen {})))
([element-gen [{:keys [num-elements min-elements max-elements max-tries ] :or {num-elements nil min-elements 0 max-elements nil max-retries 10}}]
(fmap clojure.string/join (vector char-gen ==apply-options==))))
I left out the code to handle the options properly but hopefully you get the idea.
It would be called like (to-string char {:min-elements 5 :max-elements 10}) or (to-string char-ascii {:num-elements 5})
This way it would be possible to add new character generators that could easily be converted to strings.
_Comment made by: m0smith_
I also had a thought on how to allow a function to be treated like a generator. Add a :generator-factory meta data to a function like
(defn to-string
"Generates strings of element-gen, default to char"
{:generator-factory to-string}
([] (to-string char {})))
([element-gen] (to-string element-gen {})))
([element-gen [{:keys [num-elements min-elements max-elements]}]
(fmap clojure.string/join (vector char-gen ==apply-options==))))
The generator? could then be updated to accept anything with a :generator-factory meta data
call-gen could be updated to look for the new meta data and if there, call the associated function and use the result as the Generator. | {"url":"https://ask.clojure.org/index.php/7623/create-generator-that-will-limit-the-size-generated-sequence","timestamp":"2024-11-05T04:31:12Z","content_type":"text/html","content_length":"87651","record_id":"<urn:uuid:30c7f4e4-0dce-4874-9abf-754f0c5e8888>","cc-path":"CC-MAIN-2024-46/segments/1730477027870.7/warc/CC-MAIN-20241105021014-20241105051014-00083.warc.gz"} |
APY Calculator | APY Interest Calculator | Annual Percentage Yield
APY Calculator | Annual Percentage Yield (APY) Calculator
Calculate Annual Percentage Yield using our APY Interest Calculator. with effective annual rate for an investment based on an annual interest rate and compounding frequency. The Annual Percentage
Yield (APY) represents the effective annual rate or the actual return on an investment when interest is compounded each period. Unlike standard advertised rates, which usually reflect simple
interest, APY takes compounding into account, providing a more accurate measure of an investment’s potential earnings.
The Annual Percentage Yield (APY) is the effective annual rate or the return on an investment when interest is compounded at each period. APY takes into account the effects of compounding, whereas
advertised rates usually represent returns based on simple interest.
How does this APY calculator work?
The formula for APY is as follows:
• r = Annual interest rate
• n = Number of compounding periods per year
An APY calculator, like the one below, can give you crucial information to determine the account’s profitability, without your having to do a lot of math. Within seconds, this tool can show you how
an account performs, so you can make an educated decision about what is best for your needs.
Definations of terms used in APY Calculator
• Initial deposit: The amount of money you deposit into the financial account for the first time. Usually, the financial institution will ask you at least this amount to open an account. Also, with
larger deposits getting better rates, it becomes the basis for your income. APY combines your first deposit to generate a new, higher balance.
• Monthly Deposit: You add money to your account by depositing money. Your first deposit contributes to the account, while subsequent deposits increase the principal amount, based on compound
• APY (Percentage Per Year): When looking at APY vs. APR, know that APR is an annual representation of the interest rate at which your savings will grow. Whether it’s a savings account, CD, or
other financial vehicle, your account balances are usually daily, weekly, monthly, or bi-monthly.
• Compounding frequency: Compounding refers to when you deposit money to receive interest. However, financial products have different variables that affect how much you earn. For example, an
account that compounds twice a year will earn less than an account that compounds monthly (provided the interest rate is the same).
• Intrest Earned / Earnings: This represents the interest earned from your first deposit and all subsequent deposits in a specific period of time. The APY calculator uses the interest on the
principal amount and the interest you’ve already earned to predict your total income for the year.
• Final Balance: The amount of money earned from all deposits after being made to the account. Financial institutions can limit your total free cash flow by type of fund (such as a CD that is only
allowed for the first time) or by amount (such as a $1 million limit on savings accounts down). Also check Internet Chicks site
FAQ'S Realted to APY Calculator
How is APY calculated?
APY (Annual Percentage Yield) is calculated by considering the interest rate and how frequently interest compounds. The formula for APY is:
• r is the annual interest rate.
• n is the number of times interest compounds in a year.
How do you calculate APY on a Certificate of Deposit (CD)?
To calculate APY on a CD, you need to know the interest rate and how often it compounds. If your CD compounds annually, the formula is:
How do I calculate APY on a savings account?
To calculate APY for a savings account, use the same APY formula. You will need to know the annual interest rate and the number of times the interest is compounded in a year.
How is APY calculated monthly?
If interest compounds monthly, you divide the annual interest rate by 12 (for each month). The APY formula would be adjusted to account for monthly compounding.
How do I calculate interest from APY?
To calculate the interest earned from APY, use the formula:
Interest=Principal×APYInterest = Principal \times APY
Where the principal is the initial deposit or investment.
How do you calculate APY in Excel?
To calculate APY in Excel, you can use the following formula in a cell:
APY = (1 + ( (Interest Rate) / (Number of Compounding Periods) ))^Number of Compounding Periods – 1
How do you calculate APY on a savings account with monthly compounding?
For savings accounts with monthly compounding, divide the annual interest rate by 12, and apply it to the APY formula:
APY = (1 +
Interest Rate
)^12 – 1
How do you calculate APY from an interest rate?
To calculate APY from an interest rate, apply the APY formula, which factors in how often the interest compounds. The interest rate alone does not account for compounding. | {"url":"https://techopedi.com/apy-calculator-apy-interest-calculator-annual-percentage-yield/","timestamp":"2024-11-02T05:27:26Z","content_type":"text/html","content_length":"148268","record_id":"<urn:uuid:98bd419a-e03f-4561-8b32-85784880b061>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00033.warc.gz"} |
Fraction Plus What Equals Fraction Calculator
Welcome to the Fraction Plus What Equals Fraction Calculator. This calculator calculates "what" in this sentence: "a/b plus what equals c/d?", where a/b and c/d are fractions that you enter.
Please submit your "a/b plus what equals c/d?" word problem below so we can show you how to solve it using algebra.
Here are some examples of what our Fraction Plus What Equals Fraction Calculator can answer:
1/2 plus what equals 3/4? 1/3 plus what equals 1/5? 2/5 plus what equals 3/4? 3/4 plus what equals 4/5? Copyright
Privacy Policy | {"url":"https://thefractioncalculator.com/fraction-plus-what-equals-fraction/fraction-plus-what-equals-fraction-calculator.html","timestamp":"2024-11-02T01:34:02Z","content_type":"text/html","content_length":"6118","record_id":"<urn:uuid:7e32ac8b-aae6-4e2e-b2cc-a43fc0a031df>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00342.warc.gz"} |
Observation of a vector charmoniumlike state in e+e-→ Ds+ Ds1 (2536)-+ c. c.
Using a data sample of 921.9 fb-1 collected with the Belle detector, we study the process of e+e-→Ds+Ds1(2536)-+c.c. via initial-state radiation. We report the first observation of a vector
charmoniumlike state decaying to Ds+Ds1(2536)-+c.c. with a significance of 5.9σ, including systematic uncertainties. The measured mass and width are (4625.9-6.0+6.2(stat)±0.4(syst)) MeV/c2 and
(49.8-11.5+13.9(stat)±4.0(syst)) MeV, respectively. The product of the e+e-→Ds+Ds1(2536)-+c.c. cross section and the branching fraction of Ds1(2536)-→D∗0K-is measured from the DsDs1(2536) threshold
to 5.59 GeV.
Dive into the research topics of 'Observation of a vector charmoniumlike state in e+e-→ Ds+ Ds1 (2536)-+ c. c.'. Together they form a unique fingerprint. | {"url":"https://portal.fis.tum.de/en/publications/observation-of-a-vector-charmoniumlike-state-in-ee-ds-ds1-2536-c--2","timestamp":"2024-11-14T08:53:37Z","content_type":"text/html","content_length":"99167","record_id":"<urn:uuid:f39d8d43-85e4-487d-bf07-ec9253b3f7fa>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00146.warc.gz"} |
Dark Buzz
There are a lot of people who believe that the probabilities of classical mechanics are subjective, because the underlying processes are all deterministic, and the quantum probabilities are
objective. The latter is sometimes called
the propensity theory of probability
On the other hand, Bayesians insist that probability is just an estimate of our beliefs.
A new paper tries to address the difference:
Forty some years ago David Lewis (1980) proposed a principle, dubbed the Principal Principle (PP), connecting rational credence and chance. A crude example that requires much refining is
nevertheless helpful in conveying the intuitive idea. Imagine that you are observing a coin áipping experiment. Suppose that you learn -- for the nonce never mind how -- that the objective chance
of Heads on the next flip is 1/2. The PP asserts that rationality demands that when you update your credence function on said information your degree of belief in Heads-on-the-next-áip should
equal 1/2, and this is so regardless of other information you may have about the coin, such as that, of the 100 flips you have observed so far, 72 of the outcomes were Tails.
The large and ever expanding philosophical literature that has grown up around the PP exhibits a number of curious, disturbing, and sometimes jaw-dropping features.1 To begin, there is a failure
to engage with the threshold issue of whether there is a legitimate subject matter to be investigated. Bruno de Finettiís (1990, p. x) bombastic pronouncement that "THERE IS NO PROBABILITY" was
his way of asserting that there is no objective chance, only subjective or personal degrees of belief, and hence there is no need to try to build a bridge connecting credence to a mythical
entity. Leaving doctrinaire subjectivism aside for the moment and assuming there is objective chance brings us to the next curious feature of the literature: the failure to engage with
substantive theories of chance, despite the fact that various fundamental theories of modern physicsó in particular, quantum theoryó ostensibly speak of objective chance. Of course, as soon as
one utters this complaint the de Finetti issue resurfaces since interpretive principles are needed to tease a theory of chance from a textbook on a theory of physics, and de Finettiís heirsó the
self-styled quantum Bayesians (QBians)ó maintain that the probability statements that the quantum theory provide are to be given a personalistic interpretation.2
I am not sure that any of this makes any sense.
The only way I know to make rigorous sense out of probability is the Kolmogorov probability axioms.
I don't believe there is any such thing as objective probability. It has never been an essential part of quantum mechanics.
Quantum mechanics is about observables. Probabilities are not observable. Believing in physical/objective/propensity probability goes against the spirit of the theory.
Sean M. Carroll is very good at explaining textbook physics, but when he discusses his own beliefs, he has some wacky ideas. He believes in determinism, and many-worlds theory.
(Yes, many-worlds is not deterministic, but that is not my point here.)
Here he debates panpsychism:
Theoretical physicist Sean Carroll joins us to discuss whether it make sense to think of consciousness as an emergent phenomenon, and whether contemporary physics points in this direction.
I see 3 possibilities.
1. There is no such thing as consciousness. Yes, we perceive all sorts of things, and act on those perceptions, but that's all.
2. Consciousness is real, and has a physical basis that may eventually be understood in terms of fundamental physics, chemistry, and biology.
3. Consciousness is in the mind or soul, and not the body, and it best understood in spiritual terms.
As a scientific reductionist, I lean towards (2), but the others are possible, especially since we don't even have a good definition of consciousness.
If (2) and scientific reductionism are true, and humans are composed of 10^30 or so quarks and electrons, then it seems plausible that each quark and electron has a little bit of consciousness.
Carroll's answer to this is that the behavior of electrons is completely determined by physical law, and so very strange changes to those laws would be needed to explain partially conscious
But our best laws of physics are not deterministic. Not in this universe, anyway. Those elections could be partially conscious without any change to known laws.
Carroll has elaborated on his own blog:
The idea was not to explain how consciousness actually works — I don’t really have any good ideas about that. It was to emphasize a dilemma that faces anyone who is not a physicalist, someone who
doesn’t accept the view of consciousness as a weakly-emergent way of talking about higher-level phenomena.
The dilemma flows from the following fact: the laws of physics underlying everyday life are completely known. They even have a name, the “Core Theory.” We don’t have a theory of everything, but
what we do have is a theory that works really well in a certain restricted domain, and that domain is large enough to include everything that happens in our everyday lives, including inside
ourselves. ...
That’s not to say we are certain the Core Theory is correct, even in its supposed domain of applicability.
He then launches into a discussion of zombies who appear to be just like conscious humans, but are not.
I don't see how this proves anything. He cannot define consciousness, and when he takes it away, peeople behave just the same. No. If conscious means anything, it means that people would behave
differently if they didn't have it.
Carroll calls his viewpoint physicalism, but it is really the opposite, as he refuses to accept a physical basis for consciousness.
I get why non-physicalists about consciousness are reluctant to propose explicit ways in which the dynamics of the Core Theory might be violated. Physics is really strong, very well-understood,
and backed by enormous piles of experimental data. It’s hard to mess with that.
He is assuming that a theory of consciousness would violate the Core Theory, but I doubt it.
Dr. Bee explains why particles decay, and adds a consciousness argument:
the tau can decay in many different ways. Instead of decaying into an electron, a tau-neutrino and an electron anti-neutrino, it could for example decay into a muon, a tau-neutrino and a muon
anti-neutrino. Or it could decay into a tau-neutrino and a pion. The pion is made up of two quarks. Or it could decay into a tau-neutrino and a rho. The rho is also made up of two quarks, but
different ones than the pion. And there are many other possible decay channels for the tau. ...
The taus are exactly identical. We know this because if they weren’t, they’d themselves be produced in larger numbers in particle collisions than we observe. The idea that there are different
versions of taus is therefore just incompatible with observation.
This, by the way, is also why elementary particles can’t be conscious. It’s because we know they do not have internal states. Elementary particles are called elementary because they are simple.
The only way you can assign any additional property to them, call that property “consciousness” or whatever you like, is to make that property entirely featureless and unobservable. This is why
panpsychism which assigns consciousness to everything, including elementary particles, is either bluntly wrong – that’s if the consciousness of elementary particles is actually observable,
because, well, we don’t observe it – or entirely useless – because if that thing you call consciousness isn’t observable it doesn’t explain anything.
So you could have two identical tau particles, and one decays into an electron and 2 neutrinos, and the other decays into a muon and 2 neutrinos.
And we have a Core Theory that explains the dynamics of everything that happens!
No, this is untenable. I see a couple of possibilities.
1. Those taus are not really identical. They have internal states that determine how they will decay.
2. The taus are identical, but they have some sort of conscious free will that allow them to choose how and when they decay.
Some physicists would say that the taus are identical and intrinsically random. But saying that is just a way of saying that we don't know whether it is possibility (1) or (2).
Dr. Bee gives an argument for the taus being identical. But we can never be sure that they are truly identical. Maybe they just appear identical in a particular quantum field theory, but that ignores
a deeper reality.
I know it seems crazy to say that a tau particle has a little bit of conscious free will. But the alternatives are stranger.
Now where does human consciousness come from? Carroll says that it cannot come from anything in the Core Theory, because it is dynamically complete and there is no room for any panpsychism.
There is room. Quantum mechanics is not deterministic. It predicts probabilities because there are mysterious causal factors that it cannot account for.
Jerry Coyne says that Carroll decisively refutes panpsychism. I disagree. I say Carroll has the worse argument.
After writing this, I am surprised to see Lubos Motl take the side of panpsychism.
But even before QM, it was rather clear that panpsychism was needed in any scientific world view simply because there can't be any "metaphysically sharp" boundary between objects like humans that
we consider conscious; and other objects. So some amount of the "consciousness substance" must be assigned to any object in Nature, otherwise we end up with a clearly scientifically ludicrous
anthropocentric or anthropomorphic theory. ...
OK, Carroll hasn't noticed that the current "Core Theory" is actually quantum mechanical and therefore needs conscious observers to be applied. Much of his article is a circular reasoning ...
For the 9,877th time, he can only be a "physicalist" because he doesn't do science. If he were doing science, he would be abandoning theories that conflict with the observations. And because all
classical i.e. P-world theories conflict with the observations, they are dead....
Carroll behaves exactly like you expect from a zombie: Sean Carroll is a simulation of a generic zombie
This isn't fair because Carroll's Core Theory is not classical mechanics. Carroll would say that he is very much a believer in quantum mechanics.
But Carroll doesn't really believe in textbook quantum mechanics. He believes in many-worlds theory, where there is no wave function collapse, no probabilities, no predicted events, no free will, and
no correspondence with any scientific experiments.
Yes, I do think that many-worlds theory is fundamentally incompatible with science. It is owrse than believing in astrology or witchcraft.
Nautilus has more on the pros and cons of panpsychism.
Here is some skepticism about Google:
Now though, in a paper to be submitted to a scientific journal for peer review, scientists at the Institute of Theoretical Physics under the Chinese Academy of Sciences said their algorithm on
classical computers completed the simulation for the Sycamore quantum circuits [possibly paywalled; alternative source of the same article] "in about 15 hours using 512 graphics processing units
(GPUs)" at a higher fidelity than Sycamore's. Further, the team said "if our simulation of the quantum supremacy circuits can be implemented in an upcoming exaflop supercomputer with high
efficiency, in principle, the overall simulation time can be reduced to a few dozens of seconds, which is faster than Google's hardware experiments".
I t hink this is why Scott Aaronson retracted his quantum supremacy blessing.
IBM had denied that Google reached quantum supremacy, and now makes its own supremacy claim:
IBM has created a quantum processor able to process information so complex the work can't be done or simulated on a traditional computer, CEO Arvind Krishna told "Axios on HBO" ahead of a planned
Why it matters: Quantum computing could help address problems that are too challenging for even today's most powerful supercomputers, such as figuring out how to make better batteries or
sequester carbon emissions.
Driving the news: IBM says its new Eagle processor can handle 127 qubits, a measure of quantum computing power. In topping 100 qubits, IBM says it has reached a milestone that allows quantum to
surpass the power of a traditional computer. "It is impossible to simulate it on something else, which implies it's more powerful than anything else," Krishna told "Axios on HBO...."
Krishna says the quantum computing push is one part of his approach to return the company to growth.
The comments about these news items are mostly skeptical, such as:
This is the third Quantum Computing BS story today. IBM literally "simulates" a quantum circuit and then claims it is superior to classical. Well, no shit sherlock. As I said before this is the
equivalent of claiming a pebble tossed in water is super to a classical computer because it accurately and instantly shows the interference and refraction patterns. There you go, call it "pebble
supremacy." Or a camera and flash photography setup is superior to a classical computer in rendering photorealistic ray-tracing. Technically yes, but in reality bullshit. ...
Indeed. The history of QC claims is an endless series of lies. ...
But the summary says it will help to sequester carbon. That must be true because IBM would never spew BS about something as important as sequestering carbon and the relevance of quantum computing
to carbon sequestration is totally obvious to everyone. ...
Extraordinary Popular Delusions and the Madness of Crowds, Charles Mackay. ...
Is it me, or does this quantum computing stuff starting to sound like a bunch of hooey? What are they even going to calculate with it? It never seems to have any real world application. Why do I
have this iMac on my desktop, when a quantum computer is billions of times better? Can they make a little one for me that's only a 1000 time better than my iMac? And how the hell is it gonna
solve the battery problem. That's gonna take people making things and testing them? 127 qubits, my ass!
Aaronson weighs in on these new developments:
About IBM’s new 127-qubit superconducting chip: As I told New Scientist, I look forward to seeing the actual details! As far as I could see, the marketing materials that IBM released yesterday
take a lot of words to say absolutely nothing about what, to experts, is the single most important piece of information: namely, what are the gate fidelities? How deep of a quantum circuit can
they apply? How have they benchmarked the chip? Right now, all I have to go on is a stats page for the new chip, which reports its average CNOT error as 0.9388—in other words, close to 1, or
terrible! ...
About the new simulation of Google’s 53-qubit Sycamore chip in 5 minutes on a Sunway supercomputer (see also here): This is an exciting step forward on the classical validation of quantum
supremacy experiments, and—ironically, what currently amounts to almost the same thing—on the classical spoofing of those experiments. Congratulations to the team in China that achieved this! But
there are two crucial things to understand. First, “5 minutes” refers to the time needed to calculate a single amplitude (or perhaps, several correlated amplitudes) using tensor network
contraction. It doesn’t refer to the time needed to generate millions of independent noisy samples, which is what Google’s Sycamore chip does in 3 minutes.
I am inferring that there is still no consensus on whether quantum computers are possible. Maybe IBM will convince some people, and maybe not.
Update: Aaronson also makes some political comments in support of those trying to stop Woke Leftists from stifling all alternative views in academia. But he adds:
Just for the record, I also have never considered voting Republican. The way I put it recently is that, if the Republicans disavowed their authoritarian strongman and came around on climate
change (neither of which they will), and if the Democrats continued their current descent into woke quasi-Maoism, my chance of voting Republican would surely increase to at least a snowball’s
chance in hell, from its current individual snowflake’s chance in hell. 🙂
This shows that he is very much a part of the deranged Left. He thinks Trump was an authoritarian strongman, but Pres. Biden has been much more authoritarian. Differences in climate policy have been
A argument is commonly made that everything in the world is either deterministic or random, and this leaves no room for free will. I am surprised that otherwise intelligent men make this silly
The argument essentially says that nothing good can come out of quantum randomness. But if that were true, then nothing good could come out of quantum computers.
While I have argued that quantum computers are useless, I do not make that silly argument. Of cuorse quantum indeterminacy can be part of a useful process.
From a free will essay:
A second criticism of the indeterminacy argument is that it does not allow for the type of human choices that free will advocates need. The indeterminacy of electrons is a random thing, but
genuinely free choices cannot be random: they are thoughtful and meaningful actions. If I am deciding between buying chocolate ice cream and vanilla and I randomly flip a coin to decide, that is
an arbitrary action, not a free action. If in fact all of our actions were indeterminate in the way that electrons are, we would have nonstop spasms and convulsions, not meaningfully chosen
actions. Rather than selecting either the chocolate ice cream or vanilla, I would start quivering like I am having a seizure. Thus, subatomic indeterminacy is no real help to the free will
advocate. ...
Second, regarding the contention that indeterminacy will only produce random actions, this is not necessarily the case. Quantum computers do not result in arbitrary events, like memory chips
catching on fire, or printers printing out gibberish. Rather, quantum phenomena are carefully introduced into precise spots within the computer’s hardware, the result being that it can perform
tasks with enormously greater efficiency than any other existing computer. So too with quantum biology: the results are biological processes that perform highly complex tasks with great
efficiency, such as global detection, vision, and photosynthesis. If evolution has in fact tied brain activity to quantum phenomena, it is reasonable to assume that it would similarly facilitate
an important biological process with great efficiency. None of this proves the existence of free will through indeterminacy, but it at least offers a scientifically-respectable theory for how
nature might have implanted within our brains the ability to have done otherwise.
Yes, I think it is possible that a reductionist microscopic analysis of free will would show some quantum indeterminacy.
The essence of free will is the ability to make a decision that others cannot predict. So your decision will look random to them. So saying that there is randomness in fundamental physics is an
argument for free will, not against it.
Here is philosopher Massimo Pigliucci making an argument that free will is incoherent:
The next popular argument for a truly free will invokes quantum mechanics (the last refuge of those who prefer to keep things as mysterious as possible). Quantum events, it is argued, may have
some effects that “bubble up” to the semi-macroscopic level of chemical interactions and electrical pulses in the brain. Since quantum mechanics is the only realm within which it does appear to
make sense to talk about truly uncaused events, voilà!, we have (quantistic) free will. But even assuming that quantum events do “bubble up” in that way (it is far from a certain thing), what we
gain under that scenario is random will, which seems to be an oxymoron (after all, “willing” something means to wish or direct events in a particular — most certainly not random — way). So that’s
out as well.
It now begins to look like our prospects for a coherent sense of free will are dim indeed.
Pigliucci is wrong on many levels. We invoke quantum mechanics because it is our best physical theory, and hence makes the world less mysterious, not more mysterious.
Quantum mechanics is no more about "truly uncaused events" than any other theory. It makes predictions based on causality from past info and events. And an action from free wiil is not an uncaused
He says "random will" is an oxymoron, but a free choice does indeed appear random to someone who cannot predict that choice.
While this does not prove free will, it does refute certain arguments against free will.
Nature magazine reports:
Human Betterment Foundation (HBF), one of the most prominent eugenics groups of its time, begun in Pasadena in the same decade that Caltech transformed from a sleepy small-town technical school
into a science and engineering powerhouse. ...
In June 2020, shortly after the killing of George Floyd by police in Minneapolis, Minnesota, student groups including the Socialists of Caltech, a group to which Panangaden belongs, put the
spotlight on Caltech’s most famous former president — Nobel-prizewinning physicist Robert Millikan — and his involvement with the Human Betterment Foundation as a trustee. ...
At Caltech, events progressed quickly last year. The institute assigned a committee to investigate its links to eugenics advocacy. And after a months-long process that sometimes pitted students
against administrators, leaders decided in January to remove Millikan’s name and several others from prominence on campus. This week, they announced some of the names that will replace them.
It’s a meaningful move for Panangaden, who identifies as multiracial and disabled. “I find it important to rename the buildings just because I don’t want to have that constant reminder that the
people who built this institution didn’t want me to be there, and didn’t even want me to exist.”
But she says it would be a hollow effort without further steps to address the institution’s diversity gaps.
I am not going to defend forced sterilization, but what does that have to do with George Floyd, affirmative action quotas, and a student identifying as socialist/multiracial/Indian/disabled/female?
Perhaps in another century, forced sterilization will be seen as morally similar to vaccination mandates or child support. So will today's scientists be eventually canceled if they advocated vax
Millikan was a great physicist, and a CalTech pioneer. He had no power to force any medical procedure on anyone. If he expressed some opinions about some proposed laws, why should anyone care now?
The worse accusation against Millikan is that he allowed his name on this pamphlet. The opinions expressed appear to be sincere policy suggestions to make the world better for everyone. It says:
There can be no question that a very large portion of feeblemindedness is due to inheritance. The same is tru of mental disease
This is true, but people do not like to admit it. I think the critics of this pamphlet ought to explain exactly where is goes wrong. I have my own opinions, but I suspect that the leftist critics
have other issues, and would rather not spell them out.
This weirdo students dig this stuff up as an excuse to make childish demands.
Scientific American goes deeper into partisan politics and bogus science. Here is the latest:
The recent election of Glenn Youngkin as the next governor of Virginia based on his anti–critical race theory platform is the latest episode in a longstanding conservative disinformation campaign
of falsehoods, half-truths and exaggerations designed to create, mobilize and exploit anxiety around white status to secure political power. The problem is, these lies work, and what it shows is
that Democrats have a lot of work to do if they want to come up with a successful countermessage.
Conservatives have spent close to a century galvanizing white voters around the “dangerous” idea of racial equality.
Another headline is:
Many Neuroscience Conferences Still Have No Black Speakers
The illustration is of George Floyd.
The magazine used to be outstanding at getting to the heart of scientific issues. Not promoting racial tokenism.
Update: Jerry Coyne also comments on Scientific American again posting nonscientific political editorials.
I have no idea why Scientific American is publishing editorials that have absolutely nothing to do with science. Yes, they have gone woke, and yes, they’re circling the drain, and while they of
course have the right to publish what they want, they’ve abandoned their mission to shill for the progressive Democrats.
The latest shrill editorial is a critique of CRT implying that those who oppose its teaching in schools in whatever form, and are in favor of anti-CRT bills, are white supremacists. If you don’t
believe me, read the article below. ...
But why is Scientific American publishing this kind of debatable (and misleading) progressive propaganda? Why don’t they stick with science? As a (former) scientist, I resent the intrusion of
politics of any sort into scientific journals and magazines. If I want to read stuff like the above, well, there’s Vox and Teen Vogue, and HuffPost and numerous other venues.
I wonder how long Scientific American will last. . . . .
The essence of relativity is a non-Euclidean geometry view of causality.
I have posted about the historical importance of geometry here and here, and stressed the importance to relativity here and here.
When physicists talk about non-Euclidean geometry in relativity, they usual mean gravitational masses curving space. If not that, they mean some clever formulas that relate hyperbolic space to
velocity addition formulas and other aspects of special relativity. I mean something different, and more basic.
For an excellent historical summary, see The Non-Euclidean Style of Minkowskian Relativity, by Scott Walter. See also Wikipedia.
Euclidean geometry means 3-dimensional space (or R^n) along with the metric given by the Pythagorean Theorem, and the symmetries given by rotations, translations, and reflections.
Other geometries are defined by some space with some metric-like structure, and some symmetry group.
Special relativity is spacetime with the metric dx^2 + dy^2 + dz^2 - c^2 dt^2, and the Lorentz group of symmetries. It is called the Poincare group, if translations are included.
That's it. That's why the speed of light appears constant, why nothing can go faster, why we see a FitzGerald contraction, why times are dilated, why simultaneity is tricky, and everything else. They
are all byproducts of living in a non-euclidean geometry.
I am not even referring to curved space, or hyperbolic space. I mean the minus sign in the metric that makes time so different from space. It gives flat spacetime a non-euclidean geometry.
Historically, H. Lorentz viewed relativity as an electromagnetism theory. He viewed everything as based on electromagnetism, so I am not sure he would have distinguished between a spacetime theory
and an electromagnetism theory.
Now we view electromagnetism as just one of the four fundamental forces, but Lorentz was not far off. At the time, it was not known that electromagnetism underlies all of chemistry, so he was right
to view it as much more pervasive that was commonly accepted.
Poincare was the first to declare relativity a spacetime theory, and to say it applies to electromagnetism or gravity or anything else. He was also the first to write the spacetime metric, and the
Lorentz symmetry group. He did not explicitly say that it was a geometry, but that would have been obvious to mathematicians at the time.
I credit J.C. Maxwell with being the father of relativity. He was till alive in 1972 when the Erlangen Program for studying non-euclidean geometries was announced. He probably had no idea that it
would provide the answer to what had been puzzling him most about electromagnetism.
Minkowski cited Poincare, and much more explicitly treated relativity as a non-euclidean geometry. He soon died, and his ideas caught on and were pursued by others.
Einstein understood in his famous 1905 paper that the inverse of a Lorentz transformation is another Lorentz transformation, and that the transformations can be applied to the kinematics of moving
objects. Whether he got any of this from Poincare is hard to say. Einstein rejected the geometry view as the basis for relativity. He did partially adopt Minkowski's metric about 1913, but continued
to reject relativity geometrization at least until 1925. Carlos Rovelli continues to reject it.
The geometry is what enables relativity to explain causality. It is what made J.C. Maxwell's electromagnetism the first relativistic theory, and hence the first truly causal theory. Everything is
caused by past events in the light cone. The non-euclidean geometry restricts the causality that way.
Science is all about reductionism, ie, reducing observables to simpler components. Applied to space and time, it means locality. Objects only depend on nearby objects, and not distant ones. Events
depend on recent events, and not those in the distant past. It is the Euclidean distance that defines what objects are nearby. Clocks define the recent past, but is an event recent if it is a nearby
object at a recent time?
Maybe yes, maybe no. That is where we need the non-euclidean geometry. The Minkowski metric is a fancy way of saying that the event was recent if light could have made the trip quickly.
If spacetime had a Euclidean geometry, then two events would be close if they are close in space and close in time. Causality does not work that way.
An event might seem to be spatially close, but if it is outside the light cone, then it cannot be seen, and it can have no causal effect. That is the consequence of the geometry.
Special relativity is usually taught based on the Michelson-Morley experiment on the motion of the Earth, and that is how it was historically discovered. It became widely accepted after Minkowski
convinced everyone in 1908 that it was all geometry.
Today general relativity books emphasize the non-euclidean geometry of curved space, but the textbooks do not explain that the non-euclidean geometry of flat spacetime is at the very core of special
and general relativity.
In July this year, a team in China demonstrated that it has the world’s most powerful quantum computer, finally leapfrogging Google, who claimed to have achieved quantum supremacy back in 2019.
Back then, China was touting a super-advanced 66-qubit quantum supercomputer called “Zuchongzhi” as a contender against Google’s 54-qubit Sycamore processor. But while Google’s quantum computers
have not progressed noticeably since then, China on the other hand never slowed down, coming up with more powerful quantum processors.
According to a recent study published in peer-reviewed journal Physical Review Letters and Science Bulletin, physicists in China claim they’ve constructed two quantum computers with performance
speeds that far outrival competitors in the US or indeed anywhere in the world — debuting a superconducting machine along with a speedier unit that uses light photons to obtain unprecedented
I didn't read the papers, but they are still not computing anything. They just generate some random noise, and claim that it would be hard for a regular computer to simulate it.
It will be news if they actually compute something. | {"url":"http://blog.darkbuzz.com/2021/11/","timestamp":"2024-11-12T13:53:14Z","content_type":"text/html","content_length":"150225","record_id":"<urn:uuid:b6a9be38-cd09-492a-9a40-7ae390e01037>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00737.warc.gz"} |
An object 0.680 cm tall is placed 18.5 cm to the left of the vertex of a concave spherical mirror having a radius of curvature of 24.0 cm . Calculate...
Answered You can hire a professional tutor to get the answer.
An object 0.680 cm tall is placed 18.5 cm to the left of the vertex of a concave spherical mirror having a radius of curvature of 24.0 cm . Calculate...
An object 0.680 cm tall is placed 18.5 cm to the left of the vertex of a concave spherical mirror having a radius of curvature of 24.0 cm . Calculate the position of the image? Calculate the size of
the image?
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Ask a Question | {"url":"https://studydaddy.com/question/an-object-0-680-cm-tall-is-placed-18-5-cm-to-the-left-of-the-vertex-of-a-concave","timestamp":"2024-11-03T09:55:00Z","content_type":"text/html","content_length":"26154","record_id":"<urn:uuid:96381cbf-1474-4c32-a302-5b944484e15b>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00257.warc.gz"} |
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• radical expressions worksheets | {"url":"https://softmath.com/math-com-calculator/function-range/basic-equations--algebra.html","timestamp":"2024-11-08T21:18:37Z","content_type":"text/html","content_length":"206501","record_id":"<urn:uuid:7534ba77-6319-4b95-a676-6109c2677fcd>","cc-path":"CC-MAIN-2024-46/segments/1730477028079.98/warc/CC-MAIN-20241108200128-20241108230128-00688.warc.gz"} |
Anders Gustafson - Nemo Nisi Mors
My name is Anders Gustafson. I am a software developer interested in mathematics, time handling and maps.
Nemo nisi mors is Latin for Nothing, except death (will do us part) and is my philosophy of life.
The easiest way to contact me is by sending an email to
In the different areas of Nemo Nisi Mors (NNM) you can also find:
• An appreciated and comprehensive compilation with my thoughts about the complexities and ambiguities of using time zones, 12-hour clocks and different date formats. One of the many things
discussed is if you unambiguously can know if a time you see is the correct time for the location on Earth where you are at the moment. Some of the peculiar quirks that you will learn about.
• My experiences from using timestamps. The Timestamp magician tool can help you examine different types of timestamps.
• Use current time or constant time when you want to inform about the correct time.
• A math section, with some educational pages. For example,
• Some (hopefully) useful and educational applications
• The NNM Web component library, a collection of various web components (custom elements), containing especially the following:
• For the Swedish audience:
• My love, Ingmarie Nilsson.
• Elvira, the cat.
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Comparison of Dynamic Characteristics of Gears with Different Tooth Surfaces under Different Factor Excitation
The dynamic simulation is carried out by using Benedict amp; Kelly model and time-varying friction coefficients obtained in Figure 2.8 under different micro-states of tooth surfaces.
1. Time-domain signal characteristics of dynamic displacement
Figure 1 shows the time-domain signal (Savg=0.523) of the displacement response of the active and passive gears in the X and Y directions.Fig.) N K (force rodent) N K (visible engagement line
direction (Y direction) displacement amplitude is greater than friction direction (X direction), there is obvious periodic impact on both signals.
2. Dynamic engagement force and friction force
As shown in Figure 2, the time domain signal of dynamic force between two gears is extracted from the signal of two meshing cycles in steady state, which is also convenient for analysis. The
transverse coordinate is also convenient for analysis in dimensionless time (t/tD), the transverse coordinate is also convenient for analysis in dimensionless time (t/tD), and the transverse
coordinate is expressed in dimensionless time (t/tD).The periodicity of dynamic meshing force fluctuation can be seen from the diagram. There is obvious meshing impact at single and double teeth
alternating meshing point B, D and E, up to 3.6kN, while the average meshing force is about 2.6kN, which is the main excitation source of gear vibration.Comparing the three different tooth surfaces,
with the increase of roughness, the meshing amplitude tends to decrease gradually. For example, when Savg=0.991, the maximum meshing force is 3kN and the average meshing force is 2.2kN.
Figure 2 shows that there is obvious periodic change in the dynamic friction force on the tooth surface. In the AC segment, the two teeth have opposite directions and the total friction force cancels
each other, while the direction of the friction force on the gear tooth 1 changes at joint C and the total friction force) N K (friction impact occurs when the axial Y of the bearing force increases
sharply).At points B and E, the abrupt change in the meshing force causes fluctuations in the friction force.On the whole, the friction force on the tooth surface increases with the increase of the
roughness of the tooth surface, because the variation of the friction coefficient is non-linear, and the sudden change of the friction coefficient at point C also aggravates the impact caused by the
friction force when the gear meshes through the joint.
3. Dynamic bearing force
Bearing force is the dynamic force formed by the meshing force of the gear transferred to the bearing via the gear-shaft, which ultimately excites the vibration of the box.Figure 3 shows the
time-frequency signal of bearing force of pinion in Y-direction, i.e. engagement line direction. It can be seen that the impact excitation of pinion is obvious when the gear is in rodent at time T D
and rodent at time T D. However, from the time-domain signal, the change of bearing force amplitude is not obvious, while the frequency-domain signal shows that when the tooth surface roughness
increases, the amplitude of low-frequency component increases and the high-frequency component decreases slightly.
Figure 4 shows the bearing force in the direction of pinion friction force. The time-domain signal shows that the bearing force at the joint forms impact vibration due to the change of friction force
and gradually decreases under the action of bearing damping, while the bearing force increases with the increase of tooth surface roughness.In frequency domain, the first three order amplitude of low
frequency is larger.It is found that the natural frequency of translation motion is 8517Hz, because the bearing stiffness in both directions is the same, the natural frequencies are shown in Fig. 3
and Fig. 4.
4. Dynamic Transmission Error (DTE)
Fig. 5 compares the time-domain signals of dynamic transmission errors with different roughness. It is found that the amplitudes of DTE fluctuate between -7~9um and the impact of tooth surface is
obvious. When there is gap between actual teeth, tooth detachment and slapping will occur.Comparing the error magnitude of three cases, it is found that the error decreases with the increase of
roughness, especially the magnitude of the first two orders decreases significantly, while the higher order changes little, as shown in Figure 6.
On the one hand, the results indicate that the increase of tooth surface roughness increases the friction force on the tooth surface. When the friction moment is opposite to the driving moment, the
friction force restrains the vibration of the gear in the direction of meshing line to a certain extent and thus reduces the generation of dynamic error.In the example of this study, the influence of
friction force is more obvious because the period of friction action takes up a longer part of the whole meshing process (about 4/5) for the need of experimental design; on the other hand, the
increase of roughness causes the variation of error e(t), which has no obvious influence on dynamic error.It can be seen that the dynamic signal of meshing line direction is not sensitive to the
Micro-changes of tooth surface. | {"url":"https://www.zhygear.com/comparison-of-dynamic-characteristics-of-gears-with-different-tooth-surfaces-under-different-factor-excitation/","timestamp":"2024-11-03T23:10:18Z","content_type":"text/html","content_length":"173204","record_id":"<urn:uuid:481b0657-4860-4e95-b596-ffeca103e328>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00468.warc.gz"} |
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Full-Text Articles in Education
Designing An Educational Robotics Curriculum To Teach Mathematical Concepts While Fostering A Growth Mindset: A Self-Study, Lauren Harter
Designing An Educational Robotics Curriculum To Teach Mathematical Concepts While Fostering A Growth Mindset: A Self-Study, Lauren Harter
Electronic Theses and Dissertations
This study explores the development and implementation of a five-day curriculum designed to enhance students' understanding of algebraic concepts through the integration of educational robotics and
growth mindset principles. The study is structured around three research questions that investigate influences on decision-making in curriculum design, the alignment of teaching intents with
practices, and the impact of self-study on integrating algebra, robotics, and growth mindset principles. Findings reveal themes focused on the importance of research and collaboration, using the
Understanding by Design (UbD) framework, intentional curriculum creation, starting somewhere, personal growth and self-reflection, and experiencing and embodying constructivism in action. The …
The Benefits Of Using Open-Note Assessments, Logan Schaefers
The Benefits Of Using Open-Note Assessments, Logan Schaefers
Master of Education Program Theses
This action research study investigated the impact of open-note assessments on student learning as measured by the student’s overall score on unit assessments inside of a 9th grade Algebra 1
classroom. This study included 332 freshmen: an experimental group (open-note assessments) of 72 students and a control group of 260 students. Findings of this study did not show a statistically
significant increase in the scores of students using open-note assessments. However, when looking at the different quartiles of test scores, the overwhelming evidence by the researcher revealed the
benefits that open-note assessments had on student’s academic performance resulting in better …
The Perspectives Of Using Desmos For Students’ Conceptual Understanding And Procedural Fluency To Solve Linear Equations, Larmel Dimatulac Madrilejos
The Perspectives Of Using Desmos For Students’ Conceptual Understanding And Procedural Fluency To Solve Linear Equations, Larmel Dimatulac Madrilejos
Theses and Dissertations
The study examines the perspectives of using the Desmos calculator of Algebra I students' conceptual understanding and procedural fluency to write, graph, and solve linear equations in Algebra I
STAAR. While the students have continuously used technology for mathematics assessment, emergent bilingual students in South Texas still need help passing high-stakes testing. The framework of the
study is grounded in the theory of mathematical education (knowledge of mathematics educators to teach), the theory of mathematical learning (understanding how students learn mathematics), and social
constructivism. The study seeks ways to teach all students, mainly the minority, to learn …
The Importance Of Implementing Literacy Strategies In A Mathematics Classroom, Lauren Tecca, Joanna Weaver, John Chen
The Importance Of Implementing Literacy Strategies In A Mathematics Classroom, Lauren Tecca, Joanna Weaver, John Chen
Honors Projects
The purpose of this ACTION research study is to explore the influence of literacy on mathematical proficiency levels. The correlation will use the data to formulate some strategies for the classroom
in order to increase confidence in both subject areas.
The Relationship Among Learners’ At-Risk Indicators And Ninth Grade Algebra I Achievement, Sara E. Tudon
The Relationship Among Learners’ At-Risk Indicators And Ninth Grade Algebra I Achievement, Sara E. Tudon
Theses and Dissertations
The purpose of this research is to examine the relationship between at-risk indicators including socioeconomic status, English language learners (ELL), and gender to student performance in the
Algebra I End of Course assessment. The research questions presented in the non-experimental quantitative research design were: (1) What is the impact of socioeconomic status on the Algebra I EOC
exam? (2) What is the success rate of ninth grade students identified as English Language Learners (ELL) compared to non-identified ninth grade students in Algebra I? and (3) What is the difference
in ninth grade Algebra I achievement between males and females? (4) …
Ap Physics Course Enrollments: The Impact Of Middle School Algebra And Physics First, Judi G. Luepke
Ap Physics Course Enrollments: The Impact Of Middle School Algebra And Physics First, Judi G. Luepke
Dissertations (1934 -)
The position of the United States in the global STEM economy is being challenged by other countries. There is national concern that the STEM pipeline be strengthened to ensure more students pursue
STEM degrees and join the STEM workforce. Although it is important to inspire youth in STEM programs, it is also important to provide all students access to the STEM gatekeeper courses of calculus,
chemistry, and physics. This study determined if taking algebra in middle school and Physics First impacted AP Physics enrollments in a suburban high school. Taking physics in ninth grade, or Physics
First, is part of …
The Impact Of Acceleration In Secondary Math On All Students, James Grover
The Impact Of Acceleration In Secondary Math On All Students, James Grover
Theses and Dissertations
Mathematics is a collection of mental practices, attitudes and tools that humans have developed in our quest to understand the world (Singh & Brownwell, 2019). Educators have identified math and
reading as the two core subjects that are essential for academic success. Achievement in math is considered to be the one of the most important predictors of economic success (Chazan, 2008).
Educational leaders have become increasingly interested in finding the ideal placement for students to gain access to benchmark math curriculum that opens doors for advancement. In a competitive
global market, educational and political leaders in the United States have …
Impact Of Interventions On Student Performance Among Eighth Graders In Algebra 1, Tiffany Osborne
Impact Of Interventions On Student Performance Among Eighth Graders In Algebra 1, Tiffany Osborne
All Dissertations
Educational leaders and practitioners face challenges in South Carolina schools, but through improvement science processes (Bryk, Gomez, Grunow, & LeMahieu, 2015), they can collectively develop
solutions which directly address those issues. In this Participatory Action Research (PAR) study, I partnered with participants in ongoing Plan-Do-Study-Act (PDSA) cycles (Bryk, et al., 2015) to
improve student outcomes. I triangulated multiple data points and corroborated findings with students’ own perceptions to provide evidence that students can achieve in eighth grade Algebra 1 when
given the opportunity to enroll in the course and when afforded appropriate ongoing academic interventions that foster conceptual understanding, self-efficacy, …
Effective Interventions For Secondary Students With Disabilities To Be Successful In Mathematics, Garret Atteberry
Effective Interventions For Secondary Students With Disabilities To Be Successful In Mathematics, Garret Atteberry
Culminating Projects in Special Education
This Starred Paper provides article summaries and data of different types of effective math interventions to secondary students with disabilities. This research is broken down into three main
interventions: Concrete-Representational-Abstract, Explicit Teaching, and Cognitive Strategies.
Preparing New Jersey Community College Students For The Mathematics Placement Tests, Charles Edward Haas
Preparing New Jersey Community College Students For The Mathematics Placement Tests, Charles Edward Haas
Walden Dissertations and Doctoral Studies
Although most new college students had to demonstrate algebraic and basic mathematics mastery to earn a high school diploma or the equivalent, the majority of incoming New Jersey community college
students are not showing this knowledge on the mathematics placement tests, thus placing into developmental courses, which must be successfully completed before students can attempt any college-level
mathematics courses. Guided by Knowles’ theory of andragogy and developmental mathematics as a core concept, the purpose of this study was to determine ways to help incoming New Jersey community
college students prepare for the ACCUPLACER mathematics tests. The research questions addressed testing …
Effects Of Differential Instructional Time In Algebra On Standardized Assessment And Semester Grade Outcomes, Michael S. Wojtowicz
Effects Of Differential Instructional Time In Algebra On Standardized Assessment And Semester Grade Outcomes, Michael S. Wojtowicz
Graduate Research Theses & Dissertations
Building off of other studies that examined the effectiveness of double-dose algebra programs such as Nomi and Allensworth (2009), this dissertation compared the performance outcomes of students
enrolled in one of two alternatives to traditional high school algebra, a double-dose and a single-dose algebra program. This work utilized multiple linear regression to assess the degree of
association between student race/ethnicity and selected demographic characteristics, including gender, free and reduced lunch status, and IEP status, on standardized assessment and end of semester
mathematics course grade outcomes, while controlling for initial mathematics placement test results. This project assessed these outcomes for students …
Outcomes Of A School-Wide Mathematics Intervention, Lisa M. Garrett
Outcomes Of A School-Wide Mathematics Intervention, Lisa M. Garrett
Walden Dissertations and Doctoral Studies
In response to studentsâ poor algebra achievement, Midtown High School, a pseudonym, implemented a school-wide math intervention and enrichment program during the 2014-2015 school year. The purpose
of this mixed-methods study was to assess the influence of the intervention on Algebra I and Algebra II end-of-course (EOC) exam achievement scores as well as explore math teachersâ perspectives of
the intervention program. The theoretical foundation was constructivism. A consensus sample using archival data from all 419 high school students taking Algebra before the intervention 2013-2014 and
after the intervention 2014-2015 and 2015-2016 were used with teacher interviews for triangulation. ANOVA results …
An Exploration Of Scaffolding Strategies In A Remedial High School Mathematics Course, Pauline Ofure Aikhuele
An Exploration Of Scaffolding Strategies In A Remedial High School Mathematics Course, Pauline Ofure Aikhuele
Walden Dissertations and Doctoral Studies
In a southeastern state school district, the educators understood little about the scaffolding practices of ninth-grade teachers of Foundations of Algebra (FOA), a remedial course. FOA is a
mathematics course designed for students who need substantial help to master the required standards. An increasing number of students in 2 high schools failed FOA; hence, they were not prepared for
Algebra 1. The purpose of this qualitative exploratory case study was to explore the scaffolding strategies used by FOA teachers. Bruner's constructivist theory and Vygotsky's zone of proximal
development (ZPD) theory were used to guide this study. The research questions addressed …
Implementing Technology Enhanced Mathematical Instruction In An Algebra I Course To Increase Students’ Academic Achievement In Mathematics, Carlos Marrero
Implementing Technology Enhanced Mathematical Instruction In An Algebra I Course To Increase Students’ Academic Achievement In Mathematics, Carlos Marrero
Theses and Dissertations
In July 2015, the National Council of Teachers of Mathematics established its position about the use of technology in teaching and learning mathematics. This important step forward opened a promise
for many students and teachers that deserve the excellence of high-quality education in one of the most difficult educational subjects. In the 21st century, mathematics education can be one of the
greatest recipients of all technological benefits reached by the most advanced societies of the earth.
The purpose of this applied dissertation was to measure the effects in mathematics academic achievement of implementing technology-enhanced mathematical instruction to a group of …
The Effect Of Mandating Algebra For All Students In Grade 8 Versus Grade 9 In A Small Suburban K-12 School District In New Jersey, Peter Crawley
The Effect Of Mandating Algebra For All Students In Grade 8 Versus Grade 9 In A Small Suburban K-12 School District In New Jersey, Peter Crawley
Seton Hall University Dissertations and Theses (ETDs)
The traditional sequencing of the ninth- to twelfth-grade math curriculum in the United States has students taking Algebra 1 in the ninth grade, Geometry in the tenth grade, Algebra 2 in the eleventh
grade and an optional advanced math course (e.g. pre-calculus, statistics) in the twelfth grade. In this traditional setup, talented math students are given the opportunity to take Algebra 1 in the
eighth grade, which allows them to take two or more years of advanced math before graduating from high school. In an effort to create more equitable access to advanced math courses, many districts
are considering or …
Exploring The Knowledge Of Algebra For Teaching., Jonathan David Watkins
Exploring The Knowledge Of Algebra For Teaching., Jonathan David Watkins
Electronic Theses and Dissertations
For the past few decades, researchers in mathematics education have been exploring the concept of pedagogical content knowledge (PCK)—or knowledge related to teaching content—and applying it to
various areas of mathematics, such as algebra. Research related to teacher knowledge of algebra is critical because researchers (e.g., Hill, Rowan, & Ball, 2005) have found correlations between some
types of teacher knowledge and student achievement in mathematics; students from around the world are outperforming U.S. students on international assessments of mathematics, including algebra
(Organization for Economic Cooperation and Development, 2014, 2016); and algebra plays an integral role in the K-12 mathematics curriculum …
Relationship Of Supplemental Instruction And Attitude Of Students Enrolled In College Algebra, Kele Anne Mckaig
Relationship Of Supplemental Instruction And Attitude Of Students Enrolled In College Algebra, Kele Anne Mckaig
OTS Master's Level Projects & Papers
The problem of this study was to determine the relationship of supplemental instruction on the attitudes of college algebra students at a Southeastern university. The population for this study
consisted of college algebra students enrolled in M102 and M103 courses in the Summer 2018 semester. While M102 and M103 cover the same material, M103 requires mandatory tutoring in addition to the
classroom instruction. A survey of these students provided data on their attitudes toward mathematics at the beginning and end of their college algebra course. The first research question of this
study asked to what extent attitudes differ, if at …
Teacher Graphing Practices For Linear Functions In A Covariation-Based College Algebra Classroom, Konda Jo Luckau
Teacher Graphing Practices For Linear Functions In A Covariation-Based College Algebra Classroom, Konda Jo Luckau
Theses and Dissertations
Graphing is a fundamental topic in algebra that is notoriously difficult for students. Much of the past research has focused on conceptions and misconceptions. This study extends past research by
looking at the mathematical practices of a practitioner, specifically one instructor of a function-based covariation-focused algebra class in the linear functions unit. Considering practices in
addition to conception adds dramatically to our understanding of mathematical activity because it leads to explicit descriptions of normative purposes that are connected to particular situations or
problems and also specifies how tools and symbols are coordinated to achieve these purposes. The results of this …
The Influence Of Mathematical-Instructional Minutes On The Percentage Of Proficient And Advanced Proficient Scores In Mathematics On The New Jersey Assessment Of Skills And Knowledge For Grades 6-8,
Eric Walter Kosek
The Influence Of Mathematical-Instructional Minutes On The Percentage Of Proficient And Advanced Proficient Scores In Mathematics On The New Jersey Assessment Of Skills And Knowledge For Grades 6-8,
Eric Walter Kosek
Seton Hall University Dissertations and Theses (ETDs)
The purpose of this non-experimental, cross-sectional, correlational study was to examine the influence, if any, of mathematical-instructional minutes on academic achievement as measured by the 2014
New Jersey Assessment of Skills and Knowledge (NJ ASK) 6, 7, and 8 mathematics scores. Additionally, the study accounted for other factors that influence student achievement, including selected
metrics and variables listed on the 2013-2014 New Jersey School Performance Report. The variable of interest, mathematical-instructional minutes, was obtained via survey from all schools in New
Jersey that educated students in Grades 6-8. The survey data were then matched with each responding school’s New Jersey …
Student Centered Approaches In High School Algebra, Jennifer L. Mahan
Student Centered Approaches In High School Algebra, Jennifer L. Mahan
M.S.Ed. in Educational Leadership Research Projects
This quasi-experimental study evaluated the impact of four, student centered approaches on learning outcomes for high school math students, to determine if algebraic understanding improved in an
active learning environment. Specifically, this study investigated high school algebra students’ use of learning stations, hands on manipulatives, small group collaboration and mathematical games, to
deepen their conceptual understanding of linear equations. Surveys revealed students prefered to work independently while being led by the teacher, yet this approach yielded the least amount of
improvement. Pre- and post-tests showed students from the experimental groups out-performed peers in the control group on achievement of standards …
Influence Of Application-Based Homework On Students Who Struggle In Algebra I, Charles Seipp
Influence Of Application-Based Homework On Students Who Struggle In Algebra I, Charles Seipp
Theses and Dissertations
This investigation describes a problem of practice with the academic achievement of students who struggle in Algebra I by means of an action research design. Students regularly struggle academically
for a variety of reasons, as described within and are frequently identified as at-risk due to this struggle. This investigation seeks to determine if the utilization of application-based homework
serves to increase achievement and student engagement in a course with such significant importance for future success as Algebra I. An example of application-based would be the use of specific
content outside of the classroom, such as parabolic functions to model projectile …
A Program Evaluation Of Double-Period Algebra, Jason Major
A Program Evaluation Of Double-Period Algebra, Jason Major
Students in ninth grade traditionally take algebra courses, but many students come in lacking foundational skills in mathematics. High schools have tried to solve this problem by introducing
double-period algebra courses with sporadic results. During this program evaluation, I interviewed an administrator and a teacher from two different high schools about the methods they used to begin
and evaluate the program; I found that student-teacher relationships were the most important factor in the effectiveness of the program. Using quantitative data was a good starting point to determine
the students who would benefit from the program and who would be successful, …
The Impact Of An Elementary Algebra Course On Student Success In A College-Level Liberal Arts Math Course And Persistence In College, Lori Ann Austin
The Impact Of An Elementary Algebra Course On Student Success In A College-Level Liberal Arts Math Course And Persistence In College, Lori Ann Austin
Theses and Dissertations
Many students enter community college underprepared for college-level math and are placed into developmental elementary algebra without consideration if the algebra will provide a foundation for
their needed college-level math course. Large percentages of those students are unable to succeed in the developmental course and, therefore, are unable to graduate (Bahr, 2008; Bailey, Jeong, & Cho,
2010). This quasi-experimental design focused on students who are not in math-intensive majors, needing only a general liberal arts math course. The purpose was to determine the impact of the
elementary algebra course on success in college-level math and persistence in college. Student performance …
Developing Conceptual Understanding And Procedural Fluency In Algebra For High School Students With Intellectual Disability, Andrew J. Wojcik
Developing Conceptual Understanding And Procedural Fluency In Algebra For High School Students With Intellectual Disability, Andrew J. Wojcik
Theses and Dissertations
Teaching students with Intellectual Disability (ID) is a relatively new endeavor. Beginning in 2001 with the passage of the No Child Left Behind Act, the general education curriculum integrated
algebra across the K-12 curriculum (Kendall, 2011; National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010), and expansion of the curriculum included
five intertwined skills (productive disposition, procedural fluency, strategic competence, adaptive reasoning, and conceptual understanding) (Kilpatrick, Swafford, & Findell, 2001). Researchers are
just beginning to explore the potential of students with ID with algebra (Browder, Spooner, Ahlgrim-Delzell, Harris & Wakeman, 2008; Creech-Galloway, Collins, Knight, …
The Influence Of Dragonbox On Student Attitudes And Understanding In 7th Grade Mathematics Classroom, Nihal Katirci
The Influence Of Dragonbox On Student Attitudes And Understanding In 7th Grade Mathematics Classroom, Nihal Katirci
Legacy Theses & Dissertations (2009 - 2024)
This exploratory study seeks to investigate how a mathematical education game, DragonBox12+, effects students’ learning about algebra. Data for this research was collected from middle school 7th
grade students in the Northeast region of the United States of America. The interviews and classroom observations were recorded on videotape. The research results showed that the video game DragonBox
12+ affects students’ attitude of mathematics and learning of mathematics by the help of using game mechanics to teaching algebraic rules.
Secondary Students’ Perceptions Of An Interactive Mathematics Review Program: An Action Research Study, Crystal Burroughs Wingard
Secondary Students’ Perceptions Of An Interactive Mathematics Review Program: An Action Research Study, Crystal Burroughs Wingard
Theses and Dissertations
The present action research study describes an Interactive Mathematics Review Program (IMRP) developed by the participant-researcher to enable remedial algebra students to learn in a cooperative
classroom with pedagogy that promoted collaboration and hands-on, active learning. Data are comprised of surveys, field notes, semistructured interviews, and focus group insights about the IMRP over
an 8-week period in the spring of 2017 at a southern, low-socioeconomic status high school. Findings include: (1) greater comprehension; (2) increased engagement and math-related discussions; (3)
increased motivation; (4) egalitarian principles; and (5) high-quality reciprocity. A nine-step action plan designed to enable other math teachers at …
A Matter Of Time: The Relationship Of Class Length And Demographics On The South Carolina Algebra I End-Of-Course Test In South Carolina Middle Schools, Jennifer Addie Ramsey
A Matter Of Time: The Relationship Of Class Length And Demographics On The South Carolina Algebra I End-Of-Course Test In South Carolina Middle Schools, Jennifer Addie Ramsey
Education Dissertations and Projects
For middle school students taking Algebra 1 as a high school credit, having sufficient instructional time to understand and explore the course content is crucial. While the focus of the literature
review helps lend understanding to the study, there has been limited information concerning assessment scores in middle school math classes and the length of class time. This study investigated the
differences in the End-of-Course Examination Program (EOCEP) test scores of middle school students in Algebra 1 as influenced by schedules used in South Carolina public middle schools for each
individual year in a 5-year span of the 2010-2015 academic …
Motivation For Mathematics: The Development And Initial Validation Of An Abbreviated Instrument, Kenneth Lee Butler
Motivation For Mathematics: The Development And Initial Validation Of An Abbreviated Instrument, Kenneth Lee Butler
USF Tampa Graduate Theses and Dissertations
This study outlines the development and initial validation of an abbreviated instrument intended to measure motivation for mathematics of university students in developmental algebra courses. I look
across many of the predominant theories on motivation with the aim of representing several of these theories as latent constructs in a single instrument that is short enough to be administered in a
reasonable amount of time, but inclusive enough that it could incorporate subscales representing multiple distinct latent factors. This study answers a call by researchers expressing a need to
investigate relationships between disparate theories on motivation and is a response to …
Algebraic Content And Pedagogical Knowledge Of Sixth Grade Mathematics Teachers, Mariyam Shahuneeza Naseer
Algebraic Content And Pedagogical Knowledge Of Sixth Grade Mathematics Teachers, Mariyam Shahuneeza Naseer
Walden Dissertations and Doctoral Studies
Algebra test scores of the Maldivian students from grade 6 through 12 are the lowest compared to any other area of mathematics. Algebra is a fundamental topic in mathematics and lays the foundation
for mathematical reasoning and complex problem-solving. Research shows that strengthening algebra instruction could improve student achievement. This concurrent mixed methods study examined the
algebraic content and pedagogical knowledge of 5 sixth grade mathematics teachers who teach in 5 different schools across the Maldives. Shulman's major categories of teacher knowledge and Ball,
Thames, and Phelps' domains of mathematical knowledge for teaching guided this study. The research questions examined …
Teaching An Algebraic Equation To High School Students With Moderate To Severe Intellectual Disability, Suzannah M. Chapman
Teaching An Algebraic Equation To High School Students With Moderate To Severe Intellectual Disability, Suzannah M. Chapman
Theses and Dissertations--Early Childhood, Special Education, and Counselor Education
The purpose of this study was to examine the effectiveness of using the system of least prompts and concrete representations to teach students with moderate and severe disabilities (MSD) to solve
simple linear equations. A multiple-probe (days) across participants, single case research design was used to evaluate the effectiveness of task analytic instruction along with concrete
representation on teaching students with MSD to solve algebraic equations. The results showed the system of least prompts and concrete representations were effective in teaching students with MSD to
solve simple linear equations. | {"url":"https://network.bepress.com/explore/education/?facet=subject_facet%3A%22Algebra%22&facet=publication_type%3A%22Theses%2FDissertations%22","timestamp":"2024-11-07T23:30:19Z","content_type":"text/html","content_length":"116022","record_id":"<urn:uuid:a847fcd6-f0c0-4f2a-866f-4dfdc5af143d>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00200.warc.gz"} |
maximum allowable working pressure
31 Aug 2024
Title: Maximum Allowable Working Pressure (MAWP) of Pressure Vessels: A Theoretical Analysis
Abstract: The Maximum Allowable Working Pressure (MAWP) is a critical parameter in the design and operation of pressure vessels. It represents the maximum pressure at which a vessel can be safely
operated without risking catastrophic failure. This article provides an overview of the theoretical analysis involved in determining MAWP, including the relevant formulas and equations.
Introduction: Pressure vessels are widely used in various industries, such as chemical processing, oil refining, and power generation. The safe operation of these vessels relies heavily on their
ability to withstand internal pressures without failing. The Maximum Allowable Working Pressure (MAWP) is a critical parameter that ensures the vessel’s integrity under normal operating conditions.
Theoretical Background: The MAWP of a pressure vessel is determined by considering several factors, including:
1. Material properties: The strength and ductility of the material used to construct the vessel.
2. Vessel geometry: The shape and size of the vessel, which affects its stress distribution.
3. Loading conditions: The internal pressure, external loads (e.g., wind, seismic), and other environmental factors.
1. Allowable Stress Intensity (ASI): The ASI is a measure of the maximum allowable stress intensity in the material, expressed as:
where σ_y is the yield strength of the material, and n is a safety factor.
2. Vessel Thickness: The minimum required thickness (t) of the vessel can be calculated using the following formula:
where p is the internal pressure, and r is the radius of the vessel.
3. MAWP Calculation: The MAWP can be determined by considering the maximum allowable stress intensity (ASI) and the minimum required thickness (t):
Conclusion: The Maximum Allowable Working Pressure (MAWP) is a critical parameter in the design and operation of pressure vessels. The theoretical analysis involved in determining MAWP includes
consideration of material properties, vessel geometry, and loading conditions. By applying the relevant formulas and equations, engineers can ensure the safe operation of pressure vessels under
normal operating conditions.
• ASME Boiler and Pressure Vessel Code (BPVC)
• API 650: Welded Steel Tanks for Oil Storage
• EN 12901: Metallic Gases - Cylinders and Valves
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Saccadic Eye Movements Minimize the Consequences of Motor Noise
The durations and trajectories of our saccadic eye movements are remarkably stereotyped. We have no voluntary control over these properties but they are determined by the movement amplitude and, to a
smaller extent, also by the movement direction and initial eye orientation. Here we show that the stereotyped durations and trajectories are optimal for minimizing the variability in saccade
endpoints that is caused by motor noise. The optimal duration can be understood from the nature of the motor noise, which is a combination of signal-dependent noise favoring long durations, and
constant noise, which prefers short durations. The different durations of horizontal vs. vertical and of centripetal vs. centrifugal saccades, and the somewhat surprising properties of saccades in
oblique directions are also accurately predicted by the principle of minimizing movement variability. The simple and sensible principle of minimizing the consequences of motor noise thus explains the
full stereotypy of saccadic eye movements. This suggests that saccades are so stereotyped because that is the best strategy to minimize movement errors for an open-loop motor system.
Citation: van Beers RJ (2008) Saccadic Eye Movements Minimize the Consequences of Motor Noise. PLoS ONE 3(4): e2070. https://doi.org/10.1371/journal.pone.0002070
Editor: Aldo Rustichini, University of Minnesota, United States of America
Received: January 9, 2008; Accepted: March 17, 2008; Published: April 30, 2008
Copyright: © 2008 Robert van Beers. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and
reproduction in any medium, provided the original author and source are credited.
Funding: The author was supported by Netherlands Organization for Scientific Research (NWO) Grant 451-02-013.
Competing interests: The author has declared that no competing interests exist.
We have no voluntary control over the duration and velocity of our saccadic eye movements. Normal saccades are therefore stereotyped and follow the so-called ‘main sequence’ [1]–[6]: saccade duration
increases approximately linearly with saccade amplitude (Figure 1A) whereas peak velocity increases with amplitude at a decreasing rate (Figure 1C). The empirical main sequence relationships for
horizontal saccades differ somewhat across studies because they vary across subjects [2], [7], measurement techniques [8], [9] and analysis method [10], but the general pattern is always the same.
Although it is well understood how the stereotyped saccades are generated by the brain, it is not understood why they are so stereotyped and why they have the precise properties as described by the
main sequence. The stereotyped behavior is likely to be advantageous, but in which respect are main sequence saccades advantageous?
A. Observed duration as a function of amplitude for horizontal saccades starting from the primary position or moving symmetrically about it. Different lines denote linear fits reported by different
sources: -––[2], -––[3], —[4], -––[5], ……[6]. Lines are plotted for the range of amplitudes for which the fit was made. B. Optimal duration as a function of amplitude for horizontal saccades moving
symmetrically about the primary position for three different levels of CN (k[CN]=Rk[SDN] is the best estimate of the actual level [12]). C. Observed peak velocity as a function of amplitude for
similar horizontal saccades as shown in A. Different lines denote fits or linearly connected data points reported by different sources (see legend of A for the sources). D. Peak velocity of optimal
saccades as a function of amplitude for horizontal saccades moving symmetrically about the primary position for three different levels of CN. E. Observed velocity profiles of horizontal saccades
moving symmetrically about the primary position for amplitudes of 5, 10, 20, 30, 40, 50 and 60 deg (Reprinted from [4] with permission from Wiley-Blackwell). F. Velocity profiles of the optimal
saccades (with their optimal duration) shown in E.
On top of the stereotypy, saccades display a certain level of variability [6], [11], [12]. Movement variability is undesirable because it leads to failures to reach the desired gaze direction. The
larger the variability, the larger the errors will be. A considerable proportion of the variability is caused by noise in the motor commands [12]. The detrimental effect of motor noise could be
minimized by choosing, from the infinite number of possible saccade trajectories to a target, the trajectory that produces the smallest variability in saccade endpoints [13]. The precise properties
of the motor noise determine which trajectories are optimal [14].
The noise in individual motoneurons is in a good approximation signal-dependent noise (SDN) [15]–[17], i.e., the standard deviation of the firing rate is proportional to the mean firing rate. It has
been shown that, under the assumption that motor noise is SDN, the theoretical trajectories that minimize endpoint variability are very similar to actual saccade trajectories [13]. It is however not
reasonable to assume that the actual motor command, which is the aggregate of the command activities of all motoneurons contributing to a saccade, has SDN because this aggregate command combines the
activities of many motoneurons that are distributed over six different muscles. Especially the coactivation of antagonistic muscles [18] can lead to substantial departures from SDN because the
torques generated by these muscles will partially cancel each other but the variances therein will add up. Indeed, studies aimed at identifying the properties of noise in the motor commands of
saccades [12], and also of arm movements [19], found that the noise is best characterized as a combination of SDN and constant noise (CN), which is additive noise with a standard deviation
independent of the command. There is also temporal variability, which leads to variations in speed and duration, but this is less relevant here because it does not lead to variations in saccade
endpoints [12].
The aim of this study was to determine how actual saccades relate to the theoretical movements that minimize the consequences of the actual motor noise. The results show that they are very similar,
which suggests that saccades are planned in such a way that the movement variability is minimized.
We calculated (see Materials and Methods) the trajectories that minimize the endpoint variability caused by the empirically estimated combination of SDN and CN [12]. We first consider a 5 deg
horizontal saccade. Although in normal behavior, the duration is given by the main sequence, we will consider a range of hypothetical durations and for each duration calculate the trajectory that
produces the smallest variance in saccade endpoints, averaged over a 50 ms post-movement fixation period [13]. Figure 2A shows that the endpoint variance caused by SDN decreases with duration. This
is because a saccade with a longer duration requires smaller and therefore less noisy motor commands than a saccade with a shorter duration. In contrast, the variance caused by CN increases with
duration. CN is independent of the motor command, so the amount of noise added simply increases with duration. As a result, the total endpoint variance becomes very large for very short durations
(because of SDN) and for very long durations (because of CN) and reaches a minimum at an intermediate duration. This means that there is an optimal saccade duration for which the endpoint variance is
minimal. For the 5 deg saccade, this optimal duration is 41.5 ms, which is close to the actual duration (Figure 1A). Figure 2B shows a family of total variance curves for saccades with amplitudes of
1, 2.5, 5, 10, 15, 20, 25 and 30 deg. The optimal duration, indicated by the circles, increases with saccade amplitude.
A. The optimal trajectory was calculated for a horizontal saccade of 5 deg (starting from the primary position), where the hypothetical movement duration was varied between 20 and 150 ms. The
variance resulting from SDN and CN is plotted as a function of the duration. The total variance, which is the sum of the variances caused by SDN and CN, has a minimum value for a duration of 41.5 ms,
as indicated by the arrow. This is the optimal duration. B. Total variance curves as in A for saccades with amplitudes of 1, 2.5, 5, 10, 15, 20, 25 and 30 deg (from bottom to top). The optimal
durations are indicated by the circles.
We calculated the optimal duration for horizontal saccades of amplitudes between 0.25 and 30 deg that moved the eye symmetrically about the primary position, the eye's equilibrium position when it
looks straight ahead. Figure 1B shows that the optimal duration (the bold line) increases approximately linearly with amplitude, very similar to the observed duration (Figure 1A). Note that the
larger slope that is optimal for very small amplitudes has also been observed [1], [20], [21] but is generally not included in the linear amplitude-duration fits. Peak velocity of the optimal
saccades increases with amplitude at a decreasing rate (Figure 1D), also very similar to the observations (Figure 1C). The velocity profiles of the optimal saccades (Figure 1F) have similar shapes as
observed velocity profiles (Figure 1E). The initial part of the movement is similar for all amplitudes, and velocity profiles are approximately symmetric for small saccades, and asymmetric with an
extended deceleration phase for larger saccades.
The optimal duration is determined by the ratio R of the levels of CN and SDN, and by the mechanical properties of the oculomotor system (see Materials and Methods). Since the levels of CN and SDN
are likely to vary across individuals, we calculated the optimal duration for noise ratios R that were 10% larger and smaller than the best estimate [12]. Figure 1B shows that the optimal duration
decreases when there is relatively more CN and it increases with less CN, but both curves fall within the range of observed durations (Figure 1A). The optimal peak velocity (Figure 1D) shows a
corresponding dependence on the noise ratio. These variations also fall within the range of observed peak velocities (Figure 1C).
The mechanical properties of the oculomotor system are less likely to vary much between humans but they differ strongly across different species [22], [23]. The largest time constant of the monkey
oculomotor system (modeled as a linear system), for instance, is about half that of the human system [24]. As a result, the optimal duration is considerably shorter for monkeys than for humans (when
assuming the same noise ratio R as for humans). Monkey saccades are indeed about a factor two faster than human saccades [25]. Conversely, the oculomotor systems of the cat [23] and rabbit [22], [23]
are characterized by longer time constants and their saccades are slower than human saccades [26], [27].
The duration of a human saccade is not determined by its amplitude only, but it depends also on the movement direction and the initial eye orientation. Centrifugal saccades, which move the eye from
the primary position to an eccentric position, have longer durations, lower peak velocities and more asymmetric velocity profiles than centripetal saccades, which return the eye from an eccentric
position to the primary position [4], [28] (Figure 3A). This is exactly what is optimal for minimizing the consequences of motor noise (Figure 3B). The explanation is that the elastic forces of the
eye counteract centrifugal saccades whereas they assist centripetal saccades. As a result, centripetal saccades require smaller torques, have less SDN and a shorter optimal duration than centrifugal
A. Observed velocity profiles of three 30 deg rightward saccades, starting at –▪– 20, –▴–10 and –•– 0 deg to the left of the primary position (Reprinted from [28] with permission from Elsevier). B.
Velocity profiles of the optimal saccades for the situation shown in A. C. Linear fits of observed duration as a function of amplitude for horizontal and vertical saccades. The solid lines are from
[4] and [29], and the dashed lines are from [30]. D. Optimal duration as a function of amplitude for horizontal and vertical saccades moving symmetrically about the primary position.
Saccades in the vertical direction have a longer duration than horizontal saccades of the same amplitude [4], [29], [30] (Figure 3C). This is also optimal for minimizing the consequences of motor
noise (Figure 3D). A comparison of the predicted and observed duration differences is however difficult because the observed differences vary largely across studies (see Figure 3C). The optimal
durations are different for horizontal and vertical saccades because the horizontal extraocular muscles are stronger than the vertical ones. Stronger muscles are less noisy than weaker muscles when
both produce the same torque [31]. The levels of SDN and CN are therefore lower in the horizontal than in the vertical muscles. SDN is only present for muscles that are activated. As a result, there
will be less SDN for horizontal than for vertical saccades. In contrast, the level of CN is independent of the motor commands, so there will always be CN in all muscles, even in vertical muscles
during a horizontal saccade, and vice versa. In other words, the level of CN will for each muscle pair always be the same. Summed over all muscle pairs, there will be less SDN for horizontal than for
vertical saccades but the amount of CN will be the same. This leads to a shorter optimal duration for horizontal saccades.
What is the duration of saccades in oblique directions? Let us assume that a 10 deg saccade to the right takes 56 ms and an upward one 60 ms. How long does an oblique saccade 10 deg to the right and
10 deg up then take? Since the oblique saccade requires similar horizontal muscle activations as the rightward saccade and comparable vertical muscle activations as the upward saccade, one could
expect its duration to be in the range of that of the rightward and upward 10 deg saccades, i.e., 56–60 ms. That would mean that oblique saccades would be ‘superfast’ because they would be faster
than horizontal and vertical saccades of the same amplitude (about 14 deg, taking 67–71 ms). Actual oblique saccades are however not superfast, but their duration compares to that of purely
horizontal and vertical saccades of the same amplitude [12], [32]. Why is the duration not shorter? Although the muscles could in principle generate such a superfast saccade, the endpoint variability
would be larger than necessary. For the optimal duration, the balance between SDN and CN, summed over all muscle pairs, is the same as for purely horizontal and vertical saccades. A shorter duration
would lead to an imbalance because there would be too much SDN.
Another feature of oblique saccades is that their horizontal and vertical components have approximately the same duration, even when their amplitudes are different [32], [33] (Figure 4C). The peak
velocity of each component is therefore lower and the duration longer than for a saccade for which the considered component has the same amplitude but a zero orthogonal component (Figure 4A). This
‘component stretching’ is optimal for minimizing the consequences of motor noise (Figures 4B,D). Unequal durations would lead to strongly curved trajectories, which would require a larger total
rotation angle and therefore larger and noisier motor commands, with a larger variability as the result. The optimal trajectories are therefore straight, with the same duration for the horizontal and
vertical components.
A. Observed time course of a 5 deg purely horizontal saccade (H and V denote the horizontal and vertical components, respectively) (Reprinted from [32] with permission from APS). B. Optimal time
course of a 5 deg purely horizontal saccade. C. Observed time course of an oblique saccade with a 5 deg horizontal component and a 10 deg vertical component (Reprinted from [32] with permission from
APS). D. Optimal time course of an oblique saccade as shown in C.
The trajectories of actual oblique saccades can display some curvature [34], [35]. The amount and even the direction of this curvature vary strongly across and sometimes also within subjects [34],
[35]. The curvature, when expressed as the ratio of the perpendicular deviation from the straight line between saccade onset and offset and the net amplitude of the saccade, is generally 0.1 or
smaller [34]. We performed an additional analysis to find the relation between saccade curvature and endpoint variance. Figure 5 shows the endpoint variance resulting from motor noise for a 15 deg
saccade up and to the right as a function of curvature. The figure confirms that the variance is minimal for zero curvature, and that it increases with increasing absolute curvature. The increase is
marginal (less than 3%) for absolute curvatures up to 0.1. The variance increases more rapidly for larger curvatures. For a curvature of 0.2 there is a 10% increase and for a curvature of 0.3 the
increase is almost 25%.
Oblique 15 deg saccades directed up and to the right (under 45 deg) are considered for a range of trajectory curvatures. Curvature was expressed as the ratio of the perpendicular deviation from the
straight line between saccade onset and offset and the net amplitude of the saccade, with positive values indicating detours in the anti-clockwise direction and negative values detours in the
clockwise direction. The curved paths were assumed to follow a sinusoidal shape in rotation vector space. The variance is minimal for straight trajectories and increases with curvature.
We make saccadic eye movements to direct our fovea quickly to objects of interest. Saccades thus serve vision. It can therefore be expected that the saccadic system has evolved in such a way that it
serves vision optimally. It is however not obvious what saccades should look like to support vision optimally. Saccade duration seems important for two reasons. First, when we detect an object of
interest, such as a possible predator, in our visual periphery, it is important to direct our gaze to that object as fast as possible. Second, because vision is highly degraded during a saccade,
vision is served best by making the duration of a saccade as short as possible. It could therefore be expected that saccades have evolved to be as fast as possible [36]–[38]. The duration of saccades
in oblique directions, however, argues strongly against this possibility. If saccade duration were minimized, oblique saccades would be ‘superfast’, but they clearly are not [12], [32].
Another important feature of saccades is their accuracy. Individual saccades can miss the desired destination as a result of motor noise and uncertainty in the sensed target location. Such errors can
have devastating consequences. For instance, a saccade error may preclude the timely identification of a predator (or prey). Our survival may therefore depend on saccade accuracy. This demonstrates
that minimizing variability in saccade endpoints is behaviorally relevant because the smaller the variability, the smaller the mean error will be. The relevance goes however further than this. Once
an error has been made, a secondary, corrective saccade will be generated. The number and the amplitude of the required secondary saccades, and therefore the average time needed to reach the desired
destination, will all be close to minimal when the endpoint variance is minimized. Minimizing the endpoint variance thus indirectly also approximately minimizes the total time with impaired vision
during saccades and the time needed to reach the desired gaze direction.
Our results show that the full stereotypy of saccade trajectories and durations is optimal for minimizing the variability in saccade endpoints. Given the above-mentioned advantages, we propose that
the saccade system has purposefully been optimized to minimize this variability. It is possible that this optimization process has taken place during evolution, but another possibility is that the
optimization has occurred during the development of each individual. Some support for the latter option comes from the observation that saccade duration varies somewhat across subjects [2], [7]. This
could be related to inter-individual differences in the noise levels, but more research is required to test whether this relation really exists. The finding that the sign and magnitude of the
curvature of oblique saccades vary across subjects [34], [35] provides stronger support for the latter option. Figure 5 shows that for the curvatures that oblique saccades typically have (absolute
value not greater than 0.1), the endpoint variance is only marginally larger than that of the optimal straight saccades. For larger curvatures, the variance can be substantially larger. A plausible
mechanism therefore is that the saccade optimization process is driven by the errors that are experienced after making saccades. If at a certain time during this optimization process highly curved
saccades are produced, the central nervous system could sense that the saccade errors tend to be larger than when less curved trajectories are made. This will induce a change towards planning of less
curved saccades. This process will continue until no further improvements can be made. At absolute curvatures of 0.1, the improvement that could still be made can be too small (less than 3% reduction
of variance) to be detectable. In that case, reducing the curvature will stop and the optimization process has found a solution. This solution differs somewhat from the theoretical optimum, but the
resulting variance is hardly larger. The fact that curvature can have opposite signs in different subjects is consistent with this mechanism because the optimization process will follow a different
path in every individual, due to the different realizations of motor and sensory noise in the saccades made during the optimization process.
Which trajectories and durations are optimal depends on the precise properties of the motor noise [14]. Previous studies [13], [38], [39] assumed that motor noise is pure SDN. Later work [12], [19]
has shown that this assumption is not correct. The present work can be seen as an extension of the seminal work of Harris and Wolpert [13]. In comparison to their study we have replaced the
assumption that motor noise is pure SDN by the empirically established actual motor noise. The result is that we can explain much more: not only the velocity profiles (as Harris and Wolpert did) but
the full stereotypy of saccade trajectories including the duration of saccades, and how duration and velocity vary with movement direction and initial eye orientation.
In addition to explaining what the stereotypy looks like, the principle of minimizing the consequences of motor noise also explains why there is a stereotypy in the first place. Without the
stereotypy, duration and velocity would be more variable. Many saccades would therefore be suboptimal and produce large errors. The only way to avoid this is to always choose a trajectory that is
close to the optimal trajectory, or, in other words, to produce stereotyped saccades. This may seem a very general principle that must apply to the goal-directed movements of other body parts as
well. The movements of many other body parts are however less stereotyped. We have, for instance, voluntary control over the duration and velocity of arm movements. Why are arm movements less
stereotyped? This could be related to their longer duration, which makes it possible to correct movements online on the basis of sensory feedback [40]. Online corrections can prevent movement errors
without the need to compute an entire, optimal trajectory in advance. Stereotyped movements are therefore only optimal for open-loop motor systems such as the saccade system for which movements
cannot be corrected online.
Although we have shown that a single, simple principle can explain the full stereotypy of saccade durations and velocity profiles, there is one aspect of saccade trajectories that we did not
consider. The torsion of the eye was assumed to obey Listing's law. In principle, however, torsion is not constrained to obey Listing's law but it is also a free parameter. It is unknown why the
actual eye orientation does obey Listing's law [41]. Based on the present work, an attractive hypothesis would be that also Listing's law minimizes the consequences of motor noise. Future research is
required to test this hypothesis.
In summary, we have shown that the stereotyped durations and velocities of saccadic eye movements are optimal for minimizing the variability in saccade endpoints caused by motor noise. This suggests
that the saccade system has purposefully been optimized to minimize the consequences of motor noise. This optimization process could have taken place during evolution, but it is more likely that it
takes place during the development of each individual. A key element of the study is that we minimized the consequences of the recently estimated actual motor noise, rather than that we, incorrectly,
assumed signal-dependent noise. This study therefore stresses that, in studies in which motor noise plays a role, it is very important to make correct assumptions about the properties of this noise.
Materials and Methods
Mechanics of the oculomotor system
We used the same three-dimensional model of the oculomotor system that we used to estimate the properties of motor noise [12]. In brief, the muscle torques must counteract inertial, viscous and
elastic forces [42], [43]:(1)where the eye orientation is described by a rotation of angle φ about axis n̂ from the primary position; Ω and denote the eye's angular velocity and angular acceleration,
respectively. The moment of inertia was I=2.00×10^−7 kg·m^2 [44]. The coefficient of viscosity B, and the stiffness K were chosen such that (1) corresponds to an overdamped system with time
constants of 224 and 13 ms [45].
The right hand side of (1) represents the torque generated by the extraocular muscles. These muscles were assumed to form three pairs with orthogonal insertions on the globe. The net torques
generated by these muscle pairs form the vector τ. This vector is multiplied by matrix R[M], that describes a rotation of angle about axis n̂ [46], to accommodate the effects of muscle pulleys [47]
and/or orbital fat [48] on the muscle pulling directions.
The muscles produce torques because they receive motor commands from their motoneurons. We modeled the muscles as first order lowpass filters with a time constant of t[m]=10 ms [12], [13], [39] to
define the relation between the torques τ and the aggregate motor command : , where is the temporal derivative of τ. We next expressed eye orientation as three-dimensional rotation vectors r [49].
The three elements represent the torsional, vertical and horizontal components, respectively. After making this transformation and including the muscle model, equation of motion (1) is very well
approximated by (errors <0.2% for normal saccades):(2)where r ˙, and are the first, second and third temporal derivatives of r, respectively, and J is a constant. Equation (2) describes a
three-dimensional, linear, overdamped system with time constants t[1]=224 ms, t[2]=13 ms and t[3]=10 ms, and with input (the factor arises from the transformation to rotation vectors).
When we define the state vector as: , (2) can be written in the form of the state equation:(3)where A and B are:(4)The solution of (3) is [50]:(5)
Motor noise
We assumed that motor commands have constant noise (CN) and signal-dependent noise (SDN) in their magnitude [12]. CN and SDN are zero-mean, white Gaussian noise, with standard deviations k[CN] and ,
respectively. For the horizontal muscles, k[CN]=1.37·10^−5 kg m^2 s^−2 and k[SDN]=0.172 [12]. Noise levels vary across muscle pairs as torsional∶vertical∶horizontal=n[1]∶n[2]∶n[3]=
1.41∶1.41∶1.00 to reflect the different muscle strengths [12], [31].
Optimal trajectories
We calculated optimal saccade trajectories that, on average, bring the eye to the target with minimal variance in eye orientation, summed over the horizontal, vertical and torsional components, and
averaged over a post-movement fixation interval F [13].
The shape of a saccade trajectory is fully determined by the shape of the motor command. Motor commands of saccades are generally assumed to consist of two parts. The pulse component consists of
large signals that set the eye into motion and bring it to its end position. The smaller signals of the step component are then required to keep the eye stationary after the movement. We define the
duration M of a saccade as the duration of its pulse component. Let t[F] be the time in the interval [0, F], then the variance in the fixation interval [M, M+F] in component i resulting from SDN is
[51]:(6)where u[F] is the fixation command required to keep the eye still at the target position, and p(t) is the impulse response function which for all three components is:(7)Similarly, the
variance in component i resulting from CN is:(8)The cost to be minimized is the total variance summed over the three components and averaged over the fixation interval:(9)with: , which is independent
of the trajectory and the duration so that it can be omitted from the cost function. This means that the optimal trajectory and duration are independent of the noise in the step component of the
motor command. The constant 1/F is also irrelevant for the cost function, so the cost can be simplified to:(10)with: .
The optimization problem is further specified by the constraints that the eye moves from initial state x^0 at t=0 to final state x^f at t=M. Substituting the initial and final states in (5)
defines the nine constraints as:(11)The optimization problem can thus be formulated as:(12)The optimal motor commands and the resulting optimal trajectories can be found using calculus of variations.
Let H=f+Γ^Tg be the augmented cost function, where Γ=(γ[1],…,γ[9])^T is a vector of nine Lagrange multipliers γ[i]. Then, the solution of the optimization problem can be found by solving the
Euler-Lagrange equation [52]:(13)The solution for the optimal motor command, for a given M, is:(14)where Λ is a nine dimensional vector of constants λ[i] that are determined by the nine constraint
equations. This solution is identical to the solution if there were no CN. This means that, for a given M, the optimal trajectory in the presence of both SDN and CN is identical to the optimal
trajectory in the presence of SDN only, and that was found previously [13].
The solution for the λ[i] can be shown to be: for i=1, 2, 3 and with: D=I[00](I[12]^2−I[11]I[22])+I[01](I[01]I[22]−2I[02]I[12])+I[02]^2I[11], and: , where p^(i)(t) is the ith temporal derivative
of p(t).
The trajectories of the optimal movements can be found by substituting (14) into (5).
Optimal duration
To find the optimal duration M, we consider M as a free endpoint and apply the transversality condition [52]:(15)Solving (15) leads eventually to the equation:(16)This is an implicit equation for the
optimal M that has a single solution. The equation shows that the optimal duration depends on the ratio R=k[CN]/k[SDN] of the levels of CN and SDN, not on these levels themselves. The optimal
duration depends also on the mechanics of the oculomotor system (via the impulse response function), on the fixation period F (via Q[F](M)) and, of course, on the initial and final eye orientation
(which determine the λ[i]).
We assumed that the eye orientations at movement onset and offset obeyed Listing's law. This means that the first elements of x^0 and x^f were zero. As a result, the full optimal trajectories
appeared to obey Listing's law. We also assumed that the velocity and acceleration at movement onset and offset were zero (i.e., the elements 2, 3, 5, 6, 8 and 9 of x^0 and x^f were zero).
Although we derived expressions for the optimal trajectories, these trajectories could not be calculated in closed form because the integrals I[ij] cannot be solved analytically. These integrals were
solved numerically using a time-step of 0.025 ms. The optimal duration was determined by solving (16) numerically, also using a time-step of 0.025 ms. The post-movement fixation interval F was set to
50 ms. Making this interval longer led to negligible changes to the optimal durations and trajectories.
We assumed that motor noise is a combination of SDN and CN. Actual saccades, however, also display temporal variations, which are simultaneous variations in duration and velocity across repeated
movements, such that the saccade amplitude is constant [12]. The actual durations are approximately normally distributed with a standard deviation of 0.068 times the mean duration [12]. Although this
temporal variability does not directly induce variability in saccade endpoints, it is formally not correct to assume that the duration is constant when determining the optimal durations and
trajectories. However, estimates showed that the effects of the temporal variability on the optimal duration and trajectory are negligible. The effect on the optimal duration, for instance, is
generally smaller than 0.5 ms, which is very small compared to the effect of the uncertainty in the noise levels (Fig. 1B).
Author Contributions
Conceived and designed the experiments: Rv. Performed the experiments: Rv. Analyzed the data: Rv. Wrote the paper: Rv. | {"url":"https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0002070","timestamp":"2024-11-09T04:43:12Z","content_type":"text/html","content_length":"208586","record_id":"<urn:uuid:3b9a799d-7063-441f-949f-36a0142810b8>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00715.warc.gz"} |
mteb/raw_arxiv · Datasets at Hugging Face
A fully differential calculation in perturbative quantum chromodynamics is presented for the production of massive photon pairs at hadron
colliders. All next-to-leading order perturbative contributions from quark-antiquark, gluon-(anti)quark, and gluon-gluon subprocesses are
Calculation of prompt diphoton included, as well as all-orders resummation of initial-state gluon radiation valid at next-to-next-to-leading logarithmic accuracy. The
0704.0001 production cross sections at region of phase space is specified in which the calculation is most reliable. Good agreement is demonstrated with data from the Fermilab hep-ph
Tevatron and LHC energies Tevatron, and predictions are made for more detailed tests with CDF and DO data. Predictions are shown for distributions of diphoton
pairs produced at the energy of the Large Hadron Collider (LHC). Distributions of the diphoton pairs from the decay of a Higgs boson are
contrasted with those produced from QCD processes at the LHC, showing that enhanced sensitivity to the signal can be obtained with
judicious selection of events.
We describe a new algorithm, the $(k,\ell)$-pebble game with colors, and use it obtain a characterization of the family of $(k,\ell)
$-sparse graphs and algorithmic solutions to a family of problems concerning tree decompositions of graphs. Special instances of sparse
0704.0002 Sparsity-certifying Graph graphs appear in rigidity theory and have received increased attention in recent years. In particular, our colored pebbles generalize and math.CO cs.CG
Decompositions strengthen the previous results of Lee and Streinu and give a new proof of the Tutte-Nash-Williams characterization of arboricity. We
also present a new decomposition that certifies sparsity based on the $(k,\ell)$-pebble game with colors. Our work also exposes
connections between pebble game algorithms and previous sparse graph algorithms by Gabow, Gabow and Westermann and Hendrickson.
The evolution of Earth-Moon system is described by the dark matter field fluid model proposed in the Meeting of Division of Particle and
Field 2004, American Physical Society. The current behavior of the Earth-Moon system agrees with this model very well and the general
The evolution of the Earth-Moon pattern of the evolution of the Moon-Earth system described by this model agrees with geological and fossil evidence. The closest
0704.0003 system based on the dark matter distance of the Moon to Earth was about 259000 km at 4.5 billion years ago, which is far beyond the Roche's limit. The result suggests physics.gen-ph
field fluid model that the tidal friction may not be the primary cause for the evolution of the Earth-Moon system. The average dark matter field fluid
constant derived from Earth-Moon system data is 4.39 x 10^(-22) s^(-1)m^(-1). This model predicts that the Mars's rotation is also
slowing with the angular acceleration rate about -4.38 x 10^(-22) rad s^(-2).
A determinant of Stirling cycle We show that a determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata. The proof involves a bijection from
0704.0004 numbers counts unlabeled acyclic these automata to certain marked lattice paths and a sign-reversing involution to evaluate the determinant. math.CO
single-source automata
0704.0005 From dyadic $\Lambda_{\alpha}$ In this paper we show how to compute the $\Lambda_{\alpha}$ norm, $\alpha\ge 0$, using the dyadic grid. This result is a consequence of math.CA math.FA
to $\Lambda_{\alpha}$ the description of the Hardy spaces $H^p(R^N)$ in terms of dyadic and special atoms.
We study the two-particle wave function of paired atoms in a Fermi gas with tunable interaction strengths controlled by Feshbach
resonance. The Cooper pair wave function is examined for its bosonic characters, which is quantified by the correction of Bose
Bosonic characters of atomic enhancement factor associated with the creation and annihilation composite particle operators. An example is given for a
0704.0006 Cooper pairs across resonance three-dimensional uniform gas. Two definitions of Cooper pair wave function are examined. One of which is chosen to reflect the cond-mat.mes-hall
off-diagonal long range order (ODLRO). Another one corresponds to a pair projection of a BCS state. On the side with negative scattering
length, we found that paired atoms described by ODLRO are more bosonic than the pair projected definition. It is also found that at $(k_F
a)^{-1} \ge 1$, both definitions give similar results, where more than 90% of the atoms occupy the corresponding molecular condensates.
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer
representation has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this
approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different
0704.0007 Polymer Quantum Mechanics and aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, gr-qc
its Continuum Limit we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an
appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts
from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest,
including the harmonic oscillator, the free particle and a simple cosmological model.
A general formulation was developed to represent material models for applications in dynamic loading. Numerical methods were devised to
calculate response to shock and ramp compression, and ramp decompression, generalizing previous solutions for scalar equations of state.
Numerical solution of shock and The numerical methods were found to be flexible and robust, and matched analytic results to a high accuracy. The basic ramp and shock
0704.0008 ramp compression for general solution methods were coupled to solve for composite deformation paths, such as shock-induced impacts, and shock interactions with a cond-mat.mtrl-sci
material properties planar interface between different materials. These calculations capture much of the physics of typical material dynamics experiments,
without requiring spatially-resolving simulations. Example calculations were made of loading histories in metals, illustrating the
effects of plastic work on the temperatures induced in quasi-isentropic and shock-release experiments, and the effect of a phase
We discuss the results from the combined IRAC and MIPS c2d Spitzer Legacy observations of the Serpens star-forming region. In particular
we present a set of criteria for isolating bona fide young stellar objects, YSO's, from the extensive background contamination by
extra-galactic objects. We then discuss the properties of the resulting high confidence set of YSO's. We find 235 such objects in the
0.85 deg^2 field that was covered with both IRAC and MIPS. An additional set of 51 lower confidence YSO's outside this area is identified
The Spitzer c2d Survey of Large, from the MIPS data combined with 2MASS photometry. We describe two sets of results, color-color diagrams to compare our observed source
Nearby, Insterstellar Clouds. properties with those of theoretical models for star/disk/envelope systems and our own modeling of the subset of our objects that appear
0704.0009 IX. The Serpens YSO Population to be star+disks. These objects exhibit a very wide range of disk properties, from many that can be fit with actively accreting disks to astro-ph
As Observed With IRAC and MIPS some with both passive disks and even possibly debris disks. We find that the luminosity function of YSO's in Serpens extends down to at
least a few x .001 Lsun or lower for an assumed distance of 260 pc. The lower limit may be set by our inability to distinguish YSO's from
extra-galactic sources more than by the lack of YSO's at very low luminosities. A spatial clustering analysis shows that the nominally
less-evolved YSO's are more highly clustered than the later stages and that the background extra-galactic population can be fit by the
same two-point correlation function as seen in other extra-galactic studies. We also present a table of matches between several previous
infrared and X-ray studies of the Serpens YSO population and our Spitzer data set.
Partial cubes are isometric subgraphs of hypercubes. Structures on a graph defined by means of semicubes, and Djokovi\'{c}'s and
Partial cubes: structures, Winkler's relations play an important role in the theory of partial cubes. These structures are employed in the paper to characterize
0704.0010 characterizations, and bipartite graphs and partial cubes of arbitrary dimension. New characterizations are established and new proofs of some known results are math.CO
constructions given. The operations of Cartesian product and pasting, and expansion and contraction processes are utilized in the paper to construct
new partial cubes from old ones. In particular, the isometric and lattice dimensions of finite partial cubes obtained by means of these
operations are calculated.
Computing genus 2 Hilbert-Siegel In this paper we present an algorithm for computing Hecke eigensystems of Hilbert-Siegel cusp forms over real quadratic fields of narrow
0704.0011 modular forms over $\Q(\sqrt{5}) class number one. We give some illustrative examples using the quadratic field $\Q(\sqrt{5})$. In those examples, we identify math.NT math.AG
$ via the Jacquet-Langlands Hilbert-Siegel eigenforms that are possible lifts from Hilbert eigenforms.
Distribution of integral Fourier Recently, Bruinier and Ono classified cusp forms $f(z) := \sum_{n=0}^{\infty} a_f(n)q ^n \in S_{\lambda+1/2}(\Gamma_0(N),\chi)\cap \
Coefficients of a Modular Form mathbb{Z}[[q]]$ that does not satisfy a certain distribution property for modulo odd primes $p$. In this paper, using Rankin-Cohen
0704.0012 of Half Integral Weight Modulo Bracket, we extend this result to modular forms of half integral weight for primes $p \geq 5$. As applications of our main theorem we math.NT
Primes derive distribution properties, for modulo primes $p\geq5$, of traces of singular moduli and Hurwitz class number. We also study an
analogue of Newman's conjecture for overpartitions.
Serre obtained the p-adic limit of the integral Fourier coefficient of modular forms on $SL_2(\mathbb{Z})$ for $p=2,3,5,7$. In this
$p$-adic Limit of Weakly paper, we extend the result of Serre to weakly holomorphic modular forms of half integral weight on $\Gamma_{0}(4N)$ for $N=1,2,4$. A
0704.0013 Holomorphic Modular Forms of proof is based on linear relations among Fourier coefficients of modular forms of half integral weight. As applications we obtain math.NT
Half Integral Weight congruences of Borcherds exponents, congruences of quotient of Eisentein series and congruences of values of $L$-functions at a certain
point are also studied. Furthermore, the congruences of the Fourier coefficients of Siegel modular forms on Maass Space are obtained
using Ikeda lifting.
0704.0014 Iterated integral and the loop In this article we discuss a relation between the string topology and differential forms based on the theory of Chen's iterated integrals math.CA math.AT
product and the cyclic bar complex.
Fermionic superstring loop The pure spinor formulation of the ten-dimensional superstring leads to manifestly supersymmetric loop amplitudes, expressed as integrals
0704.0015 amplitudes in the pure spinor in pure spinor superspace. This paper explores different methods to evaluate these integrals and then uses them to calculate the hep-th
formalism kinematic factors of the one-loop and two-loop massless four-point amplitudes involving two and four Ramond states.
In this work, we evaluate the lifetimes of the doubly charmed baryons $\Xi_{cc}^{+}$, $\Xi_{cc}^{++}$ and $\Omega_{cc}^{+}$. We carefully
calculate the non-spectator contributions at the quark level where the Cabibbo-suppressed diagrams are also included. The hadronic matrix
0704.0016 Lifetime of doubly charmed elements are evaluated in the simple non-relativistic harmonic oscillator model. Our numerical results are generally consistent with that hep-ph
baryons obtained by other authors who used the diquark model. However, all the theoretical predictions on the lifetimes are one order larger than
the upper limit set by the recent SELEX measurement. This discrepancy would be clarified by the future experiment, if more accurate
experiment still confirms the value of the SELEX collaboration, there must be some unknown mechanism to be explored.
Results from spectroscopic observations of the Intermediate Polar (IP) EX Hya in quiescence during 1991 and 2001 are presented.
Spin-modulated radial velocities consistent with an outer disc origin were detected for the first time in an IP. The spin pulsation was
modulated with velocities near ~500-600 km/s. These velocities are consistent with those of material circulating at the outer edge of the
accretion disc, suggesting corotation of the accretion curtain with material near the Roche lobe radius. Furthermore, spin Doppler
Spectroscopic Observations of tomograms have revealed evidence of the accretion curtain emission extending from velocities of ~500 km/s to ~1000 km/s. These findings
0704.0017 the Intermediate Polar EX Hydrae have confirmed the theoretical model predictions of King & Wynn (1999), Belle et al. (2002) and Norton et al. (2004) for EX Hya, which astro-ph
in Quiescence predict large accretion curtains that extend to a distance close to the Roche lobe radius in this system. Evidence for overflow stream of
material falling onto the magnetosphere was observed, confirming the result of Belle et al. (2005) that disc overflow in EX Hya is
present during quiescence as well as outburst. It appears that the hbeta and hgamma spin radial velocities originated from the rotation
of the funnel at the outer disc edge, while those of halpha were produced due to the flow of material along the field lines far from the
white dwarf (narrow component) and close to the white dwarf (broad-base component), in agreement with the accretion curtain model.
We give a prescription for how to compute the Callias index, using as regulator an exponential function. We find agreement with old
0704.0018 In quest of a generalized results in all odd dimensions. We show that the problem of computing the dimension of the moduli space of self-dual strings can be hep-th
Callias index theorem formulated as an index problem in even-dimensional (loop-)space. We think that the regulator used in this Letter can be applied to this
index problem.
Approximation for extinction
0704.0019 probability of the contact In this note we give a new method for getting a series of approximations for the extinction probability of the one-dimensional contact math.PR math.AG
process based on the Gr\"obner process by using the Gr\"obner basis.
The shape of the hadronic form factor f+(q2) in the decay D0 --> K- e+ nue has been measured in a model independent analysis and compared
Measurement of the Hadronic Form with theoretical calculations. We use 75 fb(-1) of data recorded by the BABAR detector at the PEPII electron-positron collider. The
0704.0020 Factor in D0 --> K- e+ nue corresponding decay branching fraction, relative to the decay D0 --> K- pi+, has also been measured to be RD = BR(D0 --> K- e+ nue)/BR(D0 hep-ex
Decays --> K- pi+) = 0.927 +/- 0.007 +/- 0.012. From these results, and using the present world average value for BR(D0 --> K- pi+), the
normalization of the form factor at q2=0 is determined to be f+(0)=0.727 +/- 0.007 +/- 0.005 +/- 0.007 where the uncertainties are
statistical, systematic, and from external inputs, respectively.
Molecular Synchronization Waves Spatiotemporal pattern formation in a product-activated enzymic reaction at high enzyme concentrations is investigated. Stochastic nlin.PS
0704.0021 in Arrays of Allosterically simulations show that catalytic turnover cycles of individual enzymes can become coherent and that complex wave patterns of molecular physics.chem-ph
Regulated Enzymes synchronization can develop. The analysis based on the mean-field approximation indicates that the observed patterns result from the q-bio.MN
presence of Hopf and wave bifurcations in the considered system.
We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution
evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the manifold, we pull back the
stochastic flow on the manifold to the Lie group via the action, and subsequently pull back the flow to the corresponding Lie algebra via
the exponential map. We construct an approximation to the stochastic flow in the Lie algebra via closed operations and then push back to
the Lie group and then to the manifold, thus ensuring our approximation lies in the manifold. We call such schemes stochastic Munthe-Kaas
0704.0022 Stochastic Lie group integrators methods after their deterministic counterparts. We also present stochastic Lie group integration schemes based on Castell--Gaines math.NA
methods. These involve using an underlying ordinary differential integrator to approximate the flow generated by a truncated stochastic
exponential Lie series. They become stochastic Lie group integrator schemes if we use Munthe-Kaas methods as the underlying ordinary
differential integrator. Further, we show that some Castell--Gaines methods are uniformly more accurate than the corresponding stochastic
Taylor schemes. Lastly we demonstrate our methods by simulating the dynamics of a free rigid body such as a satellite and an autonomous
underwater vehicle both perturbed by two independent multiplicative stochastic noise processes.
The very nature of the solar chromosphere, its structuring and dynamics, remains far from being properly understood, in spite of
intensive research. Here we point out the potential of chromospheric observations at millimeter wavelengths to resolve this long-standing
problem. Computations carried out with a sophisticated dynamic model of the solar chromosphere due to Carlsson and Stein demonstrate that
millimeter emission is extremely sensitive to dynamic processes in the chromosphere and the appropriate wavelengths to look for dynamic
ALMA as the ideal probe of the signatures are in the range 0.8-5.0 mm. The model also suggests that high resolution observations at mm wavelengths, as will be provided
0704.0023 solar chromosphere by ALMA, will have the unique property of reacting to both the hot and the cool gas, and thus will have the potential of distinguishing astro-ph
between rival models of the solar atmosphere. Thus, initial results obtained from the observations of the quiet Sun at 3.5 mm with the
BIMA array (resolution of 12 arcsec) reveal significant oscillations with amplitudes of 50-150 K and frequencies of 1.5-8 mHz with a
tendency toward short-period oscillations in internetwork and longer periods in network regions. However higher spatial resolution, such
as that provided by ALMA, is required for a clean separation between the features within the solar atmosphere and for an adequate
comparison with the output of the comprehensive dynamic simulations.
The formation of quasi-2D spin-wave waveforms in longitudinally magnetized stripes of ferrimagnetic film was observed by using time- and
Formation of quasi-solitons in space-resolved Brillouin light scattering technique. In the linear regime it was found that the confinement decreases the amplitude of
0704.0024 transverse confined dynamic magnetization near the lateral stripe edges. Thus, the so-called effective dipolar pinning of dynamic magnetization takes place nlin.PS
ferromagnetic film media at the edges. In the nonlinear regime a new stable spin wave packet propagating along a waveguide structure, for which both transversal
instability and interaction with the side walls of the waveguide are important was observed. The experiments and a numerical simulation
of the pulse evolution show that the shape of the formed waveforms and their behavior are strongly influenced by the confinement.
Spectroscopic Properties of We present recent advances in understanding of the ground and excited states of the electron-phonon coupled systems obtained by novel
Polarons in Strongly Correlated methods of Diagrammatic Monte Carlo and Stochastic Optimization, which enable the approximation-free calculation of Matsubara Green cond-mat.str-el
0704.0025 Systems by Exact Diagrammatic function in imaginary times and perform unbiased analytic continuation to real frequencies. We present exact numeric results on the cond-mat.stat-mech
Monte Carlo Method ground state properties, Lehmann spectral function and optical conductivity of different strongly correlated systems: Frohlich polaron,
Rashba-Pekar exciton-polaron, pseudo Jahn-Teller polaron, exciton, and interacting with phonons hole in the t-J model.
Placeholder Substructures II: Zero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from N-dimensional hypercomplex numbers (N a power of 2, at least 4) can
Meta-Fractals, Made of represent singularities and, as N approaches infinite, fractals -- and thereby,scale-free networks. Any integer greater than 8 and not a
0704.0026 Box-Kites, Fill power of 2 generates a meta-fractal or "Sky" when it is interpreted as the "strut constant" (S) of an ensemble of octahedral vertex math.RA
Infinite-Dimensional Skies figures called "Box-Kites" (the fundamental building blocks of ZDs). Remarkably simple bit-manipulation rules or "recipes" provide tools
for transforming one fractal genus into others within the context of Wolfram's Class 4 complexity.
We describe a peculiar fine structure acquired by the in-plane optical phonon at the Gamma-point in graphene when it is brought into
Filling-Factor-Dependent resonance with one of the inter-Landau-level transitions in this material. The effect is most pronounced when this lattice mode
0704.0027 Magnetophonon Resonance in (associated with the G-band in graphene Raman spectrum) is in resonance with inter-Landau-level transitions 0 -> (+,1) and (-,1) -> 0, at cond-mat.mes-hall
Graphene a magnetic field B_0 ~ 30 T. It can be used to measure the strength of the electron-phonon coupling directly, and its filling-factor
dependence can be used experimentally to detect circularly polarized lattice modes.
Pfaffians, hafnians and products We prove pfaffian and hafnian versions of Lieb's inequalities on determinants and permanents of positive semi-definite matrices. We use
0704.0028 of real linear functionals the hafnian inequality to improve the lower bound of R\'ev\'esz and Sarantopoulos on the norm of a product of linear functionals on a math.CA math.PR
real Euclidean space (this subject is sometimes called the `real linear polarization constant' problem).
Understanding the Flavor In $\XQM$, a quark can emit Goldstone bosons. The flavor symmetry breaking in the Goldstone boson emission process is used to intepret
Symmetry Breaking and Nucleon the nucleon flavor-spin structure. In this paper, we study the inner structure of constituent quarks implied in $\XQM$ caused by the
0704.0029 Flavor-Spin Structure within Goldstone boson emission process in nucleon. From a simplified model Hamiltonian derived from $\XQM$, the intrinsic wave functions of hep-ph
Chiral Quark Model constituent quarks are determined. Then the obtained transition probabilities of the emission of Goldstone boson from a quark can give a
reasonable interpretation to the flavor symmetry breaking in nucleon flavor-spin structure.
We investigate the effect of tuning the phonon energy on the correlation effects in models of electron-phonon interactions using DMFT. In
the regime where itinerant electrons, instantaneous electron-phonon driven correlations and static distortions compete on similar energy
0704.0030 Tuning correlation effects with scales, we find several interesting results including (1) A crossover from band to Mott behavior in the spectral function, leading to cond-mat.str-el
electron-phonon interactions hybrid band/Mott features in the spectral function for phonon frequencies slightly larger than the band width. (2) Since the optical
conductivity depends sensitively on the form of the spectral function, we show that such a regime should be observable through the low
frequency form of the optical conductivity. (3) The resistivity has a double kondo peak arrangement
We show that crystal can trap a broad (x, x', y, y', E) distribution of particles and channel it preserved with a high precision. This
Crystal channeling of LHC sampled-and-hold distribution can be steered by a bent crystal for analysis downstream. In simulations for the 7 TeV Large Hadron
0704.0031 forward protons with preserved Collider, a crystal adapted to the accelerator lattice traps 90% of diffractively scattered protons emerging from the interaction point hep-ph
distribution in phase space with a divergence 100 times the critical angle. We set the criterion for crystal adaptation improving efficiency ~100-fold. Proton angles
are preserved in crystal transmission with accuracy down to 0.1 microrad. This makes feasible a crystal application for measuring very
forward protons at the LHC.
We analyze the possibility of probing non-standard neutrino interactions (NSI, for short) through the detection of neutrinos produced in
a future galactic supernova (SN).We consider the effect of NSI on the neutrino propagation through the SN envelope within a
Probing non-standard neutrino three-neutrino framework, paying special attention to the inclusion of NSI-induced resonant conversions, which may take place in the most
0704.0032 interactions with supernova deleptonised inner layers. We study the possibility of detecting NSI effects in a Megaton water Cherenkov detector, either through hep-ph
neutrinos modulation effects in the $\bar\nu_e$ spectrum due to (i) the passage of shock waves through the SN envelope, (ii) the time dependence of
the electron fraction and (iii) the Earth matter effects; or, finally, through the possible detectability of the neutronization $\nu_e$
burst. We find that the $\bar\nu_e$ spectrum can exhibit dramatic features due to the internal NSI-induced resonant conversion. This
occurs for non-universal NSI strengths of a few %, and for very small flavor-changing NSI above a few$\times 10^{-5}$.
We performed a rigorous theoretical convergence analysis of the discrete dipole approximation (DDA). We prove that errors in any measured
quantity are bounded by a sum of a linear and quadratic term in the size of a dipole d, when the latter is in the range of DDA
Convergence of the discrete applicability. Moreover, the linear term is significantly smaller for cubically than for non-cubically shaped scatterers. Therefore, for physics.optics
0704.0033 dipole approximation. I. small d errors for cubically shaped particles are much smaller than for non-cubically shaped. The relative importance of the linear term physics.comp-ph
Theoretical analysis decreases with increasing size, hence convergence of DDA for large enough scatterers is quadratic in the common range of d. Extensive
numerical simulations were carried out for a wide range of d. Finally we discuss a number of new developments in DDA and their
consequences for convergence.
0704.0034 Origin of adaptive mutants: a This is a supplement to the paper arXiv:q-bio/0701050, containing the text of correspondence sent to Nature in 1990. q-bio.PE q-bio.CB
quantum measurement? quant-ph
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance
Convergence of the discrete of this technique was studied empirically based on extensive simulations for 5 test cases using many different discretizations. The
0704.0035 dipole approximation. II. An quality of the extrapolation improves with refining discretization reaching extraordinary performance especially for cubically shaped physics.optics
extrapolation technique to particles. A two order of magnitude decrease of error was demonstrated. We also propose estimates of the extrapolation error, which were physics.comp-ph
increase the accuracy proven to be reliable. Finally we propose a simple method to directly separate shape and discretization errors and illustrated this for
one test case.
The multisite phosphorylation-dephosphorylation cycle is a motif repeatedly used in cell signaling. This motif itself can generate a
variety of dynamic behaviors like bistability and ultrasensitivity without direct positive feedbacks. In this paper, we study the number
A remark on the number of steady of positive steady states of a general multisite phosphorylation-dephosphorylation cycle, and how the number of positive steady states
0704.0036 states in a multiple futile varies by changing the biological parameters. We show analytically that (1) for some parameter ranges, there are at least n+1 (if n is q-bio.QM q-bio.MN
cycle even) or n (if n is odd) steady states; (2) there never are more than 2n-1 steady states (in particular, this implies that for n=2,
including single levels of MAPK cascades, there are at most three steady states); (3) for parameters near the standard Michaelis-Menten
quasi-steady state conditions, there are at most n+1 steady states; and (4) for parameters far from the standard Michaelis-Menten
quasi-steady state conditions, there is at most one steady state.
In this manuscript we investigate the capabilities of the Discrete Dipole Approximation (DDA) to simulate scattering from particles that
are much larger than the wavelength of the incident light, and describe an optimized publicly available DDA computer program that
The discrete dipole processes the large number of dipoles required for such simulations. Numerical simulations of light scattering by spheres with size
approximation for simulation of parameters x up to 160 and 40 for refractive index m=1.05 and 2 respectively are presented and compared with exact results of the Mie physics.optics
0704.0037 light scattering by particles theory. Errors of both integral and angle-resolved scattering quantities generally increase with m and show no systematic dependence on physics.comp-ph
much larger than the wavelength x. Computational times increase steeply with both x and m, reaching values of more than 2 weeks on a cluster of 64 processors. The main
distinctive feature of the computer program is the ability to parallelize a single DDA simulation over a cluster of computers, which
allows it to simulate light scattering by very large particles, like the ones that are considered in this manuscript. Current limitations
and possible ways for improvement are discussed.
We present a review of the discrete dipole approximation (DDA), which is a general method to simulate light scattering by arbitrarily
The discrete dipole shaped particles. We put the method in historical context and discuss recent developments, taking the viewpoint of a general framework physics.optics
0704.0038 approximation: an overview and based on the integral equations for the electric field. We review both the theory of the DDA and its numerical aspects, the latter being physics.comp-ph
recent developments of critical importance for any practical application of the method. Finally, the position of the DDA among other methods of light
scattering simulation is shown and possible future developments are discussed.
The quadratic pion scalar radius, \la r^2\ra^\pi_s, plays an important role for present precise determinations of \pi\pi scattering.
Recently, Yndur\'ain, using an Omn\`es representation of the null isospin(I) non-strange pion scalar form factor, obtains \la r^2\ra^\
pi_s=0.75\pm 0.07 fm^2. This value is larger than the one calculated by solving the corresponding Muskhelishvili-Omn\`es equations, \la r
Scalar radius of the pion and ^2\ra^\pi_s=0.61\pm 0.04 fm^2. A large discrepancy between both values, given the precision, then results. We reanalyze Yndur\'ain's hep-ph hep-lat
0704.0039 zeros in the form factor method and show that by imposing continuity of the resulting pion scalar form factor under tiny changes in the input \pi\pi phase shifts, nucl-th
a zero in the form factor for some S-wave I=0 T-matrices is then required. Once this is accounted for, the resulting value is \la r^2\
ra_s^\pi=0.65\pm 0.05 fm^2. The main source of error in our determination is present experimental uncertainties in low energy S-wave I=0
\pi\pi phase shifts. Another important contribution to our error is the not yet settled asymptotic behaviour of the phase of the scalar
form factor from QCD.
Multilinear function series in As in the cases of freeness and monotonic independence, the notion of conditional freeness is meaningful when complex-valued states are
0704.0040 conditionally free probability replaced by positive conditional expectations. In this framework, the paper presents several positivity results, a version of the central math.OA math.FA
with amalgamation limit theorem and an analogue of the conditionally free R-transform constructed by means of multilinear function series.
We formulate a quantum generalization of the notion of the group of Riemannian isometries for a compact Riemannian manifold, by
introducing a natural notion of smooth and isometric action by a compact quantum group on a classical or noncommutative manifold
described by spectral triples, and then proving the existence of a universal object (called the quantum isometry group) in the category
Quantum Group of Isometries in of compact quantum groups acting smoothly and isometrically on a given (possibly noncommutative) manifold satisfying certain regularity
0704.0041 Classical and Noncommutative assumptions. In fact, we identify the quantum isometry group with the universal object in a bigger category, namely the category of math.QA math-ph
Geometry `quantum families of smooth isometries', defined along the line of Woronowicz and Soltan. We also construct a spectral triple on the math.MP
Hilbert space of forms on a noncommutative manifold which is equivariant with respect to a natural unitary representation of the quantum
isometry group. We give explicit description of quantum isometry groups of commutative and noncommutative tori, and in this context,
obtain the quantum double torus defined in \cite{hajac} as the universal quantum group of holomorphic isometries of the noncommutative
General System theory, It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be
0704.0042 Like-Quantum Semantics and Fuzzy done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so possible taking into account the physics.gen-ph
Sets logical openness relationship between observer and system. We are going to show how considering the truth-values of quantum propositions quant-ph
within the context of the fuzzy sets is here more useful for systemics . In conclusion we propose an example of formal quantum coherence.
We construct a system of nonequilibrium entropy limiters for the lattice Boltzmann methods (LBM). These limiters erase spurious
oscillations without blurring of shocks, and do not affect smooth solutions. In general, they do the same work for LBM as flux limiters
do for finite differences, finite volumes and finite elements methods, but for LBM the main idea behind the construction of
Nonequilibrium entropy limiters nonequilibrium entropy limiter schemes is to transform a field of a scalar quantity - nonequilibrium entropy. There are two families of cond-mat.stat-mech
0704.0043 in lattice Boltzmann methods limiters: (i) based on restriction of nonequilibrium entropy (entropy "trimming") and (ii) based on filtering of nonequilibrium entropy cond-mat.mtrl-sci
(entropy filtering). The physical properties of LBM provide some additional benefits: the control of entropy production and accurate
estimate of introduced artificial dissipation are possible. The constructed limiters are tested on classical numerical examples: 1D
athermal shock tubes with an initial density ratio 1:2 and the 2D lid-driven cavity for Reynolds numbers Re between 2000 and 7500 on a
coarse 100*100 grid. All limiter constructions are applicable for both entropic and non-entropic quasiequilibria.
We present a theoretical framework for plasma turbulence in astrophysical plasmas (solar wind, interstellar medium, galaxy clusters,
accretion disks). The key assumptions are that the turbulence is anisotropic with respect to the mean magnetic field and frequencies are
low compared to the ion cyclotron frequency. The energy injected at the outer scale scale has to be converted into heat, which ultimately
cannot be done without collisions. A KINETIC CASCADE develops that brings the energy to collisional scales both in space and velocity.
Its nature depends on the physics of plasma fluctuations. In each of the physically distinct scale ranges, the kinetic problem is
Astrophysical gyrokinetics: systematically reduced to a more tractable set of equations. In the "inertial range" above the ion gyroscale, the kinetic cascade splits astro-ph nlin.CD
0704.0044 kinetic and fluid turbulent into a cascade of Alfvenic fluctuations, which are governed by the RMHD equations at both the collisional and collisionless scales, and a physics.plasm-ph
cascades in magnetized weakly passive cascade of compressive fluctuations, which obey a linear kinetic equation along the moving field lines associated with the physics.space-ph
collisional plasmas Alfvenic component. In the "dissipation range" between the ion and electron gyroscales, there are again two cascades: the
kinetic-Alfven-wave (KAW) cascade governed by two fluid-like Electron RMHD equations and a passive phase-space cascade of ion entropy
fluctuations. The latter cascade brings the energy of the inertial-range fluctuations that was damped by collisionless wave-particle
interaction at the ion gyroscale to collisional scales in the phase space and leads to ion heating. The KAW energy is similarly damped at
the electron gyroscale and converted into electron heat. Kolmogorov-style scaling relations are derived for these cascades. Astrophysical
and space-physical applications are discussed in detail.
This paper considers the propagation of shallow-water solitary and nonlinear periodic waves over a gradual slope with bottom friction in
the framework of a variable-coefficient Korteweg-de Vries equation. We use the Whitham averaging method, using a recent development of
this theory for perturbed integrable equations. This general approach enables us not only to improve known results on the adiabatic
Evolution of solitary waves and evolution of isolated solitary waves and periodic wave trains in the presence of variable topography and bottom friction, modeled by the
0704.0045 undular bores in shallow-water Chezy law, but also importantly, to study the effects of these factors on the propagation of undular bores, which are essentially nlin.PS nlin.SI
flows over a gradual slope with unsteady in the system under consideration. In particular, it is shown that the combined action of variable topography and bottom
bottom friction friction generally imposes certain global restrictions on the undular bore propagation so that the evolution of the leading solitary wave
can be substantially different from that of an isolated solitary wave with the same initial amplitude. This non-local effect is due to
nonlinear wave interactions within the undular bore and can lead to an additional solitary wave amplitude growth, which cannot be
predicted in the framework of the traditional adiabatic approach to the propagation of solitary waves in slowly varying media.
In a quantum mechanical model, Diosi, Feldmann and Kosloff arrived at a conjecture stating that the limit of the entropy of certain
0704.0046 A limit relation for entropy and mixtures is the relative entropy as system size goes to infinity. The conjecture is proven in this paper for density matrices. The first quant-ph cs.IT
channel capacity per unit cost proof is analytic and uses the quantum law of large numbers. The second one clarifies the relation to channel capacity per unit cost for math.IT
classical-quantum channels. Both proofs lead to generalization of the conjecture.
The intelligent acoustic emission locator is described in Part I, while Part II discusses blind source separation, time delay estimation
and location of two simultaneously active continuous acoustic emission sources. The location of acoustic emission on complicated aircraft
frame structures is a difficult problem of non-destructive testing. This article describes an intelligent acoustic emission source
Intelligent location of locator. The intelligent locator comprises a sensor antenna and a general regression neural network, which solves the location problem
0704.0047 simultaneously active acoustic based on learning from examples. Locator performance was tested on different test specimens. Tests have shown that the accuracy of cs.NE cs.AI
emission sources: Part I location depends on sound velocity and attenuation in the specimen, the dimensions of the tested area, and the properties of stored data.
The location accuracy achieved by the intelligent locator is comparable to that obtained by the conventional triangulation method, while
the applicability of the intelligent locator is more general since analysis of sonic ray paths is avoided. This is a promising method for
non-destructive testing of aircraft frame structures by the acoustic emission method.
We report on the analysis of selected single source data sets from the first round of the Mock LISA Data Challenges (MLDC) for white
Inference on white dwarf binary dwarf binaries. We implemented an end-to-end pipeline consisting of a grid-based coherent pre-processing unit for signal detection, and
0704.0048 systems using the first round an automatic Markov Chain Monte Carlo post-processing unit for signal evaluation. We demonstrate that signal detection with our coherent gr-qc astro-ph
Mock LISA Data Challenges data approach is secure and accurate, and is increased in accuracy and supplemented with additional information on the signal parameters by
sets our Markov Chain Monte Carlo approach. We also demonstrate that the Markov Chain Monte Carlo routine is additionally able to determine
accurately the noise level in the frequency window of interest.
An algorithm for the We present an algorithm that produces the classification list of smooth Fano d-polytopes for any given d. The input of the algorithm is a
0704.0049 classification of smooth Fano single number, namely the positive integer d. The algorithm has been used to classify smooth Fano d-polytopes for d<=7. There are 7622 math.CO
polytopes isomorphism classes of smooth Fano 6-polytopes and 72256 isomorphism classes of smooth Fano 7-polytopes.
Part I describes an intelligent acoustic emission locator, while Part II discusses blind source separation, time delay estimation and
location of two continuous acoustic emission sources. Acoustic emission (AE) analysis is used for characterization and location of
Intelligent location of developing defects in materials. AE sources often generate a mixture of various statistically independent signals. A difficult problem of
0704.0050 simultaneously active acoustic AE analysis is separation and characterization of signal components when the signals from various sources and the mode of mixing are cs.NE cs.AI
emission sources: Part II unknown. Recently, blind source separation (BSS) by independent component analysis (ICA) has been used to solve these problems. The
purpose of this paper is to demonstrate the applicability of ICA to locate two independent simultaneously active acoustic emission
sources on an aluminum band specimen. The method is promising for non-destructive testing of aircraft frame structures by acoustic
emission analysis.
A novel way of picturing the processing of quantum information is described, allowing a direct visualization of teleportation of quantum
0704.0051 Visualizing Teleportation states and providing a simple and intuitive understanding of this fascinating phenomenon. The discussion is aimed at providing physicists physics.ed-ph
a method of explaining teleportation to non-scientists. The basic ideas of quantum physics are first explained in lay terms, after which quant-ph
these ideas are used with a graphical description, out of which teleportation arises naturally.
We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider
Quantum Field Theory on Curved Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is generated by one-parameter subgroups
0704.0052 Backgrounds. II. Spacetime which have either self-adjoint or unitary quantizations. We analytically continue the self-adjoint semigroups to one-parameter unitary hep-th
Symmetries groups, and thus construct a unitary representation of the isometry group of the associated Lorentzian manifold. The method is
illustrated for the example of hyperbolic space, whose Lorentzian continuation is Anti-de Sitter space.
The aim of the present paper is to provide a global presentation of the theory of special Finsler manifolds. We introduce and investigate
globally (or intrinsically, free from local coordinates) many of the most important and most commonly used special Finsler manifolds:
locally Minkowskian, Berwald, Landesberg, general Landesberg, $P$-reducible, $C$-reducible, semi-$C$-reducible, quasi-$C$-reducible, $P^
{*}$-Finsler, $C^{h}$-recurrent, $C^{v}$-recurrent, $C^{0}$-recurrent, $S^{v}$-recurrent, $S^{v}$-recurrent of the second order, $C_{2}
A Global Approach to the Theory $-like, $S_{3}$-like, $S_{4}$-like, $P_{2}$-like, $R_{3}$-like, $P$-symmetric, $h$-isotropic, of scalar curvature, of constant curvature,
0704.0053 of Special Finsler Manifolds of $p$-scalar curvature, of $s$-$ps$-curvature. The global definitions of these special Finsler manifolds are introduced. Various math.DG gr-qc
relationships between the different types of the considered special Finsler manifolds are found. Many local results, known in the
literature, are proved globally and several new results are obtained. As a by-product, interesting identities and properties concerning
the torsion tensor fields and the curvature tensor fields are deduced. Although our investigation is entirely global, we provide; for
comparison reasons, an appendix presenting a local counterpart of our global approach and the local definitions of the special Finsler
spaces considered.
The Hardy-Lorentz Spaces $H^ In this paper we consider the Hardy-Lorentz spaces $H^{p,q}(R^n)$, with $0<p\le 1$, $0<q\le \infty$. We discuss the atomic decomposition
0704.0054 {p,q}(R^n)$ of the elements in these spaces, their interpolation properties, and the behavior of singular integrals and other operators acting on math.CA math.FA
Potassium intercalation in graphite is investigated by first-principles theory. The bonding in the potassium-graphite compound is
reasonably well accounted for by traditional semilocal density functional theory (DFT) calculations. However, to investigate the
intercalate formation energy from pure potassium atoms and graphite requires use of a description of the graphite interlayer binding and
Potassium intercalation in thus a consistent account of the nonlocal dispersive interactions. This is included seamlessly with ordinary DFT by a van der Waals cond-mat.soft
0704.0055 graphite: A van der Waals density functional (vdW-DF) approach [Phys. Rev. Lett. 92, 246401 (2004)]. The use of the vdW-DF is found to stabilize the graphite cond-mat.mtrl-sci
density-functional study crystal, with crystal parameters in fair agreement with experiments. For graphite and potassium-intercalated graphite structural
parameters such as binding separation, layer binding energy, formation energy, and bulk modulus are reported. Also the adsorption and
sub-surface potassium absorption energies are reported. The vdW-DF description, compared with the traditional semilocal approach, is
found to weakly soften the elastic response.
We study a simple model of a nematic liquid crystal made of parallel ellipsoidal particles interacting via a repulsive Gaussian law.
Phase diagram of Gaussian-core After identifying the relevant solid phases of the system through a careful zero-temperature scrutiny of as many as eleven candidate cond-mat.soft
0704.0056 nematics crystal structures, we determine the melting temperature for various pressure values, also with the help of exact free energy cond-mat.mtrl-sci
calculations. Among the prominent features of this model are pressure-driven reentrant melting and the stabilization of a columnar phase
for intermediate temperatures.
We study the interplay of crystal field splitting and Hund coupling in a two-orbital model which captures the essential physics of
High-spin to low-spin and systems with two electrons or holes in the e_g shell. We use single site dynamical mean field theory with a recently developed impurity
0704.0057 orbital polarization transitions solver which is able to access strong couplings and low temperatures. The fillings of the orbitals and the location of phase boundaries cond-mat.str-el
in multiorbital Mott systems are computed as a function of Coulomb repulsion, exchange coupling and crystal field splitting. We find that the Hund coupling can drive
the system into a novel Mott insulating phase with vanishing orbital susceptibility. Away from half-filling, the crystal field splitting
can induce an orbital selective Mott state.
I shall present three arguments for the proposition that intelligent life is very rare in the universe. First, I shall summarize the
consensus opinion of the founders of the Modern Synthesis (Simpson, Dobzhanski, and Mayr) that the evolution of intelligent life is
exceedingly improbable. Second, I shall develop the Fermi Paradox: if they existed they'd be here. Third, I shall show that if
0704.0058 Intelligent Life in Cosmology intelligent life were too common, it would use up all available resources and die out. But I shall show that the quantum mechanical physics.pop-ph
principle of unitarity (actually a form of teleology!) requires intelligent life to survive to the end of time. Finally, I shall argue
that, if the universe is indeed accelerating, then survival to the end of time requires that intelligent life, though rare, to have
evolved several times in the visible universe. I shall argue that the acceleration is a consequence of the excess of matter over
antimatter in the universe. I shall suggest experiments to test these claims.
We derive masses and radii for both components in the single-lined eclipsing binary HAT-TR-205-013, which consists of a F7V primary and a
late M-dwarf secondary. The system's period is short, $P=2.230736 \pm 0.000010$ days, with an orbit indistinguishable from circular, $e=
0.012 \pm 0.021$. We demonstrate generally that the surface gravity of the secondary star in a single-lined binary undergoing total
eclipses can be derived from characteristics of the light curve and spectroscopic orbit. This constrains the secondary to a unique line
The Mass and Radius of the in the mass-radius diagram with $M/R^2$ = constant. For HAT-TR-205-013, we assume the orbit has been tidally circularized, and that the
0704.0059 Unseen M-Dwarf Companion in the primary's rotation has been synchronized and aligned with the orbital axis. Our observed line broadening, $V_{\rm rot} \sin i_{\rm rot} = astro-ph
Single-Lined Eclipsing Binary 28.9 \pm 1.0$ \kms, gives a primary radius of $R_{\rm A} = 1.28 \pm 0.04$ \rsun. Our light curve analysis leads to the radius of the
HAT-TR-205-013 secondary, $R_{\rm B} = 0.167 \pm 0.006$ \rsun, and the semimajor axis of the orbit, $a = 7.54 \pm 0.30 \rsun = 0.0351 \pm 0.0014$ AU.
Our single-lined spectroscopic orbit and the semimajor axis then yield the individual masses, $M_{\rm B} = 0.124 \pm 0.010$ \msun and $M_
{\rm A} = 1.04 \pm 0.13$ \msun. Our result for HAT-TR-205-013 B lies above the theoretical mass-radius models from the Lyon group,
consistent with results from double-lined eclipsing binaries. The method we describe offers the opportunity to study the very low end of
the stellar mass-radius relation.
We investigate the Coulomb excitation of low-lying states of unstable nuclei in intermediate energy collisions ($E_{lab}\sim10-500$ MeV/
0704.0060 Coulomb excitation of unstable nucleon). It is shown that the cross sections for the $E1$ and $E2$ transitions are larger at lower energies, much less than 10 MeV/ nucl-th
nuclei at intermediate energies nucleon. Retardation effects and Coulomb distortion are found to be both relevant for energies as low as 10 MeV/nucleon and as high as
500 MeV/nucleon. Implications for studies at radioactive beam facilities are discussed.
Intersection bodies represent a remarkable class of geometric objects associated with sections of star bodies and invoking Radon
transforms, generalized cosine transforms, and the relevant Fourier analysis. The main focus of this article is interrelation between
generalized cosine transforms of different kinds in the context of their application to investigation of a certain family of intersection
0704.0061 Intersection Bodies and bodies, which we call $\lam$-intersection bodies. The latter include $k$-intersection bodies (in the sense of A. Koldobsky) and unit math.FA
Generalized Cosine Transforms balls of finite-dimensional subspaces of $L_p$-spaces. In particular, we show that restrictions onto lower dimensional subspaces of the
spherical Radon transforms and the generalized cosine transforms preserve their integral-geometric structure. We apply this result to the
study of sections of $\lam$-intersection bodies. New characterizations of this class of bodies are obtained and examples are given. We
also review some known facts and give them new proofs.
In this paper, we introduce the on-line Viterbi algorithm for decoding hidden Markov models (HMMs) in much smaller than linear space. Our
analysis on two-state HMMs suggests that the expected maximum memory used to decode sequence of length $n$ with $m$-state HMM can be as
0704.0062 On-line Viterbi Algorithm and low as $\Theta(m\log n)$, without a significant slow-down compared to the classical Viterbi algorithm. Classical Viterbi algorithm cs.DS
Its Relationship to Random Walks requires $O(mn)$ space, which is impractical for analysis of long DNA sequences (such as complete human genome chromosomes) and for
continuous data streams. We also experimentally demonstrate the performance of the on-line Viterbi algorithm on a simple HMM for gene
finding on both simulated and real DNA sequences.
Neutrinoless double beta decay is one of the most sensitive approaches in non-accelerator particle physics to take us into a regime of
Experimental efforts in search physics beyond the standard model. This article is a brief review of the experiments in search of neutrinoless double beta decay from
0704.0063 of 76Ge Neutrinoless Double Beta 76Ge. Following a brief introduction of the process of double beta decay from 76Ge, the results of the very first experiments IGEX and hep-ph
Decay Heidelberg-Moscow which give indications of the existence of possible neutrinoless double beta decay mode has been reviewed. Then ongoing
efforts to substantiate the early findings are presented and the Majorana experiment as a future experimental approach which will allow a
very detailed study of the neutrinoless decay mode is discussed.
We capture the off-shell as well as the on-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the
Lagrangian densities of the four (3 + 1)-dimensional (4D) (non-)Abelian 1-form gauge theories within the framework of the superfield
Nilpotent symmetry invariance in formalism. In particular, we provide the geometrical interpretations for (i) the above nilpotent symmetry invariance, and (ii) the above
the superfield formulation: the Lagrangian densities, in the language of the specific quantities defined in the domain of the above superfield formalism. Some of the
0704.0064 (non-)Abelian 1-form gauge subtle points, connected with the 4D (non-)Abelian 1-form gauge theories, are clarified within the framework of the above superfield hep-th
theories formalism where the 4D ordinary gauge theories are considered on the (4, 2)-dimensional supermanifold parametrized by the four spacetime
coordinates x^\mu (with \mu = 0, 1, 2, 3) and a pair of Grassmannian variables \theta and \bar\theta. One of the key results of our
present investigation is a great deal of simplification in the geometrical understanding of the nilpotent (anti-)BRST symmetry
We introduce a family of rings of symmetric functions depending on an infinite sequence of parameters. A distinguished basis of such a
ring is comprised by analogues of the Schur functions. The corresponding structure coefficients are polynomials in the parameters which
we call the Littlewood-Richardson polynomials. We give a combinatorial rule for their calculation by modifying an earlier result of B.
Littlewood-Richardson Sagan and the author. The new rule provides a formula for these polynomials which is manifestly positive in the sense of W. Graham. We
0704.0065 polynomials apply this formula for the calculation of the product of equivariant Schubert classes on Grassmannians which implies a stability property math.AG math.CO
of the structure coefficients. The first manifestly positive formula for such an expansion was given by A. Knutson and T. Tao by using
combinatorics of puzzles while the stability property was not apparent from that formula. We also use the Littlewood-Richardson
polynomials to describe the multiplication rule in the algebra of the Casimir elements for the general linear Lie algebra in the basis of
the quantum immanants constructed by A. Okounkov and G. Olshanski.
Possible (algebraic) commutation relations in the Lagrangian quantum theory of free (scalar, spinor and vector) fields are considered
from mathematical view-point. As sources of these relations are employed the Heisenberg equations/relations for the dynamical variables
and a specific condition for uniqueness of the operators of the dynamical variables (with respect to some class of Lagrangians). The
Lagrangian quantum field theory paracommutation relations or some their generalizations are pointed as the most general ones that entail the validity of all Heisenberg
in momentum picture. IV. equations. The simultaneous fulfillment of the Heisenberg equations and the uniqueness requirement turn to be impossible. This problem is
0704.0066 Commutation relations for free solved via a redefinition of the dynamical variables, similar to the normal ordering procedure and containing it as a special case. That hep-th
fields implies corresponding changes in the admissible commutation relations. The introduction of the concept of the vacuum makes narrow the
class of the possible commutation relations; in particular, the mentioned redefinition of the dynamical variables is reduced to normal
ordering. As a last restriction on that class is imposed the requirement for existing of an effective procedure for calculating vacuum
mean values. The standard bilinear commutation relations are pointed as the only known ones that satisfy all of the mentioned conditions
and do not contradict to the existing data.
Epitaxial self-assembled quantum dots (SAQDs) are of interest for nanostructured optoelectronic and electronic devices such as lasers,
photodetectors and nanoscale logic. Spatial order and size order of SAQDs are important to the development of usable devices. It is
likely that these two types of order are strongly linked; thus, a study of spatial order will also have strong implications for size
Order of Epitaxial order. Here a study of spatial order is undertaken using a linear analysis of a commonly used model of SAQD formation based on surface
0704.0067 Self-Assembled Quantum Dots: diffusion. Analytic formulas for film-height correlation functions are found that characterize quantum dot spatial order and cond-mat.mtrl-sci
Linear Analysis corresponding correlation lengths that quantify order. Initial atomic-scale random fluctuations result in relatively small correlation
lengths (about two dots) when the effect of a wetting potential is negligible; however, the correlation lengths diverge when SAQDs are
allowed to form at a near-critical film height. The present work reinforces previous findings about anisotropy and SAQD order and
presents as explicit and transparent mechanism for ordering with corresponding analytic equations. In addition, SAQD formation is by its
nature a stochastic process, and various mathematical aspects regarding statistical analysis of SAQD formation and order are presented.
A Note About the {Ki(z)} In the article [Petojevic 2006], A. Petojevi\' c verified useful properties of the $K_{i}(z)$ functions which generalize Kurepa's [Kurepa
0704.0068 Functions 1971] left factorial function. In this note, we present simplified proofs of two of these results and we answer the open question stated math.NT math.CV
in [Petojevic 2006]. Finally, we discuss the differential transcendency of the $K_{i}(z)$ functions.
The goal of this paper is to construct invariant dynamical objects for a (not necessarily invertible) smooth self map of a compact
manifold. We prove a result that takes advantage of differences in rates of expansion in the terms of a sheaf cohomological long exact
sequence to create unique lifts of finite dimensional invariant subspaces of one term of the sequence to invariant subspaces of the
preceding term. This allows us to take invariant cohomological classes and under the right circumstances construct unique currents of a
given type, including unique measures of a given type, that represent those classes and are invariant under pullback. A dynamically
0704.0069 Dynamical Objects for interesting self map may have a plethora of invariant measures, so the uniquess of the constructed currents is important. It means that math.DS
Cohomologically Expanding Maps if local growth is not too big compared to the growth rate of the cohomological class then the expanding cohomological class gives
sufficient "marching orders" to the system to prohibit the formation of any other such invariant current of the same type (say from some
local dynamical subsystem). Because we use subsheaves of the sheaf of currents we give conditions under which a subsheaf will have the
same cohomology as the sheaf containing it. Using a smoothing argument this allows us to show that the sheaf cohomology of the currents
under consideration can be canonically identified with the deRham cohomology groups. Our main theorem can be applied in both the smooth
and holomorphic setting.
Coincidence of the oscillations The fractional Aharonov-Bohm oscillation (FABO) of narrow quantum rings with two electrons has been studied and has been explained in an
0704.0070 in the dipole transition and in analytical way, the evolution of the period and amplitudes against the magnetic field can be exactly described. Furthermore, the dipole cond-mat.mes-hall
the persistent current of narrow transition of the ground state was found to have essentially two frequencies, their difference appears as an oscillation matching the
quantum rings with two electrons oscillation of the persistent current exactly. A number of equalities relating the observables and dynamical parameters have been found.
Pairwise comparisons of
0704.0071 typological profiles (of No abstract given; compares pairs of languages from World Atlas of Language Structures. physics.soc-ph
In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is
The decomposition method and based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that decomposition process can be
Maple procedure for finding done by iterative procedure(s), each step of which is reduced to solution of some auxiliary PDEs system(s) for one dependent variable.
0704.0072 first integrals of nonlinear Moreover, we find on this way the explicit expression of the first-order PDE(s) for first integral of decomposable initial PDE. math-ph math.MP
PDEs of any order with any Remarkably that this first-order PDE is linear if initial PDE is linear in its highest derivatives. The developed method is implemented
number of independent variables in Maple procedure, which can really solve many of different order PDEs with different number of independent variables. Examples of PDEs
with calculated their general solutions demonstrate a potential of the method for automatic solving of nonlinear PDEs.
We treat Koll\'ar's injectivity theorem from the analytic (or differential geometric) viewpoint. More precisely, we give a curvature
0704.0073 A transcendental approach to condition which implies Koll\'ar type cohomology injectivity theorems. Our main theorem is formulated for a compact K\"ahler manifold, math.AG
Koll\'ar's injectivity theorem but the proof uses the space of harmonic forms on a Zariski open set with a suitable complete K\"ahler metric. We need neither covering
tricks, desingularizations, nor Leray's spectral sequence.
This paper is an exposition of the so-called injective Morita contexts (in which the connecting bimodule morphisms are injective) and
Morita $\alpha$contexts (in which the connecting bimodules enjoy some local projectivity in the sense of Zimmermann-Huisgen). Motivated
Injective Morita contexts by situations in which only one trace ideal is in action, or the compatibility between the bimodule morphisms is not needed, we introduce
0704.0074 (revisited) the notions of Morita semi-contexts and Morita data, and investigate them. Injective Morita data will be used (with the help of static math.RA
and adstatic modules) to establish equivalences between some intersecting subcategories related to subcategories of modules that are
localized or colocalized by trace ideals of a Morita datum. We end up with applications of Morita $\alpha$-contexts to $\ast$-modules and
injective right wide Morita contexts.
There has been important experimental progress in the sector of heavy baryons in the past several years. We study the strong decays of
0704.0075 Strong decays of charmed baryons the S-wave, P-wave, D-wave and radially excited charmed baryons using the $^3P_0$ model. After comparing the calculated decay pattern and hep-ph hep-ex
total width with the available data, we discuss the possible internal structure and quantum numbers of those charmed baryons observed nucl-ex
0704.0076 CP violation in beauty decays Precision tests of the Kobayashi-Maskawa model of CP violation are discussed, pointing out possible signatures for other sources of CP hep-ph hep-ex
violation and for new flavor-changing operators. The current status of the most accurate tests is summarized.
The Dark Energy problem is forcing us to re-examine our models and our understanding of relativity and space-time. Here a novel idea of
0704.0077 Universal Forces and the Dark Fundamental Forces is introduced. This allows us to perceive the General Theory of Relativity and Einstein's Equation from a new physics.gen-ph
Energy Problem pesrpective. In addition to providing us with an improved understanding of space and time, it will be shown how it leads to a resolution
of the Dark Energy problem.
Linear perturbations of matched We present a critical review about the study of linear perturbations of matched spacetimes including gauge problems. We analyse the
0704.0078 spacetimes: the gauge problem freedom introduced in the perturbed matching by the presence of background symmetries and revisit the particular case of spherically gr-qc
and background symmetries symmetry in n-dimensions. This analysis includes settings with boundary layers such as brane world models and shell cosmologies.
Operator algebras associated We define nonselfadjoint operator algebras with generators $L_{e_1},..., L_{e_n}, L_{f_1},...,L_{f_m}$ subject to the unitary commutation
0704.0079 with unitary commutation relations of the form \[ L_{e_i}L_{f_j} = \sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}\] where $u= (u_{i,j,k,l})$ is an $nm \times nm$ unitary math.OA
relations matrix. These algebras, which generalise the analytic Toeplitz algebras of rank 2 graphs with a single vertex, are classified up to
isometric isomorphism in terms of the matrix $u$.
We show that the globular cluster mass function (GCMF) in the Milky Way depends on cluster half-mass density (rho_h) in the sense that
the turnover mass M_TO increases with rho_h while the width of the GCMF decreases. We argue that this is the expected signature of the
slow erosion of a mass function that initially rose towards low masses, predominantly through cluster evaporation driven by internal
two-body relaxation. We find excellent agreement between the observed GCMF -- including its dependence on internal density rho_h, central
concentration c, and Galactocentric distance r_gc -- and a simple model in which the relaxation-driven mass-loss rates of clusters are
Shaping the Globular Cluster approximated by -dM/dt = mu_ev ~ rho_h^{1/2}. In particular, we recover the well-known insensitivity of M_TO to r_gc. This feature does
0704.0080 Mass Function by not derive from a literal ``universality'' of the GCMF turnover mass, but rather from a significant variation of M_TO with rho_h -- the astro-ph
Stellar-Dynamical Evaporation expected outcome of relaxation-driven cluster disruption -- plus significant scatter in rho_h as a function of r_gc. Our conclusions are
the same if the evaporation rates are assumed to depend instead on the mean volume or surface densities of clusters inside their tidal
radii, as mu_ev ~ rho_t^{1/2} or mu_ev ~ Sigma_t^{3/4} -- alternative prescriptions that are physically motivated but involve cluster
properties (rho_t and Sigma_t) that are not as well defined or as readily observable as rho_h. In all cases, the normalization of mu_ev
required to fit the GCMF implies cluster lifetimes that are within the range of standard values (although falling towards the low end of
this range). Our analysis does not depend on any assumptions or information about velocity anisotropy in the globular cluster system.
Quantum Deformations of We discussed quantum deformations of D=4 Lorentz and Poincare algebras. In the case of Poincare algebra it is shown that almost all math.QA hep-th
0704.0081 Relativistic Symmetries classical r-matrices of S. Zakrzewski classification correspond to twisted deformations of Abelian and Jordanian types. A part of twists math-ph math.MP
corresponding to the r-matrices of Zakrzewski classification are given in explicit form. math.RT
We investigate dynamical properties of bright solitons with a finite background in the F=1 spinor Bose-Einstein condensate (BEC), based
on an integrable spinor model which is equivalent to the matrix nonlinear Schr\"{o}dinger equation with a self-focusing nonlineality. We
apply the inverse scattering method formulated for nonvanishing boundary conditions. The resulting soliton solutions can be regarded as a
Matter-Wave Bright Solitons with generalization of those under vanishing boundary conditions. One-soliton solutions are derived in an explicit manner. According to the cond-mat.other
0704.0082 a Finite Background in Spinor behaviors at the infinity, they are classified into two kinds, domain-wall (DW) type and phase-shift (PS) type. The DW-type implies the cond-mat.stat-mech
Bose-Einstein Condensates ferromagnetic state with nonzero total spin and the PS-type implies the polar state, where the total spin amounts to zero. We also
discuss two-soliton collisions. In particular, the spin-mixing phenomenon is confirmed in a collision involving the DW-type. The results
are consistent with those of the previous studies for bright solitons under vanishing boundary conditions and dark solitons. As a result,
we establish the robustness and the usefulness of the multiple matter-wave solitons in the spinor BECs.
The path integral over Euclidean geometries for the recently suggested density matrix of the Universe is shown to describe a
microcanonical ensemble in quantum cosmology. This ensemble corresponds to a uniform (weight one) distribution in phase space of true
physical variables, but in terms of the observable spacetime geometry it is peaked about complex saddle-points of the {\em Lorentzian}
Why there is something rather path integral. They are represented by the recently obtained cosmological instantons limited to a bounded range of the cosmological
0704.0083 than nothing (out of constant. Inflationary cosmologies generated by these instantons at late stages of expansion undergo acceleration whose low-energy scale hep-th
everything)? can be attained within the concept of dynamically evolving extra dimensions. Thus, together with the bounded range of the early
cosmological constant, this cosmological ensemble suggests the mechanism of constraining the landscape of string vacua and,
simultaneously, a possible solution to the dark energy problem in the form of the quasi-equilibrium decay of the microcanonical state of
the Universe.
We employ granular hydrodynamics to investigate a paradigmatic problem of clustering of particles in a freely cooling dilute granular
gas. We consider large-scale hydrodynamic motions where the viscosity and heat conduction can be neglected, and one arrives at the
equations of ideal gas dynamics with an additional term describing bulk energy losses due to inelastic collisions. We employ Lagrangian
coordinates and derive a broad family of exact non-stationary analytical solutions that depend only on one spatial coordinate. These
Formation of density solutions exhibit a new type of singularity, where the gas density blows up in a finite time when starting from smooth initial
singularities in ideal conditions. The density blowups signal formation of close-packed clusters of particles. As the density blow-up time $t_c$ is approached, cond-mat.soft
0704.0084 hydrodynamics of freely cooling the maximum density exhibits a power law $\sim (t_c-t)^{-2}$. The velocity gradient blows up as $\sim - (t_c-t)^{-1}$ while the velocity nlin.PS
inelastic gases: a family of itself remains continuous and develops a cusp (rather than a shock discontinuity) at the singularity. The gas temperature vanishes at the physics.flu-dyn
exact solutions singularity, and the singularity follows the isobaric scenario: the gas pressure remains finite and approximately uniform in space and
constant in time close to the singularity. An additional exact solution shows that the density blowup, of the same type, may coexist with
an "ordinary" shock, at which the hydrodynamic fields are discontinuous but finite. We confirm stability of the exact solutions with
respect to small one-dimensional perturbations by solving the ideal hydrodynamic equations numerically. Furthermore, numerical solutions
show that the local features of the density blowup hold universally, independently of details of the initial and boundary conditions.
We discuss a universality property of any covariant field theory in space-time expanded around pp-wave backgrounds. According to this
property the space-time lagrangian density evaluated on a restricted set of field configurations, called universal sector, turns out to
be same around all the pp-waves, even off-shell, with same transverse space and same profiles for the background scalars. In this paper
we restrict our discussion to tensorial fields only. In the context of bosonic string theory we consider on-shell pp-waves and argue that
universality requires the existence of a universal sector of world-sheet operators whose correlation functions are insensitive to the
0704.0085 A Universality in PP-Waves pp-wave nature of the metric and the background gauge flux. Such results can also be reproduced using the world-sheet conformal field hep-th
theory. We also study such pp-waves in non-polynomial closed string field theory (CSFT). In particular, we argue that for an off-shell
pp-wave ansatz with flat transverse space and dilaton independent of transverse coordinates the field redefinition relating the low
energy effective field theory and CSFT with all the massive modes integrated out is at most quadratic in fields. Because of this
simplification it is expected that the off-shell pp-waves can be identified on the two sides. Furthermore, given the massless pp-wave
field configurations, an iterative method for computing the higher massive modes using the CSFT equations of motion has been discussed.
All our bosonic string theory analyses can be generalised to the common Neveu-Schwarz sector of superstrings.
We give a quantitative analysis of clustering in a stochastic model of one-dimensional gas. At time zero, the gas consists of $n$
identical particles that are randomly distributed on the real line and have zero initial speeds. Particles begin to move under the forces
Clustering in a stochastic model of mutual attraction. When particles collide, they stick together forming a new particle, called cluster, whose mass and speed are
0704.0086 of one-dimensional gas defined by the laws of conservation. We are interested in the asymptotic behavior of $K_n(t)$ as $n\to \infty$, where $K_n(t)$ denotes math.PR
the number of clusters at time $t$ in the system with $n$ initial particles. Our main result is a functional limit theorem for $K_n(t)$.
Its proof is based on the discovered localization property of the aggregation process, which states that the behavior of each particle is
essentially defined by the motion of neighbor particles.
Approximate solutions to the Our main result in this paper is the following: Given $H^m, H^n$ hyperbolic spaces of dimensional $m$ and $n$ corresponding, and given a
0704.0087 Dirichlet problem for harmonic Holder function $f=(s^1,...,f^{n-1}):\partial H^m\to \partial H^n$ between geometric boundaries of $H^m$ and $H^n$. Then for each $\ math.DG
maps between hyperbolic spaces epsilon >0$ there exists a harmonic map $u:H^m\to H^n$ which is continuous up to the boundary (in the sense of Euclidean) and $u|_{\
partial H^m}=(f^1,...,f^{n-1},\epsilon)$.
The results of the spectral, energetical and temporal characteristics of radiation in the presence of the photonic flame effect are
presented. Artificial opal posed on Cu plate at the temperature of liquid nitrogen boiling point (77 K) being irradiated by nanosecond
ruby laser pulse produces long- term luminiscence with a duration till ten seconds with a finely structured spectrum in the the
0704.0088 Some new experimental photonic antistocks part of the spectrum. Analogous visible luminescence manifesting time delay appeared in other samples of the artificial opals physics.optics
flame effect features posed on the same plate. In the case of the opal infiltrated with different nonlinear liquids the threshold of the luminiscence is
reduced and the spatial disribution of the bright emmiting area on the opal surface is being changed. In the case of the putting the
frozen nonlinear liquids on the Cu plate long-term blue bright luminiscence took place in the frozen species of the liquids. Temporal
characteristics of this luminiscence are nearly the same as in opal matrixes.
Statistical modeling of experimental physical laws is based on the probability density function of measured variables. It is expressed by
experimental data via a kernel estimator. The kernel is determined objectively by the scattering of data during calibration of
A general approach to experimental setup. A physical law, which relates measured variables, is optimally extracted from experimental data by the conditional
0704.0089 statistical modeling of physical average estimator. It is derived directly from the kernel estimator and corresponds to a general nonparametric regression. The proposed physics.data-an
laws: nonparametric regression method is demonstrated by the modeling of a return map of noisy chaotic data. In this example, the nonparametric regression is used to physics.gen-ph
predict a future value of chaotic time series from the present one. The mean predictor error is used in the definition of predictor
quality, while the redundancy is expressed by the mean square distance between data points. Both statistics are used in a new definition
of predictor cost function. From the minimum of the predictor cost function, a proper number of data in the model is estimated.
Real Options for Project Schedules (ROPS) has three recursive sampling/optimization shells. An outer Adaptive Simulated Annealing (ASA) cs.CE
Real Options for Project optimization shell optimizes parameters of strategic Plans containing multiple Projects containing ordered Tasks. A middle shell samples cond-mat.stat-mech
0704.0090 Schedules (ROPS) probability distributions of durations of Tasks. An inner shell samples probability distributions of costs of Tasks. PATHTREE is used to cs.MS cs.NA
develop options on schedules.. Algorithms used for Trading in Risk Dimensions (TRD) are applied to develop a relative risk analysis among physics.data-an
We combine classical methods of combinatorial group theory with the theory of small cancellations over relatively hyperbolic groups to
Groups with finitely many construct finitely generated torsion-free groups that have only finitely many classes of conjugate elements. Moreover, we present several
0704.0091 conjugacy classes and their results concerning embeddings into such groups. As another application of these techniques, we prove that every countable group $C$ can math.GR
automorphisms be realized as a group of outer automorphisms of a group $N$, where $N$ is a finitely generated group having Kazhdan's property (T) and
containing exactly two conjugacy classes.
Energy density for chiral We study a recently proposed formulation of overlap fermions at finite density. In particular we compute the energy density as a function
0704.0092 lattice fermions with chemical of the chemical potential and the temperature. It is shown that overlap fermions with chemical potential reproduce the correct continuum hep-lat hep-ph
potential behavior.
Lattice contribution to the electronic self-energy in complex correlated oxides is a fascinating subject that has lately stimulated
Aspects of Electron-Phonon lively discussions. Expectations of electron-phonon self-energy effects for simpler materials, such as Pd and Al, have resulted in
0704.0093 Self-Energy Revealed from several misconceptions in strongly correlated oxides. Here we analyze a number of arguments claiming that phonons cannot be the origin of cond-mat.supr-con
Angle-Resolved Photoemission certain self-energy effects seen in high-$T_c$ cuprate superconductors via angle resolved photoemission experiments (ARPES), including cond-mat.str-el
Spectroscopy the temperature dependence, doping dependence of the renormalization effects, the inter-band scattering in the bilayer systems, and
impurity substitution. We show that in light of experimental evidences and detailed simulations, these arguments are not well founded.
We present semi-analytical constraint on the amount of dark matter in the merging bullet galaxy cluster using the classical Local Group
timing arguments. We consider particle orbits in potential models which fit the lensing data. {\it Marginally consistent} CDM models in
Newtonian gravity are found with a total mass M_{CDM} = 1 x 10^{15}Msun of Cold DM: the bullet subhalo can move with V_{DM}=3000km/s, and
Timing and Lensing of the the "bullet" X-ray gas can move with V_{gas}=4200km/s. These are nearly the {\it maximum speeds} that are accelerable by the gravity of
0704.0094 Colliding Bullet Clusters: two truncated CDM halos in a Hubble time even without the ram pressure. Consistency breaks down if one adopts higher end of the error astro-ph
barely enough time and gravity bars for the bullet gas speed (5000-5400km/s), and the bullet gas would not be bound by the sub-cluster halo for the Hubble time. Models
to accelerate the bullet with V_{DM}~ 4500km/s ~ V_{gas} would invoke unrealistic large amount M_{CDM}=7x 10^{15}Msun of CDM for a cluster containing only ~ 10^
{14}Msun of gas. Our results are generalisable beyond General Relativity, e.g., a speed of $4500\kms$ is easily obtained in the
relativistic MONDian lensing model of Angus et al. (2007). However, MONDian model with little hot dark matter $M_{HDM} \le 0.6\times 10^
{15}\msun$ and CDM model with a small halo mass $\le 1\times 10^{15}\msun$ are barely consistent with lensing and velocity data.
We get asymptotics for the volume of large balls in an arbitrary locally compact group G with polynomial growth. This is done via a study
Geometry of Locally Compact of the geometry of G and a generalization of P. Pansu's thesis. In particular, we show that any such G is weakly commensurable to some
0704.0095 Groups of Polynomial Growth and simply connected solvable Lie group S, the Lie shadow of G. We also show that large balls in G have an asymptotic shape, i.e. after a math.GR math.DG
Shape of Large Balls suitable renormalization, they converge to a limiting compact set which can be interpreted geometrically. We then discuss the speed of
convergence, treat some examples and give an application to ergodic theory. We also answer a question of Burago about left invariant
metrics and recover some results of Stoll on the irrationality of growth series of nilpotent groups.
In this note we present three representations of a 248-dimensional Lie algebra, namely the algebra of Lie point symmetries admitted by a
0704.0096 Much ado about 248 system of five trivial ordinary differential equations each of order forty-four, that admitted by a system of seven trivial ordinary nlin.SI
differential equations each of order twenty-eight and that admitted by one trivial ordinary differential equation of order two hundred
and forty-four.
0704.0097 Conformal Field Theory and We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation math-ph math.MP
Operator Algebras theory in classification theory. This is based on a series of joint works with R. Longo. math.OA
Sparse Code Division Multiple Access (CDMA), a variation on the standard CDMA method in which the spreading (signature) matrix contains
Sparsely-spread CDMA - a only a relatively small number of non-zero elements, is presented and analysed using methods of statistical physics. The analysis
0704.0098 statistical mechanics based provides results on the performance of maximum likelihood decoding for sparse spreading codes in the large system limit. We present cs.IT math.IT
analysis results for both cases of regular and irregular spreading matrices for the binary additive white Gaussian noise channel (BIAWGN) with a
comparison to the canonical (dense) random spreading code.
For positive semidefinite matrices $A$ and $B$, Ando and Zhan proved the inequalities $||| f(A)+f(B) ||| \ge ||| f(A+B) |||$ and $||| g
(A)+g(B) ||| \le ||| g(A+B) |||$, for any unitarily invariant norm, and for any non-negative operator monotone $f$ on $[0,\infty)$ with
inverse function $g$. These inequalities have very recently been generalised to non-negative concave functions $f$ and non-negative
convex functions $g$, by Bourin and Uchiyama, and Kosem, respectively. In this paper we consider the related question whether the
0704.0099 On Ando's inequalities for inequalities $||| f(A)-f(B) ||| \le ||| f(|A-B|) |||$, and $||| g(A)-g(B) ||| \ge ||| g(|A-B|) |||$, obtained by Ando, for operator math.FA
convex and concave functions monotone $f$ with inverse $g$, also have a similar generalisation to non-negative concave $f$ and convex $g$. We answer exactly this
question, in the negative for general matrices, and affirmatively in the special case when $A\ge ||B||$. In the course of this work, we
introduce the novel notion of $Y$-dominated majorisation between the spectra of two Hermitian matrices, where $Y$ is itself a Hermitian
matrix, and prove a certain property of this relation that allows to strengthen the results of Bourin-Uchiyama and Kosem, mentioned
The topological structure of the event horizon has been investigated in terms of the Morse theory. The elementary process of topological
evolution can be understood as a handle attachment. It has been found that there are certain constraints on the nature of black hole
0704.0100 Topology Change of Black Holes topological evolution: (i) There are n kinds of handle attachments in (n+1)-dimensional black hole space-times. (ii) Handles are further gr-qc
classified as either of black or white type, and only black handles appear in real black hole space-times. (iii) The spatial section of
an exterior of the black hole region is always connected. As a corollary, it is shown that the formation of a black hole with an S**(n-2)
x S**1 horizon from that with an S**(n-1) horizon must be non-axisymmetric in asymptotically flat space-times.
README.md exists but content is empty. Use the Edit dataset card button to edit it.
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Models trained or fine-tuned on mteb/raw_arxiv | {"url":"https://huggingface.co/datasets/mteb/raw_arxiv","timestamp":"2024-11-09T20:48:50Z","content_type":"text/html","content_length":"417400","record_id":"<urn:uuid:2f688231-3d62-4c3d-b3c6-e5491dc9ff1e>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00555.warc.gz"} |
Determine 10 or 100 less with and without a place value chart
Curriculum>Grade 2> Module 3>Topic F: Finding 1, 10, and 100 More or Less Than a Number
Students determine a 2- or 3-digit number based on a disk model. They subtract a ten or hundred disk from the chart and determine the new total. They then solve similar problems without the disk | {"url":"https://happynumbers.com/demo/cards/444740/","timestamp":"2024-11-08T10:50:11Z","content_type":"text/html","content_length":"15228","record_id":"<urn:uuid:288d25e5-e09c-4565-a971-f9dd299a3904>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00582.warc.gz"} |
What is a line parallel to y 4x 3?
When you see the word “parallel”, you know the new line will have the same slope. parallel to y=4x-3. So, the new line will have a slope of 4.
How do you know which lines are parallel?
We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes
are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.
What is the slope of any line parallel to Y 3 4x?
Combine 34 3 4 and x x . Rewrite in slope-intercept form. Using the slope-intercept form, the slope is 34 . All lines that are parallel to y=3×4 y = 3 x 4 have the same slope of 34 .
What is the slope of a line perpendicular to Y =- 4x 3?
Slope of a line perpendicular to y=4x+3 is −14 .
What is true about the slope of the function below y 4x 3?
Slope is -3.
How do you graph y 4×3?
To graph y=4x−3 you would first graph the y-intercept, -3, and then using the slope, 4, to complete the rest of the graph. Start at point (0,-3) then go up 4 right one which would leave you at point
(1,1), the second point and you would continue going up 4 right one to plot each point.
What slope is parallel to 4?
Algebra Examples Since x=4 is a vertical line, the slope is undefined. All lines that are parallel to x=4 have the same slope of Undefined .
What line is perpendicular to Y 3 4x?
The slope of Perpendicular lines are reciprocal and have opposite signs. As the value written next to “x” indicates the value of Slope in this equatiuon the slope of the line is given as “3/4”. Thus
the line perpendicular to this line will have a slope of “-4/3”.
What is the slope of a line that is parallel to Y 5x 3?
The equation given is y=5x+3 and since the 5 is in the place of m from the general equation, 5 is the slope. Since parallel lines have the same slope, 5 is the answer. The slope is 5.
What is the perpendicular line of Y =- 4x 3?
y = 4x – 3. Hence, slope is 4. So slope of line perpendicular to this line will be -1/4.
What is the slope of the line y =- 4x 3?
The slope is −4 . The equation is in slope-intercept form, y=mx+c , where m is the slope. | {"url":"https://yoursagetip.com/lifehacks/what-is-a-line-parallel-to-y-4x-3/","timestamp":"2024-11-08T18:33:30Z","content_type":"text/html","content_length":"53030","record_id":"<urn:uuid:121ee438-aedf-4ca8-8601-da89915a994f>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00675.warc.gz"} |
The syntax for defining the denominator array den is incorrect. In MATLAB, array elements should be separated by commas or spaces within square brackets. The current syntax will result in an error.
Solution: Correct the syntax by adding a comma or space between the elements:
Y_cos = ifft(H_s * fft(cos_input)); Y_exp = ifft(H_s * fft(exp_input.*heaviside(t))); Y_u = ifft(H_s * fft(u));
The use of ifft and fft for computing the output response of the system is not appropriate. The ifft and fft functions are used for Fourier transforms, not for simulating the response of a transfer
function to an input signal. Instead, you should use the lsim function to simulate the time response of the system.
Y_cos = lsim(H_s, cos_input, t); Y_exp = lsim(H_s, exp_input.*heaviside(t), t); Y_u = lsim(H_s, u, t);
The syntax for defining the den array is incorrect. In MATLAB, array elements should be separated by commas or spaces within square brackets. The current syntax will result in an error.
The use of conv for convolution with dimpulse is incorrect. The conv function performs a convolution of two discrete sequences, but dimpulse returns the impulse response of a discrete-time system.
Instead, you should use the lsim function to simulate the time response of the system to the input U1.
The use of tf and laplace functions in this context is incorrect. The tf function is used to create transfer functions in the control system toolbox, and laplace is used for Laplace transforms, not
Fourier transforms. This will lead to incorrect results.
Recommended Solution: Use the freqs function to compute the frequency response of the analog filter described by the transfer function.
Y1 = ifourier(H_jw * fourier(U1, t), w, t); Y2 = ifourier(H_jw * fourier(U2, t), w, t); Y3 = ifourier(H_jw * fourier(U3, t), w, t);
The ifourier and fourier functions are not standard MATLAB functions. This will result in errors unless these functions are defined elsewhere in the code, which is not shown in the provided fragment.
Recommended Solution: Use the ifft and fft functions for inverse Fourier and Fourier transforms, respectively.
Y1 = ifft(H_jw .* fft(U1)); Y2 = ifft(H_jw .* fft(U2)); Y3 = ifft(H_jw .* fft(U3));
The length of the result from the conv function will be greater than the length of t, which will cause a dimension mismatch error when plotting. The conv function returns a vector of length length
(U1) + length(impulse(tf(num, den))) - 1.
Solution: Use the filter function instead of conv to ensure the output Y1 has the same length as t:
Using input to get the transfer function from the user can be risky as it allows for arbitrary code execution. This can be a significant security vulnerability.
Recommendation: Use a safer method to parse the input, such as inputdlg for a GUI input or str2num to convert a string input to numerical values.
prompt = 'Enter the numerator coefficients (e.g., [1 0]): '; numerator = str2num(input(prompt, 's')); prompt = 'Enter the denominator coefficients (e.g., [1 1]): '; denominator = str2num(input
(prompt, 's')); tf_input = {numerator, denominator};
Y_cos = ifourier(H_jw * fourier(cos_input, t), w, t); Y_exp = ifourier(H_jw * fourier(exp_input.*heaviside(t), t), w, t); Y_u = ifourier(H_jw * fourier(u, t), w, t);
The functions fourier and ifourier are not standard MATLAB functions. This will result in errors unless they are defined elsewhere in the code or provided by a specific toolbox.
Recommendation: Ensure that these functions are defined or replace them with the appropriate MATLAB functions. For Fourier transforms, you might use fft and ifft for numerical computation or fourier
and ifourier from the Symbolic Math Toolbox if symbolic computation is intended.
% Example using Symbolic Math Toolbox syms t w Y_cos = ifourier(H_jw * fourier(cos(t), t), w, t); Y_exp = ifourier(H_jw * fourier(exp(-t) * heaviside(t), t), w, t); Y_u = ifourier(H_jw * fourier(1,
t), w, t);
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website's cookie use as described in our Cookie Policy. | {"url":"https://codereviewbot.ai/tags/en-US/function-usage","timestamp":"2024-11-02T02:48:44Z","content_type":"text/html","content_length":"24723","record_id":"<urn:uuid:f87333bb-757f-4633-b88a-de768ac729b8>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00336.warc.gz"} |
Interface C with basic ASM 64 bit arithmetic
I have written some simple arithmetic routines in 64 bit assembly that work with what C names long type; i.e., 64 bit signed integers (Linux platform).
I attach 2 files:
- asm64_long.asm
the routines in 64 bit assembly
- test_asm64_long.c
a C program to test the routines against their C counterparts
By itself, the routines are too simple to be of any use in a big project, but show the way they can be interfaced in C. Take into account that in Windows the way arguments are passed is different.
(See NASM documentation).
To compile the files without the Makefile:
$ nasm -f elf64 asm64_long.asm
$ gcc -Wall test_asm64_long.c asm64_long.o -o test_asm64_long
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Book Knot Simplifier
Description of Book Knot Simplifier
Maria Andreeva, Ivan Dynnikov, Sergey Koval, Konrad Polthier, Iskander Taimanov
Here we offer a set of tools for manipulating knots and links in the three-space by using the three-page presentation of links, which was proposed and developed by I. Dynnikov in [1][2][3].
The approach is based on a simple and very well known observation that every link in the three-space is topologically equivalent to a link that lies entirely in a three-page book, i.e. the union of
three half-planes with common boundary. Though being not convenient for human perception, this way of presenting links seems to be very efficient for handling knots by computer. It provides a very
quick way from a combinatorial description of a link to its three-dimensional presentation. A three-page link admits a lot of transformations that preserve its isotopy class and can be easily found.
This fact is used in the knot simplifying tool included herein.
This software for knot manipulation and simplification builds on the JavaView library [5].
Currently available ...
View a knot available on the server
Input your own knot as a 3D curve or a Gauss code
Tools being developed ...
More editing tools
Converting to/from other formats
Comparing and recognizing knots
View a knot
To download a knot from the server click "Choose knot" button. At the present time, we have a collection of knots presented in
format, as
3D curve
(.txt files), and as a
Gauss code
(.gc files).
Files 31.jkb, 141.jkb, 322.jkb, and 539 have been generated automatically from hand-made (ID) planar diagrams of unknots having 31, 141, 322, and 539 crossings respectively. These unknots were used
to test the simplifier. The unknot with 31 crossings is shown below.
The unknot with 539 crossings is a satellite of this unknot (see [1] for a picture).
The source of the knots in TXT format is the Knot-Plot web site created by Robert Scharein [4] which contains a collection of knots and links with small crossing number (less than or equal to 10).
The files with .gc extension contain Gauss codes of the same links. These codes were generated automatically (SK) from the .txt files.
For converting a planar diagram to a three-page diagram the algorithm described in [1] is used.
Input a knot
To input your own knot click "Input knot" button and choose a method of input. Now available methods are by using
3D curve
or the
Gauss code
. If you are already using some other knot presentation with another software, you are welcome to let us know the specification of the format you are using by sending e-mail at
dynnikov@mech.math.msu.su. Then, we may make it possible to input a knot in your favorite format.
Simplify a knot
If you press the "Simplify" button, the knot simplifier starts. It implements an algorithm described in [1]. We shall explain very shortly the idea of the algorithm.
In the case of the three-page presentation of knots, a natural measure of complexity is the number of intersection points of the knot with the binding line of the three-page book. The simplifier
performs operations on the knot that preserve the isotopy class of the knot and tries to make the complexity as less as possible. Let us consider how this works. Look at the following three-page
knot, which is the trefoil knot in fact.
Its complexity equals 9. What if we replace the part of the knot marked in red with the curve marked in blue in the figure below?
We obtain a topologically equivalent knot of the same complexity, but now we obviously can simplify it by contracting the arc connecting the two rightmost points:
After doing that, we obtain a three-page knot of complexity 8.
The knot simplifier just tries to simplify a given knot by transformations of this kind. If sufficiently many subsequent trials are not successful, i.e. the knot is not simplified for a long time,
the simplifier stops. More details about the transformations used in the simplifier see [1].
At the present state, the simplifier does not search among all three-page diagrams that can be obtain from the current one by available transforms and does not make a "canonical" choice. So, if you
click the "Simplify" button again, the picture may change.
Edit a knot
The only available editing tool for now is cyclic permutation of vertices on the binding line, which is achieved by pressing the "Vertex permutation" button. Other editing tools coming soon.
Input a knot as a 3D curve
To input a knot presented by a 3D polygon just type coordinates of all vertices in the order they follow on the knot. Coordinates must be separated by blank spaces or new lines.
For example the trefoil knot is presented by a polygon with vertices (0,0,0), (3,0,1), (0,2,0), (1,0,1), (0,4,0), (4,0,1), (0,1,0), (2,0,1), (0,3,0), (0,0,1). To input it, type
and click "ok" button. The Gauss code of the knot appears. Click "ok" button again to see the three-page picture of the knot.
If your link consists of more than one connected component, separate records for different components by a blank line.
Warning: at the present state, for converting a 3D polygon to a planar diagram of a knot, projection along the z-axis is used. If the projection of your knot along the z-axis is not generic (i.e. two
vertices are projected to the same point, a vertex is projected to an internal point of an edge, or a triple crossing occurs), then the conversion may fail.
Input the Gauss code of a knot
If you have planar diagram of a knot or link you may input it by typing its Gauss code. The diagram must be connected and have at least one crossing. We use an encoding a little different from what
is usually called Gauss code, providing additional information that allows to distinguish knots from their mirror images. To input the link do the following.
For each component, choose an orientation and a starting point.
Assign different indices, which must be natural numbers, to all the crossings.
For each connected component, go along it starting from the marked point in the chosen direction, and each time you come through a crossing, write down the index of the crossing preceded by two
symbols: the first one must be + or - indicating whether you go over or under the crossing, and the second must be > or < sign indicating whether you see the arc that you intersect going from left
two the right or from right to the left, respectively. Entries for different crossings must be separated by spaces.
When you come back to the starting point of the chosen component, proceed with the next one. Separate entries for different components by keyword "component".
For example, for the diagram below
you get the following Gauss code:
->5 +<6 component +<5 ->6 ->4 +<3 -<1 +>2 ->3 +<4 -<2 +>1
This way of inputting links seems to take much time. We are now working on a better format for input.
Description of the .jkb format
Still has to be written...
Editing tools being developed
Adding/removing vertices/arcs, coloring components, taking connected sum, and more.
Converting to/from other formats
In order to make the package more convenient for those who want to use it in their own research we are going to provide converters to and from all popular formats for presenting knots. In particular,
it will be possible to input a knot as a closure of a braid or a tangle word. If you are already using some format for presenting knots, please, send the specification of the format at
] I. A. Dynnikov. Three-page link presentation and an untangling algorithm.
Proc. of the International Conference
Low-Dimensional Topology and Combinatorial Group Theory
Chelyabinsk, July, 31 - August 7, 1999; Kiev, 2000; pp. 112--130.
[2] I. A. Dynnikov. Three-page approach to knot theory. Universal semigroup. (Russian) Funktsional'nyi Analiz i Ego Prilozhenija, 34 (2000), no. 1, 29--40; translation in Functional Analysis and Its
Appl. 34 (2000), no. 1, 24--32.
[3] I. A. Dynnikov. Three-page approach to knot theory. Encoding and local moves. (Russian)
Funktsional'nyi Analiz i Ego Prilozhenija, 33 (1999), no. 4, 25--37; translation in Functional Analysis and Its Appl. 33 (1999), no. 4, 260--269. MR 2000m:57007
[4] Robert Scharein Knot-Plot Homepage at http://www.pims.math.ca/knotplot.
[5] JavaView Homepage at http://www.javaview.de. | {"url":"http://javaview.de/services/knots/doc/description.html","timestamp":"2024-11-10T02:10:39Z","content_type":"application/xhtml+xml","content_length":"15681","record_id":"<urn:uuid:7b1652c3-8ba0-4fd5-8ec6-ab5b73179331>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00761.warc.gz"} |
Q1. If A=[2−132], then show that A2−4A+7I=0 Hence find A5.
(N... | Filo
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Q1. If , then show that Hence find . (NCERT EXEMPLAR)
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Question Text Q1. If , then show that Hence find . (NCERT EXEMPLAR)
Updated On Dec 25, 2022
Topic Algebra
Subject Mathematics
Class Class 12
Answer Type Video solution: 1
Upvotes 88
Avg. Video Duration 8 min | {"url":"https://askfilo.com/user-question-answers-mathematics/q1-if-then-show-that-hence-find-ncert-exemplar-33353238383331","timestamp":"2024-11-06T21:16:52Z","content_type":"text/html","content_length":"386170","record_id":"<urn:uuid:b421a19b-df84-45b2-bb41-e5798a6de0b7>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00541.warc.gz"} |
Sora's Memories
Not open for further replies.
May 24, 2004
I just had an interesting thought. Sora fought and defeated Organization XIII in kh2. Yet he only fought 7 of the members and encountered one. Did he ever wonder what happened to the other members.
Or if he did remember what happened in Com, would that change his feelings and opinions about the organization. For example Axel.
i thought the same thing. i guess he finds out cuz jiminy(sp?) put it in his journal. (first post. woooo)
Aug 9, 2007
i thought the same thing. i guess he finds out cuz jiminy(sp?) put it in his journal. (first post. woooo)
no, everything in his journal waz erased except for thank namine
Feb 9, 2008
maybe he thought riku and mickey killed them
May 24, 2004
That is a possibility. Although Riku only killed one member ironically. He couldn't even defeat Vexen.
i was refering to kh2 when the other org members magical appeared at one time
Feb 9, 2008
i was refering to kh2 when the other org members magical appeared at one time
are u talking bout at hollow bastion?
Mar 8, 2008
I bet Sora just assumed they were eliminated because why wouldn't they have confronted him?
Interesting, but i think eastwood is right. I mean Sora also assumed that the heartless were eliminate
Jan 19, 2008
Maybe Sora didn't really care?
Dec 13, 2006
hmm good question. I guess he wasnt bothered about that. he just killed all in his way and taking out the number one would mean they would fall.
Oct 28, 2007
That is a possibility. Although Riku only killed one member ironically. He couldn't even defeat Vexen.
It's not like he couldn't, Vexen ran away like Axel and Larxene the first time they fought Sora.
About Sora's memories....... I think maybe he remembered, there is a certain scene in KH II: FM+ were he says he forgot thanking Naminé (or something like that) during the fight against Xemnas, so I
think he remembered. Maybe before that he though Riku and Mickey killed them.
Aug 29, 2007
Isn't this what coded is supposed to explain, what happened to the other organization members him, Riku, and Axel killed in CoM? Thats what I thought people said atleast.
Jan 22, 2008
You fought all the Org members that were left in KHII after the events of CoM, which I think has the rest of them being eliminated, in the words of Jiminy.
Random Question: Anyone know if Jiminy has one M or two?
Mar 17, 2007
He could have also gotten wind that the Organization had split, and assumed they'd decimated themselves from within.
Also, Jiminy has one 'M"
Oct 31, 2007
He already fogot what happen in CoM, ye?
are u talking bout at hollow bastion?
Sorry. I meant that they appeared in his journal at one point in the game.
yeah, did that happen as soon as Roxas and Sora became one again. If thats true then perhaps.....ah nevermind
We may never know.
just kidding. Did Riku lose his memories?
We may never know.
just kidding. Did Riku lose his memories?
Riku lost his memories, when he became Ansem, but then he retrieved them back.
Not open for further replies. | {"url":"https://mail.khinsider.com/forums/index.php?threads/soras-memories.102253/#post-2816051","timestamp":"2024-11-13T06:43:56Z","content_type":"text/html","content_length":"162795","record_id":"<urn:uuid:d962ba8a-32b2-4c50-8656-d3fa3f8bc1f4>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00791.warc.gz"} |
Distance Tyre Maths Problem | Best Riddles and Brain Teasers
A man always keeps a spare tyre in his car. To make full use of all the five tyres, he changes the tyres in a manner that for a distance of 1, 00,000 km, each of them runs the same distance.
Can you calculate the distance traveled by each tyre in that journey ?
We need to calculate the 4/5th of the total distance to solve the problem.
4/5 * 1, 00,000 km = 80, 000 km
Thus, each tyre traveled 80, 000 km. | {"url":"https://www.briddles.com/2015/03/distance-tyre-maths-problem.html","timestamp":"2024-11-08T14:16:40Z","content_type":"text/html","content_length":"40970","record_id":"<urn:uuid:75a3fb0d-ac7a-44d9-b3b4-9de31c0a2c87>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00616.warc.gz"} |
What is skip counting chart?
What is skip counting chart?
The skip counting charts cover the numbers from 2 up to 15. The number pages up to 12 each have a little ‘rhyme’ at the top, show how skip counting with that number works, and then skip counts up to
whatever 15x that particular number would be.
How do you calculate skip count?
To skip count, we keep adding the same number each time to the previous number. Here, we are skip counting by 2 on a number line. So, starting at 0, the next number will be 0 + 2 = 2, then, 2 + 2 =
4, then 4 + 2 = 6, then 6 + 2 = 8, and then, 10, 12, 14, 16, 18 and so on. We can skip count by any number.
How do I create a print chart?
Print a chart
1. Click the chart within your workbook.
2. Click File > Print. Tip: You can also use the keyboard shortcut, Ctrl + P, to open the Print option.
3. Click the Printer drop-down menu, and select the printer you want to use.
4. Click Print.
What is the skip count by 4 chart?
Our Skip Count by 4 Chart is exactly what you need. It’s a free counting printable using the hundreds chart to follow the by 4s sequence. Our Skip Count by 5 Chart allows your student to practice
counting in 5s. Use the shade boxes to keep focus on skip counting by 5s.
How can I use the skip counting generator in the classroom?
You can also let students use the generator to practice skip-counting concepts. Ask them for example to make a number chart of odd numbers, a chart for a specific skip-counting pattern, or a chart
where multiples of 4 are colored yellow. .
What do the charts in the hundreds chart Teach?
The first slide contains a full hundreds chart to teach counting by ones, skip counting, and place value. The second and third charts will help students learn to count by fives and 10s as well as
money skills. Print this PDF and reproduce copies as needed.
How do you skip count twos?
Direct students or teams of students to skip count twos and fours in primary colors, and overlay them on an overhead projector when they are done. Also, skip count fives and 10’s, and put on these
numbers on the overhead. Alternatively, use yellow, red, and orange for skip counting threes, sixes, and nines, and then look at the color pattern. | {"url":"https://fistofawesome.com/contributing/what-is-skip-counting-chart/","timestamp":"2024-11-12T17:02:42Z","content_type":"text/html","content_length":"43754","record_id":"<urn:uuid:8abf65c5-9974-42fb-a8f2-f4a113362249>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00636.warc.gz"} |
Online Watts to Amps - bimmodeller.com - BIM Modeling services Provider
• The watt is a unit of power or radiant flux.In the International System of Units and then it is defined as a derived unit of 1 kg·m²·s³ or, equivalently, 1 joule per second.
• Then, It is used to quantify the rate of energy transfer.
• Amp is the base unit of electrical current in the International System of Units (SI). Then, Amps is a short form of ampere.
• One ampere is equal to 6.241509074×10¹⁸ electrons worth of charge moving past a point in a second.
• It is used to convert the electric power in watts (W) to the current in amps (A).
• Amps refers to the measure of how much electrical energy is being supplies through a particular electrical line.
• Watts can be define as the overall working capacity of the electrical energy.
• I (A) = P (W) / V (V). Then, the current in amps can be compute by dividing the power in watts by the voltage in volts.
AC Single Phase Watts to Amps :
• I (A) = P (W) / (PF x V (V). Then, the phase current in amps is calculated by dividing the real power in watts by the power factor multiplied by voltage in volts.
AC Three Phase Watts to Amps ,
• I (A) = P (W) / (√3 x PF x V L-L (V)). Then, it means that the phase current in amps is computed by dividing the real power in watts by the multiplication of square root of three, time the power
• Then the result is multiplied by the line to line voltage RMS in volts.
Line to Neutral Voltage :
• I (A) = P (W) / (3 x PF x V L-N (V)). Then, it means that the phase current in amps is computed by dividing the real power in watts by the multiplication of three by the power factor multiplied
by the line to neutral voltage in volts.
• You can easily use this online watts to amps calculator for converting watts to amps.
• First, Select the current type. Then, Second : Enter the watts. Then, Third : Enter the volts.
• Click “Calculate” to get the result and then if you want to clear values Click “Reset” in addition to clear the values.
• Besides, the formula this calculator works.
• Finally, follow these steps to get the results.
• Then you will get as a result in Amps. | {"url":"https://www.bimmodeller.com/watts-to-amps/","timestamp":"2024-11-13T04:53:05Z","content_type":"text/html","content_length":"218587","record_id":"<urn:uuid:51d8a013-0b32-4e1a-b3b4-fc19b519a79c>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00751.warc.gz"} |
How do you simplify (5^(2/3))^(4/5)?
| HIX Tutor
How do you simplify #(5^(2/3))^(4/5)#?
Answer 1
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Answer 2
To simplify (5^(2/3))^(4/5), you apply the rule of exponents, which states that when you raise a power to another power, you multiply the exponents. So, (5^(2/3))^(4/5) simplifies to 5^(2/3 * 4/5).
When you multiply the exponents, you get 5^(8/15). Therefore, (5^(2/3))^(4/5) simplifies to 5^(8/15).
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Answer from HIX Tutor
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some
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Intro to Word Problems
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This content provides a comprehensive guide to tackling word problems on the GRE, emphasizing algebraic techniques and alternative problem-solving strategies.
• Word problems are a significant category in the GRE, requiring the translation of words into algebraic expressions and equations.
• Key types of word problems include age, motion, work, growth and decay, and mixture questions.
• The process involves assigning variables, writing equations, and then solving these equations using algebraic methods or alternative strategies like backsolving or picking numbers.
• The module covers general strategies for solving word problems, detailed approaches for specific types of problems, and introduces alternative strategies for finding solutions.
Introduction to Word Problems
Assigning Variables and Writing Equations
General Strategies for Solving Word Problems
Alternative Problem-Solving Strategies | {"url":"https://gre.magoosh.com/lessons/70-intro-to-word-problems?study_item=1048?utm_source=greblog&utm_medium=blog&utm_campaign=90daybeginners&utm_term=inline","timestamp":"2024-11-10T12:54:54Z","content_type":"text/html","content_length":"80075","record_id":"<urn:uuid:b1282add-7eb1-4df7-a3ec-f35fb9c929eb>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00164.warc.gz"} |
Algorithm to Add [Sum] two numbers - DSA
In this tutorial, we are going to write an algorithm to Add or Sum of two numbers. using this algorithm we can write a program to Add [Sum] two numbers in most programming languages like C, C++,
Java, and Python.
Algorithm to Add [Sum] of two numbers.
1. Read A and B.
2. Set SUM := A + B.
3. Write SUM.
4. Exit.
Here in the above algorithm we first read two integer inputs A and B. Then we set the value of the A and B variables into the SUM variable. and then write the SUM variable value on the output screen
and exit from the program.
Also, Read | {"url":"https://datastructuresandalgorithm.com/algorithm-to-add-sum-two-numbers.html","timestamp":"2024-11-10T09:13:32Z","content_type":"text/html","content_length":"65115","record_id":"<urn:uuid:e2eea403-ea26-4dc4-88f3-b23a069dd9e0>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00484.warc.gz"} |
Earnings Before Interest, Taxes, Depreciation, and Amortization is what is fully referred to as EBITDA. It is an alternative way of calculating net income profitability. It eliminates the capital
structure-dependent non-cash depreciation, amortization expense, taxes, and debt costs.
The cash profit generated by the company's operations is attempted to be displayed in the earnings before interest, taxes, depreciation, and amortization. Here is everything about EBITDA in detail.
What is EBITDA
A substitute metric for net income as a measure of profitability is EBITDA, or earnings before interest, taxes, depreciation, and amortization. To approximate the cash profit generated by the
company's operations, EBITDA includes depreciation and amortization in addition to taxes and debt payment costs.
According to generally accepted accounting principles, EBITDA is not a recognized metric (GAAP). A few publicly traded companies include adjusted EBITDA figures in their quarterly results, which
typically exclude additional expenses like stock-based compensation.
How is EBITDA Calculated?
It is primarily computed by deducting from net income the costs incurred by the business other than interest, taxes, depreciation, and amortization.
There are two formulas that can be used for the same:
EBITDA = Net Profit + interest + Taxes + Depreciation + Amortization
EBITDA = Operating Income + Depreciation + Amortization
Businesses use these formulas to efficiently determine a particular facet of their operations. Since it is a non-GAAP calculation, the user can choose which expenses to include in the net income.
For example, an investor can choose to exclude only taxes and depreciation in order to examine the potential impact of debt on a company's financial standing.
Assume that ABC Manufacturing Company has the data below, which was taken from the annual earnings report for 2022:
• Net income = Rs. 10,000,000
• Depreciation and amortization = Rs. 3,000,000
• Taxes = Rs. 5,000,000
• Interest expense = Rs, 5,000,000
• Operating income = Rs. 20,000,000
First Formula:
EBITDA = Net Profit + Interest + Taxes + Depreciation + Amortization
EBITDA = Rs 10,000,000 + Rs. 5,000,000 + Rs. 5,000,000 + Rs. 3,000,000 = Rs. 23,000,000
Second Formula:
EBITDA = Operating Income + Depreciation + Amortization
EBITDA = Rs. 20,000,000 + Rs. 3,000,000 = Rs. 23,000,000
EBITDA vs Gross Profit
While both EBITDA and gross profit measure a company's profitability, they do so in different ways. Earnings Before Interest, Taxes, Depreciation, and Amortization, or EBITDA, measures operational
effectiveness by taking into account expenses that are under the company's direct control. It excludes external factors. Gross profit, on the other hand, measures how well a business uses its labor
by comparing the difference between production costs and sales revenue.
Formulas for EBITDA and Gross Profits
These formulas can be used to determine the correct values if you want to calculate a company's gross profits or EBITDA. It is useful to review the accounting documents provided by the company before
starting your calculations. A crucial step in ensuring the accuracy of your results is to make sure you have access to the most recent data. The following are the EBITDA and gross profit formulas,
along with usage guidelines:
Formula for EBITDA
EBITDA = OI + Depreciation + Amortization
This formula uses operating income (OI) to represent a company's earnings after operating costs are deducted. Operating costs can involve many different factors, so it is important to look up all the
pertinent values in the accounting books before calculating a company's EBITDA. Prior to starting your analysis, it can be a good idea to look over the company's books as you can find the values for
asset amortization and depreciation on the balance sheet.
Formula for Gross Profits
Gross profit = revenue − COGS
Revenue is the total amount a business makes from selling the product, while COGS stands for cost of goods sold. You can determine how much value the company creates from sales by deducting COGS from
total revenue. If you want to compare different companies that sell similar products to determine which ones have the best profit margins, this formula can be helpful.
How to Calculate EBITDA for Gross Profit
You need to consider more than just the gross profit in order to calculate EBITDA (Earnings Before Interest, Taxes, Depreciation, and Amortization) based on profit. Here's a quick guide you can use:
Begin with Gross Profit: Calculate the profit by subtracting the Cost of Goods Sold (COGS) from Revenue using this formula;
Gross Profit = Revenue. COGS
Determine Operating Expenses: Make a list of all the operating costs the business has to pay. These costs include things like rent, utilities, employee salaries, marketing expenses, and any other
costs that are directly related to operating the business.
Compute Operating Income (OI): Deduct operating expenses from the profit to obtain the operating income (OI). The formula is;
OI = Gross Profit. Operating Expenses
Include Depreciation and Amortization: Refer to the depreciation and amortization values in the company's reports. These figures illustrate both the dispersion of intangible asset costs and the
gradual loss of value of tangible assets.
Combine Elements for EBITDA: Add depreciation and amortization to the operating income (OI) calculated in step 3. The EBITDA formula is;
EBITDA = OI + Depreciation + Amortization
By following these steps and using information from the company's records, you can determine EBITDA starting from gross profit. | {"url":"https://www.jordensky.com/tools/ebitda-calculator","timestamp":"2024-11-12T23:40:35Z","content_type":"text/html","content_length":"35243","record_id":"<urn:uuid:78b5770d-3ef3-46fe-a70d-dd8ab5c78610>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00812.warc.gz"} |
Minimal representations of a finite distributive lattice by principal congruences of a lattice
Grätzer George A. and Lakser Harry: Minimal representations of a finite distributive lattice by principal congruences of a lattice. In: Acta scientiarum mathematicarum, (85) 1-2. pp. 69-96. (2019)
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Let the finite distributive lattice D be isomorphic to the congruence lattice of a finite lattice L. Let Q denote those elements of D that correspond to principal congruences under this isomorphism.
Then Q contains 0, 1 ∈ D and all the join-irreducible elements of D. If Q contains exactly these elements, we say that L is a minimal representation of D by principal congruences of the lattice L. We
characterize finite distributive lattices D with a minimal representation by principal congruences with the property that D has at most two dual atoms.
Item Type: Article
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2019
Volume: 85
Number: 1-2
ISSN: 2064-8316
Page Range: pp. 69-96
Official URL: http://www.acta.hu
Related URLs: http://acta.bibl.u-szeged.hu/62105/
DOI: 10.14232/actasm-017-060-9
Uncontrolled Keywords: Matematika
Additional Information: Bibliogr.: p. 95-96. ; összefoglalás angol nyelven
Date Deposited: 2019. Sep. 25. 10:01
Last Modified: 2021. Mar. 25. 15:30
URI: http://acta.bibl.u-szeged.hu/id/eprint/62134
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2020 Dodge Charger Tire Size
Your Dodge was manufactured with different tire sizes. To determine the best tire size for your specific 2020 Dodge Charger, we first need to determine your rim size. Please review the information
How to Determine Rim Size
Check your existing tires. Your Dodge Charger's rim size is the number to the right of the R. In the example pictured here, the tire size fits 16-inch rims.
Rim Size Selection
Now that you know your rim size, make a selection below to filter your results.
17-Inch Rims
2020 Dodge Charger
The original tire size for your 2020 Dodge Charger is listed below. Tap on the box to view a color-coded explanation of your Dodge Charger's' tire size.
Trim Options:
SXT (RWD)
P215/65R17 98
Simplified Size: 215-65-17
Simplified size is useful for shopping and buying tires.
The original tire size for your 2020 Dodge Charger is P215/65R17 98T. A color-coded explanation of the 2020 Dodge Charger's tire size is shown below.
This letter denotes the intended use of the tire.
P P Passenger Vehicle
LT Light Truck
C Commercial Vehicle
215 This number indicates that your tire has a width of 215 millimeters.
17 The tire size was designed to fit rims or wheels that are 17 inches in diameter.
98 This tire has a load index of 98, which means it's capable of carrying a load of 1650 pounds (750 kg) or less. A higher number means the tire can carry more weight. A lower number means the
65 This number means that your tire has an aspect ratio of 65%. In other words, your tire's sidewall height (from the edge of the rim to the tire's tread) is 65% of the width. In this case, the
sidewall height works out to be 139 millimeters.
This letter denotes how your tire was constructed. Radial is the standard construction method for about 99% of all tires sold today.
R R Radial
B Bias Belt
D Diagonal
This tire has a speed rating of T, which means 118 mph (190 km/h) is the maximum speed that can be sustained for 10 minutes. A higher speed becomes dangerous.
18-Inch Rims
2020 Dodge Charger
Your 2020 Dodge Charger was manufactured with multiple tire sizes. Choose a tire size below to get a color-coded explanation of the differences. Then pick the best tire size for your 2020 Dodge
Trim Options:
Pursuit Police
245/55R18 103
Simplified Size: 245-55-18
Simplified size is useful for shopping and buying tires.
The original tire size for your 2020 Dodge Charger is 245/55R18 103V. A color-coded explanation of the 2020 Dodge Charger's tire size is shown below.
245 This number indicates that your tire has a width of 245 millimeters.
18 The tire size was designed to fit rims or wheels that are 18 inches in diameter.
103 This tire has a load index of 103, which means it's capable of carrying a load of 1925 pounds (875 kg) or less. A higher number means the tire can carry more weight. A lower number means the
55 This number means that your tire has an aspect ratio of 55%. In other words, your tire's sidewall height (from the edge of the rim to the tire's tread) is 55% of the width. In this case, the
sidewall height works out to be 134 millimeters.
This letter denotes how your tire was constructed. Radial is the standard construction method for about 99% of all tires sold today.
R R Radial
B Bias Belt
D Diagonal
This tire has a speed rating of V, which means 149 mph (240 km/h) is the maximum speed that can be sustained for 10 minutes. A higher speed becomes dangerous.
Trim Options:
Pursuit Police
P225/60R18 99
Simplified Size: 225-60-18
Simplified size is useful for shopping and buying tires.
The original tire size for your 2020 Dodge Charger is P225/60R18 99W. A color-coded explanation of the 2020 Dodge Charger's tire size is shown below.
This letter denotes the intended use of the tire.
P P Passenger Vehicle
LT Light Truck
C Commercial Vehicle
225 This number indicates that your tire has a width of 225 millimeters.
18 The tire size was designed to fit rims or wheels that are 18 inches in diameter.
99 This tire has a load index of 99, which means it's capable of carrying a load of 1705 pounds (775 kg) or less. A higher number means the tire can carry more weight. A lower number means the
60 This number means that your tire has an aspect ratio of 60%. In other words, your tire's sidewall height (from the edge of the rim to the tire's tread) is 60% of the width. In this case, the
sidewall height works out to be 135 millimeters.
This letter denotes how your tire was constructed. Radial is the standard construction method for about 99% of all tires sold today.
R R Radial
B Bias Belt
D Diagonal
This tire has a speed rating of W, which means 167 mph (270 km/h) is the maximum speed that can be sustained for 10 minutes. A higher speed becomes dangerous.
19-Inch Rims
2020 Dodge Charger
The original tire size for your 2020 Dodge Charger is listed below. Tap on the box to view a color-coded explanation of your Dodge Charger's' tire size.
Trim Options:
SXT (AWD)
235/55R19 101
Simplified Size: 235-55-19
Simplified size is useful for shopping and buying tires.
The original tire size for your 2020 Dodge Charger is 235/55R19 101H. A color-coded explanation of the 2020 Dodge Charger's tire size is shown below.
235 This number indicates that your tire has a width of 235 millimeters.
19 The tire size was designed to fit rims or wheels that are 19 inches in diameter.
101 This tire has a load index of 101, which means it's capable of carrying a load of 1815 pounds (825 kg) or less. A higher number means the tire can carry more weight. A lower number means the
55 This number means that your tire has an aspect ratio of 55%. In other words, your tire's sidewall height (from the edge of the rim to the tire's tread) is 55% of the width. In this case, the
sidewall height works out to be 129 millimeters.
This letter denotes how your tire was constructed. Radial is the standard construction method for about 99% of all tires sold today.
R R Radial
B Bias Belt
D Diagonal
This tire has a speed rating of H, which means 130 mph (210 km/h) is the maximum speed that can be sustained for 10 minutes. A higher speed becomes dangerous.
20-Inch Rims
2020 Dodge Charger
There are multiple tire sizes for your 2020 Dodge Charger that depend upon the trim level. Look for your trim level below to get a color-coded explanation of your tire size. Then pick the best tire
size for your 2020 Dodge Charger.
Trim Options:
SXT (RWD)
245/45R20 99
Simplified Size: 245-45-20
Simplified size is useful for shopping and buying tires.
The original tire size for your 2020 Dodge Charger is 245/45R20 99V. A color-coded explanation of the 2020 Dodge Charger's tire size is shown below.
245 This number indicates that your tire has a width of 245 millimeters.
20 The tire size was designed to fit rims or wheels that are 20 inches in diameter.
99 This tire has a load index of 99, which means it's capable of carrying a load of 1705 pounds (775 kg) or less. A higher number means the tire can carry more weight. A lower number means the
45 This number means that your tire has an aspect ratio of 45%. In other words, your tire's sidewall height (from the edge of the rim to the tire's tread) is 45% of the width. In this case, the
sidewall height works out to be 110 millimeters.
This letter denotes how your tire was constructed. Radial is the standard construction method for about 99% of all tires sold today.
R R Radial
B Bias Belt
D Diagonal
This tire has a speed rating of V, which means 149 mph (240 km/h) is the maximum speed that can be sustained for 10 minutes. A higher speed becomes dangerous.
Trim Options:
GT (RWD)R/TScat Pack
245/45ZR20 99
Simplified Size: 245-45-20
Simplified size is useful for shopping and buying tires.
The original tire size for your 2020 Dodge Charger is 245/45ZR20 99Y. A color-coded explanation of the 2020 Dodge Charger's tire size is shown below.
245 This number indicates that your tire has a width of 245 millimeters.
20 The tire size was designed to fit rims or wheels that are 20 inches in diameter.
99 This tire has a load index of 99, which means it's capable of carrying a load of 1705 pounds (775 kg) or less. A higher number means the tire can carry more weight. A lower number means the
Z This tire has a speed class of Z, which means it's part of an elite speed class of 149 mph or more (240 km/h). A tire's speed class is less specific than the speed rating.
45 This number means that your tire has an aspect ratio of 45%. In other words, your tire's sidewall height (from the edge of the rim to the tire's tread) is 45% of the width. In this case, the
sidewall height works out to be 110 millimeters.
This letter denotes how your tire was constructed. Radial is the standard construction method for about 99% of all tires sold today.
R R Radial
B Bias Belt
D Diagonal
This tire has a speed rating of Y, which means 186 mph (300 km/h) is the maximum speed that can be sustained for 10 minutes. A higher speed becomes dangerous.
Trim Options:
Scat Pack
275/40ZR20/XL (106)
Simplified Size: 275-40-20
Simplified size is useful for shopping and buying tires.
The original tire size for your 2020 Dodge Charger is 275/40ZR20/XL 106(Y). A color-coded explanation of the 2020 Dodge Charger's tire size is shown below.
275 This number indicates that your tire has a width of 275 millimeters.
20 The tire size was designed to fit rims or wheels that are 20 inches in diameter.
XL The mark of XL means extra load. A tire with this designation can handle higher inflation pressures than a regular tire, which increases its maximum load.
106 This tire has a load index of 106, which means it's capable of carrying a load of 2090 pounds (950 kg) or less. A higher number means the tire can carry more weight. A lower number means the
Z This tire has a speed class of Z, which means it's part of an elite speed class of 149 mph or more (240 km/h). A tire's speed class is less specific than the speed rating.
40 This number means that your tire has an aspect ratio of 40%. In other words, your tire's sidewall height (from the edge of the rim to the tire's tread) is 40% of the width. In this case, the
sidewall height works out to be 110 millimeters.
This letter denotes how your tire was constructed. Radial is the standard construction method for about 99% of all tires sold today.
R R Radial
B Bias Belt
D Diagonal
This tire has a speed rating of Y, which means 186 mph (300 km/h) is the maximum speed that can be sustained for 10 minutes. A higher speed becomes dangerous.
Trim Options:
SRT Hellcat WidebodyScat Pack 392 Widebody
305/35ZR20/XL (107)
Simplified Size: 305-35-20
Simplified size is useful for shopping and buying tires.
The original tire size for your 2020 Dodge Charger is 305/35ZR20/XL 107(Y). A color-coded explanation of the 2020 Dodge Charger's tire size is shown below.
305 This number indicates that your tire has a width of 305 millimeters.
20 The tire size was designed to fit rims or wheels that are 20 inches in diameter.
XL The mark of XL means extra load. A tire with this designation can handle higher inflation pressures than a regular tire, which increases its maximum load.
107 This tire has a load index of 107, which means it's capable of carrying a load of 2145 pounds (975 kg) or less. A higher number means the tire can carry more weight. A lower number means the
Z This tire has a speed class of Z, which means it's part of an elite speed class of 149 mph or more (240 km/h). A tire's speed class is less specific than the speed rating.
35 This number means that your tire has an aspect ratio of 35%. In other words, your tire's sidewall height (from the edge of the rim to the tire's tread) is 35% of the width. In this case, the
sidewall height works out to be 106 millimeters.
This letter denotes how your tire was constructed. Radial is the standard construction method for about 99% of all tires sold today.
R R Radial
B Bias Belt
D Diagonal
This tire has a speed rating of Y, which means 186 mph (300 km/h) is the maximum speed that can be sustained for 10 minutes. A higher speed becomes dangerous. | {"url":"https://www.sizemytires.com/vehicle/2020/dodge/charger","timestamp":"2024-11-08T11:16:00Z","content_type":"text/html","content_length":"55919","record_id":"<urn:uuid:2acf5cd9-ab62-43b0-8819-7cdec7fb0aa6>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00523.warc.gz"} |
LoopUnrollRuntime: Add weights to all branches
Make sure every conditional branch constructed by LoopUnrollRuntime code sets branch weights.
• Add new 1:127 weights for the conditional jumps checking whether the whole (unrolled) loop should be skipped in the generated prolog or epilog code.
• Remove updateLatchBranchWeightsForRemainderLoop function and just add weights immediately when constructing the relevant branches. This leads to simpler code and makes the code more obvious as
every call to CreateCondBr now has a BranchWeights parameter.
• Rework formula for epilogue latch weights, to assume equal distribution of remainders and remove assert (as I was able to reach this code when forcing small unroll factors on the commandline). | {"url":"https://reviews.llvm.org/D158642","timestamp":"2024-11-09T19:30:21Z","content_type":"text/html","content_length":"441006","record_id":"<urn:uuid:053a8263-b239-43b3-8a71-22d1f688abbd>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00485.warc.gz"} |
Convex Optimization I
EE364A - Convex Optimization I
EE364A: Convex Optimization I (Stanford Univ.). Taught by Professor Stephen Boyd, this course concentrates on recognizing and solving convex optimization problems that arise in engineering. Convex
sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality
conditions, duality theory, theorems of alternative, and applications. Interiorpoint methods. Applications to signal processing, control, digital and analog circuit design, computational geometry,
statistics, and mechanical engineering. (from see.stanford.edu)
Lecture 01 - Introduction
Lecture 02 - Guest Lecturer: Jacob Mattingley, Convex Sets and Their Applications
Lecture 03 - Logistics, Convex Functions, Examples
Lecture 04 - Quasiconvex Functions, Examples, Log-Concave and Log-Convex Functions
Lecture 05 - Optimal and Locally Optimal Points, Convex Optimization Problem, Quasiconvex Optimization
Lecture 06 - Linear-Fractional Program, Quadratic Program
Lecture 07 - Generalized Inequality Constraints, Semidefinite Program (SDP)
Lecture 08 - Lagrangian, Least-Norm Solution Of Linear Equations, Dual Problem, Weak and Strong Duality
Lecture 09 - Complementary Slackness, Karush-Kuhn-Tucker (KKT) Conditions, Sensitivity, Duality
Lecture 10 - Applications: Norm Approximation, Penalty Function Approximation, Least-Norm Problems, etc.
Lecture 11 - Statistical Estimation, Maximum Likelihood Estimation
Lecture 12 - Geometric Problems
Lecture 13 - Linear Discrimination, Nonlinear Discrimination, Numerical Linear Algebra Background
Lecture 14 - Numerical Linear Algebra Background, Factorizations
Lecture 15 - Algorithm - Unconstrained Minimization
Lecture 16 - Unconstrained Minimization (cont.), Equality Constrained Minimization
Lecture 17 - Equality Constrained Minimization (cont.), Interior-Point Methods
Lecture 18 - Logarithmic Barrier, Central Path, Barrier Method, Feasibility and Phase I Methods
Lecture 19 - Interior-Point Methods, Barrier Method (Review), Generalized Inequalities
EE364A - Convex Optimization I
Instructors: Professor Stephen Boyd. Handouts. Assignments. Exams. This course concentrates on recognizing and solving convex optimization problems that arise in engineering. | {"url":"http://www.infocobuild.com/education/audio-video-courses/electronics/ee364a-convex-optimization-i-systems-stanford.html","timestamp":"2024-11-06T20:30:36Z","content_type":"text/html","content_length":"11725","record_id":"<urn:uuid:b2e99bc1-69fb-4c41-89c3-c7f034963f45>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00687.warc.gz"} |
Ring Theory/Integral domains and Fields - Wikibooks, open books for an open world
Definition 1: A non zero element 'a' of a commutative ring R is called a zero divisor if there exists some non zero element b in R such that ab=0.
For example, in the ring of 2-by-2 matrices, the matrix
${\displaystyle {\begin{pmatrix}1&1\\2&2\end{pmatrix}}}$
is a zero divisor because
${\displaystyle {\begin{pmatrix}1&1\\2&2\end{pmatrix}}\cdot {\begin{pmatrix}1&1\\-1&-1\end{pmatrix}}={\begin{pmatrix}-2&1\\-2&1\end{pmatrix}}\cdot {\begin{pmatrix}1&1\\2&2\end{pmatrix}}={\begin
Definition 2: A commutative ring is called an integral domain, if it has no zero divisors. Equivalently, a commutative ring is called an integral domain if ${\displaystyle ab=0\Rightarrow a=0\ or\ b=
0}$ or in other words ${\displaystyle aeq 0,beq 0\Rightarrow abeq 0\forall a,b\in R}$.
For example ${\displaystyle \mathbb {Z} ,\mathbb {Q} ,\mathbb {R} ,\mathbb {C} }$ are all integral domains. ${\displaystyle \mathbb {Z} _{6}}$ is not an integral domain (2.3=0 here) but ${\
displaystyle \mathbb {Z} _{5}}$ is.
Definition 3: A ring (R,+,.) is called a division ring if it forms a group with respect to the operation '.'. If that group is abelian then the ring is called a field. We will emphasize the
properties of a field again:
A field F is a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold:
• Closure of F under addition and multiplication
For all a, b in F, both a + b and a · b are in F (or more formally, + and · are binary operations on F).
• Associativity of addition and multiplication
For all a, b, and c in F, the following equalities hold: a + (b + c) = (a + b) + c and a · (b · c) = (a · b) · c.
• Commutativity of addition and multiplication
For all a and b in F, the following equalities hold: a + b = b + a and a · b = b · a.
• Additive and multiplicative identity
There exists an element of F, called the additive identity element and denoted by 0, such that for all a in F, a + 0 = a. Likewise, there is an element, called the multiplicative identity element and
denoted by 1, such that for all a in F, a · 1 = a. For technical reasons, the additive identity and the multiplicative identity are required to be distinct.
• Additive and multiplicative inverses
For every a in F, there exists an element −a in F, such that a + (−a) = 0. Similarly, for any a in F other than 0, there exists an element a−1 in F, such that a · a−1 = 1. (The elements a + (−b) and
a · b−1 are also denoted a − b and a/b, respectively.) In other words, subtraction and division operations exist.
• Distributivity of multiplication over addition
For all a, b and c in F, the following equality holds: a · (b + c) = (a · b) + (a · c).
Clearly every field is a division ring. The easiest examples of fields are ${\displaystyle \mathbb {Q} ,\mathbb {R} }$ and ${\displaystyle \mathbb {C} }$. A division ring which is not a field is the
field of quaternions, described as follows:
Consider ${\displaystyle \mathbb {R} ^{4}}$. Let the symbol 1 stand for (1,0,0,0); i for (0,1,0,0); j for (0,0,1,0) and k for (0,0,0,1). Clearly every element of ${\displaystyle \mathbb {R} ^{4}}$
can be represented as ${\displaystyle \alpha _{0}(1)+\alpha _{1}(i)+\alpha _{2}(j)+\alpha _{3}(k)}$ where ${\displaystyle \alpha _{i}}$ is some real number. We endow addition and multiplication on $
{\displaystyle \mathbb {R} ^{4}}$ according to the following rules: Addition of two elements ${\displaystyle \alpha _{0}(1)+\alpha _{1}(i)+\alpha _{2}(j)+\alpha _{3}(k)}$ and ${\displaystyle \beta _
{0}(1)+\beta _{1}(i)+\beta _{2}(j)+\beta _{3}(k)}$ is simply ${\displaystyle (\alpha _{0}+\beta _{0})(1)+(\alpha _{1}+\beta _{1})(i)+(\alpha _{2}+\beta _{2})(j)+(\alpha _{3}+\beta _{3})(k)}$. For
multiplication note that if we impose the following rules:
${\displaystyle i^{2}=j^{2}=k^{2}=ijk=-1,}$
then these determine all the possible products of i, j, and k.
For example, since
${\displaystyle -1=ijk,}$
right-multiplying both sides by k gives
{\displaystyle {\begin{aligned}-k&=ijkk,\\-k&=ij(-1),\\k&=ij.\end{aligned}}}
All the other possible products can be determined by similar methods, and this gives the following table:
{\displaystyle {\begin{alignedat}{2}ij&=k,&\qquad ji&=-k,\\jk&=i,&kj&=-i,\\ki&=j,&ik&=-j.\end{alignedat}}}
For two elements ${\displaystyle \alpha _{0}(1)+\alpha _{1}(i)+\alpha _{2}(j)+\alpha _{3}(k)}$ and ${\displaystyle \beta _{0}(1)+\beta _{1}(i)+\beta _{2}(j)+\beta _{3}(k)}$, their product is
determined by the products of the i,j,k's according to the above rules and the distributive law. This gives the following expression:
${\displaystyle \alpha _{0}\beta _{0}-\alpha _{1}\beta _{1}-\alpha _{2}\beta _{2}-\alpha _{3}\beta _{3})(1)+(\alpha _{0}\beta _{1}+\alpha _{1}\beta _{0}+\alpha _{2}\beta _{3}-\alpha _{3}\beta _{2})
(i)+(\alpha _{0}\beta _{2}-\alpha _{1}\beta _{3}+\alpha _{2}\beta _{0}+\alpha _{3}\beta _{1})(j)+(\alpha _{0}\beta _{3}-\alpha _{1}\beta _{2}-\alpha _{2}\beta _{1}+\alpha _{3}\beta _{0})(k)}$
It is left to the reader to verify that the thus obtained algebraic structure is indeed a division ring.
Basic Theorems on Integral domains and fields
Theorem 1.11: Let R be a commutative ring. Then R is an integral domain if and only if ${\displaystyle ab=ac\Rightarrow b=c}$ where ${\displaystyle a,b,c\in R,aeq 0}$ .
Proof: ${\displaystyle \Rightarrow }$ : Clearly ab=ac implies a(b-c)=0. As a is non zero and R is an integral domain so b-c=0 or b=c.
${\displaystyle \Leftarrow }$ : Suppose that for some nonzero a we have ab=0. But then ab=a0 and by our hypothesis b=0.${\displaystyle \Box }$ .
Remark: Basically the above theorem means that integral domains are the rings where cancellation laws hold. In rings where cancellation laws do not hold we are bound to have some zero divisors.
Theorem 1.12: Every field is an integral domain.
Proof: Let R be any field. Let ab=ac, where ${\displaystyle a,b,c\in R}$ and ${\displaystyle aeq 0}$ . Then as ${\displaystyle a^{-1}}$ exists so multiplying it on both sides of ab=ac we have b=c,
i.e. cancellation laws hold. By the previous theorem R is an integral domain.${\displaystyle \Box }$
Remark: The converse of the above result may not be true as is evident from ${\displaystyle \mathbb {Z} }$ .
Theorem 1.13: Every finite integral domain is a field.
Proof: Let R be a finite integral domain and let ${\displaystyle x\in R}$ where ${\displaystyle xeq 0,1}$ . It suffices to show that x is a unit. Now the list 1,x,x^2,x^3... can't go on forever as R
is finite. Suppose, without losing generality that for some i<j, x^i=x^j. Then x^i-x^j=0 and since i<j, so x^j-i is a legitimate member of R (in fact so is x^j-i-1). We have x^i(1-x^j-i)=x^i-x^j=0.
As x is non zero and R is an integral domain so x^i is non zero. But then 1-x^j-i=0 or x^j-i=1. It follows that as x^j-i-1x=1. Hence x is a unit with inverse x^j-i-1.${\displaystyle \Box }$
Corollary: The ring ${\displaystyle {\frac {\mathbb {Z} }{p\mathbb {Z} }}}$ is a field iff p is prime.
Proof: ${\displaystyle \Rightarrow }$ : We will denote elements of ${\displaystyle {\frac {\mathbb {Z} }{p\mathbb {Z} }}}$ by numbers 0,1,...p-1. Now suppose p was composite and p=ab where 1<a,b<p.
Now ab=0 in ${\displaystyle {\frac {\mathbb {Z} }{p\mathbb {Z} }}}$ although a,b are themselves nonzero. This contradicts the fact that ${\displaystyle {\frac {\mathbb {Z} }{p\mathbb {Z} }}}$ is an
integral domain.
${\displaystyle \Leftarrow }$ Suppose p is prime. It suffices to show that ${\displaystyle {\frac {\mathbb {Z} }{p\mathbb {Z} }}}$ is an integral domain. Let a,b be nonzero elements of ${\
displaystyle {\frac {\mathbb {Z} }{p\mathbb {Z} }}}$ such that ab=0 there. But then p|ab and as p is prime so p|a or p|b. That's just another way of saying that a=0 or b=0 in ${\displaystyle {\frac
{\mathbb {Z} }{p\mathbb {Z} }}}$ and so ${\displaystyle {\frac {\mathbb {Z} }{p\mathbb {Z} }}}$ is an integral domain.${\displaystyle \Box }$
Theorem 1.14: Let R be a ring such that the equation ax=b has a solution for all ${\displaystyle a(eq 0)\in R}$ and for all ${\displaystyle b\in R}$ . Then R is a division ring.
Proof: We first show that R has no zero divisors followed by the fact that it has a unity. Let ab=0 where a,b are non zero. Now abx=0 for each x in R. Ler r be any element of R. Now by the hypothesis
there exists an x such that bx=r. Using this x we see that ar=0 for any r in R. Now consider ax=a. Clearly there is a c such that ac=a. But ar=0 implies that ac=0=a. This contradicts the fact that a
was chosen to be nonzero. So R has no zero divisors. Now let e be the solution of ax=a. Obviously e is nonzero. Then ae=a and a(e-e^2)=ae-ae^2=a-ae=0 and so e=e^2. Then for any x (xe-x)e=xe-xe=0 and
as e is nonzero so xe=x following which R has unity. (The fact that ex=x is similarly proved.)
Now if a is non zero, then ax=e has a solution a^-1. Also (a^-1a-e)a^-1=a^-1e-ea^-1=0 and so as a^-1 is non zero we have a^-1a-e=0 or a^-1a=e. Then aa^-1=a^-1a=e and so a is a unit. Similarly all non
zero elements are units.${\displaystyle \Box }$ | {"url":"https://en.m.wikibooks.org/wiki/Ring_Theory/Integral_domains_and_Fields","timestamp":"2024-11-09T09:39:29Z","content_type":"text/html","content_length":"108940","record_id":"<urn:uuid:eaeb678d-1027-4fed-9bb9-01db0356dbf0>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00055.warc.gz"} |
Max-margin classification of data with absent features
We consider the problem of learning classifiers in structured domains, where some objects have a subset of features that are inherently absent due to complex relationships between the features.
Unlike the case where a feature exists but its value is not observed, here we focus on the case where a feature may not even exist (structurally absent) for some of the samples. The common approach
for handling missing features in discriminative models is to first complete their unknown values, and then use a standard classification procedure over the completed data. This paper focuses on
features that are known to be non-existing, rather than have an unknown value. We show how incomplete data can be classified directly without any completion of the missing features using a max-margin
learning framework. We formulate an objective function, based on the geometric interpretation of the margin, that aims to maximize the margin of each sample in its own relevant subspace. In this
formulation, the linearly separable case can be transformed into a binary search over a series of second order cone programs (SOCP), a convex problem that can be solved efficiently. We also describe
two approaches for optimizing the general case: an approximation that can be solved as a standard quadratic program (QP) and an iterative approach for solving the exact problem. By avoiding the
pre-processing phase in which the data is completed, both of these approaches could offer considerable computational savings. More importantly, we show that the elegant handling of missing values by
our approach allows it to both outperform other methods when the missing values have non-trivial structure, and be competitive with other methods when the values are missing at random. We demonstrate
our results on several standard benchmarks and two real-world problems: edge prediction in metabolic pathways, and automobile detection in natural images.
• Max margin
• Metabolic pathways
• Missing features
• Network reconstruction
Dive into the research topics of 'Max-margin classification of data with absent features'. Together they form a unique fingerprint. | {"url":"https://cris.biu.ac.il/en/publications/max-margin-classification-of-data-with-absent-features-3","timestamp":"2024-11-14T14:49:40Z","content_type":"text/html","content_length":"56961","record_id":"<urn:uuid:e6e27919-bf98-4f59-bd79-9dc36f3e0f98>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00157.warc.gz"} |
Analytic non-supersymmetric background dual of a confining gauge theory and the corresponding plane wave theory of hadrons
We find a regular analytic 1st order deformation of the Klebanov-Strassler background. From the dual gauge theory point of view the deformation describes supersymmetry soft breaking gaugino mass
terms. We calculate the difference in vacuum energies between the supersymmetric and the non-supersymmetric solutions and find that it matches the field theory prediction. We also discuss the
breaking of the U(1)[R] symmetry and the space-time dependence of the gaugino bilinears two point function. Finally, we determine the Penrose limit of the non-supersymmetric background and write down
the corresponding plane wave string theory. This string describes "annulons"-heavy hadrons with mass proportional to large global charge. Surprisingly the string spectrum has two fermionic zero
modes. This implies that the sector in the non-supersymmetric gauge theory which is the dual of the annulons is supersymmetric.
• Ads-CFT and dS-CFT Correspondence
• D-branes
• Penrose limit and pp-wave background
• Supersymmetry Breaking
Dive into the research topics of 'Analytic non-supersymmetric background dual of a confining gauge theory and the corresponding plane wave theory of hadrons'. Together they form a unique fingerprint. | {"url":"https://cris.tau.ac.il/en/publications/analytic-non-supersymmetric-background-dual-of-a-confining-gauge-","timestamp":"2024-11-01T23:29:13Z","content_type":"text/html","content_length":"48365","record_id":"<urn:uuid:7b9423d9-e37c-4715-a76d-932edcf5d035>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00706.warc.gz"} |
Is Arctangent the same as tan 1?
Arctangent, written as arctan or tan-1 (not to be confused with ) is the inverse tangent function.
How do you convert tan to degrees?
Places x is equal to 36.87 degrees now if you wanted to let’s just say another example tangent of y is equal to negative 0.1 do the same.
How do you calculate tan?
In any right triangle, the tangent of an angle is the length of the opposite side (O) divided by the length of the adjacent side (A).
Is tan inverse equal to cot?
Cot x is the multiplicative inverse of tan x. The reciprocal of cotangent function is equal to the tangent function, i.e. Hence, the product of tan x and cot x is equal to 1.
What is the formula of tan inverse?
Inverse Tan Formula
In a right-angled triangle, the tangent of an angle (θ) is the ratio of its opposite side to the adjacent side. i.e., tan θ = (opposite side) / (adjacent side). Then by the definition of inverse tan,
the inverse tan formula is, θ = tan-1[ (opposite side) / (adjacent side) ] .
What is the value of 1 tan?
We know that a tan of 90 degrees is defined as infinity. Thus for tan-1 the value is 90 degrees.
Why do you use tan-1?
The tangent formula is used to tan of an angle in a right-angled triangle. The inverse tangent formula is used to find the angle when the side opposite to that angle and adjacent side are known to
us. The inverse of Tangent is represented by arctan or tan-1.
What is the tangent of a 30 angle?
The exact value of tan 30° is 0.57735. The value of tangent of angle 30 degrees can also be evaluated using the values of sin 30 degrees and cos 30 degrees.
How do you find tangent without a calculator?
Ex: Solve tan(x)=a Without a Calculator – YouTube
What is the value of tan?
Deriving the Value of Tan Degrees
Angles (in degrees) 0° 45°
Sin 0 1 2
Cos 1 1 2
tan 0 1
What is the cot of 1?
Cot 1 degrees is the value of cotangent trigonometric function for an angle equal to 1 degrees. The value of cot 1° is 57.29 (approx).
What is the tan inverse of negative 1?
Tan(-1)= -pi/4. Knowing that tan is negative in quadrants 2 and 4.
What is the value of tan inverse 2?
The value of arctan 2 in degrees is 63.435° and in radians is 1.107 (both values are rounded to 3 decimals).
What is the value of tan inverse 4?
The value of tan 4 degrees is 0.0699268. . .. Tan 4 degrees in radians is written as tan (4° × π/180°), i.e., tan (π/45) or tan (0.069813. . .).
What is the tan inverse of 2?
The approximate value of tan ⁻2 is 63.
Is value of cot215 tan215?
∴ cot2 15° + tan2 15° = 14
A total number of 400 vacancies will be filled for the UPSC NDA II 2022 exam.
What is tan to the negative 1?
tan x−1, sometimes interpreted as (tan(x))−1 = 1tan(x) = cot(x) or cotangent of x, the multiplicative inverse (or reciprocal) of the trigonometric function tangent (see above for ambiguity)
What is the inverse of tan 0?
Since the other name of arctan is “tan inverse”, we can say that tan inverse 0 is 0. Since 0 degrees is same as 0 radians: arctan 0 in degrees is 0°.
How do you solve a 30 60 90 Triangle?
30°-60°-90° Triangles
In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.
How do you find tan 30 without a calculator?
Memorise (sin/cos/tan) 30, 45, 60 without using a calculator – YouTube
How do you find sine cosine and tangent by hand?
How to Calculate Sin, Cos & Tan With No Calculator : Math Lessons & Tips
What is tan θ?
tan θ is also called as law of tangent. The tangent formula for a right-angled triangle can be defined as the ratio of the opposite side of a triangle to the adjacent side. It can also be represented
as a ratio of the sine of the angle to the cosine of the angle.
Why is tan 30?
The value of tan 30 degrees is 1/√3. The value of tan π/6 can be evaluated with the help of a unit circle, graphically. In trigonometry, the tangent of an angle in a right-angled triangle is equal to
the ratio of opposite side and the adjacent side of the angle.
What is the value of cot 45?
Tangent and cotangent of an angle is the quotient of 2 catheti, which are equal, so finally tan 45 = cot 45 = 1.
What is the value of cot 30?
What is Cot 30 Degrees? Cot 30 degrees is the value of cotangent trigonometric function for an angle equal to 30 degrees. The value of cot 30° is √3 or 1.7321 (approx). | {"url":"https://www.trentonsocial.com/is-arctangent-the-same-as-tan-1/","timestamp":"2024-11-03T07:25:55Z","content_type":"text/html","content_length":"60639","record_id":"<urn:uuid:e8df9667-a8e3-4a95-85c7-680784f7eff1>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00839.warc.gz"} |
Documentation/kdump/vmcoreinfo.txt - linux - Git at Google
What is it?
VMCOREINFO is a special ELF note section. It contains various
information from the kernel like structure size, page size, symbol
values, field offsets, etc. These data are packed into an ELF note
section and used by user-space tools like crash and makedumpfile to
analyze a kernel's memory layout.
Common variables
The version of the Linux kernel. Used to find the corresponding source
code from which the kernel has been built. For example, crash uses it to
find the corresponding vmlinux in order to process vmcore.
The size of a page. It is the smallest unit of data used by the memory
management facilities. It is usually 4096 bytes of size and a page is
aligned on 4096 bytes. Used for computing page addresses.
The UTS namespace which is used to isolate two specific elements of the
system that relate to the uname(2) system call. It is named after the
data structure used to store information returned by the uname(2) system
User-space tools can get the kernel name, host name, kernel release
number, kernel version, architecture name and OS type from it.
An array node_states[N_ONLINE] which represents the set of online nodes
in a system, one bit position per node number. Used to keep track of
which nodes are in the system and online.
The global page directory pointer of the kernel. Used to translate
virtual to physical addresses.
Defines the beginning of the text section. In general, _stext indicates
the kernel start address. Used to convert a virtual address from the
direct kernel map to a physical address.
Stores the virtual area list. makedumpfile gets the vmalloc start value
from this variable and its value is necessary for vmalloc translation.
Physical addresses are translated to struct pages by treating them as
an index into the mem_map array. Right-shifting a physical address
PAGE_SHIFT bits converts it into a page frame number which is an index
into that mem_map array.
Used to map an address to the corresponding struct page.
Makedumpfile gets the pglist_data structure from this symbol, which is
used to describe the memory layout.
User-space tools use this to exclude free pages when dumping memory.
mem_section|(mem_section, NR_SECTION_ROOTS)|(mem_section, section_mem_map)
The address of the mem_section array, its length, structure size, and
the section_mem_map offset.
It exists in the sparse memory mapping model, and it is also somewhat
similar to the mem_map variable, both of them are used to translate an
The size of a page structure. struct page is an important data structure
and it is widely used to compute contiguous memory.
The size of a pglist_data structure. This value is used to check if the
pglist_data structure is valid. It is also used for checking the memory
The size of a zone structure. This value is used to check if the zone
structure has been found. It is also used for excluding free pages.
The size of a free_area structure. It indicates whether the free_area
structure is valid or not. Useful when excluding free pages.
The size of a list_head structure. Used when iterating lists in a
post-mortem analysis session.
The size of a nodemask_t type. Used to compute the number of online
(page, flags|_refcount|mapping|lru|_mapcount|private|compound_dtor|
User-space tools compute their values based on the offset of these
variables. The variables are used when excluding unnecessary pages.
(pglist_data, node_zones|nr_zones|node_mem_map|node_start_pfn|node_
On NUMA machines, each NUMA node has a pg_data_t to describe its memory
layout. On UMA machines there is a single pglist_data which describes the
whole memory.
These values are used to check the memory type and to compute the
virtual address for memory map.
(zone, free_area|vm_stat|spanned_pages)
Each node is divided into a number of blocks called zones which
represent ranges within memory. A zone is described by a structure zone.
User-space tools compute required values based on the offset of these
(free_area, free_list)
Offset of the free_list's member. This value is used to compute the number
of free pages.
Each zone has a free_area structure array called free_area[MAX_ORDER].
The free_list represents a linked list of free page blocks.
(list_head, next|prev)
Offsets of the list_head's members. list_head is used to define a
circular linked list. User-space tools need these in order to traverse
(vmap_area, va_start|list)
Offsets of the vmap_area's members. They carry vmalloc-specific
information. Makedumpfile gets the start address of the vmalloc region
from this.
(zone.free_area, MAX_ORDER)
Free areas descriptor. User-space tools use this value to iterate the
free_area ranges. MAX_ORDER is used by the zone buddy allocator.
Index of the first record stored in the buffer log_buf. Used by
user-space tools to read the strings in the log_buf.
Console output is written to the ring buffer log_buf at index
log_first_idx. Used to get the kernel log.
log_buf's length.
The index that the next printk() record to read after the last clear
command. It indicates the first record after the last SYSLOG_ACTION
_CLEAR, like issued by 'dmesg -c'. Used by user-space tools to dump
the dmesg log.
The index of the next record to store in the buffer log_buf. Used to
compute the index of the current buffer position.
The size of a structure printk_log. Used to compute the size of
messages, and extract dmesg log. It encapsulates header information for
log_buf, such as timestamp, syslog level, etc.
(printk_log, ts_nsec|len|text_len|dict_len)
It represents field offsets in struct printk_log. User space tools
parse it and check whether the values of printk_log's members have been
(free_area.free_list, MIGRATE_TYPES)
The number of migrate types for pages. The free_list is described by the
array. Used by tools to compute the number of free pages.
On linux-2.6.21 or later, the number of free pages is in
vm_stat[NR_FREE_PAGES]. Used to get the number of free pages.
Page attributes. These flags are used to filter various unnecessary for
dumping pages.
The HUGETLB_PAGE_DTOR flag denotes hugetlbfs pages. Makedumpfile
excludes these pages.
Used to convert the virtual address of an exported kernel symbol to its
corresponding physical address.
Used to walk through the whole page table and convert virtual addresses
to physical addresses. The init_top_pgt is somewhat similar to
swapper_pg_dir, but it is only used in x86_64.
User-space tools need to know whether the crash kernel was in 5-level
paging mode.
This is a struct pglist_data array and stores all NUMA nodes
information. Makedumpfile gets the pglist_data structure from it.
(node_data, MAX_NUMNODES)
The maximum number of nodes in system.
The kernel randomization offset. Used to compute the page offset. If
KASLR is disabled, this value is zero.
Currently unused by Makedumpfile. Used to compute the module virtual
address by Crash.
AMD-specific with SME support: it indicates the secure memory encryption
mask. Makedumpfile tools need to know whether the crash kernel was
encrypted. If SME is enabled in the first kernel, the crash kernel's
page table entries (pgd/pud/pmd/pte) contain the memory encryption
mask. This is used to remove the SME mask and obtain the true physical
Currently, sme_mask stores the value of the C-bit position. If needed,
additional SME-relevant info can be placed in that variable.
For example:
[ misc ][ enc bit ][ other misc SME info ]
63 59 55 51 47 43 39 35 31 27 ... 3
Denotes whether physical address extensions are enabled. It has the cost
of a higher page table lookup overhead, and also consumes more page
table space per process. Used to check whether PAE was enabled in the
crash kernel when converting virtual addresses to physical addresses.
pgdat_list|(pgdat_list, MAX_NUMNODES)
pg_data_t array storing all NUMA nodes information. MAX_NUMNODES
indicates the number of the nodes.
node_memblk|(node_memblk, NR_NODE_MEMBLKS)
List of node memory chunks. Filled when parsing the SRAT table to obtain
information about memory nodes. NR_NODE_MEMBLKS indicates the number of
node memory chunks.
These values are used to compute the number of nodes the crashed kernel used.
node_memblk_s|(node_memblk_s, start_paddr)|(node_memblk_s, size)
The size of a struct node_memblk_s and the offsets of the
node_memblk_s's members. Used to compute the number of nodes.
User-space tools need to know whether the crash kernel was in 3-level or
4-level paging mode. Used to distinguish the page table.
The maximum number of bits for virtual addresses. Used to compute the
virtual memory ranges.
The offset between the kernel virtual and physical mappings. Used to
translate virtual to physical addresses.
Indicates the physical address of the start of memory. Similar to
kimage_voffset, which is used to translate virtual to physical
The kernel randomization offset. Used to compute the page offset. If
KASLR is disabled, this value is zero.
It indicates whether the crash kernel supports large physical address
extensions. Used to translate virtual to physical addresses.
An array with a pointer to the lowcore of every CPU. Used to print the
psw and all registers information.
Used to get the vmalloc_start address from the high_memory symbol.
(lowcore_ptr, NR_CPUS)
The maximum number of CPUs.
node_data|(node_data, MAX_NUMNODES)
See above.
See above.
The vmemmap_list maintains the entire vmemmap physical mapping. Used
to get vmemmap list count and populated vmemmap regions info. If the
vmemmap address translation information is stored in the crash kernel,
it is used to translate vmemmap kernel virtual addresses.
The size of a page. Used to translate virtual to physical addresses.
Page size definitions, i.e. 4k, 64k, or 16M.
Used to make vtop translations.
vmemmap_backing|(vmemmap_backing, list)|(vmemmap_backing, phys)|
(vmemmap_backing, virt_addr)
The vmemmap virtual address space management does not have a traditional
page table to track which virtual struct pages are backed by a physical
mapping. The virtual to physical mappings are tracked in a simple linked
list format.
User-space tools need to know the offset of list, phys and virt_addr
when computing the count of vmemmap regions.
mmu_psize_def|(mmu_psize_def, shift)
The size of a struct mmu_psize_def and the offset of mmu_psize_def's
Used in vtop translations.
node_data|(node_data, MAX_NUMNODES)
See above.
Indicates whether the crashed kernel enabled SH extended mode. | {"url":"https://kunit.googlesource.com/linux/+/kunit/rfc/v5.1/v4/Documentation/kdump/vmcoreinfo.txt?autodive=0%2F%2F%2F%2F","timestamp":"2024-11-03T07:40:52Z","content_type":"text/html","content_length":"117231","record_id":"<urn:uuid:2c56f3f2-c3db-402c-8ed7-adf3bce04b2f>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00810.warc.gz"} |
Blog - QuantPedia - Page 94
We are really excited that we can announce, that Quantopian started to publish series of articles where they will really deeply analyze some of Quantpedia's suggested strategies.
We think, that Soeng Lee from Quantopian did a really good job with a first article, so we just wanted to point that article to you as something interesting to read for people with an interest in
"quant trading". Click on a "View Notebook" button to read a complete analysis:
First article analyses strategy #271 – Earnings Announcements Combined with Stock Repurchases. Quantopian's analysis confirms initial findings of Amini & Singal academic paper:
Earnings are a highly studied event with much of the alpha in traditional earnings strategies squeezed out. However, the research here suggests that there is some level of predictability surrounding
earnings and corporate actions (Buyback announcements). In order to validate the authors' research, Soeng Lee from Quantopian attempts an OOS implementation of the methods used in the Amini&Singal
whitepaper. He examines share buybacks and earnings announcements from 2011 till 2016 finding similar results to the authors with positive returns of 1.115% in a (-10, +15) day window surrounding
earnings. The results hold true for different time windows (0, +15) and sample selection criteria.
Soeng finds the highest positive returns for earnings that are (5, 15) days after a buyback announcement (abnormal returns of 2.67%). Also, the main study by Amini&Singal was focused on buybacks
greater than 5%. However, the robustness test that included all buybacks appears to outperform the main study. The test looking at buybacks 1 ~ 30 days before an earnings announcement also performed
better than the 16 ~ 31 days criteria (as suggested in Amini&Singal) with a greater sample size.
The final Quantopian OOS equity curve looks really promising:
This Quantopian's analysis is the first of the longer series of articles. We are already looking forward to the next one … | {"url":"https://quantpedia.com/blog/page/94/","timestamp":"2024-11-13T11:24:55Z","content_type":"text/html","content_length":"153052","record_id":"<urn:uuid:c83485b0-9141-4887-b612-dea550f9f8ce>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00529.warc.gz"} |
positive definite
positive definite的意思
positive definite中文翻譯：
positive definiteness───[數]正定性
past definite───過去時
positive effect───積極的效果；明顯效果
positive electricity───[物]正電；陽電
positive attitude───積極態度
positive change───正向的改變
positive emotion───正性情緒
positive feeling───積極情感
positive light───正光
Results linear complementary problem have unique solution when m is generalized positive definite matrix.───結果得到了當m是廣義正定矩陣時，線性互補問題存在唯一解。
Results linear complementary problem have unique solution when M is generalized positive definite matrix.───結果得到了當M是廣義正定矩陣時,線性互補問題存在唯一解.
Moreover, the condition is also sufficient if the positive definite matrix is included in this set.───當這個集合中包含有正定矩陣時, 上述必要條件也是充分的.
If a symmetrical matrix is positive definite, the determinants of all its minors are also positive.───如果對稱矩陣是為正定者, 它的所有子式的行列式也都是正的.
Positive definite matrix occupies a very important position in matrix theory, and has great value in practice.───正定矩陣在矩陣論中占有十分重要的地位，在實際中也有廣泛的應用價值。
A region decomposition method to solve a positive definite quadratic programming is presented.───給出了一個求解正定二次規劃的區域分解方法。
Positive semi - definite matrices are positive definite if and only if they are nonsingular.───正半定矩陣是正定的,當且僅當它們是非奇異矩陣.
The method can guarantee global stability without searching a common positive definite matrix.───該方法無需求正定矩陣就能保證系統全局穩定.
Positive definite matrix occupies a very important position in matrix theory, and has great value in practice.
When a common positive definite matrix can not be found to design fuzzy model-based controller, the improved adaptive reconfigurable control scheme based on fuzzy model and neural network is
General solutions of above inverse problem in positive definite matrix and in orthogonal matrix are given here by using factorization method of matrix.
Based on the definitions of generalized positive definite matrix, a further study of it is made in the present paper, and several new results are obtained as a consequence.
In this paper, we discuss properties of positive definite complex matrix, and the relation between it and the Hermite positive definite matrix.
Moreover, the condition is also sufficient if the positive definite matrix is included in this set.
Positive semi - definite matrices are positive definite if and only if they are nonsingular.
If a symmetrical matrix is positive definite, the determinants of all its minors are also positive.
A unified simple condition for stable matrix, positive definite matrix and M matrix is presented in this paper. | {"url":"https://www.qjyouth.com/ec/286533.html","timestamp":"2024-11-11T18:15:32Z","content_type":"text/html","content_length":"9949","record_id":"<urn:uuid:8da635d9-0b4c-4ffc-9ab3-c0e851781a99>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00836.warc.gz"} |
The area of the right triangle ABC is 4 times greater than
Question Stats:
60% 40% (02:06) based on 613 sessions
The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB?
(1) Angles ABC and KLM are each equal to 55 degrees.
(2) LM is 6 inches.
I thought the answer was D because Statement 1 tells us that the triangles are similar and statement 2 tells us that KLM = a right 6-8-10 triangle. So the area of KLM is 24 which would make ABC’s
area = 96 and which makes ABC = 12-16-20 triangle.
The above solution is not right.
Properties of Similar Triangles:
• Corresponding angles are the same.
• Corresponding sides are all in the same
• It is only necessary to determine that two sets of angles are identical in order to conclude that two triangles are similar; the third set will be identical because all of the angles of a triangle
always sum to 180º.
• In similar triangles, the sides of the triangles are in some proportion to one another. For example, a triangle with lengths 3, 4, and 5 has the same angle measures as a triangle with lengths 6, 8,
and 10. The two triangles are similar, and all of the sides of the larger triangle are twice the size of the corresponding legs on the smaller triangle.
• If two similar triangles have sides in the ratio \(\frac{x}{y}\), then their areas are in the ratio \(\frac{x^2}{y^2}\).
OR in another way: in two similar triangles, the ratio of their areas is the square of the ratio of their sides: \(\frac{AREA}{area}=\frac{SIDE^2}{side^2}\).
For more on triangles please check Triangles chapter of the Math Book (link in my signature).
Back to original question:
The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB?
(1) Angles ABC and KLM are each equal to 55 degrees --> ABC and KLM are similar triangles --> \(\frac{AREA_{ABC}}{area_{KLM}}=\frac{4}{1}\), so the sides are in ratio 2/1 --> hypotenuse KL=10 -->
hypotenuse AB=2*10=20. Sufficient.
(2) LM is 6 inches --> KM=8 --> \(area_{KLM}=24\) --> \(AREA_{ABC}=96\). But just knowing the are of ABC is not enough to determine hypotenuse AB. For instance: legs of ABC can be 96 and 2 OR 48 and
4 and you'll get different values for hypotenuse. Not sufficient.
Answer: A.
Hope it helps. | {"url":"https://gmatclub.com/forum/the-area-of-the-right-triangle-abc-is-4-times-greater-than-94037.html","timestamp":"2024-11-05T06:51:00Z","content_type":"application/xhtml+xml","content_length":"705295","record_id":"<urn:uuid:dcbf5588-b7fe-44a0-b030-1ead3e3ec0e3>","cc-path":"CC-MAIN-2024-46/segments/1730477027871.46/warc/CC-MAIN-20241105052136-20241105082136-00756.warc.gz"} |
April 2017
The BITX 40’s microphone amp has a flaw that may shorten the lifespan of microphones by overstressing their components. Here’s what I found and how I fixed it so far.
Here’s the BITX 40 mic amp schematic:
The mic bias is supplied by the TX line through 4.9K of resistance. TX is the DC power supply, 12-15V.
Most electret microphones have a maximum voltage of 10 V, though I’ve seen a few datasheets with a 9 V limit. The data sheets also say that the mics draw 0.5 mA maximum. No minimum is given.
Now, applying Ohm’s law,
$(0.5 \mathrm{mA}) * (4.9 \mathrm{k\Omega}) = 2.45 \mathrm{V}$
Subtracting that from 12 V gives us 9.55 V, so one might think that everything is great.
Not really.
From the books of Bob Pease I learned the importance of worst case design. In worst case design, one looks at the datasheet minimum and maximum specifications and designs the circuit to work under
the worst combination of specifications. Ignore the datasheet typical ratings, because those describe the best case. No one wants a circuit that only works in the best possible circumstances.
The BITX 40 docs specify a maximum power supply of 15 V, so that is the worst-case TX. The worst case microphone current is the minimum current, but I haven’t seen a mic datasheet that lists a
minimum. Therefore, I have to make a guess. I need the guess to be on the safe side without being ridiculous. Knowing that the current is set by a JFET and knowing about both the variability of JFETs
and how data sheet maximums are chosen, I could guess that the typical current is maybe half of the maximum and the minimum half of that, so 0.125 mA. If I want to make a truly robust circuit I could
assume a minimum current of zero. I know a JFET can’t create current out of nothing, so the lowest possible current it draws is zero.
Let’s look at what voltages that creates:
$(15 V) - (0.125 \mathrm{mA})(4.9 \mathrm{k\Omega}) = 14.388$
Uh-oh. That’s well above the 10 V maximum for the mic.
The zero current case is easier to work out. With zero current through the resistor, the mic sees the full 15 V.
A simple fix is to put a resistor in parallel with MIC1, making a voltage divider. I use a computer headset with my BITX, and I know that computer mics are typically fed with 5 V through a 2.2 kΩ
resistor. Knowing that, I picked a 4.3 kΩ resistor across MIC1 to form a voltage divider equivalent to 2.3 kΩ fed by 7 V. That’s close enough, and 7 V is well below the maximum for most electret
The 4.3 kohm resistor on the underside of the BITX 40 PCB. The wires are for the Si5351 BFO mod I added.
Unfortunately, the mic now drives an impedance about 30% lower than before, reducing its output. The RF drive, R136, should be adjusted to compensate.
One could fix the issue a different way, of course. A Zener diode in series with R121 could drop the voltage just as effectively without lowering the amplifier’s input impedance. An LM780x regulator
could do the job, too, albeit with more components. I happened to have 1% resistors within reach and Zener diodes on a different floor of the house. I chose the resistor.
Is this a real problem?
No one else seems to have noticed this issue, so it’s worth asking whether it matters. One answer is that it is worthwhile, and pleasing, to do things right. There is a place for bodging a circuit
together that works as a one-off, but I enjoy the n-dimensional puzzle of getting the details right.
The other answer is that it might be killing microphones, but not often enough that anyone has noticed. The BITX 20 mailing list, home to BITX 40 discussion, has seen a few comments from hams whose
microphone capsules worked for a while, then failed. Some have been able to trace the problems to bad solder joints or physical damage, but I have to wonder if any of the remaining unsolved cases
were caused by overvoltage.
Manufacturer maximum specifications are based on an assumption about the device’s expected lifetime. Operating beyond that specification can be expected to shorten the device’s lifetime. Sometimes
that shortened lifetime is dramatic, with a flash of light, a puff of smoke, or an outpouring of heat. Other times it is subtle and takes longer. Perhaps mic elements will fail faster than usual.
Perhaps their average lifespan will be 2 years instead of 20.
The difference might not be enough to notice, but we can fix it anyway. Worst case design will save the day.
Replacing the BITX 40 BFO
The BITX 40 is all about modifications. The design itself is “cheap and cheerful”, and the circuit board is laid out to invite changes and experiments. I have a list of quirks I intend to fix in
mine, and with that the mods began.
First up was a misalignment of the BFO. Each BITX 40 uses a set of 5 matched crystals, four for the IF filter and the fifth for the BFO. The BFO is set up to pull the crystal frequency slightly to
put the audio passband in the right place, or at least it is supposed to. On mine, the BFO frequency was just inside the IF passband.
Having the BFO in the wrong place had several consequences. First, receive audio was bassy, running from about 0 Hz to 1800 Hz. This transmits audio frequencies that are not useful for communications
and omits the ones around 2 kHz that are especially important. Worse, the passband actually stretch below 0 Hz, into the upper sideband, which meant that my transmitter was not suppressing the
carrier. It was sending VSB, vestigial sideband, not SSB. That may be fine if you’re a TV transmitter, but it’s not the kind of clean SSB signal hams expect.
One solution, which Wayne NB6M used on his BITX 40, is to change the “pulling” capacitor in the BFO to put the frequency where it belongs. Instead, I replaced the BFO entirely with a spare channel on
the Si5351 frequency synthesizer.
I started off by attaching wires to pins 8 and 9 of the Raduino board. These are Si5351 channel 0 and ground, respectively. For quick progress, I used a twisted pair. When I box it up, I will switch
to coax and use a connector to make maintenance easier.
At the other end, I attached the wires to pins 1 and 6 of T4. This supplies the BFO to the second mixer.
Finally, I unsoldered R101 and C106 to remove power from the analog BFO and disconnect it from the second mixer.
With the hardware work done, I turned to the Arduino code. I downloaded Ashhar Farhan’s original bitx40 sketch and added one line of code near the bottom of setup().
si5351.set_freq(bfo_freq * 100ULL, SI5351_CLK0);
Then I turned it on, saw that the BFO was now too far above the IF passband, and with a couple of experiments, came up with the following edit near the top of the sketch:
#define INIT_BFO_FREQ (11997000L)
unsigned long baseTune = 7100000L;
unsigned long bfo_freq = INIT_BFO_FREQ;
With that, I was done. The rig sounds better and works better. I still haven’t transmitted, though. That will take one more mod which I will write about next.
BITX 40!
I’ve decided to build a BITX 40. This petite SSB transceiver sells for a mere $59, some assembly required. As it comes, it puts out approx. 7W, and with some straightforward upgrades it can produce
25W. It comes as a fully-assembled PCB plus most of the parts needed to hook it up. A case, speaker, and a few other incidentals are not included. The board and radio are designed to invite hacking
and customization. It is also designed to serve as an introduction to homebrewing for hams who may not be ready to build a radio from scratch. For more information on the BITX-40, see its supplier
http://www.hfsigs.com/ and the active and helpful support community at groups.io.
My BITX 40 is operable “al fresco” on my workbench. The included Arduino/Si5351 VFO works fine and tunes the full 40m band. It needs a little bit of work before I can transmit with it. It’s important
to understand that the BITX 40 is not a turnkey rig. Many of them ship with small flaws, and figuring out and fixing the flaws is part of the fun. (This is why that helpful community at groups.io is
so important.) Mine shares a flaw with Wayne, N6BM’s BITX 40 — the BFO frequency is inside the IF passband, instead of about 300 Hz below the passband like it should. This means that stations I tune
sound bassy, I can hear part of the opposite sideband, and when I transmit, the carrier is not suppressed.
(I suppose I could call it “vestigial sideband”, like what NTSC TV uses, but it’s supposed to be SSB…)
Wayne fixed the problem by changing a capacitor in the BFO circuit to pull the frequency where it needed to be. I plan to fix it by disabling the analog BFO and instead use a spare Si5351 output.
Having a tunable VFO will let me put the passband exactly where I want. With a little more code, it will also give me passband tuning.
I think I found a bug in the microphone amp that I’m going to take a closer look at, and I found a perfect case at the Mike and Key hamfest in Puyallup last month. I didn’t even try to negotiate the
price. It was free!
I’ll have more on my BITX 40 project in upcoming posts. | {"url":"http://skywired.net/blog/2017/04/","timestamp":"2024-11-06T20:57:42Z","content_type":"text/html","content_length":"50944","record_id":"<urn:uuid:55a677e5-004a-4b24-8008-54a2d3485377>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00248.warc.gz"} |
[Solved] Exercise 2 Several years ago, ballots in | SolutionInn
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Exercise 2 Several years ago, ballots in Champaign-Urbana contained the following question to assess public opinion on an issue: Should the State of Illinois legalize
Exercise 2 Several years ago, ballots in Champaign-Urbana contained the following question to assess public opinion on an issue: \"Should the State of Illinois legalize and regulate the sale and use
of marijuana in a similar fashion as the State of Colorado?\" Suppose we obtain a random sample of 80 Champaign voters, of which 55 support marijuana legalization. We also obtain a random sample of
100 Urbana voters, of which 75 support marijuana legalization. Let pc be the true proportion of Champaign voters who support marijuana legalization, and let pu be the true proportion of Urbana voters
who support marijuana legalization. (a) Calculate a 95% confidence interval for pu - pc. (b) Calculate the p-value for the test Ho: pu = pc versus H1: pu # pc. Using a level of significance of a=
0.05, make a decision about the null hypothesis and provide a concluding statement in the context of this situation
There are 3 Steps involved in it
Step: 1
1 Define the Proportions Let p c pc pc be the true proportion of Champaign voters who support marijuana legalization Let p u pu pu be the true proport...
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MANOVA.RM 0.5.4
• fixing minor errors and bugs, including order of factors
• removing GUI since package RGtk2 no longer exists
MANOVA.RM 0.5.1
• improve RM function such that
□ no interaction term necessary
□ within-subjects factor can be explicitely specified (instead of no.subf)
• speed up computation time by removing parallel computing
MANOVA.RM 0.4.3
• fix ordering of data for multRM
• update documentation
• fix bug in simCI without interactions
• improve error messages for missing data
MANOVA.RM 0.4.1
• include new function multRM for multivariate repeated measures designs
• update documentation and vignette
• update output of RM (now also states the names of the within-subject factors)
• improve post-hoc comparisons
MANOVA.RM 0.3.4
• include warning for incorrectly labelled subjects (in RM designs with more than one whole-plot factor)
• include graphics for example documentation
• update package description
• implement checks for missing values in RM
MANOVA.RM 0.3.1
• implementation of post-hoc comparisons
• formula without interaction term possible (in MANOVA)
• warning message for singular covariance matrices (RM)
• improve runtime for permutation
• improve output
• allow for univariate calculations in MANOVA.wide
MANOVA.RM 0.2.3
• add documentation for S3 methods
• improve documentation in vignette
• fix handling of variables coded as factors in nested designs
MANOVA.RM 0.2.2
• warning message for singular covariance matrices
• implement output of confidence intervals for interactions (RM design, option: CI.info in plot(…))
MANOVA.RM 0.2.1
• improved plotting routine for RM models, now allowing for more user-specified parameters
• parametric bootstrap now also implemented for the ATS in RM-Designs
• excluded calculation for ATS in multivariate settings (no sensible test statistic in this context)
• fixed some bugs in ordering of data for multivariate higher-way layouts and setting of random seed in permutation procedure
• CIs can now also be calculated using the resampling quantiles of the WTS
• include factor AgeGroup in EEGwide data
MANOVA 0.1.2
• included EEG data example in wide format
• fixed a bug in the calculation of mean values and covariances in the MANOVA() function (one-way layout)
MANOVA 0.1.1
• included new function MANOVA.wide() for data provided in wide format
• fixed a bug in the calculation of mean values and covariance matrices in two- and higher-way layouts
• re-structured the analysis of nested designs
MANOVA 0.0.5
• included calculation and plotting options for confidence ellipsoids for contrasts in multivariate factorial designs
• fixed some bugs in Wild bootstrap routine and one-way designs
• included modified ATS (MATS) and parametric and wild bootstrap thereof in MANOVA()
MANOVA 0.0.4
• fixed small bug in the parametric bootstrap routine in the RM() function
MANOVA 0.0.3
• fixed some bugs in the MANOVA() function, especially in the parametric bootstrap | {"url":"https://cran.opencpu.org/web/packages/MANOVA.RM/news/news.html","timestamp":"2024-11-09T22:48:56Z","content_type":"application/xhtml+xml","content_length":"5488","record_id":"<urn:uuid:6dd34d00-d43c-44aa-8923-46a52b3303ab>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.10/warc/CC-MAIN-20241109214337-20241110004337-00098.warc.gz"} |
Evelyn Agard | Calculus Tutor on HIX Tutor
Evelyn Agard
Calvin University
Calculus teacher | Tutor for 10 years
I hold a degree in Calculus from Calvin University. My passion lies in unraveling the intricacies of mathematical concepts and sharing my knowledge with students. With a keen eye for detail and years
of experience, I specialize in simplifying complex calculus topics. My approachable demeanor fosters an environment where students feel comfortable asking questions and exploring mathematical
theories. I am dedicated to helping learners build a strong foundation in calculus and achieve academic success. Let's embark on this mathematical journey together. | {"url":"https://tutor.hix.ai/tutors/evelyn-agard","timestamp":"2024-11-13T22:41:22Z","content_type":"text/html","content_length":"563370","record_id":"<urn:uuid:858352da-a638-42cf-8b75-5cb1afadbe79>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00495.warc.gz"} |
The What & More Importantly, The Why of the Weibull Analysis - HP Reliability, an Eruditio LLC company.The What & More Importantly, The Why of the Weibull Analysis
How to conduct a Weibull analysis and the questions the analysis will generate.
Often the message is not obvious.
There is the immediate failure. And, if we’re paying attention we can sort out the root cause of the failure along with replacing or repairing the damaged parts. Sometimes though the damage is caused
by another issue with the system.
Something was hidden.
Keep in mind that for any complex system there are thousands of possible ways it can manifest a failure. From alignment errors to lubrication mistakes, to material degradation or wear, there are
clues and indications in every failure.
The Time Element of Data
As you track and record your team’s corrective maintenance activities, you are also gathering essential information to learn about your equipment. Beyond the components involved in the repair, what
else did you learn:
• The time of the failure (reported)
• The failure mode or symptoms
• The root cause, possibly
• The corrective action taken to restore the system
I would say the most important element learned is the time of the failure. The time of day isn’t all the important, yet the time since installation or since the last failure involving that part is
As you know, there are different ways, say, a motor can fail. It could be defective or damaged when installed, and it will likely fail shortly after installation. It could be accumulating damage and
slowing losing its ability to operating under peak loads. Or, the bearings may be wearing out.
In each case, the remedy, to really fix the issue is different. We need to look at the repair data including the time to failure information.
The Data Analysis
Given any set of data, the first step in the analysis is nearly always a plot. No different when given time to failure data.
Let’s say we have 10 identical motors (same size and from the same vendor) installed across the production line. We know when each motor was placed into service.
Five of the motors have failed and have been replaced. Five have not. A histogram, boxplot or timeline may provide some information. My choice for this type of data is a Weibull cumulative
distribution function (CDF) plot.
The Weibull CDF plot is on a log-log set of scales. The horizontal axis is time (could be cycles, operating or calendar time, etc.). The vertical access is the probability of failure, from near zero
to 1, often we use 0.01 to 0.99 indicating a 1% to 99% chance of failure.
To plot the data we need to know how long each motor has been in operation. From installation to failure or till the last time we knew the motor was still working (we call this right censoring as we
do not know when it will fail in the future, just that it is still running at this point).
Therefore, if one of our motors of the five that have failed, failed 100 days after installation, we will plot the first point above the 100-day point on the x-axis.
One way to do this is to estimate the CDF (or the cumulative percent failure). Intuitively we could use 100 ( i / n ) with my failures out of n units under test. Thus if with 10 motors, the first
failure (i=1) time would be plotted at the 10% point on the vertical axis. This method is generally an overestimate or biased.
The approximate median rank estimate is generally accepted as addressing the bias adequately and relatively simple to use. For each time t[i], of the i-th failure, calculate the CDF or percentile
using 100 ( i – 0.3 ) / n + 0.4 ).
If we have 10 units that have failed out of 10 units or complete data that first point plotted would be at 6.73% and the time of the first failure. And, the 10th point would be at 93.3% and the time
of the last failure.
If the 5 failures were from a group of 10 units, as in our motor example, then 5 of the motors are right censored. Using the median rank estimate formula the first point would be at 6.73% and the
time of the first failure., in this case, 100 days.
The 5th point would be at 45.19% and the time of the fifth failure.
The Weibull Analysis Basics
After plotting the points on a log-log scale, properly accounting for the motors that have not yet failed (right censored). We have a few dots on a graph. What does this tell us?
Without getting into regression algorithms, like least squares, median ranks, or maximum likelihood, we can simply take out our ruler and align a best-fit line to the data. Draw a straight line that
generally describes the location of the data.
If the line fits the data as a straight line (not a convex or concave pattern to the data points) then we may have data that can be described by the Weibull distribution. Basically, if the data
describes a straight line as plotted on a log-log graph, the Weibull distribution may adequately describe the time to failure data.
This has a few advantages since the slope of the line, provides information concerning the nature of the failures. It may help us in an investigation concerning the motor failures. Plus, the plot
provides a crude indication of the chance of failure over time for the remaining motors.
The beta, β, value is called the shape parameter and describes the shape of the distribution, think histogram. It ranges from describing data with a decreasing failure rate over time, β <1, to a
data with an increasing failure rate, β >1. When β =1 the Weibull distribution exactly equals an Exponential distribution, and describes a constant failure rate (which is very rare).
If the slope is less than one, the likely causes are faulty motors out of the box, shipping or installation damage, improper installation or similar. A detailed failure analysis may reveal the issue
only impacts a small percentage of all motors or impacts all motors, yet the longer the motors run, the less chance that this particular failure mechanism will occur.
I should mention that if the data does describe straight line it generally means there is a single failure mechanism involved. If the line is not straight, it is likely there are two or more
underlying causes of the failures. With only five failures, you should rely on root cause analysis as the plot itself may be misleading.
Now, if the slope of the fitted line is greater than one, it indicates an increasing chance of failure over time. This is wear out. The causes are as you would suspect, wear, corrosion, drift,
accumulated damage, etc.
What Action Do We Take?
We gather time to failure data, account for censored data, plot data and fit a line. The analysis considers the slope of the line (if straight) and gleans a few clues about the source of the
That’s not all we can learn from the analysis. We can also make a decision about the remaining motors still operating in the plant. Based on the slope of the fitted line, we can decide to leave the
remaining motors on the line in operation or plan to conduct some preventative maintenance to replace the motors likely to fail soon.
If the slope is less than one, the remaining motors have a reduced chance of failure than previously. Leave them in operation as replacing them will only increase the chance of failure. Of course,
over time other failure mechanisms will appear, so continue to monitor the time to failure data.
If the slope is greater than one, the remaining motors are likely wearing out. This means these motors have an increasing chance of failure with time. Thus, depending on the steepness of the slope,
you can project the probability of failure for the remaining units.
If the cost of unplanned downtime is high and replacing a failure motor is expensive, plan on replacing the motors before they fail (or the probability of failure becomes unacceptable.)
For non-repairable data, a Weibull analysis is a great way to visualize and understand the time to failure data you likely already have available. There are various software packages and tools
available to make the fitting the line process more accurate, yet the basics of simply plotting the data can be done on log paper or via your favorite spreadsheet.
Plot the data – a great first step with any data analysis. Learn to read these plots and take appropriate action to improve your program.
I would like to thank Fred for sharing his knowledge on the Weibull Analysis. In the next post, we will explore the Crow-AMSAA Analysis (or Reliability Growth Analysis). Do you use Weibull in your
organization? If not, why?
Fred Schenkelberg is an experienced reliability engineering and management consultant with his firm FMS Reliability. His passion is working with teams to create cost-effective reliability programs
that solve problems, create durable and reliable products, increase customer satisfaction, and reduce warranty costs. If you enjoyed this article, consider subscribing to the ongoing series
at Accendo Reliability.
The other articles in the series include:
Post 1 – Using the Maintenance Data You Already Have
Post 2 – The What & More Importantly, The Why of the Weibull Analysis
Post 3 – Quantify the Improvements with a Crow-AMSAA (or RGA)
Post 4 – Using a Mean Cumulative Plot
Post 5 – The Next Step in Data
Post 6 – The Next Step in Your Data Analysis
Post 7 – Data Q&A with Fred & James
Fred Schenkelberg
FMS Reliability
Accendo Reliability
New Weibull Handbook
By James Kovacevic|2019-04-19T15:50:01-04:00June 13th, 2016|Defect Elimination, Reliability Engineering|Comments Off on The What & More Importantly, The Why of the Weibull Analysis
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Algebraic and Geometric Methods in Engineering and Physics — 1st Semester
Lecturer: José Natário
Email: jnatar@math.tecnico.ulisboa.pt
Office: Mathematics Building, 4th floor, room 4.29
Classes: Mondays from 12:00 to 14:00 in classroom P1 and Tuesdays from 9:00 to 11:00 in classroom Q4.2
Office Hours: Wednesdays from 14:00 to 16:00 in this Zoom session
The seminars will be held on 15 February (from 14:30) and on 22 February (from 10:00 and from 14:30) on this Zoom session, and will have the duration of 25 minutes (+5 minutes for questions).
A PDF file containing the slides for the presentation must be handed in by the end of the day of the presentation (at the latest).
The subject may be any application of algebra, geometry or topology to physics or engineering, and should be explained at a level appropriate for students of this course (all of whom will be
Here are some suggestions of possible seminar subjects:
Crystallographic groups;
Error-correcting linear codes;
Finite geometry and the card game Dobble;
Frieze groups;
Gauge theories and the Standard Model of particle physics;
Molecular symmetries;
Noether's theorem;
Representations of SU(2) and spin;
Representations of SU(3) and quarks;
Rubik's cube group
Spherical harmonics and atomic orbitals;
Topological data analysis.
Topics of algebra and applications: Rings, fields and modules. Groups, actions and representations of finite groups. Applications: Information security, vibrations of symmetric structures, structural
optimization using representations of finite groups.
Topics of geometry and topology and applications: Elements of topology. Topological spaces and metric spaces. Fundamental group and coverings. Simplicial complexes and homology. Manifolds and tensor
fields. Riemannian manifolds. Forms and integration. De Rham cohomology. Flows of vector fields. Lie derivatives and symmetry group of a tensor field. Morse theory. Aplications: data science and
persitent homology, applications of Morse theory to big data, cosmological models.
Lie algebras, Lie groups and applications: Lie groups and Lie algebras. Compact Lie groups and their Lie algebras. Root systems. Elements of the theory of representations. Lie group actions on
manifolds. Aplications: Statics and dynamics of robots, grassmanians and flag manifolds, particle physics and theories of unification.
We will use these lecture notes, which will be updated as the course progresses. See the bibliography in the notes for more references.
Seminar: Students must prepare and present a seminar explaining some application of algebra, geometry or topology to physics or engineering. The classification obtained in this presentation will make
up 50% of the final grade.
Exam: There will be an exam counting 50% towards the final grade. Students will be able to repeat this exam if necessary. | {"url":"https://www.math.tecnico.ulisboa.pt/~jnatar/MAGEF-20/","timestamp":"2024-11-05T13:21:05Z","content_type":"application/xhtml+xml","content_length":"16574","record_id":"<urn:uuid:38faca9d-b6ee-47dd-ad54-282d16341b62>","cc-path":"CC-MAIN-2024-46/segments/1730477027881.88/warc/CC-MAIN-20241105114407-20241105144407-00539.warc.gz"} |
10,475 research outputs found
Eighteen high dispersion International Ultraviolet Exploration spectra of 6 stars in the large magellanic cloud (LMC) 3 stars in the small magellanic cloud (SMC) and 2 foreground stars were studied.
Fourteen spectra cover the wavelengths lambda 1150-2000 A and 4 cover lambda 1900-3200 A. All the Magellanic Cloud star spectra exhibit exceedingly strong interstellar absorption lines due to a wide
range of ionization stages at galactic velocities and at velocities associated with the LMC or SMC. The analysis is restricted to the Milky Way absorption features. Toward the LMC stars, the strong
interstellar lines have a positive velocity extension, which exceeds the extension recorded toward the SMC stars. The most straightforward interpretation of these velocity extensions is obtained by
assuming that gas at large distances away from the plane of the galaxy participates in the rotation of the galaxy as found in the galactic disk
Using molecular dynamics (MD) simulations, we find the formation of heaps in a system of granular particles contained in a box with oscillating bottom and fixed sidewalls. The simulation includes the
effect of static friction, which is found to be crucial in maintaining a stable heap. We also find another mechanism for heap formation in systems under constant vertical shear. In both systems,
heaps are formed due to a net downward shear by the sidewalls. We discuss the origin of net downward shear for the vibration induced heap.Comment: 11 pages, 4 figures available upon request, Plain
TeX, HLRZ-101/9
We report experimental measurements of avalanche behavior of thin granular layers on an inclined plane for low volume flow rate. The dynamical properties of avalanches were quantitatively and
qualitatively different for smooth glass beads compared to irregular granular materials such as sand. Two scenarios for granular avalanches on an incline are identified and a theoretical explanation
for these different scenarios is developed based on a depth-averaged approach that takes into account the differing rheologies of the granular materials.Comment: 4 pages, 4 figures, accepted to Phys.
Rev. Let
We present an implementation of realistic static friction in molecular dynamics (MD) simulations of granular particles. In our model, to break contacts between two particles, one has to apply a
finite amount of force, determined by the Coulomb criterion. Using a two dimensional model, we show that piles generated by avalanches have a {\it finite} angle of repose $\theta_R$ (finite slopes).
Furthermore, these piles are stable under tilting by an angle smaller than a non-zero tilting angle $\theta_T$, showing that $\theta_R$ is different from the angle of marginal stability $\theta_{MS}$
, which is the maximum angle of stable piles. These measured angles are compared to a theoretical approximation. We also measure $\theta_{MS}$ by continuously adding particles on the top of a stable
pile.Comment: 14 pages, Plain Te
We discuss the fragmentation of a heavy quark to a baryon containing two heavy quarks of mass $m_Q\gg\Lambda_{\rm QCD}$. In this limit the heavy quarks first combine perturbatively into a compact
diquark with a radius small compared to $1/\Lambda_{\rm QCD}$, which interacts with the light hadronic degrees of freedom exactly as does a heavy antiquark. The subsequent evolution of this $QQ$
diquark to a $QQq$ baryon is identical to the fragmentation of a heavy antiquark to a meson. We apply this analysis to the production of baryons of the form $ccq$, $bbq$, and $bcq$.Comment: 9 pages,
1 figure included, uses harvmac.tex and epsf.tex, UCSD/PTH 93-11, CALT-68-1868, SLAC-PUB-622
We perform the first numerical three-dimensional studies of quantum field effects in the Bosenova experiment on collapsing condensates by E. Donley et al. [Nature 415, 39 (2002)] using the exact
experimental geometry. In a stochastic truncated Wigner simulation of the collapse, the collapse times are larger than the experimentally measured values. We find that a finite temperature initial
state leads to an increased creation rate of uncondensed atoms, but not to a reduction of the collapse time. A comparison of the time-dependent Hartree-Fock-Bogoliubov and Wigner methods for the more
tractable spherical trap shows excellent agreement between the uncondensed populations. We conclude that the discrepancy between the experimental and theoretical values of the collapse time cannot be
explained by Gaussian quantum fluctuations or finite temperature effects.Comment: 9 pages, 4 figures, replaced with published versio
For a solar flare occurring on 2010 November 3, we present observations using several SDO/AIA extreme-ultraviolet (EUV) passbands of an erupting flux rope followed by inflows sweeping into a current
sheet region. The inflows are soon followed by outflows appearing to originate from near the termination point of the inflowing motion - an observation in line with standard magnetic reconnection
models. We measure average inflow plane-of-sky speeds to range from ~150-690 km/s with the initial, high-temperature inflows being the fastest. Using the inflow speeds and a range of Alfven speeds,
we estimate the Alfvenic Mach number which appears to decrease with time. We also provide inflow and outflow times with respect to RHESSI count rates and find that the fast, high-temperature inflows
occur simultaneously with a peak in the RHESSI thermal lightcurve. Five candidate inflow-outflow pairs are identified with no more than a minute delay between detections. The inflow speeds of these
pairs are measured to be 10^2 km/s with outflow speeds ranging from 10^2-10^3 km/s - indicating acceleration during the reconnection process. The fastest of these outflows are in the form of
apparently traveling density enhancements along the legs of the loops rather than the loop apexes themselves. These flows could either be accelerated plasma, shocks, or waves prompted by
reconnection. The measurements presented here show an order of magnitude difference between the retraction speeds of the loops and the speed of the density enhancements within the loops - presumably
exiting the reconnection site.Comment: 31 pages, 13 figures, 1 table, Accepted to ApJ (expected publication ~July 2012
A time-domain simulation program has been developed to provide an accurate description of interferometric gravitational wave detectors. This is being utilized to build a model of LIGO with the aim of
aiding in the shakedown and integration of the interferometer subsystems, and ultimately the optimization of detector sensitivity | {"url":"https://core.ac.uk/search/?q=authors%3A(S.%20B.%20Savage)","timestamp":"2024-11-11T07:24:25Z","content_type":"text/html","content_length":"151165","record_id":"<urn:uuid:811af3ae-67fa-46bd-9a49-d6892a243855>","cc-path":"CC-MAIN-2024-46/segments/1730477028220.42/warc/CC-MAIN-20241111060327-20241111090327-00550.warc.gz"} |
Free Printable Loco Sudoku Puzzles Sudoku Printable | Sudoku Printables
Free Printable Loco Sudoku Puzzles Sudoku Printable
Free Printable Loco Sudoku Puzzles Sudoku Printable – If you’ve had any issues with sudoku, you’re aware that there are several kinds of puzzles to choose from and it’s hard for you to pick which
ones you’ll need to solve. There are many different ways to solve them. In fact, it is likely that an printable version of sudoku can be an excellent method to begin. The guidelines for solving
sudoku are similar to the rules for solving other puzzles however, the format of sudoku varies slightly.
What Does the Word ‘Sudoku’ Mean?
The word “Sudoku” is derived from the Japanese words suji and dokushin which translate to ‘number’ and ‘unmarried person as well as ‘unmarried. The objective of the puzzle is to fill in every box
with numbers such that each number from one to nine appears only once on each horizontal line. The word Sudoku is an emblem from the Japanese puzzle manufacturer Nikoli which was established in
The name Sudoku originates by the Japanese word shuji wa dokushin ni kagiru meaning ‘numbers should be single’. The game is comprised of nine 3×3 squares and nine smaller squares inside. In the
beginning, it was called Number Place, Sudoku was an educational puzzle that encouraged mathematical development. While the origins of this game remain a mystery, Sudoku is known to have roots that
go back to the earliest number puzzles.
Why is Sudoku So Addicting?
If you’ve played Sudoku, you’ll know how addictive the game can be. The Sudoku addicted person will be unable to stop thinking about the next puzzle they can solve. They’re always thinking about
their next puzzle, while different aspects of their lives tend to be left to sidelines. Sudoku is a game that can be addictive, but it’s important that you keep the addictive potential of the game in
check. If you’ve become addicted to Sudoku Here are some methods to reduce your dependence.
One of the most common methods to determine if your addiction to Sudoku is to look at your behavior. Most people carry books and magazines with them While others just scroll through social media
updates. Sudoku addicts carry newspapers, books, exercise books, as well as smartphones wherever they travel. They are constantly solving puzzles, and they cannot stop! Some people even find it
easier to solve Sudoku puzzles than standard crosswords, and they’re able to stop.
Printable Loco Sudoku
What is the Key to Solving a Sudoku Puzzle?
A good strategy for solving the printable sudoku puzzle is to practice and experiment with different approaches. The top Sudoku puzzle solvers don’t use the same method for each puzzle. The key is to
try out and test various methods until you can find the one that is effective for you. After a while, you will be able solve puzzles without a problem! But how do you learn to solve sudoku puzzles
that are printable sudoku problem?
In the beginning, you must grasp the basics of suduko. It is a game of reasoning and deduction, and you need to examine the puzzle from a variety of angles to spot patterns and work out the puzzle.
When solving a suduko puzzle, you should not try to figure out the numbers; instead, you should look over the grid for clues to spot patterns. It is also possible to apply this strategy to squares
and rows.
Related For Sudoku Puzzles Printable | {"url":"https://sudokuprintables.net/printable-loco-sudoku/free-printable-loco-sudoku-puzzles-sudoku-printable/","timestamp":"2024-11-08T20:20:48Z","content_type":"text/html","content_length":"24346","record_id":"<urn:uuid:7cc671fd-c48c-4ef4-8757-512ef30a86b0>","cc-path":"CC-MAIN-2024-46/segments/1730477028079.98/warc/CC-MAIN-20241108200128-20241108230128-00148.warc.gz"} |
Summer Undergraduate Math Research at Yale
This is the list of projects for 2019.
Closed geodesic on flat spaces
In Euclidean space, the shortest path between two points is a straight line. In non-Euclidean spaces, geodesics abstract the notion of a straight line. For example, on the sphere the shortest paths
are the great circle geodesics, and we fly “over the pole” when traveling from NYC to Paris. Last summer students studied closed geodesics on doubled polygons, where geodesics billiard off the
edges. This summer, we’ll consider closed geodesics on flat surfaces, generalizations of doubled polygons which locally exhibit Euclidean geometry while globally having properties of negative
Mentor: Ian Adelstein and Aaron Calderon
Primitive sets of polynomials
A set of integers is primitive if no number in the set divides another. For example, the prime numbers form a primitive set, however there are many other examples. There are even primitive sets
which are `”larger” than the primes. In this project we will look at primitive sets of polynomials with coefficients from a finite field. This ring of polynomials over a finite field behaves in
many ways like the integers, but the techniques for studying problems over this ring are often more combinatorial than over the integers. We will investigate what the “largest” primitive sets are in
this setting, as well as counting how many primitive sets there are. A convenient way to model the situation is using divisibility graphs, and so related questions involving independent vertex sets
of graphs may be considered as well.
Mentor: Nathan McNew
Multiscale Analysis on Graphs
Kernel-based techniques are a set of Harmonic Analysis tools for graphs and manifolds that address critical challenges in the analysis and storage of large datasets. Diffusion Maps, introduced by
Coifman and Lafon, is a multiscale, non-linear algorithm in this family. This technique unveils the underlying manifold, usually a lower-dimensional in which the data is embedded, using the
eigenvalues and eigenvectors of the diffusion operator on the data. Diffusion Maps have gained popularity in many applications that require dimensionality reduction and feature extraction. This
project is two-folds: first, we use Diffusion Maps in conjunction with other machine learning tools, e.g., neural nets, to analyze medical data, and second, we look at Diffusion Maps in the broader
context of Harmonic Analysis and establish links between diffusion methods and composite dilation methods on Euclidean spaces. Some coding experience is recommended but not required.
Mentor: Karamatou Yacoubou Djima
Geometry Group (Isoperimetric Problems)
In Euclidean space (and in hyperbolic space) the round sphere provides the least-area way to enclose given volume—solves the isoperimetric problem. What happens if you give space a density that
weights both area and volume? In the Euclidean plane the regular hexagonal provides the least-perimeter tile of fixed area. What happens in the hyperbolic plane? For some earlier results and
references, see “Geometry Group 2019” at
and also
July 13-27 we’ll go on a retreat to Ocean City, New Jersey, living and working together free from the usual distractions; the four of you will be provided with two bedrooms to share (each with two
beds, or other options). In the past, this retreat has been crucial to making headway in parts that require a great deal of focused attention.
Mentor: Frank Morgan
Intersections of virtual multistrings
In this project, we will explore the interplay between the combinatorial and geometric models of closed curves on surfaces. Turaev, Henrich, and Cahn used the combinatorial model to develop a based
matrix associated to a single closed curve, an object that captures various geometric properties of the curve. More recently, this notion was extended to multiple curves, but it is unknown how much
geometric data is captured by this generalized based matrix. Of particular interest is the minimal number of intersection points between two curves. Based matrices and other operations provide lower
bounds on this quantity and we want to develop a better classification of the strengths of each of these techniques. All of these questions should be accessible to undergraduates and can be tailored
to their backgrounds.
Mentor: David Freund | {"url":"https://sumry.yale.edu/sumry-2020/2019-project-descriptions","timestamp":"2024-11-02T02:44:58Z","content_type":"text/html","content_length":"26234","record_id":"<urn:uuid:95a86eb5-054f-4009-8905-afc4be534395>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00228.warc.gz"} |
Why Homework Assignments Are Important
College homework is an essential part of the learning process. Besides helping students revise the information taught in class, it also contributes to the overall performance of the students. Thus,
ensuring that your college homework is excellent can be a priority. Moreover, a well-researched assignment contributes to the overall performance of the students. Thus, it can be challenging to
produce eye-catching papers if you have no clue how to go about it. On the other hand, it is advantageous to students that they can organize their papers systematically https://www.privatewriting.com
/. Hence, your lecturer will expect you to produce an excellent article if you committed yourself adequately. A well-researched assignment can help you to develop a pattern of evaluating your
classmates. For instance, you can look at the frequency of letters that students reply to their assignments. If you conclude that these comments show a clear correlation between the homework and
performance, you can get a hint of the kind of assessment you can expect.
Benefits of College Homework
Some of our benefits include:
1. Homework helps students to develop a routine that ensures all the assignments they give are done effectively.
2. college students help improve their academic skills. It allows them to gain a better understanding of the English language.
3. Homework enables students to create a foundation of conduct that allows them to stay on track with the assignments.
4. College homework assignments help students to establish a standard of their performance. Thus, it allows them to build on the skills they have acquired over time.
Parts of the Homework Assignment Test
The tests cover everything from simple simple questions like a vocabulary check to complex math problems. Therefore, you should be prepared to tackle any question that you throw at you. Remember, if
you do not understand any concept, chances are you will not answer the questions as required. Therefore, you should comprehensively analyze your college homework. Take the time to understand the
questions and derive the answer. If you end up not finding an answer, you should revise your task accordingly. Moreover, you should take the time to practice your skills in the area of
problem-solving. Furthermore, regular practice will help you to identify the areas where you do not understand. As such, you will have ample time to correct your mistakes. Additionally, you will have
a clear idea of what you should work on in the future. Competently, you should not be afraid to put in the work. | {"url":"https://towering-shadow-angelfish.glitch.me/","timestamp":"2024-11-13T12:09:30Z","content_type":"text/html","content_length":"3339","record_id":"<urn:uuid:3ce168c5-1b18-4d9a-9b0c-fe809b2eebe7>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00468.warc.gz"} |
magnet gauss - Osenc
Last Updated on
February 10th, 2023 10:50 pm
In this business, we often hear about Magnet Gauss, but we have a question now, what is Gauss? How much can Gauss be achieved with magnetism? How do we know how much Gauss does the magnet has? How
much can Gauss be used for the commonly used N35 and N38? In this post, we would like to explain it to you, one by one in an easy way:
Gauss is a unit of the magnetic field. This unit is part of the Gaussian system of units, which was inherited from the older CGS-EMU system. 5000 Gauss represents your magnet with a maximum magnetic
field of 5,000 Gauss. But please note,if you use a gauss meter to check the magnetic strength field. That is to measure the Gauss value of a certain point. It means that the magnetic field strength
of a certain point on the magnet is 5000 Gauss, while the Gauss value of other points is not the same.
How Much Can Gauss Be Achieved By Magnetism?
This question is very general, and we don’t know how to answer it and make you satisfied. Because the magnet’s magnetic level is related to many factors, such as the grade of magnets, the
specifications of the magnet, the thickness, and so on.
But we have collected some common specifications of magnet Gauss for your reference
• Such as 10 * 4 N35 Gauss material can reach about 3,000-3,200 Gauss, 10 * 5 to about 3,400-3,600 Gauss.
The surface magnetic field of a single NdFeB magnet is 3,000-7,000G, ferrite 300-800G, samarium cobalt, and AlNiCo 2,000G. Neodymium iron boron should be considered a very high permanent magnet, but
it is difficult to reach 5,000 or more.
N35 and N38 are probably up to 2,000GS. If the size is bigger, N35 can reach 3,500GS at most, and N38 can reach 3,800GS. If there anyone tells you that he can produce a large magnet with 10,000
gausses, you must marry him first, because he has new technology.
In general, the Gauss surface of the magnet is such that it is inversely proportional to the area and is proportional to the thickness.
How to check Gauss value?
We usually use a Gauss meter to measure the Gauss magnet surface. However, the Gauss values measured at different positions on the surface of the magnet are different, the Gaussmeters have different
measured data, and the error is relatively large.
What Is The Difference Between A Gauss Magnet And A Magnetic Flux?
Both Gauss and flux measurements are made to determine the performance of the magnet. The reproducibility of magnetic flux is better than Gauss, more stable, and the error is not too big.
Note: Gauss (Gs) is the unit of measure for magnetic field lines. 1T=10,000 Gs
1Gauss = 1,000 Milligauss
Ordinary gauss meters cannot measure. It should be a dedicated tool to check it. This is a fairly small unit of measurement that the average citizen does not need to use. The more commonly used
situation is to measure whether the magnetic field strength of a package meets the shipping standards of the IATA (International Air Transport Association). The IATA requires that the magnetic field
of the package cannot exceed 0.00525Gauss (525Milligauss)
10,000gauss= 1 Tesla
10 Gauss = 1 Mt
Tesla is the new unit of the International System of Units (SI). This is why we can see that some products are sometimes expressed as Tesla and sometimes as Gauss to express the magnetic field | {"url":"https://osenc.com/magnet-gauss/","timestamp":"2024-11-06T04:19:38Z","content_type":"text/html","content_length":"302080","record_id":"<urn:uuid:0444b9c6-107e-4699-925b-d8bbff3f3660>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00333.warc.gz"} |
To solve this question, we need to use the formula for the heat conducted across a conductor per unit time. We need to assume the dimensions of the rod and the temperature of the reservoir. Putting
these in the formula, we will get the expression for \[Q\]. Then applying the same formula for the second case, we will get the expression for the heat conducted in time $t$, which when compared with
the previous expression will come in terms of \[Q\].
Formula used: The formula used to solve this question is given by
$\dfrac{q}{T} = k\dfrac{{A\Delta T}}{l}$, here $Q$ is the heat conducted in time $t$ across a conductor of length $l$, area of cross section $A$ and the material of thermal conductivity of $k$, and
is subjected to the temperature difference of $\Delta T$ across its ends.
Complete step-by-step solution:
Let the length, the area of cross section, and the thermal conductivity of the metallic rod be $L$, ${A_1}$, and $K$ respectively. Also, let the temperature of the thermal reservoirs be ${T_1}$ and $
{T_2}$. We can represent this situation in the below figure.
We know that the rate of heat conducted per unit time is given by
$\dfrac{q}{T} = k\dfrac{{A\Delta T}}{l}$ (1)
Substituting $k = K$, \[A = {A_1}\], $l = L$, $\Delta T = {T_2} - {T_1}$, $q = Q$ and $T = t$, we get
$\dfrac{Q}{t} = K\dfrac{{{A_1}\left( {{T_2} - {T_1}} \right)}}{L}$....................(2)
Now, according to the question, the rod is melted and from that a new rod of half the radius is formed. We know that the area of cross section is related to the radius as
${A_1} = \pi {r^2}$................(3)
Putting $r' = \dfrac{r}{2}$, we get
${A_2} = \pi {\left( {\dfrac{r}{2}} \right)^2}$
${A_2} = \dfrac{{\pi {r^2}}}{4}$
Putting (3) in the above equation, we get
${A_2} = \dfrac{{{A_1}}}{4}$...................(4)
Since the material of the rod is still the same, there is no change in the thermal conductivity. Also, there is no change in the length and the temperature of the reservoirs. Therefore, if $Q'$ is
the heat conducted by the new rod in time $t$, then it is given by
$\dfrac{{Q'}}{t} = K\dfrac{{{A_2}\left( {{T_2} - {T_1}} \right)}}{L}$ ……………...(5)
Dividing (5) by (2) we get
$\dfrac{{\dfrac{{Q'}}{t}}}{{\dfrac{Q}{t}}} = \dfrac{{K\dfrac{{{A_2}\left( {{T_2} - {T_1}} \right)}}{L}}}{{K\dfrac{{{A_1}\left( {{T_2} - {T_1}} \right)}}{L}}}$
\[ \Rightarrow \dfrac{{Q'}}{Q} = \dfrac{{{A_2}}}{{{A_1}}}\]
Putting (4) above, we get
\[\dfrac{{Q'}}{Q} = \dfrac{{{A_1}}}{{4{A_1}}}\]
\[ \Rightarrow Q' = \dfrac{Q}{4}\]
Hence, the correct answer is option A.Note:
If we do not remember the formula for the heat conducted per unit time, then we can use the analogy between the electric current and the heat to derive the same. As we know that the resistance is
given by $R = \rho \dfrac{l}{A}$ and the electric current is given by $I = \dfrac{V}{R}$. Combining these two, we get the current as $I = \dfrac{{AV}}{{\rho l}}$. The electric current is equivalent
to the heat per unit time, the potential difference is equivalent to the temperature difference, and the reciprocal of resistivity is equivalent to the thermal conductivity. | {"url":"https://www.vedantu.com/question-answer/a-cylindrical-metallic-rod-in-thermal-contact-class-11-physics-cbse-60092883ae05980992f6e1fb","timestamp":"2024-11-10T10:49:45Z","content_type":"text/html","content_length":"179908","record_id":"<urn:uuid:f42e282c-2a5f-4c44-a402-b9302dd1e29a>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00520.warc.gz"} |
Comparison of SARS-CoV-2 Exit Strategies Building Blocks
We consider and compare various exit strategy building blocks and key measures to mitigate the current SARS-CoV-2 pandemic, some already proposed as well as improvements we suggest. Our comparison is
based on a computerized simulation integrating accumulated SARS-CoV-2 epidemiological knowledge. Our results stress the importance of immediate on-symptom isolation of suspected cases and household
members, and the beneficial effects of prompt testing capacity. Our findings expose significant epidemic-suppression differences among strategies with seemingly similar economic cost stressing the
importance of not just the portion of population and business that is released, but also the pattern. The most effective building blocks are the ones that integrate several base strategies - they
allow to release large portions of the population while still achieving diminishing viral spread. However, it may come with a price on somewhat more complex schemes. For example, our simulations
indicate that a personal isolation of 4 days once every two weeks, for example a long weekend (Fri-Mon) self-isolation once every two weeks, while protecting the 5% most sensitive population would
reduce R well below 1 even if ten percent of the population do not follow it. This kind of integrated strategy can be either voluntary or mandatory and enforced. We further simulate the contrasting
approach of a stratified population release in a hope to achieve herd immunity, which for the time being seems inferior to other suggested building blocks. Knowing the tradeoff between building
blocks could help optimize exit strategies to be more effective and suitable for a particular area or country, while maximizing human life as well as economic value. Given our results, we believe
that pandemic can be controlled within a reasonable amount of time and at a reasonable socio-economic burden.
Coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was declared as a pandemic by the World Health Organization ^1. Unfortunately, no vaccine is
available at this time. Therefore, mitigation actions are being taken to minimize both the adverse effects of the pandemic on the economy and the spread of the virus. Currently taken measures are
mostly social distancing, isolation of cases and suspected cases, contact tracing, higher levels of hygiene, facial masks wearing, and mass population quarantines which cause vast socio-economical
damage ^2–6. Going forward there’s a need to easen some of the measures to allow economic activity, while minimizing viral health damage.
One extreme approach is a stratified release of population, lower risk first. The idea is that lower risk individuals would contract the virus, recover and gain immunity, thus slowing the epidemic
rate for future uninfected individuals. The hope is that by the time higher risk individuals are released, the infection probability is greatly reduced and thus infection of the higher risk group is
largely reduced. Hence the term “Herd Immunity”. Care is taken to release at a rate that would not overload the healthcare system.
In the other extreme there are mitigation building blocks based on “social distancing”. These are deliberate measures taken to restrict, slow and limit the spread of the virus such that only a very
small number of individuals will end up infected until the disease is eradicated or a vaccination is available. Social distancing measures could reduce the probability of contracting the virus given
a contact, for example using facial masks, or reducing the rate of contacts of infected and susceptible individuals - thus reducing the spread of the virus ^4–7. These measures typically include
keeping a large portion of the population at home either constantly or intermittently. The challenge is how to reduce the economic and social cost of such measures to an acceptable level while
controlling for viral spread.
The mid-term goal is keeping R[t]<1 through social distancing measures, where R[t] indicates at every time (t) how many secondary infections are caused on average by a single infected case. R[t]>1
means the disease is spreading at an exponential growth rate as each case causes more than a new single case, and R[t]<1 means the disease is diminishing as each case causes less than a new single
case. The special case of R[t]=1 or very close to one is not so theoretic, and suggests the disease continues at a fixed rate of new daily cases. In such a case, a short intervention can reduce the
number of daily cases and then we can continue with the same measures, but in a lower rate of new daily cases. Reduction of new daily cases could also assist in contact tracing, if done manually -
which further slows the epidemic.
R[t] at time zero is called the basic reproduction number R[0]. For SARS-CoV-2 the exact number is under active research and it could change from one country to another or given different
environmental conditions ^8–10, with many estimated values in the range of 2.2-3.2 which means each case causes 2.2-3.2 new cases, unless people have already been infected and cannot get infected
twice. When social distancing measures are taken, the reproduction rate changes, and it is then denoted by R instead of R[0].
Social distancing measures have a potentially high price tag attached to them, both economically and socially. Therefore, once the rate of new infections is low enough, we want to keep R[t]<1 but
close to 1 with measures that cost the least. The situation is constantly changing and keeping R[t]<1 but close to 1 is a moving target - for example there are constant changes in human behaviour,
public attention and public resilience, weather ^11,12 changes, local outbreaks and so on and all could affect R[t]. We need to dynamically try different measures so we keep R[t]<1 but close to 1
while probing and estimating the current situation. Therefore, we could occasionally cross the line to R[t]>1, which means growing infection rates until we take actions to reduce R[t]. The price paid
for social distancing interventions is also in the difficulty of implementing them. Complex measures could mean less compliance and less success in implementation and eventual effectiveness.
As the current goal is to keep R[t] around 1 and the situation is constantly changing, information and response speed are the key. The consequences of quick feedback are priceless compared with
alternatives. If the feedback loop for an action taken is 14-21 days, and during this time the virus could be back propagating at doubling the number of cases every 3-4 days. We could be expecting
3-7 sequential multiplications, i.e., 8-128 fold increase (2^3 to 2^7) in the number of new infections, and following a similar increase in ICU beds. Therefore, lack of prompt feedback, typically
through mass-testing leads to a need to maintain a large spare capacity. Maintaining spare capacity has a large cost associated with it, both monetary and possibly in human life. We propose how to
promptly estimate the number of new infections and thus gain a short response time to actions taken.
In the first part of the paper, key mitigation measures are suggested. Our findings stress the importance of self-isolation upon symptoms until a SARS-CoV-2 test result, and further isolation of
household members if no fast testing is available or if a test returns positive for the virus.
The second part of the paper focuses on comparison between building blocks in terms of their effectiveness in controlling R[t]<1, and effectiveness in terms of percent of population business-day that
is released. Surprisingly, there is a large difference in epidemic-control effectiveness of strategies, while having similar economic costs by releasing the population to a similar extent. The key is
not just the portion of the population that is released, but also the release pattern. This finding suggests that exit strategies could be optimized for both viral spread and economic value. The more
successful strategies were the more complex ones, integrating several ideas. Gaining understanding of the tradeoff is important as it could assist in building an exit strategy suited for a specific
area, in a way that is cost effective and communicable to the public so compliance would be high. For each building block, we give the resulting reduction in R as indicated by our simulation.
For example, to reduce R well below 1 it suffices that every person enters a four-day isolation at their pre-chosen time within each two weeks period while protecting the 5% most sensitive
population. This suggestion works even if people would take their isolation over a long weekend once every two weeks (Fri-Mon), and even if ten percent of the population do not follow it. It works
even if in addition every person in a household chooses a different isolation period, and no isolation is kept among household members.
The reason such a strategy works is three-fold:
1. Interaction is greatly reduced 4 out of 14 days - 28.5% of time is significant in terms of virus spread.
2. Infectiousness onset 3 days on average after contracting the virus. Those that contract the virus during their 10 release days have a good chance to enter their pre-planned isolation shortly
after or before they become infectious and thus infect less.
3. As symptoms typically onset on day 5 from contraction, those that contract the virus during their 10 release days have good chances that symptoms onset would occur during their pre-planned
isolation or shortly after. With self isolation upon symptoms they are likely to be removed from further infecting others.
Together with general social distancing measures such as self-isolation on symptoms and wearing facial masks while outside of home, the result is a reduction of R well below 1.
We give special consideration to the herd immunity approach. Given the knowledge that has already accumulated, our results indicate that for now social distancing is expected to be a significantly
more effective approach than herd immunity, with significantly less casualties across all age groups.
Part I: Key Mitigation Measures
A word of caution. Our results are based on a SEIR agent-based simulator, which we built based on Israeli population structure of nine million people, and based on existing knowledge on SARS-CoV-2
epidemiological behavior. The simulations are performed in a 1-day iteration cycle simulating a period of one year. We distinguish between infection within a household and outside, as existing
literature shows the virus spreads significantly in familial infection clusters ^13. Various exit-strategy building blocks are fed into the simulator so their outcome can be assessed given the
existing knowledge. The simulation is executed 10 times over each set of parameters, but with different random choices. Standard deviation of the results in these runs are given in time-based
figures, when a point value is given it corresponds to the mean result. The exact structure and full list of assumptions is given in the supplementary at the end of this paper.
Proposal 1: Immediate household self-isolation upon first symptom
We propose that the single most cost-effective epidemic control is immediate self-isolation of the entire household upon the first symptom ^14 suspected as related to coronavirus of someone in the
household. Release from isolation is only after a negative laboratory result of the first person in the household to have shown a symptom, and provided that the other members of the household do not
show any symptoms related to coronavirus.
In our simulations, after this measure is taken, R dropped from R[0]=3.03 to R=1.54. This is a dramatic drop by a factor of 1.54/3.03 = 0.508. This drop is compared to the second-best epidemic
control measure: immediate self-isolation on the first symptom of a person (without other household members), which results in R=2.2, a 2.2/3.03=0.726 factor drop. If the symptomatic person
self-isolates on symptoms but we wait with household isolation until the virus test for the symptomatic person returns positive, and assuming a 5-day delay we get a much inferior situation with R=
1.65. The effect size in this case between an immediate household isolation to a delayed one 1.54/1.65 = 0.93 is comparable to the effect of facial masks with protection factor of 10% 2.83/3.03=0.93,
see Figure 2. These few days post symptoms and before diagnosis could be critical for reducing further infections directly or through other household members ^15. See Figure 1. If vast and prompt
tests are in place, the difference between household isolation and personal isolation upon symptoms diminishes, as household members are assumed to enter isolation upon a positive test for one
household member, and get checked themselves.
Immediate self-isolation of the entire household achieves an immediate stop to further spreading of the virus of both possibly affected but asymptomatic members and possibly other affected but
presymptomatic household members. Without fast and prompt testing it would probably not be enough to isolate just the symptomatic person, as research based on experience in China shows that a large
proportion of the infections occur within households ^13,16, see particular example ^17. Patients are pre-symptomatic in the first few days after infection while still being possibly infecting.
Furthermore, it’s estimated that a vast portion of the infections are made by pre-symptomatic or asymptomatic ^18–23. Social distancing measures taken outside the household, reduces non-household
infections. The declining infection rate between households means that relatively, more infection occurs within a household. It is also interesting to notice that areas with larger households are
likely to suffer from a higher R even if all other parameters are the same. Our simulations show that a self household isolation, even on the basis of fever alone of one of the members, has a
dramatic effect in preventing the spread of the epidemic, and should be used together with any other measures taken ^24.
Self-isolation upon symptoms dramatically shortens the spreading period. A study on Chinese experience in Shenzhen shows it took an average of 4.6 days after symptoms onset to isolate an infected
person, which was reduced to 2.7 days if the person was isolated due to contact tracing and not symptoms ^13.
One implementation option is that every person of a household shall self-test for fever every day, with possible daily online compulsory reporting of body temperature as well as onset of other
symptoms. Body temperature could also be checked in key public locations or entry points. We estimate the daily number of new people with fever by assuming 0.3 percent of the adult population shows
fever signs of above 38 Celsius at any given day ^25, and dividing by an average conservative duration of a non-COVID-19 fever disease of 1-4 days^26–28. Therefore, an order of 7,500 to 30,000
isolations shall occur daily and thus this number of daily tests for this purpose would be needed for a country the size of Israel about 9 million people. Only if the first symptomatic household
member is found to be infected, a test would be carried out to the other family members - so the extra tests due to infected household members is expected to be insignificant compared to the
background symptomatic non-SARS-CoV-2 cases.
An improvement to reduce the amount of tests would be using machine learning algorithms utilizing additional external data to release a household from self-isolation without the need for a laboratory
test for the virus. Such external data can include the prevalence of coronavirus in the surrounding area, prevalence of other infectious diseases in the area, workplace, or by information on personal
location voluntarily collected and stored on household members’ mobile phones ^29 etc.
Proposal 2: Focus testing capacity on self-isolated households
Focus testing capacity on quickly testing self-isolated households. This approach simultaneously serves three important purposes in parallel:
1. Quick and accurate measure of actual coronavirus spread - as on average symptoms onset about 5.2 days after infection ^30, and households enter immediate self-isolation, immediate testing gives
an accurate and near real-time measure of virus spread in the community, and could prevent the need for population survey-testing for the virus.
2. Effective contact tracing - Given self-isolated households contain the population with the highest risk of being infected that could have already continued unidentified infection chains, there’s
importance in locating those that are really infected and trace their contacts to isolate them. When testing is done quickly enough, we have better chances of isolating the non-household
individuals that got infected by the detected cases, before they infect others. We note that we did not include contact tracing effects in our simulations, so the total combined effect of
isolation and quick testing could be even stronger than we report.
3. Public Compliance and fast reporting - when the logic behind self-household isolation is shared with the public, and the public knows that they would be released in a short time from
self-isolation if they didn’t contract coronavirus, the public is more likely to comply with the instructions, and with compliance the virus spread would reduce. As symptoms might be mild to
begin with, people might delay the request for a test. In the simulations we assume this delay would be half a day on average as we conservatively assumed people would only comply when having
fever symptoms, and fever can be tested when entering the workplace, schools, and in a variety of other public places. If testing is fast enough, it suffices to isolate only the symptomatic
person until results arrive.
In the unfortunate scenario that there is not enough testing capacity to cover all the new symptomatic candidates, the importance of the proposed self-household isolation is even greater, as
effective contact tracing would not be possible and infection has a significant familial base ^13. In such a case, sample testing of the isolated households might still provide a good proxy for the
spread of the infection.
It should be noted that not testing all the isolated population could lead to increasing public in-acceptance. Perhaps when the number of new infections is high and it’s likely the symptoms are due
to SARS-CoV-2 infection, people would accept a delay in testing. Probably less when the number of new infections shall drop to a few a day, and the chances of justified isolation shall be minimal yet
crucial in preventing relapse.
Proposal 3: Vaccinate population for common influenza towards the upcoming winter
Many countries regularly recommend the entire population (unless contraindicated) to vaccinate against seasonal influenza towards the winter ^31. We suggest strengthening this recommendation towards
the winter this year. Seasonal influenza could cause coronavirus-like initial symptoms ^32, and vaccination shall reduce the background noise of seasonal influenza symptoms, which could reduce the
number of needed tests. In addition, reduction in influenza reduces pressure on the healthcare system and keeps the population in a healthier starting point. In short, reduction in influenza allows
to focus scarce resources on the coronavirus front. Likewise, the standard vaccination schedule should be kept and its importance communicated to the public.
Proposal 4: Facial Masks and Hygiene Measures
As the cost of facial masks is low, and absent information, counties are tempted to instruct the population to wear facial masks in addition to increased hygiene ^4–6. The hope is that these measures
could reduce random infection by SARS-CoV-2 ^2,3. Whether these alone could stop the epidemic and what their contribution would be, if any, is unknown at this time. Nevertheless, in Figure 2, we
provide three simulations, assuming facial masks and hygiene measures reduce infection outside home by 10%, 30%, and 50% respectively. Note we assume the measures are taken only while outside home,
so household infection remains the same. See further analysis in the supplementary.
Part 2: Improvement and Comparison of Exit Strategies Building-Blocks
We compare the efficiency of several key exit strategies building blocks, comparing how much they are efficient in stopping the epidemic in terms of R, while in relation to how effective they are the
amount of average released business days they allow for the population. We summarize results of the partial release options in Figure 3.
Exit strategies building blocks we consider:
1. Do nothing - let the virus swipe the population (DN)
2. Immediate self-isolation upon symptoms (ISI)
3. Self-isolation of entire households only after a positive test (5 days delay)
4. Immediate self-household-isolation upon symptoms (ISHI)
5. Immediate self-isolation of symptomatic, household joins after a positive test (5 days delay)
6. DN + wearing facial masks when outside home (DN+masks)
7. ISHI + wearing facial masks when outside home (ISHI+masks)
8. Intermittent Release. Intermittent release of population, see ^33
9. Release certain percent of the population, quarantine the rest. The released group does not change across days.
10. Release 95% of the population with 1-week quarantines as needed: Release 95% healthiest by households, then a week quarantine is entered if virus spread causes above 2e^-5 (2 in 100,000) true
positive new household isolations daily averaged for a week.
11. Improved Two-Group intermittent release. Suggested below.
12. Improved Two-Group intermittent with fixed 10% release. Suggested below.
13. Random shift with fixed 10% release. Suggested below.
A special category of its own of deliberate exposure while controlling exposure order:
14. Herd immunity - described below.
In all strategies except DN, ISI, and herd immunity, we isolated households upon the first symptom. For all simulations, we assumed leakage of infection from the released population to the
quarantined population, such that being quarantined reduces the probability of infection from outside sources by a factor of 100 compared to the released population. While we cannot justify the exact
factor, the need to model leakage is undoubted as there’s always some level of incompliance, special needs that require going outside, need to buy supplies, human mistakes etc.
Personal risk prediction was based on a mocked personal coronavirus mortality prediction - see supplementary, and for a household as the average risk for the household members. Alternatively, risk
can be evaluated by age based on SARS-CoV-2 estimated infection fatality rate. In all simulations except DN, ISI, ISHI,DN+masks and ISHI+masks, we kept the top 5% highest-risk household in isolation
to protect them. In practice, other protection measures for sensitive populations are required, together with sensitive locations - these are outside the scope of the current paper.
Improved intermittent release
In this family of strategies we greatly improve an earlier proposed family of strategy ^33. In these strategies, we release the population based on 14-day cycles, for a varying number of consecutive
days depending on the particular variant. In the remainder of the days in the cycle, the previously released population is set on quarantine which we refer to as washout period. During the washout
period, some of those who contracted the virus in the preceding release days would become symptomatic. Hence, they will be “washed out” from further infecting others before the next cycle begins.
Another advantage of this family of strategies is that during the washout days R[t] is smaller due to the reduction in interactions.
We suggest a few improvements that together with ISHI make a big difference:
1. Dynamic and gradual number of release days, vs. quarantine days.
The object is to add as many release days while keeping R[t] below 1. Based on measured near real-time R[t] (discussed above), if R[t] is below 1, and the load on the healthcare system is
reasonable and the number of new true-positive daily household isolations is below desired threshold, we add a release day on expense of a quarantine day in a cycle. If R is growing above 1, we
deduct a release day on the expense of a quarantine day in each 14-days cycle. We manage to significantly increase the number of release days in a cycle from 4 suggested in the original idea ^33
to 9, thanks to our ISHI isolation procedure, and despite that we assumed R[0]=3.03. Additional measures could further increase the number of release days while keeping R[t] < 1.
2. Two-group approach reduces R and allows more release days.
We suggest to divide the population into two groups A and B, whose quarantine days are disjoint but their release days can be joined. The population can be divided household-wise.
The strength of this improvement is that while it keeps the washout periods in place, it further reduces infection on days that only one group is released. On each day that only one group is
released, the number of interactions decrease and limit further infection in the group. Thus, R is effectively reduced.
Of the possible day-divisions between the groups, we suggest divisions which maximizes the number of business days in an equal manner between the groups. We give several examples in the tables
below, and note that with this adaptation, we can improve to 10 workdays out of a 14 days cycle, while keeping R below 1. In other words a long weekend (Fri-Mon) once every two weeks suffices to
reduce R below 1 under our model assumptions.
3. Division to groups on a personal rather than household basis
One of the possible difficulties in implementing a two-group approach is dividing into two groups based on households rather than on a person by person basis. Surprisingly, our simulations show
that the difference in the basis of division is not significant in respect to R, while it could make a big difference in the ease of implementation. Therefore, we suggest this improvement of
dividing to groups based on a personal basis. This basis can also be set by the workplace, as long as it makes sure the division is such that it lowers in-workplace physical interaction.
4. Two-Group approach with a fixed release
Although effective, a two-group approach could appear more difficult compared to other building blocks, mainly as some employees are essential and are needed at their workplace more than their
group designates them or the group division is violated due to poor compliance. Therefore, we present an option allowing a fixed release rate in parallel to the two groups. For example, a fixed
10% of the population could be released all the time, regardless of the group division. This improvement makes the scheme more real, at the cost of somewhat elevated R - see Figure 4 for 80%
business days. As we see, while the cost in terms of R is significant, rising from R=0.98 for Two groups 10-4 days division on personal based group-division, to R=1.03 with additional 10% fixed
population release - it’s still very close to 1. Even with just the addition of facial masks (or hygiene) at 10% protection it would bring us to R=0.93. This improvement allows for a long weekend
(Fri-Mon) once every two weeks with division on a personal basis, with 10% of the people in complete noncompliance - a dramatic improvement in implementability while still keeping R below 1.
5. Random shift with a fixed release
The maximum level of freedom can be given, allowing people to choose their 4 isolation days along 14 days, allowing 10% noncompliance and no masks. If the choice is random, it shows better
performance in terms of R (R=0.92) compared to the same building block with two groups (R=1.03), and in terms of business days it’s 70.52% vs. 77.31% respectively. Business days average is lower
as isolation can fall over business days instead of weekends - but this is a personal choice. For R, the division is sensitive to people coordinating their isolation period to align and maximize
interaction. In such a case we shall end up in a situation similar to two groups, or in the worst case to a single group R value. However, as circles in life are diverse, we assume it would be
nearly impossible for the public to completely synchronize their isolation days.
This strategy can be either voluntary, or enforced for example by having individuals fill-in online in advance their chosen self-isolation days for future 14-day periods, and this strategy building
block can come on top of other strategies such as wearing masks - leading to an even better epidemiological result.
We give a few examples:
Two Groups 8-6: 8 release days followed by 6 quarantine days:
Two Group 9-5: 9 release days followed by 5 quarantine days:
Two Group 10-4: 10 release days followed by 4 quarantine days:
Two Group 11-3: 11 release days followed by 3 quarantine days:
Protection of population at Risk - Expected Mechanical Ventilation by Household
The higher-risk percentiles take an enormous amount of medical resources relative to their size, where the top 5% risk-group take a 544-fold more resources vs. the lower risk group (using the fitted
predictor for risk assessment - see supplementary), or 178-fold more resources if we use age alone for risk assessment. The resources go hand in hand with their risk, which demonstrates why this
population needs special protection also from the standpoint of resource usage, especially in the top 5%-10% percentiles.
Herd Immunity
We discuss herd immunity separately from other strategy building blocks, as it is the only strategy that aims at increasing infection rates - even if only in certain age groups in an attempt to
protect the rest and perhaps the economy. All other strategies are focused on preventing further infection. As such, herd immunity has one big advantage over all other strategies - immunity from
relapse, under the assumption that a person cannot get infected twice. This advantage is believed to be only a temporary one, as the general belief is that if we wait long enough - there will be a
vaccine that will provide immunity without the need to get large portions of the population sick, or that global efforts of social distancing and testing will eventually eradicate the disease.
The logic behind the herd immunity approach is that the lowest risk households are released first, and as they are low-risk they shall have a reduced demand rate of healthcare resources and reduced
casualties rate. The low-risk groups shall then be first to contract the virus, recover and gain immunity. Thus, the virus transmission is reduced as those that recover do not infect others and
cannot get sick again. Further groups of increasing risk are then released too, in a measured rate as not to exceed healthcare capacity. The extremely high-risk groups shall be released last once the
epidemic is over.
Therefore, we release the lowest-risk 25% immediately, and release further 5% of the population every two weeks until ICU is at 1% capacity. As a result, ICU utilization peaks and slightly
overshoots, and we continue releasing higher risk groups every two weeks once ICU capacity is back to at least 50% capacity again.
The herd immunity approach tries to infect as many of the released population as fast as possible in the beginning, so we did not isolate symptomatic households at start. We employ the ISHI procedure
to slow virus transmission only after 60% of the population has been released.
We depict simulation results for herd immunity in Figure 5 vs. a Two Group 10-4 strategy with division into two groups on personal basis, allowing up to 10% complete noncompliance and using facial
masks outside hume assuming 10% protection. The later strategy allows more release business days on average in a 1-year period - 77.8% vs. 71% for herd immunity.
Herd immunity should probably wait
There are several points that push away from a herd immunity strategy at this stage:
1. Too many need to get infected. Herd immunity is by far an outlier strategy with the largest amount of infections. From what we currently know, we don’t expect herd immunity to appear before over
60% of the population contracts the virus. While it’s reasonable to assume that a person shall not contract the virus twice in a short period, it’s still an unknown risk. Even for a small country
the size of Israel of about 9 million people, it means about 5,400,000 million people need to get infected - and just for Israel. Infecting that many people could result in mistakes being
multiplied in very large numbers, and almost definite leakage of infection to more sensitive populations that cannot be really protected in 100% of total isolation for months - resulting in many
2. Closes the door to potential luck. We might get lucky and have the summer eliminate the epidemic, as happened with some other viral infections - or other measure being successful. We might have
an effective medicine that will allow people to get infected without serious consequences. With herd immunity at this point - we won’t enjoy this luck, or enjoy it in a limited way.
3. Inefficient, costly for the economy and inhumane, as it will take too long to implement. We take for example Israel which has a relatively young and healthy population structure. It is expected
to take many months of quarantine given the limited capacity of the healthcare system, keeping a large portion of the population under quarantine for a prolonged period of time - which can be
considered inhumane. We simulate a year ahead, and give the herd immunity approach the advantage that we ignore death after a 1-year period. As can be seen in Figure 3 and Figure 5, we have other
strategies that can, at least potentially, hold the situation with minimal number of infections and casualties for for a relatively low cost, until we have a vaccine for example.
4. Too many will die and die young. While mortality rate is becoming clearer and much lower than initial estimates, it’s still relatively high ^34. Herd immunity approach could lead not only to
higher mortality than alternatives, but out of the casualties a high proportion would be young. At this time, we don’t have medical knowledge that hints that the young people who get to critical
condition have some a priori hidden condition that is expected to shorten their life anyhow. So we have to assume at this point that we would be losing many life-years under this strategy. See
Figure 5 for distribution of mortality across age groups.
5. Healthcare system strain will kill even more. A herd immunity approach will strain the healthcare systems to its limits for many months. Healthcare personnel and resources will find themself
recruited to care for the critical coronavirus patients, inevitably neglecting regular care. Many health situations that would normally end in recovery will end in otherwise avoidable death due
to lack of care.
6. Long term health damage. It could well be that some portion of surviving patients would suffer long-term or permanent health consequences post recovery, with mid-term damage almost certain for
those mechanically ventilated. Waiting for a vaccine could prevent it.
In light of the above, and given there appear to be other effective and relatively low-economical-damage containment strategies, it appears that sticking to containment strategies is more efficient
at this stage.
Our results show that seemingly similar strategies in terms of the amount of population-business-days they allow, can have a very different epidemic supression outcome, based on the pattern the
population is released. The more effective building blocks are a combination of both partial planned intermittent quaranties and partial population release, such as a two-group intermittent release
or random shift. As such, these mixed intermittent approaches are better performing, and are reasonable to implement given they can be relaxed to allow some fixed population noncompliance - 10
percent in our example. Division to groups on a personal, rather than on a household basis make these building blocks easier to live with. It should be noted, however, that partial release schemes
are sensitive to a special division into two groups that does not reduce interaction. For example, the resulting R of dividing the population into two groups on a city basis would resemble the
resulting R of a single-group and less the R of two groups. In other words, if the division is not made in a way that shall reduce interaction we will get an R closer to that of a single group
intermittent scheme.
Intermittent schemes without partial release of population seem less effective at reducing R compared to mixed schemes, though they are probably somewhat easier to enforce. Constant release of a
fixed certain percent of population while keeping the rest quarantined also seems less effective too compared to mixed schemes where the population that is being released changes. Releasing the
population, and then quarantining as the epidemic relapses seems less effective compared to planned intermittent release schemes that achieve better results while also less predictable business-wise.
The decision on using one building-block or the other is not just a numerical one, but should take into consideration other measures and factors including population compliance, effectiveness of
economy, etc. The factors and their weight could change by population and region. Actual decisions are outside the scope of this paper.
A large untreated question is reopening schools. Unfortunately, there is just no data available ^35 to make a truly informed decision, mostly because schools closed up very quickly globally with the
appearance of the pandemic, with the exception of Sweden for the lower age-groups ^36. Children are less symptomatic than adults ^37. Furthermore, there is conflicting information on whether
asymptomatic are less infectious ^38 than symptomatic. Based on experience in China, Korea and Israel, it seems children contracted the virus less ^39. According to Israeli ministry of health data ^
40, the percent of positive tests for children aged 0-9 years old is lower compared to adults and in the range of adults for ages 10-19, suggesting this phenomena of lower contraction in children is
not merely an ascertainment bias due to milder symptoms. It could be argued the latter phenomena can be attributed to the fact the main importers of the virus were travelling adults and schools
closed up relatively fast. In Sweden, the infection rates of children are also very low ^41 - though testing was limited. In household secondary infection in China, children were less likely to get
infected ^16,39. In the municipality of Vo’, Italy, almost the entire municipality was tested twice as part of a survey in the early outbreak in Italy ^42. While the infection prevalence was about
2.6%, none of the 234 children aged 0-10 were infected, despite some of them sharing a household with a case. According to Israeli ministry of health information, the education system accounted for
only 3-11 percent of virus contraction. On top of things, and perhaps the bottom line - there is no real and reasonable solution for parents to go to work, if their children cannot go to their school
- so opening of schools seems unavoidable. Limited mitigation can be partially achieved by noticing symptoms at school, and bi-daily measurements of body temperature for early detection of symptoms,
as children tend to be less symptomatic.
We assume the epidemic shall last many months, and that schools will reopen before it’s eradicated. Therefore, we will have to accomodate for the school effect anyhow, whatever it is, so that R<1
despite schools being open. However, it could be that R would be very close to 1 after schools reopen, and so there could be benefits from reducing the number of new daily infections to a smaller
level which would stay there after schools are reopened as R would be close to 1. Opening schools with our suggested strategy provides a layer of protection that would slow-down possible relapses.
We compare key mitigation measures of SARS-CoV-2 spread, and compare various exit strategies building blocks. Our results stress the importance of not just the amount of population that is released,
but also the pattern. Our findings demonstrate the importance of mixed strategies, as each strategy is effective through somewhat other means. Some of our mixed schemes can allow relatively
convenient life while controlling for the epidemic spread.
Therefore, and given our results, we believe that pandemic can be controlled within a reasonable amount of time and at a reasonable socio-economic burden.
Data Availability
No data is available
Simulator and Underlying Assumptions
Our simulation is based on a SEIR (Susceptible, Exposed, Infectious, Recovered) agent-based model that we programmed in Python and adapted to Israeli population and parameters of SARS-CoV-2 epidemic.
Therefore, in our database, we hold about 9 million rows, one for each resident of Israel, but for efficiency purposes we run the simulation on a subsampling of 1:10 on a reduced 900,000
representative lines. For each person, we hold an index, age, sex, and household identifier together with simulation data.
Population Structure
We assumed each person is living with their children, unless they have children of their own. This construction resulted in a somewhat smaller household than real Israeli data. From Israeli bureau of
statistics, the average Israeli household is 3.3 people ^43, while in our simulation the average is 2.15, perhaps due to multi-generation households, or several families living together.
Estimation of personal probability of death and mechanical ventilation
To mock coronavirus outcomes of mortality and mechanical ventilation for subjects, we used a combination of 3-year all-cause mortality predictor trained on Clalit healthcare data and have the results
in cross-validation, and age-specific infection-fatality-rate (IFR) and ventilation estimates from the existing literature on SARS-CoV-2.
We manually fitted the mortality predictor to coronavirus mortality and mechanical ventilation probabilities as follows, where missing values were imputed by the reference value per appropriate age
Temporal modeling
The simulation was based on the following temporal assumptions:
Note that available literature of these parameters has a wide confidence interval, which could affect our results.
Simulation Temporal Course
The simulation is executed with a 1-day cycle simulating a year. Totals are counted for mortality, infections, ICU usage - all based on the above detailed assumptions. We did not take into account
actual ICU resources in the simulation, but counted the needed resources and assumed they are available. It is up to the strategy to avoid a situation of exhausting resources.
At initialization, each subject receives concrete values of their personal disease course relative to infection, if they get infected. To that end we draw random variables of the relevant
distribution detailed above. For each person we also hold a boolean flag indicating if they are infected, and a counter to count the relative number of days since each person’s infection. We also
keep a flag to note if a person is in quarantine (isolation) or released. We assumed isolation is at home and with household members. People in ICU are considered removed and stop infecting others.
There are three types of infections modeled: infection of family members, infection of released population, and leakage infection to those in quarantine. The infection of each group is performed in
complete mix, i.e., the probabilities to get infected by an infector are identical within a group, and the population within a group is uniformly infected based on that probability.
Daily infection of the released population is based on R[0_Released] and the relative infectiousness for that day for an infector, whose product we denote as Φ[i]^d. Thus, Φ[i]^d denotes the number
of expected infectious interactions an infector i makes on day d, assuming no-one else is infected and all population is released. We define infectious interactions as the number of people that would
be infected if no one else was infected yet. Then, when just a fraction f of the population is released, under complete mix assumption we assume the number of daily interactions per person drops by a
factor f. Therefore, under complete mix, the number of infectious interactions an infector makes also drops by a factor f, and each infector shall now have only f·Φ[i]^d daily infectious
Interestingly, under the complete mix assumption, the probability of a released person to have an infectious interaction with a single infector is identical as in full release. However, there is a
factor f less candidates to infect, so the total number of new cases drop by a factor of f. The probability of a released person to have an infectious interaction with an infected person is therefore
equal to Φ[i]^d/(T-1), where T is the total initial population - and one person is infecting the others. As T>>1 we neglect 1, and remain with infectious interaction probability of Φ[i]^d/T.
Given there are C infectors released, under the complete mix assumption, the probability of a released person to be infected by one of them is:
Using the approximation (1-1/x)^x is about e^-1 for large x, where x=T/Φ[i]^d, i.e., T>>Φ[i]^d, it follows that the probability for a released individual to be infected in a day (if not already
infected) is:
Our simulation tries to infect released individuals daily based on this probability. Note that when , using the approximation that e^x = 1 + x for small x, the probability reduces to . Though this
approximation is used in classic analytical SIR/SEIR models, we did not have the need to use it in our simulations.
We can decompose R[0] to contribution from household infections, and all the rest:R[0]=R[HH]+R[Rest]
Where CDF’ is the cumulative density function of the chosen gamma probability for infectiousness scaled for the length of the infection period for this person. i.e., CDF’(d)=CDF(9.21(d/L)), where L
is the personal length of infectiousness.
Simulation Applied on a Strategy Building Block
The various strategies that are evaluated were fed separately into the simulator. A strategy can set for each person if they are quarantined or released, based on all prior information (age, sex,
probabilities - but not actual random choices), and can measure actual ICU usage, and perform viral tests, require to put masks when out of home, etc.. The strategy is invoked each day and has a
chance to intervene prior to the infections taking course for that day.
Modelling Facial Masks
If two people are wearing masks, it reduces droplets and aerosol that contain the virus. Averaging the numbers in ^7, we assume it reduces droplets and aerosol by about 29.1% to 18.2%, without change
in the viral load, i.e., a mask on an affected individual reduces spread by a factor of 0.625 in a period of 30 minutes ^7. Numbers are small so we assume about 30% spread both aerosols and droplets.
We cannot make an accurate assumption on how much surgical masks shall reduce infection to a wearer of the mask, though based on ^49 it would be about a six-fold protection factor. If we follow these
numbers we expect infection to drop by a factor of 0.625/6 to 0.625, i.e., from 0.1 to 0.625. Another cause of inclarity is the possibility that droplets or aerosol are infecting through unprotected
eyes, or other transmission from hands to the eyes ^50,51, which are not protected by a surgical mask, and later accidental transfer from hands to mouth or eyes. The inclarity is further extended as
good mask usage requires careful fitting of the masks, replacing them frequently enough, smart disposal together with additional protective measures ^52.
It’s difficult to model long-exposure of several 30 minutes units, as we cannot tell if the percent of droplets are per-person due to mask-face fitting for example (although participants were
corrected if they mis-wore the mask), or due to properties of the mask itself. If it’s mask properties then an hour worth exposure would still be infecting. e.g., even if we assume the extreme value
for mask protection factor of 0.1, then for 5 hours the protection is only 1-(1-0.1)^2×5=0.651, i.e., the protection is just 30% reduction in possibility of infection. So if surgical masks are
useful, it’s probably protective for short and random exposure patterns. To provide a conservative yet useful estimate, we gace simulation results for protection levels of 10%, 30% and 50%.
Estimation of impact on R[0]
SIR models typically state the S - Susceptible, E - exposed, I - Infecting, R - Removed, and N - total number of people. Then
dS/dt = -βSI/N^2
dE/dt =βSI/N^2-κE
dI/dt = κE - νI/N
dR/dt = νI/N
R[t] is then (dE/dt + dI/dt + dR/dt)/(dR/dt), which is βS/νN and R[0] is then β/ν.
We can estimate R[0] as if the S[0] of the population is susceptible at start then: R[0]= ln(S[0]/S[∞]) / (1-S[∞] / N), where we estimate S[∞] by taking the uninfected number of uninfected people
after a year, and S[0] as the number of unaffected people at start of intervention. We do start intervening on day 14, but to allow washout of previous doing-nothing, we take S[0] as day 35 (21 days
washout). Taking S[0] at day 35 also accommodates our simulation deliberate infection by 10 people a day during the first month. | {"url":"https://www.medrxiv.org/content/10.1101/2020.04.23.20072850v2.full","timestamp":"2024-11-10T07:36:48Z","content_type":"application/xhtml+xml","content_length":"251371","record_id":"<urn:uuid:1446b861-8ebf-4c82-a056-58bf8f10143e>","cc-path":"CC-MAIN-2024-46/segments/1730477028179.55/warc/CC-MAIN-20241110072033-20241110102033-00520.warc.gz"} |
On the lax solution to the Hamilton-Jacobi equation. Part I
The review article of Crandall, Ishii, and Lions [Bull. AMS, 27, No. 1, 1-67 (1992)] devoted to viscosity solutions of first- and second-order partial differential equations contains the exact Lax
formula u(x,t) = inf [y∈Rn]{v(y) + 1/2t∥x-y∥^2} (1) for a solution to the Hamilton-Jacobi nonlinear partial differential equation ∂u/∂t + 1/2∥∇u∥^2 = 0. u|[t=0] = v, (2) where the Cauchy data v: R^n
→ R are chosen as a function properly convex and semicontinuous from below, ∥·∥ = 〈·,·) is the usual norm in R^n, n ∈ Z[+], and t ∈ R [+] is a positive evolution parameter. The article also states
that there is no exact proof of the Lax formula (1) based on general properties of the Hamiltonian-Jacobi equation (2). This work presents precisely such an exact proof of the Lax formula (1).
All Science Journal Classification (ASJC) codes
• Statistics and Probability
• General Mathematics
• Applied Mathematics
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Center for Plasma Theory and Computation Reports
UW_CPTC_24-2: “Modeling of Macroscopic Dynamics in Three-Dimensional Plasma Configurations: Final Scientific Report,” Carl Sovinec, posted October 9, 2024.
UW_CPTC_24-1: “ECH Ignition of DD in Mirror/Cusp Geometry,” Prof. Emeritus, Dept. of Nuclear Engineering, U. C. Berkeley; August 1, 2024.
UW_CPTC_22-4: “Pressure-Driven Tearing and Thermal Transport in Finite-Beta Reversed Field Pinch Computations,” U. Gupta and C. R. Sovinec, September 13, 2022.
UW_CPTC_22-3: “Gyrokinetic Modeling of Linear Tearing Mode,” by T. Jitsuk, A. Di Siena, Z. R. Williams, M. J. Pueschel, and P. W. Terry, May 27, 2022.
UW_CPTC_22-2: “Sloshing Ion Stabilization of Mirrors and Cusps” by T. K. Fowler, Prof. Emeritus, Dept. of Nuclear Engineering, U. C. Berkeley; February 2, 2022.
UW_CPTC_22-1: “Computational study of runaway electrons in MST tokamak discharges with applied resonant magnetic perturbations,” by B. S. Cornille, M. T. Beidler, S. Munaretto, B. E. Chapman, D.
Del-Castillo-Negrete, N. C. Hurst, J. S. Sarff, and C. R. Sovinec, February 4, 2022.
UW_CPTC_21-4: “A study of ITG and KBM turbulence in low-magnetic-shear, inherently-three-dimensional magnetic equilibria” by Ian J. McKinney, December 31, 2021.
UW_CPTC_21-3: “Effect of Triangularity on Ion-Temperature-Gradient-Driven Turbulence” by J.M. Duff, B.J. Faber, C.C. Hegna, M.J. Pueschel and P.W. Terry, December 9, 2021.
UW_CPTC_21-2: “Energetic particle transport in optimized stellarators” by A. Bader, D.T. Anderson, M. Drevlak, B.J. Faber, C.C. Hegna, S. Henneberg, M. Landreman, J.C. Schmitt, Y. Suzuki, A. Ware,
June 1, 2021.
UW_CPTC_21-1: “Stellarator Beta Limits with Extended MHD Modeling Using NIMROD” by Torrin A. Bechtel, April 16, 2021.
UW_CPTC_20-2: “Influence of Boundary and Edge-Plasma Modeling in Computations of Axisymmetric Vertical Displacement” by K. J. Bunkers and C. R. Sovinec. Data presented in this report is available at
bunkers_sovinec_figures.tar.gz. This article has been submitted to Physics of Plasmas. After it is published, it will be found at https://aip.scitation.org/journal/php.
UW-CPTC 20-1: “A New Optimized Quasihelically Symmetric Stellarator” by A. Bader, B.J. Faber, J.C. Schmitt, D.T. Anderson, M. Drevlak, J.M. Duff, H. Frerichs, C.C. Hegna, T.G. Kruger, M. Landreman,
I.J. McKinney, L. Singh, J.M. Schroeder, P.W. Terry, A.S. Ware, May 1, 2020.
UW-CPTC 19-2: “Conservation properties with artificial particle diffusivity” by C. R. Sovinec, June 30, 2019.
UW-CPTC 19-1: “Effects of flux surface shaping on ion temperature gradient turbulence in tokamaks” by Joey M. Duff, May 23, 2019. Data presented in this report is available at https://
uwmadison.box.com/s/270n0h422dupq19qg9pltv54cgjrcmee .
UW-CPTC 18-5rev: “Effects of asymmetries in computations of forced vertical displacement” by C. R. Sovinec and K. J. Bunkers, September 14, 2018. This article is published under a CC BY license.
The Version of Record is available online at https://doi.org/10.1088/1361-6587/aaf124 . Data presented in this report is available from https://uwmadison.box.com/s/l49uw0fn8hebn85kb8vxf06qqnuvchka .
UW-CPTC 18-4: “The role of three-dimensional geometry on turbulence in quasi-helically symmetric stellarators” by Benjamin J. Faber, July 27, 2018.
UW CPTC 18-3: “Mode Penetration Induced By Transient Magnetic Perturbations” by M.T. Beidler, J.D. Callen, C.C. Hegna, and C.R. Sovinec, June 25, 2018.
UW-CPTC 18-2: “Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport” by C.C. Hegna, P.W. Terry and B.J. Faber, March 4, 2018.
UW-CPTC 18-1: “Minimum magnetic curvature for resilient divertors using Compact Toroidal Hybrid geometry” by Aaron Bader, Chris C. Hegna, M.R. Cianciosa and Greg Hartwell, March 21, 2018. zip
archive of data in figures
UW-CPTC_17-8: “Verification of Braginskii closures in NIMROD on MHD waves,” K. J. Bunkers and C. R. Sovinec, November 21, 2017.
UW-CPTC_17-5r1: “Parameter-space survey of linear g-mode and interchange in extended magnetohydrodynamics” by E. C. Howell and C. R. Sovinec, September 14, 2017. zip archive of data in figures
UW-CPTC 17-4: “Enhanced toroidal flow stabilization of edge localized modes with increased plasma density” by Shikui Cheng, Ping Zhu and Debabrata Banerjee, May 19, 2017.
UW-CPTC 17-3: “HSX as an example of a resilient non-resonant divertor” by A. Bader, A.H. Boozer, C.C. Hegna, S.A. Lazerson and J.C. Schmitt, March 30, 2017.
UW-CPTC 17-2: “Resistive Wall And Error Field Studies Using The Extended MHD Code NIMROD” by Andrea L. Becerra, January 15, 2017.
UW-CPTC 17-1_rev: “Nonlinear Modeling of Forced Magnetic Reconnection in Slab Geometry with NIMROD” M.T. Beidler, J.D. Callen, C.C. Hegna and C.R. Sovinec, updated April 18, 2017. tar archive of data
in figures
UW-CPTC 16-2: “Stellarator Turbulence: Subdominant Eigenmodes and Quasilinear Modeling” by M.J. Pueschel, B.J. Faber, J. Citrin, C.C. Hegna, P.W. Terry and D.R. Hatch, February 10, 2016. gzipped tar
archive of data in figures
UW-CPTC 16-3: “Model of ELM suppression by RMPs in DIII-D” by J.D. Callen, M.T. Beidler, N.M. Ferraro, C.C. Hegna, R.J. La Haye, R. Nazikian and C. Paz-Soldan, July 2, 2016.
UW-CPTC 16-4: “Model of n = 2 RMP ELM suppression in DIII-D” by J.D. Callen, R. Nazikian, C. Paz-Soldan, N.M. Ferraro, M.T. Beidler, C.C. Hegna and R.J. La Haye, December 19, 2016.
UW-CPTC 16-5: “Modeling of Helium Transport and Exhaust in the LHD Edge” by A. Bader, M. Kobayashi, O. Schmitz, A.R. Akerson, F. Effenberg, H. Frerichs, Y. Feng, C.C. Hegna , K. Ida and the LHD
Experimental Group, November 10, 2016.
UW-CPTC 16-6: “Extended MHD Modeling of Tearing-Driven Magnetic Relaxation” by J. P. Sauppe and C. R. Sovinec, November 17, 2016. gzipped tar archive of data
UW-CPTC 15-1_rev1: “Analytical theory of the shear Alfven continuum in the presence of a magnetic island” by C.R. Cook and C.C. Hegna, April 2, 2015.
UW-CPTC 15-2: “Gyrokinetic studies of trapped electron mode turbulence in the HSX stellarator” by B.J. Faber, M.J. Pueschel, J.H.E. Proll, P. Xanthopoulos, P.W. Terry, C.C. Hegna, G.M. Weir, K.M.
Likin and J.N. Talmadge, June 18, 2015. gzipped tar archive of data in figures
UW-CPTC 15-3: “Shear alfven continua and discrete modes in the presence of a magnetic island” by Carson Raymond Cook, June 26, 2015.
UW-CPTC 15-4: “The effect of three-dimensional fields on bounce averaged particle drifts in a tokamak” by C.C. Hegna, July 20, 2015.
UW-CPTC 15-5: “Extended MHD Study of Interchange Modes in Spheromaks” by Eric C. Howell, May 20, 2015.
UW-CPTC 15-6: “Two-Fluid and Finite Larmor Radius Effects on Helicity Evolution in a Plasma Pinch” by J.P. Sauppe and C.R. Sovinec, October 5, 2015. gzipped tar archive of data in figures
UW-CPTC 15-7_rev1: “Stabilization of Numerical Interchange in Spectral-Element Magnetohydrodynamics” by C.R. Sovinec, updated May 10, 2016. tar archive of data in figures
UW-CPTC 15-8: “Analytical and numerical treatment of resistive drift instability in a plasma slab” by V.V. Mirnov, J.P. Sauppe, C.C. Hegna and C.R. Sovinec, December 16, 2015. gzipped tar archive of
data in figures
UW-CPTC 15-9: “Extended magnetohydrodynamic modeling of plasma relaxation dynamics in the reversed-field pinch” by Joshua Paul Sauppe, November 23, 2015.
UW-CPTC 14-1: “Effects of a weakly 3-D equilibrium on ideal MHD instabilities” by C.C. Hegna, April 28, 2014.
UW-CPTC 14-2: “Principles of toroidal geometry optimization for ITG modes” by Mordechai N. Rorvig, August 27, 2014.
UW-CPTC 13-1: “Simulations of Edge Configurations in Quasi-Helically Symmetric Geometry using EMC3-EIRENE” by A. Bader, D.T. Anderson, C.C. Hegna, Y. Feng, J.D. Lore and J.N. Talmadge, February 25,
UW-CPTC 13-2: “Solving the Grad-Shafranov Equation with Spectral Elements” by E.C. Howell and C.R. Sovinec, August 21, 2013.
UW-CPTC 13-3_rev2: “Coulomb collision effects on linear Landau damping” by J.D. Callen, April 8, 2014.
UW-CPTC 13-4: “Collisional effects in low collisionality plasmas” by J.D. Callen, November 22, 2013.
UW-CPTC 13-5: “Pedestal Structure Without And With 3D Fields” by J.D. Callen, November 6, 2013.
UW-CPTC 13-6: “Simulated Flux-rope Evolution during Non-inductive Current Drive in Pegasus” by J.B. O’Bryan and C.R. Sovinec, October 7, 2013.
UW-CPTC 13-7: “Steady-state Force Balance in the DEBS Code” by D.D. Schnack, November 10, 2013.
UW-CPTC 13-8: “Flow Damping Due to a Model of Fluctuation Induced Viscosity in DEBS” by D.D. Schnack, November 11, 2013.
UW-CPTC 13-9: “Dependence of Single- and Multi-Helicity States on Θ and the Harmann number in the Force-free Visco-resistive MHD Model” by D.D. Schnack, November 11, 2013.
UW-CPTC 12-1: “The Internal Kink Mode and Giant Sawteeth in Tokamaks” by Dalton D. Schnack, March 5, 2012.
UW-CPTC 12-2: “Local ITG-like Instability in the Two-fluid and Extended MHD Models in Slab Geometry” by D.D. Schnack, D.C. Barnes, Ping Zhu, C.C. Hegna & C.R. Sovinec, April 16, 2012.
UW-CPTC 12-3: “Gravitational Instability as a Test Case for Extended MHD Computations” by D.D. Schnack, September 12, 2005.
UW-CPTC 12-4: “Simulation of current-filament dynamics and relaxation in the Pegasus Spherical Tokamak” by J.B. O’Bryan, C.R. Sovinec & T.M. Bird, August 10, 2012.
UW-CPTC 12-5: “Numerical simulation of current evolution in the Compact Toroidal Hybrid” by M.G. Schlutt, C.C Hegna, C.R. Sovinec, S.F. Knowlton & J.D. Hebert, June 21, 2012.
UW-CPTC 12-6_rev2: “Magnetic-flutter-induced pedestal plasma transport” by J.D. Callen, C.C Hegna & A.J.Cole, July 1, 2013.
UW-CPTC 12-7: “Investigation of 3D effects in stellarator configurations using extended MHD” by M.G. Schlutt, September 5, 2012.
UW-CPTC 12-8: “Self-consistent simulations of nonlinear magnetohydrodynamics and profile evolution in stellarator configurations” by M.G. Schlutt, C.C. Hegna, C.R. Sovinec, E.D. Held & S.E. Kruger,
November 30, 2012.
UW-CPTC 12-9: “A model for microinstability destabilization and enhanced transport in the presence of shielded 3-D magnetic perturbations” by T.M. Bird & C.C. Hegna, November 23, 2012.
UW-CPTC 11-1_rev3: “The effect of anisotropic heat transport on magnetic islands in 3-D configurations” by M.G. Schlutt & C.C. Hegna, August 1, 2012.
UW-CPTC 11-2: “Zero-B modeling of coaxial helicity injection in the HIT-II spherical torus” by R.A. Bayliss, C.R. Sovinec & A.J. Redd, May 24, 2011.
UW-CPTC 11-3_rev: “Pedestal Structure Model” by J.D. Callen, J.M. Canik & S.P. Smith, November 8, 2011.
UW-CPTC 11-4_rev: “Model for pedestal structure” by J.D. Callen, November 7, 2011.
UW-CPTC 11-5: “Parallel Neoclassical Resistivity Evaluation” by J.D. Callen, July 11, 2011.
UW-CPTC 11-7: “Healing of magnetic islands in stellarators by plasma flow” by C.C. Hegna, June 7, 2011.
UW-CPTC 11-8: “Nonlinear Evolution of Kink Unstable Jets” by C.S. Carey, C.R. Sovinec and S. Heinz, July 22, 2011.
UW-CPTC 11-9: “Nature of axial tail instability and bubble-blob formation in near-Earth plasma sheet” by P. Zhu, J. Raeder, C.C. Hegna & C.R. Sovinec, August 11, 2011.
UW-CPTC 11-10: “The Effect of Three Dimensional Shaping on the Ballooning Stability Properties of Stellarator Equilibria and Tokamak Equilibria with Resonant Magnetic Perturbations” by Thomas M.
Bird, August 11, 2011.
UW-CPTC 11-11: “Plasma flow healing of magnetic islands in stellarators” by C.C. Hegna, August 19, 2011.
UW-CPTC 11-13_rev: “Resonant magnetic perturbation effects on pedestal structure and ELMs” by J.D. Callen, A.J. Cole, C.C. Hegna, S. Mordijck & R.A. Moyer, March 19, 2012.
UW-CPTC 11-14: “Stabilizing Effects of Edge Current Density on Peeling-Ballooning Instability” by P. Zhu, C.C. Hegna & C.R. Sovinec, September 21, 2011.
UW-CPTC 11-15_rev: “Resonant-magnetic-perturbation-induced plasma transport in H-mode pedestals” by J.D.Callen. A.J. Cole & C.C. Hegna, September 6, 2012.
UW-CPTC 10-1: “Observation of peak neoclassical toroidal viscous force in the DIII-D tokamak” by A.J. Cole, J.D. Callen, W.M. Solomon, A.M. Garofalo, C.C. Hegna, H. Reimerdes and the DIII-D Team,
July 21, 2010.
UW-CPTC 10-2_rev: “Determining the Bohm criterion in plasmas with two ion species” by S.D. Baalrud & C.C. Hegna, November 28, 2010.
UW-CPTC 10-3: “Kinetic Theory of the Presheath and the Bohm Criterion” by S.D. Baalrud & C.C. Hegna, October 26, 2010.
UW-CPTC 10-4: “Kinetic theory of instability-enhanced collective interactions in plasma” by S.D. Baalrud, May 12, 2010.
UW-CPTC 10-5_rev: “Kinetic shielding of magnetic islands in 3-D equilibria” by C.C. Hegna, October 21, 2010.
UW-CPTC 10-6: “A Model Of Pedestal Structure” by J.D. Callen, August 30, 2010.
UW-CPTC 10-7: “Peak neoclassical toroidal viscosity at low toroidal rotation in the DIII-D tokamak” by A.J. Cole, J.D. Callen, W.M. Solomon, C.C. Hegna, M.J. Lanctot, H. Reimerdes and the DIII-D
Team, April 27, 2011.
UW-CPTC 10-8_rev: “Effects of 3D Magnetic Perturbations on Toroidal Plasmas” by J.D. Callen (Daejeon IAEA FEC paper OV/4-3), October 28, 2010.
UW-CPTC 10-9: “High-beta physics of magnetic islands in 3-D equilibria” by C.C. Hegna, M.G. Schlutt, E.D. Held, S.E. Kruger & C.R. Sovinec, September 24, 2010.
UW-CPTC 10-10_rev: “Effects of 3D Magnetic Perturbations on Toroidal Plasmas” by J.D. Callen (submitted to Nucl. Fusion), June 17, 2011.
UW-CPTC 09-1: “Initiation of ballooning instability in the near-Earth plasma sheet prior to the March 23, 2007 THEMIS substorm expansion onset” by P. Zhu, J. Raeder, K. Germaschewski & C.C. Hegna,
January 2009.
UW-CPTC 09-2_rev: “Note on Kinetic Alfven Waves” by Carl R. Sovinec, revised February 27, 2009.
UW-CPTC 09-3: “Computational Needs for Reversed-Field Pinch and Spheromak Development” by Carl R. Sovinec, February 27, 2009.
UW-CPTC 09-4: “Instability-Enhanced Collisional Effects and Langmuir’s Paradox” by S.D. Baalrud, J.D. Callen & C.C. Hegna, April 7, 2009.
UW-CPTC 09-5_rev: “Instability-Enhanced Collisional Friction Determines the Bohm Criterion in Multiple-Ion-Species Plasmas” by S.D. Baalrud, C.C. Hegna & J.D. Callen, revised October 31, 2009.
UW-CPTC 09-6_rev: “Viscous Forces Due To Collisional Parallel Stresses For Extended MHD Codes” by J.D. Callen, revised February 4, 2010.
UW-CPTC 09-7: “Drift-resistive-inertial ballooning modes in the HSX Stellarator” by T. Rafiq, C.C. Hegna, J.D. Callen & A.H. Kritz, August 12, 2009.
UW-CPTC 09-8: “Unified theory of resistive and inertial ballooning modes in three-dimensional configurations” by T. Rafiq, C.C. Hegna, J.D. Callen & A.H. Kritz, August 13, 2009.
UW-CPTC 09-9: “A closure scheme for modeling RF modifications to the fluid equations” by C.C. Hegna & J.D. Callen, August 20, 2009.
UW-CPTC 09-10_rev: “Analysis of pedestal plasma transport” by J.D. Callen, R.J. Groebner, T.H. Osborne, J.M. Canik, L.W. Owen, A.Y. Pankin, T. Rafiq, T.D. Rognlien & W.M. Stacey, revised March 31,
UW-CPTC 09-11_rev: “Transport equations in tokamak plasmas” by J.D. Callen, C.C. Hegna & A.J. Cole, revised February 4, 2010.
UW-CPTC 09-12_rev: “Kinetic theory of instability-enhanced collisional effects” by S.D. Baalrud, J.D. Callen & C.C. Hegna, revised February 11, 2010.
UW-CPTC 09-13: “Analysis of a Semi-Implicit Algorithm for Low-Frequency Two-Fluid Plasma Modeling” by C.R. Sovinec, J.R. King & the NIMROD Team, December 4, 2009.
UW-CPTC 08-1: “Global axisymmetric simulations of two-fluid reconnection in an experimentally relevant geometry” by Nicholas A. Murphy and Carl R. Sovinec, January 22, 2008.
UW-CPTC 08-2: “Ballooning stability of near-Earth plasma sheet during the March 23, 2007 THEMIS substorm event: A local analysis” by P. Zhu, J. Raeder, K. Germaschewski, A. Bhattacharjee & C.C.
Hegna, February 2008.
UW-CPTC 08-3: “Nonlinear MHD dynamics of pulsed parallel current drive in reversed-field pinches” by J.M. Reynolds, C.R. Sovinec & S.C. Prager, April 2008.
UW-CPTC 08-4_rev: “A kinetic equation for unstable plasmas in a finite space-time domain” by S.D. Baalrud, J.D. Callen & C.C. Hegna, revised September 16, 2008.
UW-CPTC 08-5: “Unified theory of resistive and inertial ballooning modes in three-dimensional configurations” by T. Rafiq, C.C. Hegna, J.D. Callen, G. Bateman, A.Y. Pankin & A.H. Kritz, June 16,
UW-CPTC 08-6_rev: “Toroidal Rotation In Tokamak Plasmas” by J.D. Callen, A.J. Cole & C.C. Hegna, (2008 IAEA Geneva paper TH/P8-36), revised November 13, 2008.
UW-CPTC 08-7_rev: “Toroidal flow and radial particle flux in tokamak plasmas” by J.D. Callen, A.J. Cole & C.C. Hegna, revised July 23, 2009.
UW-CPTC 08-8: “Low Collisionality Neoclassical Toroidal Viscosity in Tokamaks and Quasi-symmetric Stellarators Using an Integral-truncation Technique” by A.J. Cole, C.C. Hegna & J.D. Callen, June 17,
UW-CPTC 08-9: “Intermediate Nonlinear Regimes of Line-tied g Mode and Ballooning Instability” by P. Zhu, C.C. Hegna, C.R. Sovinec, A. Bhattacharjee & K. Germaschewski, September 2008.
UW-CPTC 08-10: “Exponential Growth of Nonlinear Ballooning Instability” by P. Zhu, C.C. Hegna & C.R. Sovinec, November 2008.
UW-CPTC 08-11: “Initiation of ballooning instability by reconnection in the near-Earth plasma sheet” by P. Zhu, J. Raeder, K. Germaschewski & C.C. Hegna, December 2008.
UW-CPTC 08-12: “Rotational Stabilization of Magnetically Collimated Jets” by C.S. Carey & C.R. Sovinec, January 2009.
UW-CPTC 07-1: “Axisymmetric Interchange Calculations with NIMROD” by C.R. Sovinec, January 9, 2007.
UW-CPTC 07-2: “Effect of neoclassical toroidal viscosity on error-field penetration thresholds in tokamak plasmas” by A.J. Cole, C.C. Hegna & J.D. Callen, March 13, 2007.
UW-CPTC 07-3_rev: “Scaling of Ohmic Tokamak Error-field Penetration Thresholds in the Presence of Neoclassical Toroidal Viscosity” by A.J. Cole, C.C. Hegna & J.D. Callen, revised January 4, 2008.
UW-CPTC 07-4: “ECRH and its effects on neoclassical transport in stellarators” by JaeChun Seol, C.C. Hegna & J.D. Callen, April 6, 2007.
UW-CPTC 07-5: “Paleoclassical electron heat transport model” by J.D. Callen, December 14, 2007.
UW-CPTC 07-6: “Non-ideal MHD ballooning modes in three-dimensional configurations” by T. Rafiq, C.C. Hegna & J.D. Callen, October 2007.
UW-CPTC 07-7_rev: “Neoclassical toroidal viscosity and error-field penetration in tokamaks” by A.J. Cole, C.C. Hegna & J.D. Callen, revised January 4, 2008.
UW-CPTC 07-8: “The absence of complete FLR stabilization in extended MHD” by P. Zhu, D.D. Schnack, F. Ebrahimi, E.G. Zweibel, M. Suzuki, C.C. Hegna & C.R. Sovinec, December 2007.
UW-CPTC 07-9: “Current sheet formation due to a localized interchange mode” by P. Zhu, C.R. Sovinec and C.C. Hegna, December 2007.
UW-CPTC 07-10: “Ballooning filament growth in the intermediate nonlinear regime” by P. Zhu and C.C. Hegna, December 2007.
UW-CPTC 06-1: “Dissipative trapped-electron instability in quasi-helically symmetric stellarators” by T. Rafiq & C.C. Hegna, revised April 18, 2006.
UW-CPTC 06-2: “Nonlinear Ballooning Instability in the Near-Earth Magnetotail: Growth, Structure, and Possible Roles in Substorms” by P. Zhu, C.R. Sovinec, C.C. Hegna, K. Germaschewski & A.
Bhattacharjee, March 2006.
UW-CPTC 06-3: “Key hypothesis of paleoclassical model” by J.D. Callen, September 5, 2006.
UW-CPTC 06-4: “Final Report on the OFES ELM Milestone for FY2006” by D.C. Barnes, R.A. Bayliss, D.P. Brennan, E.D. Held, S.E. Kruger, A.Y. Pankin, D.D. Schnack, C.R. Sovinec, and the NIMROD Team,
September 30, 2006.
UW-CPTC 06-5: “Experimental Tests of Paleoclassical Transport” by J.D. Callen et al., October 2006.
UW-CPTC 06-6: “Paleoclassical model for edge electron temperature pedestal” by J.D. Callen et al., March 22, 2007.
UW-CPTC 06-7: “Intermediate nonlinear regime of a line-tied g mode” by P. Zhu, C.C. Hegna, C.R. Sovinec, A. Bhattacharjee & K. Germaschewski, November 2006.
UW-CPTC 06-8_rev: “Derivation of paleoclassical key hypothesis” by J.D. Callen, revised January 25, 2007.
UW-CPTC 05-1: “An Analysis of Mass Matrix Lumping in NIMROD” by Nick Murphy and Carl Sovinec, January 26, 2005.
UW-CPTC 05-2: “Time and Space Dependent Parallel Viscous Force” by Ana Laura Garcia-Perciante, March 2005.
UW-CPTC 05-3: “Nonlinear extended magnetohydrodynamics simulation using high-order finite elements” by C.R. Sovinec, et al., 2005.
UW-CPTC 05-4: “Banana regime pressure anisotropy in a bumpy cylinder magnetic field” by A.L. Garcia-Perciante, J.D. Callen, K.C. Shaing & C.C. Hegna, August 7, 2005.
UW-CPTC 05-5: “Drift waves in helically symmetric stellarators” by T. Rafiq and C.C. Hegna, July 6, 2005.
UW-CPTC 05-6: “Numerical Studies of Magnetohydrodynamic Activity Resulting from Inductive Transients” by C.R. Sovinec, August 2005.
UW-CPTC 05-7_rev: “Sheared flow effects on ballooning instabilities in three-dimensional equilibria” by C.C. Hegna, revised September 14, 2005.
UW-CPTC 05-8: “Final Report on the OFES ELM Milestone for FY2005” by D.P. Brennan, E.D. Held, S.E. Kruger, A.Y. Pankin, D.D. Schnack and C.R. Sovinec, September 30, 2005.
UW-CPTC 05-9: “Resistive Ballooning Modes In HSX?” by J.D. Callen, October 11, 2005.
UW-CPTC 05-10: “Nonlinear Growth of a Line-tied g-Mode Near Marginal Stability” by P. Zhu, C.C. Hegna and C.R. Sovinec, December 2005.
UW-CPTC 04-1_rev2: “Most Electron Heat Transport Is Not Anomalous; It’s A Paleoclassical Process In Toroidal Plasmas” by J.D. Callen, second revision October 25, 2004.
UW-CPTC 04-2: “Stabilization of Line Tied Resistive Wall Kink Modes with Rotating Walls” by C.C. Hegna, April 14, 2004.
UW-CPTC 04-3_rev3: “Paleoclassical Transport In Low Collisionality Toroidal Plasmas” by J.D. Callen, third revision June 30, 2005.
UW-CPTC 04-4: “Compressibility effect on magnetic-shear-localized ideal magnetohydrodynamic interchange instability” by Sangeeta Gupta, J.D. Callen and C.C. Hegna, July 8, 2004.
UW-CPTC 04-5: “Perturbing Ideal Magnetohydrodynamic Stability for Toroidal Plasmas” by Kate Comer, August 2004.
UW-CPTC 04-6: “Time-dependent neoclassical viscosity” by A.L. Garcia-Perciante, J.D. Callen, K.C. Shaing and C.C. Hegna, October 4, 2004.
UW-CPTC 04-7: “Numerical Investigation of Transients in the SSPX Spheromak” by C.R. Sovinec, B.I. Cohen, G.A. Cone, E.B. Hooper and H.S. McLean, October 2004.
UW-CPTC 04-8_rev: “Paleoclassical Electron Heat Transport” by J.D. Callen, revised October 2004.
UW-CPTC 04-9_rev: “Paleoclassical electron heat transport” by J.D. Callen, revised June 30, 2005.
UW-CPTC 03-1: “Magnetic Island Effects on Axisymmetric Equilibria” by X. Liu, J.D. Callen and C.C. Hegna, December 2003.
UW-CPTC 03-2: “Hybrid Kinetic-MHS Simulations in General Geometry” by Charlson C. Kim, Carl R. Sovinec and Scott E. Parker, November 19, 2003.
UW-CPTC 03-3: “Time-Dependent Neoclassical Viscosity” by A.L. Garcia-Perciante, December 19, 2003.
UW-CPTC 03-4_rev: “Role of Bumpy Fields on Single Particle Orbit in near Quasi-Helically Symmetric Stellarators” by JaeChun Seol and C.C. Hegna, revised April 2004.
UW-CPTC 03-5: “Linear Resistive Layer Equations in the Presence of Sheared Torodial Rotation” by C.C. Hegna, December 2003.
UW-CPTC 02-1: “On the Poloidal Beta Evolution of Fixed-q Heating in Tokamaks” by M.W. Kissick, J.-N. Leboeuf & S.E. Kruger, January 2002.
UW-CPTC 01-3: “A Tutorial on NIMROD Physics Kernel Code Development” by Carl R. Sovinec, August 2001.
NE/Physics/ECE 922 Seminar
Hurst-Noah_Oct23_2023.pdf: “Non-disruptive tokamak operation far beyond traditional safety factor and density limits”
Royce-James_Sept18_2023.pdf: “Rising Tides Lift all Boats: Fusion Energy Science, Plasma, Diversity, Equity, Inclusion, & Accessibility (DEIA) – the Intersectionality of a Healthy to Innovative
Spaces and a ‘People Centered’ Focus to Drive Outcomes and Discovery”
John-Edwards_Sept8-9_2014.pdf: “In pursuit of Ignition – recent progress and directions at the National Ignition Facility” by John Edwards, LLNL.
Oliver-Schmitz_and_Gavin-Weir_abstracts_Oct20_2014.pdf: Oliver Schmitz and Gavin Weir abstracts Oct20, 2014. | {"url":"https://cptc.wisc.edu/report/","timestamp":"2024-11-09T06:38:19Z","content_type":"text/html","content_length":"90113","record_id":"<urn:uuid:9087544c-0bef-4c13-88c5-9572c3f92a77>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.30/warc/CC-MAIN-20241109053958-20241109083958-00200.warc.gz"} |
Example to illustrate idea that likelihood ratio must be computed from same data
Last updated: 2017-01-02
Code version: 55e11cf8f7785ad926b716fb52e4e87b342f38e1
Suppose that we are considering whether to model some data \(X\) as normal or log-normal. In this case we’ll assume the truth is that the data are log normal, which we can simulate as follows:
X = exp(rnorm(1000,-5,2))
We will use \(Z\) to denote \(\log(X)\):
Z = log(X)
And let’s check by graphing which looks more normal:
\(M_2: \log(X)\) is normal" is better than the model “\(M_1: X\) is normal”.
Now consider computing a “log-likelihood” for each model.
To compute a log-likelihood under the model “X is normal” we need to also specify a mean and variance (or standard deviation). We use the sample mean and variance here:
sum(dnorm(X, mean=mean(X), sd=sd(X),log=TRUE))
[1] -135.3375
Doing the same for \(Z\) we obtain:
sum(dnorm(Z, mean=mean(Z), sd=sd(Z),log=TRUE))
[1] -2125.232
Done this way the log-likelihood for \(M_1\) appears much larger than the log-likelihood for \(M_2\), contradicting both the graphical evidence and the way the data were simulated.
The right way
The explanation here is that it does not make sense to compare a likelihood for \(Z\) with a likelihood for \(X\) because even though \(Z\) and \(X\) are 1-1 mappings of one another (\(Z\) is
determined by \(X\), and vice versa), they are formally not the same data. That is, it does not make sense to compute \[\text{"LLR"} := \log(p(X|M_1)/p(Z|M_2))\].
However, we could compute a log-likelihood ratio for this problem as \[\text{LLR} := log(p(X|M_1)/p(X|M_2)).\] Here we are using the fact that the model \(M_2\) for \(Z\) actually implies a model for
\(X\): \(Z\) is normal if and only if \(X\) is log-normal. So a sensible LLR would be given by:
sum(dnorm(X, mean=mean(X), sd=sd(X),log=TRUE)) - sum(dlnorm(X, meanlog=mean(Z), sdlog=sd(Z),log=TRUE))
[1] -3080.778
The fact that the LLR is very negative supports the graphical evidence that \(M_2\) is a much better fitting model (and indeed, as we know – since we simulated the data – \(M_2\) is the true model).
Session information
R version 3.3.2 (2016-10-31)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 14.04.5 LTS
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] rmarkdown_1.1
loaded via a namespace (and not attached):
[1] magrittr_1.5 assertthat_0.1 formatR_1.4 htmltools_0.3.5
[5] tools_3.3.2 yaml_2.1.13 tibble_1.2 Rcpp_0.12.7
[9] stringi_1.1.1 knitr_1.14 stringr_1.0.0 digest_0.6.9
[13] gtools_3.5.0 evaluate_0.9
This site was created with R Markdown | {"url":"https://rawcdn.githack.com/stephens999/fiveMinuteStats/0713277eda2ef15ef7f1bc52f287a9027db4e017/docs/LR_error.html","timestamp":"2024-11-03T13:24:40Z","content_type":"application/xhtml+xml","content_length":"14039","record_id":"<urn:uuid:9cf8cbe1-8f7e-45ac-bb49-cd44606de669>","cc-path":"CC-MAIN-2024-46/segments/1730477027776.9/warc/CC-MAIN-20241103114942-20241103144942-00011.warc.gz"} |
Extreme Gradient Boosting with XGBoost and Cluster Analysis in Python
Gradient boosting is currently one of the most popular techniques for the efficient modeling of tabular datasets of all sizes. XGboost is a very fast, scalable implementation of gradient boosting,
with models using XGBoost regularly winning online data science competitions and being used at scale across different industries. Extreme Gradient Boosting is a tree-based method that belongs to
Machine Learning's supervised branch. While the approach can be used for both classification and regression problems, this story's formulas and examples all apply to classification.
A classification problem involves predicting the category a given data point belongs to out of a finite set of possible categories. Depending on how many possible categories there are to predict, a
classification problem can be either binary or multi-class. An example of a Binary Classification problem would be predicting whether a given image contains a cat or not. Binary Classification
involves picking between two choices.
To create a XGBoost model we can use the scikit-learn .fit() / .predict() paradigm , as the xgboost library has a scikit-learn compatible API!
We will be working with churn data. This dataset contains imaginary data from a ride-sharing app with user behaviors over their first month of app usage in a set of imaginary cities as well as
whether they used the service 5 months after sign-up. the DataFrame create is called churn_data.
Our goal is to use the first month's worth of data to predict whether the app's users will remain users of the service at the 5-month mark. To do this, we'll split the data into training and test
sets, fit a small xgboost model on the training set, and evaluate its performance on the test set by computing its accuracy.
# Import xgboost
import xgboost as xgb
# Create arrays for the features and the target: X, y
X, y = churn_data.iloc[:,:-1], churn_data.iloc[:,-1]
# Create the training and test sets
X_train, X_test, y_train, y_test= train_test_split(X, y, test_size=0.2, random_state=123)
# Instantiate the XGBClassifier: xg_cl
xg_cl = xgb.XGBClassifier(objective='binary:logistic', n_estimators=10, seed=123)
# Fit the classifier to the training set
xg_cl.fit(X_train, y_train)
# Predict the labels of the test set: preds
preds = xg_cl.predict(X_test)
# Compute the accuracy: accuracy
accuracy = float(np.sum(preds==y_test))/y_test.shape[0]
print("accuracy: %f" % (accuracy))
XGBoost gets its lauded performance and efficiency gains by utilizing its own optimized data structure for datasets called a DMatrix.
# Create arrays for the features and the target: X, y
X, y = churn_data.iloc[:,:-1], churn_data.iloc[:,-1]
# Create the DMatrix from X and y: churn_dmatrix
churn_dmatrix = xgb.DMatrix(data=X, label=y)
# Create the parameter dictionary: params
params = {"objective":"reg:logistic", "max_depth":3}
# Perform cross-validation: cv_results
cv_results = xgb.cv(dtrain=churn_dmatrix, params=params,
nfold=3, num_boost_round=5,
metrics="error", as_pandas=True, seed=123)
# Print cv_results
# Print the accuracy
Hence we can conclude that XGBoost helps in increasing ht performance sig its own data structures and packages.
Cluster Analysis in Python
We all have used Google News, which automatically groups similar news articles under a topic. have you ever wondered what process runs in the background to arrive at these groups?
Clustering is an unsupervised machine learning model. It involves automatically discovering natural grouping in data. A cluster is often an area of density in the feature space where examples from
the domain (observations or rows of data) are closer to the cluster than other clusters. The cluster may have a center (the centroid) that is a sample or a point feature space and may have a boundary
or extent.
For this article, we will be taking the pokemon sighting problem. There have been reports of sightings of rare, legendary Pokémon. First, we will plot the coordinates of sightings to find out where
the Pokémon might be.
# Import plotting class from matplotlib library
from matplotlib import pyplot as plt
# Create a scatter plot
plt.scatter(x, y)
# Display the scatter plot
Notice the area that are dense, they helps us to understand that there are two legendary Pokémon
This means that the points seem to separate into two clusters. In this exercise, we will form two clusters of sightings using hierarchical clustering.
# Import linkage and fcluster functions
from scipy.cluster.hierarchy import linkage, fcluster
# Use the linkage() function to compute distance
Z = linkage(df, 'ward')
# Generate cluster labels
df['cluster_labels'] = fcluster(Z, 2, criterion='maxclust')
# Plot the points with seaborn
sns.scatterplot(x='x', y='y', hue='cluster_labels', data=df)
The clusters are plotted in two different colors now.
Now we do clustering of the sightings using k-means clustering.
# Import kmeans and vq functions
from scipy.cluster.vq import kmeans, vq
# Compute cluster centers
centroids,_ = kmeans(df, 2)
# Assign cluster labels
df['cluster_labels'], _ = vq(df, centroids)
# Plot the points with seaborn
sns.scatterplot(x='x', y='y', hue='cluster_labels', data=df)
Hence, we can conclude that clustering can be helpful as a data analysis activity in order to learn more about the problem domain, so-called pattern discovery or knowledge discovery. | {"url":"https://www.datainsightonline.com/post/extreme-gradient-boosting-with-xgboost-and-cluster-analysis-in-python-1","timestamp":"2024-11-14T21:09:57Z","content_type":"text/html","content_length":"1050377","record_id":"<urn:uuid:3366baee-0392-43a0-bf5b-86c7c5cbc69b>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00485.warc.gz"} |
Problem 1304 - USTC Online Judge
Problem 1304
The least cost
Time Limit: 1000ms
Memory Limit: 65536kb
There is an undirected graph with V verticals and E edges. Can you find the least-cost path between source vertex S and destination vertex D according to the following rules?
First, each edge has two costs A and B, and you have two skills named Skill-One and Skill-Two. When passing an edge, you can choose whether using skills or not.
If you want to use skills when passing an edge, Skill-One or Skill-Two can be chosen (but can't choose both simultaneously). What's more, Skill-One (or Skill-Two) can be only used on one edge of the
path at most. Skill-Two only can be used after Skill-One. More details about the two skills are as below:
1) Skill-One can help you to pass the edge by costing A/2 or B/2(such as 5/2=2).
2) Skill-Two can help you to pass the edge by costing A/3 or B/3(such as 5/3=1).
If you do not want to use skills when passing an edge, the passing cost depends on the conditions of your using of past skill. More details as follows:
1) Paying A or B if Skill One and Skill Two both have been used before.
2) Paying A + B if Skill One and Skill Two neither have been used before.
3) Paying A if Skill One have been used and Skill Two have not been used before.
Can you find the least cost between between S and D?
Notice: As you know, there is no condition that Skill-Two is used but Skill-One has not been used.
The first line, an integer T, indicates number of test cases (T<=10). For each test case:
The first line: four numbers V, E, S, D, indicating verticals, edges, source, and destination respectively.
Each of the following E lines contains four numbers X, Y, A, B, indicating there exists an undirected edge with two costs A and B between vertex X and vertex Y.
2<=N<=1000, 1<=M<=2000, 1<=S, D<=N.
1<=X, Y<=N, X! =Y, 1<=A, B<=100.
All numbers in the input are integers
For each test, output the least-cost path, or output "-1" if not existing a path connecting S and D directly or indirectly.
Sample Input
Sample Output | {"url":"https://acm.ustc.edu.cn/ustcoj/problem.php?id=1304","timestamp":"2024-11-13T07:53:08Z","content_type":"text/html","content_length":"4748","record_id":"<urn:uuid:551b6366-2ad8-4ee4-a9bd-a6bb91d6f785>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00253.warc.gz"} |