s duality as fourier transform for arbitrary ϵ1 ϵ2 the alday gaiotto tachikawa relations reduce s duality to the modular transformations of conformal blocks it was recently conjectured that for the four point conformal block the modular transform up to the non perturbative contributions can be written in the form of the ordinary fourier transform when 1 2 1 here i extend this conjecture to general values of 1 2 namely i argue that for a properly normalized four point conformal block the s duality is perturbatively given by the fourier transform for arbitrary values of the deformation parameters 1 2 the conjecture is based on explicit perturbative computations in the first few orders of the string coupling constant g2 1 2 and hypermultiplet masses

some matrix factorization identities for discrete inverse scattering this note analyzes the relationships between several inverse scattering methods and points out that all classical approaches implicitly construct a lower upper triangular factorization of a given positive definite toeplitz matrix it is shown that the various inversion methods implicitly obtain the factorization by solving different nested sets of linear equations and expressing the factors in terms of the solutions obtained the fact that the triangular factorization of a matrix with nonzero leading minors is unique immediately yields various identities e g involving the so called central mass sequence that were derived in the literature with considerably more manipulation in fact our basic factorization results are somewhat more general since they do not require the toeplitz assumption

structure property and design of nonbinary regular cycle codes in this paper we study nonbinary regular ldpc cycle codes whose parity check matrix h has fixed column weight j 2 and fixed row weight d through graph analysis we show that the parity check matrix h of a regular cycle code can be put into an equivalent structure in the form of concatenation of row permuted block diagonal matrices if d is even or if d is odd and the code s associated graph contains at least one spanning subgraph that consists of disjoint edges this equivalent structure of h enables i parallel processing in lineartime encoding ii considerable resource reduction on the code storage for encoding and decoding and iii parallel processing in sequential belief propagation decoding which increases the throughput without compromising performance or complexity on the code s structure design we propose a novel design methodology based on the equivalent structure of h finally we present various numerical results on the code performance and the decoding complexity

on the dotsenko fateev representation of the toric conformal blocks we demonstrate that the recent ansatz of maruyoshi and yagi 2010 arxiv 1009 5553 inspired by the original remark of r dijkgraaf and c vafa reproduces the toric conformal blocks in the same sense as the spherical blocks given by the integral representation of mironov et al 2010 j high energy phys jhep02 2010 030 arxiv 0911 5721 and mironov et al 2010 arxiv 1001 0563 with a peculiar choice of open integration contours for screening insertions in other words we provide some evidence that the toric conformal blocks are reproduced by appropriate ensembles not only in the large n limit but also at finite n the check is explicitly performed at the first two levels for the 1 point toric functions generalizations to higher genera are briefly discussed

sequential message passing decoding of ldpc codes by partitioning check nodes in this paper we analyze the sequential message passing decoding algorithm of low density parity check ldpc codes by partitioning check nodes this decoding algorithm shows better bit error rate ber performance than the conventional message passing decoding algorithm especially for the small number of iterations analytical results indicate that as the number of partitioned subsets of check nodes increases the ber performance is improved we also derive the recursive equations for mean values of messages at check and variable nodes by using density evolution with a gaussian approximation from these equations the mean values are obtained at each iteration of the sequential decoding algorithm and the corresponding ber values are calculated they show that the sequential decoding algorithm converges faster than the conventional one finally the analytical results are confirmed by the simulation results

cascading parity check error correcting codes a method for improving the performance of sparse matrix based parity check codes is proposed based on insight gained from methods of statistical physics the advantages of this approach are demonstrated on an existing encoding decoding paradigm suggested by sourlas we also discuss the application of the same method to more advanced codes of a similar type

finite size effects and error free communication in gaussian channels the efficacy of a specially constructed gallager type error correcting code to communication in a gaussian channel is examined the construction is based on the introduction of complex matrices used in both encoding and decoding which comprise sub matrices of cascading connection values the finite size effects are estimated for comparing the results with the bounds set by shannon the critical noise level achieved for certain code rates and infinitely large systems nearly saturates the bounds set by shannon even when the connectivity used is low

parallel versus sequential updating for belief propagation decoding abstract a sequential updating scheme sus for the belief propagation algorithm is proposed and is compared with the parallel regular updating scheme pus simulation results on various codes indicate that the number of iterations of the belief algorithm for the sus is about one half of the required iterations for the pus where both decoding algorithms have the same error correction properties the complexity per iteration for both schemes is similar resulting in a lower total complexity for the sus furthermore the sus utilizes significantly less memory during the decoding process we demonstrate that the acceleration in convergence time is related to the inter iteration information sharing which is a property of only the sus and which increases the correction gain per iteration finally the connection between the dynamics of error correcting codes and physical systems is discussed

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

q vertex operator from 5d nekrasov function the five dimensional agt correspondence implies the connection between the q deformed virasoro block and the 5d nekrasov partition function in this paper we determine a q deformation of the four point block in the coulomb gas representation from the 5d nekrasov function and obtain an expression of the q deformed vertex operator if we use only one kind of the q vertex operators one of the insertion points of them must be modified in order to hold the 2d 5d correspondence

iterative approximate linear programming decoding of ldpc codes with linear complexity the problem of low complexity linear programming lp decoding of low density parity check ldpc codes is considered an iterative algorithm similar to min sum and belief propagation for efficient approximate solution of this problem was proposed by vontobel and koetter in this paper the convergence rate and computational complexity of this algorithm are studied using a scheduling scheme that we propose in particular we are interested in obtaining a feasible vector in the lp decoding problem that is close to optimal in the following sense the distance normalized by the block length between the minimum and the objective function value of this approximate solution can be made arbitrarily small it is shown that such a feasible vector can be obtained with a computational complexity which scales linearly with the block length combined with previous results that have shown that the lp decoder can correct some fixed fraction of errors we conclude that this error correction can be achieved with linear computational complexity this is achieved by first applying the iterative lp decoder that decodes the correct transmitted codeword up to an arbitrarily small fraction of erroneous bits and then correcting the remaining errors using some standard method these conclusions are also extended to generalized ldpc codes

exact wkb and abelianization for the t_3 equation we describe the exact wkb method from the point of view of abelianization both for schrodinger operators and for their higher order analogues opers the main new example which we consider is the t 3 equation an order 3 equation on the thrice punctured sphere with regular singularities at the punctures in this case the exact wkb analysis leads to consideration of a new sort of darboux coordinate system on a moduli space of flat mathrm sl 3 connections we give the simplest example of such a coordinate system and verify numerically that in these coordinates the monodromy of the t 3 equation has the expected asymptotic properties we also briefly revisit the schrodinger equation with cubic potential and the mathieu equation from the point of view of abelianization

quantum hitchin systems via beta deformed matrix models we study the quantization of hitchin systems in terms of beta deformations of generalized matrix models related to conformal blocks of liouville theory on punctured riemann surfaces we show that in a suitable limit corresponding to the nekrasov shatashvili one the loop equations of the matrix model reproduce the hamiltonians of the quantum hitchin system on the sphere and the torus with marked points the eigenvalues of these hamiltonians are shown to be the epsilon 1 deformation of the chiral observables of the corresponding mathcal n 2 four dimensional gauge theory moreover we find the exact wave functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions

nekrasov functions from exact bohr sommerfeld periods the case of su n we suggested in 2009 that the nekrasov function with one non vanishing deformation parameter is obtained by the standard seiberg witten sw contour integral construction the only difference is that the sw differential pdx is substituted by its quantized version for the corresponding integrable system and contour integrals become exact monodromies of the wavefunction this provides an explicit formulation of the earlier guess by nekrasov and shatashvili in 2009 in this paper we successfully check this suggestion in the first order in 2 and the first order in instanton expansion for the su n model where the consistency of the so deformed sw equations is already non trivial

integrating over higgs branches we develop some useful techniques for integrating over higgs branches in supersymmetric theories with 4 and 8 supercharges in particular we define a regularized volume for hyperkahler quotients we evaluate this volume for certain ale and alf spaces in terms of the hyperkahler periods we also reduce these volumes for a large class of hyperkahler quotients to simpler integrals these quotients include complex coadjoint orbits instanton moduli spaces on 4 and ale manifolds hitchin spaces and moduli spaces of parabolic higgs bundles on riemann surfaces in the case of hitchin spaces the evaluation of the volume reduces to a summation over solutions of bethe ansatz equations for the non linear schrodinger system we discuss some applications of our results

low density parity check codes with 2 state trellis decoding a class of low density parity check ldpc codes with a simple 2 state trellis structure is presented for ldpc decoding the conventional belief propagation bp algorithm consists of numerous sub decoders of single parity check codes and exchanges information between sub decoders in an iterative manner if the single parity check codes can be constructed and grouped in a proper way the decoder can be decomposed into few identical 2 state trellis decoders therefore instead of numerous sub decoders of single parity check codes an iterative decoding algorithm based on few sub decoders over 2 state trellis is proposed the proposed decoding algorithm improves the efficiency of message passing between sub decoders and hence provides a fast convergent rate as compared to the standard bp algorithm simulation results show that the proposed scheme provides a better performance and a fast convergent rate as compared to those of standard bp algorithm the result also shows that the proposed algorithm has a similar performance as that of asynchronous replica shuffled bp algorithm and has a slightly inferior performance than that of synchronous replica shuffled bp algorithm however complexity analysis shows that our proposed algorithm has complexity that is lower than that of the replica shuffled bp algorithm

error correcting codes that nearly saturate shannon s bound gallager type error correcting codes that nearly saturate shannon s bound are constructed using insight gained from mapping the problem onto that of an ising spin system the performance of the suggested codes is evaluated for different code rates in both finite and infinite message length

parallel vs sequential belief propagation decoding of ldpc codes over gf q and markov sources abstract a sequential updating scheme sus for belief propagation bp decoding of ldpc codes over galois fields gf q and correlated markov sources is proposed and compared with the standard parallel updating scheme pus a thorough experimental study of various transmission settings indicates that the convergence rate in iterations of the bp algorithm for the sus is about one half of that for the pus independent of the finite field size q moreover this 1 2 factor appears regardless of the correlations of the source and the channel s noise model while the error correction performance remains unchanged these results may imply on the universality of the one half convergence speed up of sus decoding a comparison to the dynamics of physical spin systems is also addressed

properties and applications of gaussian autoregressive processes in detection theory corresp a sufficient statistic having dimension 3p 1 is constructed for p th order stationary gaussian autoregressive processes a computationally efficient discriminator based on the statistic is obtained a derivation of the whitening filter correlator detector for known signals in autoregressive noise is presented a new formula for the signal to noise ratio of an optimal detector for a constant signal in stationary correlated gaussian noise is presented and used to help study the nature of autoregressive approximations to more general processes in this application

mathcal w algebras and surface operators in mathcal n 2 gauge theories a general class of algebras can be constructed from the affine sl n algebra by quantum drinfeld sokolov reduction and are classified by partitions of n surface operators in an su n 4d gauge theory are also classified by partitions of n we argue that instanton partition functions of gauge theories in the presence of a surface operator can also be computed from the corresponding algebra we test this proposal by analysing the polyakov bershadsky algebra obtaining results that are in agreement with the known partition functions for su 3 gauge theories with a so called simple surface operator as a byproduct our proposal implies relations between and algebras

an inverse problem for toeplitz matrices abstract a simplified solution to an inverse problem for toeplitz matrices using central mass sequences is presented some connections with discrete transmission lines are mentioned

superfast tikhonov regularization of toeplitz systems toeplitz structured linear systems arise often in practical engineering problems correspondingly a number of algorithms have been developed that exploit toeplitz structure to gain computational efficiency when solving these systems the earliest fast algorithms for toeplitz systems required o n 2 operations while more recent superfast algorithms reduce the cost to o n log n 2 or below in this work we present a superfast algorithm for tikhonov regularization of toeplitz systems using an extension and transformation technique our algorithm translates a tikhonov regularized toeplitz system into a type of specialized polynomial problem known as tangential interpolation under this formulation we can compute the solution in only o n log n 2 operations we use numerical simulations to demonstrate our algorithm s complexity and verify that it returns stable solutions

cluster variation method in statistical physics and probabilistic graphical models the cluster variation method cvm is a hierarchy of approximate variational techniques for discrete ising like models in equilibrium statistical mechanics improving on the mean field approximation and the bethe peierls approximation which can be regarded as the lowest level of the cvm in recent years it has been applied both in statistical physics and to inference and optimization problems formulated in terms of probabilistic graphical models the foundations of the cvm are briefly reviewed and the relations with similar techniques are discussed the main properties of the method are considered with emphasis on its exactness for particular models and on its asymptotic properties the problem of the minimization of the variational free energy which arises in the cvm is also addressed and recent results about both provably convergent and message passing algorithms are discussed

serial schedules for belief propagation analysis of convergence time low density parity check ldpc codes are usually decoded by running an iterative belief propagation algorithm over the factor graph of the code in the traditional message passing schedule in each iteration all the variable nodes and subsequently all the factor nodes pass new messages to their neighbors recently several studies show that serial scheduling in which messages are generated using the latest available information significantly improves the convergence speed in terms of number of iterations it was observed experimentally in several studies that the serial schedule converges in exactly half the number of iterations compared to the standard parallel schedule in this correspondence we provide a theoretical motivation for this observation by proving it for single path graphs

shuffled iterative decoding shuffled versions of iterative decoding of low density parity check codes and turbo codes are presented the proposed schemes have about the same computational complexity as the standard versions and converge faster simulations show that the new schedules offer better performance complexity tradeoffs especially when the maximum number of iterations has to remain small

addendum to on the variation in the cohomology of the symplectic form of the reduced phase space here we have used the notation rlx for the inner product of the vector field x with the form a and ix m x j m for the x component of a in an earlier paper 4 it was shown that the push forward j dm of the liouville measure dm on m under the momentum mapping j is a piecewise polynomial measure on moreover in case x has isolated isolated zeros on m an explicit formula for the integral

iterative decoding with replicas replica shuffled versions of iterative decoders for low density parity check ldpc codes and turbo codes are presented the proposed schemes can converge faster than standard and plain shuffled approaches two methods density evolution and extrinsic information transfer exit charts are used to analyze the performance of the proposed algorithms both theoretical analysis and simulations show that the new schedules offer good tradeoffs with respect to performance complexity latency and connectivity

an inverse problem for toeplitz matrices and the synthesis of discrete transmission lines abstract let a m be a positive definite m x m toeplitz matrix let a k be its k x k principal minor for any k m which is also positive definite and toeplitz define the central mass sequence 1 m by k sup a k k 0 in which k is the k x k matrix of all 1 s we show how knowledge of the sequence k is equivalent to knowledge of the matrix a m this result has application to the direct and inverse problems for a transmission line which consists of piecewise constant components knowing the impulse response of the transmission line we can calculate the capacitance taper of the line and vice versa

on some properties of positive definite toeplitz matrices and their possible applications abstract various properties of a real symmetric toeplitz matrix m with elements jk a j k 1 j k m are reviewed here matrices of this kind often arise in applications in statistics econometrics psychometrics structural engineering multichannel filtering reflection seismology etc and it is desirable to have techniques which exploit their special structure possible applications of the results related to their inverse determinant and eigenvalue problem are suggested

improved low density parity check codes using irregular graphs we construct new families of error correcting codes based on gallager s 1973 low density parity check codes we improve on gallager s results by introducing irregular parity check matrices and a new rigorous analysis of hard decision decoding of these codes we also provide efficient methods for finding good irregular structures for such decoding algorithms our rigorous analysis based on martingales our methodology for constructing good irregular codes and the demonstration that irregular structure improves performance constitute key points of our contribution we also consider irregular codes under belief propagation we report the results of experiments testing the efficacy of irregular codes on both binary symmetric and gaussian channels for example using belief propagation for rate 1 4 codes on 16000 bits over a binary symmetric channel previous low density parity check codes can correct up to approximately 16 errors while our codes correct over 17 in some cases our results come very close to reported results for turbo codes suggesting that variations of irregular low density parity check codes may be able to match or beat turbo code performance

synchronous of asynchronous parallel dynamics which is more efficient abstract the convergence time of parallel dynamics is compared analytically with that of random sequential dynamics in parallel dynamics all elements are updated simultaneously whereas in random sequential dynamics the elements are updated only on average at the same speed one dimensional and infinite range interactions are studied the relevance of the results to neural networks and monte carlo simulations is discussed