secret sharing and non shannon information inequalities the known secret sharing schemes for most access structures are not efficient even for a one bit secret the length of the shares in the schemes is 2o n where n is the number of participants in the access structure it is a long standing open problem to improve these schemes or prove that they cannot be improved the best known lower bound is by csirmaz who proved that there exist access structures with n participants such that the size of the share of at least one party is n logn times the secret size csirmaz s proof uses shannon information inequalities which were the only information inequalities known when csirmaz published his result on the negative side csirmaz proved that by only using shannon information inequalities one cannot prove a lower bound of n on the share size in the last decade a sequence of non shannon information inequalities were discovered in fact it was proved that there are infinity many independent information inequalities even in four variables this raises the hope that these inequalities can help in improving the lower bounds beyond n however we show that any information inequality with four or five variables cannot prove a lower bound of n on the share size in addition we show that the same negative result holds for all information inequalities with more than five variables that are known to date

a recursive construction of the set of binary entropy vectors and related algorithmic inner bounds for the entropy region a method for checking membership in the region of entropic vectors generated from n bits is presented a general technique for utilizing this method to create inner bounds for regions of entropic vectors as a function of outer bounds is then presented these two algorithms are then used to provide new insights regarding relationships among well known bounds for the region of entropic vectors

universal amplitudes in finite size scaling the antiperiodic 3d spherical model the antiperiodic 3d spherical model is studied on a hypercube lattice two sides of which are finite and the other infinite the universal correlation length finite size scaling amplitude in the conjectured relationship xi l a x is calculated exactly and found to be a 0 1361 which should be compared with the antiperiodic 3d ising model value of a approximately 0 12

stabilizer information inequalities from phase space distributions the shannon entropy of a collection of random variables is subject to a number of constraints the best known examples being monotonicity and strong subadditivity it remains an open question to decide which of these laws of information theory are also respected by the von neumann entropy of many body quantum states in this article we consider a toy version of this difficult problem by analyzing the von neumann entropy of stabilizer states we find that the von neumann entropy of stabilizer states satisfies all balanced information inequalities that hold in the classical case our argument is built on the fact that stabilizer states have a classical model provided by the discrete wigner function the phase space entropy of the wigner function corresponds directly to the von neumann entropy of the state which allows us to reduce to the classical case our result has a natural counterpart for multi mode gaussian states which sheds some light on the general properties of the construction we also discuss the relation of our results to recent work by linden ruskai and winter the quantum entropy cone of stabiliser states e print arxiv 1302 5453

a conditional information inequality and its combinatorial applications we show that the inequality h a b x h a b y leqslant h a b for jointly distributed random variables a b x y which does not hold in general case holds under some natural condition on the support of the probability distribution of a b x y this result generalizes a version of the conditional ingleton inequality if for some distribution i x mskip 5mu mskip 5mu y a h a x y 0 then i a mskip 5mu mskip 5mu b leqslant i a mskip 5mu mskip 5mu b x i a mskip 5mu mskip 5mu b y i x mskip 5mu mskip 5mu y we present two applications of our result the first one is the following easy to formulate theorem on edge colorings of bipartite graphs assume that the edges of a bipartite graph are colored in k colors so that each two edges sharing a vertex have different colors and for each pair left vertex x right vertex y there is at most one color a such both x and y are incident to edges with color a assume further that the degree of each left vertex is at least l and the degree of each right vertex is at least r then k geqslant lr the second application is a new method to prove lower bounds for biclique cover of bipartite graphs

an approximate numerical method for the complex eigenproblem in systems characterised by a structural damping matrix this paper presents an efficient numerical method that approximates the complex eigenvalues and eigenvectors in structural systems with viscoelastic damping materials characterised by the complex structural damping matrix this new method begins from the solution of the undamped system and approximates the complex eigenpair by finite increments using the eigenvector derivatives and the rayleigh quotient it is implemented in three different approaches single step incremental and iterative schemes the single step technique is presented for systems with low and medium damping from numerical examples it can be verified that the errors committed by the approximate single step technique with respect to the exact solutions obtained by the iram method are less than 0 2 when the loss factor of the material damping is lower than 1 this is a considerable improvement on other approximate methods for higher damped systems an improvement to the previous approach is proposed by an incremental technique that keeps the accuracy without significantly increasing the computational time the complex eigenproblem for materials whose mechanical properties are dependent on frequency is solved by a fast iterative approach whose validity is proved using a four parameter fractional derivative model

analysis of four parameter fractional derivative model of real solid materials the introduction of fractional derivatives into the constitutive equation of the differential operator type of linear solid materials has led to the development of the so called fractional derivative models one of these models characterized by four parameters has been found usable for describing the variation of dynamics elastic and damping properties in a wide frequency range provided that there is only one loss peak in this paper this four parameter model is theoretically analyzed the effect of the parameters on the frequency curves is demonstrated and it is shown that there is a strict relation between the dispersion of the dynamic modulus the loss peak and the slope of the frequency curves the half value bandwidth of the loss modulus frequency curve is investigated and conditions are developed to establish the applicability of the model for a class of materials moreover it is shown that the model can be used to predict the frequency dependences of dynamic properties for a wide range even if measurements are made in only a narrow frequency range around the loss peak

lattice sums of generalized hypergeometric functions representations and convergence criteria for one dimensional 1d and two dimensional 2d lattice sums of generalized hypergeometric functions pfp 1 are derived by using apparently new integral representations for the latter functions and 1d and 2d forms of the poisson summation formula these lattice sum representations concisely unify and generalize various specializations given previously by several authors and should prove useful in analysing finite size effects in systems subjected to non periodic boundary conditions

from log determinant inequalities to gaussian entanglement via recoverability theory many determinantal inequalities for positive definite block matrices are consequences of general entropy inequalities specialized to gaussian distributed vectors with prescribed covariances in particular strong subadditivity ssa yields ln det v ac ln det v bc ln det v abc ln det v c geq 0 for all 3 times 3 block matrices v abc where subscripts identify principal submatrices we shall refer to the above mentioned inequality as ssa of log det entropy in this paper we develop further insights on the properties of the above mentioned inequality and its applications to classical and quantum information theory in the first part of this paper we show how to find known and new necessary and sufficient conditions under which saturation with equality occurs subsequently we discuss the role of the classical transpose channel also known as petz recovery map in this problem and find its action explicitly we then prove some extensions of the saturation theorem by finding faithful lower bounds on a log det conditional mutual information in the second part we focus on quantum gaussian states whose covariance matrices are not only positive but obey additional constraints due to the uncertainty relation for gaussian states the log det entropy is equivalent to the renyi entropy of order 2 we provide a strengthening of log det ssa for quantum covariance matrices that involves the so called gaussian renyi 2 entanglement of formation a well behaved entanglement measure defined via a gaussian convex roof construction we then employ this result to define a log det entropy equivalent of the squashed entanglement measure which is remarkably shown to coincide with the gaussian renyi 2 entanglement of formation this allows us to establish useful properties of such measure s such as monogamy faithfulness and additivity on gaussian states

on the hardness of approximating the network coding capacity this work addresses the computational complexity of achieving the capacity of a general network coding instance it has been shown lehman and lehman soda 2005 that determining the scalar linear capacity of a general network coding instance is np hard in this paper we address the notion of approximation in the context of both linear and nonlinear network coding loosely speaking we show that given an instance of the general network coding problem of capacity c constructing a code of rate c for any universal i e independent of the size of the instance constant 1 is hard specifically finding such network codes would solve a long standing open problem in the field of graph coloring our results refer to scalar linear vector linear and nonlinear encoding functions and are the first results that address the computational complexity of achieving the network coding capacity in both the vector linear and general network coding scenarios in addition we consider the problem of determining the scalar linear capacity of a planar network coding instance i e an instance in which the underlying graph is planar we show that even for planar networks this problem remains np hard

dualities between entropy functions and network codes in communications networks the capacity region of multisource network coding is given in terms of the set of entropy functions gamma more broadly determination of gamma would have an impact on converse theorems for multi terminal problems in information theory this paper provides several new dualities between entropy functions and network codes given a function g ges 0 defined on all subsets of n random variables we provide a construction for a network multicast problem which is ldquosolvablerdquo if and only if g is the entropy function of a set of quasi uniform random variables the underlying network topology is fixed and the multicast problem depends on g only through link capacities and source rates a corresponding duality is developed for linear network codes where the constructed multicast problem is linearly solvable if and only if g is linear group characterizable relaxing the requirement that the domain of g be subsets of random variables we obtain a similar duality between polymatroids and the linear programming bound these duality results provide an alternative proof of the insufficiency of linear and abelian network codes and demonstrate the utility of non shannon inequalities to tighten outer bounds on network coding capacity regions

fractional calculus a different approach to the analysis of viscoelastically damped structures fractional calculus is used to construct stress strain relationships for viscoelastic materials these relationships are used in the finite element analysis of viscoelastically damped structures and closed form solutions to the equations of motion are found the attractive feature of this approach is that very few empirical parameters are required to model the viscoelastic material and calculate the response of the structure for general loading conditions

truncation technique for characterizing linear polymatroids linear polymatroids have a strong connection to network coding the problem of finding the linear network coding capacity region is equivalent to the characterization of all linear polymatroids it is well known that linear polymatroids must satisfy the inequalities of ingleton combin math appln 1971 however it has been an open question for years as to whether these inequalities are sufficient it was until recently that new subspace rank inequalities have been discovered independently by kinser and dougherty in this paper we propose a new approach to investigate properties of linear polymatroids specifically we demonstrate how to construct a new polymatroid that satisfies not only the ingleton and dfz inequalities but also lies outside the minimal closed and convex cone containing all linear polymatroids using this polymatroid we prove that all truncation preserving inequalities including ingleton inequalities and dfz inequalities are insufficient to characterize linear polymatroids

on the conjectures of henkel and weston recent conjectures of henkel and weston 1992 on certain two dimensional sums are examined and some significant generalizations of these sums are developed the results so obtained should be useful in analysing finite size effects in systems subjected to non periodic boundary conditions

maximum independence and mutual information if i sub 1 i sub 2 i sub k are random boolean variables and the joint probabilities up to the k 1 th order are known the values of the kth order probabilities maximizing the overall entropy have been defined as the maximum independence estimate in this article some contributions deriving from the definition of maximum independence probabilities are proposed first it is shown that the maximum independence values are reached when the product of the probabilities of the minterms i sub 1 i sub 2 i sub k containing an even number of complemented variables is equal to the products of the probabilities of the other minterms second the new definition of group mutual information as the difference between the maximum independence entropy and the real entropy is proposed and discussed finally the new concept of mutual information is applied to the determination of dependencies in data mining problems

size and treewidth bounds for conjunctive queries this article provides new worst case bounds for the size and treewith of the result q d of a conjunctive query q applied to a database d we derive bounds for the result size q d in terms of structural properties of q both in the absence and in the presence of keys and functional dependencies these bounds are based on a novel coloring of the query variables that associates a coloring number c q to each query q intuitively each color used represents some possible entropy of that variable using this coloring number we derive tight bounds for the size of q d in case i no functional dependencies or keys are specified and ii simple functional dependencies keys are given these results generalize recent size bounds for join queries obtained by atserias et al 2008 in the case of arbitrary compound functional dependencies we use tools from information theory to provide lower and upper bounds establishing a close connection between size bounds and a basic question in information theory our new coloring scheme also allows us to precisely characterize both in the absence of keys and with simple keys the treewidth preserving queries the queries for which the treewidth of the output relation is bounded by a function of the treewidth of the input database finally we give some results on the computational complexity of determining the size bounds and of deciding whether the treewidth is preserved

computation of eigenvalues in proportionally damped viscoelastic structures based on the fixed point iteration abstract linear viscoelastic structures are characterized by dissipative forces that depend on the history of the velocity response via hereditary damping functions the free motion equation leads to a nonlinear eigenvalue problem characterized by a frequency dependent damping matrix in the present paper a novel and efficient numerical method for the computation of the eigenvalues of linear and proportional or lightly non proportional viscoelastic structures is developed the central idea is the construction of two complex valued functions of a complex variable whose fixed points are precisely the eigenvalues this important property allows the use of these functions in a fixed point iterative scheme with help of some results in fixed point theory necessary conditions for global and local convergence are provided it is demonstrated that the speed of convergence is linear and directly depends on the level of induced damping in addition under certain conditions the recursive method can also be used for the calculation of non viscous real eigenvalues in order to validate the mathematical results two numerical examples are analyzed one for single degree of freedom systems and another for multiple ones

on certain schlomilch type series abstract by using a form of the poisson summation formula together with a generalization due to srivastava and exton of the discontinuous integral of weber and schafheitlin and the heretofore not readily available cosine transform of the hypergeometric function 1 f 2 b 2 t 2 b 0 several new schlomilch and fourier type series are evaluated by specialization of the latter series numerous results appearing in the literature are obtained in a unified way

capacity and achievable rate regions for linear network coding over ring alphabets the rate of a network code is the ratio of the block size of the network s messages to that of its edge codewords we compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general cases of arbitrary ring and module alphabets for non commutative rings two sided linearity is allowed specifically we prove the following for directed acyclic networks first the linear rate region and the linear capacity of any network over a finite field depend only on the characteristic of the field furthermore any two fields with different characteristics yield different linear capacities for at least one network second whenever the characteristic of a given finite field divides the size of a given finite ring each network s linear rate region over the ring is contained in its linear rate region over the field thus any network s linear capacity over a field is at least its linear capacity over any other ring of the same size an analogous result also holds for linear network codes over module alphabets third whenever the characteristic of a given finite field does not divide the size of a given finite ring there is some network whose linear capacity over the ring is strictly greater than its linear capacity over the field thus for any finite field there always exist rings over which some networks have higher linear capacities than over the field

lattice sums for the helmholtz equation a survey of different representations for lattice sums for the helmholtz equation is made these sums arise naturally when dealing with wave scattering by periodic structures one of the main objectives is to show how the various forms depend on the dimension d of the underlying space and the lattice dimension d lambda lattice sums are related to and can be calculated from the quasi periodic green s function and this object serves as the starting point of the analysis

monotonicity under local operations linear entropic formulas all correlation measures classical and quantum must be monotonic under local operations in this paper we characterize monotonic formulas that are linear combinations of the von neumann entropies associated with the quantum state of a physical system that has n parts we show that these formulas form a polyhedral convex cone which we call the monotonicity cone and enumerate its facets we illustrate its structure and prove that it is equivalent to the cone of monotonic formulas implied by strong subadditivity we explicitly compute its extremal rays for n leq5 we also consider the symmetric monotonicity cone in which the formulas are required to be invariant under subsystem permutations we describe this cone fully for all n

networks matroids and non shannon information inequalities we define a class of networks called matroidal networks which includes as special cases all scalar linearly solvable networks and in particular solvable multicast networks we then present a method for constructing matroidal networks from known matroids we specifically construct networks that play an important role in proving results in the literature such as the insufficiency of linear network coding and the unachievability of network coding capacity we also construct a new network from the vamos matroid which we call the vamos network and use it to prove that shannon type information inequalities are in general not sufficient for computing network coding capacities to accomplish this we obtain a capacity upper bound for the vamos network using a non shannon type information inequality discovered in 1998 by zhang and yeung and then show that it is smaller than any such bound derived from shannon type information inequalities this is the first application of a non shannon type inequality to network coding we also compute the exact routing capacity and linear coding capacity of the vamos network finally using a variation of the vamos network we prove that shannon type information inequalities are insufficient even for computing network coding capacities of multiple unicast networks

two constructions on limits of entropy functions the correspondence between the subvectors of a random vector and their shannon entropies gives rise to an entropy function limits of the entropy functions are closed to convolutions with modular polymatroids and when integer valued also to free expansions the problem of description of the limits of entropy functions is reduced to those limits that correspond to matroids related results on entropy functions are reviewed with regard to polymatroid and matroid theories and perfect and ideal secret sharing

conditional information inequalities for entropic and almost entropic points we study conditional linear information inequalities i e linear inequalities for shannon entropy that hold for distributions whose joint entropies meet some linear constraints we prove that some conditional information inequalities cannot be extended to any unconditional linear inequalities some of these conditional inequalities hold for almost entropic points while others do not we also discuss some counterparts of conditional information inequalities for kolmogorov complexity

on a relation between information inequalities and group theory we establish a one to one correspondence between information inequalities and group inequalities the major implication of our result is that we can prove information inequalities by proving the corresponding group inequalities and vice versa by giving a group theoretic proof for all shannon type inequalities we suggest that new inequalities could be discovered by making use of the rich set of tools in group theory on the other hand via a non shannon type information inequality discovered by zhang and yeung 1997 we obtain a new inequality in group theory whose meaning is yet to be understood

the minimal set of ingleton inequalities the ingleton inequalities are the inequality constraints known to be required of representable matroids for a matroid of n elements there are 16n ingleton inequalities in this paper we show that many of these inequalities are redundant we explicitly determine the unique minimal set of ingleton inequalities which number on the order of 6n 4 o 5n in information theory these inequalities are required of the entropy functions of certain random variables constructed from linear subspaces as a result these inequalities appear as constraints in linear programming outer bounds for the capacity region of multisource network coding where the codes are required to be linear ingleton inequalities have also played an instrumental role in demonstrating the insufficiency of linear codes for multisource network coding the reduction that we obtain for ingleton inequalities is sufficiently large to meaningfully reduce the complexity of these linear programming bounds

closure solvability for network coding and secret sharing network coding is a new technique to transmit data through a network by letting the intermediate nodes combine the packets they receive given a network the network coding solvability problem decides whether all the packets requested by the destinations can be transmitted in this paper we introduce a new approach to this problem we define a closure operator on a digraph closely related to the network coding instance and we show that the constraints for network coding can all be expressed according to that closure operator thus a solution for the network coding problem is equivalent to a so called solution of the closure operator we can then define the closure solvability problem in general which surprisingly reduces to finding secret sharing matroids when the closure operator is a matroid based on this reformulation we can easily prove that any multiple unicast where each node receives at least as many arcs as there are sources solvable by linear functions we also give an alternative proof that any nontrivial multiple unicast with two source receiver pairs is always solvable over all sufficiently large alphabets based on singular properties of the closure operator we are able to generalize the way in which networks can be split into two distinct parts we also provide a new way of identifying and removing useless nodes in a network we also introduce the concept of network sharing where one solvable network can be used to accommodate another solvable network coding instance finally the guessing graph approach to network coding solvability is generalized to any closure operator which yields bounds on the amount of information that can be transmitted through a network

a framework for linear information inequalities we present a framework for information inequalities namely inequalities involving only shannon s information measures for discrete random variables a region in ir 2 sup n 1 denoted by spl gamma is identified to be the origin of all information inequalities involving n random variables in the sense that all such inequalities are partial characterizations of spl gamma a product from this framework is a simple calculus for verifying all unconstrained and constrained linear information identities and inequalities which can be proved by conventional techniques these include all information identities and inequalities of such types in the literature as a consequence of this work most identities and inequalities involving a definite number of random variables can now be verified by a software called itip which is available on the world wide web our work suggests the possibility of the existence of information inequalities which cannot be proved by conventional techniques we also point out the relation between spl gamma and some important problems in probability theory and information theory

on ingleton violating finite groups given n discrete random variables its entropy vector is the 2 n 1 dimensional vector obtained from the joint entropies of all non empty subsets of the random variables it is well known that there is a close relation between such an entropy vector and a certain group characterizable vector obtained from a finite group and n of its subgroups indeed roughly speaking knowing the region of all such group characterizable vectors is equivalent to knowing the region of all entropy vectors this correspondence may be useful for characterizing the space of entropic vectors and for designing network codes if one restricts attention to abelian groups then not all entropy vectors can be obtained this is an explanation for the fact shown by dougherty et al that linear network codes cannot achieve capacity in general network coding problems since linear network codes come from abelian groups all abelian group characterizable vectors and by fiat all entropy vectors generated by linear network codes satisfy a linear inequality called the ingleton inequality general entropy vectors however do not necessarily have this property it is therefore of interest to identify groups that violate the ingleton inequality in this paper we study the problem of finding nonabelian finite groups that yield characterizable vectors which violate the ingleton inequality using a refined computer search we find the symmetric group s 5 to be the smallest group that violates the ingleton inequality careful study of the structure of this group and its subgroups reveals that it belongs to the ingleton violating family pgl 2 q with a prime power q geq 5 i e the projective group of 2 times 2 nonsingular matrices with entries in mathbb f q we further interpret this family of groups and their subgroups using the theory of group actions and identify the subgroups as certain stabilizers we also extend the construction to more general groups such as pgl n q and gl n q the families of groups identified here are therefore good candidates for constructing network codes more powerful than linear network codes and we discuss some considerations for constructing such group network codes

multiround private information retrieval capacity and storage overhead private information retrieval pir is the problem of retrieving one message out of k messages from n non communicating replicated databases where each database stores all k messages in such a way that each database learns no information about which message is being retrieved the capacity of pir is the maximum number of bits of desired information per bit of downloaded information among all pir schemes the capacity has recently been characterized for pir as well as several of its variants in every case it is assumed that all the queries are generated by the user simultaneously here we consider multiround pir where the queries in each round are allowed to depend on the answers received in previous rounds we show that the capacity of multiround pir is the same as the capacity of single round pir the result is generalized to also include t privacy constraints combined with previous results this shows that there is no capacity advantage from multiround over single round schemes non linear over linear schemes or from epsilon error over zero error schemes however we show through an example that there is an advantage in terms of storage overhead we provide an example of a multiround non linear epsilon error pir scheme that requires a strictly smaller storage overhead than the best possible with single round linear zero error pir schemes

quasi uniform codes and their applications quasi uniform random vectors have probability distributions that are uniform over their projections they are of fundamental interest because a linear information inequality is valid if and only if it is satisfied by all quasi uniform random vectors in this paper we investigate properties of codes induced by quasi uniform random vectors we prove that quasi uniform codes which include linear and almost affine codes as special cases are distance invariant and that greene s theorem and the critical theorem of crapo and rota hold in the setting of quasi uniform codes we show that both theorems are essentially combinatorial but not algebraical in nature linear programming bounds proposed by delsarte are extended for quasi uniform codes

on information divergence measures and a unified typicality strong typicality which is more powerful for theorem proving than weak typicality can be applied to finite alphabets only while weak typicality can be applied to countable alphabets in this paper the relation between typicality and information divergence measures is discussed the new definition of information divergence measure in this paper leads to the definition of a unified typicality for finite or countably infinite alphabets which is stronger than both weak typicality and strong typicality unified typicality retains the asymptotic equipartition property and the structural properties of strong typicality and it can potentially be used to generalize those theorems which are previously established by strong typicality to countable alphabets the applications in rate distortion theory and multisource network coding problems are discussed

on information theoretic characterizations of markov random fields and subfields let x i i in v form a markov random field mrf represented by an undirected graph g v e and v be a subset of v we determine the smallest graph that can always represent the subfield x i i in v as an mrf based on this result we obtain a necessary and sufficient condition for a subfield of a markov tree to be also a markov tree when g is a path so that x i i in v form a markov chain it is known that the i measure is always nonnegative kawabata and yeung in 1992 we prove that markov chain is essentially the only mrf such that the i measure is always nonnegative by applying our characterization of the smallest graph representation of a subfield of an mrf we develop a recursive approach for constructing information diagrams for mrfs our work is built on the set theoretic characterization of an mrf yeung et al in 2002

probabilistic inequalities for evaluating structural network measures proving interrelations between structural graph measures analytically has been intricate generally relations between structural graph measures describe the interplay between measures which turned out to be useful for better understanding the properties of such quantities the results which have been achieved so far are restricted to simple measures or special graph classes such as trees in this paper we introduce a probabilistic approach for establishing inequalities between quantitative network measures on random networks those inequalities between different graph measures lead to a deeper understanding of the mathematical apparatus and in particular to a discussion of quality aspects of structural graph measures which is a major contribution of this paper

entropy region and convolution the entropy region is constructed from vectors of random variables by collecting shannon entropies of all subvectors its shape is studied here by means of polymatroidal constructions notably by convolution the closure of the region is decomposed into the direct sum of tight and modular parts reducing the study to the tight part the relative interior of the reduction belongs to the entropy region behavior of the decomposition under self adhesivity is clarified results are specialized and extended to the region constructed from four tuples of random variables this and computer experiments help to visualize approximations of a symmetrized part of the entropy region the four atom conjecture on the minimal ingleton score is refuted

on certain two dimensional schlomilch series by using representations for one dimensional 1d schlomilch series lommel s expansion for bessel functions of the first kind and elementary series manipulations several algebraic formulae for two dimensional 2d schlomilch series are derived one of these formulae contains as a special case an identity involving a certain trigonometric lattice sum conjectured by henkel and weston 1993 which has recently been derived by boersma and de doelder 1993 using the 2d poisson summation formula the latter method is used to give an alternative derivation for 2d schlomilch series further it is shown that representation by 2d schlomilch series of a null function is not unique in addition representations for several other 1d type series are given

balanced information inequalities in this correspondence we are interested in linear information inequalities both discrete and continuous ones we show that every discrete information inequality is associated with a balanced information inequality and a set of residual weights to prove the inequality it is necessary and sufficient to prove that its balanced version is valid and all its residual weights are nonnegative for a continuous information inequality we prove that it is valid if and only if its discrete counterpart is balanced and valid

insufficiency of linear coding in network information flow it is known that every solvable multicast network has a scalar linear solution over a sufficiently large finite field alphabet it is also known that this result does not generalize to arbitrary networks there are several examples in the literature of solvable networks with no scalar linear solution over any finite field however each example has a linear solution for some vector dimension greater than one it has been conjectured that every solvable network has a linear solution over some finite field alphabet and some vector dimension we provide a counterexample to this conjecture we also show that if a network has no linear solution over any finite field then it has no linear solution over any finite commutative ring with identity our counterexample network has no linear solution even in the more general algebraic context of modules which includes as special cases all finite rings and abelian groups furthermore we show that the network coding capacity of this network is strictly greater than the maximum linear coding capacity over any finite field exactly 10 greater so the network is not even asymptotically linearly solvable it follows that even for more general versions of linearity such as convolutional coding filter bank coding or linear time sharing the network has no linear solution

index coding capacity how far can one go with only shannon inequalities an interference alignment perspective is used to identify the simplest instances minimum possible number of edges in the alignment graph not more than 2 interfering messages at any destination of index coding problems where non shannon information inequalities are necessary for capacity characterization in particular this includes the first known example of a multiple unicast one destination per message index coding problem where non shannon information inequalities are shown to be necessary the simplest multiple unicast example has 7 edges in the alignment graph and 11 messages the simplest multiple groupcast multiple destinations per message example has 6 edges in the alignment graph 6 messages and 10 receivers for both the simplest multiple unicast and multiple groupcast instances the best outer bound based on only shannon inequalities is 2 5 which is tightened to 11 28 by the use of the zhang yeung non shannon type information inequality and the linear capacity is shown to be 5 13 using the ingleton inequality conversely identifying the minimal challenging aspects of the index coding problem allows an expansion of the class of solved index coding problems up to but not including these instances

sensor networks consider the two related problems of sensor selection and sensor fusion in the first given a set of sensors one wishes to identify a subset of the sensors which while small in size captures the essence of the data gathered by the sensors in the second one wishes to construct a fused sensor which utilizes the data from the sensors possibly after discarding dependent ones in order to create a single sensor which is more reliable than each of the individual ones in this work we rigorously define the dependence among sensors in terms of joint empirical measures and incremental parsing we show that these measures adhere to a polymatroid structure which in turn facilitates the application of efficient algorithms for sensor selection we suggest both a random and a greedy algorithm for sensor selection given an independent set we then turn to the fusion problem and suggest a novel variant of the exponential weighting algorithm in the suggested algorithm one competes against an augmented set of sensors which allows it to converge to the best fused sensor in a family of sensors without having any prior data on the sensors performance

a new inequality for the von neumann entropy strong subadditivity of von neumann entropy proved in 1973 by lieb and ruskai is a cornerstone of quantum coding theory all other known inequalities for entropies of quantum systems may be derived from it here we prove a new inequality for the von neumann entropy which we prove is independent of strong subadditivity it is an inequality which is true for any four party quantum state provided that it satisfies three linear relations constraints on the entropies of certain reduced states

optimality and approximate optimality of source channel separation in networks we consider the source channel separation architecture for lossy source coding in communication networks it is shown that the separation approach is optimal in two general scenarios and is approximately optimal in a third scenario the two scenarios for which separation is optimal complement each other the first is when the memoryless sources at source nodes are arbitrarily correlated each of which is to be reconstructed at possibly multiple destinations within certain distortions but the channels in this network are synchronized orthogonal and memoryless point to point channels the second is when the memoryless sources are mutually independent each of which is to be reconstructed only at one destination within a certain distortion but the channels are general including multi user channels such as multiple access broadcast interference and relay channels possibly with feedback the third scenario for which we demonstrate approximate optimality of source channel separation generalizes the second scenario by allowing each source to be reconstructed at multiple destinations with different distortions for this case the loss from optimality using the separation approach can be upper bounded when a difference distortion measure is taken and in the special case of quadratic distortion measure this leads to universal constant bounds

cut set bounds on network information flow explicit characterization of the capacity region of communication networks is a long standing problem while it is known that network coding can outperform routing and replication the set of feasible rates is not known in general characterizing the network coding capacity region requires the determination of the set of all entropic vectors furthermore computing the explicitly known linear programming bound is infeasible in practice due to an exponential growth in complexity as a function of network size this paper focuses on the fundamental problems of characterization and computation of outer bounds for multi source multi sink networks starting from the known local functional dependence induced by the communication network we introduce the notion of irreducible sets which characterize implied functional dependence we provide recursions for the computation of all maximal irreducible sets these sets act as information theoretic bottlenecks and provide an easily computable outer bound for networks with correlated sources we extend the notion of irreducible sets and resulting outer bound for networks with independent sources we compare our bounds with existing bounds in the literature we find that our new bounds are the best among the known graph theoretic bounds for networks with correlated sources and for networks with independent sources

a class of non linearly solvable networks for each positive composite integer m a network is constructed which is solvable over an alphabet of size m but is not solvable over any smaller alphabet these networks have no linear solutions over any module alphabets and are not asymptotically linearly solvable over any finite field alphabets the networks capacities are all shown to equal one and their linear capacities are all shown to be bounded away from one for all finite field alphabets in addition if m is a non power of prime composite number then such a network is not solvable over any prime power size alphabet

the inequalities of quantum information theory let spl rho denote the density matrix of a quantum state having n parts 1 n for i spl sube n 1 n let spl rho sub i tr sub n spl bsol i spl rho denote the density matrix of the state comprising those parts i such that i spl isin i and let s spl rho sub i denote the von neumann 1927 entropy of the state spl rho sub i the collection of spl nu 2 sup n numbers s spl rho sub i sub i spl sube n may be regarded as a point called the allocation of entropy for spl rho in the vector space r sup spl nu let a sub n denote the set of points in r sup spl nu that are allocations of entropy for n part quantum states we show that a sub n the topological closure of a sub n is a closed convex cone in r sup spl nu this implies that the approximate achievability of a point as an allocation of entropy is determined by the linear inequalities that it satisfies lieb and ruskai 1973 have established a number of inequalities for multipartite quantum states strong subadditivity and weak monotonicity we give a finite set of instances of these inequalities that is complete in the sense that any valid linear inequality for allocations of entropy can be deduced from them by taking positive linear combinations and independent in the sense that none of them can be deduced from the others by taking positive linear combinations let b sub n denote the polyhedral cone in r sup spl nu determined by these inequalities we show that a sub n b sub n for n spl les 3 the status of this equality is open for n spl ges 4 we also consider a symmetric version of this situation in which s spl rho sub i depends on i only through the number i spl ne i of indexes in i and can thus be denoted s spl rho sub i in this case we give for each n a finite complete and independent set of inequalities governing the symmetric allocations of entropy s spl rho sub i sub 0 spl les i spl les n in r sup n 1

randomness and dependencies extraction via polarization with applications to slepian wolf coding and secrecy the polarization phenomenon for a single source is extended to a framework with multiple correlated sources it is shown in addition to extracting the randomness of the source the polar transforms take the original arbitrary dependencies to extremal dependencies polar coding schemes for the slepian wolf sw coding problem and for secret key generations are then proposed based on this phenomenon in particular secret keys achieving the secrecy capacity and compression schemes achieving the sw capacity region are obtained with a complexity of o n log n

an implicit characterization of the achievable rate region for acyclic multisource multisink network coding the achievable information rate region problem of multisource multisink network coding for general acyclic networks with arbitrary transmission requirements has previously been studied where inner and outer bounds on the region were derived in terms of gamma ast the fundamental region of entropy functions in this paper we derive the exact characterization of the achievable rate region in terms of entropic functions thus closing the gap between the existing inner and outer bounds

information theoretic characterizations of conditional mutual independence and markov random fields we take the point of view that a markov random field is a collection of so called full conditional mutual independencies using the theory of i measure we have obtained a number of fundamental characterizations related to conditional mutual independence and markov random fields we show that many aspects of conditional mutual independence and markov random fields have very simple set theoretic descriptions new insights into the structure of conditional mutual independence and markov random fields are obtained our results have immediate applications in the implication problem of probabilistic conditional independency and relational database we obtain a hypergraph characterization of a markov random field which makes it legitimate to view a markov random field as a hypergraph based on this result we naturally employ the graham reduction a tool from relational database theory to recognize a markov forest this connection between markov random fields and hypergraph sheds some light on the possible role of hypergraph theory in the study of markov random fields

a general formula for channel capacity a formula for the capacity of arbitrary single user channels without feedback not necessarily information stable stationary etc is proved capacity is shown to equal the supremum over all input processes of the input output inf information rate defined as the liminf in probability of the normalized information density the key to this result is a new converse approach based on a simple new lower bound on the error probability of m ary hypothesis tests among equiprobable hypotheses a necessary and sufficient condition for the validity of the strong converse is given as well as general expressions for spl epsiv capacity

multicasting multiple correlated sources to multiple sinks over a noisy channel network the problem of network coding for multicasting a single source to multiple sinks has first been studied by ahlswede cai li and yeung in 2000 in which they have established the celebrated max flow min cut theorem on nonphysical information flow over a network of independent channels on the other hand in 1980 han has studied the case with multiple correlated sources and a single sink from the viewpoint of polymatroidal functions in which a necessary and sufficient condition has been demonstrated for reliable transmission over the network this paper presents an attempt to unify both cases which leads to establish a necessary and sufficient condition for reliable transmission over a network for multicasting multiple correlated sources to multiple sinks here the problem of separation of source coding and network coding is also discussed

abstract functional dependency structures abstract the functional dependency fd structures known mainly from database relationships theory appear to include other kinds of dependencies among objects like functions boolean or random variables etc we examine the representations of fd relations in the matroid theory manner a galois connection of the fd relations with closure system is elaborated

an equivalence between network coding and index coding we show that the network coding and index coding problems are equivalent this equivalence holds in the general setting which includes linear and nonlinear codes specifically we present a reduction that maps a network coding instance to an index coding instance while preserving feasibility i e the network coding instance has a feasible solution if and only if the corresponding index coding instance is feasible in addition we show that one can determine the capacity region of a given network coding instance with colocated sources by studying the capacity region of a corresponding index coding instance previous connections between network and index coding were restricted to the linear case

entropic inequalities and marginal problems a marginal problem asks whether a given family of marginal distributions for some set of random variables arises from some joint distribution of these variables here we point out that the existence of such a joint distribution imposes nontrivial conditions already on the level of shannon entropies of the given marginals these entropic inequalities are necessary but not sufficient criteria for the existence of a joint distribution for every marginal problem a list of such shannon type entropic inequalities can be calculated by fourier motzkin elimination and we offer a software interface to a fourier motzkin solver for doing so for the case that the hypergraph of given marginals is a cycle graph we provide a complete analytic solution to the problem of classifying all relevant entropic inequalities and use this result to bound the decay of correlations in stochastic processes furthermore we show that shannon type inequalities for differential entropies are not relevant for continuous variable marginal problems non shannon type inequalities are both in the discrete and in the continuous case in contrast to other approaches our general framework easily adapts to situations where one has additional conditional independence requirements on the joint distribution as in the case of graphical models we end with a list of open problems a complementary article discusses applications to quantum nonlocality and contextuality

a theory of network equivalence part i point to point channels a family of equivalence tools for bounding network capacities is introduced given a network n with node set v the capacity of n is a set of non negative vectors with elements corresponding to all possible multicast connections in n a vector is in the capacity region for n if and only if it is possible to simultaneously and reliably establish all multicast connections across n at the given rates any other demand type with independent messages is a special case of this multiple multicast problem and is therefore included in the given rate region in part i we show that the capacity of a network n is unchanged if any independent memoryless point to point channel in n is replaced by a noiseless bit pipe with throughput equal to the removed channel s capacity it follows that the capacity of a network comprised entirely of such point to point channels equals the capacity of an error free network that replaces each channel by a noiseless bit pipe of the corresponding capacity a related separation result was known previously for a single multicast connection over an acyclic network of independent memoryless point to point channels our result treats general connections e g a collection of simultaneous unicasts and allows cyclic or acyclic networks

switching based filter based on dempster s combination rule for image processing in this work a two pass switching rank ordered arithmetic mean tsram filter that preserves image details while effectively suppressing impulse noise is proposed to improve the performance of switching based median filters the proposed filter mechanism includes an efficient impulse detector based on the dempster shafer d s evidence theory and a rank ordered arithmetic mean filter that works by estimating the noise free ordered mean values excluding the current pixel a modified dempster s combination rule is applied to the impulse detector to improve filtering performance a simple switching median filter is included to perform second pass filtering experimental results show that the proposed filter outperforms many well accepted switching based median filters in terms of both noise suppression and detail preservation providing excellent robustness at various percentages of impulse noise

the structure of renyi entropic inequalities we investigate the universal inequalities relating the rnyi entropies of the marginals of a multi partite quantum state this is in analogy to the same question for the shannon and von neumann ent

linear codes for sources and source networks error exponents universal coding for slepian wolf source networks the error exponents obtained by korner marton and the author are shown to be universally attainable by linear codes also improved exponents are derived for linear codes with large rates specializing the results to simple discrete memoryless sources reveals their relationship to the random coding and expurgated bounds for channels with additive noise one corollary is that there are universal linear codes for this class of channels which attain the random coding error exponent for each channel in the class the combinatorial approach of csiszar korner marton is used in particular all results are derived from a lemma specifying good encoders in terms of purely combinatorial properties

a non shannon type conditional inequality of information quantities given n discrete random variables spl omega x sub 1 x sub n associated with any subset spl alpha of 1 2 n there is a joint entropy h x sub spl alpha where x sub spl alpha x sub i i spl isin spl alpha this can be viewed as a function defined on 2 sup 1 2 n taking values in 0 spl infin we call this function the entropy function of spl omega the nonnegativity of the joint entropies implies that this function is nonnegative the nonnegativity of the conditional joint entropies implies that this function is nondecreasing and the nonnegativity of the conditional mutual information implies that this function is two alternative these properties are the so called basic information inequalities of shannon s information measures an entropy function can be viewed as a 2 sup n 1 dimensional vector where the coordinates are indexed by the subsets of the ground set 1 2 n as introduced by yeng see ibid vol 43 no 6 p 1923 34 1997 spl gamma sub n stands for the cone in ir 2 sup n 1 consisting of all vectors which have all these properties let spl gamma sub n be the set of all 2 sup n 1 dimensional vectors which correspond to the entropy functions of some sets of n discrete random variables a fundamental information theoretic problem is whether or not spl gamma sub n spl gamma sub n here spl gamma sub n stands for the closure of the set spl gamma sub n we show that spl gamma sub n is a convex cone spl gamma sub 2 spl gamma sub 2 spl gamma sub 3 spl ne spl gamma sub 3 but spl gamma sub 3 spl gamma sub 3 for four random variables we have discovered a conditional inequality which is not implied by the basic information inequalities of the same set of random variables this lends an evidence to the plausible conjecture that spl gamma sub n spl ne spl gamma sub n for n 3

eigensolutions of nonviscously damped systems based on the fixed point iteration abstract in this paper nonviscous nonproportional symmetric vibrating structures are considered nonviscously damped systems present dissipative forces depending on the time history of the response via kernel hereditary functions solutions of the free motion equation leads to a nonlinear eigenvalue problem involving mass stiffness and damping matrices this latter as dependent on frequency viscous damping can be considered as a particular case involving damping forces as function of the instantaneous velocity of the degrees of freedom in this work a new numerical procedure to compute eigensolutions is proposed the method is based on the construction of certain recursive functions which under a iterative scheme allow to reach eigenvalues and eigenvectors simultaneously and avoiding computation of eigensensitivities eigenvalues can be read then as fixed points of those functions a deep analysis of the convergence is carried out focusing specially on relating the convergence conditions and error decay rate to the damping model features such as the nonproportionality and the viscoelasticity the method is validated using two 6 degrees of freedom numerical examples involving both nonviscous and viscous damping and a continuous system with a local nonviscous damper the convergence and the sequences behavior are in agreement with the results foreseen by the theory

sensitivity analysis of discrete structural systems methods for calculating sensitivity derivatives for discrete structural systems are surveyed primarily covering literature published during the past two decades methods are described for calculating derivatives of static displacements and stresses eigenvalues and eigenvectors transient structural response and derivatives of optimum structural designs with respect to problem parameters the survey is focused on publications developed in nonstructural fields such as electronics controls and physical chemistry which are directly applicable to structural problems most notable among the nonstructural based methods are the adjoint variable technique from control theory and the green s function and fast methods from physical chemistry

derivatives of eigenvalues and eigenvectors of a general complex matrix a survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non hermitian matrices is presented in addition a modification of one method based on a better normalizing condition is proposed methods are classified as direct or adjoint and are evaluated for efficiency operation counts are presented in terms of matrix size number of design variables and number of eigenvalues and eigenvectors of interest the effect of the sparsity of the matrix and its derivatives is also considered and typical solution times are given general guidelines are established for the selection of the most efficient method

iterative method for calculating derivatives of eigenvectors the modified modal method uses the static solution to account for the contribution of truncated higher eigenvectors which significantly improves the accuracy or effectiveness of the tuncated modal superposition in this paper we extended this method to an iterative procedure

on secure network coding with nonuniform or restricted wiretap sets the secrecy capacity of a network for a given collection of permissible wiretap sets is the maximum rate of communication such that observing links in any permissible wiretap set reveal no information about the message this paper considers secure network coding with nonuniform or restricted wiretap sets for example networks with unequal link capacities where a wiretapper can wiretap any subset of k links or networks where only a subset of links can be wiretapped existing results show that for the case of uniform wiretap sets networks with equal capacity links packets where any k can be wiretapped the secrecy capacity is given by a cut set bound if random keys are injected at the source and decoded at the sink whether or not the communicating users have information about the choice of wiretap set in contrast we show that for the nonuniform case this secrecy rate is achievable for the case of known but not unknown wiretap set we give achievable linear optimization based strategies where random keys are canceled at intermediate nonsink nodes or injected at intermediate nonsource nodes finally we show that determining the secrecy capacity is an np hard problem

piecewise linear conditional information inequality a new information inequality of non shannon type is proved for three discrete random variables under conditional independence constraints using the framework of entropy functions and polymatroids tightness of the inequality is described via quasi groups

frequency dependences of complex moduli and complex poisson s ratio of real solid materials abstract the concept of a complex modulus of elasticity is a powerful and widely used tool for characterizing the linear dynamic elastic and damping properties of solid materials in the frequency domain it is shown in this paper that typical characters of frequency dependences of all complex moduli shear young s etc and complex poisson s ratios of real solid materials can be determined by transforming the causal and real relaxation and creep responses respectively from the time domain into the frequency domain even without having to specify the processes of relaxation and creep it is proved that all dynamic moduli monotonically increase and the dynamic poisson s ratio monotonically decreases with increasing frequency and all respective loss factors pass through at least one maximum these frequency dependences are generally valid for any real solid material regardless of the actual damping mechanisms some experimental results are presented and interpreted in the light of the theory the usefulness of theoretical predictions in materials engineering measurements of dynamic properties and in modelling dynamic behaviour is discussed

higher order eigensensitivities based numerical method for the harmonic analysis of viscoelastically damped structures this paper presents an efficient numerical method for the harmonic analysis of viscoelastically damped structural systems characterized by a frequency dependent structural damping matrix making use of the complex mode superposition method departing from the undamped eigensolution the proposed numerical method updates the complex and frequency dependent eigenpair avoiding the solution of a complex eigenproblem for each computational frequency the complex eigenvalues and eigenvectors are updated within the desired tolerance by an adaptive step size control scheme using the first and higher order eigenderivatives the influence on the computation time of the considered number of eigenderivatives and the tolerance is discussed and the efficiency of the proposed numerical method for the harmonic analysis of viscoelastically damped large ordered structural systems is proved finally a practical application is presented where the harmonic response of a constrained layer damping cantilever beam subjected to a base motion is analyzed the complex and frequency dependent eigenvalues and eigenvectors are computed the modal contributions to the total response are determined and the total response is approximated by the complex mode superposition method finally the approximated response is validated with the exact one computed by the direct frequency method and with that experimentally measured copyright 2011 john wiley sons ltd

capacity bounds for networks with correlated sources and characterisation of distributions by entropies characterising the capacity region for a network can be extremely difficult even with independent sources determining the capacity region can be as hard as the open problem of characterising all information inequalities the majority of computable outer bounds in the literature are relaxations of the linear programming bound which involves entropy functions of random variables related to the sources and link messages when sources are not independent the problem is even more complicated extension of linear programming bounds to networks with correlated sources is largely open source dependence is usually specified through a joint probability distribution and one of the main challenges in extending linear program bounds is the difficulty or impossibility of characterising arbitrary dependences via entropy functions this paper tackles the problem by answering the question of how well entropy functions can characterise correlation among sources we show that by using carefully chosen auxiliary random variables the characterisation can be fairly accurate using such auxiliary random variables we also give implicit and explicit outer bounds on the capacity of networks with correlated sources the characterisation of correlation or joint distribution via shannon entropy functions is also applicable to other information measures such as renyi entropy and tsallis entropy