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# Matrix - Science topic

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Questions related to Matrix

y=Ax+e where y is observed vector A is observation matrix n x is signal to be estimated by observing less than required as dimension of y is k n x is m(k<m).

I need to determine only the first natural frequency of the elastic beam, in order to continue to take the optimization of certain parameters of the beam. Given that the proposed model matrix occur with larger dimensions in symbolic form, the determination of the frequency is very slow. Therefore, I need a way to quickly determine only the first eigenvalues
of the matrix with dimensions nxn in symbolic form.

Does anyone have a good source for correcting for spatial auto correlation when comparing a species assemblage (site X species matrix) to a geographic distance matrix? I know a mantel test will tell me how correlated the variables are but how do you correct for this effect in subsequent analyses?

In general it is assumed to be positive semi definite. What are the consequences of assuming the cov matrix as positive definite

Is there any good reference to the conditions on matrices A,B,C,D such that

the equation of the form:

XCX+XD-AX-B=0

have any solution over a general finite field F ?

If affirmative, is there any description of all the solutions ?

Also, is there any formula for the number of solutions ?

Specifically, are there any known conditions for a unique solution and a formula for the unique solution ?

How can I use HIFOO in order to find a minimal-norm static-output-feedback ? Specifically, if A,B,C are the state space matrices of a continuous time linear system, how can I find, using HIFOO, a matrix K such that A-BKC would be stable and has a minimal norm ?

Also, if the system is a descrete time system, can I use HIFOO in the same way ?

Is there any possibility to approximate any general/square matrix to an idempotent matrix?

I want to do a long term experiment with photocatalytic TiO2 under outdoor conditions and I am looking for a matrix that does not inhibit TiO2 photocatalysis very much and on the other hand itself is stable against the photocatalysis. Has anyone experience with that?

In formula (7) the min operator look to applied only to matrix B

_{j1 , }but in my understanding it should be applied to the whole formula. Am i correct?Hi.

I used PCA to extract the principal components of a set of 5 variables. The eigenvalue of the first component is 1.98, and for the second is 0.98. So I retain the first PC (because it is >1). The loadings matrix (prcomp.object$rotation) is:

Standard deviations:

[1] 1.8964529 0.9809027 0.5126452 0.4047367 0.1211575

Rotation:

PC1 PC2 PC3 PC4 PC5

v1 0.4854578 -0.1426120 -0.3791216 -0.7605055 -0.14795533

v2 -0.4461265 -0.3337826 -0.8067325 0.1899892 -0.05144943

v3 -0.3395503 -0.7385043 0.3986846 -0.3292091 0.26830763

v4 -0.4364794 0.5355879 -0.1179392 -0.4308451 0.56841368

v5 -0.5094048 0.1897576 0.1805279 -0.3025383 0.76182615

It strikes me a bit that the loadings of all the variables in PC1 (the only component to be retained) are quite low (<0.51).

How should I interpret this result?

Isn't PCA appropiate here?

Or is it just normal (and the correlation between the original variables and PC1 is just low)?

Thanks!

I am about to collect data for my project which is about wound healing. I will use Oasis as a collagen based matrix. I looked to the literature and I didn't get enough information.

Hi.

I want to build the Fock Matrix in Gaussian.

First of all, I create the Z-matrix using

**Avogadro**software, and later I use**Gaussian**with IOP (iop(5/33=3)), but I don't know how to search this matrix....sometimes appear "Fock matrix is not symmetric: symmetry in diagonalization turned off" in the log txt.How have to search the fock matrix, when appear it?

Thanks in advance.

Where can use composites that have a higher storage modulus than the matrix.

Please help.

Is there a relation between rank of a matrix polynomial and its eigenvalues? Somewhat like what exists between rank a matrix and its eigenvalues.

Can we have a matrix and determinant, whose elements are other matrices?

If this exists then how can we find eigenvalues of such matrices?

In the structural soil interaction, is it possible the non-diagonal element of the mass matrix to be zero? In what condition is it possible?

Thanks in advance

I have a 3D heat transfer model. I want to get state space of 3D, but when I got state space, the matrix is so large. Does anyone know how to reduce matrix or how to convert 3D to 2D model so that I can get smaller matrix. Thank you very much for you help.

I need to invert a large singular matrix

I'm making use of AUC values got from weka tool as result.....found that tool is using trapezoidal approximation method... but not yet very clear.....

How do I normalize a matrix?

How do I normalize any matrix?
Is it column or row wise normalization?
Is it right that we have to divide each column of a matrix by the square root of the sum of each element of that column?

Is it possible to create a geographical distance matrix without the pop coords worksheet for the Mantel test using Genalex software?

I am using GenALEx software for my codominant microsatellite data. In the genalex tutorial 3 ex 3.3 mantel test for isolation of distance they have mentioned a worksheet named pop coords which contains UTM values this worksheet is activated for geographic distance matrix.
Is it possible to create geographical distance matrix without pop coords worksheet. If not how to create that sheet.

Second phase/particles can have coherent/semi-coherent/non-coherent bonding with the metal matrix. Is there a way to have a feeling about the second phase coherency using EBSD? Can KAM analysis around the second phase show us anything in this regard?

Can interface coherency be analyzed by Geometrical Necessary Dislocation measurements?

Of course one challenge would be the EBSD resolution that is a few ten nm..

Using the Neel mechanism, we hope that the size can be fairly well controlled so that a predictable relaxation rate results. The particles would probably end up in a matrix of surfactant or something similar. We hope that the bulk susceptibility (blocking/DC) will be at least 2.

I have found that sometimes inverse and pseudo inverse of a covariance matrix are the same whereas it is not true always. is there any relation between pseudoinverse and nonsingularity?

I have a matrix and i have shown the output of matrix one by one element in FortranForm.

the problem is i want to put "&" continuation charater in output because when I am copying the data into fortran Code, Fortran is showing warning that it exceeds 2048 characters .

So i wanted to put ampersand character in each output of matrix element in FortranForm. please help

I would like to test dissimilarities among different groups in a dist matrix. For instance, if I have a dist matrix with three factors a, b, c, functions like adonis and betadisper in R will test the aa, bb and cc combinations. However, I am interested in testing the ba, ca, and cb combinations. How can I test for these combinations?

**a a a b b b c c c**

**a**aa

**a**aa aa

**a**aa aa aa

**b**ba ba ba bb

**b**ba ba ba bb bb

**b**ba ba ba bb bb bb

**c**ca ca ca cb cb cb cc

**c**ca ca ca cb cb cb cc cc

**c**ca ca ca cb cb cb cc cc cc

If I have some symmetric vector, representing radial distribution of data (the Line Spread Function (LSF) of the optical system, in my case, and a priori I know that PSF has circular symmetry), how, from this vector, can I create a circularly symmetric matrix (representing the PSF of the system)? And vise versa?

For example, I have a vector representing 1D Gaussian, and I want matrix of 2D Gaussian.

Thank you in advance!

If the Wave Function of a quantum system is known, how do I obtain the dipole transition matrix elements?

Can anyone send me or tell me where i may find the piezoelectric, the dielectric and elastic properties parameters/constants matrixes of the following compositions or any other compositions of PVDF copolymers and the terypolymers?

P(VDF-TrFE)56/44 mol%-P(VDF-TrFE)68/32 mol%

P(VDF-HFP) 85/15 mol%

P(VDF-CTFE)88/12 mol% and

P(VDF–TrFE–CFE) 68/32/9 mol%

Thank You !

Any suggestion/resources are appreciated.

where [KL] is stiffness matrix linear and [KNL] is stiffness matrix non-linear?

[

**M**]{d2**D**/dt2}+[**G**]{d**D**/dt}([**KL**]+[**KNL**]){**D**}={0}a c 0 … 0 1

b a c 0 … 0

0 b a c 0 … 0

0 0

. a c 0

. b a c

1 0 … 0 b a

I have 12 constructs meant to be measuring different aspects of the same construct - will I have remove some of these? or are there other remedies

This is for stable isotope analysis

Hi all,

I am trying to prepare a computational model of a particular protein (matrix metaloproteinaise 1 (MMP1)) found in the extracellular matrix of humans. However, I am struggling to find a reliable source for the measurement of water density in this environment. If anyone knows of an article with this values, and/or a description of the ion-solvent composition, I would be extremely grateful.

Many thanks

All possible combinations should be used.

By "solution", I mean a PseudoInverse. By "exact", I mean a formula, not a fit (such as SVD) or a decomposition.

Or why are good dispersion and bad distribution of filler good for electrical conductivity? Thanks in advance

We have known that the asymptotic determinant of the covariance matrix when its order goes to infinity.

I am wondering whether there is the close form in the finite case? Thanks,

>> A = sym('A', [2 4]) % symbolic matrix without having to define its elements.

A =

[ A1_1, A1_2, A1_3, A1_4]

[ A2_1, A2_2, A2_3, A2_4]

>> A' % transpose of A

ans =

[ conj(A1_1), conj(A2_1)]

[ conj(A1_2), conj(A2_2)]

[ conj(A1_3), conj(A2_3)]

[ conj(A1_4), conj(A2_4)]

**By default Matlab sets symbolic elements as 'Complex Number'.**

>> syms x y real % x y declared a 'Real'

>> f=[x y]

f =

[ x, y]

>> f'

ans =

x

y

I need a way to declare the elements in the matrix as 'Real'.

My Y axis values are overlapping. (attached the image below) it seems I need an .m2p file.

COMMANDS I USED

do_dssp -s md.tpr -f md.trr -o dssp.xpm

xpm2ps -f dssp.xpm -di scale.m2p -do scale.m2p -o dssp

scale.m2p

; Command line options of xpm2ps override the parameters in this file

black&white = no ; Obsolete

titlefont = Times-Roman ; A PostScript Font

titlefontsize = 20 ; Font size (pt)

legend = yes ; Show the legend

legendfont = Times-Roman ; A PostScript Font

legendlabel = ; Used when there is none in the .xpm

legend2label = ; Used when merging two xpm's

legendfontsize = 14 ; Font size (pt)

xbox = 2.0 ; x-size of a matrix element

ybox = 2.0 ; y-size of a matrix element

matrixspacing = 20.0 ; Space between 2 matrices

xoffset = 0.0 ; Between matrix and bounding box

yoffset = 0.0 ; Between matrix and bounding box

x-major = 20 ; Major ticks on x axis every .. frames

x-minor = 5 ; Id. Minor ticks

x-firstmajor = 0 ; First frame for major tick

x-majorat0 = no ; Major tick at first frame

x-majorticklen = 8.0 ; x-majorticklength

x-minorticklen = 4.0 ; x-minorticklength

x-label = ; Used when there is none in the .xpm

x-fontsize = 16 ; Font size (pt)

x-font = Times-Roman ; A PostScript Font

x-tickfontsize = 10 ; Font size (pt)

x-tickfont = Helvetica ; A PostScript Font

y-major = 20

y-minor = 5

y-firstmajor = 0

y-majorat0 = no

y-majorticklen = 8.0

y-minorticklen = 4.0

y-label =

y-fontsize = 16

y-font = Times-Roman

y-tickfontsize = 10

y-tickfont = Helvetica

The equation of the system is

dx(t)/dt=A(t)x(t) where A is 2*2 matrix

In floquet-lyaponov theory it is said that using two independent initial conditions we can calculate PHI(t) matrix which is state transition matrix.

let A=[0 exp(t) ;

0 1]

By taking independent initial conditions [1;0] and [0;1] how we can calculate phi matrix?

First at all, thanks (Afendras) for your help. I really appreciate it. I want to apply resultants matrices in Legendre base to avoid change of basis and apply resultants matrices in the non monomial basis such as in legendre or chebysheve base without conversion between basis. Can you please suggest some papers or other helpful information? Thanks

In fact, I downloaded it and I face a problem with the output of the ([label_vector, instance_matrix] = libsvmread('../data');)

It gives me usually as empty matrix, and I usually get the same error. although the input matrix for the libsvmwrite a sparse matrix(double).Please,could you help me as faster as you can.

Notes:

I'm working on matlab with windows 7, and I'm working on multi classification problem.

Thank you in advance.

Let a matrix contains a11= 2^2+a^2

then how to show the output to be like a11=2.d0**2+a**2

Mathematica user can solve this problem.

we must determine Cr in the matrix "air", we can collect samples of dust by high and low volume sampler. What are the best techniques for sampling, pretreatment and analysis?

Hi, guys. I got a problem in my recent research. It can be sketched as follows:

How to theoretically choose a positive \alpha such that the matrix D=B*B^T/\alpha+B*inv(A)*B^T is nonsingular or well-conditioned? Here B is an m-by-n matrix (n >=m) and A is an n-by-n nonsingular matrix .

(SHHY) Algorithm The standard Hussein, Hind and Yahya method for removable salt and pepper image noise.

I want to make a double layered system consist of Hydrogel and electrospun matrix. How to place a hydrogel on the top of electrospun fibrous matrix?

My question is quite simple. I am implementing a greedy algorithm technique over the coefficients of a matrix and selecting the best coefficient according to some criteria. The matrix size is 50x1000. In every iteration a single coefficient is selected for operations. The problem before the initiation of the algorithm is out of 50,000 coefficients I have 25,000 candidate coefficients which I should process. Now in the first iteration I have to select the best coefficient among the 25,000 and in the successive iterations I have to select one from 24999, 24998, 24997. So as you see, the algorithm is quite time consuming because in each iteration I have to calculate the benefit of all the coefficients and select the best one according to the benefit and this benefit processing is a further matrix operation which is also time consuming. Do you have any idea how to reduce the computation time of the algorithm? My implementation language is java. Any help or ideas are appreciated.

I'm looking for the efficient matrix manipulation free (open source/GPL/etc.) library for the .NET framework (v.4.5 would be the best).

I have a matrix X with n*f dimensions and a matrix A with f*f dimensions.

I need to calculate for each row of matrix X, X(i,:)* A* X(i,:)' where X(i,:)' is transpose of X(i,:),

because of speed issues, I don't want to use loop, is there any way to do this multiplication without loop in MATLAB?

I have developed a mass and stiffnes matrix for my problem..natural frequency and modeshapes are also calculated..damping ratio is given..how can i develop damping matrix? Which equation should I use? If I use the equation 2*si*w*M, will i get d correct damping matrix?

Is it related to the rank of the Jacobian matrix? I know in continuous time this is true, but I am not sure about discrete time. Any references and links are welcome.

I want to use some hybrid functions of orthogonal functions for approximation and the problem of finding Operational Matrix of Integration, Product, Delay of Hybrid Functions (i.e block pulse with Taylor, chebyshev, hermite, B-Spline, Bernstein,...)

I have measured the scattering parameters of carbon matrix in GHz frequencies, results indicate the dielectric constant is very high

Does anyone know some applications of the smallest or largest singular value and vector of an M-matrix? I have learnt some in the synchronization and asynchronization of coupled chaotic dynamical systems, where these quantities of the M-matrix are desired. Any more description or references are much appreciated.

I need to convert a similarity matrix into a vector, ie, a variable that represents the matrix.

I have a .txt file that contains information in the following pattern :

The data is separated in the form of

255,205,0 102,235,39 206,89,165 ....... (that is, 3 uint8 integers separated by commas, and the groups of 3 separated by whitespaces). There are a total of 30*60 = 1800 triplets of numbers separated by commas and the triplets are separated by spaces.

Basically, these are pixel intensities of the 3 channels in an RGB image. I need to store them in a 2 dimensional array such that the first element of each triplet goes into the 1st column, the second element into the 2nd column and the 3rd element into the 3rd column. Effectively, at the end of this operation, I should have a 2 dimensional matrix of 1800x3 size.

Please help me with this. I have attached a sample text file. Thanks in advance.

I am doing in vitro matrix degradation assay with Enatmoeba histolytica and I observe different behavior of the pathogen towards two different components of the ECM viz Fibronectin and collagen type I. The pathogen infects the intestine and in severe infections can breach the mucosal lining of the gut and escape to the liver causing liver abscess but still persons infected with it can also act as asymptomatic carriers and some people show severe infection with the infection flaring up and causing massive tissue damage.

So, can the ECM composition trigger such kind of response, which can vary from one person to the other?

Any suggestion for an open-source matrix library?

I am finalizing my algorithm on Matlab so I need to transfer the code to C++ language in order to test it on large-scale problems by using PC clusters. Do you have any suggestion for an open-source linear algebra matrix library? Reliability, memory and computation efficient implementation and flexibilty in usage is requested.

For example, consider shaft as shown in the picture and consider the elements type as shown below.

In many practical problems, we get a large sparse matrix. Can we find determinant of this matrix efficiently?

I am modeling a pipe. I have to calculate a mass matrix and stiffness matrix using the finite element method. Every node has two degrees of freedom.

c = all(b>=-100*eps);

b is a matrix I already have.

what can you say about matrix c?

2.2204e-16 is the value of eps which command window shows.

. I have Ax = Iy, where A matrix and I Identity matrix.

We found the following rather simple result. We suspect its been proven decades ago, but we couldn't turn up this fact after several searchers. (If this is known, please provide a reference.)

Let B be a square matrix over a finite commutative ring with unity. Then det(B) equals zero or is a zero divisor if and only if the set of row vectors of B is dependent.

Constrained generalized inverse of a non square matrix?

Suppose that we have a system of linear equations given by:
Ax = b ; $ A \in R^{m,n}$
subject to: x_min < x < x_max
How can we obtain the minimum norm solution respecting the constraint "without optimization"?

I have got a data matrix generated on some plant species as proportions from certain quantitative measurements. Since such data (proportions, percentages, probabilities) are generally known to be skewed with unequal variances, I intend to transform mine before ANOVA. I understand that the arcsine or logit transform can be the best for such data. However I am constrained by the fact that the proportions obtained by me do not only lie between 0 and 1. Many of them include values above 1 (i.e. percent increase, giving values greater than 100%). How best (with reasons) can the data be transformed prior to the proposed analysis?

I have some problem related to matrix inversion.

What has present day spectrometry inherited from the low-level gamma ray scintillation methods introduced by Leonidas D. Marinelli, beginning in 1950?

In 1950 Marinelli invented and developed a "twin" scintillator method for dosimetry and spectrometry of fast neutrons and its application to the measurement of cosmic-ray neutron background." (Patent 27795-703, June 11, 1957.) By 1953 he achieved the sensitivity of the method to the measurement of the natural K-40 content of man and animals. In 1958 he presented the Janeway Lecture on "Radioactivity and the Human Skeleton." In 1969 he published "Localization of scintillations in gamma-ray cameras by time-of-flight techniques:Linear resolutions attainable in long fluorescent rods." In 1970 he published "Time-of-flight" gamma-ray camera of large dimensions" with he objective of "measuring time intervals in the nanosecond region. This suggests the use of time-of-flight techniques in the localization of scintillations within large fluors and hence the estimate of the distribution of low-level radioactivity in vivo. We devote special attention to the solution of Fredholm's equation of the first kind, linking the scintillation matrix to the radioactivity distribution matrix to develop the kernel of the equation (and hence the physical collimation) most appropriate to the objective."

I got the scheme graph as attached. Can I determine the molecular weight of the polymer? I don't understand whether the data is correct or not.

Different anions have no same infects on bacterial,How to choose the functional group? Any articles I can consult in?

I have a hollow tapered vertical tower..I have developed stiffness matrix considering translational and rotational using the function defined in BATHE's book..but, since I need to use tuned liquid column damper at the top, I have to develop stiffness matrix in such away that only translational motion along horizontal should be considered. Can you suggest any method? I couldn't find any suitable method. I tried to do in ansys also using beam 54 element restricting ROTZ and UY..but my frequencies are not matching with the previously calculated frequency.

I dont have the analytical expression of the periodic solution at which i compute the monodromy matrix but i have proved that it exists through the gaines and Mahwin continuation theorem.

Actually I already downloaded and installed markovchain package in R but I have difficulty following the instruction guide of the developer. I am estimating the transition probabilities of loan data from different states of delinquencies.

I have established a SMC/EC 3D co culture system. Now I am trying to do Immunofluorescence of the co culture. I am having troubles like the ECs form a uniform monolayer on the top of the SMCs. The SMCs are in a collagen matrix. So I need to do anti alpha actin IF of SMCs. How can I do it? I can fix the sample and use triton x for permeabilization, but it would disrupt the ECs adhesions. Also if I do collagenase and make cells suspensions, it might interfere with the cell morphology and what not. Is there a way to do IF without disturbing both cells? I am using µ slides from ibidi.

In doping, Whether increment of metal percentage on SC matrix or phase control of SC or varies metal on SC or some other important.

What are the advantages of using pearson correlation matrix instead of using polycoric corelation matrix in factor analysis?

I am writing an article and I need convincing reasons to use pearson correlation matrix I did not find an answer anywhere.

Thanks for your help

With my best wishes

As I understand the working of guass quadrature and calculation of global displacements in FE method,

Gauss quadrature is used to quickly calculate the values in the stiffness matrix which is much easier to do in element's local co-ordinate system eta and zhi.

On using a single point integration for this purpose a much softer value is returned in the global stiffness matrix which is later solved for displacements.

So, finally there will be non-zero nodal displacements and thus a strain is induced in the Finite element. Why is it said that there is no strain energy in hourglass mode?

I have read some articles which explain this using the concept of integration points. According to them, the integration point has not moved - so there will be no strain. But arent we calculating all values on nodes in global equation [K][X]=[F] than on integration points?

- Do you have any references about this topic?
- I am working on UHTCs (e.g. ZrB2-SiC composites)

In the attached paper by Francois Leyvraz, I could not get past eqs.(6-7b) for the following reason: if you differentiate eq.(5) with respect to t, you obtain R(dot) super T times R + R super T times R(dot) = 0 , or, using nomenclature from the paper, Omega sub b + R(dot) super T times R = 0. Omega sub l does not appear. Moreover, if R is antisymmetric (as it must be), that does not imply that R(dot) is also antisymmetric. The product of any matrix with an antisymmetric one does not have to be antisymmetric...

I need to determine Pb in food samples by VARIAN 240FS AAS. What Is the best matrix modifier for the determination of Pb by VARIAN 240FS AA fast sequential atomic absorption? What type of chemical modifiers would you suggest?

Deleted!

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For a linear measurement equation l=Ax+v and a linear equality constraint Cx+d=0, where l is the measurement vector, A is the design matrix, x is the parameter vector to be estimated, v is the measurement error which is zero-mean with known covariance matrix R, I known how to estimate x using the Lagrange multiplier, the question is how to calculate the covariance matrix associated with this estimate?

How can I solve a system of matrix equations?

For example if I have system of matrix equations like this:
(A *X*B) -(C*Y*D)-(I*X'*G)= Q1, [EQ1]
(E*X*F)+(G*Y*H)= Q2.[EQ2]
** || all the matrices are of size n*n ||** Where A,B,C,D,E,F,G,H,I,G,Q1,Q2 are known matrices[all are invertible ] and X&Y are unknown matrices. I tried to use vectorization technique but because of X' &X together in EQ1 i am unable to do that. Can anyone suggest me some method to solve it (Preferably by using MATLAB) ? Thanks in advance.

I transferred 2D slices in 3D single Matrix.

A[4,4] is divided into 4 blocks of a

_{n}[2 2] then, A_{xx -> }a_{n}(y,z)The eigenvalues of εA+(1-ε)B (0<ε<1) locate inside the convex hull formed by all eigenvalues of both A and B.

Is the above statement true or false? (I guess is true)

How to prove it?

If S matrix is given for a general optical waveguide, I need to know about effective index & loss associated with that. The real part of the complex propagation constant gives effective index & imaginary part gives me attenuation coefficient.

Suppose that A is a matrix which is marginally stable and K stabilizes A through the fact that A+K is asymptotically stable. Then is it true that A+εK must also be asymptotically stable for any arbitrarily ε subject to ε>0? So how to prove it?

Is this matrix a positive or semi-positive definite matrix ?

[ 2 0 0 0

0 2 0 0

0 0 2 0

0 0 0 0 ]

Quadratic matrix equation:

such as A R

^{2}+ B R + C = 0.where A, B, C are matrices of nXn order. its solution is needed in order to get A minimal matrix.

In a Quantitative measurements using thick targets by relative method, how to correct for stopping power when the proton beam has different range in standard and sample. Also standard and sample are of slight different in matrix. Since beam will completely stop in the targets, so I am thinking how to use stopping power correction or Range correction of data when samples are thick?

I want to prepare the arlequin input file for my 0 and 1 matrix data (dominant marker). The data are huge. I want to mention the numbers of haplotypes that there are between individuals of one population and also between populations of one group and so on. But how can I find the haplotypes in my huge data? Is there any software or suitable way of doing it?

I am trying to develop polymer matrix patch. Can anyone please explain what will be minimum and maximum polymer % concentration in transdermal polymer matrix patch?

I am not able to find Apriori algorithm with boolean matrix generation algorithm.CAn anyone provide me code for it?

My second question is,using sampling technique ,if accuracy doesn't fall then,the algorithm with sampling of original algorithm can be called as enhanced algorithm??for my research?