correlation factors describing primary and spatial sensations of sound fields abstract the theory of subjective preference of the sound field in a concert hall is established based on the model of human auditory brain system the model consists of the autocorrelation function acf mechanism and the interaural crosscorrelation function iacf mechanism for signals arriving at two ear entrances and the specialization of human cerebral hemispheres this theory can be developed to describe primary sensations such as pitch or missing fundamental loudness timbre and in addition duration sensation which is introduced here as a fourth these four primary sensations may be formulated by the temporal factors extracted from the acf associated with the left hemisphere and spatial sensations such as localization in the horizontal plane apparent source width and subjective diffuseness are described by the spatial factors extracted from the iacf associated with the right hemisphere any important subjective responses of sound fields may be described by both temporal and spatial factors

on the minimum output entropy of random orthogonal quantum channels we consider the sequences of random quantum channels defined by using the stinespring formula with haar distributed random orthogonal matrices for any fixed sequence of input states we study the asymptotic eigenvalue distribution of the outputs through the tensor powers of random channels we show that the input states achieving minimum output entropy are tensor products of maximally entangled states bell states when the tensor power is even this phenomenon is completely different from the one for random quantum channels constructed from haar distributed random unitary matrices which leads us to formulate some conjectures about the regularized minimum output entropy

linear free resolutions and minimal multiplicity let s k x x be a polynomial ring over a field and let a4 a m be a finitely generated graded module in the most interesting case a4 is an ideal of s for a given natural number p there is a great interest in the question can m be generated by homogeneous elements of degree p no simple answer say in terms of the local cohomology of m is known but somewhat surprisingly the stronger question can the jth syzygy of m be generated by elements of degree qp j for all j 0 l n does admit a simple response the following is neither new nor difficult to prove though it seems not well known

the c 3 theorem and a d 2 algorithm for large scale stochastic mixed integer programming set convexification this paper considers the two stage stochastic integer programming problem with an emphasis on instances in which integer variables appear in the second stage drawing heavily on the theory of disjunctive programming we characterize convexifications of the second stage problem and develop a decomposition based algorithm for the solution of such problems in particular we verify that problems with fixed recourse are characterized by scenario dependent second stage convexifications that have a great deal in common we refer to this characterization as the c3 common cut coefficients theorem based on the c3 theorem we develop a decomposition algorithm which we refer to as disjunctive decomposition d2 in this new class of algorithms we work with master and subproblems that result from convexifications of two coupled disjunctive programs we show that when the second stage consists of 0 1 milp problems we can obtain accurate second stage objective function estimates after finitely many steps this result implies the convergence of the d2 algorithm

the proper formula for relative entropy and its asymptotics in quantum probability umegaki s relative entropys trd logd logd of states and with density operatorsd andd respectively is shown to be an asymptotic exponent considered from the quantum hypothesis testing viewpoint it is also proved that some other versions of the relative entropy give rise to the same asymptotics as umegaki s one as a byproduct the inequality tra logab tra loga logb is obtained for positive definite matricesa andb

neighborhood systems for production sets with indivisibilities a production set with indivisibilities is described by an activity analysis matrix with activity levels which can assume arbitrary integral values a neighborhood system is an association with each integral vector of activity levels of a finite set of neighboring vectors the neighborhood relation is assumed to be symmetric and translation invariant each such neighborhood system can be used to define a local maximum for the associated integer programs obtained by selecting a single commodity whose level is to be maximized subject to specified factor endowments of the remaining commodities it is shown that each technology matrix subject to mild regularity assumptions has a unique minimal neighborhood system for which a local maximum is global the complexity of such minimal neighborhood systems is examined for several examples

a finite branch and bound algorithm for two stage stochastic integer programs this paper addresses a general class of two stage stochastic programs with integer recourse and discrete distributions we exploit the structure of the value function of the second stage integer problem to develop a novel global optimization algorithm the proposed scheme departs from those in the current literature in that it avoids explicit enumeration of the search space while guaranteeing finite termination computational experiments on standard test problems indicate superior performance of the proposed algorithm in comparison to those in the existing literature

integer hulls of linear polyhedra and scl in families the integer hull of a polyhedron is the convex hull of the integer points contained in it we show that the vertices of the integer hulls of a rational family of polyhedra of size o n have eventually quasipolynomial coordinates as a corollary we show that the stable commutator length of elements in a surgery family is eventually a ratio of quasipolynomials and that unit balls in the scl norm eventually quasiconverge in finite dimensional surgery families

the complexity of generic primal algorithms for solving general integer programs primal methods constitute a common approach to solving combinatorial optimization problems starting from a given feasible solution they successively produce new feasible solutions with increasingly better objective function value until an optimal solution is reached from an abstract point of view an augmentation problem is solved in each iteration that is given a feasible point these methods find an augmenting vector if one exists usually augmenting vectors with certain properties are sought to guarantee the polynomial running time of the overall algorithm in this paper we show that one can solve every integer programming problem in polynomial time provided one can efficiently solve the directed augmentation problem the directed augmentation problem arises from the ordinary augmentation problem by splitting each direction into its positive and its negative part and by considering linear objectives on these parts our main result states that in order to get a polynomial time algorithm for optimization it is sufficient to efficiently find for any linear objective function in the positive and negative part an arbitrary augmenting vector this result also provides a general framework for the design of polynomial time algorithms for specific combinatorial optimization problems we demonstrate its applicability by considering the min cost flow problem by giving a novel algorithm for linear programming over unimodular spaces and by providing a different proof that for 0 1 integer programming an efficient algorithm solving the ordinary augmentation problem suffices for efficient optimization our main result also implies that directed augmentation is at least as hard as optimization in other words for an np hard problem already the task of finding a directed augmenting vector in polynomial time is hopeless unless p np we illustrate this kind of consequence with the help of the knapsack problem

general formulas for capacity of classical quantum channels the capacity of a classical quantum channel or in other words the classical capacity of a quantum channel is considered in the most general setting where no structural assumptions such as the stationary memoryless property are made on a channel a capacity formula as well as a characterization of the strong converse property is given just in parallel with the corresponding classical results of verdu han 1994 which are based on the so called information spectrum method the general results are applied to the stationary memoryless case with or without cost constraint on inputs whereby a deep relation between the channel coding theory and the hypothesis testing for two quantum states is elucidated

the coding theorem for a class of quantum channels with long term memory in this paper we consider the transmission of classical information through a class of quantum channels with long term memory which are convex combinations of memoryless channels hence the memory of such channels can be considered to be given by a markov chain which is aperiodic but not irreducible we prove the coding theorem and weak converse for this class of channels the main techniques that we employ are a quantum version of feinstein s fundamental lemma feinstein a 1954 ire trans pgit 4 2 22 khinchin a i 1957 mathematical foundations of information theory ii on the fundamental theorems of information theory new york dover chapter iv and a generalization of helstrom s theorem helstrom c w 1976 quantum detection and estimation theory mathematics in science and engineering vol 123 london academic

a convex approximation for two stage mixed integer recourse models with a uniform error bound we develop a convex approximation for two stage mixed integer recourse models and we derive an error bound for this approximation that depends on the total variations of the probability density functions of the random variables in the model we show that the error bound converges to zero if all these total variations converge to zero our convex approximation is a generalization of the one in romeijnders van der vlerk and klein haneveld math program to appear restricted to totally unimodular integer recourse models for this special case it has the best worst case error bound possible the error bound in this paper is the first in the general setting of mixed integer recourse models as main building blocks in its derivation we generalize the asymptotic periodicity results of gomory linear algebra appl 2 1969 pp 451 558 for pure integer programs to the mixed integer case and we use the total variation error bounds on the expectation of periodic functions derived in romeijnders van der v

sensitivity theorems in integer linear programming we consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right hand side vector among our results we show that for any optimal solution to a linear program max wx ax b the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant of the integral matrixa using this we strengthen several integer programming proximity results of blair and jeroslow graver and wolsey we also show that the chvatal rank of a polyhedron x ax b can be bounded above by a function of the matrixa independent of the vectorb a result which as blair observed is equivalent to blair and jeroslow s theorem that each integer programming value function is a gomory function

variation of cost functions in integer programming we study the problem of minimizingc x subject toa x b x 0 andx integral for a fixed matrixa two cost functionsc andc are considered equivalent if they give the same optimal solutions for eachb we construct a polytopest a whose normal cones are the equivalence classes explicit inequality presentations of these cones are given by the reduced grobner bases associated witha the union of the reduced grobner bases asc varies called the universal grobner basis consists precisely of the edge directions ofst a we present geometric algorithms for computingst a the graver basis and the universal grobner basis

comparison of symbolic and ordinary powers of ideals all given rings in this paper are commutative associative with identity and noetherian recently l ein r lazarsfeld and k smith els discovered a remarkable and surprising fact about the behavior of symbolic powers of ideals in affine regular rings of equal characteristic 0 if h is the largest height of an associated prime of i then i hn i n for all n 0 here if w is the complement of the union of the associated primes of i i t denotes the contraction of i t rw to r where rw is the localization of r at the multiplicative system w their proof depends on the theory of multiplier ideals including an asymptotic version and in particular requires resolution of singularities as well as vanishing theorems we want to acknowledge that without their generosity and quickness in sharing their research this manuscript would not exist our objective here is to give stronger results that can be proved by methods that are in some ways more elementary our results are valid in both equal characteristic 0 and in positive prime characteristic p but depend on reduction to characteristic p we use tight closure methods and in consequence we need neither resolution of singularities nor vanishing theorems that may fail in positive characteristic for the most basic form of the result all that we need from tight closure theory is the definition of tight closure and the fact that in a regular ring every ideal is tightly closed we note that the main argument here is closely related to a proof given in hu 5 14 16 p 45 that regular local rings in characteristic p are ufds

the regularity of tor and graded betti numbers let s k x1 xn let a b be finitely generated graded s modules and let m x1 xn s we give bounds for the regularity of the local cohomology of tork a b in terms of the graded betti numbers of a and b under the assumption that dim tor1 a b 1 we apply the results to syzygies grobner bases products and powers of ideals and to the relationship of the rees and symmetric algebras for example we show that any homogeneous linearly presented m primary ideal has some power equal to a power of m and if the first n 1 2 steps of the resolution of i are linear then i 2 is a power of m

the frequency range applicable to pitch identification based upon the auto correlation function model abstract pitch identification experiments were conducted to determine the upper boundary of the frequency range within which the autocorrelation function acf model described by ando see reference 16 is applicable to the phenomenon of the missing fundamental of a complex tone pitch matching tests were conducted using 1 complex tones consisting of 2 f 3 f and 4 f where f denotes the fundamental frequencies of 0 5 1 0 1 2 1 6 2 0 or 3 0 khz and 2 complex tones consisting of 2 f and 3 f these tests showed that for both kinds of complex tones the acf model can account for the perception of pitch when the fundamental frequency is below 1200 hz

duration sensation when listening to bandpass noises abstract the duration sensation of bandpass noise was examined while changing the factors 1 1and e extracted from the autocorrelation function the white noise and bandpass noises with six center frequencies 125 250 500 1000 2000 and 4000 hz with different bandwidths were used as stimuli a paired comparison test comparing the white noise duration with bandpass noise duration was conducted under the conditions of constant sound pressure level spl 80 db a and rise and fall times 1 ms results indicate that the duration of bandpass noise is judged to be longer than that of the white noise the duration sensation of the bandpass stimuli with longer 1is significantly longer than that of the stimuli with shorter 1 p

stochastic programming with integer variables including integer variables into traditional stochastic linear programs has considerable implications for structural analysis and algorithm design starting from mean risk approaches with different risk measures we identify corresponding two and multi stage stochastic integer programs that are large scale block structured mixed integer linear programs if the underlying probability distributions are discrete we highlight the role of mixed integer value functions for structure and stability of stochastic integer programs when applied to the block structures in stochastic integer programming well known algorithmic principles such as branch and bound lagrangian relaxation or cutting plane methods open up new directions of research we review existing results in the field and indicate departure points for their extension

cutting planes for multistage stochastic integer programs this paper addresses the problem of finding cutting planes for multistage stochastic integer programs we give a general method for generating cutting planes for multistage stochastic integer programs based on combining inequalities that are valid for the individual scenarios we apply the method to generate cuts for a stochastic version of a dynamic knapsack problem and for stochastic lot sizing problems we give computational results which show that these new inequalities are very effective in a branch and cut algorithm

constructions and complexity of secondary polytopes abstract the secondary polytope a of a configuration a of n points in affine d 1 space is an n d polytope whose vertices correspond to regular triangulations of conv a in this article we present three constructions of a and apply them to study various geometric combinatorial and computational properties of secondary polytopes the first construction is due to gel fand kapranov and zelevinsky who used it to describe the face lattice of a we introduce the universal polytope u a d r n a combinatorial object depending only on the oriented matroid of a the secondary a can be obtained as the image of u a under a canonical linear map onto r n the third construction is based upon gale transforms or oriented matroid duality it is used to analyze the complexity of computing a and to give bounds in terms of n and d for the number of faces of a

on zero error communication via quantum channels in the presence of noiseless feedback we initiate the study of zero error communication via quantum channels when the receiver and the sender have at their disposal a noiseless feedback channel of unlimited quantum capacity generalizing shannon s zero error communication theory with instantaneous feedback we first show that this capacity is only a function of the linear span of choi kraus operators of the channel which generalizes the bipartite equivocation graph of a classical channel and which we dub non commutative bipartite graph then we go on to show that the feedback assisted capacity is non zero allowing for a constant amount of activating noiseless communication if and only if the non commutative bipartite graph is non trivial and give a number of equivalent characterizations this result involves a far reaching extension of the conclusive exclusion of quantum states we then present an upper bound on the feedback assisted zero error capacity motivated by a conjecture originally made by shannon and proved later by ahlswede we demonstrate that this bound to have many good properties including being additive and given by a minimax formula we also prove a coding theorem showing that this quantity is the entanglement assisted capacity against an adversarially chosen channel from the set of all channels with the same choi kraus span which can also be interpreted as the feedback assisted unambiguous capacity the proof relies on a generalization of the postselection lemma de finetti reduction that allows to reflect additional constraints and which we believe to be of independent interest this capacity is a relaxation of the feedback assisted zero error capacity however we have to leave open the question of whether they coincide in general we illustrate our ideas with a number of examples including classical quantum channels and weyl diagonal channels and close with an extensive discussion of open questions

optimal sequence of quantum measurements in the sense of stein s lemma in quantum hypothesis testing we derive a necessary and sufficient condition for a sequence of quantum measurements to achieve the optimal performance in quantum hypothesis testing we discuss what quantum measurement we should perform in order to attain the optimal exponent of the second error probability under the condition that the first error probability goes to 0 as an asymptotically optimal measurement we propose a projection measurement characterized by the irreducible representation theory of the special linear group sl especially in the spin 1 2 system it is realized by the simultaneous measurement of the total momentum and a momentum of a specified direction as a by product we obtain another proof of quantum stein s lemma in addition an asymptotically optimal measurement is constructed in the quantum gaussian case and it is physically meaningful

a quantum version of sanov s theorem we present a quantum version of sanov s theorem focussing on a hypothesis testing aspect of the theorem there exists a sequence of typical subspaces for a given set of stationary quantum product states asymptotically separating them from another fixed stationary product state analogously to the classical case the separating rate on a logarithmic scale is equal to the infimum of the quantum relative entropy with respect to the quantum reference state over the set while in the classical case the separating subsets can be chosen universally in the sense that they depend only on the chosen set of i i d processes in the quantum case the choice of the separating subspaces depends additionally on the reference state

universal coding for classical quantum channel we construct a universal code for a stationary and memoryless classical quantum channel as a quantum version of the universal coding by csiszar and korner our code is constructed utilizing a combination of irreducible representations a decoder introduced through the quantum information spectrum and the packing lemma

algebraic algorithms for sampling from conditional distributions we construct markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic examples include contingency tables logistic regression and spectral analysis of permutation data the algorithms involve computations in polynomial rings using grobner bases

permutohedra and minimal matrices the notions of minimality uniqueness and additivity originated in discrete tomography they have applications to kronecker products of characters of the symmetric group and arise as the optimal solutions of quadratic transportation problems here we introduce the notion of real minimality and give geometric characterizations of all these notions for a matrix a by considering the intersection of the permutohedron determined by a with the transportation polytope in which a lies we also study the computational complexity of deciding if the properties of being additive real minimal unique and minimal hold for a given matrix and show how to efficiently construct some matrix with any of these properties

cancellation model of pitch perception a model of pitch perception is presented involving an array of delay lines and inhibitory gating neurons in response to a periodic sound a minimum appears in the pattern of outputs of the inhibitory neurons at a lag equal to the period of the sound the position of this minimum is the cue to pitch the model is similar to the autocorrelation model of pitch multiplication being replaced by an operation similar to subtraction and maxima by minima the two models account for a wide class of pitch phenomena in very much the same way the principal goal of this paper is to demonstrate this fact several features of the cancellation model may be to its advantage it is closely related to the operation of harmonic cancellation that can account for segregation of concurrent harmonic stimuli it can be generalized to explain the perception of multiple pitches and it shows a greater degree of sensitivity to phase than autocorrelation which may allow it to explain certain phenomena that autocorrelation cannot account for

test sets for integer programs in this paper i discuss various properties of the simplicial complex of maximal lattice free bodies associated with a matrix a if the matrix satisfies some mild conditions and is generic the edges of the complex form the minimal test set for the family of integer programs obtained by selecting a particular row of a as the objective function and using the remaining rows to impose constraints on the integer variables 1997 the mathematical programming society inc published by elsevier science b v

positivity and complexity of ideal sheaves the problem of bounding the complexity of a polynomial ideal in terms of the degrees of its generators has attracted a great deal of interest in recent years results in this direction go back at least as far as the classical work 17 of hermann on the ideal membership problem and the effective nullstellensatz of brownawell 4 and kollar 21 marks a major recent advance with the development of computational algebraic geometry the question has taken on increasing importance and it came into particularly clear focus through the influential paper 3 of bayer andmumford more recently the theorem of 8 and 20 concerning regularity of powers raises the question of bounding the complexity of powers of an ideal and suggests that asymptotically the picture should become very clean the aim of the present paper is to examine some of the results and questions of 3 30 and 7 from a geometric perspective in the spirit of 12 our thesis is that much of this material is clarified and parts rendered transparent when viewed through the lenses of vanishing theorems and intersection theory specifically motivated by thework 25 26 of paolettiwe introduce an invariant s j thatmeasures in effect howmuchonehas to twist an idealj in order tomake

neighbors of the origin for four by three matrices scarf has defined a neighborhood system for families of integer programs where the right hand side is allowed to vary this system depends on a matrix a of constraint and objective function coefficients of the integer programs this paper characterizes the set of neighbors of the origin when a is four by three showing that it may be described as the set of integer vectors in a union of two dimensional polyhedra where the number of polyhedra is quadratic in the bit size of a

strong converse to the quantum channel coding theorem a lower bound on the probability of decoding error for a quantum communication channel is presented from which the strong converse to the quantum channel coding theorem is immediately shown the results and their derivations are mostly straightforward extensions of the classical counterparts which were established by arimoto 1973 except that more careful treatment is necessary here due to the noncommutativity of operators

total variation bounds on the expectation of periodic functions with applications to recourse approximations we derive a lower and upper bound for the expectation of periodic functions depending on the total variation of the probability density function of the underlying random variable using worst case analysis we derive tighter bounds for functions that are periodically monotone these bounds can be used to evaluate the performance of approximations for both continuous and integer recourse models in this paper we introduce a new convex approximation for totally unimodular recourse models and we show that this convex approximation has the best worst case error bound possible improving previous bounds with a factor 2 moreover we use similar analysis to derive error bounds for two types of discrete approximations of continuous recourse models with continuous random variables furthermore we derive a tractable lipschitz constant for pure integer recourse models

classical capacities of compound and averaged quantum channels we determine the capacity of compound classical quantum channels as a consequence we obtain the capacity formula for the averaged classical quantum channels the capacity result for compound channels demonstrates as in the classical setting the existence of reliable universal classical quantum codes in scenarios where the only a priori information about the channel used for the transmission of information is that it belongs to a given set of memoryless classical quantum channels our approach is based on a universal classical approximation of the quantum relative entropy which in turn relies on a universal hypothesis testing result

the capacity of the quantum channel with general signal states it is shown that the capacity of a classical quantum channel with arbitrary possibly mixed states equals the maximum of the entropy bound with respect to all a priori distributions this completes the recent result of hausladen jozsa schumacher westmoreland and wootters 1996 who proved the equality for the pure state channel

asymptotic linear bounds for the castelnuovo mumford regularity we prove asymptotic linear bounds for the castelnuovo mumford regularity of certain filtrations of homogeneous ideals whose rees algebras need not be noetherian

uniform bounds and symbolic powers on smooth varieties the purpose of this note is to show how one can use multiplier ideals toestablish effective uniform bounds on the multiplicative behavior of certainfamilies of ideal sheaves on a smooth algebraic variety in particular weprove a quick but rather surprising result concerning the symbolic powersof radical ideals on such a variety let

asymptotics of quantum relative entropy from a representation theoretical viewpoint in this paper it is proved that the quantum relative entropy d can be asymptotically attained by the relative entropy of probabilities given by a certain sequence of positive operator valued measures povms the sequence of povms depends on but is independent of the choice of

a smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels we use the smooth entropy approach to treat the problems of binary quantum hypothesis testing and the transmission of classical information through a quantum channel we provide lower and upper bounds on the optimal type ii error of quantum hypothesis testing in terms of the smooth max relative entropy of the two states representing the two hypotheses then using a relative entropy version of the quantum asymptotic equipartition property qaep we can recover the strong converse rate of the i i d hypothesis testing problem in the asymptotics on the other hand combining stein s lemma with our bounds we obtain a stronger e independent version of the relative entropy qaep similarly we provide bounds on the one shot e error classical capacity of a quantum channel in terms of a smooth max relative entropy variant of its holevo capacity using these bounds and the e independent version of the relative entropy qaep we can recover both the holevo schumacher westmoreland theorem about the optimal direct rate of a memoryless quantum channel with product state encoding as well as its strong converse counterpart

decomposition of test sets in stochastic integer programming we study graver test sets for linear two stage stochastic integer programs and show that test sets can be decomposed into finitely many building blocks whose number is independent on the number of scenarios of the stochastic program we present a finite algorithm to compute the building blocks directly without prior knowledge of test set vectors once computed building blocks can be employed to solve the stochastic program by a simple augmentation scheme again without explicit knowledge of test set vectors finally we report preliminary computational experience

vanishing theorems a theorem of severi and the equations defining projective varieties in 1903 severi s proved that if x x c p are smooth surfaces whose union is the complete intersection of r 2 hypersurfaces of degrees di dr 2 then hypersurfaces of degree k z di r cut out a complete linear series on x cf sr xiii 9 8 the purpose of this paper is first of all to show that elementary arguments using the kodaira vanishing theorem lead to a simple variant of severi s statement theorem 7 below which extends it in serval directions more importantly we hope to convince the reader that this result has a surprising number of applications to questions involving the equations defining projective varieties consider to begin with a smooth complex projective variety x c pr of dimension n and codimension e r n in this setting our theorem asserts the vanishing of the higher cohomology of suitable twists of the ath power of the ideal sheaf yx of x in apr proposition 1 assume that x is cut out scheme theoretically in p by hypersurfaces of degrees d1 d2 d then h p r k 0 for i 1 provided k ad d2 de r note that only the degrees of the first e codim x pr defining equations come into play here when n 2 and a 1 this is a consequence of severi s

a geometric buchberger algorithm for integer programming let ip a c denote the family of integer programs of the form min cx ax b x nn obtained by varying the right hand side vector b but keeping a and c fixed a test set for ipa c is a set of vectors in zn such that for each nonoptimal solution to a program in this family there is at least one element g in this set such that g has an improved cost value as compared to we describe a unique minimal test set for this family called the reduced grobner basis of ip a c an algorithm for its construction is presented which we call a geometric buchberger algorithm for integer programming and we show how an integer program may be solved using this test set the reduced grobner basis is then compared with some other known test sets from the literature we also indicate an easy procedure to construct test sets with respect to all cost functions for a matrix a zn 2 n of full row rank

entanglement transmission and generation under channel uncertainty universal quantum channel coding we determine the optimal rates of universal quantum codes for entanglement transmission and generation under channel uncertainty in the simplest scenario the sender and receiver are provided merely with the information that the channel they use belongs to a given set of channels so that they are forced to use quantum codes that are reliable for the whole set of channels this is precisely the quantum analog of the compound channel coding problem we determine the entanglement transmission and entanglement generating capacities of compound quantum channels and show that they are equal moreover we investigate two variants of that basic scenario namely the cases of informed decoder or informed encoder and derive corresponding capacity results

symbolic powers of monomial ideals and vertex cover algebras abstract we introduce and study vertex cover algebras of weighted simplicial complexes these algebras are special classes of symbolic rees algebras we show that symbolic rees algebras of monomial ideals are finitely generated and that such an algebra is normal and cohen macaulay if the monomial ideal is squarefree for a simple graph the vertex cover algebra is generated by elements of degree 2 and it is standard graded if and only if the graph is bipartite we also give a general upper bound for the maximal degree of the generators of vertex cover algebras

constructing arrangements of lines and hyperplanes with applications a finite set of lines partitions the euclidean plane into a cell complex similarly a finite set of d 1 dimensional hyperplanes partitions d dimensional euclidean space an algorithm is presented that constructs a representation for the cell complex defined by n hyperplanes in optimal o n d time in d dimensions it relies on a combinatorial result that is of interest in its own right the algorithm is shown to lead to new methods for computing lambda matrices constructing all higher order voronoi diagrams halfspatial range estimation degeneracy testing and finding minimum measure simplices in all five applications the new algorithms are asymptotically faster than previous results and in several cases are the only known methods that generalize to arbitrary dimensions the algorithm also implies an upper bound of 2 cn d c a positive constant for the number of combinatorially distinct arrangements of n hyperplanes in e d

non linear behaviour of castelnuovo mumford regularity abstract it is shown that the castelnuovo mumford regularity of lex segment ideals of ordinary powers as well as of frobenius powers of a homogeneous polynomial ideal is a function of polynomial type of huge degree

alternatives for testing total dual integrality in this paper we provide characterizing properties of totally dual integral tdi systems among others the following a system of linear inequalities is tdi if and only if its coefficient vectors form a hilbert basis and there exists a test set for the system s dual integer programs where all test vectors have positive entries equal to 1 reformulations of this provide relations between computational algebra and integer programming and they contain applegate cook and mccormick s sufficient condition for the tdi property and sturmfels theorem relating toric initial ideals generated by square free monomials to unimodular triangulations we also study the theoretical and practical efficiency and limits of the characterizations of the tdi property presented here in the particular case of set packing polyhedra our results correspond to endowing the weak perfect graph theorem with an additional computationally interesting geometric feature the normal fan of the stable set polytope of a perfect graph can be refined into a regular triangulation consisting only of unimodular cones

solving stochastic programs with integer recourse by enumeration a framework using gro bner basis reductions in this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right hand side vector using grobner basis methods from computational algebra to solve the numerous second stage integer programs using structural properties of the expected integer recourse function we prove that under mild conditions an optimal solution is contained in a finite set furthermore we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed

asymptotic behavior of integer programming and the stability of the castelnuovo mumford regularity the paper provides a connection between commutative algebra and integer programming and contains two parts the first one is devoted to the asymptotic behavior of integer programs with a fixed cost linear functional and the constraint sets consisting of a finite system of linear equations or inequalities with integer coefficients depending linearly on n an integer n is determined such that the optima of these integer programs are a quasi linear function of n for all n ge n using results in the first part one can bound in the second part the indices of stability of the castelnuovo mumford regularities of integral closures of powers of a monomial ideal and that of symbolic powers of a square free monomial ideal

coding theorems for compound problems via quantum renyi divergences recently a new notion of quantum renyi divergences has been introduced by muller lennert dupuis szehr fehr and tomamichel and wilde winter and yang which found a number of applications in strong converse theorems here we show that these new renyi divergences are also useful tools to obtain coding theorems in the direct domain of various problems we demonstrate this by giving new and considerably simplified proofs for the achievability parts of stein s lemma with composite null hypothesis universal state compression and the classical capacity of compound classical quantum channels based on single shot error bounds already available in the literature and simple properties of the quantum renyi divergences the novelty of our proofs is that the composite compound coding theorems can be almost directly obtained from the single shot error bounds essentially with the same effort as for the case of simple null hypothesis single source single channel

coding theorem and strong converse for quantum channels we present a new proof of holevo s 1973 1977 coding theorem for transmitting classical information through quantum channels and its strong converse the technique is largely inspired by wolfwitz s 1964 combinatorial approach using types of sequences as a byproduct of our approach which is independent of previous ones both in the coding theorem and the converse we can give a new proof of holevo s information bound

the value function of an integer program we consider integer programs in which the objective function and constraint matrix are fixed while the right hand side varies the value function gives for each feasible right hand side the criterion value of the optimal solution we provide a precise characterization of the closed form expression for any value function

pitch of iterated rippled noise iterated rippled noise irn stimuli are generated by a cascade of delay d gain g and add networks the matched pitch of irn stimuli was determined as a function of the type of network used to generate irn stimuli the delay d 2 4 and 8 ms the number of iterations n 1 2 3 4 6 8 of the delay and add networks and whether the delayed noise was added g 1 to or subtracted g 1 from the undelayed noise the matched pitch of irn stimuli did not depend on the type of network when g 1 addition the matched pitch did not depend on the number of stages of iterations n and was always equal to the reciprocal of the delay 1 d when g 1 subtraction the match pitch depended on n when n 1 the matched pitch of irn stimuli was ambiguous having two pitches in the region of 1 d 10 when n 8 the match pitch was equal to 1 2d this change in the pitch occurred between n 2 and 6 the results are discussed in terms of spectral and temporal models of complex pitch processing a temporal model based on autocorrelation was able to provide quantitative predictions for the pitch of these irn stimuli however a spectral type of model can also account for the pitch of these irn stimuli

classical capacity of quantum channels with general markovian correlated noise the classical capacity of a quantum channel with arbitrary markovian correlated noise is evaluated for the general case of a channel with long term memory which corresponds to a markov chain which does not converge to equilibrium the capacity is expressed in terms of the communicating classes of the markov chain for an irreducible and aperiodic markov chain the channel is forgetful and one retrieves the known expression kretschmann and werner in phys rev a 72 062323 2005 for the capacity

loudness of sharply 2068 db octave filtered noises in relation to the factors extracted from the autocorrelation function this study examines the loudness of bandpass noises with center frequencies of 250 500 and 1000hz while changing the autocorrelation function acf the bandwidth of the source signal was altered with a 2068 db octave sharp filter to control the acf of the source signal the scale values of loudness were obtained using a paired comparison method it is shown that the loudness of the bandpass noises inside the critical band is not constant the loudness of the pure tone is greater than that of sharply filtered noises the loudness of the bandpass noises increases with increasing effective duration of the acf e of the source signal

simple integer recourse models convexity and convex approximations we consider the objective function of a simple recourse problem with fixed technology matrix and integer second stage variables separability due to the simple recourse structure allows to study a one dimensional version instead based on an explicit formula for the objective function we derive a complete description of the class of probability density functions such that the objective function is convex this result is also stated in terms of random variables next we present a class of convex approximations of the objective function which are obtained by perturbing the distributions of the right hand side parameters we derive a uniform bound on the absolute error of the approximation finally we give a representation of convex simple integer recourse problems as continuous simple recourse problems so that they can be solved by existing special purpose algorithms

the multiparametric 0 1 integer linear programming problem a unified approach abstract we designed an algorithm for the multiparametric 0 1 integer linear programming ilp problem with the perturbation of the constraint matrix the objective function and the right hand side vector simultaneously considered our algorithm works by choosing an appropriate finite sequence of non parametric mixed integer linear programming milp problems in order to obtain a complete multiparametrical analysis the algorithm may be implemented by using any software capable of solving milp problems

an exact algorithm for solving large scale two stage stochastic mixed integer problems some theoretical and experimental aspects abstract we present an algorithmic framework so called bfc tsmip for solving two stage stochastic mixed 0 1 problems the constraints in the deterministic equivalent model have 0 1 variables and continuous variables at any stage the approach uses the twin node family tnf concept within an adaptation of the algorithmic framework so called branch and fix coordination for satisfying the nonanticipativity constraints for the first stage 0 1 variables jointly we solve the mixed 0 1 submodels defined at each tnf integer set for satisfying the nonanticipativity constraints for the first stage continuous variables in these submodels the only integer variables are the second stage 0 1 variables a numerical example and some theoretical and computational results are presented to show the performance of the proposed approach

on the castelnuovo mumford regularity and the arithmetic degree of monomial ideals in the first part of this paper we show that the castelnuovo mumford regularity of a monomial ideal is bounded above by its arithmetic degree the second part gives upper bounds for the castelnuovo mumford regularity and the arithmetic degree of a monomial ideal in terms of the degrees of its generators these bounds can be formulated for an arbitrary homogeneous ideal in terms of any grobner basis

diagnostic system based on the human auditory brain model for measuring environmental noise an application to railway noise abstract measurements of railway noise were conducted by use of a diagnostic system of regional environmental noise the system is based on the model of the human auditory brain system the model consists of the interplay of autocorrelators and an interaural crosscorrelator acting on the pressure signals arriving at the ear entrances and takes into account the specialization of left and right human cerebral hemispheres different kinds of railway noise were measured through binaural microphones of a dummy head to characterize the railway noise physical factors extracted from the autocorrelation functions acf and interaural crosscorrelation function iacf of binaural signals were used the factors extracted from acf were 1 energy represented at the origin of the delay 0 2 effective duration of the envelope of the normalized acf e 3 the delay time of the first peak 1 and 4 its amplitude o 1 the factors extracted from iacf were 5 iacc 6 interaural delay time at which the iacc is defined iacc and 7 width of the iacf at the iacc w iacc the factor 0 can be represented as a geometrical mean of energies at both ears as listening level ll

an algebraic geometry algorithm for scheduling in presence of setups and correlated demands we study here a problem of schedulingn job types onm parallel machines when setups are required and the demands for the products are correlated random variables we model this problem as a chance constrained integer program

regularity of powers of cover ideals of unimodular hypergraphs abstract let h be a unimodular hypergraph over the vertex set n and let j h be the cover ideal of h in the polynomial ring r k x 1 x n we show that reg j h s is a linear function in s for all s r n 2 1 where r is the rank of h moreover for every i a i r j h s is also a linear function in s for s n 2

heralded channel holevo superadditivity bounds from entanglement monogamy we introduce a class of channels called heralded channels which generalize the quantum erasure channel composed with an arbitrary other quantum channel we show that monogamy of squashed entanglem

a time domain description for the pitch strength of iterated rippled noise two versions of a cascaded add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose strength relative to the noise can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds or the number of iterations n 1 2 3 4 7 and 9 performance was determined for irn stimuli generated with delays of 2 4 and 8 ms and for four bandpass filter conditions 0 2000 250 2000 500 2000 and 750 2000 hz some irn stimuli were extremely difficult to discriminate despite relatively large spectral differences while other irn stimuli produced readily discriminable changes in perception despite small spectral differences these contrasting results are inconsistent with simple spectral explanations for the perception of irn stimuli an explanation based on the first peak of the autocorrelation function of irn stimuli is consistent with the results simulations of the processing performed by the peripheral auditory system i e interval histograms and correlograms produce results which are consistent with the involvement of these temporal processes in the perception of irn stimuli

cohen macaulayness of powers of two dimensional squarefree monomial ideals abstract two dimensional squarefree monomial ideals can be seen as the stanley reisner ideals of graphs the main results of this paper are combinatorial characterizations for the cohen macaulayness of ordinary and symbolic powers of such an ideal in terms of the associated graph