analytical and belief propagation studies of random constraint satisfaction problems with growing domains we study solution space structure and solution finding algorithms of a representative hard random constraint satisfaction problem with growing domains known as model rb using rigorous methods we show that solutions are grouped into disconnected clusters before the theoretical satisfiability phase transition point using the cavity method it is shown that the entropy density obtained by belief propagation bp on random model rb instances which corresponds well to the analytical results vanishes as the control parameter constraint tightness approaches the satisfiability threshold from an algorithmic point of view we find that reinforced bp which performs much better than all existing algorithms allows us to find solutions efficiently for instances in the regime that is very close to the satisfiability transition these results also can shed light on the effectiveness of bp reinforcement on problems with a large number of states

the normalized correlation accounting for binaural detection across center frequency bernstein and trahiotis l r bernstein and c trahiotis j acoust soc am 100 1754 1763 1996 recently reported the results of experiments designed to determine the form of interaural correlation that accounts for listeners sensitivities to interaural disparities within high frequency stimuli overall those results demonstrated that listeners abilities to discriminate changes in the interaural correlation of the envelope from a base correlation of 1 0 were well accounted for by the use of the normalized correlation the purpose of this study was to determine how well the normalized correlation computed subsequent to half wave rectification and low pass filtering could account for binaural detection data at low intermediate and high frequencies respectively in a four interval two alternative task listeners detected which interval contained a tone between 500 hz and 2 khz added antiphasically to diotic 100 hz wide noise nos nonsignal intervals contained the tone added homophasically noso performance was measured for signal to noise ratios between 30 and 30 db results indicated that a low pass filter function based on physiological measures of synchrony in cochlear nerve fibers in conjunction with the assumption of half wave square law rectification accounted for typically 80 of the variance in the behavioral data

a discrete multiple scales analysis of a discrete version of the korteweg de vries equation abstract a more elaborate discrete multiple scales analysis than that used by newell in 1977 is performed on the zabusky kruskal discretization of the korteweg de vries kdv equation this eventually leads to a set of partial difference equations describing the modulational behavior of a small harmonic wave modulated by a slowly varying envelope in the case of certain modes of the carrier wave the multiple scales analysis breaks down indicating that in these cases the numerical solution deviates in behavior from that of the kdv equation numerical experiments are reported which confirm this

controllability and maximum matchings of complex networks previously the controllability problem of a linear time invariant dynamical system was mapped to the maximum matching mm problem on the bipartite representation of the underlying directed graph and the sizes of mms on random bipartite graphs were calculated analytically with the cavity method at zero temperature limit here we present an alternative theory to estimate mm sizes based on the core percolation theory and the perfect matching of cores our theory is much more simplified and easily interpreted and can estimate mm sizes on random graphs with or without symmetry between out and in degree distributions our result helps to illuminate the fundamental connection between the controllability problem and the underlying structure of complex systems

the effect of spatial separation on informational and energetic masking of speech the effect of spatial separation of sources on the masking of a speech signal was investigated for three types of maskers ranging from energetic to informational normal hearing listeners performed a closed set speech identification task in the presence of a masker at various signal to noise ratios stimuli were presented in a quiet sound field the signal was played from 0 azimuth and a masker was played either from the same location or from 90 to the right signals and maskers were derived from sentences that were preprocessed by a modified cochlear implant simulation program that filtered each sentence into 15 frequency bands extracted the envelopes from each band and used these envelopes to modulate pure tones at the center frequencies of the bands in each trial the signal was generated by summing together eight randomly selected frequency bands from the preprocessed signal sentence three maskers were derived from the preprocessed masker sentences 1 different band sentence which was generated by summing together six randomly selected frequency bands out of the seven bands not present in the signal resulting in primarily informational masking 2 different band noise which was generated by convolving the different band sentence with gaussian noise and 3 same band noise which was generated by summing the same eight bands from the preprocessed masker sentence that were used in the signal sentence and convolving the result with gaussian noise resulting in primarily energetic masking results revealed that in the different band sentence masker the effect of spatial separation averaged 18 db at 51 correct while in the different band and same band noise maskers the effect was less than 10 db these results suggest that in these conditions the advantage due to spatial separation of sources is greater for informational masking than for energetic masking

statistical mechanics of the vertex cover problem we review recent progress in the study of the vertex cover problem vc the vc belongs to the class of np complete graph theoretical problems which plays a central role in theoretical computer science on ensembles of random graphs vc exhibits a coverable uncoverable phase transition very close to this transition depending on the solution algorithm easy hard transitions in the typical running time of the algorithms occur we explain a statistical mechanics approach which works by mapping the vc to a hard core lattice gas and then applying techniques such as the replica trick or the cavity approach using these methods the phase diagram of the vc could be obtained exactly for connectivities c e the solution of the vc exhibits full replica symmetry breaking the statistical mechanics approach can also be used to study analytically the typical running time of simple complete and incomplete algorithms for the vc finally we describe recent results for the vc when studied on other ensembles of finite and infinite dimensional graphs

ground state entropy of the random vertex cover problem counting the number of ground states for a spin glass or nondeterministic polynomial complete combinatorial optimization problem is even more difficult than the already hard task of finding a single ground state in this paper the entropy of minimum vertex covers of random graphs is estimated through a set of iterative equations based on the cavity method of statistical mechanics during the iteration both the cavity entropy contributions and cavity magnetizations for each vertex are updated this approach overcomes the difficulty of iterative divergence encountered in the zero temperature first step replica symmetry breaking 1rsb spin glass theory it is still applicable when the 1rsb mean field theory is no longer stable the method can be extended to compute the entropies of ground states and metastable minimal energy states for other random graph spin glass systems

t 0 mean field population dynamics approach for the random 3 satisfiability problem during the past decade phase transition phenomena in the random 3 satisfiability 3 sat problem has been intensively studied by statistical physics methods in this work we study the random 3 sat problem by the mean field first step replica symmetry broken cavity theory at the limit of temperature t 0 the reweighting parameter y of the cavity theory is allowed to approach infinity together with the inverse temperature beta with fixed ratio r y beta focusing on the system s space of satisfiable configurations we carry out extensive population dynamics simulations using the technique of importance sampling and we obtain the entropy density s r and complexity sigma r of zero energy clusters at different r values we demonstrate that the population dynamics may reach different fixed points with different types of initial conditions by knowing the trends of s r and sigma r with r we can judge whether a certain type of initial condition is appropriate at a given r value this work complements and confirms the results of several other very recent theoretical studies

performance of modularity maximization in practical contexts although widely used in practice the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts here we present a broad characterization of its performance in such situations first we revisit and clarify the resolution limit phenomenon for modularity maximization second we show that the modularity function q exhibits extreme degeneracies it typically admits an exponential number of distinct high scoring solutions and typically lacks a clear global maximum third we derive the limiting behavior of the maximum modularity q max for one model of infinitely modular networks showing that it depends strongly both on the size of the network and on the number of modules it contains finally using three real world metabolic networks as examples we show that the degenerate solutions can fundamentally disagree on many but not all partition properties such as the composition of the largest modules and the distribution of module sizes these results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts they also explain why many heuristics are often successful at finding high scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network we conclude by discussing avenues for mitigating some of these behaviors such as combining information from many degenerate solutions or using generative models

high frequency induced instability in nystrom methods for the van der pol equation in this paper several nystrom methods for the van der pol equation are considered in an earlier study by cai aoyagi and abe it was shown that the second order nystrom or leapfrog method fails to approximate the limit cycle of the van der pol equation exhibiting a periodic modulation of the amplitude and sporadic high frequency noise instead cai et al did a linear analysis and concluded that the spurious behavior was due to the interaction of the main part of the solution with a high frequency computational mode in this paper we also apply a third and fourth order nystrom method to the van der pol equation numerical experiments show that in these cases the high frequency mode causes blowup after some time the onset of the instability can be delayed by decreasing the time step we also improve on their analysis of the second order scheme by doing a nonlinear analysis to wit a discrete multiple scales analysis by this means we are able to explain the spurious behavior of this system completely

the effect of tone vocoding on spatial release from masking for old hearing impaired listeners old hearing impaired listeners generally benefit little from lateral separation of multiple talkers when listening to one of them this study aimed to determine how spatial release from masking srm in such listeners is affected when the interaural time differences itds in the temporal fine structure tfs are manipulated by tone vocoding tvc at the ears by a master hearing aid system word recall was compared with and without tvc when target and masker sentences from a closed set were played simultaneously from the front loudspeaker co located and when the maskers were played 45 to the left and right of the listener separated for 20 hearing impaired listeners aged 64 to 86 srm was 3 7 db smaller with tvc than without tvc this difference in srm correlated with mean audiometric thresholds below 1 5 khz even when monaural tfs sensitivity discrimination of frequency shifts in identically filtered complexes was partialed out suggesting that low frequency audiometric thresholds may be a good indicator of candidacy for hearing aids that preserve itds the tvc difference in srm was not correlated with age pure tone itd thresholds nor fundamental frequency difference limens and only with monaural tfs sensitivity before control for low frequency audiometric thresholds

typical approximation performance for maximum coverage problem this study investigated the typical performance of approximation algorithms known as belief propagation the greedy algorithm and linear programming relaxation for maximum coverage problems in sparse biregular random graphs after we used the cavity method for a corresponding hard core lattice gas model results showed that two distinct thresholds of replica symmetry and its breaking exist in the typical performance threshold of belief propagation in the low density region the superiority of three algorithms in terms of a typical performance threshold is obtained by some theoretical analyses although the greedy algorithm and linear programming relaxation have the same approximation ratio in worst case performance their typical performance thresholds are mutually different indicating the importance of typical performance results of numerical simulations validate the theoretical analyses and imply further mutual relations of approximation algorithms

near optimal configurations in mean field disordered systems we present a general technique to compute how the energy of a configuration varies as a function of its overlap with the ground state in the case of optimization problems our approach is based on a generalization of the cavity method to a system interacting with its ground state with this technique we study the random matching problem as well as the mean field diluted spin glass as a by product of this approach we calculate the de almeida thouless transition line of the spin glass on a fixed connectivity random graph

prediction of speech intelligibility in spatial noise and reverberation for normal hearing and hearing impaired listeners binaural speech intelligibility of individual listeners under realistic conditions was predicted using a model consisting of a gammatone filter bank an independent equalization cancellation ec process in each frequency band a gammatone resynthesis and the speech intelligibility index sii hearing loss was simulated by adding uncorrelated masking noises according to the pure tone audiogram to the ear channels speech intelligibility measurements were carried out with 8 normal hearing and 15 hearing impaired listeners collecting speech reception threshold srt data for three different room acoustic conditions anechoic office room cafeteria hall and eight directions of a single noise source speech in front artificial ec processing errors derived from binaural masking level difference data using pure tones were incorporated into the model except for an adjustment of the sii to intelligibility mapping function no model parameter was fitted to the srt data of this study the overall correlation coefficient between predicted and observed srts was 0 95 the dependence of the srt of an individual listener on the noise direction and on room acoustics was predicted with a median correlation coefficient of 0 91 the effect of individual hearing impairment was predicted with a median correlation coefficient of 0 95 however for mild hearing losses the release from masking was overestimated

predicting binaural speech intelligibility using the signal to noise ratio in the envelope power spectrum domain this study proposes a binaural extension to the multi resolution speech based envelope power spectrum model mr sepsm jorgensen ewert and dau 2013 j acoust soc am 134 436 446 it consists of a combination of better ear be and binaural unmasking processes implemented as two monaural realizations of the mr sepsm combined with a short term equalization cancellation process and uses the signal to noise ratio in the envelope domain snrenv as the decision metric the model requires only two parameters to be fitted per speech material and does not require an explicit frequency weighting the model was validated against three data sets from the literature which covered the following effects the number of maskers the masker types speech shaped noise ssn speech modulated ssn babble and reversed speech the masker s azimuths reverberation on the target and masker and the interaural time difference of the target and masker the pearson correlation coefficient between the simulated spee

statistical mechanics of maximal independent sets the graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory a maximal independent set is defined by the set of occupied nodes that satisfy some packing and covering constraints it is known that finding minimum and maximum density maximal independent sets are hard optimization problems in this paper we use cavity method of statistical physics and monte carlo simulations to study the corresponding constraint satisfaction problem on random graphs we obtain the entropy of maximal independent sets within the replica symmetric and one step replica symmetry breaking frameworks shedding light on the metric structure of the landscape of solutions and suggesting a class of possible algorithms this is of particular relevance for the application to the study of strategic interactions in social and economic networks where maximal independent sets correspond to pure nash equilibria of a graphical game of public goods allocation

the effect of spatial separation in distance on the intelligibility of speech in rooms the influence of spatial separation in source distance on speech reception thresholds srts is investigated in one scenario the target was presented at 0 5 m distance and the masker varied from 0 5 m distance up to 10 m in a second scenario the masker was presented at 0 5 m distance and the target distance varied the stimuli were synthesized using convolution with binaural room impulse responses brirs measured on a dummy head in a reverberant auditorium and were equalized to compensate for distance dependent spectral and intensity changes all sources were simulated directly in front of the listener srts decreased monotonically when the target was at 0 5 m and the speech masker was moved further away resulting in a srt improvement of up to 10 db when the speech masker was at 0 5 m and the target was moved away a large variation across subjects was observed neither short term signal to noise ratio snr improvements nor cross ear glimpsing could account for the observed improvement in intelligibility however the effect might be explained by an improvement in the snr in the modulation domain and a decrease in informational masking this study demonstrates that distance related cues can play a significant role when listening in complex environments

statistical mechanics of the minimum vertex cover problem in stochastic block models the minimum vertex cover min vc problem is a well known np hard problem earlier studies illustrate that the problem defined over the erdos renyi random graph with a mean degree c exhibits computational difficulty in searching the min vc set above a critical point c e 2 718 here we address how this difficulty is influenced by the mesoscopic structures of graphs for this we evaluate the critical condition of difficulty for the stochastic block model we perform a detailed examination of the specific cases of two equal size communities characterized by in and out degrees which are denoted by c in and c out respectively our analysis based on the cavity method indicates that the solution search once becomes difficult when c in c out exceeds e from below but becomes easy again when c out is sufficiently larger than c in in the region c out e experiments based on various search algorithms support the theoretical prediction

spin glass model for the c dismantling problem c dismantling cd problem aims at finding the minimum vertex set d of a graph g v e after removing which the remaining graph will break into connected components with the size not larger than c in this paper we introduce a spin glass model with c 1 integer value states into the cd problem and then study the properties of this spin glass model by the belief propagation bp equations under the replica symmetry ansatz we give the lower bound rho c of the relative size of d with finite c on regular random graphs and erdos renyi random graphs we find rho c will decrease gradually with growing c and it converges to rho infty as c to infty the cd problem is called dismantling problem when c is a small finite fraction of v therefore rho infty is also the lower bound of the dismantling problem when v to infty to reduce the computation complexity of the bp equations taking the knowledge of the probability of a random selected vertex belonging to a remaining connected component with the size a the original bp equations can be simplified to one with only three states when c to infty the simplified bp equations are very similar to the bp equations of the feedback vertex set spin glass model h j zhou eur phys j b 86 455 2013 at last we develop two practical belief propagation guide decimation algorithms based on the original bp equations cd bpd and the simplified bp equations scd bpd to solve the cd problem on a certain graph our bpd algorithms and two other state of art heuristic algorithms are applied on various random graphs and some real world networks computation results show that the cd bpd is the best in all tested algorithms in the case of small c but considering the performance and computation consumption we recommend using scd bpd for the network with small clustering coefficient when c is large

fault tolerance of random graphs with respect to connectivity mean field approximation for semidense random graphs the fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated which relates to the reliability of wireless sensor networks with unreliable relay nodes the model evaluates the network breakdown probability that a graph is disconnected after stochastic node removal to establish a mean field approximation for the model we propose the cavity method for finite systems the analysis enables us to obtain an approximation formula for random graphs with any number of nodes and an arbitrary degree distribution in addition its asymptotic analysis reveals that the phase transition occurs in semidense random graphs whose average degree grows logarithmically these results which are supported by numerical simulations coincide with the mathematical results indicating successful predictions by the mean field approximation for unbounded but not dense random graphs

statistical mechanics of the hitting set problem in this paper we present a detailed study of the hitting set hs problem this problem is a generalization of the standard vertex cover to hypergraphs one seeks a configuration of particles with minimal density such that every hyperedge of the hypergraph contains at least one particle it can also be used in important practical tasks such as the group testing procedures where one wants to detect defective items in a large group by pool testing using a statistical mechanics approach based on the cavity method we study the phase diagram of the hs problem in the case of random regular hypergraphs depending on the values of the variables and tests degrees different situations can occur the hs problem can be either in a replica symmetric phase or in a one step replica symmetry breaking one in these two cases we give explicit results on the minimal density of particles and the structure of the phase space these problems are thus in some sense simpler than the original vertex cover problem where the need for a full replica symmetry breaking has prevented the derivation of exact results so far finally we show that decimation procedures based on the belief propagation and the survey propagation algorithms provide very efficient strategies to solve large individual instances of the hitting set problem

maximum independent set on diluted triangular lattices core percolation and maximum independent set on random graphs have recently been characterized using the methods of statistical physics here we present a statistical physics study of these problems on bond diluted triangular lattices core percolation critical behavior is found to be consistent with the standard percolation values though there are strong finite size effects a transfer matrix method is developed and applied to find accurate values of the density and degeneracy of the maximum independent set on lattices of limited width but large length an extrapolation of these results to the infinite lattice limit yields high precision results which are tabulated these results are compared to results found using both vertex based and edge based local probability recursion algorithms which have proven useful in the analysis of hard computational problems such as the satisfiability problem

minimal vertex covers on finite connectivity random graphs a hard sphere lattice gas picture the minimal vertex cover or maximal independent set problem is studied on random graphs of finite connectivity analytical results are obtained by a mapping to a lattice gas of hard spheres of chemical radius 1 and they are found to be in excellent agreement with numerical simulations we give a detailed description of the replica symmetric phase including the size and entropy of the minimal vertex covers and the structure of the unfrozen component which is found to percolate at a connectivity c approximately 1 43 the replica symmetric solution breaks down at c e approximately 2 72 we give a simple one step replica symmetry broken solution and discuss the problems in the interpretation and generalization of this solution

community detection in complex networks using extremal optimization we propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity the method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure we present the results of the algorithm for computer simulated and real networks and compare them with other approaches the efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks

the effect of better ear glimpsing on spatial release from masking the current experiment investigated whether better ear glimpsing can explain the spatial release achieved by normal hearing adults when situations are high in informational masking both modeling and behavioral methods were used the speech reception thresholds of 38 young adults were measured for co located spatially separated and two better ear glimpsed conditions in the better ear glimpsed conditions the binaural signals were processed so that in each time frequency segment the signal with the better snr left or right ear was presented diotically to investigate the effect of widening auditory filters on better ear glimpsing adjacent frequency bands were combined in one of the better ear glimpsing conditions twenty two participants were tested with maskers high in informational masking while 16 participants were tested with maskers lower in informational masking the mean speech reception thresholds achieved in the glimpsed conditions were significantly worse than in the spatially separated condition this suggests that better ear glimpsing can explain some but not all of the observed spatial release from masking the difference between performance in the spatially separated and glimpsed conditions was largest when informational masking was high suggesting better ear glimpsing may release energetic rather than informational masking reducing the number of frequency bands sampled had a small effect on performance

on modulational instabilities in discretisations of the korteweg devries equation abstract w l briggs a c newell and t sarie j comput phys 51 83 1983 have studied nonlinear instabilities in discretisations of the equation u 1 u u u x 0 where u is a constant they demonstrated that solutions of leap frog discretisations of this equation could be destabilised by a dynamical process which can localise noise on the spatial grid d m sloan and a r mitchell j comput phys 67 1986 examined these instabilities by considering perturbations of the basic solution which take the form of side band fourier modes here this latter work is extended to cover analogous discretisations of the korteweg de vries equation

clustering analysis of the ground state structure of the vertex cover problem vertex cover is one of the classical np complete problems in theoretical computer science a vertex cover of a graph is a subset of vertices such that for each edge at least one of the two endpoints is contained in the subset when studied on erd os r enyi random graphs with connectivity c one observes a threshold behavior in the thermodynamic limit the size of the minimal vertex cover is independent of the specific graph recent analytical studies show that on the phase boundary for small connectivities cle the system is replica symmetric while for larger connectivities replica symmetry breaking occurs this change coincides with a change of the typical running time of algorithms from polynomial to exponential to understand the reasons for this behavior and to compare with the analytical results we numerically analyze the structure of the solution landscape for this purpose we have also developed an algorithm which allows the calculation of the backbone without the need to enumerate all solutions we study exact solutions found with a branch and bound algorithm as well as configurations obtained via a monte carlo simulation we analyze the cluster structure of the solution landscape by direct clustering of the states by analyzing the eigenvalue spectrum of correlation matrices and by using a hierarchical clustering method all results are compatible with a change at c e for small connectivities the solutions are collected in a finite small number of clusters while the number of clusters diverges slowly with system size for larger connectivities and replica symmetry breaking but not one step replica symmetry breaking 1 rsb occurs

number of guards needed by a museum a phase transition in vertex covering of random graphs in this letter we study the np complete vertex cover problem on finite connectivity random graphs when the allowed size of the cover set is decreased a discontinuous transition in solvability and typical case complexity occurs this transition is characterized by means of exact numerical simulations as well as by analytical replica calculations the replica symmetric phase diagram is in excellent agreement with numerical findings up to average connectivity e where replica symmetry becomes locally unstable

a discrete linearizability test based on multiscale analysis in this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad graph by the multiple scale reduction around their harmonic solution we show that the a1 a2 and a3 linearizability conditions restrain the number of the parameters which enter into the equation a subclass of the equations which pass the a3 c integrability conditions can be linearized by a mobius transformation

curvilinear component analysis a self organizing neural network for nonlinear mapping of data sets we present a new strategy called curvilinear component analysis cca for dimensionality reduction and representation of multidimensional data sets the principle of cca is a self organized neural network performing two tasks vector quantization vq of the submanifold in the data set input space and nonlinear projection p of these quantizing vectors toward an output space providing a revealing unfolding of the submanifold after learning the network has the ability to continuously map any new point from one space into another forward mapping of new points in the input space or backward mapping of an arbitrary position in the output space

constructing free energy approximations and generalized belief propagation algorithms important inference problems in statistical physics computer vision error correcting coding theory and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs the belief propagation bp algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree but only approximate when the factor graph has cycles we show that bp fixed points correspond to the stationary points of the bethe approximation of the free energy for a factor graph we explain how to obtain region based free energy approximations that improve the bethe approximation and corresponding generalized belief propagation gbp algorithms we emphasize the conditions a free energy approximation must satisfy in order to be a valid or maxent normal approximation we describe the relationship between four different methods that can be used to generate valid approximations the bethe method the junction graph method the cluster variation method and the region graph method finally we explain how to tell whether a region based approximation and its corresponding gbp algorithm is likely to be accurate and describe empirical results showing that gbp can significantly outperform bp

covering problems and core percolations on hypergraphs we introduce two generalizations of core percolation in graphs to hypergraphs related to the minimum hyperedge cover problem and the minimum vertex cover problem on hypergraphs respectively we offer analytical solutions of these two core percolations for uncorrelated random hypergraphs whose vertex degree and hyperedge cardinality distributions are arbitrary but have nondiverging moments we find that for several real world hypergraphs their two cores tend to be much smaller than those of their null models suggesting that covering problems in those real world hypergraphs can actually be solved in polynomial time

binaural speech intelligibility in noise for hearing impaired listeners the effect of head induced interaural time delay itd and interaural level differences ild on binaural speech intelligibility in noise was studied for listeners with symmetrical and asymmetrical sensorineural hearing losses the material recorded with a kemar manikin in an anechoic room consisted of speech presented from the front 0 and noise presented at azimuths of 0 30 and 90 derived noise signals containing either only itd or only ild were generated using a computer for both groups of subjects speech reception thresholds srt for sentences in noise were determined as a function of 1 noise azimuth 2 binaural cue and 3 an interaural difference in overall presentation level simulating the effect of a monaural hearing aid comparison of the mean results with corresponding data obtained previously from normal hearing listeners shows that the hearing impaired have a 2 5 db higher srt in noise when both speech and noise are presented from the front and 2 6 5 1 db less binaural gain when the noise azimuth is changed from 0 to 90 the gain due to ild varies among the hearing impaired listeners between o db and normal values of 7 db or more it depends on the high frequency hearing loss at the side presented with the most favorable signal to noise s n ratio the gain due to itd is nearly normal for the symmetrically impaired 4 2 db compared with 4 7 db for the normal hearing but only 2 5 db in the case of asymmetrical impairment when itd is introduced in noise already containing ild the resulting gain is 2 2 5 db for all groups the only marked effect of the interaural difference in overall presentation level is a reduction of the gain due to ild when the level at the ear with the better s n ratio is decreased this implies that an optimal monaural hearing aid with a moderate gain will hardly interfere with unmasking through itd while it may increase the gain due to ild by preventing or diminishing threshold effects

two solutions to diluted p spin models and xorsat problems we derive analytical solutions for p spin models with finite connectivity at zero temperature these models are the statistical mechanics equivalent of p xorsat problems in theoretical computer science we give a full characterization of the phase diagram location of the phase transitions static and dynamic together with a description of the clustering phenomenon taking place in configurational space we use two alternative methods the cavity approach and a rigorous derivation

polynomial iterative algorithms for coloring and analyzing random graphs we study the graph coloring problem over random graphs of finite average connectivity c given a number q of available colors we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable depending on q we find with a one step replica symmetry breaking approximation the precise value of the critical average connectivity c q moreover we show that below c q there exists a clustering phase c in c d c q in which ground states spontaneously divide into an exponential number of clusters furthermore we extended our considerations to the case of single instances showing consistent results this leads us to propose a different algorithm that is able to color in polynomial time random graphs in the hard but colorable region i e when c in c d c q

generalization of core percolation on complex networks we introduce a k leaf removal algorithm as a generalization of the so called leaf removal algorithm in this pruning algorithm vertices of degree smaller than k together with their first nearest neighbors and all incident edges are progressively removed from a random network as the result of this pruning the network is reduced to a subgraph which we call the generalized k core gk core performing this pruning for the sequence of natural numbers k we decompose the network into a hierarchy of progressively nested gk cores we present an analytical framework for description of gk core percolation for undirected uncorrelated networks with arbitrary degree distributions configuration model to confirm our results we also derive rate equations for the k leaf removal algorithm which enable us to obtain the structural characteristics of the gk cores in another way also we apply our algorithm to a number of real world networks and perform the gk core decomposition for them

detecting the solution space of vertex cover by mutual determinations and backbones to solve the combinatorial optimization problems especially the minimal vertex cover problem with high efficiency is a significant task in theoretical computer science and many other subjects aiming at detecting the solution space of vertex cover a new structure named mutual determination is defined and discovered for vertex cover on general graphs which results in the emergence of strong correlations among the unfrozen nodes based on the backbones and mutual determinations with node ranks by leaf removal we propose a mutual determination and backbone evolution algorithm to achieve the reduced solution graph which provides a graphical expression of the solution space of vertex cover by this algorithm the whole solution space and detailed structures such as backbones can be obtained strictly when there is no leaf removal core on the given graph compared with the current algorithms the mutual determination and backbone evolution algorithm performs as well as the replica symmetry one in a certain interval but has a small gap higher than the replica symmetric breaking one and has a relatively small error for the exact results the algorithm with the mutual determination provides a new viewpoint to solve vertex cover and understand the organizations of the solution spaces and the reduced solution graph gives an alternative way to catch detailed information of the ground steady states

gibbs states and the set of solutions of random constraint satisfaction problems abstract an instance of a random constraint satisfaction problem defines a random subset the set of solutions of a large product space x n the set of assignments we consider two prototypical problem ensembles random k satisfiability and q coloring of random regular graphs and study the uniform measure with support on s as the number of constraints per variable increases this measure first decomposes into an exponential number of pure states clusters and subsequently condensates over the largest such states above the condensation point the mass carried by the n largest states follows a poisson dirichlet process for typical large instances the two transitions are sharp we determine their precise location further we provide a formal definition of each phase transition in terms of different notions of correlation between distinct variables in the problem the degree of correlation naturally affects the performances of many search sampling algorithms empirical evidence suggests that local monte carlo markov chain strategies are effective up to the clustering phase transition and belief propagation up to the condensation point finally refined message passing techniques such as survey propagation may also beat this threshold message passing algorithms phase transitions random graphs

phase diagram of the 1 in 3 satisfiability problem we study typical case properties of the 1 in 3 satisfiability problem the boolean satisfaction problem where a clause is satisfied by exactly one literal in an enlarged random ensemble parametrized by average connectivity and probability of negation of a variable in a clause random 1 in 3 satisfiability and exact 3 cover are special cases of this ensemble we interpolate between these cases from a region where satisfiability can be typically decided for all connectivities in polynomial time to a region where deciding satisfiability is hard in some interval of connectivities we derive several rigorous results in the first region and develop a one step replica symmetry breaking cavity analysis in the second one we discuss the prediction for the transition between the almost surely satisfiable and the almost surely unsatisfiable phase and other structural properties of the phase diagram in light of cavity method results

dynamical replica analysis of processes on finitely connected random graphs i vertex covering we study the stochastic dynamics of ising spin models with random bonds interacting on finitely connected poissonian random graphs we use the dynamical replica method to derive closed dynamical equations for the joint spin field probability distribution and solve these within the replica symmetry ansatz although the theory is developed in a general setting with a view to future applications in various other fields in this paper we apply it mainly to the dynamics of the glauber algorithm extended with cooling schedules when running on the so called vertex cover optimization problem our theoretical predictions are tested against both monte carlo simulations and known results from equilibrium studies in contrast to previous dynamical analyses based on deriving closed equations for only a small number of scalar order parameters the agreement between theory and experiment in the present study is nearly perfect

message passing for vertex covers constructing a minimal vertex cover of a graph can be seen as a prototype for a combinatorial optimization problem under hard constraints in this paper we develop and analyze message passing techniques namely warning and survey propagation which serve as efficient heuristic algorithms for solving these computational hard problems we show also how previously obtained results on the typical case behavior of vertex covers of random graphs can be recovered starting from the message passing equations and how they can be extended

computational complexity arising from degree correlations in networks we apply a bethe peierls approach to statistical mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices using the nondeterministic polynomial time hard optimization problem of finding minimal vertex covers on these graphs we show that such correlations may lead to a qualitatively different solution structure as compared to uncorrelated networks this results in a higher complexity of the network in a computational sense simple heuristic algorithms fail to find a minimal vertex cover in the highly correlated case whereas uncorrelated networks seem to be simple from the point of view of combinatorial optimization

an explicit finite difference scheme with exact conservation properties abstract a finite difference scheme for the numerical study of the korteweg de vries equation is constructed it is explicit and yet conserves exactly the energy of the computed solutions the underlying idea can also be applied to more general equations or systems numerical experiments are included

measurements of the binaural temporal window using a detection task two experiments investigated the shape of the binaural temporal window using a detection task in experiment 1 a 10 ms tone burst was presented binaurally out of phase during a burst of white noise which changed from being interaurally uncorrelated to correlated and back to uncorrelated the tone occurred during the correlated portion of the noise in one interval of each 2i fc trial detection thresholds were recorded using a 2 down 1 up adaptive procedure thresholds were measured for different durations of correlated noise 0 960 ms frequencies of tone burst 125 250 500 and 1000 hz and levels of noise 20 30 40 and 50 db spl hz window shapes based on nine candidate functions were fitted to the data using the assumption that the binaural masking release was related to the overall interaural correlation of noise admitted by the window fitted windows included both a forward and a backward lobe gaussian functions tended to give closer fits than exponential and rounded exponential functions and simple functions gave more parsimonious fits that those which included dynamic range limiting terms using simple gaussian fits the shape of the window was largely independent of frequency and level and the windows for individual listeners had equivalent rectangular durations ranging from 55 to 188 ms the asymmetry was variable although forward lobes were generally shorter than backward lobes experiment 2 ruled out the possibility that the forward lobe might be an artefact caused by distraction of the listener when the interaural phase change in the noise closely followed the signal in this experiment the out of phase tone was presented during a burst of partially correlated noise which changed after a variable interval to a fully correlated noise thresholds for detecting the tone rose i e performance worsened as the interval was increased distraction would have produced the opposite effect

threshold values stability analysis and high q asymptotics for the coloring problem on random graphs we consider the problem of coloring erdos renyi and regular random graphs of finite connectivity using q colors it has been studied so far using the cavity approach within the so called one step replica symmetry breaking 1rsb ansatz we derive a general criterion for the validity of this ansatz and applying it to the ground state we provide evidence that the 1rsb solution gives exact threshold values c q for the transition from the colorable to the uncolorable phase with q colors we also study the asymptotic thresholds for q 1 finding c q 2q ln q ln q 1 o 1 in perfect agreement with rigorous mathematical bounds as well as the nature of excited states and give a global phase diagram of the problem

group testing with random pools phase transitions and optimal strategy the problem of group testing is to identify defective items out of a set of objects by means of pool queries of the form does the pool contain at least a defective the aim is of course to perform detection with the fewest possible queries a problem which has relevant practical applications in different fields including molecular biology and computer science here we study gt in the probabilistic setting focusing on the regime of small defective probability and large number of objects p 0 and n we construct and analyze one stage algorithms for which we establish the occurrence of a non detection detection phase transition resulting in a sharp threshold overline m for the number of tests by optimizing the pool design we construct algorithms whose detection threshold follows the optimal scaling overline m propto np log p then we consider two stages algorithms and analyze their performance for different choices of the first stage pools in particular via a proper random choice of the pools we construct algorithms which attain the optimal value previously determined in mezard and toninelli arxiv 0706 3104 for the mean number of tests required for complete detection we finally discuss the optimal pool design in the case of finite p

spin models on random graphs with controlled topologies beyond degree constraints we study ising spin models on finitely connected random interaction graphs which are drawn from an ensemble in which not only the degree distribution p k can be chosen arbitrarily but which allows for further fine tuning of the topology via preferential attachment of edges on the basis of an arbitrary function q k k of the degrees of the vertices involved we solve these models using finite connectivity equilibrium replica theory within the replica symmetric ansatz in our ensemble of graphs phase diagrams of the spin system are found to depend no longer only on the chosen degree distribution but also on the choice made for q k k the increased ability to control interaction topology in solvable models beyond prescribing only the degree distribution of the interaction graph enables a more accurate modeling of real world interacting particle systems by spin systems on suitably defined random graphs

spin glass phase transitions and minimum energy of the random feedback vertex set problem a feedback vertex set fvs of an undirected graph contains vertices from every cycle of this graph constructing a fvs of sufficiently small cardinality is very difficult in the worst cases but for random graphs this problem can be efficiently solved by converting it into an appropriate spin glass model h j zhou eur phys j b 86 455 2013 in the present work we study the spin glass phase transitions and the minimum energy density of the random fvs problem by the first step replica symmetry breaking 1rsb mean field theory for both regular random graphs and erdos renyi graphs we determine the inverse temperature beta 1 at which the replica symmetric mean field theory loses its local stability the inverse temperature beta d of the dynamical clustering phase transition and the inverse temperature beta s of the static condensation phase transition these critical inverse temperatures all change with the mean vertex degree in a nonmonotonic way and beta d is distinct from beta s for regular random graphs of vertex degrees k 60 while beta d are identical to beta s for erdos renyi graphs at least up to mean vertex degree c 512 we then derive the zero temperature limit of the 1rsb theory and use it to compute the minimum fvs cardinality

spurious resonance in semidiscrete methods for the korteweg de vries equation a multiple scales analysis of semidiscrete methods for the korteweg de vries equation is conducted methods that approximate the spatial derivatives by finite differences with arbitrary order accuracy and the limiting method the fourier pseudospectral method are considered the analysis reveals that a resonance effect can occur in the semidiscrete solution but not in the solution of the continuous equation it is shown for the fourier pseudospectral discretization that resonance can only be caused by aliased modes the spurious semidiscrete solutions are investigated in numerical experiments and we suggest methods for avoiding spurious resonance

parasitic waves and solitons in the numerical solution of the korteweg de vries and modified korteweg de vries equation abstract by means of numerical experiments the zabusky kruskal discretization of the korteweg de vries equation is shown to have solitary saw toothed wave packet solutions an analysis is presented to explain the properties of this type of solution this as well as numerical experiments indicate that the solution is stable only for small amplitude wave packets and that the propagation of the wave packet is essentially linear similar experiments and analysis for a discretized modified korteweg de vries equation show that large amplitude solitary wave packet solutions are possible for this equation and that their propagation is governed by an mkdv equation which differs from the one which is consistent with the discretized equation this makes it possible to construct sawtoothed wave packets which behave like mkdv solitons the results of several numerical experiments showing collisions between wave packets and solitons are also reported

core organization of directed complex networks the recursive removal of leaves dead end vertices and their neighbors from an undirected network results when this pruning algorithm stops in a so called core of the network this specific subgraph should be distinguished from k cores which are principally different subgraphs in networks if the vertex mean degree of a network is sufficiently large the core is a giant cluster containing a finite fraction of vertices we find that generalization of this pruning algorithm to directed networks provides a significantly more complex picture of cores by implementing a rate equation approach to this pruning procedure for directed uncorrelated networks we identify a set of cores progressively embedded into each other in a network and describe their birth points and structure

sentence reception in noise from one versus two sources effects of aging and hearing loss sentence reception thresholds srts and babble detection thresholds bdts were measured for signals presented from loudspeakers located at 0 deg and 90 deg azimuth in addition the s b ratios necessary to achieve srt in the presence of a 12 talker babble were determined under three conditions in which the speech and babble were presented from the same or spatially separated loudspeakers in the first experiment normal hearing subjects were tested on two occasions the results were highly reliable with standard errors of the test retest differences of less than 1db for all conditions in the second experiment srts bdts and s b ratios were measured for three normal hearing groups 39 40 54 and 55 years and for a fourth group with presbycusis 55 years presbycusics had higher srts and bdts than all other groups regardless of age and the oldest normals had higher thresholds than younger subjects presbycusics required higher s b ratios than any of the normal groups and the oldest normal group needed a higher s b ratio compared to the youngest group all groups demonstrated a significant advantage in s b ratio when the sentences and babble sources were spatially separated compared to when they were presented from the same loudspeaker there was no significant difference in the magnitude of advantage due to spatial separation of speech and noise between the normal groups regardless of age but the presbycusics had significantly smaller advantages than all normals these findings suggest that aging alone does not impair the ability to take advantage of the spatial separation of speech and noise and that the speech reception problems of aging individuals involve various components that depend upon the nature of the listening task

coloring random graphs we study the graph coloring problem over random graphs of finite average connectivity c given a number q of available colors we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable depending on q we find the precise value of the critical average connectivity c q moreover we show that below c q there exists a clustering phase c e c d c q in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity in local search algorithms

statistical mechanics perspective on the phase transition in vertex covering offinite connectivity random graphs the vertex cover problem is studied for random graphs gn cn having n vertices and cn edges exact numerical results are obtained by a branch and bound algorithm it is found that a transition in the coverability at a c dependent threshold x xc c appears where xn is the cardinality of the vertex cover this transition coincides with a sharp peak of the typical numerical e1ort which is needed to decide whether there exists a cover with xn vertices or not for small edge concentrations c two less than arrows one inside the other 0 5 a cluster expansion is performed giving very accurate results in this regime these results are extended using methods developed in statistical physics the so called annealed approximation reproduces a rigorous bound on xc c which was known previously the main part of the paper contains an application of the replica method within the replicasymmetric ansatz the threshold xc c and various statistical properties of minimal vertex covers can be calculated for c e 2 the results show an excellent agreement with the numerical findings at average vertex degree 2c e an instability of the simple replica symmetric solution occurs

the effects of age and cochlear hearing loss on temporal fine structure sensitivity frequency selectivity and speech reception in noise temporal fine structure tfs sensitivity frequency selectivity and speech reception in noise were measured for young normal hearing nhy old normal hearing nho and hearing impaired hi subjects two measures of tfs sensitivity were used the tfs lf test interaural phase difference discrimination and the tfs2 test discrimination of harmonic and frequency shifted tones these measures were not significantly correlated with frequency selectivity after partialing out the effect of audiometric threshold suggesting that insensitivity to tfs cannot be wholly explained by a broadening of auditory filters the results of the two tests of tfs sensitivity were significantly but modestly correlated suggesting that performance of the tests may be partly influenced by different factors the nho group performed significantly more poorly than the nhy group for both measures of tfs sensitivity but not frequency selectivity suggesting that tfs sensitivity declines with age in the absence of elevated audiometric thresholds or broadened auditory filters when the effect of mean audiometric threshold was partialed out speech reception thresholds in modulated noise were correlated with tfs2 scores but not measures of frequency selectivity or tfs lf test scores suggesting that a reduction in sensitivity to tfs can partly account for the speech perception difficulties experienced by hearing impaired subjects

random graph coloring statistical physics approach the problem of vertex coloring in random graphs is studied using methods of statistical physics and probability our analytical results are compared to those obtained by exact enumeration and monte carlo simulations we critically discuss the merits and shortcomings of the various methods and interpret the results obtained we present an exact analytical expression for the two coloring problem as well as general replica symmetric approximated solutions for the thermodynamics of the graph coloring problem with p colors and k body edges

the influence of non spatial factors on measures of spatial release from masking this study tested the hypothesis that the reduction in spatial release from masking srm resulting from sensorineural hearing loss in competing speech mixtures is influenced by the characteristics of the interfering speech a frontal speech target was presented simultaneously with two intelligible or two time reversed unintelligible speech maskers that were either colocated with the target or were symmetrically separated from the target in the horizontal plane the difference in srm between listeners with hearing impairment and listeners with normal hearing was substantially larger for the forward maskers deficit of 5 8 db than for the reversed maskers deficit of 1 6 db this was driven by the fact that all listeners regardless of hearing abilities performed similarly and poorly in the colocated condition with intelligible maskers the same conditions were then tested in listeners with normal hearing using headphone stimuli that were degraded by noise vocoding reducing the number of available spectral channels systematically reduced the measured srm and again more so for forward reduction of 3 8 db than for reversed speech maskers reduction of 1 8 db the results suggest that non spatial factors can strongly influence both the magnitude of srm and the apparent deficit in srm for listeners with impaired hearing

a multi resolution envelope power based model for speech intelligibility the speech based envelope power spectrum model sepsm presented by jorgensen and dau 2011 j acoust soc am 130 1475 1487 estimates the envelope power signal to noise ratio snrenv after modulation frequency selective processing changes in this metric were shown to account well for changes of speech intelligibility for normal hearing listeners in conditions with additive stationary noise reverberation and nonlinear processing with spectral subtraction in the latter condition the standardized speech transmission index 2003 iec 60268 16 fails however the sepsm is limited to conditions with stationary interferers due to the long term integration of the envelope power and cannot account for increased intelligibility typically obtained with fluctuating maskers here a multi resolution version of the sepsm is presented where the snrenv is estimated in temporal segments with a modulation filter dependent duration the multi resolution sepsm is demonstrated to account for intelligibility

phase transition for cutting plane approach to vertex cover problem we study the vertex cover problem which is a nondeterministic polynomial time hard optimization problem and a prototypical model exhibiting phase transitions on random graphs such as erd s renyi er random graphs these phase transitions coincide with changes of the solution space structure e g for the er ensemble at connectivity c e 2 7183 from replica symmetric to replica symmetry broken for the vertex cover problem the typical complexity of exact branch and bound algorithms which proceed by exploring the landscape of feasible configurations also changes close to this phase transition from easy to hard in this work we consider an algorithm which has a completely different strategy the problem is mapped onto a linear programming problem augmented by a cutting plane approach hence the algorithm operates in a space outside the space of feasible configurations until the final step where a solution is found here we show that this type of algorithm also exhibits an easy hard transition around c e which strongly indicates that the typical hardness of a problem is fundamental to the problem and not due to a specific representation of the problem

the network source location problem ground state energy entropy and effects of freezing ground state entropy of the network source location problem is evaluated at both the replica symmetric level and one step replica symmetry breaking level using the entropic cavity method the regime that is a focus of this study is closely related to the vertex cover problem with randomly quenched covered nodes the resulting entropic message passing inspired decimation and reinforcement algorithms are used to identify the optimal location of sources in single instances of transportation networks the conventional belief propagation without taking the entropic effect into account is also compared we find that in the glassy phase the entropic message passing inspired decimation yields a lower ground state energy compared to the belief propagation without taking the entropic effect using the extremal optimization algorithm we study the ground state energy and the fraction of frozen hubs and extend the algorithm to collect statistics of the entropy the theoretical results are compared with the extremal optimization results

optimal vertex cover for the small world hanoi networks the vertex cover problem on the hanoi networks hn3 and hn5 is analyzed with an exact renormalization group and parallel tempering monte carlo simulations the grand canonical partition function of the equivalent hard core repulsive lattice gas problem is recast first as an ising like canonical partition function which allows for a closed set of renormalization group equations the flow of these equations is analyzed for the limit of infinite chemical potential at which the vertex cover problem is attained the relevant fixed point and its neighborhood are analyzed and nontrivial results are obtained both for the coverage as well as for the ground state entropy density which indicates the complex structure of the solution space using special hierarchy dependent operators in the renormalization group and monte carlo simulations structural details of optimal configurations are revealed these studies indicate that the optimal coverages or packings are not related by a simple symmetry using a clustering analysis of the solutions obtained in the monte carlo simulations a complex solution space structure is revealed for each system size nevertheless in the thermodynamic limit the solution landscape is dominated by one huge set of very similar solutions

on the nonlinear schro dinger limit of the korteweg de vries equation abstract using the multiscale approach of zakharov and kuznetsov it is shown that the nonlinear schrodinger periodic scattering data is related to the korteweg de vries periodic scattering data via an average over the korteweg de vries carrier oscillation this allows a complete elucidation of the physical meaning of the nonlinear schrodinger scattering data conservation laws theta function solutions and reality constraint

phase transitions in the coloring of random graphs we consider the problem of coloring the vertices of a large sparse random graph with a given number of colors so that no adjacent vertices have the same color using the cavity method we present a detailed and systematic analytical study of the space of proper colorings solutions we show that for a fixed number of colors and as the average vertex degree number of constraints increases the set of solutions undergoes several phase transitions similar to those observed in the mean field theory of glasses first at the clustering transition the entropically dominant part of the phase space decomposes into an exponential number of pure states so that beyond this transition a uniform sampling of solutions becomes hard afterward the space of solutions condenses over a finite number of the largest states and consequently the total entropy of solutions becomes smaller than the annealed one another transition takes place when in all the entropically dominant states a finite fraction of nodes freezes so that each of these nodes is allowed a single color in all the solutions inside the state eventually above the coloring threshold no more solutions are available

nonlinear instability in dissipative finite difference schemes a unified analysis of reaction diffusion equations and their finite difference representations is presented the parallel treatment of the two problems shows clearly when and why the finite difference approximations break down the approach used provides a general framework for the analysis and interpretation of numerical instability in approximations of dissipative nonlinear partial differential equations continuous and discrete problems are studied from the perspective of bifurcation theory and numerical instability is shown to be associated with the bifurcation of periodic orbits in discrete systems an asymptotic approach due to newell siam j appl math 33 1977 133 160 is used to investigate the instability phenomenon further in particular equations are derived that describe the interaction of the dynamics of the partial differential equation with the artefacts of the discretization

random k satisfiability problem from an analytic solution to an efficient algorithm we study the problem of satisfiability of randomly chosen clauses each with k boolean variables using the cavity method at zero temperature we find the phase diagram for the k 3 case we show the existence of an intermediate phase in the satisfiable region where the proliferation of metastable states is at the origin of the slowdown of search algorithms the fundamental order parameter introduced in the cavity method which consists of surveys of local magnetic fields in the various possible states of the system can be computed for one given sample these surveys can be used to invent new types of algorithms for solving hard combinatorial optimizations problems one such algorithm is shown here for the k 3 satisfiability problem with very good performances

minimum vertex cover problems on random hypergraphs replica symmetric solution and a leaf removal algorithm the minimum vertex cover problems on random ensuremath alpha uniform hypergraphs are studied using two different approaches a replica method in statistical mechanics of random systems and a leaf removal algorithm it is found that there exists a phase transition at the critical average degree e ensuremath alpha ensuremath 1 below which a replica symmetric ansatz in the replica method holds and the algorithm estimates exactly the same solution of the problem as that by the replica method in contrast above the critical degree the replica symmetric solution becomes unstable and the leaf removal algorithm fails to estimate the optimal solution because of the emergence of a large size core these results strongly suggest a close relation between the replica symmetry and the performance of an approximation algorithm critical properties of the core percolation are also examined numerically by a finite size scaling

multi scale expansions in the theory of systems integrable by the inverse scattering transform abstract it is shown that using multi scale expansions conventionally employed in the theory of nonlinear waves one can transform systems integrable by the ist method into other systems of this type

witness of unsatisfiability for a random 3 satisfiability formula the random 3 satisfiability 3 sat problem is in the unsatisfiable unsat phase when the clause density alpha exceeds a critical value alpha s approximate to 4 267 rigorously proving the unsatisfiability of a given large 3 sat instance is however extremely difficult in this paper we apply the mean field theory of statistical physics to the unsatisfiability problem and show that a reduction to 3 xorsat which permits the construction of a specific type of unsat witnesses feige kim ofek witnesses is possible when the clause density alpha 19 we then construct feige kim ofek witnesses for single 3 sat instances through a simple random sampling algorithm and a focused local search algorithm the random sampling algorithm works only when a scales at least linearly with the variable number n but the focused local search algorithm works for clause density alpha cn b with b approximate to 0 59 and prefactor c approximate to 8 the exponent b can be further decreased by enlarging the single parameter s of the focused local search algorithm

stability analysis on the finite temperature replica symmetric and first step replica symmetry broken cavity solutions of the random vertex cover problem the vertex cover problem is a prototypical hard combinatorial optimization problem it was studied in recent years by physicists using the cavity method of statistical mechanics in this paper the stability of the finite temperature replica symmetric rs and the first step replica symmetry broken 1rsb cavity solutions of the vertex cover problem on random regular graphs of finite vertex degree k are analyzed by population dynamics simulations we found that 1 the lowest temperature for the rs solution to be stable t rs k is not a monotonic function of k 2 at relatively large connectivity k and temperature t slightly below the dynamic transition temperature t d k the 1rsb solutions with small but non negative complexity values are stable and 3 the dynamical transition temperature t d and kauzmann temperature t k is equal to each other similar results are obtained on random poissonian graphs

revision extension and evaluation of a binaural speech intelligibility model this study presents revision extension and evaluation of a binaural speech intelligibility model beutelmann r and brand t 2006 j acoust soc am 120 331 342 that yields accurate predictions of speech reception thresholds srts in the presence of a stationary noise source at arbitrary azimuths and in different rooms the modified model is based on an analytical expression of binaural unmasking for arbitrary input signals and is computationally more efficient while maintaining the prediction quality of the original model an extension for nonstationary interferers was realized by applying the model to short time frames of the input signals and averaging over the predicted srt results binaural srts from 8 normal hearing and 12 hearing impaired subjects incorporating all combinations of four rooms three source setups and three noise types were measured and compared to the model s predictions depending on the noise type the parametric correlation coefficients between observed and predicted srts were 0 80 0 93 for normal hearing subjects and 0 59 0 80 for hearing impaired subjects the mean absolute prediction error was 3 db for the mean normal hearing data and 4 db for the individual hearing impaired data 70 of the variance of the srts of hearing impaired subjects could be explained by the model which is based only on the audiogram

instability of one step replica symmetry broken phase in satisfiability problems we reconsider the one step replica symmetry breaking 1rsb solutions of two random combinatorial problems k xorsat and k sat we present a general method for establishing the stability of these solutions with respect to further steps of replica symmetry breaking our approach extends the ideas of montanari and ricci tersenghi 2003 eur phys j b 33 339 to more general combinatorial problems it turns out that 1rsb is always unstable at sufficiently small clause density or high energy in particular the recent 1rsb solution to 3 sat is unstable at zero energy for m with m 4 153 on the other hand the sat unsat phase transition seems to be correctly described within 1rsb