53,582 research outputs found
An ontology-based approach to the optimization of non-binary (2,v)-regular LDPC codes
A non-binary (2,v)-regular LDPC code is defined by a parity-check matrix with
column weight 2 and row weight v. In this report, we give an ontology-based
approach to the optimization for this class of codes. All possible
inter-connected cycle patterns that lead to low symbol-weight codewords are
identified to put together the ontology. The optimization goal is to improve
the distance property of equivalent binary images. Using the proposed method,
the estimation and optimization of bit-distance spectrum becomes easily
handleable. Three codes in the CCSDS recommendation are analyzed and several
codes with good minimum bit-distance are designed.Comment: Technical Repor
Distribution of Coefficients of Modular Forms and the Partition Function
Let be an odd prime and be positive integers. We study the
distribution of the coefficients of integer and half-integral weight modular
forms modulo odd positive integer . As a consequence, we prove that for each
integer , Comment: 8page
Symmetry Partition Sort
In this paper, we propose a useful replacement for quicksort-style utility
functions. The replacement is called Symmetry Partition Sort, which has
essentially the same principle as Proportion Extend Sort. The maximal
difference between them is that the new algorithm always places already
partially sorted inputs (used as a basis for the proportional extension) on
both ends when entering the partition routine. This is advantageous to speeding
up the partition routine. The library function based on the new algorithm is
more attractive than Psort which is a library function introduced in 2004. Its
implementation mechanism is simple. The source code is clearer. The speed is
faster, with O(n log n) performance guarantee. Both the robustness and
adaptivity are better. As a library function, it is competitive
Linear Statistics of Matrix Ensembles in Classical Background
Given a joint probability density function of real random variables,
obtained from the eigenvector-eigenvalue decomposition of
random matrices, one constructs a random variable, the linear
statistics, defined by the sum of smooth functions evaluated at the eigenvalues
or singular values of the random matrix, namely, For
the jpdfs obtained from the Gaussian and Laguerre ensembles, we compute, in
this paper the moment generating function where denotes expectation
value over the Orthogonal () and Symplectic ( ensembles, in
the form one plus a Schwartz function, none vanishing over for the
Gaussian ensembles and for the Laguerre ensembles. These are
ultimately expressed in the form of the determinants of identity plus a scalar
operator, from which we obtained the large asymptotic of the linear
statistics from suitably scaled $F(\cdot).
Dealing With 4-Variables by Resolution: An Improved MaxSAT Algorithm
We study techniques for solving the Maximum Satisfiability problem (MaxSAT).
Our focus is on variables of degree 4. We identify cases for degree-4 variables
and show how the resolution principle and the kernelization techniques can be
nicely integrated to achieve more efficient algorithms for the MaxSAT problem.
As a result, we present an algorithm of time for the MaxSAT
problem, improving the previous best upper bound by Ivan
Bliznets and Alexander
Gap Probability Distribution of the Jacobi Unitary Ensemble: An Elementary Treatment, from Finite to Double Scaling
In this paper, we study the gap probability problem of the (symmetric) Jacobi
unitary ensemble of Hermitian random matrices, namely the probability that the
interval is free of eigenvalues. Using the ladder operator
technique for orthogonal polynomials and the associated supplementary
conditions, we derive three quantities instrumental in the gap probability,
denoted by , and . We find that each one
satisfies a second order differential equation. We show that after a double
scaling, the large second order differential equation in the variable with
as parameter satisfied by , can be reduced to the
Jimbo-Miwa-Okamoto form of the Painlev\'{e} V equation.Comment: 20 page
On the variance of linear statistics of Hermitian random matrices
Linear statistics, a random variable build out of the sum of the evaluation
of functions at the eigenvalues of a N times N random matrix,sum[j=1 to N]f(xj)
or tr f(M), is an ubiquitous statistical characteristics in random matrix
theory. Hermitian random matrix ensembles, under the eigenvalue-eigenvector
decomposition give rise to the joint probability density functions of N random
variables. We show that if f(.) is a polynomial of degree K, then the variance
of trf(M), is of the form,sum[n=1 to K] n(d[n])square, and d[n] is related to
the expansion coefficients c[n] of the polynomial f(x) =sum[n=0 to K] c[n] b
Pn(x), where Pn(x) are polynomials of degree n, orthogonal with respect to the
weights 1/[(b-x)(x-a)]^(1/2), [(b -x)(x -a)]^(1/2), [(b-x)(x-a)]^(1/2)/x; (0 <
a < x < b), [(b-x)(x-a)]^(1/2)/[x(1-x)] ; (0 < a < x < b < 1), respectively.Comment: 17 pages, 0 figures, variance of linear statistic
Linear Statistics of Random Matrix Ensembles at the Spectrum Edge Associated with the Airy Kernel
In this paper, we study the large behavior of the moment-generating
function (MGF) of the linear statistics of Hermitian matrices in
the Gaussian unitary, symplectic, orthogonal ensembles (GUE, GSE, GOE) and
Laguerre unitary, symplectic, orthogonal ensembles (LUE, LSE, LOE) at the edge
of the spectrum. From the finite Fredholm determinant expression of the MGF
of the linear statistics, we find the large asymptotics of the MGF
associated with the Airy kernel in these Gaussian and Laguerre ensembles. Then
we obtain the mean and variance of the suitably scaled linear statistics. We
show that there is an equivalence between the large behavior of the MGF of
the scaled linear statistics in Gaussian and Laguerre ensembles, which leads to
the statistical equivalence between the mean and variance of suitably scaled
linear statistics in Gaussian and Laguerre ensembles. In the end, we use the
Coulomb fluid method to obtain the mean and variance of another type of linear
statistics in GUE, which reproduces the result of Basor and Widom.Comment: 32 page
Three Dimensional Steady Subsonic Euler Flows in Bounded Nozzles
In this paper, we study the existence and uniqueness of three dimensional
steady Euler flows in rectangular nozzles when prescribing normal component of
momentum at both the entrance and exit. If, in addition, the normal component
of the voriticity and the variation of Bernoulli's function at the exit are
both zero, then there exists a unique subsonic potential flow when the
magnitude of the normal component of the momentum is less than a critical
number. As the magnitude of the normal component of the momentum approaches the
critical number, the associated flows converge to a subsonic-sonic flow.
Furthermore, when the normal component of vorticity and the variation of
Bernoulli's function are both small, the existence of subsonic Euler flows is
established. The proof of these results is based on a new formulation for the
Euler system, a priori estimate for nonlinear elliptic equations with nonlinear
boundary conditions, detailed study for a linear div-curl system, and delicate
estimate for the transport equations
Computational Optimal Control of the Saint-Venant PDE Model Using the Time-scaling Technique
This paper proposes a new time-scaling approach for computational optimal
control of a distributed parameter system governed by the Saint-Venant PDEs. We
propose the time-scaling approach, which can change a uniform time partition to
a nonuniform one. We also derive the gradient formulas by using the variational
method. Then the method of lines (MOL) is applied to compute the Saint-Venant
PDEs after implementing the time-scaling transformation and the associate
costate PDEs. Finally, we compare the optimization results using the proposed
time-scaling approach with the one not using it. The simulation result
demonstrates the effectiveness of the proposed time-scaling method
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