exact closed form performance analysis of optimum combining with multiple cochannel interferers and rayleigh fading a new closed form expression is derived for the exact bit error probability bep for optimum combining with binary phase shift keying the exact bep expression is for multiple equal power cochannel interferers and multiple reception branches it is assumed that the aggregate interference and noise is gaussian and that both the desired signal and interference are subject to rayleigh fading the derivation starts by expressing the optimum combining decision statistic as a sum of quadratic forms of gaussian random variables and it proceeds to average over the fading interference the new bep expression has low complexity as it contains only finite sums and products

hodge laplacians on graphs this is an elementary introduction to the hodge laplacian on a graph a higher order generalization of the graph laplacian we will discuss basic properties including cohomology and hodge theory t

characteristic functions for optimum combining output sinr with awgn and correlated interference optimum combining oc is a powerful means for combatting co channel interference its performance however is difficult to analyze the prevailing methodology in current use is to neglect the influence of additive white gaussian noise awgn inclusion of awgn into the analysis usually leads to mathematical intractability except for some extreme cases in this letter we formulate the problem in the framework of hypergeometric functions so that their good properties can be exploited to enable the analysis to account for the influence of awgn and co channel interference simultaneously we obtain closed form solutions to the characteristic function chf of the signal to interference plus noise ratio at the oc output for three important operational scenarios in rayleigh fading although the general solution still needs further effort to simplify the assumptions made here are that both signal and interferers suffer from rayleigh fading and the number of interferers is not less than the number of antennas the use of resulting chf formulas is illustrated through their application to the bit error and outage performance evaluation of oc

random walks among time increasing conductances heat kernel estimates for any graph having a suitable uniform poincare inequality and volume growth regularity we establish two sided gaussian transition density estimates and parabolic harnack inequality for constant speed continuous time random walks evolving via time varying uniformly elliptic conductances provided the vertex conductances i e reversing measures increase in time such transition density upper bounds apply for discrete time uniformly lazy walks with the matching lower bounds holding once the parabolic harnack inequality is proved

a note on the finite time behavior of simulated annealing simulated annealing has proven to be a very successful heuristic for various combinatorial optimization problems it is a randomized algorithm that attempts to find the global optimum with high probability by local exchanges in this paper we give a new proof of the convergence of simulated annealing by applying results about rapidly mixing markov chains with this proof technique it is possible to obtain better bounds for the finite time behavior of simulated annealing than previously known

spectral properties of metastable markov semigroups abstract it is shown that if a symmetric markov semigroup e ht on the hilbert space l 2 x is hypercontractive then the approximate degeneracy of the ground state has several consequences concerning other parts of the spectrum of h and concerning the unitary group e iht in particular in the presence of a space inversion symmetry all the eigenvalues occur in pairs with gaps comparable to the gap between the bottom two eigenvalues

absence of mass gap for a class of stochastic contour models we study a class of markovian stochastic processes in which the state space is a space of lattice contours and the elementary motions are local deformations we show under suitable hypotheses on the jump rates that the infinitesimal generator has zero mass gap this result covers among others the bfacf dynamics for fixed endpoint self avoiding walks and the sterling greensite dynamics for fixed boundary self avoiding surfaces our models also mimic the glauber dynamics for the low temperature ising model the proofs are based on two new general principles the minimum hitting time argument and the mean or mean exponential hitting time argument

mass fractal dimension and the compactness of proteins vibrational dynamics and energy flow in a protein are related by alexander orbach theory to the protein s mass fractal dimension d and spectral dimension d proteins struct funct bioinf 55 529 2004 recently proposed a relation between d and protein size based on their computational analysis of a set of proteins ranging from about 100 to several thousand amino acids we report here values for d computed for 200 proteins from the protein data bank pdb ranging from about 100 to over 10 000 amino acids and examine variation of d with protein size the average d is found to be 2 5 significantly smaller than a completely compact three dimensional collapsed polymer indeed we find that on average a protein in its pdb configuration fills about three quarters of the volume within the protein surface protein mass is also found to scale with radius of gyration with an exponent of 2 5 for this set of proteins

relations entre isoperimetrie et trou spectral pour les chaines de markov finies let g be a finite and connected graph we will note by l g the maximum length of an injective path in g we will show by two dictinct proofs one using sub trees of g and the other based on multiflows of paths that sup p g i p p l g where the supremum is taken over all markovian kernels p reversible with respect to a probability and whose allowed transitions are given by the edges of g and where i p respectively p is the isoperimetric constant resp the spectral gap associated to the couple p then we will study more precisely the same supremum but where the probability is also fixed these results give optimal minorations of the spectral gap which are linear with respect to the isoperimetric constant and not quadratic as in the cheeger inequality and we will give several examples on infinite graphs

on the layering transition of an sos surface interacting with a wall ii the glauber dynamics we continue our study of the statistical mechanics of a 2d surface above a fixed wall and attracted towards it by means of a very weak positive magnetic fieldh in the solid on solid sos approximation when the inverse temperature is very large in particular we consider a glauber dynamics for the above model and study the rate of approach to equilibrium in a large cube with arbitrary boundary conditions using the results proved in the first paper of this series we show that for allh h k 1 h k h k being the critical values of the magnetic field found in the previous paper the gap in the spectrum of the generator of the dynamics is bounded away from zero uniformly in the size of the box and in the boundary conditions on the contrary forh h k and free boundary conditions we show that the gap in a cube of sidel is bounded from above and from below by a negative exponential ofl our results provide a strong indication that contrary to what happens in two dimensions for the three dimensional dynamical ising model in a finite cube at low temperature and very small positive external field with boundary conditions that are opposite to the field on one face of the cube and are absent free on the remaining faces the rate of exponential convergence to equilibrium which is positive in infinite volume may go to zero exponentially fast in the side of the cube

approximate counting uniform generation and rapidly mixing markov chains the paper studies effective approximate solutions to combinatorial counting and uniform generation problems using a technique based on the simulation of ergodic markov chains it is shown that for self reducible structures almost uniform generation is possible in polynomial time provided only that randomised approximate counting to within some arbitrary polynomial factor is possible in polynomial time it follows that for self reducible structures polynomial time randomised algorithms for counting to within factors of the form 1 n are available either for all fl e r or for no fi e r a substantial part of the paper is devoted to investigating the rate of convergence of finite ergodic markov chains and a simple but powerful characterisation of rapid convergence for a broad class of chains based on a structural property of the underlying graph is established finally the general techniques of the paper are used to derive an almost uniform generation procedure for labelled graphs with a given degree sequence which is valid over a much wider range of degrees than previous methods this in turn leads to randomised approximate counting algorithms for these graphs with very good

self avoiding random loops a random loop or polygon is a simple random walk whose trajectory is a simple jordan curve the study of random loops is extended in two ways first the probability p sub n x y that a random n step loop contains a point x y in the interior of the loop is studied and 1 2 1 2 is shown to be 1 2 1 n it is plausible that p sub n x y tends toward 1 2 for all x y but this is not proved even for x y 3 2 1 2 a way is offered to simulate random n step self avoiding loops numerical evidence obtained with this simulation procedure suggests that the probability p sub n 3 2 1 2 approximately 1 2 c n for some fixed c

ground state and lowest eigenvalue of the laplacian for non compact hyperbolic surfaces letm be a complete riemannian surface with constant curvature 1 infinite volume and a finitely generated fundamental group denote by m the lowest eigenvalue of the laplacian onm and let m be the associated eigenfunction we estimate the size of m and the shape of m by a finite procedure which has an electrical circuit analogue using the margulis lemma we decomposem into its thick and thin parts on the compact thick components we show that m varies from a constant value by no more thano sqrt lambda m the estimate for m is calculable in terms of the topology ofm and the lengths of short geodesics ofm an analogous theorem of the compact case was treated in swy

dynamical stability of metastable states abstract we continue our study of symmetric markov semigroups for which the zero eigenvalue is almost but not quite degenerate we show that the metastable states of the semigroup are dynamically stable under small perturbations without any of the technical restrictions or approximations of our earlier papers

diffusions and random shadows in negatively curved manifolds abstract let m be a d dimensional complete simply connected negatively curved manifold there is a natural notion of hausdorff dimension for its boundary at infinity this is shown to provide a notion of global curvature or average rate of growth in two probabilistic senses first on surfaces d 2 it is twice the critical drift separating transience from recurrence for brownian motion with constant length radial drift equivalently it is twice the critical for the existence of a green function for the operator 2 r second for any d it is the critical intensity for almost sure coverage of the boundary by random shadows cast by balls appropriately scaled produced from a constant intensity poisson point process

on the two dimensional dynamical ising model in the phase coexistence region we consider a glauber dynamics reversible with respect to the two dimensional ising model in a finite square of sidel in the absence of an external field and at large inverse temperature we first consider the gap in the spectrum of the generator of the dynamics in two different cases with plus and open boundary conditions we prove that when the symmetry under global spin flip is broken by the boundary conditions the gap is much larger than the case in which the symmetry is present for this latter we compute exactly the asymptotics of 1 l log gap asl and show that it coincides with the surface tension along one of the coordinate axes as a consequence we are able to study quite precisely the large deviations in time of the magnetization and to obtain an upper bound on the spin spin time correlation in the infinite volume plus phase our results establish a connection between the dynamical large deviations and those of the equilibrium gibbs measure studied by shlosman in the framework of the rigorous description of the wulff shape for the ising model finally we show that in the case of open boundary conditions it is possible to rescale the time withl in such a way that asl the finite dimensional distributions of the time rescaled magnetization converge to those of a symmetric continuous time markov chain on the two state space m m m being the spontaneous magnetization our methods rely upon a novel combination of techniques for bounding from below the gap of symmetric markov chains on complicated graphs developed by jerrum and sinclair in their markov chain approach to hard computational problems and the idea of introducing block glauber dynamics instead of the standard single site dynamics in order to put in evidence more effectively the effect of the boundary conditions in the approach to equilibrium

approach to equilibrium for random walks on graphs and for stochastic infinite particle processes associated with a finite connected graph g is a doubly stochastic laplacian matrix g g a lower bound on the mass gap for g g is obtained i e the first nonzero eigenvalue of g g this estimate is then used to estimate the mass gap for some infinite particle stochastic generators with corresponding processes that are closely related to monte carlo methods employed in statistical mechanics calculations

biased random walks on galton watson trees we consider random walks with a bias toward the root on the family tree t of a supercritical galton watson branching process and show that the speed is positive whenever the walk is transient the corresponding harmonic measures are carried by subsets of the boundary of dimension smaller than that of the whole boundary when the bias is directed away from the root and the extinction probability is positive the speed may be zero even though the walk is transient the critical bias for positive speed is determined

polymer dynamics in the depinned phase metastability with logarithmic barriers we consider the stochastic evolution of a 1 1 dimensional polymer in the depinned regime at equilibrium the system exhibits a double well structure the polymer lies essentially either above or below the repulsive line as a consequence one expects a metastable behavior with rare jumps between the two phases combined with a fast thermalization inside each phase however the energy barrier between these two phases is only logarithmic in the system size l and therefore the two relevant time scales are only polynomial in l with no clear cut separation between them the whole evolution is governed by a subtle competition between the diffusive behavior inside one phase and the jumps across the energy barriers our main results are i a proof that the mixing time of the system lies between l frac 5 2 and l frac 5 2 2 ii the identification of two regions associated with the positive and negative phase of the polymer together with the proof of the asymptotic exponentiality of the tunneling time between them with rate equal to a half of the spectral gap

non equivalence of dynamical ensembles and emergent non ergodicity dynamical ensembles have been introduced to study constrained stochastic processes in the microcanonical ensemble the value of a dynamical observable is constrained to a given value in the canonical ensemble a bias is introduced in the process to move the mean value of this observable the equivalence between the two ensembles means that calculations in one or the other ensemble lead to the same result in this paper we study the physical conditions associated with ensemble equivalence and the consequences of non equivalence for continuous time markov jump processes we show that ergodicity guarantees ensemble equivalence for non ergodic systems or systems with emergent ergodicity breaking we adapt a method developed for equilibrium ensembles to compute asymptotic probabilities while caring about the initial condition we illustrate our results on the infinite range ising model by characterizing the fluctuations of magnetization and activity we discuss the emergence of non ergodicity by showing that the initial condition can only be forgotten after a time that scales exponentially with the number of spins

difference equations isoperimetric inequality and transience of certain random walks the difference laplacian on a square lattice in rn has been stud ied by many authors in this paper an analogous difference operator is studied for an arbitrary graph it is shown that many properties of the laplacian in the continuous setting e g the maximum principle the harnack inequality and cheeger s bound for the lowest eigenvalue hold for this difference oper ator the difference laplacian governs the random walk on a graph just as the laplace operator governs the brownian motion as an application of the theory of the difference laplacian it is shown that the random walk on a class of graphs is transient the random walks we consider are defined as follows let k be a connected graph i e a one dimensional simplicial complex for a vertex x e k let m x denote the number of edges emanating from x the probability that a particle moves from x to another vertex y e k is l m x if x and y are connected by an edge and it is zero otherwise as observed by courant friedrichs and lewy cfl for the case of a square lattice in the plane this random walk is intimately related to the difference analog of the laplacian

central limit theorem for additive functionals of reversible markov processes and applications to simple exclusions we prove a functional central limit theorem for additive functionals of stationary reversible ergodic markov chains under virtually no assumptions other than the necessary ones we use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk

on the spectral gap of kawasaki dynamics under a mixing condition revisited we consider a conservative stochastic spin exchange dynamics which is reversible with respect to the canonical gibbs measure of a lattice gas model we assume that the corresponding grand canonical measure satisfies a suitable strong mixing condition we give an alternative and quite natural from the physical point of view proof of the famous lu yau result which states that the relaxation time in a box of side l scales like l2 we then show how to use such an estimate to prove a decay to equilibrium for local functions of the form 1 t e where e is positive and arbitrarily small and 12 for d 1 1 for d 2

phase transitions on nonamenable graphs we survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph most attention is devoted to transitive graphs and trees

approximating the permanent a randomised approximation scheme for the permanent of a 0 1s presented the task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph the latter is accomplished by simulating a markov chain whose states are the matchings in the graph for a wide class of 0 1 matrices the approximation scheme is fully polynomial i e runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output this class includes all dense matrices those that contain sufficiently many 1 s and almost all sparse matrices in some reasonable probabilistic model for 0 1 matrices of given density for the approach sketched above to be computationally efficient the markov chain must be rapidly mixing informally it must converge in a short time to its stationary distribution a major portion of the paper is devoted to demonstrating that the matchings chain is rapidly mixing apparently the first such result for a markov chain with genuinely c

tight bounds for mixing of the swendsen wang algorithm at the potts transition point we study two widely used algorithms for the potts model on rectangular subsets of the hypercubic lattice mathbb z d heat bath dynamics and the swendsen wang algorithm and prove that under certain circumstances the mixing in these algorithms is torpid or slow in particular we show that for heat bath dynamics throughout the region of phase coexistence and for the swendsen wang algorithm at the transition point the mixing time in a box of side length l with periodic boundary conditions has upper and lower bounds which are exponential in ld 1 this work provides the first upper bound of this form for the swendsen wang algorithm and gives lower bounds for both algorithms which significantly improve the previous lower bounds that were exponential in l log l 2

on the outage probability of optimum combining and maximal ratio combining schemes in an interference limited rice fading channel in this letter we study the performance of optimum combining oc and maximal ratio combining mrc diversity schemes in wireless digital communication systems with rice fading and cochannel interference new simplified closed form expressions are derived for the probability density function pdf as well as the outage probability for oc and mrc when the desired signal has a line of sight and the interferers are assumed to be scattered and further away from the receiver it is assumed that the interferers have equal powers and their number l is larger than the diversity order m i e l m

relationship between the fractal dimension and the power law index for a time series a numerical investigation abstract a time series showing self affine over all time scales follows a power law spectrum when such a time series x j j 1 2 n is transformed into the discrete fourier transformation i e x j n 2 k 0 c k cos 2 jkn k where c k and k are the amplitude and phase for wavenumber k respectively the power spectrum density for wavenumber k is given by p k c 2 k n k the relationship between the power law index and the fractal dimension d for a time series following a power law spectrum is investigated by using a numerical experiment it should be noted that the time series with the same power law index shows various behaviors in a time domain depending on distribution of k and gives different values of the fractal dimension accordingly in short the phase distribution strongly affects the irregularity represented in terms of the fractal dimension in addition the relationships between and d are also examined both for the differenced and for the integrated time series

variational method for estimating the rate of convergence of markov chain monte carlo algorithms we demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of markov chain monte carlo mcmc algorithms as a function of the target density and proposal density the bound relies on approximating the second largest eigenvalue in the spectrum of the mcmc operator using a variational principle and the approach is applicable to problems with continuous state spaces we apply the method to one dimensional examples with gaussian and quartic target densities and we contrast the performance of the random walk metropolis hastings algorithm with a smart variant that incorporates gradient information into the trial moves a generalization of the metropolis adjusted langevin algorithm we find that the variational method agrees quite closely with numerical simulations we also see that the smart mcmc algorithm often fails to converge geometrically in the tails of the target density except in the simplest case we examine and even then care must be taken to choose the appropriate scaling of the deterministic and random parts of the proposed moves again this calls into question the utility of smart mcmc in more complex problems finally we apply the same method to approximate the rate of convergence in multidimensional gaussian problems with and without importance sampling there we demonstrate the necessity of importance sampling for target densities which depend on variables with a wide range of scales

new monte carlo method for the self avoiding walk we introduce a new monte carlo algorithm for the self avoiding walk saw and show that it is particularly efficient in the critical region long chains we also introduce new and more efficient statistical techniques we employ these methods to extract numerical estimates for the critical parameters of the saw on the square lattice we find 2 63820 0 00004 0 00030 1 352 0 006 0 025 v 0 7590 0 0062 0 0042 where the first error bar represents systematic error due to corrections to scaling subjective 95 confidence limits and the second bar represents statistical error classical 95 confidence limits these results are based on saws of average length 166 using 340 hours cpu time on a cdc cyber 170 730 we compare our results to previous work and indicate some directions for future research

convergence rates of markov chains for some self assembly and non saturated ising models algorithms based on markov chains are ubiquitous across scientific disciplines as they provide a method for extracting statistical information about large complicated systems for some self assembly models markov chains can be used to predict both equilibrium and non equilibrium dynamics in fact the efficiency of these self assembly algorithms can be related to the rate at which simple chains converge to their stationary distribution we give an overview of the theory of markov chains and show how many natural chains including some relevant in the context of self assembly undergo a phase transition as a parameter representing temperature is varied in the model we illustrate this behavior for the non saturated ising model in which there are two types of tiles that prefer to be next to other tiles of the same type unlike the standard ising model we also allow empty spaces that are not occupied by either type of tile we prove that for a local markov chain that allows tiles to attach and detach from the lattice the rate of convergence is fast at high temperature and slow at low temperature

exponential convergence to equilibrium for a class of random walk models we prove exponential convergence to equilibrium l 2 geometric ergodicity for a random walk with inward drift on a sub cayley rooted tree this randomwalk model generalizes a monte carlo algorithm for the self avoiding walk proposed by berretti and sokal if the number of vertices of leveln in the tree grows asc n n n 1 we prove that the autocorrelation time satisfies n 2 n 1

on eigenfunctions of markov processes on trees we begin by studying the eigenvectors associated to irreducible finite birth and death processes showing that the i nontrivial eigenvector i admits a succession of i decreasing or increasing stages each of them crossing zero imbedding naturally the finite state space into a continuous segment one can unequivocally define the zeros of i which are interlaced with those of i 1 these kind of results are deduced from a general investigation of minimax multi sets dirichlet eigenproblems which leads to a direct construction of the eigenvectors associated to birth and death processes this approach can be generically extended to eigenvectors of markov processes living on trees this enables to reinterpret the eigenvalues and the eigenvectors in terms of the previous dirichlet eigenproblems and a more general conjecture is presented about related higher order cheeger inequalities finally we carefully study the geometric structure of the eigenspace associated to the spectral gap on trees

isoperimetry in two dimensional percolation we study isoperimetric sets i e sets with minimal boundary for a prescribed volume on the unique infinite connected component of supercritical bond percolation on the square lattice in the limit of the volume tending to infinity properly scaled isoperimetric sets are shown to converge in the hausdorff metric to the solution of an isoperimetric problem in 2 with respect to a particular norm as part of the proof we also show that the anchored isoperimetric profile as well as the cheeger constant of the giant component in finite boxes scale to deterministic quantities this settles a conjecture of itai benjamini for the square lattice 2015 wiley periodicals inc

the spectra of multiplicative attribute graphs abstract a multiplicative attribute graph is a random graph in which vertices are represented by random words of length t in a finite alphabet and the probability of adjacency is a symmetric function t t 0 1 these graphs are a generalization of stochastic kronecker graphs and both classes have been shown to exhibit several useful real world properties we establish asymptotic bounds on the spectra of the adjacency matrix and the normalized laplacian matrix for these two families of graphs under certain mild conditions as an application we examine various properties of the stochastic kronecker graph and the multiplicative attribute graph including the diameter clustering coefficient chromatic number and bounds on low congestion routing

proteins coexistence of stability and flexibility we introduce an equation for protein native topology based on recent analysis of data from the protein data bank and on a generalization of the landau peierls instability criterion for fractals the equation relates the protein fractal dimension df the spectral dimension ds and the number of amino acids n deviations from the equation may render a protein unfolded the fractal nature of proteins is shown to bridge their seemingly conflicting properties of stability and flexibility over 500 proteins have been analyzed df ds and n and found to obey this equation of state

protein sequence complexity revisited relationship with fractal 3d structure topological and kinetic parameters abstract the study of protein sequence complexity is not a new area and several methodological approaches are available in order to describe or represent the protein sequence information the present study explored the relationship between sequence complexity and structural fractal dimension secondary structure information number of domains and also kinetic parameters considering several methodologies our results indicate that some sequence complexity indexes are sensitive enough to differentiate native from random sequences even when the differences are small we also found that proteins with increased complexity present a higher number of domains increased length and mean solvent accessibility moreover proteins with lower complexity revealed an increased folding and unfolding constant rate interestingly we found a significant correlation between protein sequence complexity and structural fractal dimension and a significant effect of the secondary structure classes

diffusion on hierarchical systems of weakly coupled networks abstract we analyzed diffusion dynamics on weakly coupled networks interconnected networks by means of separation of time scales using an adiabatic approximation we reduced the system dynamics to a markov chain with aggregated variables and derived a transport equation that is analogous to fick s first law and includes a driving force entropy production is a sum of microscopic entropy transport which results from the particle s migration between networks of different topologies and macroscopic entropy production of the markov chain equilibrium particles partition between different sub networks depends only on internal sub network parameters by changing structure of networks one can not only modify diffusion constants but can also induce or reverse the direction of the particles flow between different networks our framework confirmed by numerical simulations is also useful for considering diffusion in nested systems corresponding to hierarchical networks with several different time scales thus it can serve to uncover hidden hierarchy levels from observations of diffusion processes

censored glauber dynamics for the mean field ising model we study glauber dynamics for the ising model on the complete graph on n vertices known as the curie weiss model it is well known that at high temperature 1 it is exp n recently levin luczak and peres considered a censored version of this dynamics which is restricted to non negative magnetization they proved that for fixed 1 the mixing time of this model is nlog n analogous to the high temperature regime of the original dynamics furthermore they showed cutoff for the original dynamics for fixed 1 the question whether the censored dynamics also exhibits cutoff remained unsettled

the spectral gap for the kawasaki dynamics at low temperature in this paper we analyze the convergence to equilibrium of kawasaki dynamics for the ising model in the phase coexistence region first we show in strict analogy with the nonconservative case that in any lattice dimension for any boundary condition and any positive temperature and particle density the spectral gap in a box of side l does not shrink faster than a negative exponential of the surface ld 1 then we prove that in two dimensions and for free boundary condition the spectral gap in a box of side l is smaller than a negative exponential of l provided that the temperature is below the critical one and the particle density satisfies where represents the particle density of the plus and minus phase respectively

self testing algorithms for self avoiding walks we present a markov chain monte carlo algorithm for almost uniformly generating and approximately counting self avoiding walks in rectangular lattices zd these are classical problems that arise for example in the study of long polymer chains while there are a number of monte carlo algorithms used to solve these problems in practice these are heuristic and their correctness relies on unproven conjectures in contrast our algorithm is shown rigorously to produce answers with specified accuracy and confidence only the efficiency of the algorithm relies on a widely believed conjecture and a novel feature is that this conjecture can be tested as the algorithm proceeds with this self testing feature incorporated the algorithm has polynomially bounded running time and is completely reliable in the sense that it either outputs answers that are guaranteed to be within the specified accuracy and confidence bounds or finds a counter example to the conjecture

exact bit error probability for optimum combining with a rayleigh fading gaussian cochannel interferer we derive expressions for the exact bit error probability bep for the detection of coherent binary phase shift keying signals of the optimum combiner employing space diversity when both the desired signal and a gaussian cochannel interferer are subject to flat rayleigh fading two different methods are employed to reach two different but numerically identical expressions with the direct method the conditional bep is averaged over the fading of both signal and interference with the moment generating function based method expressions are derived from an alternative representation of the gaussian q function

on hyperboundedness and spectrum of markov operators consider an ergodic markov operator m reversible with respect to a probability measure mu on a general measurable space it is shown that if m is bounded from mathbb l 2 mu to mathbb l p mu where p 2 then it admits a spectral gap this result answers positively a conjecture raised by hoegh krohn and simon j funct anal 9 121 80 1972 in the more restricted semi group context the proof is based on isoperimetric considerations and especially on cheeger inequalities of higher order for weighted finite graphs recently obtained by lee et al proceedings of the 2012 acm symposium on theory of computing 1131 1140 acm new york 2012 it provides a quantitative link between hyperboundedness and an eigenvalue different from the spectral gap in general in addition the usual cheeger inequality is extended to the higher eigenvalues in the compact riemannian setting and the exponential behaviors of the small eigenvalues of witten laplacians at small temperature are recovered

bounds on the spectrum for markov chains and markov processes a generalization of cheeger s inequality we prove a general version of cheeger s inequality for discrete time markov chains and continuous time markovian jump processes both reversible and nonreversible with general state space we also prove a version of cheeger s inequality for markov chains and processes with killing as an application we prove l 2 exponential convergence to equilibrium for random walk with inward drift on a class of countable rooted graphs

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

multi way dual cheeger constants and spectral bounds of graphs we introduce a set of multi way dual cheeger constants and prove universal higher order dual cheeger inequalities for eigenvalues of normalized laplace operators on weighted finite graphs our proof proposes a new spectral clustering phenomenon deduced from metrics on real projective spaces we further extend those results to a general reversible markov operator and find applications in characterizing its essential spectrum

modulus of continuity eigenvalue bounds for homogeneous graphs and convex subgraphs with applications to quantum hamiltonians abstract we adapt modulus of continuity estimates to the study of spectra of combinatorial graph laplacians as well as the dirichlet spectra of certain weighted laplacians the latter case is equivalent to stoquastic hamiltonians and is of current interest in both condensed matter physics and quantum computing in particular we introduce a new technique which bounds the spectral gap of such laplacians hamiltonians by studying the limiting behavior of the oscillations of their solutions when introduced into the heat equation our approach is based on recent advances in the pde literature which include a proof of the fundamental gap theorem by andrews and clutterbuck

metastability and the ising model we discuss a recent theorem which establishes a precise connection between i the approximate degeneracy of the zero eigenvalue for the generator of the glauber dynamics of the ising model in a small nonzero field and below the critical temperature ii the existence of a partition of the configuration space into a normal region and a metastable region this enables us to demonstrate that the recent approach to metastability of davies and martin may be viewed as a simple although in some ways fairly crude approximation to the conventional approach we also obtain what appear to be the first results concerning the stability of metastable states under small perturbations