generalized entropic uncertainty relations a new class of uncertainty relations is derived for pairs of observables in a finite dimensional hilbert space which do not have any common eigenvector this class contains an entropic uncertainty relation which improves a previous result of deutsch and confirms a recent conjecture by kraus some comments are made on the extension of these relations to the case where the hilbert space is infinite dimensional

discrete solitons in nonlinear schrodinger lattices with a power law nonlinearity abstract we study the discrete nonlinear schrodinger lattice model with the onsite nonlinearity of the general form u 2 u we systematically verify the conditions for the existence and stability of discrete solitons in the one dimensional version of the model predicted by means of the variational approximation va and demonstrate the following monostability of fundamental solitons fss in the case of the weak nonlinearity 2 1 3 68 bistability in a finite range of values of the soliton s power for 3 68 2 1 5 and the presence of a threshold minimum norm of the fs for 2 1 5 we also perform systematic numerical simulations to study higher order solitons in the same general model i e bound states of the fss while all in phase bound states are unstable stability regions are identified for antisymmetric double solitons and their triple counterparts these numerical findings are supplemented by an analytical treatment of the stability problem which allows quantitively accurate predictions for the stability features of such multipulses when these waveforms are found to be unstable we show by means of direct simulations that they self trap into a persistent lattice breather or relax into a stable fs or sometimes decay completely

decomposition rules for quantum renyi mutual information with an application to information exclusion relations we prove decomposition rules for quantum renyi mutual information generalizing the relation i a b h a h a b to inequalities between renyi mutual information and renyi entropy of different orders the proof uses beigi s generalization of reisz thorin interpolation to operator norms j math phys 54 12 122202 2013 and a variation of the argument developed by dupuis j math phys 56 022203 2015 which was used to show chain rules for conditional renyi entropies the resulting decomposition rule is then applied to establish an information exclusion relation for renyi mutual information generalizing the original relation by hall phys rev lett 74 3307 1995

characterization of ergodic hidden markov sources an algebraic criterion for the ergodicity of discrete random sources is presented for finite dimensional sources which contain hidden markov sources as a subclass the criterion can be effectively computed this result is obtained on the background of a novel elementary theory of discrete random sources which is based on linear spaces spanned by word functions and linear operators on these spaces an outline of basic elements of this theory is provided

on the existence of homoclinic solutions of a class of discrete nonlinear periodic systems abstract in this paper we obtain a new sufficient condition on the existence of homoclinic solutions of a class of discrete nonlinear periodic systems by using critical point theory in combination with periodic approximations we prove that it is also necessary in some special cases

efficient tests for equivalence of hidden markov processes and quantum random walks while two hidden markov process hmp resp quantum random walk qrw parametrizations can differ from one another the stochastic processes arising from them can be equivalent here a polynomial time algorithm is presented which can determine equivalence of two hmp parametrizations m1 m2 resp two qrw parametrizations q1 q2 in time o max n1 n2 4 where n1 n2 are the number of hidden states in m1 m2 resp the dimension of the state spaces associated with q1 q2 and is the set of output symbols previously avail able algorithms for testing equivalence of hmps were exponential in the number of hidden states in case of qrws algorithms for testing equivalence had not yet been presented the core subrou tines of this algorithm can also be used to efficiently test hidden markov processes and quantum random walks for ergodicity

observable operator models for discrete stochastic time series a widely used class of models for stochastic systems is hidden markov models systems that can be modeled by hidden markov models are a proper subclass of linearly dependent processes a class of s

chain rules for quantum renyi entropies we present chain rules for a new definition of the quantum renyi conditional entropy sometimes called the sandwiched renyi conditional entropy more precisely we prove analogues of the equation h ab c h a bc h b c which holds as an identity for the von neumann conditional entropy in the case of the renyi entropy this relation no longer holds as an equality but survives as an inequality of the form h ab c h a bc h b c where the parameters obey the relation 1 1 1 and 1 1 1 1 if 1 1 1 1 the direction of the inequality is reversed

breathers in nonlinear lattices existence linear stability and quantization abstract it has been proved by the principle of anti integrable limit renamed here anti continuous limit and the implicit function theorem that under rather weak hypotheses there exist spatially localized and time periodic solutions breathers in arrays of nonlinear coupled classical oscillators provided the coupling is not too strong the models can be translationally invariant or not and be of any dimension there are also time periodic solutions corresponding to arbitrary distributions on the lattice of such solutions multibreathers the whole set of these solutions can be labeled by a discrete coding sequence the condition that the frequency of the breather or multibreather solution has no harmonics in the phonon spectrum can be discarded for a large subset of spatially extended time periodic solutions called phonobreather which correspond to special codes which can be also spatially chaotic and where no oscillator is at rest these results extend almost without change to models with coupled rotors the existence of rotobreathers which are exact solutions consisting of a single rotor rotating while the other rotors oscillate is proved there are also multirotobreather solutions and phono rotobreathers etc it is also shown that the phase of the single breathers constituting a multibreather or multirotobreather solution can be submitted to a phase torsion these new dynamical structures carry a nonzero energy flow in models with two dimensions and more the phase torsion of multibreather solutions can generate new dynamical solutions with vortices in the energy flow the dynamics of a quantum electron coupled to a classical lattice is also studied within the same approach from the anti continuous limit the existence of two kinds of polarobreathers which are spatially exponentially localized dynamical solutions is proved for a small enough electronic transfer integral the polarobreathers of the first kind include the standard static polaron the lattice configuration is static time independent when the electron is in an excited state i e the electronic oscillator oscillates periodically they can be spatially chaotic a polarobreather of the second kind corresponds to a localized periodic lattice oscillation associated with a localized quasiperiodic electronic oscillation the most simple of these solutions are those for which both the lattice oscillation and the electron wave function are mostly concentrated close to the same single site the standard floquet analysis of the linear stability of the breather and multibreather solutions is shown to be related with the band spectrum property of the newton operator involved in the implicit function theorem the krein theory of bifurcations is reinterpreted from this point of view the linear stability of the single breather and rotobreather solutions is then proved at least at small enough coupling finally it is shown that in the quantum version of translationally invariant classical models where there cannot exist in principle any strictly localized excitation there are narrow bands of excitations consisting of bound states of many bosons which are the quantum counterpart of the classical breathers the bandwidth of these excitations goes exponentially to zero with the number of bound phonons this theory provides simultaneously existence theorems and a new powerful and accurate numerical method for calculating practically any of the solutions which has been formally predicted to exist these numerical applications are currently written elsewhere

asymptotic mean stationarity of sources with finite evolution dimension the notion of the evolution of a discrete random source with finite alphabet is introduced and its behavior under the action of an associated linear evolution operator is studied viewing these sources as possibly stable dynamical systems it is proved that all random sources with finite evolution dimension are asymptotically mean stationary which implies that such random sources have ergodic properties and a well defined entropy rate it is shown that the class of random sources with finite evolution dimension properly generalizes the well studied class of finitary stochastic processes which includes hidden markov sources as special cases

the quantum reverse shannon theorem based on one shot information theory the quantum reverse shannon theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel s entanglement assisted classical capacity in this paper we provide a new proof of this theorem which has previously been proved by bennett devetak harrow shor and winter our proof has a clear structure being based on two recent information theoretic results one shot quantum state merging and the post selection technique for quantum channels

an element free based solution for nonlinear schrodinger equations using the icvmls ritz method an improved complex variable moving least squares ritz icvmls ritz method is proposed for predicting numerical solution of the two dimensional nonlinear schrodinger equation in this element free solution procedure the icvmls approximation is employed to reduce the number of unknown coefficients in the trial function it follows by the ritz procedure to derive the final algebraic equation system through discretizing the constructed energy formulation of the nonlinear schrodinger equation the central differencing scheme and newton s algorithm are adopted to solve the nonlinear equation system numerical experiments are conducted on the final form of the governing equation system to demonstrate the accuracy and efficiency of the element free icvmls ritz method by comparing the computed results with the available analytical solutions

homoclinic solutions of discrete nonlinear schrodinger equations with asymptotically or super linear terms abstract in this paper we study the following periodic discrete nonlinear schrodinger equation u n n u n n g n u n n z where the nonlinearity g n is asymptotically or super linear the sufficient conditions on the existence and on the nonexistence of nontrivial solitons was established by using critical point theory

existence of gap solitons in periodic discrete nonlinear schrodinger equations in this paper we discuss how to use the critical point theory to study the existence of gap solitons for periodic discrete nonlinear schrodinger equations an open problem proposed by professor alexander pankov is solved

a bound on modeling error in observable operator models and an associated learning algorithm observable operator models ooms generalize hidden markov models hmms and can be represented in a structurally similar matrix formalism the mathematical theory of ooms gives rise to a family of constructive fast and asymptotically correct learning algorithms whose statistical efficiency however depends crucially on the optimization of two auxiliary transformation matrices this optimization task is nontrivial indeed even formulating computationally accessible optimality criteria is not easy here we derive how a bound on the modeling error of an oom can be expressed in terms of these auxiliary matrices which in turn yields an optimization procedure for them and finally affords us with a complete learning algorithm the error controlling algorithm models learned by this algorithm have an assured error bound on their parameters the performance of this algorithm is illuminated by comparisons with two types of hmms trained by the expectation maximization algorithm with the efficiency sharpening algorithm another recently found learning algorithm for ooms and with predictive state representations littman sutton 2001 trained by methods representing the state of the art in that field

discrete nonlinear schrodinger equations with superlinear nonlinearities abstract in this paper we study the discrete nonlinear equation lu n u n n g n u n n z where belongs to a finite spectral gap of the operator l or it is a lower edge of a finite spectral gap by using a variant generalized weak linking theorem for strongly indefinite problem developed by schechter and zou we will study the existence of nontrivial solitons for this equation with gn is super linear

entanglement assisted capacity of a quantum channel and the reverse shannon theorem the entanglement assisted classical capacity of a noisy quantum channel c sub e is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel assuming that the sender and receiver have access to the resource of shared quantum entanglement which may be used up by the communication protocol we show that the capacity c sub e is given by an expression parallel to that for the capacity of a purely classical channel i e the maximum over channel inputs spl rho of the entropy of the channel input plus the entropy of the channel output minus their joint entropy the latter being defined as the entropy of an entangled purification of spl rho after half of it has passed through the channel we calculate entanglement assisted capacities for two interesting quantum channels the qubit amplitude damping channel and the bosonic channel with amplification attenuation and gaussian noise we discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel alone or in the presence of ancillary resources such as prior entanglement in the classical analog of entanglement assisted communication communication over a discrete memoryless channel dmc between parties who share prior random information we show that one parameter is sufficient i e that in the presence of prior shared random information all dmcs of equal capacity can simulate one another with unit asymptotic efficiency

identifiability of hidden markov information sources and their minimum degrees of freedom if only a function of the state in a finite state markov chain is observed then the stochastic process is no longer markovian in general this type of information source is found widely and the basic problem of its identifiability remains open that is the problem of showing when two different markov chains generate the same stochastic process the identifiability problem is completely solved by linear algebra where a block structure of a markov transition matrix plays a fundamental role and from which the minimum degree of freedom for a source is revealed

norm observable operator models hidden markov models hmms are one of the most popular and successful statistical models for time series observable operator models ooms are generalizations of hmms that exhibit several attractive advantages in particular a variety of highly efficient constructive and asymptotically correct learning algorithms are available for ooms however the oom theory suffers from the negative probability problem npp a given learned oom may sometimes predict negative probabilities for certain events it was recently shown that it is undecidable whether a given oom will eventually produce such negative values we propose a novel variant of ooms called norm observable operator models nooms which avoid the npp by design like ooms nooms use a set of linear operators to update system states but differing from ooms they represent probabilities by the square of the norm of system states thus precluding negative probability values while being free of the npp nooms retain most advantages of ooms for example nooms also capture some processes that cannot be modeled by hmms more importantly in principle nooms can be learned from data in a constructive way and the learned models are asymptotically correct we also prove that nooms capture all markov chain mc describable processes this letter presents the mathematical foundations of nooms discusses the expressiveness of the model class and explains how a noom can be estimated from data constructively

periodic and decaying solutions in discrete nonlinear schrodinger with saturable nonlinearity we demonstrate the existence of solutions in the discrete nonlinear schrodinger equation dnls with saturable nonlinearity we consider two types of solutions to dnls periodic and vanishing at infinity calculus of variations and the nehari manifolds are employed to establish the existence of these solutions we present some extensions of our results combining the nehari manifold approach and the mountain pass argument

standing waves for discrete schrodinger equations in infinite lattices with saturable nonlinearities abstract in this paper we consider the periodic discrete nonlinear equation l u n u n g n u n n z lim n u n 0 where l is a jacobi operator and the nonlinearities g n s are asymptotically linear as s in the two different cases is a spectral endpoint of l or it belongs to a finite spectral gap of l we obtain the existence of nontrivial solitons of this equation by using variational methods in particular a necessary and sufficient condition is obtained for the existence of gap solitons of the nonlinear equation here solitons appear when we look for standing waves of some discrete nonlinear schrodinger equations

on analytic properties of entropy rate entropy rate is a real valued functional on the space of discrete random sources for which it exists however it lacks existence proofs and or closed formulas even for classes of random sources which have intuitive parameterizations a good way to overcome this problem is to examine its analytic properties relative to some reasonable topology a canonical choice of a topology is that of the norm of total variation as it immediately arises with the idea of a discrete random source as a probability measure on sequence space it is shown that both upper and lower entropy rate hence entropy rate itself if it exists are lipschitzian relative to this topology which by well known facts is close to differentiability an application of this theorem leads to a simple and elementary proof of the existence of entropy rate of random sources with finite evolution dimension this class of sources encompasses arbitrary hidden markov sources and quantum random walks

gap solitons in periodic discrete nonlinear schrodinger equations with saturable nonlinearities the main result of the paper concerns the existence of nontrivial exponentially decaying solutions to periodic stationary discrete nonlinear schrodinger equations with saturable nonlinearities provided that zero belongs to a spectral gap of the linear part the proof is based on the critical point theory in combination with periodic approximations of solutions as a preliminary step we prove also the existence of nontrivial periodic solutions with arbitrarily large periods

discrete schrodinger equations with sign changing nonlinearities infinitely many homoclinic solutions abstract we obtain infinitely many homoclinic solutions for a class of discrete nonlinear schrodinger equations where nonlinearities are superlinear at infinity and primitive functions of nonlinearities are allowed to be sign changing by using some weaker conditions our results extend and improve some existed results in the literature besides some examples are given to illuminate our results