an efficient ml decoder for tail biting codes based on circular trap detection tail biting codes are efficient coding techniques to eliminate the rate loss in conventional known tail convolutional codes at a cost of increased complexity in decoders in addition tail biting trellis representation of block codes makes the trellis based maximum likelihood ml decoder desirable for implementation circular viterbi algorithm cva is introduced to decode the tail biting codes for its decoding efficiency however its decoding process suffers from circular traps which degrade the decoding efficiency in this paper we propose an efficient checking rule for the detection of circular traps based on this rule a novel maximum likelihood ml decoding algorithm for tail biting codes is presented on tail biting trellis computational complexity and memory consumption of this decoder are significantly reduced comparing to other available ml decoders such as the two phase ml decoder to further reduce the decoding complexity we propose a new near optimal decoding algorithm based on a simplified trap detection strategy the performance of the above algorithms is validated with simulation

adjacency spectra of random and complete hypergraphs abstract we present progress on the problem of asymptotically describing the adjacency eigenvalues of random and complete uniform hypergraphs there is a natural conjecture arising from analogy with random matrix theory that connects these spectra to that of the all ones hypermatrix several of the ingredients along a possible path to this conjecture are established and may be of independent interest in spectral hypergraph hypermatrix theory in particular we provide a bound on the spectral radius of the symmetric bernoulli hyperensemble and show that the spectrum of the complete k uniform hypergraph for k 2 3 is close to that of an appropriately scaled all ones hypermatrix

on the gibbs states of the noncritical potts model on z 2 we prove that all gibbs states of the q state nearest neighbor potts model on mathbb z 2 below the critical temperature are convex combinations of the q pure phases in particular they are all translation invariant to achieve this goal we consider such models in large finite boxes with arbitrary boundary condition and prove that the center of the box lies deeply inside a pure phase with high probability our estimate of the finite volume error term is of essentially optimal order which stems from the brownian scaling of fluctuating interfaces the results hold at any supercritical value of the inverse temperature beta beta c q log left 1 sqrt q right

tailbiting codes bounds and search results tailbiting trellis representations of linear block codes with an arbitrary sectionalization of the time axis are studied the notations of regular and irregular tailbiting codes are introduced and their maximal state complexities are lower bounded the asymptotic behavior of the derived bound is investigated furthermore for regular tailbiting codes the product state complexity is lower bounded tables of new tailbiting trellis representations of linear block codes of rates 1 2 1 3 and 1 4 are presented almost all found trellises are optimal in the sense of the new bound on the state complexity and for most codes with nonoptimal trellises there exist time varying trellises which are optimal five of our newly found tailbiting codes are better than the previously known linear codes with the same parameters four of them are also superior to any previously known nonlinear code with the same parameters also more than 40 other quasi cyclic codes have been found that improve the parameter set of previously known quasi cyclic codes

a rigorous theory of finite size scaling at first order phase transitions a large class of classical lattice models describing the coexistence of a finite number of stable states at low temperatures is considered the dependence of the finite volume magnetizationm per h l in cubes of sizel d under periodic boundary conditions on the external fieldh is analyzed for the case where two phases coexist at the infinite volume transition pointh t we prove that independent of the details of the model the finite volume magnetization per lattice site behaves likem per h t m tanh ml d h ht withm per h denoting the infinite volume magnetization and m 1 2 m per h t 0 m per h t 0 introducing the finite size transition pointh m l as the point where the finite volume susceptibility attains the maximum we show that in the case of asymmetric field driven transitions its shift ish t h m l o l 2d in contrast to claims in the literature starting from the obvious observation that the number of stable phases has a local maximum at the transition point we propose a new way of determining the pointh t from finite size data with a shift that is exponentially small inl finally the finite size effects are discussed also in the case where more than two phases coexist

hypergraphs and hypermatrices with symmetric spectrum abstract it is well known that a graph is bipartite if and only if the spectrum of its adjacency matrix is symmetric in the present paper this assertion is dissected into three separate matrix results of wider scope which are extended to hypermatrices to this end the concept of bipartiteness is generalized by a new monotone property of cubical hypermatrices called odd colorable matrices it is shown that a nonnegative symmetric r matrix a has a symmetric spectrum if and only if r is even and a is odd colorable this result also solves a problem of pearson and zhang about hypergraphs with symmetric spectrum and disproves a conjecture of zhou sun wang and bu separately similar results are obtained for the h spectrum of hypermatrices

algorithmic pirogov sinai theory we develop an efficient algorithmic approach for approximate counting and sampling in the low temperature regime of a broad class of statistical physics models on finite subsets of the lattice mathbb z d and on the torus mathbb z n mathbb z d our approach is based on combining contour representations from pirogov sinai theory with barvinok s approach to approximate counting using truncated taylor series some consequences of our main results include an fptas for approximating the partition function of the hard core model at sufficiently high fugacity on subsets of mathbb z d with appropriate boundary conditions and an efficient sampling algorithm for the ferromagnetic potts model on the discrete torus mathbb z n mathbb z d at sufficiently low temperature

uniqueness and global markov property for euclidean fields the case of general polynomial interactions we give a general method for proving uniqueness and global markov property for euclidean quantum fields the method is based on uniform continuity of local specifications proved by using potential theoretical tools and exploitation of a suitable fkg order structure we apply this method to give a proof of uniqueness and global markov property for the gibbs states and to study extremality of gibbs states also in the case of non uniqueness in particular we prove extremality for 2 4 also in the case of non uniqueness and global markov property for weak coupling 2 4 which solves a long standing problem uniqueness and extremality holds also at any point of differentiability of the pressure with respect to the external magnetic field

an updated table of minimum distance bounds for binary linear codes in 1973 helgert and sfinaff published a table of upper and lower bounds on the maximum minimum distance for binary linear error correcting codes up to length 127 this article presents an updated table incorporating numerous improvements that have appeared since then to simplify the updating task the author has developed a computer program that systematically investigates the consequences of each improvement by applying several well known general code construction techniques this program also made it possible to check the original table furthermore it offers a quick and reliable update service for future improvements

on the principal eigenvectors of uniform hypergraphs abstract let a h be the adjacency tensor of r uniform hypergraph h if h is connected the unique positive eigenvector x x 1 x 2 x n t with x r 1 corresponding to spectral radius h is called the principal eigenvector of h the maximum and minimum entries of x are denoted by x max and x min respectively in this paper we investigate the bounds of x max and x min in the principal eigenvector of h meanwhile we also obtain some bounds of the ratio x i x j for i j n as well as the principal ratio h x max x min of h as an application of these results we finally give an estimate of the gap of spectral radii between h and its proper sub hypergraph h

agreement percolation and phase coexistence in some gibbs systems we extend some relations between percolation and the dependence of gibbs states on boundary conditions known for ising ferromagnets to other systems and investigate their general validity percolation is defined in terms of the agreement of a configuration with one of the ground states of the system this extension is studied via examples and counterexamples including the antiferromagnetic ising and hard core models on bipartite lattices potts models and many layered ising and continuum widom rowlinson models in particular our results on the hard square lattice model make rigorous observations made by hu and mak on the basis of computer simulations moreover we observe that the naturally defined clusters of the widom rowlinson model play for the wr model itself the same role that the clusters of the fortuin kasteleyn measure play for the ferromagnetic potts models the phase transition and percolation in this system can be mapped into the corresponding liquid vapor transition of a one component fluid

spectra of uniform hypergraphs abstract we present a spectral theory of uniform hypergraphs that closely parallels spectral graph theory a number of recent developments building upon classical work has led to a rich understanding of symmetric hyperdeterminants of hypermatrices a k a multidimensional arrays symmetric hyperdeterminants share many properties with determinants but the context of multilinear algebra is substantially more complicated than the linear algebra required to address spectral graph theory i e ordinary matrices nonetheless it is possible to define eigenvalues of a hypermatrix via its characteristic polynomial as well as variationally we apply this notion to the adjacency hypermatrix of a uniform hypergraph and prove a number of natural analogs of basic results in spectral graph theory open problems abound and we present a number of directions for further study

a classical wr model with q particle types a version of the widom rowlinson model is considered where particles of q types coexist subject to pairwise hard core exclusions for q le 4 in the case of large equal fugacities we give a complete description of the pure phase picture based on the theory of dominant ground states

first order phase transitions in unbounded spin systems i construction of the phase diagram the phase diagram and the corresponding infinite volume gibbs states are constructed for a large class of continuous unbounded spin models our construction relies on a partition of unity mapping our system onto an interacting contour system a generalisation of zahradnik s approach to piragov sinai theory to interacting contour systems and a suitable mean field expansion around the minimas of the hamiltonian

quantum lattice models at intermediate temperature we analyze the free energy and construct the gibbs kms states for a class of quantum lattice systems at low temperature and when the interactions are almost diagonal in a suitable basis the models we study may have continuous symmetries our results however apply to intermediate temperatures where discrete symmetries are broken but continuous symmetries are not our results are based on quantum pirogov sinai theory and a combination of high and low temperature expansions

the relationship between phase transitions and percolation in models with ground state degeneracy a criterion for the uniqueness of limiting gibbs states in classical models with unique ground states is formulated various applications of this criterion formulated in the terminology of percolation theory are discussed

forbidden gap argument for phase transitions proved by means of chessboard estimates chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest in this note we show that the method not only produces a point in the phase diagram where more than one gibbs states coexist but that it can also be used to rule out the existence of shift ergodic states that differ significantly from those proved to exist for models depending on a parameter say the temperature this shows that the values of the conjugate thermodynamic quantity the energy inside the transitional gap are forbidden in all shift ergodic gibbs states we point out several models where our result provides useful additional information concerning the set of possible thermodynamic equilibria

the q state potts model in the standard pirogov sinai theory surface tensions and wilson loops theq state potts model both scalar and gauge versions is rewritten with the help of the duality transformation into a form of the pirogov sinai theory with noninteracting contours that can be controlled by cluster expansions onceq is large enough this is then used in a new proof of the existence of a unique transition inverse temperature t where the mean internal energy is discontinuous moreover we prove for the scalar model again forq large enough that there are discontinuities at t of the magnetization and of the mass gap with the magnetization vanishing below t and the mass gap vanishing above t we also show that the surface tensions between ordered stable phases are strictly positive up to t and the surface tension between an ordered phase and the disordered one is strictly positive at t for the three dimensional gauge model the wilson parameter exhibits a direct transition from an area law decay quark confinement to a perimeter law decay deconfinement

a simple inductive approach to the problem of convergence of cluster expansions of polymer models we explain a simple inductive method for the analysis of the convergence of cluster expansions taylor expansions mayer expansions for the partition functions of polymer models we give a very simple proof of the dobrushin koteck preiss criterion and formulate a generalization usable for situations where a successive expansion of the partition function has to be used

partition function zeros at first order phase transitions a general analysis we present a general rigorous theory of partition function zeros for lattice spin models depending on one complex parameter first we formulate a set of natural assumptions which are verified for a large class of spin models in a companion paper 5 under these assumptions we derive equations whose solutions give the location of the zeros of the partition function with periodic boundary conditions up to an error which we prove is generically exponentially small in the linear size of the system for asymptotically large systems the zeros concentrate on phase boundaries which are simple curves ending in multiple points for models with an ising like plus minus symmetry we also establish a local version of the lee yang circle theorem this result allows us to control situations when in one region of the complex plane the zeros lie precisely on the unit circle while in the complement of this region the zeros concentrate on less symmetric curves

perron frobenius theorem for nonnegative multilinear forms and extensions we prove an analog of perron frobenius theorem for multilinear forms with nonnegative coefficients and more generally for polynomial maps with nonnegative coefficients we determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector

random cluster representation of the blume capel model the so called diluted random cluster model may be viewed as a random cluster representation of the blume capel model it has three parameters a vertex parameter a an edge parameter p and a cluster weighting factor q stochastic comparisons of measures are developed for the vertex marginal when q 1 2 and the edge marginal when q 1 taken in conjunction with arguments used earlier for the random cluster model these permit a rigorous study of part of the phase diagram of the blume capel model

principal eigenvectors and spectral radii of uniform hypergraphs abstract in this paper some inequalities among the principal eigenvector spectral radius and vertex degrees of a connected uniform hypergraph are established necessary and sufficient conditions of equalities holding are presented which are related to the regularity of a hypergraph furthermore we present some bounds on the spectral radius for a connected irregular uniform hypergraph in terms of some parameters such as principal ratio maximum degree diameter and the number of vertices and edges

on the singularity of the free energy at a first order phase transition at first order phase transition the free energy does not have an analytic continuation in the thermodynamical variable which is conjugate to an order parameter for the transition this result is proved at low temperature for lattice models with finite range interaction and two periodic ground states under the only condition that they satisfy the peierls condition

single polygon counting on cayley tree of order 3 we showed that one form of generalized catalan numbers is the solution to the problem of finding different connected component with finite vertices containing a fixed root for the semi infinite cayley tree of order 3 we give the formula for the full graph cayley tree of order 3 which is derived from the generalized catalan numbers using ratios of gamma functions two upper bounds are given for problem defined on semi infinite cayley tree of order 3 as well as the full graph

on the ising model with random boundary condition the infinite volume limit behavior of the 2d ising model under possibly strong random boundary conditions is studied the model exhibits chaotic size dependence at low temperatures and we prove that the and phases are the only almost sure limit gibbs measures assuming that the limit is taken along a sparse enough sequence of squares in particular we provide an argument to show that in a sufficiently large volume a typical spin configuration under a typical boundary condition contains no interfaces in order to exclude mixtures as possible limit points a detailed multi scale contour analysis is performed

tight bounds on the minimum average weight per branch for rate n 1 n convolutional codes consider a cycle in the state diagram of a convolutional code the average weight per branch of the cycle is equal to the total hamming weight of all labels on the branches divided by the number of branches let w sub 0 be the minimum average weight per branch over all cycles in the state diagram except the zero state self loop of weight zero codes with low w sub 0 result in high bit error probabilities when they are used with either viterbi or sequential decoding hemmati and costello 1980 showed that w sub 0 is upper bounded by 2 sup spl nu 2 3 spl middot 2 sup spl nu 2 1 for a class of 2 1 codes where spl nu denotes the constraint length in the present correspondence it is shown that the bound is valid for a large class of n n 1 codes n spl ges 2 examples of high rate codes with w sub 0 equal to the upper bound are also given hemmati and costello defined a class of codes to be asymptotically catastrophic if w sub 0 approaches zero for large spl nu the class of n n 1 codes constructed by wyner and ash 1963 is shown to be asymptotically catastrophic all codes in the class have minimum possible w sub 0 equal to 1 spl nu

an alternate version of pirogov sinai theory a new approach to the pirogov sinai theory of phase transitions is developed not employing the contour models with a parameter the completeness of the phase diagram is proven

ordering and demixing transitions in multicomponent widom rowlinson models we use monte carlo techniques and analytical methods to study the phase diagram of multicomponent widom rowlinson models on a square lattice there are m species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles simulations show that for m between two and six there is a direct transition from the gas phase at z mathit z mathit d m to a demixed phase consisting mostly of one species at zg mathit z mathit d m while for m ensuremath ge 7 there is an intermediate crystal phase for z lying between mathit z mathit c m and mathit z mathit d m in this phase which is driven by entropy particles independent of species preferentially occupy one of the sublattices i e spatial symmetry but not particle symmetry is broken the transition at mathit z mathit d m appears to be of the first order for m ensuremath ge 5 putting it in the potts model universality class for large m the transition between the crystalline and demixed phases at mathit z mathit d m can be proven to be of the first order with mathit z mathit d m ensuremath sim m 2 1 m while mathit z mathit c m is argued to behave as ensuremath lambda mathrm cr m with ensuremath lambda mathrm cr the critical value of the fugacity at which the one component hard core square lattice gas has a transition and to be always of the ising type explicit calculations for the bethe lattice with the coordination number q 4 give results similar to those for the square lattice except that the transition at mathit z mathit d m becomes first order at mg2 this happens for all q consistent with the model being in the potts universality class c 1995 the american physical society

tailbiting codes obtained via convolutional codes with large active distance slopes the slope of the active distances is an important parameter when investigating the error correcting capability of convolutional codes and the distance behavior of concatenated convolutional codes the slope of the active distances is equal to the minimum average weight cycle in the state transition diagram of the encoder a general upper bound on the slope depending on the free distance of the convolutional code and new upper bounds on the slope of special classes of binary convolutional codes are derived moreover a search technique resulting in new tables of rate r 1 2 and rate r 1 3 convolutional encoders with high memories and large active distance slopes is presented furthermore we show that convolutional codes with large slopes can be used to obtain new tailbiting block codes with large minimum distances tables of rate r 1 2 and rate r 1 3 tailbiting codes with larger minimum distances than the best previously known quasi cyclic codes are given two new tailbiting codes also have larger minimum distances than the best previously known binary linear block codes with same size and length one of them is also superior in terms of minimum distance to any previously known binary nonlinear block code with the same set of parameters

a beast for prowling in trees when searching for convolutional codes and tailbiting codes of high complexity it is of vital importance to use fast algorithms for computing their weight spectra which corresponds to finding low weight paths in their code trellises this can be efficiently done by a combined search in both forward and backward code trees a bidirectional efficient algorithm for searching such code trees beast is presented for large encoder memories it is shown that beast is significantly more efficient than comparable algorithms beast made it possible to find new convolutional and tailbiting codes that have larger free minimum distances than the previously best known codes with the same parameters tables of such codes are presented

non analyticity and the van der waals limit reference gr pf article 2004 001doi 10 1023 b joss 0000012506 98828 ddview record in web of science record created on 2008 11 27 modified on 2017 05 12

some properties of the laplace and normalized laplace spectra of uniform hypergraphs abstract in 8 hu and qi studied the normalized laplace tensors and normalized laplace spectra of k uniform hypergraphs they also mentioned the question about whether or not 2 is also an h eigenvalue of the normalized laplace tensor of a k uniform hypergraph when 2 is an eigenvalue of the normalized laplace tensor in this case k is necessarily even in this paper we use an expression for the normalized laplace tensor in terms of the tensor product together with the diagonal similarity of tensors the perron frobenius theorem for nonnegative tensors and nonnegative weakly irreducible tensors and the concept and properties of odd colorable hypergraphs introduced in 13 to give a complete answer to this question we show that i when k 2 mod 4 then the answer to this question is affirmative ii when k 0 mod 4 then the answer to this question is negative and in this case we give an infinite family of counterexamples we also study the signless normalized laplace spectra and the signless normalized laplace h spectra of hypergraphs we give structural characterizations of the hypergraphs having the same normalized laplace spectrum and signless normalized laplace spectrum or having the same normalized laplace h spectrum and signless normalized laplace h spectrum or both finally we determine the first two k uniform supertrees of order n with the largest laplace spectral radii and also determine the unique k uniform hypertree of order n with the smallest laplace spectral radii in the case when k is even

loss network representation of peierls contours we present a probabilistic approach for the study of systems with exclusions in the regime traditionally studied via cluster expansion methods in this paper we focus on its application for the gases of peierls contours found in the study of the ising model at low temperatures but most of the results are general we realize the equilibrium measure as the invariant measure of a loss network process whose existence is ensured by a subcriticality condition of a dominant branching process in this regime the approach yields besides existence and uniqueness of the measure properties such as exponential space convergence and mixing and a central limit theorem the loss network converges exponentially fast to the equilibrium measure without metastable traps this convergence is faster at low temperatures where it leads to the proof of an asymptotic poisson distribution of contours our results on the mixing properties of the measure are comparable to those obtained with duplicated variables expansion used to treat systems with disorder and coupled map lattices it works in a larger region of validity than usual cluster expansion formalisms and it is not tied to the analyticity of the pressure in fact it does not lead to any kind of expansion for the latter and the properties of the equilibrium measure are obtained without resorting to combinatorial or complexanalysis techniques

connected hypergraphs with small spectral radius abstract in 1970 smith classified all connected graphs with spectral radius at most 2 here the spectral radius of a graph is the largest eigenvalue of its adjacency matrix recently the definition of spectral radius has been extended to r uniform hypergraphs in this paper we generalize smith s theorem to r uniform hypergraphs we show that the smallest limit point of the spectral radii of connected r uniform hypergraphs is r 4 r we discovered a novel method for computing the spectral radius of hypergraphs and classified all connected r uniform hypergraphs with spectral radius at most r

on maximal entries in the principal eigenvector of graphs abstract for an undirected connected graph it is well known that an eigenvector belonging to the principal eigenvalue of g can be given such that all entries are positive we ask whether this vector carries information on the structure of the graph and approach this question by investigating the values that can occur in its maximal entry

the p spectral radius of k partite and k chromatic uniform hypergraphs abstract the p spectral radius of an r uniform hypergraph g of order n is defined for every real number p 1 as p g max x 1 p x n p 1 r i 1 i r e g x i 1 x i r it generalizes several hypergraph parameters including the lagrangian the spectral radius and the number of edges this paper presents solutions to several extremal problems about the p spectral radius of k partite and k chromatic hypergraphs of order n two of the main results are i let k r 2 and let g be a k partite r graph of order n for every p 1 p g p t k r n unless g t k r n where t k r n is the complete k partite r graph of order n with parts of size n k or n k ii let k 2 and let g be a k chromatic 3 graph of order n for every p 1 p g p q k 3 n unless g q k 3 n where q k 3 n is a complete k chromatic 3 graph of order n with classes of size n k or n k the latter statement generalizes a result of mubayi and talbot

nonanalytic features of the first order phase transition in the ising model the absence of the analytic continuation for the free energy near the point of the first order phase transition in thed dimensional ising model is proved it is shown that thermodynamic functions in the metastable phase do not have certain values and can be derived only with an uncertainty the asymptotic expansion near the point of the phase transition yields the values of thermodynamic functions with the same uncertainty

analyticity of low temperature phase diagrams of lattice spin models the analyticity of all strata of the pirogov sinai phase diagram is proved as a byproduct of the method a characterization of typical volumes for which the complex partition function vanishes is given for a hamiltonian that is a perturbation of the real valued one near the point of a phase transition

combinatorial methods for the spectral p norm of hypermatrices abstract the spectral p norm of r matrices generalizes the spectral 2 norm of 2 matrices in 1911 schur gave an upper bound on the spectral 2 norm of 2 matrices which was extended in 1934 by hardy littlewood and polya to r matrices recently kolotilina and independently the author strengthened schur s bound for 2 matrices the main result of this paper extends the latter result to r matrices thereby improving the result of hardy littlewood and polya the proof is based on combinatorial concepts like r partite r matrix and symmetrant of a matrix which appear to be instrumental in the study of the spectral p norm in general thus another application shows that the spectral p norm and the p spectral radius of a symmetric nonnegative r matrix are equal whenever p r this result contributes to a classical area of analysis initiated by mazur and orlicz back in 1930 additionally a number of bounds are given on the p spectral radius and the spectral p norm of r matrices and r graphs

analytic methods for uniform hypergraphs abstract this paper presents some analytic methods for studying uniform hypergraphs its starting point is the spectral theory of 2 graphs in particular the largest and the smallest eigenvalues and min of 2 graphs first these two parameters are extended to weighted uniform hypergraphs second the eigenvalues numbers and min are extended to eigenvalues functions p and min p which also encompass other graph parameters like the lagrangian and the number of edges in this way the functions p and min p seamlessly join spectral and traditional results in hypergraphs in particular this new viewpoint helps to show that spectral extremal and edge extremal problems are asymptotically equivalent naturally all results about p and min p also extend spectral hypergraph theory but delve into deeper problems than before in fact the resulting theory is new even for 2 graphs where some well settled topics become research challenges again the paper covers a multitude of topics with more than a hundred concrete statements to underpin an analytic theory for hypergraphs essential among these topics are a perron frobenius type theory and methods for extremal hypergraph problems many open problems are raised and directions for possible further research are outlined

a spectral condition for odd cycles in graphs abstract let g be a graph of sufficiently large order n and let the largest eigenvalue g of its adjacency matrix satisfies g n 2 4 then g contains a cycle of length t for every t n 320 this condition is sharp the complete bipartite graph t 2 n with parts of size n 2 and n 2 contains no odd cycles and its largest eigenvalue is equal to n 2 4 this condition is stable if g is close to n 2 4 and g fails to contain a cycle of length t for some t n 321 then g resembles t 2 n

extremal problems for the p spectral radius of berge hypergraphs abstract let g be a simple graph we say that a hypergraph h is a berge g if there is a bijection e g e h such that e e for all e e g for any r uniform hypergraph h and a real number p 1 the p spectral radius p h of h is defined as p h max x p 1 r i 1 i 2 i r e h x i 1 x i 2 x i r in this paper we study the p spectral radius of berge g g c n hypergraphs and determine the 3 uniform hypergraphs with maximum p spectral radius for p 1 among all berge g g c n hypergraphs where c n is the set of graphs of order n obtained from c n by adding an edge

partition function zeros at first order phase transitions pirogov sinai theory this paper is a continuation of our previous analysis 2 of partition functions zeros in models with first order phase transitions and periodic boundary conditions here it is shown that the assumptions under which the results of ref 2 were established are satisfied by a large class of lattice models these models are characterized by two basic properties the existence of only a finite number of ground states and the availability of an appropriate contour representation this setting includes for instance the ising potts and blume capel models at low temperatures the combined results of ref 2 and the present paper provide complete control of the zeros of the partition function with periodic boundary conditions for all models in the above class

hypergraph regularity and the multidimensional szemeredi theorem we prove analogues for hypergraphs of szemeredi s regularity lemma and the associated counting lemma for graphs as an application we give the first combinatorial proof of the multidimensional szemeredi theorem of furstenberg and katznelson and the first proof that provides an explicit bound similar results with the same consequences have been obtained independently by nagle rodl schacht and skokan

some new binary quasi cyclic codes by means of local search techniques five quasi cyclic codes have been found that have a higher minimum distance than known binary linear codes the new codes have parameters 102 17 37 60 20 17 84 21 27 105 21 36 and 100 25 30 also 39 other quasi cyclic codes have been found that improve the parameter sets of previously known quasi cyclic codes twenty four of them give a new and easier description of binary linear codes with best known parameters

active distances for convolutional codes a family of active distance measures for general convolutional codes is defined these distances are generalizations of the extended distances introduced by thommesen and justesen 1983 for unit memory convolutional codes it is shown that the error correcting capability of a convolutional code is determined by the active distances the ensemble of periodically time varying convolutional codes is defined and lower bounds on the active distances are derived for this ensemble the active distances are very useful in the analysis of concatenated convolutional encoders

woven convolutional codes i encoder properties encoders for convolutional codes with large free distances can be constructed by combining several less powerful convolutional encoders this paper is devoted to constructions in which the constituent convolutional codes are woven together in a manner that resembles the structure of a fabric the general construction is called twill and it is described together with two special cases viz woven convolutional encoders with outer warp and with inner warp the woven convolutional encoders inherit many of their structural properties such as minimality and catastrophicity from their constituent encoders for all three types of woven convolutional codes upper and lower bounds on their free distances as well as lower bounds on the active distances of their encoders are derived

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

finite size scaling for first order phase transitions rigorous results abstract recent rigorous results on finite size effects for lattice models are reviewed we consider symmetric and asymmetric first order phase transitions in cubic and cylindrical geometries and discuss the determination of transition points from finite size data

first order phase transitions in unbounded spin systems ii completeness of the phase diagram we continue our analysis of unbounded spin systems with nearest neighbor interactionw and a single spin potentialv which hasn deep and widely separated minima in this second part we show that all translation invariant phases obeying a certain regularity condition are convex combinations of the stable phases determined in the first part of this paper for periodic boundary conditions each stable phase contributes with the same weight in the infinite volume limit

random surfaces with two sided constraints an application of the theory of dominant ground states we consider some models of classical statistical mechanics which admit an investigation by means of the theory of dominant ground states our models are related to the gibbs ensemble for the multidimensional sos model with symmetric constraints x m 2 the main result is that for 0 where 0 does not depend onm the structure of thermodynamic phases in the model is determined by dominant ground states for an evenm a gibbs state is unique and for an oddm the number of space periodic pure gibbs states is two

a unified approach to phase diagrams in field theory and statistical mechanics we construct the phase diagram of any system which admits a low temperature polymer or cluster expansion such an expansion turns the system into a hard core interacting contour model with small but not necessarily positive activities the method uses some of zahradnik s ideas z1 but applies equally well to systems with complex interactions we give two applications first to low temperaturep 2 models with complex couplings and second to a computation of asymptotics of partition functions in periodic volumes if the index of a supersymmetric field theory is known the second application would help determine the number of phases in infinite volume

some best rate 1 p and rate p 1 p systematic quasi cyclic codes tables of 1 p and rate p 1 p binary quasi cyclic qc codes that extend previously published results are presented many of these codes attain bounds given by t verhoeff 1987 who composed a table of bounds on the maximum possible minimum distance of binary linear codes many of the codes presented meet or improve these bounds a best code is considered to be one which has the largest possible minimum distance for the given code dimensions n and k and class of error correcting codes a good code has the maximum known minimum distance for the class of codes an optimal code is one that achieves the maximum possible minimum distance for a linear code with the same dimensions binary power residue codes are found and used to construct qc codes

surface induced finite size effects for first order phase transitions we consider classical lattice models describing first order phase transitions and study the finite size scaling of the magnetization and susceptibility in order to model the effects of an actual surface in systems such as small magnetic clusters we consider models with free boundary conditions for a field driven transition with two coexisting phases at the infinite volume transition pointh h t we prove that the low temperature finite volume magnetizationmfree l h per site in a cubic volume of sizel d behaves like m free l h frac m m 2 frac m m 2 tanh left frac m m 2 l d h h chi l right o left frac 1 l right whereh x l is the position of the maximum of the finite volume susceptibility andm are the infinite volume magnetizations ath h t 0 andh h t 0 respectively we show thath x l is shifted by an amount proportional to 1 l with respect to the infinite volume transition pointh t provided the surface free energies of the two phases at the transition point are different this should be compared with the shift for periodic boundary conditions which for an asymmetric transition with two coexisting phases is proportional only to 1 l2d one can consider also other definitions of finite volume transition points for example the positionh u l of the maximum of the so called binder cumulantufree l h whileh u l is again shifted by an amount proportional to 1 l with respect to the infinite volume transition pointh t its shift with respect toh l is of the much smaller order 1 l2d we give explicit formulas for the proportionality factors and show that in the leading 1 l2d term the relative shift is the same as that for periodic boundary conditions

low temperature phase diagrams of quantum lattice systems i stability for quantum perturbations of classical systems with finitely many ground states starting from classical lattice systems ind 2 dimensions with a regular zerotemperature phase diagram involving a finite number of periodic ground states we prove that adding a small quantum perturbation and or increasing the temperature produce only smooth deformations of their phase diagrams the quantum perturbations can involve bosons or fermions and can be of infinite range but decaying exponentially fast with the size of the bonds for fermions the interactions must be given by monomials of even degree in creation and annihilation operators our methods can be applied to some anyonic systems as well our analysis is based on an extension of pirogov sinai theory to contour expansions ind 1 dimensions obtained by iteration of the duhamel formula

a note on asymptotically catastrophic convolutional codes of rate n 1 n convolutional codes with rate r n 1 n n spl ges 2 are defined in terms of their minimal parity check matrices the matrices are represented by a binary vector notation introduced by ytrehus 1992 the upper bounds on spl omega 0 minimum average weight per branch are presented many classes of rate n 1 n convolutional codes are shown to be asymptotically catastrophic