a justesen construction of binary concatenated codes that asymptotically meet the zyablov bound for low rate an explicit construction of a sequence of binary codes that asymptotically meet the zyablov bound for rates lower than 0 30 is given by using justesen s construction of concatenation the outer codes are constructed from generalized hermitian curves these outer codes can be described without any algebraic geometry terminology while the proofs of some properties deeply rely on algebraic geometry

an efficient algorithm to find all small size stopping sets of low density parity check matrices in this work we introduce an efficient algorithm to find all stopping sets of size less than some threshold of a fixed low density parity check ldpc matrix the solution is inspired by the algorithm proposed by rosnes and ytrehus in 2005 to find an exhaustive list of all small size turbo stopping sets in a turbo code the efficiency of the proposed algorithm is demonstrated by several numerical examples for instance we have applied the algorithm to the well known 3 5 regular 155 64 tanner code and found all stopping sets of size at most 18 in about 1 min on a standard desktop computer also we have verified that the minimum stopping set size of the 4896 2474 ramanujan margulis code is indeed 24 and that the corresponding multiplicity is exactly 204 furthermore we have applied the algorithm to the ieee 802 16e ldpc codes and determined the minimum stopping set size and the corresponding multiplicity exactly for these codes finally as an application we present a greedy algorithm to find a small number of redundant parity checks to add to the original parity check matrix in order to remove all stopping sets in the corresponding tanner graph of size less than the minimum distance an extensive case study of the 155 64 tanner code illustrates the usefulness of the algorithm and we present a 110 times 155 redundant parity check matrix for this code with no stopping sets of size less than the minimum distance simulation results of iterative decoding on the binary erasure channel show performance improvements for low to medium erasure probabilities when this redundant parity check matrix is used for decoding

eigenderivative analysis of asymmetric non conservative systems in general the damping matrix of a dynamic system or structure is such that it can not be simultaneously diagonalized with the mass and stiffness matrices by any linear transformation for this reason the eigenvalues and eigenvectors and consequently their derivatives become complex expressions for the first and second order derivatives of the eigenvalues and eigenvectors of these linear non conservative systems are given traditional restrictions of symmetry and positive definiteness have not been imposed on the mass damping and stiffness matrices the results are derived in terms of the eigenvalues and left and right eigenvectors of the second order system so that the undesirable use of the first order representation of the equations of motion can be avoided the usefulness of the derived expressions is demonstrated by considering a non proportionally damped two degree of freedom symmetric system and a damped rigid rotor on flexible supports copyright 2001 john wiley sons ltd

new algorithms for finding irreducible polynomials over finite fields we present a new algorithm for finding an irreducible polynomial of specified degree over a finite field our algorithm is deterministic and it runs in polynomial time for fields of small characteristic we in fact prove the stronger result that the problem of finding irreducible polynomials of specified degree over a finite field is deterministic polynomial time reducible to the problem of factoring polynomials over the prime field

perfectly secure index coding in this paper we investigate the index coding problem in the presence of an eavesdropper messages are to be sent from one transmitter to a number of legitimate receivers who have side information about the messages and share a set of secret keys with the transmitter to do this the transmitter communicates to the legitimate receivers the public code c which is also heard by the eavesdropper we assume perfect secrecy meaning that the eavesdropper should not be able to retrieve any information about the message set from the public communication we study the minimum key lengths for zero error and perfectly secure index coding problem on one hand this problem is a generalization of the index coding problem and thus a difficult one on the other hand it is a generalization of the shannon s cipher system we show that a generalization of shannon s one time pad strategy is optimal up to a multiplicative constant meaning that it obtains the entire boundary of the cone formed by looking at the secure rate region from the origin this shows the optimality of the generalized one time pad for minimizing the consumption of shared secret keys per message bits when public communication is free the transmitter is not charged for the rate of the public communication finally we consider relaxation of the perfect secrecy and zero error constraints to weak secrecy and asymptotically vanishing probability of error and provide a secure version of the result obtained by langberg and effros on the equivalence of zero error and epsilon error regions in the conventional index coding problem

reversible low density parity check codes low density parity check ldpc codes may be decoded using a circuit implementation of the sum product algorithm which maps the factor graph of the code by reusing the decoder for encoding both tasks can be performed using the same circuit thus reducing area and verification requirements motivated by this iterative encoding techniques based upon the graphical representation of the code are proposed code design constraints which ensure encoder convergence are presented and then used to design iteratively encodable codes while also preventing 4 cycle creation we show how the jacobi method for iterative matrix inversion can be applied to finite field matrices viewed as message passing and employed as the core of an iterative encoder we present an algebraic construction of 4 cycle free iteratively encodable codes using circulant matrices analysis of these codes identifies a weakness in their structure due to a repetitive pattern in the factor graph the graph supports pseudo codewords of low pseudo weight in order to remove the repetitive pattern in the graph we propose a recursive technique for generating iteratively encodable codes the new codes offer flexibility in the choice of code length and rate and performance that compares well to randomly generated quasi cyclic and extended euclidean geometry codes

a construction of non reed solomon type mds codes a construction is presented of long maximum distance separable mds codes that are not generalized reed solomon grs type the construction uses subsets s mod s mod m of a finite field f gf q with the property that no t distinct elements of s add up to some fixed element of f large subsets of this kind are used to construct n m 2 k t 1 non grs mds codes over f

pliable index coding we formulate a new variant of the index coding problem where instead of demanding a specific message clients are pliable and are interested in receiving any t messages that they do not have we term this problem pliable index coding or picod t we prove that with this formulation although some instances of the problem become simple in general the problem of finding the optimal linear code remains np hard however we show that it is possible to construct pliable index codes that are substantially smaller than index codes in many cases if there are n clients the server has m messages and each client has a side information set of cardinality s leq m t we show that o min t log n t log 2 n broadcast transmissions are sufficient to satisfy all the clients for t 1 this is an exponential improvement over the n messages required in index coding in the worst case for m n in addition for t gg log 2 n the number of broadcast transmissions required is only linearly dependent on t we generalize the results to instances where the side information sets are not necessarily of equal cardinality when m o n delta for some constant delta 0 we show that the codes of size o min t log 2 n t log n log 3 n are sufficient in general we also consider the scenario when the server only knows the cardinality of the side information sets of the clients and each client is interested in receiving any t messages that it does not have we term this formulation oblivious pliable index coding or ob picod t if the cardinalities of side information sets of all the clients is s with s leq m t then we show that min s t m s messages are both sufficient and necessary for linear codes finally we develop efficient heuristic approximation algorithms for picod t and show through simulations on the random instances of picod t that they perform well in practice

on the accuracy required of experimental data for finite element model updating abstract in this paper the determination is considered of the required experimental accuracy that must be attained when updating finite element models with use of measured vibration test data a theoretical basis is developed for frf based updating techniques as these use measured data directly it is shown that a well defined relationship that can be expressed as a characteristic function exists between the system s properties the correction matrices and the actual amount of experimental noise the formulation is then applied to the standard response function updating formulation where the element mass and stiffness matrices are corrected by using a single multiplier the so called p value in the presence of noise the convergence of the updating algorithm is shown to be dependent on a number of conditions which arise from two distinct cases one convergent and the other divergent the findings are illustrated in the case of a 3 d space frame and the efficacy of the proposed characteristic function is discussed in some detail finally a way of selecting the optimum excitation frequency values is presented as a means of relaxing the minimum experimental accuracy

frequency selection method for frf based model updating abstract in this paper a new frequency selection method for efficient frf based model updating is proposed using the proposed method the frequency points used for updating can be selected in an automatic way such that the selected frequencies can carry as much information as possible with a limited number of frequencies in order to demonstrate the effectiveness of the proposed method a numerical example of truss structure is used different sets of frequency points for updating are compared in terms of numerical stability as well as updated results finally the proposed method is extended to deal with rotor bearing systems

a polynomial time algorithm for pliable index coding in pliable index coding we consider a server with m messages and n clients where each client has as side information a subset of the messages we seek to minimize the number of broadcast transmissions so that each client can recover any one unknown message she does not already have previous work has shown that the pliable index coding problem is np hard and requires at most mathcal o log 2 n broadcast transmissions which indicates exponential savings over the conventional index coding that requires in the worst case mathcal o n transmissions in this paper building on a decoding criterion that we propose we first design a deterministic polynomial time algorithm that can realize the exponential benefits by achieving in the worst case a performance upper bounded by mathcal o log 2 n broadcast transmissions we extend our algorithm to the t requests case where each client requires t unknown messages that she does not have and show that our algorithm requires at most mathcal o t log n log 2 n broadcast transmissions we construct lower bound instances that require at least omega log n transmissions for linear pliable index coding and at least omega t log n transmissions for the t requests case indicating that both our upper and lower bounds are polynomials of log n and differ within a factor of mathcal o log n we provide a probabilistic analysis over random instances and show that the required number of transmissions is almost surely theta log n as compared with the theta n log n for index coding in addition we show that these upper and lower bounds also hold for vector pliable index coding in the worst case instances and the random graph instances implying that vector coding does not provide benefits in terms of these bounds our numerical experiments show that our algorithm outperforms existing algorithms for pliable index coding by up to 50 less transmissions

index coding an interference alignment perspective author s maleki h cadambe vr jafar sa abstract the index coding problem is studied from an interference alignment perspective providing new results as well as new insights into and generalizations of previously known results an equivalence is established between the capacity of multiple unicast index coding where each message is desired by exactly one receiver and groupcast index coding where a message can be desired by multiple receivers which settles the heretofore open question of insufficiency of linear codes for the multiple unicast index coding problem by equivalence with groupcast settings where this question has previously been answered necessary and sufficient conditions for the achievability of rate half per message in the index coding problem are shown to be a natural consequence of interference alignment constraints and generalizations to feasibility of rate 1 l 1 per message when each destination desires at least l messages are similarly obtained finally capacity optimal solutions are presented to a series of symmetric index coding problems inspired by the local connectivity and local interference characteristics of wireless networks the solutions are based on vector linear coding 1963 2012 ieee

a rate distortion approach to index coding we approach index coding as a special case of rate distortion with multiple receivers each with some side information about the source specifically using techniques developed for the rate distortion problem we provide two upper bounds and one lower bound on the optimal index coding rate the upper bounds involve specific choices of the auxiliary random variables in the best existing scheme for the rate distortion problem the lower bound is based on a new lower bound for the general rate distortion problem the bounds are shown to coincide for a number of groupcast index coding instances including all instances for which the number of decoders does not exceed three

the minrank of random graphs the minrank of a directed graph g is the minimum rank of a matrix m that can be obtained from the adjacency matrix of g by switching some ones to zeros i e deleting edges and then setting all diagonal entries to one this quantity is closely related to the fundamental information theoretic problems of linear index coding bar yossef et al network coding effros et al and distributed storage mazumdar isit 2014 we prove tight bounds on the minrank of directed erd s renyi random graphs g n p for all regimes of p in 0 1 in particular for any constant p we show that mathsf minrk g theta n log n with high probability where g is chosen from g n p this bound gives a near quadratic improvement over the previous best lower bound of omega sqrt n haviv and langberg and partially settles an open problem raised by lubetzky and stav our lower bound matches the well known upper bound obtained by the clique covering solution and settles the linear index coding problem for random knowledge graphs

on the intractability of permuting a block code to minimize trellis complexity an important problem in the theory and application of block code trellises is to find a coordinate permutation of a given code to minimize the trellis complexity we show that the problem of finding a coordinate permutation that minimizes the number of vertices at a given depth in the minimal trellis for a binary linear block code is np complete

the hardness of decoding linear codes with preprocessing the problem of maximum likelihood decoding of linear block codes is known to be hard the fact that the problem remains hard even if the code is known in advance and can be preprocessed for as long as desired in order to device a decoding algorithm is shown the hardness is based on the fact that existence of a polynomial time algorithm implies that the polynomial hierarchy collapses thus some linear block codes probably do not have an efficient decoder the proof is based on results in complexity theory that relate uniform and nonuniform complexity classes

interlinked cycles for index coding generalizing cycles and cliques we consider a graphical approach to index coding as cycles have been shown to provide coding gain cycles and cliques a specific type of overlapping cycles have been exploited in an existing literature in this paper we define a more general form of overlapping cycles called the interlinked cycle mathsf ic structure that generalizes cycles and cliques we propose a scheme called the interlinked cycle cover mathsf icc scheme that leverages mathsf ic structures in digraphs to construct scalar linear index codes we characterize a class of infinitely many digraphs where our proposed scheme is optimal over all linear and non linear index codes consequently for this class of digraphs we indirectly prove that scalar linear index codes are optimal furthermore we show that the mathsf icc scheme can outperform all the existing graph based schemes including partial clique cover and fractional local chromatic number schemes and a random coding scheme namely composite coding for certain graphs

fixed parameter tractability and completeness i basic results for many fixed parameter problems that are trivially soluable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as k feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is soluable in time bounded by a polynomial of degree c where c is a constant independent of k we establish the main results of a completeness program which addresses the apparent fixed parameter intractability of many parameterized problems in particular we define a hierarchy of classes of parameterized problems fpt subseteq w 1 subseteq w 2 subseteq cdots subseteq w sat subseteq w p and identify natural complete problems for w t for t geq 2 in other papers we have shown many problems complete for w 1 dominating set is shown to be complete for w 2 and thus is not fixed parameter tractable unless independent set clique irredundant set and many other natural problems in w 2 are also fixed parameter tractable we also give a compendium of currently known hardness results as an appendix

broadcasting with side information bounding and approximating the broadcast rate index coding has received considerable attention recently motivated in part by applications such as fast video on demand and efficient communication in wireless networks and in part by its connection to network coding optimal encoding schemes and efficient heuristics were studied in various settings while also leading to new results for network coding such as improved gaps between linear and non linear capacity as well as hardness of approximation the problem of broadcasting with side information a generalization of the index coding problem begins with a sender and sets of users and messages each user possesses a subset of the messages and desires an additional message from the set the sender wishes to broadcast a message so that on receipt of the broadcast each user can compute her desired message the fundamental parameter of interest is the broadcast rate the average communication cost for sufficiently long broadcasts though there have been many new nontrivial bounds on by bar yossef 2006 lubetzky and stav 2007 alon 2008 and blasiak 2011 there was no known polynomial time algorithm for approximating within a nontrivial factor and the exact value of remained unknown for all nontrivial instances using the information theoretic linear program introduced in blasiak 2011 we give a polynomial time algorithm for recognizing instances with 2 and pinpoint precisely for various classes of graphs e g various cayley graphs of cyclic groups further extending ideas from ramsey theory we give a polynomial time algorithm with a nontrivial approximation ratio for computing finally we provide insight into the quality of previous bounds by giving constructions showing separations between and the respective bounds in particular we construct graphs where is uniformly bounded while its upper bound derived from the naive encoding scheme is polynomially worse

computing the stopping distance of a tanner graph is np hard two decision problems related to the computation f stopping sets in tanner graphs are shown to be np complete it follows as a consequence that there exists no polynomial time algorithm for computing the stopping distance of a tanner graph unless p np

linear programming approximations for index coding index coding a source coding problem over broadcast channels has been a subject of both theoretical and practical interests since its introduction by birk and kol 1998 in short the problem can be defined as follows there is an input p triangleq p 1 dots p n a set of n clients who each desire a single entry p i of the input and a broadcaster whose goal is to send as few messages as possible to all clients so that each one can recover its desired entry additionally each client has some predetermined side information corresponding to the certain entries of the input p which we represent as the side information graph mathcal g the graph mathcal g has a vertex v i for client i and a directed edge v i v j indicating that client i knows the j th entry of the input given a fixed side information graph mathcal g we are interested in determining or approximating the broadcast rate of index coding on the graph i e the least number of messages the broadcaster can transmit so that every client recovers its desired information the complexity of determining this broadcast rate in the most general case is open and the best known approximations are barely better than the trivial o n approximation corresponding to sending each client their information directly without performing any coding using index coding schemes based on linear programs lps we take a two pronged approach to approximating the broadcast rate first extending earlier work on planar graphs we focus on approximating the broadcast rate for special graph families such as graphs with the small chromatic number and disk graphs in certain cases we are able to show that simple lp based schemes give constant factor approximations of the broadcast rate which seem extremely difficult to obtain in the general case second we provide several lp based schemes for the general case which are not constant factor approximations but which strictly improve on the best known schemes these can be viewed as both a strengthening of the constant factor approximations proven for special graph families as these schemes strictly improve on those which we prove are good approximations as well as another tool that can be used either in practice or in future theoretical analyses

on the complexity of some coding problems corresp it is shown that the problem of finding a codeword with least weight and whose weight is not a multiple of k in a binary linear code belongs to the class of nondeterministic polynomial np hard problems for any k geq 2 some other related problems are shown to belong to the same class these results were motivated by a conjecture due to berlekamp mceliece and van tilborg that the problem of finding the hamming distance of a code is np hard

bounds on the dimension of codes and subcodes with prescribed contraction index abstract let c be a linear code over gf q spanned by the rows of a matrix g of rank k a nonnegative integer is said to be the contraction index of c if a maximal set of pairwise linearly independent columns of g has k elements we derive several upper and lower bounds on the dimension of a proper subcode of c with a prescribed contraction index v q of length n minimum hamming distance d and contraction index for certain values of n and d the latter bound is shown to be tight for all q and this substantially generalizes the results obtained by delsarte and by duc for 1

generalized collinearity diagnostics abstract working in the context of the linear model y x e we generalize the concept of variance inflation as a measure of collinearity to a subset of parameters in denoted by 1 with the associated columns of x given by x 1 the essential idea underlying this generalization is to examine the impact on the precision of estimation in particular the size of an ellipsoidal joint confidence region for 1 of less than optimal selection of other columns of the design matrix x 2 treating still other columns x 0 as unalterable even hypothetically in typical applications x 1 contains a set of dummy regressors coding categories of a qualitative variable or a set of polynomial regressors in a quantitative variable x 2 contains all other regressors in the model save the constant which is in x 0 if 2 v denotes the realized variance of and 2 u is the variance associated with an optimal selection of x 2 then the corresponding scaled dispersion ellipsoids to be compared are v x x v

finite element analysis of saint venant torsion problem with exact integration of the elastic plastic constitutive equations abstract in this paper torsion of prismatic bars considering elastic plastic material behaviour is studied based on the presented variational formulation associated isoparametric finite elements are developed the unknown warping function is approximated using an isoparametric concept the elastic plastic stresses are obtained by an exact integration of the rate equations thus the ultimate torque can be calculated in one single load step this quantity describes the plastic reserve of a bar subjected to torsion furthermore for linear isotropic hardening no local iterations are necessary to compute the stresses at the integration points the numerical results are in very good agreement with available analytical solutions for simple geometric shapes the arbitrary shaped domains may be simply or multiple connected

meshless methods for the inverse problem related to the determination of elastoplastic properties from the torsional experiment abstract the problem of determining the elastoplastic properties of a prismatic bar from the given experimental relation between the torsional moment m and the angle of twist per unit length of the rod s length is investigated as an inverse problem the proposed method to solve the inverse problem is based on the solution of some sequences of the direct problem by applying the levenberg marquardt iteration method in the direct problem these properties are known and the torsional moment is calculated as a function of the angle of twist from the solution of a non linear boundary value problem this non linear problem results from the saint venant displacement assumption the ramberg osgood constitutive equation and the deformation theory of plasticity for the stress strain relation to solve the direct problem in each iteration step the kansa method is used for the circular cross section of the rod or the method of fundamental solutions mfs and the method of particular solutions mps are used for the prismatic cross section of the rod the non linear torsion problem in the plastic region is solved using the picard iteration

ill conditioning and multicollinearity abstract it is well known that unstability of solutions to small changes in inputs causes many problems in numerical computations existence uniqueness and stability of solutions are important features of mathematical problems problems that fail to satisfy these conditions are called ill posed the purpose of this study is to remind briefly some methods of solution to ill posed problems and to see the impacts or connections of these techniques to some statistical methods

hat guessing games hat problems have become a popular topic in recreational mathematics in a typical hat problem each of n players tries to guess the color of the hat he or she is wearing by looking at the colors of the hats worn by some of the other players in this paper we consider several variants of the problem united by the common theme that the guessing strategies are required to be deterministic and the objective is to maximize the number of correct answers in the worst case we also summarize what is currently known about the worst case analysis of deterministic hat guessing problems with a finite number of players

plastic analysis of torsion of a prismatic beam finite element formulation for stress analysis of a twisting beam is developed the formulation is effective for a prismatic beam with solid section as well as a thin walled beam and can be applied both to a pure torsion problem and a warping torsion problem the formulation is of a great advantage to an elastic plastic torsion problem the formulation does not stand on the assumption of a thin walled structure and therefore torsional rigidity of the section can be evaluated exactly without using the so called saint venant s torsional constant torsional rigidity is in this paper evaluated directly by a warping function of the section warping function is evaluated numerically due to shape of the section due to progress of plastic region and due to effect of finite displacement finite rotation small strain pure torsion and warping torsion of a rectangular beam and an h beam which have an elastic plastic material property are analysed and the extension to the finite displacement problem is discussed many numerical examples are provided in order to check the accuracy of the formulation

optimal sensor placement using frfs based clustering method the purpose of this work is to develop an optimal sensor placement method by selecting the most relevant degrees of freedom as actual measure position based on observation matrix of a structure s frequency response two optimal criteria are used to avoid the information redundancy of the candidate degrees of freedom by using principal component analysis the frequency response matrix can be decomposed into principal directions and their corresponding singular a relatively small number of principal directions will maintain a system s dominant response information according to the dynamic similarity of each degree of freedom the k means clustering algorithm is designed to classify the degrees of freedom and effective independence method deletes the sensors which are redundant of each cluster finally two numerical examples and a modal test are included to demonstrate the efficient of the derived method it is shown that the proposed method provides a way to extract sub optimal sets and the selected sensors are well distributed on the whole structure

error correction for index coding with side information a problem of index coding with side information was first considered by birk and kol in 1998 in this study a generalization of index coding scheme where transmitted symbols are subject to errors is studied error correcting methods for such a scheme and their parameters are investigated in particular the following question is discussed given the side information hypergraph of index coding scheme and the maximal number of erroneous symbols what is the shortest length of a linear index code such that every receiver is able to recover the required information this question turns out to be a generalization of the problem of finding a shortest length error correcting code with a prescribed error correcting capability in the classical coding theory the singleton bound and two other bounds referred to as the bound and the bound for the optimal length of a linear error correcting index code ecic are established for large alphabets a construction based on concatenation of an optimal index code with a maximum distance separable classical code is shown to attain the singleton bound for smaller alphabets however this construction may not be optimal a random construction is also analyzed it yields another inexplicit bound on the length of an optimal linear ecic further the problem of error correcting decoding by a linear ecic is studied it is shown that in order to decode correctly the desired symbol the decoder is required to find one of the vectors belonging to an affine space containing the actual error vector the syndrome decoding is shown to produce the correct output if the weight of the error pattern is less or equal to the error correcting capability of the corresponding ecic finally the notion of static ecic which is suitable for use with a family of instances of an index coding problem is introduced several bounds on the length of static ecics are derived and constructions for static ecics are discussed connections of these codes to weakly resilient boolean functions are established

path weights in concentration graphs a graphical model provides a compact and efficient representation of the association structure of a multivariate distribution by means of a graph relevant features of the distribution are represented by vertices edges and other higher order graphical structures such as cliques or paths typically paths play a central role in these models because they determine the independence relationships among variables however while a theory of path coefficients is available in models for directed graphs little has been investigated about the strength of the association represented by a path in an undirected graph essentially it has been shown that the covariance between two variables can be decomposed into a sum of weights associated with each of the paths connecting the two variables in the corresponding concentration graph in this context we consider concentration graph models and provide an extensive analysis of the properties of path weights and their interpretation more specifically we give an interpretation of covariance weights through their factorisation into a partial covariance and an inflation factor we then extend the covariance decomposition over the paths of an undirected graph to other measures of association such as the marginal correlation coefficient and a quantity that we call the inflated correlation the usefulness of these findings is illustrated with an application to the analysis of dietary intake networks

the intractability of computing the minimum distance of a code it is shown that the problem of computing the minimum distance of a binary linear code is np hard and the corresponding decision problem is np complete this result constitutes a proof of the conjecture of berlekamp mceliece and van tilborg 1978 extensions and applications of this result to other problems in coding theory are discussed

on the index coding problem and its relation to network coding and matroid theory the index coding problem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad hoc networks an instance of the index coding problem includes a sender that holds a set of information messages x x1 xk and a set of receivers r each receiver x h in r needs to obtain a message x x and has prior side information consisting of a subset h of x the sender uses a noiseless communication channel to broadcast encoding of messages in x to all clients the objective is to find an encoding scheme that minimizes the number of transmissions required to satisfy the demands of all the receivers in this paper we analyze the relation between the index coding problem the more general network coding problem and the problem of finding a linear representation of a matroid in particular we show that any instance of the network coding and matroid representation problems can be efficiently reduced to an instance of the index coding problem our reduction implies that many important properties of the network coding and matroid representation problems carry over to the index coding problem specifically we show that vector linear codes outperform scalar linear index codes and that vector linear codes are insufficient for achieving the optimum number of transmissions

structural damage detection using measured frf data abstract the underlying principle behind structural damage detection techniques is that vibration signature e g modal properties or frequency response function frf data is a sensitive indicator of structural physical integrity and thus can be used to detect damage since indirectly measured modal data contain accumulative errors incurred in modal parameter extraction and provide much less information than frf data it is more reasonable and reliable to use directly measured frf data for structural damage detection in this paper a new damage detection algorithm is formulated to utilize an original analytical model and frf data measured prior and posterior to damage for structural damage detection based on nonlinear perturbation equations of frf data an algorithm has been derived which can be used to determine a damage vector indicating both location and magnitude of damage from perturbation equations of frf data an additional development with respect to the proposed technique is an effective technique introduced for weighting perturbation equations of frf data at selected locations and frequencies so as to reduce influence of measurement errors on accuracy of damage detection to the minimum for extension of the proposed algorithm to cases of incomplete measurement in terms of coordinates an iterative version of the proposed algorithm has been introduced the validity and applicability of the proposed damage detection algorithm have been demonstrated through numerical and experimental studies on a practical plane 3 bay frame structure respectively

on the security of index coding with side information security aspects of the index coding with side information icsi problem are investigated building on the results of bar yossef 2006 the properties of linear index codes are further explored the notion of weak security considered by bhattad and narayanan 2005 in the context of network coding is generalized to block security it is shown that the linear index code based on a matrix l whose column space code c l has length n minimum distance d and dual distance d is d 1 t block secure and hence also weakly secure if the adversary knows in advance t d 2 messages and is completely insecure if the adversary knows in advance more than n d messages strong security is examined under the conditions that the adversary 1 possesses t messages in advance 2 eavesdrops at most transmissions 3 corrupts at most transmissions we prove that for sufficiently large q an optimal linear index code which is strongly secure against such an adversary has length q 2 here q is a generalization of the min rank over fq of the side information graph for the icsi problem in its original formulation in the work of bar yossef et al

fixed parameter tractability and completeness ii on completeness for w 1 abstract for many fixed parameter problems that are trivially solvable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is solvable in time bounded by a polynomial of degree c where c is a constant independent of k in a previous paper the w hierarchy of parameterized problems was defined and complete problems were identified for the classes w t for t 2 our main result shows that independent set is complete for w 1

on the complexity of multicovering radii the multicovering radius is a generalization of the covering radius in this correspondence we show that lower bounding the m covering radius of an arbitrary binary code is np complete when m is polynomial in the length of the code lower bounding the m covering radius of a linear code is spl sigma sub 2 sup p complete when m is polynomial in the length of the code if p is not equal to np then the m covering radius of an arbitrary binary code cannot be approximated within a constant factor or within a factor n sup spl epsi where n is the length of the code and spl epsi 1 in polynomial time note that the case when m 1 was also previously unknown if np is not equal to spl sigma sub 2 sup p then the m covering radius of a linear code cannot be approximated within a constant factor or within a factor n sup spl epsi where n is the length of the code and spl epsi 1 in polynomial time

plastic instability of beam structures using co rotational elements in a previous paper comput methods appl mech engrg 191 2002 1755 the authors have presented a 3d co rotational elastic beam element including warping effects this formulation is now further developed in order to incorporate elasto plastic deformations the element possesses seven degrees of freedom at each node and can be used to model beams with arbitrary cross sections thus within the present approach the centroid and shear center of the cross section are not necessarily coincident the main purpose of this element is to model elasto plastic instability problems in this context two methods of branch switching are tested and discussed in the first one the bifurcation point is isolated by successive bisections and the branch switching is operated by using the eigenvector associated to the negative eigenvalue in the second one introduced by petryk an energy approach is used to select automatically the stable post bifurcation path six examples including large displacement and stability problems are used in order to assess the performances of the element

network coding in node constrained line and star networks line and star networks with both node and edge constraints are studied in the network coding framework for line networks the capacity region of the general multiple multicast problem is established the coding theorem is based on a binary linear coding scheme while the converse requires new upper bounds that improve on standard cut based bounds for star networks the multiple unicast problem is examined capacity upper bounds are derived and a simple linear coding scheme is proposed which is based on the combinatorial optimization problem of cycle packing in directed graphs the optimality of this scheme is established for a broad class of demands the connection of node constrained network coding in star networks and index coding with side information is discussed and used to partially characterize the optimal linear code for general rates

nonlinear index coding outperforming the linear optimum the following source coding problem was introduced by birk and kol a sender holds a word x isin 0 1 n and wishes to broadcast a codeword to n receivers rn rn the receiver ri is interested in xi and has prior side information comprising some subset of the n bits this corresponds to a directed graph g on n vertices where i j is an edge ri ri knows the bit xj an index code for g is an encoding scheme which enables each ri to always reconstruct xi given his side information the minimal word length of an index code was studied by bar yossef birk jayram and kol focs 06 they introduced a graph parameter minrk2 g which completely characterizes the length of an optimal linear index code for g they showed that in various cases linear codes attain the optimal word length and conjectured that linear index coding is in fact always optimal in this work we disprove the main conjecture of bar yossef birk jayram and kol in the following strong sense for any epsiv 0 and sufficiently large n there is an n vertex graph g so that every linear index code for g requires codewords of length at least nepsiv and yet a nonlinear index code for g has a word length of ne this is achieved by an explicit construction which extends alon s variant of the celebrated ramsey construction of frankl and wilson in addition we study optimal index codes in various less restricted natural models and prove several related properties of the graph parameter minrk g

optimal finite length and asymptotic index codes for five or fewer receivers index coding models broadcast networks in which a sender sends different messages to different receivers simultaneously where each receiver may know some of the messages a priori the aim is to find the minimum normalized index codelength that the sender sends this paper considers unicast index coding where each receiver requests exactly one message and each message is requested by exactly one receiver each unicast index coding instances can be fully described by a directed graph and vice versa where each vertex corresponds to one receiver for any directed graph representing a unicast index coding instance we show that if a maximum acyclic induced subgraph mais is obtained by removing two or fewer vertices from the graph then the minimum index codelength equals the number of vertices in the mais and linear codes are optimal for the corresponding index coding instance using this result we solved all unicast index coding instances with up to five receivers which correspond to all graphs with up to five vertices for 9818 non isomorphic graphs among all graphs up to five vertices we obtained the minimum index codelength for all message alphabet sizes for the remaining 28 graphs we obtained the minimum index codelength if the message alphabet size is k 2 for any positive integer k this work complements the result by arbabjolfaei et al isit 2013 who solved all unicast index coding instances with up to five receivers in the asymptotic regime where the message alphabet size tends to infinity