consistent estimation of a general nonparametric regression function in time series abstract we propose an estimator of the conditional distribution of x t x t 1 x t 2 and the corresponding regression function e x t x t 1 x t 2 where the conditioning set is of infinite order we establish consistency of our estimator under stationarity and ergodicity conditions plus a mild smoothness condition

using dual approximation algorithms for scheduling problems theoretical and practical results the problem of scheduling a set of n jobs on m identical machines so as to minimize the makespan time is perhaps the most well studied problem in the theory of approximation algorithms for np hard optimization problems in this paper the strongest possible type of result for this problem a polynomial approximation scheme is presented more precisely for each e an algorithm that runs in time o n e 1 e 2 and has relative error at most e is given in addition more practical algorithms for e 1 5 2 k and e 1 6 2 k which have running times o n k log n and o n km 4 log n are presented the techniques of analysis used in proving these results are extremely simple especially in comparison with the baroque weighting techniques used previously the scheme is based on a new approach to constructing approximation algorithms which is called dual approximation algorithms where the aim is to find superoptimal but infeasible solutions and the performance is measured by the degree of infeasibility allowed this notion should find wide applicability in its own right and should be considered for any optimization problem where traditional approximation algorithms have been particularly elusive

universal tests for memory words the main result is a universal pointwise test that when presented with a set of words s on a finite or countable alphabet x that purports to be a set of memory words for a stationary process will eventually almost surely return the value yes precisely when all positive probability words in s are memory words for example if s consists of all of the single letters in x then the test will eventually say yes if and only if the process is a markov chain various further positive and negative results of this type are also given

effects of degree biased transmission rate and nonlinear infectivity on rumor spreading in complex social networks we introduce a generalized rumor spreading model and analytically investigate the spreading of rumors on scale free sf networks in the standard rumor spreading model each node has an infectivity equal to its degree and connectivity is uniform across all links to generalize this model we introduce an infectivity function that determines the number of simultaneous contacts that a given node individual may establish with its connected neighbors and a connectivity strength function csf for the direct link between two connected nodes these lead to a degree biased propagation of rumors for nonlinear functions this generalization is reflected in the infectivity s exponent ensuremath alpha and the csf s exponent ensuremath beta we show that by adjusting exponents ensuremath alpha and ensuremath beta the epidemic threshold can be controlled this feature is absent in the standard rumor spreading model in addition we obtain a critical threshold we show that the critical threshold for our generalized model is greater than that of the standard model on a finite sf network theoretically we show that ensuremath beta ensuremath 1 leads to a maximum spreading of rumors and computation results on different networks verify our theoretical prediction also we show that a smaller ensuremath alpha leads to a larger spreading of rumors our results are interesting since we obtain these results regardless of the network topology and configuration

global convergence of a reaction diffusion predator prey model with stage structure and nonlocal delays in this paper a lotka volterra type reaction diffusion predator prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated in the case of a general domain sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function method numerical simulations are carried out to illustrate the main results

fully dynamic algorithms for bin packing being mostly myopic helps the problem of maintaining an approximate solution for one dimensional bin packing when items may arrive and depart dynamically is studied in accordance with various work on fully dynamic algorithms and in contrast to prior work on bin packing it is assumed that the packing may be arbitrarily rearranged to accommodate arriving and departing items in this context our main result is a fully dynamic approximation algorithm for bin packing mmp that is frac 5 4 competitive and requires theta log n time per operation i e for an insert or a delete of an item this competitive ratio of frac 5 4 is nearly as good as that of the best practical off line algorithms our algorithm utilizes the technique introduced here whereby the packing of an item is done with a total disregard for already packed items of a smaller size this myopic packing of an item may then cause several smaller items to be repacked in a similar fashion with a bit of additional sophistication to avoid certain bad cases the number of items either individual items or bundles of very small items treated as a whole that needs to be repacked is bounded by a constant

critical behavior of propagation on small world networks we report numerical evidence that an epidemiclike model which can be interpreted as the propagation of a rumor exhibits critical behavior at a finite randomness of the underlying small world network the transition occurs between a regime where the rumor dies in a small neighborhood of its origin and a regime where it spreads over a finite fraction of the whole population critical exponents are evaluated through finite size scaling analysis and the dependence of the critical randomness with the network connectivity is studied the behavior of this system as a function of the small network randomness bears noticeable similarities with an epidemiological model reported recently m kuperman and g abramson phys rev lett 86 2909 2001 in spite of substantial differences in the respective dynamical rules

complex dynamic behavior of a rumor propagation model with spatial temporal diffusion terms a spatial temporal rumor propagation model with discrete and non local delays is regarded stability and hopf bifurcation are proved in a strict mathematical way sensitivity analysis is applied to search active parameters hopf bifurcation causes an oscillation phenomenon in this model numerical simulations provide a new insight into rumor spreading in online social networks rumor propagation as a typical form of social communication in online social networks has had a significant negative impact on a harmonious and stable society with the rapid development of mobile communication equipments traditional rumor propagation models which depend on ordinary differential equations ode may not be suitable for describing rumor propagation in an online social network in this paper based on reaction diffusion equations we propose a novel epidemic like model with both discrete and nonlocal delays for investigating the spatial temporal dynamics of rumor propagation by analyzing the corresponding characteristic equations of this model the local stability conditions of a boundary equilibrium point and a positive equilibrium point are established by applying the linear approximation method of nonlinear systems sufficient conditions are derived for the existence of hopf bifurcation at the above two kinds of equilibrium points moreover a sensitivity analysis method based on the density of spreading users is proposed and then in theoretical and experimental aspect we identify some sensitive parameters in the process of rumor propagation finally numerical simulations are performed to illustrate the theoretical results

dynamics of rumor propagation on small world networks we study the dynamics of an epidemiclike model for the spread of a rumor on a small world network it has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of the network randomness here by numerical means we perform a quantitative characterization of the evolution in the two regimes the variant of dynamic small worlds where the quenched disorder of small world networks is replaced by randomly changing connections between individuals is also analyzed in detail and compared with a mean field approximation

algorithms for the relaxed online bin packing model the typical online bin packing problem requires the fitting of a sequence of rationals in 0 1 into a minimum number of bins of unit capacity by packing the ith input element without any knowledge of the sizes or the number of input elements that follow moreover unlike typical online problems this one issue does not admit any data reorganization i e no element can be moved from one bin to another in this paper first of all the relaxed online bin packing model will be formalized this model allows a constant number of elements to move from one bin to another as a consequence of the arrival of a new input element then in the context of this new model two online algorithms will be described the first presents linear time and space complexities with a 1 5 approximation ratio and moves at most once only small elements the second instead is an o n log n time and linear space algorithm with a 1 33 approximation ratio and moves each element a constant number of times in the worst case as a result of the arrival of a new input element the first algorithm moves no more than three elements while the second moves as many as seven elements please note that the number of movements performed is explicitly considered in the complexity analysis both algorithms are below the theoretical 1 536 lower bound effective for the online bin packing algorithms without the movement of elements moreover our algorithms are more online than any other linear space online bin packing algorithm because unlike the algorithms already known they allow the return of a possibly relevant fraction of bins before the work is carried out

a rumor spreading model with variable forgetting rate abstract a rumor spreading model with the consideration of forgetting rate changing over time is examined in small world networks the mean field equations are derived to describe the dynamics of rumor spreading in small world networks further numerical solutions are conducted on livejournal an online social blogging platform to better understand the performance of the model results show that the forgetting rate has a significant impact on the final size of rumor spreading the larger the initial forgetting rate or the faster the forgetting speed the smaller the final size of the rumor spreading numerical solutions also show that the final size of rumor spreading is much larger under a variable forgetting rate compared to that under a constant forgetting rate

deinterleaving finite memory processes via penalized maximum likelihood we study the problem of deinterleaving a set of finite memory markov processes over disjoint finite alphabets which have been randomly interleaved by a finite memory switch the deinterleaver has access to a sample of the resulting interleaved process but no knowledge of the number or structure of the component markov processes or of the switch we study conditions for uniqueness of the interleaved representation of a process showing that certain switch configurations as well as memoryless component processes can cause ambiguities in the representation we show that a deinterleaving scheme based on minimizing a penalized maximum likelihood cost function is strongly consistent in the sense of reconstructing almost surely as the observed sequence length tends to infinity a set of component and switch markov processes compatible with the original interleaved process furthermore under certain conditions on the structure of the switch including the special case of a memoryless switch we show that the scheme recovers all possible interleaved representations of the original process experimental results are presented demonstrating that the proposed scheme performs well in practice even for relatively short input samples

intermittent estimation for gaussian processes let xn n 0 be a stationary real valued gaussian time series we estimate the conditional expectation e xn 1 x0 xn from a growing number of observations x0 xn in a pointwise consistent way along a sequence of stopping times

space efficient representation of truncated suffix trees with applications to markov order estimation suffix trees st are useful in many text processing applications for example to determine the number of occurrences of patterns of arbitrary length in an input string x if the length n of x is large the memory required to represent the st may become a practical performance bottleneck this problem can be alleviated in cases where a nontrivial upper bound is known on the lengths of the patterns of interest by using a truncated st tst however conventional tst implementations still require n bits of memory since they store x we describe a new tst representation that avoids this limitation by storing all the information necessary to reconstruct the tst edge labels in a string y that is often much shorter than x we apply tsts to the implementation of markov order estimators where an upper bound k n on the estimated order can be derived or it is imposed for consistency for example the new representation allows for estimator implementations with sublinear space complexity in some cases of interest in other cases we show experimentally that even when the new representation does not have an asymptotic advantage it still achieves very significant memory savings in practice

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

revealing the efficiency of information diffusion in online social networks of microblog abstract online social networks osns such as microblogs enable people to simultaneously share information with a large number of peers and revealing the properties of the formed network structure and the corresponding impacts on information diffusion are important in this article we empirically study 10 millions user profiles from the largest chinese mircoblog sina weibo and 41 7 millions profiles from twitter by studying followers topology we find an invariant characteristic that the followers count of users obeys a power law distribution with exponent near 2 we then investigate the reason from the theoretical view and find this network structure achieves the optimal information diffusion in terms of inducing a minimal propagation times our study thus reveals the efficiency of information diffusion in osns of microblogs which is validated by experimental examination theoretical analysis and numerical simulation

estimation of the number of communities in the stochastic block model in this article we introduce an estimator for the number of communities in the stochastic block model sbm based on the maximization of a penalized version of the so called krichevsky trofimov mixture distribution we prove its eventual almost sure convergence to the underlying number of communities without assuming a known upper bound on that quantity our results apply to both the dense and the sparse regimes to our knowledge this is the first consistency result for the estimation of the number of communities in the sbm in the unbounded case that is when the number of communities is allowed to grow with the same size

consistent order estimation and minimal penalties consider an i i d sequence of random variables whose distribution f lies in one of the nested families of models mq q 1 the smallest index q such that mq contains f is called the model order the aim of this paper is to explore the consistency properties of penalized likelihood model order estimators such as bayesian information criterion we show in a general setting that the minimal strongly consistent penalty is of order q loglogn where q is a dimensional quantity in contrast to previous work an a priori upper bound on the model order is not assumed the results rely on a sharp characterization of the pathwise fluctuations of the generalized likelihood ratio statistic under entropy assumptions on the model classes our results are applied to the geometrically complex problem of location mixture order estimation which is widely used but poorly understood

performance analysis of grammar based codes revisited the compression performance of grammar based codes is revisited from a new perspective previously the compression performance of grammar based codes was evaluated against that of the best arithmetic coding algorithm with finite contexts in this correspondence we first define semifinite state sources and finite order semi markov sources based on the definitions of semifinite state sources and finite order semi markov sources and the idea of run length encoding rle we then extend traditional rle algorithms to context based rle algorithms rle algorithms with k contexts and rle algorithms of order k where k is a nonnegative integer for each individual sequence x let r sup sub sr k x and r sup sub sr k x be the best compression rate given by rle algorithms with k contexts and by rle algorithms of order k respectively it is proved that for any x r sup sub sr k is no greater than the best compression rate among all arithmetic coding algorithms with k contexts furthermore it is shown that there exist stationary ergodic semi markov sources for which the best rle algorithms without any context outperform the best arithmetic coding algorithms with any finite number of contexts finally we show that the worst case redundancies of grammar based codes against r sup sub sr k x and r sup sub sr k x among all length n individual sequences x from a finite alphabet are upper bounded by d sub 1 loglogn logn and d sub 2 loglogn logn respectively where d sub 1 and d sub 2 are constants this redundancy result is stronger than all previous corresponding results

on the online bin packing problem a new framework for analyzing online bin packing algorithms is presented this framework presents a unified way of explaining the performance of algorithms based on the harmonic approach within this framework it is shown that a new algorithm harmonic has asymptotic performance ratio at most 1 58889 it is also shown that the analysis of harmonic 1 presented in richey 1991 is incorrect this is a fundamental logical flaw not an error in calculation or an omitted case the asymptotic performance ratio of harmonic 1 is at least 1 59217 thus harmonic provides the best upper bound for the online bin packing problem to date

prediction for discrete time series let x n be a stationary and ergodic time series taking values from a finite or countably infinite set assume that the distribution of the process is otherwise unknown we propose a sequence of stopping times n along which we will be able to estimate the conditional probability p x x0 from data segment x0 in a pointwise consistent way for a restricted class of stationary and ergodic finite or countably infinite alphabet time series which includes among others all stationary and ergodic finitarily markovian processes if the stationary and ergodic process turns out to be finitarily markovian among others all stationary and ergodic markov chains are included in this class then almost surely if the stationary and ergodic process turns out to possess finite entropy rate then n is upperbounded by a polynomial eventually almost surely

the consistency of the bic markov order estimator the bayesian information criterion bic estimates the order of a markov chain with finite alphabet a from observation of a sample path x 1 x 2 x n as that value k k that minimizes the sum of the negative logarithm of the kth order maximum likelihood and the penalty term a k a 1 2 log n we show that k equals the correct order of the chain eventually almost surely as n oo thereby strengthening earlier consistency results that assumed an apriori bound on the order a key tool is a strong ratio typicality result for markov sample paths we also show that the bayesian estimator or minimum description length estimator of which the bic estimator is regarded as an approximation fails to be consistent for the uniformly distributed i i d process

stability and hopf bifurcation analysis of an eco epidemic model with a stage structure abstract in this paper an eco epidemiological model with a stage structure is considered the asymptotical stability of the five equilibria the existence of stability switches about positive equilibrium is investigated it is found that hopf bifurcation occurs when the delay passes though a critical value some explicit formulae determining the stability and the direction of the hopf bifurcation periodic solutions bifurcating from hopf bifurcations are obtained by using the normal form theory and center manifold theory some numerical simulations for justifying the theoretical analysis are also provided finally biological explanations and main conclusions are given

fully dynamic bin packing revisited we consider the fully dynamic bin packing problem where items arrive and depart in an online fashion and repacking of previously packed items is allowed the goal is of course to minimize both the number of bins used as well as the amount of repacking a recently introduced way of measuring the repacking costs at each timestep is the migration factor defined as the total size of repacked items divided by the size of an arriving or departing item concerning the trade off between number of bins and migration factor if we wish to achieve an asymptotic competitive ratio of 1 epsilon for the number of bins a relatively simple argument proves a lower bound of omega 1 epsilon for the migration factor we establish a nearly matching upper bound of o 1 epsilon 4 log 1 epsilon using a new dynamic rounding technique and new ideas to handle small items in a dynamic setting such that no amortization is needed the running time of our algorithm is polynomial in the number of items nand in 1 epsilon the previous best trade off was for an asymptotic competitive ratio of 5 4 for the bins rather than 1 epsilon and needed an amortized number of o log n repackings while in our scheme the number of repackings is independent of n and non amortized

a robust aptas for the classical bin packing problem bin packing is a well studied problem which has many applications in this paper we design a robust aptas for the problem the robust aptas receives a single input item to be added to the packing at each step it maintains an approximate solution throughout this process by slightly adjusting the solution for each new item at each step the total size of items which may migrate between bins must be bounded by a constant factor times the size of the new item we show that such a property cannot be maintained with respect to optimal solutions

partial differential equation modeling of malware propagation in social networks with mixed delays abstract with the wide applications of social networks government and individuals increasingly emphasize information networks security this paper is devoted to investigating a reaction diffusion malware propagation model with mixed delays to describe the process of social networks applying matrix theory for characteristic values we establish the local stability conditions of a positive equilibrium point based on the linear approximation method of nonlinear systems the hopf bifurcation at the positive equilibrium point is considered additionally we identify some sensitive parameters in the process of malware propagation that are significant for control theory finally numerical simulations are performed to illustrate the theoretical results

limits to consistent on line forecasting for ergodic time series this article concerns problems of time series forecasting under the weakest of assumptions related results are surveyed and are points of departure for the developments here some of which are new and others are new derivations of previous findings the contributions in this study are all negative showing that various plausible prediction problems are unsolvable or in other cases are not solvable by predictors which are known to be consistent when mixing conditions hold

estimating the lengths of memory words for a stationary stochastic process xn with values in some set a a finite word w isin ak is called a memory word if the conditional probability of x 0 given the past is constant on the cylinder set defined by x k 1 w it is a called a minimal memory word if no proper suffix of w is also a memory word for example in a k step markov processes all words of length k are memory words but not necessarily minimal we consider the problem of determining the lengths of the longest minimal memory words and the shortest memory words of an unknown process xn based on sequentially observing the outputs of a single sample xi1 xi2 xin we will give a universal estimator which converges almost surely to the length of the longest minimal memory word and show that no such universal estimator exists for the length of the shortest memory word the alphabet a may be finite or countable

hidden markov models with applications in cell adhesion experiments estimation of the number of hidden states is challenging in hidden markov models motivated by the analysis of a specific type of cell adhesion experiments a new framework based on a hidden markov model and double penalized order selection is proposed the order selection procedure is shown to be consistent in estimating the number of states a modified expectation maximization algorithm is introduced to efficiently estimate parameters in the model simulations show that the proposed framework outperforms existing methods applications of the proposed methodology to real data demonstrate the accuracy of estimating receptor ligand bond lifetimes and waiting times which are essential in kinetic parameter estimation supplementary materials for this article are available online

large scale typicality of markov sample paths and consistency of mdl order estimators for markov chains of arbitrary order with finite alphabet a almost sure sense limit theorems are proved on relative frequencies of k blocks and of symbols preceded by a given k block when k is permitted to grow as the sample size n grows as an application the consistency of two kinds of minimum description length mdl markov order estimators is proved with upper bound o log n respectively spl alpha log n with spl alpha 1 log a on the permissible value of the estimated order it was shown by csiszar and shields see ann statist vol 28 p 1601 1619 2000 that in the absence of any bound or with bound spl alpha log n with large spl alpha consistency fails

theory of rumour spreading in complex social networks we introduce a general stochastic model for the spread of rumours and derive mean field equations that describe the dynamics of the model on complex social networks in particular those mediated by the internet we use analytical and numerical solutions of these equations to examine the threshold behaviour and dynamics of the model on several models of such networks random graphs uncorrelated scale free networks and scale free networks with assortative degree correlations we show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system in the case of scale free networks on the other hand this threshold becomes vanishingly small in the limit of infinite system size we find that the initial rate at which a rumour spreads is much higher in scale free networks than in random graphs and that the rate at which the spreading proceeds on scale free networks is further increased when assortative degree correlations are introduced the impact of degree correlations on the final fraction of nodes that ever hears a rumour however depends on the interplay between network topology and the rumour spreading rate our results show that scale free social networks are prone to the spreading of rumours just as they are to the spreading of infections they are relevant to the spreading dynamics of chain emails viral advertising and large scale information dissemination algorithms on the internet

scaling fields in the two dimensional abelian sandpile model we consider the unoriented two dimensional abelian sandpile model from a perspective based on two dimensional conformal field theory we compute lattice correlation functions for various cluster variables at and off criticality from which we infer the field theoretic description in the scaling limit we find perfect agreement with the predictions of a c 2 conformal field theory and its massive perturbation thereby providing direct evidence for conformal invariance and more generally for a description in terms of a local field theory the question of the height 2 variable is also addressed with however no definite conclusion yet

super mediator a new centrality measure of node importance for information diffusion over social network we propose an efficient method to discover a new type of influential nodes in a social network which we name super mediators i e those nodes which if removed decrease information spread it is formulated mathematically as a problem of difference maximization of the average influence degree with respect to removal of a node i e a node that contributes to making the difference large is influential this definition requires use of information diffusion model for their identification and thus is model driven the other definition which is more empirical is that super mediators are those nodes that appear frequently in long diffusion sequences but much less frequently in short diffusion sequences this definition does not require any model but does require abundant information diffusion data and thus is data driven we attempt to characterize the property of super mediators from various angles how the resulting super mediators are different between these two definitions and which is more reasonable how super mediators are compared with nodes identified by other centralities e g betweenness degree closeness etc how super mediators are different from the solution of well studied influence maximization problem i e nodes capable of widely spreading information to other recipient nodes and the solution of reverse influence maximization problem i e nodes capable of widely receiving information from other information source nodes we conducted extensive experiments using three real world social networks the major findings are 1 model driven super mediator degree has the best discrimination capability while influence degree reverse influence degree and data driven super mediator degree are much less discriminative all flat for high ranked nodes 2 model driven super mediators have high scores for either influence degree or reverse influence degree while data driven super mediators have high scores for both and 3 model driven super mediators are closely correlated with betweenness centrality but the strength of the correlation depends on the value of diffusion probability

a simple on line bin packing algorithm the one dimensional on line bin packing problem is considered a simple o 1 space and o n time algorithm called harmonic m is presented it is shown that this algorithm can achieve a worst case performance ratio of less than 1 692 which is better than that of the o n space and o n log n time algorithm first fit also shown is that 1 691 is a lower bound for all 0 1 space on line bin packing algorithms finally a revised version of harmonic m an o n space and o n time algorithm is presented and is shown to have a worst case performance ratio of less than 1 636 d

stability and hopf bifurcation analysis on a ring of four neurons with delays we consider a four neuron ring with self feedback and delays by analyzing the associated characteristic equation linear stability is investigated and hopf bifurcations are demonstrated as well as the stability and direction of the hopf bifurcation are determined by employing the normal form method and the center manifold reduction numerical simulations are presented to illustrate the results

order estimation of markov chains estimators spl chi sub n x sub 0 x sub 1 x sub n are described which when applied to an unknown stationary process taking values from a countable alphabet spl chi converge almost surely to k in case the process is a kth order markov chain and to infinity otherwise