a nonlinear elliptic equation arising from gauge field theory and cosmology we study radially symmetric solutions of a nonlinear elliptic partial differential equation in r 2 with critical sobolev growth i e the nonlinearity is of exponential type this problem arises from a wide variety of important areas in theoretical physics including superconductivity and cosmology our results lead to many interesting implications for the physical problems considered for example for the self dual chern simons theory we are able to conclude that the electric charge magnetic flux or energy of a non topological n vortex solution may assume any prescribed value above an explicit lower bound for the einstein matter gauge equations we find a necessary and sufficient condition for the existence of a self dual cosmic string solution such a condition imposes an obstruction for the winding number of a string in terms of the universal gravitational constant

self duality equations for ginzburg landau and seiberg witten type functionals with 6th order potentials the abelian chern simons higgs model of hong kim pac and jackiw weinberg leads to a ginzburg landau type functional with a 6th order potential on a compact riemann surface we derive the existence of two solutions with different asymptotic behavior as the coupling parameter tends to 0 for any number of prescribed vortices we also introduce a seiberg witten type functional with a 6th order potential and again show the existence of two asymptotically different solutions on a compact kahler surface the analysis is based on maximum principle arguments and applies to a general class of scalar equations

time dependent ginzburg landau equations of superconductivity abstract we study in this article the existence uniqueness and long time behavior of the solutions of a nonstationary ginzburg landau superconductivity model we first prove the existence and uniqueness of solutions with h 1 initial data which are crucial for the study of the global attractor we also obtain for the first time the existence of global weak solutions of the model with l 2 initial data it is then proved that the ginzburg landau system admits a global attractor which represents exactly all the long time dynamics of the system the global attractor obtained consists of exactly the set of steady state solutions and its unstable manifold its hausdorff and fractal dimensions are estimated in terms of the physically relevant ginzburg landau parameter diffusion parameter and applied magnetic field we construct explicitly absorbing sets for some abstract semigroups having a lyapunov functional and consequently prove the existence of global attractors this abstract result is applied to the ginzburg landau system for which the existence of global attractor does not seem to be the direct consequence of some a priori estimates of solutions

extensions of the i mmse relationship to gaussian channels with feedback and memory unveiling a fundamental link between information theory and estimation theory the i mmse relationship by guo et al together with its numerous extensions has great theoretical significance and various practical applications on the other hand its influences to date have been restricted to channels without feedback or memory due to the absence of its extensions to such channels in this paper we propose the extensions of the i mmse relationship to discrete time and continuous time gaussian channels with feedback and or memory our approach is based on a very simple observation which can be applied to other scenarios such as a simple and direct proof of the classical de bruijn s identity

mixed type solutions of the su 3 models on a torus in this paper we study mixed type solutions of su 3 chern simons system see 1 4 below on a two dimensional flat torus nolasco and tarantello commun math phys 213 599 639 2000 among other things nolasco and tarantello obtained solutions of 1 4 as minimizers of several functionals closely related to 1 4 and showed that if n 1 n 2 1 then one of those minimizers turns out to be a mixed type solution that is one component tends to ln frac 1 2 pointwise a e and the other component converges to a solution of a mean field equation we call these kinds of solutions mixed type i solutions in this paper we prove two main results i the asymptotic analysis of mixed type i solutions with arbitrary configuration of vortex points and ii the existence of mixed type i solutions under a non degenerate condition this non degenerate condition also ensures some uniqueness result in particular our results imply that when n 1 n 2 1 there are only two mixed type i solutions of 1 4

the cauchy problem for coupled yang mills and scalar fields in the temporal gauge we study the cauchy problem for minimally coupled classical yang mills and scalar fields inn 1 dimensional space time in the temporal gauge we prove the existence and uniqueness of solutions for small time intervals and for anyn we then develop a general theory of solutions in local spaces and extend the previous local in time results to this more general setting in space time dimensions two and three we prove the existence of global in time solutions by the method of a priori estimates both in global and local spaces in space time dimension four our estimates yield only partial results on the global existence problem

cauchy problems of the gauged sigma model we study the gauged sigma model in r1 1 the existence of the global smooth solution will be proved furthermore we show that the global weak solutions exist in rn 1 n 2 3

a large family of semi classical polynomials the perturbed chebyshev some results concerning finite perturbations of order s of the chebyshev polynomials are shown their semi classical character follows from the stieltjes transform of their orthogonality measure according to the choice of the perturbation parameters polynomials of arbitrary class can be generated the second order differential equation satisfied by these polynomials is obtained and several examples are worked out some particular cases of this differential equation had already been obtained by shohat and allaway

analyticity of entropy rate of hidden markov chains with continuous alphabet we first prove that under certain mild assumptions the entropy rate of a hidden markov chain observed when passing a finite state stationary markov chain through a discrete time continuous output channel is analytic with respect to the input markov chain parameters we then further prove under strengthened assumptions on the channel that the entropy rate is jointly analytic as a function of both the input markov chain parameters and the channel parameters in particular the main theorems establish the analyticity of the entropy rate for two representative channels 1 cauchy and 2 gaussian the analyticity results obtained are expected to be helpful in computation estimation of entropy rate of hidden markov chains and capacity of finite state channels with continuous output alphabet

on the absolute continuity of the blackwell measure in 1957 blackwell expressed the entropy of hidden markov chains using a measure which can be characterised as an invariant measure for an iterated function system with place dependent weights this measure called the blackwell measure plays a central role in understanding the entropy rate and other important characteristics of fundamental models in information theory we show that for a suitable set of parameter values the blackwell measure is absolutely continuous for almost every parameter in the case of binary symmetric channels

limit theorems in hidden markov models in this paper under mild assumptions we derive a law of large numbers a central limit theorem with an error estimate an almost sure invariance principle and a variant of the chernoff bound in finite state hidden markov models these limit theorems are of interest in certain areas of information theory and statistics particularly we apply the limit theorems to derive the rate of convergence of the maximum likelihood estimator in finite state hidden markov models

renormalization group and analyticity in one dimension a proof of dobrushin s theorem we consider one dimensional systems described by many body potentials with finite first moment and prove that the correlation functions are analytic in the interaction parameters this result is not new dobrushin 1973 but our proof is simpler and physically more transparent we show that by introducing suitable blocks and averaging over the variables associated to a subset of the blocks decimation procedure the resulting effective interaction is such that the system can always be dealt with as a high temperature system

on affinity relating two positive measures and the connection coefficients between polynomials orthogonalized by these measures we consider two positive normalized measures da x and db x related by the relationship da x cx ddb x or by da x cx 2 edb x and db x is symmetric we show that then the polynomial sequences a n x b n x orthogonal with respect to these measures are related by the relationship a n x b n x email protected nb n 1 x or by a n x b n x email protected nb n 2 x for some sequences k n and l n we present several examples illustrating this fact and also present some attempts for extensions and generalizations we also give some universal identities involving polynomials b n x and the sequence k n that have a form of the fourier series expansion of the radon nikodym derivative of one measure with respect to the other

on the entropy of a hidden markov process we study the entropy rate of a hidden markov process hmp defined by observing the output of a binary symmetric channel whose input is a first order binary markov process despite the simplicity of the models involved the characterization of this entropy is a long standing open problem by presenting the probability of a sequence under the model as a product of random matrices one can see that the entropy rate sought is equal to a top lyapunov exponent of the product this offers an explanation for the elusiveness of explicit expressions for the hmp entropy rate as lyapunov exponents are notoriously difficult to compute consequently we focus on asymptotic estimates and apply the same product of random matrices to derive an explicit expression for a taylor approximation of the entropy rate with respect to the parameter of the binary symmetric channel the accuracy of the approximation is validated against empirical simulation results we also extend our results to higher order markov processes and to renyi entropies of any order

asymptotic behavior of condensate solutions in the chern simons higgs theory we study the asymptotic behavior of condensate solutions in the chern simons higgs model as the chern simons coupling parameter tends to zero using the variational method we prove that there exist condensate solutions which show concentration phenomena

multiple geronimus transformations abstract we consider multiple geronimus transformations and show that they lead to discrete non diagonal sobolev type inner products moreover it is shown that every discrete sobolev inner product can be obtained as a multiple geronimus transformation a connection with geronimus spectral transformations for matrix orthogonal polynomials is also considered

stationary measures for projective transformations the blackwell and furstenberg measures in this paper we study the blackwell and furstenberg measures which play an important role in information theory and the study of lyapunov exponents for the blackwell measure we determine parameter domains of singularity and give upper bounds for the hausdorff dimension for the furstenberg measure we establish absolute continuity for some parameter values our method is to analyze linear fractional iterated function schemes which are contracting on average have no separation properties that is we do not assume that the open set condition holds see hutchinson in indiana univ math j 30 713 747 1981 and in the case of the blackwell measure have place dependent probabilities in such a general setting even an effective upper bound on the dimension of the measure is difficult to achieve

a boundary value problem related to the ginzburg landau model we analyze the ginzburg landau equation for a superconductor in the case of a 2 dimensional model a cylindrical conductor with a magnetic field parallel to the axis this amounts to find the extrema of the free energy mathcal a kappa 1 2 int limits omega nabla ia phi 2 b a 2 kappa 4 phi 2 1 2 dx where is a bounded domain with smooth boundary in 2 a a1 a2 the vector potential ba 1a2 2a1 the magnetic field a complex field we describe the connected components of the maximal configuration space i e of the set of all a with components in the sobolev spaceh1 and such that 1 on the boundary modulo the action of the gauge group in the critical case 1 we give a complete description of the minimal configurations in each component

qualitative properties of solutions to some nonlinear elliptic equations in r 2 o introduction elliptic equations in this paper we investigate properties of the solutions to the au r x e u x x r 2 for functions r x which are positive near infinity equations of this kind arise from a variety of situations such as from prescribing gaussian curvature in geometry i 2 and from combustion theory in physics 3 recently a series ofworks have been sought to understand the existence and the qualitative properties of the solutions of ni i 5 and ni cheng 4 1 considered the case where r x is nonpositive mcowen 6 1 and aviles 7 investigated the situation where r x 0 in some order as ixl in our previous paper 1 we consider a special case where r is a constant we proved that the solutions are radially symmetric and hence classified all the solutions in this paper we consider more general functions r x first we obtain the asymptotic behavior of the solution near infinity consequently we prove that all the solutions satisfy an identity which is somewhat of a generalization of the well known kazdan warner condition finally using the asymptotic behavior together with the further development of the method employed in our previous paper i 1 we show that all the solutions are radially symmetric provided r is radially symmetric and nonincreasing this part can be viewed as the completion of 1 throughout this paper we assume that the function r x is positive near infinity in 1 we study the asymptotic behavior of the solution u x of let fl 1 2n r2 r x e dx under some appropriate conditions we show that the solutions approach

nonself dual chern simons and maxwell chern simons vortices on bounded domains abstract we first show the existence of the multivortex solutions of maxwell chern simons higgs mcsh model on bounded domains and prove that the solutions of the euler lagrange equations of the mcsh energy functional converge to those of the abelian higgs ah model and the chern simons higgs csh model in suitable limits respectively we also show the existence of the multivortex solutions of the nonself dual csh model on bounded domains besides we study asymptotics for the minimizers of mcsh energy functional when the gauge field vanishes

the existence of chern simons vortices a new type of vortices called chern simons vortices is considered and the existence is established

topological multivortex solutions of the self dual maxwell chern simons higgs system abstract we study the existence and various behaviors of topological multivortex solutions of the relativistic self dual maxwell chern simons higgs system we first prove the existence of general topological solutions by applying variational methods to the newly discovered minimizing functional then by an iteration method we prove the existence of topological solutions satisfying some extra conditions which we call admissible solutions we establish asymptotic exponential decay estimates for these topological solutions we also investigate the limiting behavior of the admissible solutions as parameters in our system go to some limits for the abelian higgs limit we obtain strong convergence result while for the chern simons limit we only obtained that our admissible solutions weakly approximate one of the chern simons solutions

geronimus transformations of bivariate linear functionals abstract given a linear functional u in the linear space of polynomials in two variables with real coefficients and a polynomial x y in this contribution we deal with geronimus transformations of u i e those linear functionals v such that u x y v the connection formulas between the sequences of bivariate orthogonal polynomials with respect to u and v are given a matrix interpretation of such transformations by using lu and ul factorizations of the block jacobi matrices associated with such polynomials is given finally some illustrative examples of geronimus transformations of weight function supported in domains of r 2 are discussed

the global existence in the cauchy problem of the maxwell chern simons higgs system in this article we prove the global existence of solution of the classical maxwell chern simons higgs equations in 2 1 dimensional minkowski space time in the lorentz gauge we also prove that the topological solution of the maxwell chern simons higgs system converges to that of maxwell higgs system as the chern simons constant goes to zero reproducing the classical result by moncrief j math phys 21 2291 1980 on the global existence of the maxwell klein gordon system in 2 1 dimension

analyticity of entropy rates of continuous state hidden markov models the analyticity of the entropy and relative entropy rates of continuous state hidden markov models is studied here using the analytic continuation principle and the stability properties of the optimal filter the analyticity of these rates is established for analytically parameterized models the obtained results hold under relatively mild conditions and cover several useful classes of hidden markov models these results are relevant for several theoretically and practically important problems arising in statistical inference system identification and information theory

variations around classical orthogonal polynomials connected problems abstract we survey and prove the principal characterizations of the classical orthogonal polynomials with the method of the dual sequence two new characterizations are given connected problems are discussed

asymptotics of entropy rate in special families of hidden markov chains we derive an asymptotic formula for entropy rate of a hidden markov chain under certain parameterizations we also discuss applications of the asymptotic formula to the asymptotic behaviors of entropy rate of hidden markov chains as outputs of certain channels such as binary symmetric channel binary erasure channel and some special gilbert elliot channel

asymptotics for maxwell chern simons multivortices chern simons gauge theories are of interest in several areas of physics including high tc superconductivity as they can describe particles which are both electrically and magnetically charged on the other hand the introduction of the chern simons term into the lagrangian results in serious di5culties for a rigorous treatment of the corresponding equations of motion therefore a considerable e7ort has been devoted in recent years to the study of models with a self dual structure such a structure allows us to obtain time independent energy minimizer solutions to the full second order equations of motion by solving appropriate rst order equations also known as the bogomol nyi equations 11 these particular solutions are called multivortices for an overview of self dual chern simons theories see the monograph of dunne 8 in 9 10 hong et al and jackiw and weinberg introduced a chern simons model where the maxwell term is neglected in order to achieve self duality we call this model the cs model the cs multivortices have proved to be particularly interesting from the mathematical viewpoint and have been extensively analyzed see references

existence of multivortex solutions in the self dual chern simons higgs theory in a background metric in this paper we show the existence of the multiple multivortex solutions of the self duality equations of 2 1 dimensional chern simons higgs model in a background metric of the form g diag 1 b x b x with b x o x l as x for some l 2

analyticity convergence and convergence rate of recursive maximum likelihood estimation in hidden markov models this paper considers the asymptotic properties of the recursive maximum likelihood estimator for hidden markov models the paper is focused on the analytic properties of the asymptotic log likelihood and on the point convergence and convergence rate of the recursive maximum likelihood estimator using the principle of analytic continuation the analyticity of the asymptotic log likelihood is shown for analytically parameterized hidden markov models relying on this fact and some results from differential geometry lojasiewicz inequality the almost sure point convergence of the recursive maximum likelihood algorithm is demonstrated and relatively tight bounds on the convergence rate are derived as opposed to the existing result on the asymptotic behavior of maximum likelihood estimation in hidden markov models the results of this paper are obtained without assuming that the log likelihood function has an isolated maximum at which the hessian is strictly negative definite

bubbling solutions for relativistic abelian chern simons model on a torus we prove the existence of bubbling solutions for the following chern simons higgs equation delta u frac 1 varepsilon 2 e u 1 e u 4 pi sum j 1 n delta p j quad rm in omega where is a torus we show that if n 4 and p 1 p j j 2 n then for small e 0 the above problem has a solution u e and as e 0 u e blows up at the vertex point p 1 and satisfies frac 1 varepsilon 2 e u 1 e u to 4 pi n delta p 1 this is the first result for the existence of a solution which blows up at a vertex point

concavity of the mutual information rate for input restricted memoryless channels at high snr we consider a memoryless channel with an input markov process supported on a mixing finite type constraint we continue the development of asymptotics for the entropy rate of the output hidden markov chain and deduce that at high signal to noise ratio the mutual information rate of such a channel is concave with respect to almost all input markov chains of a given order

remark on a relation between magnetic field and topological degree of order parameter in a type ii superconductivity model abstract it is proved that in the absence of an applied magnetic field the two space dimensional steady state helmholtz free energy which models the type ii superconductors admits no minimizer in the following admissible function set u a h 1 c h 1 r 2 u 1 1 2 i u d u ud u d 2k here c is the complex plane k is a fixed nonzero integer which is the topological degree of u with respect to its value 0 the case k 0 is discussed separately under different assumptions

differentiation of srb states abstract let f be a diffeomorphism of a manifold m and f a generalized srb state for f if supp f is a hyperbolic compact set we show that the map is differentiable in a suitable functional setup and we compute the derivative when supp f is an attractor the derivative is given by where x is the vector field this formula can be extended to time dependent situations and also at least formally to nonuniformly hyperbolic situations the above results will find their use in the study of the onsager reciprocity relations and the fluctuation dissipation formula of nonequilibrium statistical mechanics

periodic maxwell chern simons vortices with concentrating property in order to study electrically and magnetically charged vortices in fractional quantum hall effect and anyonic superconductivity the maxwell chern simons mcs model was introduced by lee et al phys lett b 252 79 83 1990 as a unified system of the classical abelian higgs model ah and the chern simons cs model in this article the first goal is to obtain the uniform cs limit result of mcs model with respect to the chern simons parameter without any restriction on either a particular class of solutions or the number of vortex points as the chern simons mass scale tends to infinity the most important step for this purpose is to derive the relation between the higgs field and the neutral scalar field our cs limit result also provides the critical clue to answer the open problems raised by ricciardi and tarantello comm pure appl math 53 811 851 2000 and tarantello milan j math 72 29 80 2004 and we succeed to establish the existence of periodic maxwell chern simons vortices satisfying the concentrating property of the density of superconductive electron pairs furthermore we expect that the cs limit analysis in this paper would help to study the stability multiplicity and bubbling phenomena for solutions of the mcs model

transformations of gibbs measures we study local transformations of gibbs measures we establish sufficient conditions for the quasilocality of the images and obtain results on the existence and continuity properties of their relative energies general results are illustrated by simple examples

analyticity of entropy rate of hidden markov chains we prove that under mild positivity assumptions the entropy rate of a hidden markov chain varies analytically as a function of the underlying markov chain parameters a general principle to determine the domain of analyticity is stated an example is given to estimate the radius of convergence for the entropy rate we then show that the positivity assumptions can be relaxed and examples are given for the relaxed conditions we study a special class of hidden markov chains in more detail binary hidden markov chains with an unambiguous symbol and we give necessary and sufficient conditions for analyticity of the entropy rate for this case finally we show that under the positivity assumptions the hidden markov chain itself varies analytically in a strong sense as a function of the underlying markov chain parameters

bubbling solutions for the su 3 chern simons model on a torus we consider the following nonlinear system derived from the su 3 chern simons models on a torus where denotes the dirac measure at when if we look for a solution with then 0 1 is reduced to the chern simons higgs equation the existence of bubbling solutions to 0 1 has been a longstanding problem in this paper we prove the existence of such solutions such that even if 2012 wiley periodicals inc

on a sharp sobolev type inequality on two dimensional compact manifolds motivated by the asymptotic analysis of double vortex condensates in the chern simons higgs theory we construct a suitable minimizing sequence for a sharp sobolev inequality a la moser for two dimensional compact manifolds as a consequence we first obtain a direct proof of the sharp character of such an inequality secondly and more interestingly we use such minimizing sequence to show that for the flat torus the corresponding extremal problem attains its infimum

noisy constrained capacity for bsc channels we study the classical problem of noisy constrained capacity in the case of the binary symmetric channel bsc namely the capacity of a bsc whose input is a sequence from a constrained set as stated by fan while calculation of the noise free capacity of constrained sequences is well known the computation of the capacity of a constraint in the presence of noise has been an unsolved problem in the half century since shannon s landmark paper we first express the constrained capacity of a binary symmetric channel with d k constrained input as a limit of the top lyapunov exponents of certain matrix random processes then we compute asymptotic approximations of the noisy constrained capacity for cases where the noise parameter e is small in particular we show that when k 2d the error term excess of capacity beyond the noise free capacity is o e whereas it is o eloge when k 2d in both cases we compute the coefficient of the error term in the course of establishing these findings we also extend our previous results on the entropy of a hidden markov process to higher order finite memory processes these conclusions are proved by a combination of analytic and combinatorial methods

event based state estimation of hidden markov models through a gilbert elliott channel in this note the problem of event based state estimation for a finite state hidden markov model under a generic stochastic event triggering condition and an unreliable communication channel is investigated the effect of packet dropout is characterized with a gilbert elliott process utilizing the change of probability measure approach the packet dropout model and the event triggered measurement information available to the estimator analytical expressions for the conditional probability distributions of the states are obtained based on which the optimal event based state estimates can be further calculated together with a closed form expression of the average sensor to estimator communication rate the effectiveness of the proposed results is illustrated by an application to a wireless automated machine health monitoring problem

uniqueness of the topological multivortex solution in the self dual chern simons theory we establish a uniqueness result for the topological multivortex solution to the self dual equations of the abelian relativistic self dual chern simons higgs model we prove that the topological multivortex solution is unique if the chern simons coupling parameter 0 is sufficiently small we also establish a uniqueness result for 0 sufficiently large

projection of markov measures may be gibbsian we study the induced measure obtained from a 1 step markov measure supported by a topological markov chain after the mapping of the original alphabet onto another one we give sufficient conditions for the induced measure to be a gibbs measure in the sense of bowen when the factor system is again a topological markov chain this amounts to constructing when it does exist the induced potential and proving its holder continuity this is achieved through a matrix method we provide examples and counterexamples to illustrate our results

derivatives of entropy rate in special families of hidden markov chains consider a hidden markov chain obtained as the observation process of an ordinary markov chain corrupted by noise recently zuk et al showed how in principle one can explicitly compute the derivatives of the entropy rate of at extreme values of the noise namely they showed that the derivatives of standard upper approximations to the entropy rate actually stabilize at an explicit finite time we generalize this result to a natural class of hidden markov chains called black holes we also discuss in depth special cases of binary markov chains observed in binary symmetric noise and give an abstract formula for the first derivative in terms of a measure on the simplex due to blackwell

asymmetric domain walls of small angle in soft ferromagnetic films we focus on a special type of domain wall appearing in the landau lifshitz theory for soft ferromagnetic films these domain walls are divergence free mathbb s 2 valued transition layers that connect two directions m theta pm in mathbb s 2 differing by an angle 2 theta and minimize the dirichlet energy our main result is the rigorous derivation of the asymptotic structure and energy of such asymmetric domain walls in the limit theta downarrow 0 as an application we deduce that a supercritical bifurcation causes the transition from symmetric to asymmetric walls in the full micromagnetic model

orthogonal polynomials associated with an inverse quadratic spectral transform let p n n 0 be a sequence of monic orthogonal polynomials with respect to a quasi definite linear functional u and q n n 0 a sequence of polynomials defined by q n x p n x s np n 1 x t np n 2 x n 1 with t n 0 for n 2 we obtain a new characterization of the orthogonality of the sequence q n n 0 with respect to a linear functional v in terms of the coefficients of a quadratic polynomial h such that h x v u we also study some cases in which the parameters s n and t n can be computed more easily and give several examples finally the interpretation of such a perturbation in terms of the jacobi matrices associated with p n n 0 and q n n 0 is presented

the entropy of a binary hidden markov process the entropy of a binary symmetric hidden markov process is calculated as an expansion in the noise parameter e we map the problem onto a one dimensional ising model in a large field of random signs and calculate the expansion coefficients up to second order in e using a conjecture we extend the calculation to 11th order and discuss the convergence of the resulting series

on the optimality of symbol by symbol filtering and denoising we consider the problem of optimally recovering a finite alphabet discrete time stochastic process x sub t from its noise corrupted observation process z sub t in general the optimal estimate of x sub t will depend on all the components of z sub t on which it can be based we characterize nontrivial situations i e beyond the case where x sub t z sub t are independent for which optimum performance is attained using symbol by symbol operations a k a singlet decoding meaning that the optimum estimate of x sub t depends solely on z sub t for the case where x sub t is a stationary binary markov process corrupted by a memoryless channel we characterize the necessary and sufficient condition for optimality of symbol by symbol operations both for the filtering problem where the estimate of x sub t is allowed to depend only on z sub t sub t spl les t and the denoising problem where the estimate of x sub t is allowed dependence on the entire noisy process it is then illustrated how our approach which consists of characterizing the support of the conditional distribution of the noise free symbol given the observations can be used for characterizing the entropy rate of the binary markov process corrupted by the binary symmetric channel bsc in various asymptotic regimes for general noise free processes not necessarily markov general noise processes not necessarily memoryless and general index sets random fields we obtain an easily verifiable sufficient condition for the optimality of symbol by symbol operations and illustrate its use in a few special cases for example for binary processes corrupted by a bsc we establish under mild conditions the existence of a spl delta sup 0 such that the say what you see scheme is optimal provided the channel crossover probability is less than spl delta sup finally we show how for the case of a memoryless channel the large deviations ld performance of a symbol by symbol filter is easy to obtain thus characterizing the ld behavior of the optimal schemes when these are singlet decoders and constituting the only known cases where such explicit characterization is available

global existence and nonrelativistic limit for the vlasov maxwell chern simons system the vlasov maxwell chern simons system is studied global existence of classical solutions is proved and then its nonrelativistic limit is investigated when the speed of light tends to infinity it is proved that solutions of the vlasov maxwell chern simons system converge to solutions of the vlasov yukawa system in a suitable sense

the existence of non topological multivortex solutions in the relativistic self dual chern simons theory we construct a general type of multivortex solutions of the self duality equations the bogomol nyi equations of 2 1 dimensional relativistic chern simons model with the non topological boundary condition near infinity for such construction we use a perturbation argument around the explicit solutions of the liouville equation

an upper bound for the largest lyapunov exponent of a markovian product of nonnegative matrices we derive an upper bound for the largest lyapunov exponent of a markovian product of nonnegative matrices using markovian type counting arguments the bound is expressed as the maximum of a nonlinear concave function over a finite dimensional convex polytope of probability distributions

a randomized algorithm for the capacity of finite state channels inspired by ideas from the field of stochastic approximation we propose a randomized algorithm to compute the capacity of a finite state channel with a markovian input when the mutual information rate of the channel is concave with respect to the chosen parameterization the proposed algorithm proves to be convergent to the capacity of the channel almost surely with the derived convergence rate we also discuss the convergence behavior of the algorithm without the concavity assumption

on the inverse problem of the product of a semi classical form by a polynomial abstract a form linear functional u is called regular if there exists a sequence of polynomials pn n 0 deg pn n which is orthogonal with respect to u such a form is said to be semi classical if there exist polynomials and such that d u u 0 where d designs the derivative operator on certain regularity conditions the product of a semi classical form by a polynomial gives a semi classical form in this paper we consider the inverse problem given a semi classical form v find all regular forms u which satisfy the relation x2u v c we give the structure relation differential recurrence relation of the orthogonal polynomial sequence relatively to u an example is treated with a nonsymmetric form v

lower bounds for the energy of unit vector fields and applications we prove lower bounds for the dirichlet energy of a unit vector field defined in a perforated domain of r2with nonzero degree on the outer boundary in terms of the total diameter of the holes we use this to derive lower bounds and then compactness results for sequences ue of minimizers or almost minimizers of ginzburg landau functionals with coupling constant 1 e2tending to

entropy of hidden markov processes via cycle expansion hidden markov processes hmp is one of the basic tools of the modern probabilistic modeling the characterization of their entropy remains however an open problem here the entropy of hmp is calculated via the cycle expansion of the zeta function a method adopted from the theory of dynamical systems for a class of hmp this method produces exact results both for the entropy and the moment generating function the latter allows to estimate via the chernoff bound the probabilities of large deviations for the hmp more generally the method offers a representation of the moment generating function and of the entropy via convergent series

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

gamma limit of the nonself dual chern simons higgs energy abstract we consider the gamma limit of the abelian chern simons higgs energy g csh 1 2 u a e u e 2 2 4 curl a e h ex 2 u e 2 1 e 2 u e 2 1 u e 2 2 d x on a bounded simply connected two dimensional domain under the e 0 limit as a first step we study the gamma limit of e csh 1 2 u u e 2 1 e 2 u e 2 1 u e 2 2 d x under two different scalings e csh log e and e csh log e 2 we apply the log e 2 scaling result to the full chern simons higgs energy g csh and as a consequence we are able to compute the first critical field h 1 h 1 u for the nucleation of a vortex the method entails estimating in certain weak topologies the jacobian j u e det u e in terms of the chern simons higgs energy e csh

minimum memory for generating rare events we classify the rare events of structured memoryful stochastic processes and use this to analyze sequential and parallel generators for these events given a stochastic process we introduce a method to construct a process whose typical realizations are a given process rare events this leads to an expression for the minimum memory required to generate rare events we then show that the recently discovered classical quantum ambiguity of simplicity also occurs when comparing the structure of process fluctuations