classical solutions of the quantum yang baxter equation the classical analogue is developed here for part of the construction in which knot and link invariants are produced from representations of quantum groups whereas previous work begins with a quantum group obtained by deforming the multiplication of functions on a poisson lie group we work directly with a poisson lie groupg and its associated symplectic groupoid the classical analog of the quantumr matrix is a lagrangian submanifold open image in new window in the cartesian square of the symplectic groupoid for any symplectic leafs ing open image in new window induces a symplectic automorphism ofs s which satisfies the set theoretic yang baxter equation when combined with the flip map exchanging components and suitably implanted in each cartesian powers n generates a symplectic action of the braid groupb n ons n application of a symplectic trace formula to the fixed point set of the action of braids should lead to link invariants but work on this last step is still in progress

error exponents of modulo additive noise channels with side information at the transmitter consider the optimum strategy for using channel state side information in transmission over a modulo additive noise channel with state dependent noise where the receiver does not have access to the side information si previous work showed that capacity wise the optimum transmitter shifts each code letter by a prediction of the noise sample based on the si we show that this structure achieves also the random coding error exponent and therefore is optimum at some range of rates below capacity specifically the optimum transmitter predictor minimizes the renyi entropy of the prediction error the renyi order depends on the rate and goes to one corresponding to shannon entropy for rates close to capacity in contrast it is shown that this prediction strategy may not be optimal at low transmission rates

grassmann extensions of yang baxter maps in this paper we show that there are explicit yang baxter yb maps with darboux lax representation between grassman extensions of algebraic varieties motivated by some recent results on noncommutative extensions of darboux transformations we first derive a darboux matrix associated with the grassmann extended derivative nonlinear schrodinger dnls equation and then we deduce novel endomorphisms of grassmann varieties which possess the yb property in particular we present ten dimensional maps which can be restricted to eight dimensional yb maps on invariant leaves related to the grassmann extended nls and dnls equations we consider their vector generalisations

3d compatible ternary systems and yang baxter maps according to shibukawa ternary systems defined on quasi groups and satisfying certain conditions provide a way of constructing dynamical yang baxter yb maps after noting that these conditions can be interpreted as three dimensional compatibility of equations on quad graphs we investigate when the associated dynamical yb maps are in fact parametric yb maps in some cases these maps can be obtained as reductions of higher dimensional maps through compatible constraints conversely parametric yb maps on quasi groups with an invariance condition give rise to three dimensional compatible systems the application of this method on spaces with certain quasi group structures provides new examples of multi parametric yb maps and three dimensional compatible systems

classification of integrable equations on quad graphs the consistency approach a classification of discrete integrable systems on quad graphs i e on surface cell decompositions with quadrilateral faces is given the notion of integrability laid in the basis of the classification is the three dimensional consistency this property yields among other features the existence of the discrete zero curvature representation with a spectral parameter for all integrable systems of the obtained exhaustive list the so called three leg forms are found this establishes lagrangian and symplectic structures for these systems and the connection to discrete systems of the toda type on arbitrary graphs generalizations of these ideas to the three dimensional integrable systems and to the quantum context are also discussed

wiretap channels implications of the more capable condition and cyclic shift symmetry characterization of the rate equivocation region of a general wiretap channel involves two auxiliary random variables u for rate splitting and v for channel prefixing in this paper we explore specific classes of wiretap channels for which the evaluation of the rate equivocation region is simpler we show that if the wiretap channel is more capable v x is optimal and the boundary of the rate equivocation region is achieved by varying rate splitting u alone conversely we show under a mild condition that if the wiretap channel is not more capable then v x is strictly suboptimal next we focus on the class of cyclic shift symmetric wiretap channels we show that optimal rate splitting u that achieves the boundary of the rate equivocation region is uniform with cardinality vert cal x vert and the prefix channel between optimal u and v is expressed as cyclic shifts of the solution of an auxiliary optimization problem over a single variable we provide a special class of cyclic shift symmetric wiretap channels for which u phi is optimal we apply our results to the binary input cyclic shift symmetric wiretap channels and thoroughly characterize the rate equivocation regions of the bsc bec and bec bsc wiretap channels

explicit auto transformations of integrable chains a construction scheme for explicit auto transformations of integrable discrete differential equations chains is presented these transformations are rather convenient to obtain the exact solutions for chains as well as associated partial differential systems on the other hand they exemplify new integrable discrete mappings their group properties are also of great interest the scheme is illustrated by several examples of integrable systems which contains the nonlinear schrodinger system and the landau lifshits model

poisson yang baxter maps with binomial lax matrices a construction of multidimensional parametric yang baxter maps is presented the corresponding lax matrices are the symplectic leaves of first degree matrix polynomials equipped with the sklyanin bracket these maps are symplectic with respect to the reduced symplectic structure on these leaves and provide examples of integrable mappings an interesting family of quadrirational symplectic yb maps on c4 c4 with 3 3 lax matrices is also presented

integrable two component systems of difference equations we present two lists of two component systems of integrable difference equations defined on the edges of the z2 graph the integrability of these systems is manifested by their lax formulation whic

darboux transformations finite reduction groups and related yang baxter maps in this paper we construct yang baxter yb maps using darboux matrices which are invariant under the action of finite reduction groups we present six dimensional yb maps corresponding to darboux transformations for the nonlinear schrodinger nls equation and the derivative nonlinear schrodinger dnls equation these yb maps can be restricted to four dimensional yb maps on invariant leaves the former are completely integrable and they also have applications to a recent theory of maps preserving functions with symmetries fordy a and kassotakis a 2013 j phys a math theor 46 205201 we give a six dimensional yb map corresponding to the darboux transformation for a deformation of the dnls equation we also consider vector generalizations of the yb maps corresponding to the nls and dnls equations

capacity and lattice strategies for canceling known interference we consider the generalized dirty paper channel y x s n e x sup 2 spl les p sub x where n is not necessarily gaussian and the interference s is known causally or noncausally to the transmitter we derive worst case capacity formulas and strategies for strong or arbitrarily varying interference in the causal side information si case we develop a capacity formula based on minimum noise entropy strategies we then show that strategies associated with entropy constrained quantizers provide lower and upper bounds on the capacity at high signal to noise ratio snr conditions i e if n is weak relative to the power constraint p sub x these bounds coincide the optimum strategies take the form of scalar lattice quantizers and the capacity loss due to not having s at the receiver is shown to be exactly the shaping gain 1 2log 2 spl pi e 12 spl ap 0 254 bit we extend the schemes to obtain achievable rates at any snr and to noncausal si by incorporating minimum mean squared error mmse scaling and by using k dimensional lattices for gaussian n the capacity loss of this scheme is upper bounded by 1 2log2 spl pi eg spl lambda where g spl lambda is the normalized second moment of the lattice with a proper choice of lattice the loss goes to zero as the dimension k goes to infinity in agreement with the results of costa these results provide an information theoretic framework for the study of common communication problems such as precoding for intersymbol interference isi channels and broadcast channels

affine linear and d4 symmetric lattice equations symmetry analysis and reductions we consider lattice equations on which are autonomous affine linear and possess the symmetries of the square some basic properties of equations of this type are derived as well as a sufficient linearization condition and a conservation law a systematic analysis of the lie point and the generalized three and five point symmetries is presented it leads to the generic form of the symmetry generators of all the equations in this class which satisfy a certain non degeneracy condition finally symmetry reductions of certain lattice equations to discrete analogs of the painleve equations are considered

feedback does not increase the capacity of discrete channels with additive noise we consider discrete time finite alphabet channels with additive random noise we show that output feedback does not increase the capacity of such channels this result holds in the most general case i e for arbitrary additive noise processes

channels with block interference a new class of channel models with memory is presented in order to study various kinds of interference phenomena it is shown among other things that when all other parameters are held fixed channel capacity c is an em increasing function of the memory length while the cutoff rate r 0 generally is a em decreasing function calculations with various explicit coding schemes indicate that c is better than r 0 as a performance measure for these channel models as a partial resolution of this c versus r 0 paradox the conjecture is offered that r 0 is more properly a measure of coding delay rather than of coding complexity

yang baxter maps and symmetries of integrable equations on quad graphs a connection between the yang baxter relation for maps and the multidimensional consistency property of integrable equations on quad graphs is investigated the approach is based on the symmetry analysis of the corresponding equations it is shown that the yang baxter variables can be chosen as invariants of the multiparameter symmetry groups of the equations we use the classification results by adler bobenko and suris to demonstrate this method some new examples of yang baxter maps are derived in this way from multifield integrable equations

design of quantizers for decentralized estimation systems the authors consider parameter estimation in decentralized systems with distributed processors they restrict the local processors to be quantizers and consider the optimal design of the systems to minimize the estimation error they present necessary conditions for the optimal system based on the bayes distortion functions and fisher s information the numerical results compare the resulting quantizers obtained by different distortion criteria

noise prediction for channels with side information at the transmitter the computation of channel capacity with side information at the transmitter side but not at the receiver side requires in general extension of the input alphabet to a space of strategies and is often hard we consider the special case of a discrete memoryless module additive noise channel y x z sub s where the encoder observes causally the random state s spl isin s that governs the distribution of the noise z sub s we show that the capacity of this channel is given by c log spl chi min sub t s spl rarr spl chi h z sub s t s this capacity is realized by a state independent code followed by a shift by the noise prediction t sub min s that minimizes the entropy of z sub s t s if the set of conditional noise distributions p z s s spl isin s is such that the optimum predictor t sub min spl middot is independent of the state weights then c is also the capacity for a noncausal encoder that observes the entire state sequence in advance furthermore for this case we also derive a simple formula for the capacity when the state process has memory

yang baxter maps and multi field integrable lattice equations a variety of yang baxter maps are obtained from integrable multi field equations on quad graphs a systematic framework for investigating this connection relies on the symmetry groups of the equations the method is applied to lattice equations introduced by adler and yamilov which are related to the nonlinear superposition formulae for the backlund transformations of the nonlinear schrodinger system and specific ferromagnetic models

memoryless multiple access channel with asymmetric noisy state information at the encoders the problem of reliable communication over the memoryless state dependent multiple access channel mac is considered where the encoders and the decoder are provided with various degrees of asymmetric noisy channel state information csi for the case where the encoders observe causal asymmetric noisy csi and the decoder observes complete csi inner and outer bounds to the capacity region which are tight for the sum rate capacity are provided next single letter characterizations for the channel capacity regions under each of the following system settings are established 1 the csi at the encoders are asymmetric deterministic functions of the csi at the decoder and the encoders have noncausal noisy csi 2 the encoders observe asymmetric noisy csi with asymmetric delays and the decoder observes complete csi 3 a degraded message set scenario with asymmetric noisy csi at the encoders and complete and or noisy csi at the decoder the main component in these results is a generalization of a recently introduced converse coding approach for the mac with asymmetric quantized csi at the encoders and herein considerably extended and adapted for the noisy csi setup

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

sequential convexification in reverse convex and disjunctive programming this paper is about a property of certain combinatorial structures called sequential convexifiability shown by balas 1974 1979 to hold for facial disjunctive programs sequential convexifiability means that the convex hull of a nonconvex set defined by a collection of constraints can be generated by imposing the constraints one by one sequentially and generating each time the convex hull of the resulting set here we extend the class of problems considered to disjunctive programs with infinitely many terms also known as reverse convex programs and give necessary and sufficient conditions for the solution sets of such problems to be sequentially convexifiable we point out important classes of problems in addition to facial disjunctive programs for instance reverse convex programs with equations only for which the conditions are always satisfied finally we give examples of disjunctive programs for which the conditions are violated and so the procedure breaks down

on discrete 2d integrable equations of higher order we study two dimensional discrete integrable equations of order 1 with respect to one independent variable and m with respect to another one a generalization of the multidimensional consistency property is proposed for this type of equations the examples are related to the backlund darboux transformations for the lattice equations of bogoyavlensky type

quantization for decentralized hypothesis testing under communication constraints in a decentralized hypothesis testing network several peripheral nodes observe an environment and communicate their observations to a central node for the final decision the presence of capacity constraints introduces theoretical and practical problems the following problem is addressed given that the peripheral encoders that satisfy these constraints are scalar quantizers how should they be designed in order that the central test to be performed on their output indices is most powerful the scheme is called cooperative design separate encoding since the quantizers process separate observations but have a common goal they seek to maximize a system wide performance measure the bhattacharyya distance of the joint index space as such a criterion is suggested and a design algorithm to optimize arbitrarily many quantizers cyclically is proposed a simplified version of the algorithm namely an independent design separate encoding scheme where the correlation is either absent or neglected for the sake of simplicity is outlined performances are compared through worked examples

a noncommutative discrete potential kdv lift in this paper we construct a grassmann extension of a yang baxter map which first appeared in the work of kouloukas and papageorgiou j phys a math theor 42 404012 2009 and can be considered as a lift of the discrete potential korteweg de vries dpkdv equation this noncommutative extension satisfies the yang baxter equation and it admits a 3 3 lax matrix moreover we show that it can be squeezed down to a novel system of lattice equations which possesses a lax representation and whose bosonic limit is the dpkdv equation finally we consider commutative analogs of the constructed yang baxter map and its associated quad graph system and we discuss their integrability

integrable lattice equations with vertex and bond variables we present integrable lattice equations on a two dimensional square lattice with coupled vertex and bond variables in some of the models the vertex dynamics is independent of the evolution of the bond variables and one can write the equations as non autonomous yang baxter maps we also present a model in which the vertex and bond variables are fully coupled integrability is tested with algebraic entropy as well as multidimensional consistency

entropy amplification property and the loss for writing on dirty paper costa s celebrated ldquowriting on dirty paperrdquo wdp shows that the power constrained channel y x s z with gaussian z has the same capacity as the standard awgn channel y x z provided that the ldquointerferencerdquo s no matter how strong it is is known at the transmitter while this ability for perfect interference cancelation is very appealing it relies heavily on the gaussianity of the unknown noise z we construct an example of ldquobadrdquo noise for writing on dirty paper namely ldquodifference set noiserdquo if the interference s is strong then difference set noise limits the wdp capacity to at most 2 bits at the same time like in the awgn case the zero interference capacity grows without bound with the input constraint thus almost 100 of the available capacity is lost in wdp in the presence of difference set noise this high capacity loss is due to the ldquoentropy amplification propertyrdquo eap of noise with an aperiodic probability distribution using the eap and the duality between wdp and wyner ziv source coding we also give an example of dramatic rate loss in quantizing encrypted source