transverse vibrations of non homogeneous orthotropic rectangular plates of variable thickness a spline technique an analysis and numerical results are presented for free transverse vibrations of non homogeneous orthotropic rectangular plates of non uniform thickness and resting on an elastic foundation of winkler type on the basis of classical plate theory the non homogeneity of the plate material is assumed to arise due to the exponential variation in young s moduli and density along one direction following levy approach i e the two parallel edges are simply supported the fourth order differential equation governing the motion of such plates of exponentially varying thickness in one direction has been solved by using the quintic splines interpolation technique for three different combinations of clamped simply supported and free boundary conditions at the other two edges effect of the non homogeneity and elastic foundation together with other plate parameters such as orthotropy aspect ratio and thickness variation on the natural frequencies of vibration is illustrated for the first three modes of vibration normalized displacements are presented for specified plates for all the three boundary conditions

skew spectra of graphs without even cycles abstract the study of the invariance of the skew spectrum of an oriented graph under different orientations leads to the special family g of graphs without even cycles basic graphical and spectral properties of g are observed as a result the hosoya index of a graph in g can be computed via its skew spectrum we also focus on friendship graphs a subfamily of g in particular the condition under which the skew spectrum of a friendship graph is actually i times the spectrum of some graph is determined where i 1

dimer monomer model on the sierpinski gasket abstract we present the numbers of dimer monomers m d n on the sierpinski gasket s g d n at stage n with dimension d equal to two three and four the upper and lower bounds for the asymptotic growth constant defined as z s g d lim v ln m d n v where v is the number of vertices on s g d n are derived in terms of the results at a certain stage as the difference between these bounds converges quickly to zero as the calculated stage increases the numerical value of z s g d can be evaluated with more than a hundred significant figures accurate from the results for d 2 3 4 we conjecture the upper and lower bounds of z s g d for general dimension the corresponding results on the generalized sierpinski gasket s g d b n with d 2 and b 3 4 are also obtained

time scales of spike train correlation for neural oscillators with common drive we examine the effect of the phase resetting curve on the transfer of correlated input signals into correlated output spikes in a class of neural models receiving noisy superthreshold stimulation we use linear response theory to approximate the spike correlation coefficient in terms of moments of the associated exit time problem and contrast the results for type i vs type ii models and across the different time scales over which spike correlations can be assessed we find that on long time scales type i oscillators transfer correlations much more efficiently than type ii oscillators on short time scales this trend reverses with the relative efficiency switching at a time scale that depends on the mean and standard deviation of input currents this switch occurs over time scales that could be exploited by downstream circuits

representational accuracy of stochastic neural populations fisher information is used to analyze the accuracy with which a neural population encodes d stimulus features it turns out that the form of response variability has a major impact on the encoding capacity and therefore plays an important role in the selection of an appropriate neural model in particular in the presence of baseline firing the reconstruction error rapidly increases with d in the case of poissonian noise but not for additive noise the existence of limited range correlations of the type found in cortical tissue yields a saturation of the fisher information content as a function of the population size only for an additive noise model we also show that random variability in the correlation coefficient within a neural population as found empirically considerably improves the average encoding quality finally the representational accuracy of populations with inhomogeneous tuning properties either with variability in the tuning widths or fragmented into specialized subpopulations is superior to the case of identical and radially symmetric tuning curves usually considered in the literature

monomer dimer problem on random planar honeycomb lattice we consider the monomer dimer md problem on a random planar honeycomb lattice model namely the random multiple chain this is a lattice system with non periodic boundary condition whose generating process is inspired by the growth of single walled zigzag carbon nanotubes by applying algebraic and combinatorial techniques we establish a calculating expression of the md partition function for bipartite graphs which corresponds to the permanent of a matrix further by using the transfer matrix argument we show that the computing problem of the permanent of high order matrix can be converted into some lower order matrices for this family of lattices based on which we derive an explicit recurrence formula for evaluating the md partition function of multiple chains and random multiple chains finally we analyze the expectation of the number of monomer dimer arrangements on a random multiple chain and the asymptotic behavior of the annealed md entropy when the multiple chain becomes infinite in width and length respectively

on the validations of the asymptotic matching conjectures in this paper we review the asymptotic matching conjectures for r regular bipartite graphs and their connections in estimating the monomer dimer entropies in d dimensional integer lattice and beth

packing dimers on 2p 1 x 2q 1 lattices we use computational method to investigate the number of ways to pack dimers on m x n lattices where both m and n are odd in this case there is always a single vacancy in the lattices we show that the dimer configuration numbers on 2k 1 x 2k 1 odd square lattices have some remarkable number theoretical properties in parallel to those of close packed dimers on 2k x 2k even square lattices for which an exact solution exists furthermore we demonstrate that there is an unambiguous logarithmic term in the finite size correction of free energy of odd by odd lattice strips with any width n or 1 this logarithmic term determines the distinct behavior of the free energy of odd square lattices these findings reveal a deep and previously unexplored connection between statistical physics models and number theory and indicate the possibility that the monomer dimer problem might be solvable

recursion transform method for computing resistance of the complex resistor network with three arbitrary boundaries we develop a general recursion transform r t method for a two dimensional resistor network with a zero resistor boundary as applications of the r t method we consider a significant example to illuminate the usefulness for calculating resistance of a rectangular m ifmmode times else texttimes fi n resistor network with a null resistor and three arbitrary boundaries a problem never solved before since green s function techniques and laplacian matrix approaches are invalid in this case looking for the exact calculation of the resistance of a binary resistor network is important but difficult in the case of an arbitrary boundary since the boundary is like a wall or trap which affects the behavior of finite network in this paper we obtain several general formulas of resistance between any two nodes in a nonregular m ifmmode times else texttimes fi n resistor network in both finite and infinite cases in particular 12 special cases are given by reducing one of the general formulas to understand its applications and meanings and an integral identity is found when we compare the equivalent resistance of two different structures of the same problem in a resistor network

a quadratic identity for the number of perfect matchings of plane graphs we present a quadratic identity on the number of perfect matchings of plane graphs by the method of graphical condensation which generalizes the results found by propp j propp generalized domino shuffling theoret comput sci 303 2003 267 301 kuo e h kuo applications of graphical condensation for enumerating matchings and tilings theoret comput sci 319 2004 29 57 and yan yeh and zhang w g yan y n yeh f j zhang graphical condensation of plane graphs a combinatorial approach theoret comput sci 349 2005 452 461

computing the numbers of independent sets and matchings of all sizes for graphs with bounded treewidth abstract in the theory and applications of graphs it is a basic problem to compute the numbers of independent sets and matchings of given sizes since the problem of computing the total number of independent sets and that of matchings of graphs is p complete it is unlikely to give efficient algorithms to find the numbers of independent sets and matchings of given sizes in this paper for graphs with order n and treewidth at most p we present two dynamic algorithms to compute the numbers of independent sets of all sizes with runtime o 2p pn3 and the numbers of matchings of all sizes with runtime o 22p pn3 respectively by the algorithms presented in this paper for graphs with small treewidths the numbers of independent sets and matchings of all possible sizes can be computed efficiently

the free vibrations of tapered rectangular plates using a new set of beam functions with the rayleigh ritz method abstract in19991999 academic pressacademic pressthis paper the free vibrations of a wide range of non uniform rectangular plates in one or two directions are considered the domain of the plate is bounded by copyright x 1a a and y 1b b in rectangular co ordinates the thickness of the plate is continuously varying and proportional to the power functionxsyt a variety of tapered rectangular plates can be described by giving the taper factors s and t different values s and t may be given arbitrary real numbers if both 1 0 and 1 0 or arbitrary non negative numbers if 1 0 or 1 0 the uniform rectangular plate is a special case by letting both s and t equal to zero a new set of admissible functions which are the static solutions of the tapered beam or a strip taken from the tapered rectangular plate under an arbitrary static load expanded into a taylor series is developed unlike conventional admissible functions the set of static beam functions will vary appropriately with the thickness variation of the plate the eigenfrequency equation is obtained by the use of the rayleigh ritz method a general computer program has been compiled and some numerical results are tabulated on the basis of comparison with available results in the literature it is shown that the first few eigenfrequencies can be obtained with good accuracy by using only a small number of terms of the static beam functions

population coding with correlation and an unfaithful model this study investigates a population decoding paradigm in which the maximum likelihood inference is based on an unfaithful decoding model umli this is usually the case for neural population decoding because the encoding process of the brain is not exactly known or because a simplified decoding model is preferred for saving computational cost we consider an unfaithful decoding model that neglects the pair wise correlation between neuronal activities and prove that umli is asymptotically efficient when the neuronal correlation is uniform or of limited range the performance of umli is compared with that of the maximum likelihood inference based on the faithful model and that of the center of mass decoding method it turns out that umli has advantages of decreasing the computational complexity remarkably and maintaining high level decoding accuracy moreover it can be implemented by a biologically feasible recurrent network pouget zhang deneve latham 1998 the effect of correlation on the decoding accuracy is also discussed

graphs determined by polynomial invariants many polynomials have been defined associated to graphs like the characteristic matchings chromatic and tutte polynomials besides their intrinsic interest they encode useful combinatorial information about the given graph it is natural then to ask to what extent any of these polynomials determines a graph and in particular whether one can find graphs that can be uniquely determined by a given polynomial in this paper we survey known results in this area and at the same time we present some new results

fa yueh wu s contributions in physics abstract we sketch a subset of professor f y wu s contributions in lattice statistical mechanics solid state physics graph theory enumerative combinatorics and other domains of physics and mathematics we will recall some of f y wu s most important and well known classic results and we will also sketch some of his most recent researches dedicated to the connections of lattice statistical mechanical models with deep problems in pure mathematics

enumeration of spanning trees in planar unclustered networks abstract among a variety of subgraphs spanning trees are one of the most important and fundamental categories they are relevant to diverse aspects of networks including reliability transport self organized criticality loop erased random walks and so on in this paper we introduce a family of modular self similar planar networks with zero clustering relevant properties of this family are comparable to those networks associated with technological systems having low clustering like power grids some electronic circuits the internet and some biological systems so it is very significant to research on spanning trees of planar networks however for a large network evaluating the relevant determinant is intractable in this paper we propose a fairly generic linear algorithm for counting the number of spanning trees of a planar network using the algorithm we derive analytically the exact numbers of spanning trees in planar networks our result shows that the computational complexity is o t which is better than that of the matrix tree theorem with o m 2 t 2 where t is the number of steps and m is the girth of the planar network we also obtain the entropy for the spanning trees of a given planar network we find that the entropy of spanning trees in the studied network is small which is in sharp contrast to the previous result for planar networks with the same average degree we also determine an upper bound and a lower bound for the numbers of spanning trees in the family of planar networks by the algorithm as another application of the algorithm we give a formula for the number of spanning trees in an outerplanar network with small world features

amplitude ratios for critical systems in the c 2 universality class we study the finite size corrections of the critical dense polymer cdp and the dimer models on n rectangular lattice we find that the finite size corrections in the cdp and dimer models depend in a crucial way on the parity of n and a change of the parity of n is equivalent to the change of boundary conditions we present a set of universal amplitude ratios for amplitudes in finite size correction terms of critical systems in the universality class with central charge c 2 the results are in perfect agreement with a perturbated conformal field theory under the assumption that all analytical corrections coming from the operators which belongs to the tower of the identity our results inspire many interesting problems for further studies

decorrelation of spiking variability and improved information transfer through feedforward divisive normalization response variability is often positively correlated in pairs of similarly tuned neurons in the visual cortex many authors have considered correlated variability to prevent postsynaptic neurons from averaging across large groups of inputs to obtain reliable stimulus estimates however a simple average of variability ignores nonlinearities in cortical signal integration this study shows that feedforward divisive normalization of a neuron s inputs effectively decorrelates their variability furthermore we show that optimal linear estimates of a stimulus parameter that are based on normalized inputs are more accurate than those based on nonnormalized inputs due partly to reduced correlations and that these estimates improve with increasing population size up to several thousand neurons this suggests that neurons may possess a simple mechanism for substantially decorrelating noise in their inputs further work is needed to reconcile this conclusion with past evidence that correlated noise impairs visual perception

grassmannian representation of the two dimensional monomer dimer model we present an application of the grassmann algebra to the problem of the monomer dimer statistics on a two dimensional square lattice the exact partition function or total number of possible configurations of a system of dimers with a finite set of n monomers at fixed positions can be expressed via a quadratic fermionic theory we give an answer in terms of a product of two pfaffians and the solution is closely related to the kasteleyn result of the pure dimer problem correlation functions are in agreement with previous results both for monomers on the boundary where a simple exact expression is available in the discrete and continuous case and in the bulk where the expression is evaluated numerically

on the hosoya index of a family of deterministic recursive trees abstract in this paper we calculate the hosoya index in a family of deterministic recursive trees with a special feature that includes new nodes which are connected to existing nodes with a certain rule we then obtain a recursive solution of the hosoya index based on the operations of a determinant the computational complexity of our proposed algorithm is o log 2 n with n being the network size which is lower than that of the existing numerical methods finally we give a weighted tree shrinking method as a graphical interpretation of the recurrence formula for the hosoya index

stimulus dependent correlations and population codes the magnitude of correlations between stimulus driven responses of pairs of neurons can itself be stimulus dependent we examine how this dependence affects the information carried by neural populations about the stimuli that drive them stimulus dependent changes in correlations can both carry information directly and modulate the information separately carried by the firing rates and variances we use fisher information to quantify these effects and show that although stimulus dependent correlations often carry little information directly their modulatory effects on the overall information can be large in particular if the stimulus dependence is such that correlations increase with stimulus induced firing rates this can significantly enhance the information of the population when the structure of correlations is determined solely by the stimulus however in the presence of additional strong spatial decay of correlations such stimulus dependence may have a negative impact opposite relationships hold when correlations decrease with firing rates

a causal perspective on the analysis of signal and noise correlations and their role in population coding the role of correlations between neuronal responses is crucial to understanding the neural code a framework used to study this role comprises a breakdown of the mutual information between stimuli and responses into terms that aim to account for different coding modalities and the distinction between different notions of independence here we complete the list of types of independence and distinguish activity independence related to total correlations conditional independence related to noise correlations signal independence related to signal correlations coding independence related to information transmission and information independence related to redundancy for each type we identify the probabilistic criterion that defines it indicate the information theoretic measure used as statistic to test for it and provide a graphical criterion to recognize the causal configurations of stimuli and responses that lead to its existence using this causal analysis we first provide sufficiency conditions relating these types second we differentiate the use of the measures as statistics to test for the existence of independence from their use for quantification we indicate that signal and noise correlation cannot be quantified separately third we explicitly define alternative system configurations used to construct the measures in which noise correlations or noise and signal correlations are eliminated accordingly we examine which measures are meaningful only as a comparison across configurations and which ones provide a characterization of the actually observed responses without resorting to other configurations fourth we compare the commonly used nonparametric approach to eliminate noise correlations with a functional model based approach showing that the former approach does not remove those effects of noise correlations captured by the tuning properties of the individual neurons and implies nonlocal causal structure manipulations these results improve the interpretation of the measures on the framework and help in understanding how to apply it to analyze the role of correlations

population coding in neuronal systems with correlated noise neuronal representations of external events are often distributed across large populations of cells we study the effect of correlated noise on the accuracy of these neuronal population codes our main question is whether the inherent error in the population code can be suppressed by increasing the size of the population n in the presence of correlated noise we address this issue using a model of a population of neurons that are broadly tuned to an angular variable in two dimensions the fluctuations in the neuronal activities are modeled as gaussian noises with pairwise correlations that decay exponentially with the difference between the preferred angles of the correlated cells we assume that the system is broadly tuned which means that both the correlation length and the width of the tuning curves of the mean responses span a substantial fraction of the entire system length the performance of the system is measured by the fisher information fi which bounds its estimation error by calculating the fi in the limit of a large n we show that positive correlations decrease the estimation capability of the network relative to the uncorrelated population the information capacity saturates to a finite value as the number of cells in the population grows in contrast negative correlations substantially increase the information capacity of the neuronal population these results are supplemented by the effect of correlations on the mutual information of the system our analysis provides an estimate of the effective number of statistically independent degrees of freedom denoted n mathrm eff that a large correlated system can have according to our theory n mathrm eff remains finite in the limit of a large n estimating the parameters of the correlations and tuning curves from experimental data in some cortical areas that code for angles we predict that the number of effective degrees of freedom embedded in localized populations in these areas is less than or of the order of ensuremath approx 10 2

a pfaffian formula for monomer dimer partition functions we consider the monomer dimer partition function on arbitrary finite planar graphs and arbitrary monomer and dimer weights with the restriction that the only non zero monomer weights are those on the boundary we prove a pfaffian formula for the corresponding partition function as a consequence of this result multipoint boundary monomer correlation functions at close packing are shown to satisfy fermionic statistics our proof is based on the celebrated kasteleyn theorem combined with a theorem on pfaffians proved by one of the authors and a careful labeling and directing procedure of the vertices and edges of the graph

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

the complexity of counting in sparse regular and planar graphs we show that a number of graph theoretic counting problems remain cal np hard indeed cal p complete in very restricted classes of graphs in particular we prove that the problems of counting matchings vertex covers independent sets and extremal variants of these all remain hard when restricted to planar bipartite graphs of bounded degree or regular graphs of constant degree we obtain corollaries about counting cliques in restricted classes of graphs and counting satisfying assignments to restricted classes of monotone 2 cnf formulae to achieve these results a new interpolation based reduction technique which preserves properties such as constant degree is introduced

correlation transfer in stochastically driven neural oscillators over long and short time scales in the absence of synaptic coupling two or more neural oscillators may become synchronized by virtue of the statistical correlations in their noisy input streams recent work has shown that the degree of correlation transfer from input currents to output spikes depends not only on intrinsic oscillator dynamics but also on the length of the observation window over which the correlation is calculated in this paper we use stochastic phase reduction and regular perturbations to derive the correlation of the total phase elapsed over long time scales a quantity that provides a convenient proxy for the spike count correlation over short time scales we derive the spike count correlation directly using straightforward probabilistic reasoning applied to the density of the phase difference our approximations show that output correlation scales with the autocorrelation of the phase resetting curve over long time scales we also find a concise expression for the influence of the shape of the phase resetting curve on the initial slope of the output correlation over short time scales these analytic results together with numerical simulations provide new intuitions for the recent counterintuitive finding that type i oscillators transfer correlations more faithfully than do type ii over long time scales while the reverse holds true for the better understood case of short time scales

vibration of elastically restrained cross ply laminated plates with variable thickness abstract the natural frequencies of symmetrically laminated plates of variable thickness are analyzed using the finite strip transition matrix technique in this paper the natural frequencies of such plates are determined for edges with being elastically restrained against both rotation and transition or both a successive conjunction of the classical finite strip method and the transition matrix method is applied to develop a new modification of the finite strip method to reduce the complexity of the problem the displacement function is expressed as the product of a basic trigonometric series function in the longitudinal direction and an unknown function that has to be determined in the other direction using the new transition matrix after necessary simplification and the satisfaction of the boundary conditions yields a set of simultaneous equations that leads to the characteristic matrix of vibration the mode shapes and the frequency parameters for different combinations of elastic or translational restraint coefficients have been presented and compared with those available from other methods in the literature also the effect of the tapered ratio and the aspect ratio on the natural frequencies and the mode shapes of the plates are presented the good agreement with other methods demonstrates the validity and the reliability of the proposed method

dimers on a simple quartic net with a vacancy a seminal milestone in lattice statistics is the exact solution of the enumeration of dimers on a simple quartic net obtained by fisher kasteleyn and temperley fkt in 1961 an outstanding related and yet unsolved problem is the enumeration of dimers on a net with vacant sites here we consider this vacant site problem with a single vacancy occurring at certain specific sites on the boundary of a simple quartic net first using a bijection between dimer and spanning tree configurations due to temperley kenyon propp and wilson we establish that the dimer generating function is independent of the location of the vacancy and deduce a closed form expression for the generating function we next carry out finite size analyses of this solution as well as that of the fkt solution our analyses lead to a logarithmic correction term in the large size expansion for the vacancy problem with free boundary conditions a concrete example exhibiting this difference is given we also find the central charge c 2 in the language of conformal field theory for the vacancy problem as versus the value c 1 when there is no vacancy

two dimensional monomer dimer systems are computationally intractable the classic problem of counting monomer dimer arrangements on a two dimensional lattice is analyzed using techniques from theoretical computer science under a certain assumption made precise in the text it can be shown that the general problem is computationally intractable this negative result contrasts with the special case of a system with monomer density zero for which efficient solutions have been known for some time a second much easier result obtained under the same assumption is that the partition function of a three dimensional ising system is computationally intractable again the negative result contrasts with known efficient techniques for evaluating the partition function of a two dimensional system

logarithmic corrections in the free energy of monomer dimer model on plane lattices with free boundaries using exact computations we study the classical hard core monomer dimer models on m x n plane lattice strips with free boundaries for an arbitrary number v of monomers or vacancies we found a logarithmic correction term in the finite size correction of the free energy per lattice site the coefficient of the logarithmic correction term depends on the number of monomers present v and the parity of the width n of the lattice strip the coefficient equals to v when n is odd and v 2 when n is even the results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers we also study the finite size correction in the low dimer density limit where the number of dimers d is fixed in this case the coefficient of the logarithmic correction term equals to d for both odd and even n

long range properties of spanning trees we compute some large scale properties of the uniform spanning tree process on bounded regions in z2 in particular we compute the distribution of the meeting point of the branches of the tree issued from three boundary points we also compute the crossing probabilities of branches of the tree on rectangular and annular regions as well as the winding number of the branches of the tree

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

pfaffian solution of a dimer monomer problem single monomer on the boundary we consider the dimer monomer problem for the rectangular lattice by mapping the problem into one of close packed dimers on an extended lattice we rederive the tzeng wu solution for a single monomer on the boundary by evaluating a pfaffian we also clarify the mathematical content of the tzeng wu solution by identifying it as the product of the nonzero eigenvalues of the kasteleyn matrix

holographic algorithms the power of dimensionality resolved valiant s theory of holographic algorithms is a novel methodology to achieve exponential speed ups in computation a fundamental parameter in holographic algorithms is the dimension of the linear basis vectors we completely resolve the problem of the power of higher dimensional bases we prove that 2 dimensional bases are universal for holographic algorithms

nonlinear population codes theoretical and experimental studies of distributed neuronal representations of sensory and behavioral variables usually assume that the tuning of the mean firing rates is the main source of information however recent theoretical studies have investigated the effect of crosscorrelations in the trial to trial fluctuations of the neuronal responses on the accuracy of the representation assuming that only the first order statistics of the neuronal responses are tuned to the stimulus these studies have shown that in the presence of correlations similar to those observed experimentally in cortical ensembles of neurons the amount of information in the population is limited yielding nonzero error levels even in the limit of infinitely large populations of neurons in this letter we study correlated neuronal populations whose higher order statistics and in particular response variances are also modulated by the stimulus we ask two questions does the correlated noise limit the accuracy of the neuronal representation of the stimulus and how can a biological mechanism extract most of the information embedded in the higher order statistics of the neuronal responses specifically we address these questions in the context of a population of neurons coding an angular variable we show that the information embedded in the variances grows linearly with the population size despite the presence of strong correlated noise this information cannot be extracted by linear readout schemes including the linear population vector instead we propose a bilinear readout scheme that involves spatial decorrelation quadratic non linearity and population vector summation we show that this nonlinear population vector scheme yields accurate estimates of stimulus parameters with an efficiency that grows linearly with the population size this code can be implemented using biologically plausible neurons

ensemble inhibition and excitation in the human cortex an ising model analysis with uncertainties the pairwise maximum entropy model also known as the ising model has been widely used to analyze the collective activity of neurons however controversy persists in the literature about seemingly inconsistent findings whose significance is unclear due to lack of reliable error estimates we therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive markov chain monte carlo after the convergence of the main optimization algorithm we apply our method to the activity patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake sleep cycle our analysis shows that the ising model captures neuronal collective behavior much better than the independent model during wakefulness light sleep and deep sleep when both excitatory e and inhibitory i neurons are modeled ignoring the inhibitory effects of i neurons dramatically overestimates synchrony among e neurons furthermore information theoretic measures reveal that the ising model explains about 80 95 of the correlations depending on sleep state and neuron type thermodynamic measures show signatures of criticality although we take this with a grain of salt as it may be merely a reflection of long range neural correlations

monomer dimer model on a scale free small world network abstract the explicit determination of the number of monomer dimer arrangements on a network is a theoretical challenge and exact solutions to monomer dimer problem are available only for few limiting graphs with a single monomer on the boundary e g rectangular lattice and quartic lattice however analytical research even numerical result for monomer dimer problem on scale free small world networks is still missing despite the fact that a vast variety of real systems display simultaneously scale free and small world structures in this paper we address the monomer dimer problem defined on a scale free small world network and obtain the exact formula for the number of all possible monomer dimer arrangements on the network based on which we also determine the asymptotic growth constant of the number of monomer dimer arrangements in the network we show that the obtained asymptotic growth constant is much less than its counterparts corresponding to two dimensional lattice and sierpinski fractal having the same average degree as the studied network which indicates from another aspect that scale free networks have a fundamentally distinct architecture as opposed to regular lattices and fractals without power law behavior

boundary monomers in the dimer model the correlation functions of an arbitrary number of boundary monomers in the system of close packed dimers on the square lattice are computed exactly in the scaling limit the equivalence of the 2n point correlation functions with those of a complex free fermion is proved thereby reinforcing the description of the monomer dimer model by a conformal free field theory with central charge c 1 comment 15 pages 2 figures

finite size effects for the ising model on helical tori we analyze the exact partition function of the ising model on a square lattice under helical boundary conditions obtained by liaw et al phys rev e 73 055101 r 2006 based on such an expression we then extend the algorithm of ivashkevich izmailian and hu j phys a 35 5543 2002 to derive an exact asymptotic expansion of the logarithm of the partition function and its first to fourth derivatives at the critical point from such results we find that the shift exponent for the specific heat is ensuremath lambda 1 for all values of the helicity factor d we also find that finite size corrections for the free energy the internal energy and the specific heat of the model in a crucial way depend on the helicity factor of the lattice

vacancy localization in the square dimer model we study the classical dimer model on a square lattice with a single vacancy by developing a graph theoretic classification of the set of all configurations which extends the spanning tree formulation of close packed dimers with this formalism we can address the question of the possible motion of the vacancy induced by dimer slidings we find a probability 57 4 ensuremath 10 sqrt 2 for the vacancy to be strictly jammed in an infinite system more generally the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 9 8 on a finite system the probability that a vacancy in the bulk can reach the boundary falls off as a power law of the system size with exponent 1 4 the resultant weak localization of vacancies still allows for unbounded diffusion characterized by a diffusion exponent that we relate to that of diffusion on spanning trees we also implement numerical simulations of the model with both free and periodic boundary conditions

dimer coverings on the sierpinski gasket we present the number of dimer coverings nd n on the sierpinski gasket sgd n at stage n with dimension d equal to two three four or five when the number of vertices denoted as v n of the sierpinski gasket is an even number nd n is the number of close packed dimers when the number of vertices is an odd number no close packed configurations are possible and we allow one of the outmost vertices uncovered the entropy of absorption of diatomic molecules per site defined as s mathit sg d lim n to infty ln n d n v n is calculated to be ln 2 3 exactly for sg2 the numbers of dimers on the generalized sierpinski gasket sgd b n with d 2 and b 3 4 5 are also obtained exactly with entropies equal to ln 6 7 ln 28 12 ln 200 18 respectively the number of dimer coverings for sg3 is given by an exact product expression such that its entropy is given by an exact summation expression the upper and lower bounds for the entropy are derived in terms of the results at a certain stage for sgd n with d 3 4 5 as the difference between these bounds converges quickly to zero as the calculated stage increases the numerical value of s mathit sg d with d 3 4 5 can be evaluated with more than a hundred significant figures accurate

monomer dimer problem on some networks abstract zhang et al 2012 obtained the exact formula for the number of all possible monomer dimer arrangements and the asymptotic growth constant on a scale free small world network in this note we generalize this result and obtain the exact solution on the monomer dimer model on many networks particularly we prove that these networks have the same asymptotic growth constant of the number of monomer dimer arrangements

counting spanning trees in a small world farey graph the problem of spanning trees is closely related to various interesting problems in the area of statistical physics but determining the number of spanning trees in general networks is computationally intractable in this paper we perform a study on the enumeration of spanning trees in a specific small world network with an exponential distribution of vertex degrees which is called a farey graph since it is associated with the famous farey sequence according to the particular network structure we provide some recursive relations governing the laplacian characteristic polynomials of a farey graph and its subgraphs then making use of these relations obtained here we derive the exact number of spanning trees in the farey graph as well as an approximate numerical solution for the asymptotic growth constant characterizing the network finally we compare our results with those of different types of networks previously investigated

approximating the permanent via importance sampling with application to the dimer covering problem we estimate the asymptotic growth rate of the number of dimer covers of a cubic lattice our estimate 3 0 4466 0 0006 is consistent with the lower bounds obtained by hammersley and later schrijver and the more recent improved upper bound obtained by ciucu obtaining this estimate is an important step toward approximating the partition function of the cubic monomer dimer system from the partition function all of the standard thermodynamic quantities can be evaluated it is well known that computing 3 is equivalent to computing the permanent of a certain 0 1 matrix we describe an extremely efficient monte carlo algorithm for approximating the permanent previous work on monte carlo approaches includes the pioneering results of jerrum and sinclair who use a rapidly mixing random walk our method is inspired by results of soules on convergence of sinkhorn balancing to obtain a maximum entropy doubly stochastic matrix we use the sinkhorn balanced matrix to generate an importance function that allows us to do direct random sampling rather than a random walk that converges to a limiting distribution

approximating the number of monomer dimer coverings of a lattice we study the problem of counting the number of coverings of ad dimensional rectangular lattice by a specified number of monomers and dimers this problem arises in several models in statistical physics and has been widely studied a classical technique due to fisher kasteleyn and temperley solves the problem exactly in two dimensions when the number of monomers is zero the dimer covering problem but is not applicable in higher dimensions or in the presence of monomers this paper presents the first provably polynomial time approximation algorithms for computing the number of coverings with any specified number of monomers ind dimensional rectangular lattices with periodic boundaries for any fixed dimensiond and in two dimensional lattices with fixed boundaries the algorithms are based on monte carlo simulation of a suitable markov chain and in constrast to most monte carlo algorithms in statistical physics have rigorously derived performance guarantees that do not rely on any assumptions the method generalizes to counting coverings of any finite vertex transitive graph a class which includes most natural finite lattices with periodic boundary conditions