stochastic upscaling in solid mechanics an excercise in machine learning this paper presents a consistent theoretical and computational framework for upscaling in random microstructures we adopt an information theoretic approach in order to quantify the informational content of the microstructural details and find ways to condense it while assessing quantitatively the approximation introduced in particular we substitute the high dimensional microscale description by a lower dimensional representation corresponding for example to an equivalent homogeneous medium the probabilistic characteristics of the latter are determined by minimizing the distortion between actual macroscale predictions and the predictions made using the coarse model a machine learning framework is essentially adopted in which a vector quantizer is trained using data generated computationally or collected experimentally several parallels and differences with similar problems in source coding theory are pointed out and an efficient computational tool is employed various applications in linear and non linear problems in solid mechanics are examined

a near tight lower bound on the time complexity of distributed minimum weight spanning tree construction this paper presents a lower bound of omega d sqrt n log n on the time required for the distributed construction of a minimum weight spanning tree mst in weighted n vertex networks of diameter d omega log n in the bounded message model this establishes the asymptotic near optimality of existing time efficient distributed algorithms for the problem whose complexity is o d sqrt n log n

learning overcomplete representations in an overcomplete basis the number of basis vectors is greater than the dimensionality of the input and the representation of an input is not a unique combination of basis vectors overcomplete representations have been advocated because they have greater robustness in the presence of noise can be sparser and can have greater flexibility in matching structure in the data overcomplete codes have also been proposed as a model of some of the response properties of neurons in primary visual cortex previous work has focused on finding the best representation of a signal using a fixed overcomplete basis or dictionary we present an algorithm for learning an overcomplete basis by viewing it as probabilistic model of the observed data we show that overcomplete bases can yield a better approximation of the underlying statistical distribution of the data and can thus lead to greater coding efficiency this can be viewed as a generalization of the technique of independent component analysis and provides a method for bayesian reconstruction of signals in the presence of noise and for blind source separation when there are more sources than mixtures

a bayesian approach to multiscale inverse problems with on the fly scale determination abstract a bayesian computational approach is presented to provide a multi resolution estimate of an unknown spatially varying parameter from indirect measurement data in particular we are interested in spatially varying parameters with multiscale characteristics in our work we consider the challenge of not knowing the characteristic length scale s of the unknown a priori and present an algorithm for on the fly scale determination our approach is based on representing the spatial field with a wavelet expansion wavelet basis functions are hierarchically structured localized in both spatial and frequency domains and tend to provide sparse representations in that a large number of wavelet coefficients are approximately zero for these reasons wavelet bases are suitable for representing permeability fields with non trivial correlation structures moreover the intra scale correlations between wavelet coefficients form a quadtree and this structure is exploited to identify additional basis functions to refine the model bayesian inference is performed using a sequential monte carlo smc sampler with a markov chain monte carlo mcmc transition kernel the smc sampler is used to move between posterior densities defined on different scales thereby providing a computationally efficient method for adaptive refinement of the wavelet representation we gain insight from the marginal likelihoods by computing bayes factors for model comparison and model selection the marginal likelihoods provide a termination criterion for our scale determination algorithm the bayesian computational approach is rather general and applicable to several inverse problems concerning the estimation of a spatially varying parameter the approach is demonstrated with permeability estimation for groundwater flow using pressure sensor measurements

master equation for the degree distribution of a duplication and divergence network abstract network growth as described by the duplication divergence model proposes a simple general idea for the evolution dynamics of natural networks in particular it is an alternative to the well known barabasi albert model when applied to protein protein interaction networks in this work we derive a master equation for the node degree distribution of networks growing via duplication and divergence and we obtain an expression for the total number of links and for the degree distribution as a function of the number of nodes using algebra tools we investigate the degree distribution asymptotic behavior analytic results show that the network nodes average degree converges if the total mutation rate is greater than 0 5 and diverges otherwise treating original and duplicated node mutation rates as independent parameters has no effect on this result however difference in these parameters results in a slower rate of convergence and in different degree distributions the more different these parameters are the denser the tail of the distribution we compare the solutions obtained with simulated networks these results are in good agreement with the expected values from the derived expressions the method developed is a robust tool to investigate other models for network growing dynamics

central limit theorem for sequential monte carlo methods and its application to bayesian inference the term sequential monte carlo methods or equivalently particle filters refers to a general class of iterative algorithms that performs monte carlo approximations of a given sequence of distributions of interest t we establish in this paper a central limit theorem for the monte carlo estimates produced by these computational methods this result holds under minimal assumptions on the distributions t and applies in a general framework which encompasses most of the sequential monte carlo methods that have been considered in the literature including the resample move algorithm of gilks and berzuini j r stat soc ser b stat methodol 63 2001 127 146 and the residual resampling scheme the corresponding asymptotic variances provide a convenient measurement of the precision of a given particle filter we study in particular in some typical examples of bayesian applications whether and at which rate these asymptotic variances diverge in time in order to assess the long term reliability of the considered algorithm

a variational bayesian method to inverse problems with impulsive noise we propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers the approach is of bayesian type and it exploits a heavy tailed t distribution for data noise to achieve robustness with respect to outliers a hierarchical model with all hyper parameters automatically determined from the given data is described an algorithm of variational type by minimizing the kullback leibler divergence between the true posteriori distribution and a separable approximation is developed the numerical method is illustrated on several one and two dimensional linear and nonlinear inverse problems arising from heat conduction including estimating boundary temperature heat flux and heat transfer coefficient the results show its robustness to outliers and the fast and steady convergence of the algorithm

two absolute bounds for distributed bit complexity the concept of distributed communication bit complexity was introduced by dinitz rajsbaum and moran they studied the bit complexity of consensus and leader election arriving at more or less exact bounds this paper answers two questions on leader election which remained there open the first is to close the gap between the known upper and lower bounds for electing a leader by two linked processors the second is whether the suggested algorithm sending 1 5n bits while electing a leader in a chain of even length n is optimal in the case when n is known to the processors for both problems absolutely exact bounds are found moreover the presented lower bound proofs show that there is no optimal algorithm other than the suggested ones

sensor placement for calibration of spatially varying model parameters abstract this paper presents a sensor placement optimization framework for the calibration of spatially varying model parameters to account for the randomness of the calibration parameters over space and across specimens the spatially varying parameter is represented as a random field based on this representation bayesian calibration of spatially varying parameter is investigated to reduce the required computational effort during bayesian calibration the original computer simulation model is substituted with kriging surrogate models based on the singular value decomposition svd of the model response and the karhunen loeve expansion kle of the spatially varying parameters a sensor placement optimization problem is then formulated based on the bayesian calibration to maximize the expected information gain measured by the expected kullback leibler k l divergence the optimization problem needs to evaluate the expected k l divergence repeatedly which requires repeated calibration of the spatially varying parameter and this significantly increases the computational effort of solving the optimization problem to overcome this challenge an approximation for the posterior distribution is employed within the optimization problem to facilitate the identification of the optimal sensor locations using the simulated annealing algorithm a heat transfer problem with spatially varying thermal conductivity is used to demonstrate the effectiveness of the proposed method

exactly solvable random graph ensemble with extensively many short cycles we introduce and analyse ensembles of 2 regular random graphs with a tuneable distribution of short cycles the phenomenology of these graphs depends critically on the scaling of the ensembles control parameters relative to the number of nodes a phase diagram is presented showing a second order phase transition from a connected to a disconnected phase we study both the canonical formulation where the size is large but fixed and the grand canonical formulation where the size is sampled from a discrete distribution and show their equivalence in the thermodynamical limit we also compute analytically the spectral density which consists of a discrete set of isolated eigenvalues representing short cycles and a continuous part representing cycles of diverging size

randomised distributed mis and colouring algorithms for rings with oriented edges in o log ź n bit rounds we present and analyse las vegas distributed algorithms which compute a mis or a colouring for anonymous rings with an arbitrary orientation of the edges their bit complexity and time complexity are o log n with high probability these algorithms are optimal modulo a multiplicative constant

exact leaf powers we define and study the new notion of exact k leaf powers where a graph g v g e g is an exact k leaf power if and only if there exists a tree t v t e t an exact k leaf root of g whose set of leaves equals v g such that email protected e g holds for u email protected v g if and only if the distance of u and v in t is exactly k this new notion is closely related to but different from leaf powers and neighbourhood subtree tolerance graphs we prove characterizations of exact 3 and 4 leaf powers which imply that such graphs can be recognized in linear time and that also the corresponding exact leaf roots can be found in linear time furthermore we characterize all exact 5 leaf roots of chordless cycles and derive several properties of exact 5 leaf powers

distributed coloring algorithms for triangle free graphs vertex coloring is a central concept in graph theory and an important symmetry breaking primitive in distributed computing whereas degree graphs may require palettes of 1 colors in the worst case it is well known that the chromatic number of many natural graph classes can be much smaller in this paper we give new distributed algorithms to find k coloring in graphs of girth 4 triangle free graphs girth 5 and trees the parameter k can be at most 1 4 o 1 ln in triangle free graphs and at most 1 o 1 ln in girth 5 graphs and trees where o 1 is a function of specifically for sufficiently large we can find such a coloring in o k log n time moreover for any we can compute such colorings in roughly logarithmic time for triangle free and girth 5 graphs and in o log log log n time on trees as a byproduct our algorithm shows that the chromatic number of triangle free graphs is at most 4 o 1 ln which improves on jamall s recent bound of 67 o 1 ln finally we show that 1 coloring for triangle free graphs can be obtained in sublogarithmic time for any

a distributed enumeration algorithm and applications to all pairs shortest paths diameter we consider the standard message passing model we assume the system is fully synchronous all processes start at the same time and time proceeds in synchronised rounds in each round each vertex can transmit a different message of size o 1 to each of its neighbours this paper proposes and analyses a distributed enumeration algorithm of vertices of a graph having a distinguished vertex which satisfies that two vertices with consecutive numbers are at distance at most 3 we prove that its time complexity is o n where n is the number of vertices of the graph furthermore the size of each message is o 1 thus its bit complexity is also o n we provide some links between this enumeration and hamiltonian graphs from which we deduce that this enumeration is optimal in the sense that there does not exist an enumeration which satisfies that two vertices with consecutive numbers are at distance at most 2 we deduce from this enumeration algorithms which compute all pairs shortest paths and the diameter with a time complexity and a bit complexity equal to o n

a fast network decomposition algorithm and its applications to constant time distributed computation abstract a partition c 1 c 2 c q of g v e into clusters of strong respectively weak diameter d such that the supergraph obtained by contracting each c i is l colorable is called a strong resp weak d l network decomposition network decompositions were introduced in a seminal paper by awerbuch goldberg luby and plotkin in 1989 awerbuch et al showed that strong d l network decompositions with d l exp o log n log log n can be computed in distributed deterministic time o d even more importantly they demonstrated that network decompositions can be used for a great variety of applications in the message passing model of distributed computing the result of awerbuch et al was improved by panconesi and srinivasan in 1992 in the latter result d l exp o log n and the running time is o d as well in another remarkable breakthrough linial and saks in 1992 showed that weak o log n o log n network decompositions can be computed in distributed randomized time o log 2 n much more recently barenboim 2012 devised a distributed randomized constant time algorithm for computing strong network decompositions with d o 1 however the parameter l in his result is o n 1 2 in this paper we drastically improve the result of barenboim and devise a distributed randomized constant time algorithm for computing strong o 1 o n network decompositions as a corollary we derive a constant time randomized o n approximation algorithm for the distributed minimum coloring problem improving the previously best known o n 1 2 approximation guarantee we also derive other improved distributed algorithms for a variety of problems most notably for the extremely well studied distributed minimum dominating set problem currently there is no known deterministic polylogarithmic time algorithm we devise a deterministic polylogarithmic time approximation algorithm for this problem addressing an open problem of lenzen and wattenhofer 2010

local algorithms for edge colorings in udgs in this paper we consider two problems the edge coloring and the strong edge coloring problems on unit disk graphs udgs both problems have important applications in wireless sensor networks as they can be used to model link scheduling problems in such networks it is well known that both problems are np complete and approximation algorithms for them have been extensively studied under the centralized model of computation centralized algorithms however are not suitable for ad hoc wireless sensor networks whose devices typically have limited resources and lack the centralized coordination we develop local distributed approximation algorithms for the edge coloring and the strong edge coloring problems on unit disk graphs for the edge coloring problem our local distributed algorithm has approximation ratio 2 and locality 50 for the strong edge coloring problem on udgs we present two local distributed algorithms with different tradeoffs between their approximation ratio and locality the first algorithm has ratio 128 and locality 22 whereas the second algorithm has ratio 10 and locality 180

selection of model discrepancy priors in bayesian calibration abstract in the kennedy and o hagan framework for bayesian calibration of physics models selection of an appropriate prior form for the model discrepancy function is a challenging issue due to the lack of physics knowledge regarding model inadequacy aiming to address the uncertainty arising from the selection of a particular prior this paper first conducts a study on possible formulations of the model discrepancy function a first order taylor series expansion based method is developed to investigate the potential redundancy caused by adding a discrepancy function to the original physics model further we propose a three step calibration validation and combination approach in order to inform the decision on the construction of model discrepancy priors in the validation step a reliability based metric is used to evaluate posterior model predictions in the validation domain the validation metric serves as a quantitative measure of how well the discrepancy formulation captures the missing physics in the model in the combination step the posterior distributions of model parameters and discrepancy corresponding to different priors are combined into a single distribution based on the probabilistic weights derived from the validation step the combined distribution acknowledges the uncertainty in the prior formulation of model discrepancy function

generalised gibbs sampler and multigrid monte carlo for bayesian computation summary although monte carlo methods have frequently been applied with success indiscriminate use of markov chain monte carlo leads to unsatisfactory performances in numerous applications we present a generalised version of the gibbs sampler that is based on conditional moves along the traces of groups of transformations in the sample space we explore its connection with the multigrid monte carlo method and its use in designing more efficient samplers the generalised gibbs sampler provides a framework encompassing a class of recently proposed tricks such as parameter expansion and reparameterisation to illustrate we apply this new method to bayesian inference problems for nonlinear state space models ordinal data and stochastic differential equations with discrete observations

improved distributed approximate matching we present distributed network algorithms to compute weighted and unweighted matchings with improved approximation ratios and running times the computational model is a network of processors exchanging o log n bit messages the congest model for unweighted graphs we give an algorithm providing 1 e approximation in o log n time for any constant e 0 improving on the classical approximation in olog n time of israeli and itai 1986 the time complexity of the algorithm depends on 1he exponentially in the general case and polynomially in bipartite graphs for weighted graphs we present another algorithm which provides e approximation in general graphs in o loge 1log n time improving on the previously known algorithms which attain e approximation in o log n time or approximation in o n time all our algorithms are randomized the complexity bounds hold both with high probability and for the expected running time

a multi resolution non parametric bayesian framework for identification of spatially varying model parameters this paper proposes a hierarchical multi resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output such parameters are frequently encountered in pde based models and correspond to quantities such as density or pressure fields elasto plastic moduli and internal variables in solid mechanics conductivity fields in heat diffusion problems permeability fields in fluid flow through porous media etc the proposed model has all the advantages of traditional bayesian formulations such as the ability to produce measures of confidence for the inferences made and providing not only predictive estimates but also quantitative measures of the predictive uncertainty in contrast to existing approaches it utilizes a parsimonious non parametric formulation that favors sparse representations and whose complexity can be determined from the data the proposed framework in non intrusive and makes use of a sequence of forward solvers operating at various resolutions as a result inexpensive coarse solvers are used to identify the most salient features of the unknown field s which are subsequently enriched by invoking solvers operating at finer resolutions this leads to significant computational savings particularly in problems involving computationally demanding forward models but also improvements in accuracy it is based on a novel adaptive scheme based on sequential monte carlo sampling which is embarrassingly parallelizable and circumvents issues with slow mixing encountered in markov chain monte carlo schemes the capabilities of the proposed methodology are illustrated in problems from nonlinear solid mechanics with special attention to cases where the data is contaminated with random noise and the scale of variability of the unknown field is smaller than the scale of the grid where observations are collected

a mathematical model for generating bipartite graphs and its application to protein networks complex systems arise in many different contexts from large communication systems and transportation infrastructures to molecular biology most of these systems can be organized into networks composed of nodes and interacting edges here we present a theoretical model that constructs bipartite networks with the particular feature that the degree distribution can be tuned depending on the probability rate of fundamental processes we then use this model to investigate protein domain networks a protein can be composed of up to hundreds of domains each domain represents a conserved sequence segment with specific functional tasks we analyze the distribution of domains in homo sapiens and arabidopsis thaliana organisms and the statistical analysis shows that while a the number of domain types shared by k proteins exhibits a power law distribution b the number of proteins composed of k types of domains decays as an exponential distribution the proposed mathematical model generates bipartite graphs and predicts the emergence of this mixing of a power law and b exponential distributions our theoretical and computational results show that this model requires 1 growth process and 2 copy mechanism

efficient quantum algorithms for simulating sparse hamiltonians we present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse hamiltonian h over a given time t in terms of a procedure for computing the matrix entries of h in particular when h acts on n qubits has at most a constant number of nonzero entries in each row column and h is bounded by a constant we may select any positive integer k such that the simulation requires o log n t1 1 2k accesses to matrix entries of h we also show that the temporal scaling cannot be significantly improved beyond this because sublinear time scaling is not possible

a bayesian approach to characterizing uncertainty in inverse problems using coarse and fine scale information the bayesian approach allows one to easily quantify uncertainty at least in theory in practice however the markov chain monte carlo mcmc method can be computationally expensive particularly in complicated inverse problems we present a methodology for improving the speed and efficiency of an mcmc analysis by combining runs on different scales by using a coarser scale the chain can run faster particularly when there is an external forward simulator involved in the likelihood evaluation and better explore the posterior being less likely to become stuck in local maxima we discuss methods for linking the coarse chain back to the original fine scale chain of interest the resulting coupled chain can thus be run more efficiently without sacrificing the accuracy achieved at the finer scale

low weight superimposed codes and related combinatorial structures bounds and applications abstract a k n superimposed code is a well known and widely used combinatorial structure that can be represented by a t n binary matrix such that for any k columns of the matrix and for any column c chosen among these k columns there exists a row in correspondence of which column c has an entry equal to 1 and the remaining k 1 columns have entries equal to 0 due to the many situations in which superimposed codes find applications there is an abundant literature that studies the problem of constructing k n superimposed codes with a small number t of rows motivated by applications to conflict free communication in multiple access networks group testing and data security we study the problem of constructing superimposed codes that have the additional constraints that the number of 1 s in each column of the matrix is constant and equal to an input parameter w our results improve on the known literature in the area we also extend our findings to other important combinatorial structures like selectors generalized superimposed codes and z error correcting superimposed codes

wavelet based numerical homogenization a numerical homogenization procedure for elliptic differential equations is presented it is based on wavelet decompositions of discrete operators in fine and coarse scale components followed by the elimination of the fine scale contributions if the operator is in divergence form this is preserved by the homogenization procedure for periodic problems results similar to classical effective coefficient theory are proved the procedure can be applied to problems that are not cell periodic

stochastic identification of imperfections in a submerged shell structure abstract accurate predictions of the buckling load in imperfection sensitive shell structures requires precise knowledge of the location and magnitude of any geometric imperfections in the shell e g dents this work describes a non contact approach to identifying such imperfections in a submerged shell structure by monitoring the acoustic pressure field at discrete points proximal to a shell structure excited by a cyclic membrane i e in plane loading it is noticed that parameters describing small scale denting can be identified in order to perform the identification a fluid structure model that predicts the spatio temporal pressure field is required this model is described in detail and includes the predicted effects of the imperfection on the observations a bayesian markov chain monte carlo approach is then used to generate the imperfection parameter estimates and quantify the uncertainty in those estimates additionally for cases involving the occurrence of an unknown number of dents reversible jump markov chain monte carlo rjmcmc methods are employed in this work

the local nature of list colorings for graphs of high girth we consider list coloring problems for graphs mathcal g of girth larger than c log delta 1 n where n and delta geq3 are respectively the order and the maximum degree of mathcal g and c is a suitable constant first we determine that the edge and total list chromatic numbers of these graphs are chi l mathcal g delta and chi l mathcal g delta 1 this proves that the general conjectures of bollobas and harris graphs combin 1 1985 pp 115 127 behzad the total chromatic number in combinatorial mathematics and its applications proc conf oxford 1969 academic press london 1971 pp 1 8 vizing diskret analiz 3 1964 pp 25 30 and juvan mohar and skrekovski combin probab comput 7 1998 pp 181 188 hold for this particular class of graphs moreover our proofs exhibit a certain degree of locality which we exploit to obtain an efficient distributed algorithm able to compute both kinds of optimal list colorings also using an argument similar to one of erdos we show that our algorithm can compute k list vertex colorings of graphs having girth larger than c log k 1 n

locality in distributed graph algorithms this paper concerns a number of algorithmic problems on graphs and how they may be solved in a distributed fashion the computational model is such that each node of the graph is occupied by a processor which has its own id processors are restricted to collecting data from others which are at a distance at most t away from them in t time units but are otherwise computationally unbounded this model focuses on the issue of locality in distributed processing namely to what extent a global solution to a computational problem can be obtained from locally available data three results are proved within this model a 3 coloring of an n cycle requires time omega log n this bound is tight by previous work of cole and vishkin any algorithm for coloring the d regular tree of radius r which runs for time at most 2r 3 requires at least omega sqrt d colors in an n vertex graph of largest degree delta an o delta 2 coloring may be found in time o log n

deterministic broadcasting time with partial knowledge of the network we consider the time of deterministic broadcasting in networks whose nodes have limited knowledge of network topology each node v knows only the part of the network within knowledge radiusr from it i e it knows the graph induced by all nodes at distance at most r from v apart from that each node knows the maximum degree of the network one node of the network called the source has a message which has to reach all other nodes we adopt the widely studied communication model called the one way model in which in every round each node can communicate with at most one neighbor and in each pair of nodes communicating in a given round one can only send a message while the other can only receive it this is the weakest of all store and forward models for point to point networks and hence our algorithms work for other models as well in at most the same time we show trade offs between knowledge radius and time of deterministic broadcasting when the knowledge radius is small i e when nodes are only aware of their close vicinity while for knowledge radius 0 minimum broadcasting time is e where e is the number of edges in the network broadcasting can be usually completed faster for positive knowledge radius our main results concern knowledge radius 1 we develop fast broadcasting algorithms and analyze their execution time we also prove lower bounds on broadcasting time showing that our algorithms are close to optimal

improved distributed algorithms for coloring interval graphs with application to multicoloring trees we give a distributed 1 epsilon approximation algorithm for the minimum vertex coloring problem on interval graphs which runs in the mathcal local model and operates in mathrm o frac 1 epsilon log n rounds if nodes are aware of their interval representations then the algorithm can be adapted to the mathcal congest model using the same number of rounds prior to this work only constant factor approximations using mathrm o log n rounds were known 12 linial s ring coloring lower bound implies that the dependency on log n cannot be improved we further prove that the dependency on frac 1 epsilon is also optimal

patterns from nature a well established problem in global optimization is the problem of colouring the vertices of an arbitrary graph using the minimal number of colours such that adjacent vertices are assigned different colours one way to restrict the number of colours used is to allow only greedy colourings a greedy colouring is an assignment of colours to the vertices of a graph that can be obtained by an algorithm that considers each vertex in turn and assigns the first colour that is not already assigned to some neighbour an optimal colouring can always be obtained in this way by choosing an appropriate order on the vertices recently a new bio inspired approach to distributed pattern formation has been proposed based on modelling the neurological development of the fruit fly building on that approach we propose a new simple randomised algorithm for distributed greedy colouring using only local processing at the vertices and messages along the edges in our approach the processors exchange only simple messages representing potential colour values and each processor has minimal graph knowledge we discuss two variations of this algorithm and investigate their time complexity and message complexity both theoretically and experimentally in addition we show experimentally that the number of colours used turns out to be optimal or near optimal for many standard graph colouring benchmarks thus for distributed networks our algorithm serves as an effective heuristic approach to computing a colouring with a small number of colours

new lower bound techniques for distributed leader finding and other problems on rings of processors several new lower bounds are derived for deterministic and randomized extrema finding and some other problems on asynchronous non anonymous rings of processors where the ring size n is known in advance to the processors with a new technique using results from extremal graph theory an n log n lower bounds is obtained for the average number of messages for distributed leader finding on rings where the processors know the ring size n and processors take identities from a set i with size as small as cn for any constant c 1 formerly this bound was only known for special values of n and exponential size of i also improvements are made on the constant factor of the n log n bound an elementary but powerful result shows that the same bounds hold for randomized algorithms it is shown the n log n lower bounds can be derived for the expected message complexity for computing and on an input 1n or on an input 0n or xor over all inputs even when processors have unique identities this confirms a conjecture of abrahamson et al 2

impact of observational incompleteness on the structural properties of protein interaction networks abstract the observed structure of protein interaction networks is corrupted by many false positive negative links this observational incompleteness is abstracted as random link removal and a specific experimentally motivated spoke link rearrangement their impact on the structural properties of gene duplication and mutation network models is studied for the degree distribution a curve collapse is found showing no sensitive dependence on the link removal rearrangement strengths and disallowing a quantitative extraction of model parameters the spoke link rearrangement process moves other structural observables like degree correlations cluster coefficient and motif frequencies closer to their counterparts extracted from the yeast data this underlines the importance to take a precise modeling of the observational incompleteness into account when network structure models are to be quantitatively compared to data

coarse gradient langevin algorithms for dynamic data integration and uncertainty quantification the main goal of this paper is to design an efficient sampling technique for dynamic data integration using the langevin algorithms based on a coarse scale model of the problem we compute the proposals of the langevin algorithms using the coarse scale gradient of the target distribution to guarantee a correct and efficient sampling each proposal is first tested by a metropolis acceptance rejection step with a coarse scale distribution if the proposal is accepted in the first stage then a fine scale simulation is performed at the second stage to determine the acceptance probability comparing with the direct langevin algorithm the new method generates a modified markov chain by incorporating the coarse scale information of the problem under some mild technical conditions we prove that the modified markov chain converges to the correct posterior distribution we would like to note that the coarse scale models used in the simulations need to be inexpensive but not necessarily very accurate as our analysis and numerical simulations demonstrate we present numerical examples for sampling permeability fields using two point geostatistics karhunen loeve expansion is used to represent the realizations of the permeability field conditioned to the dynamic data such as the production data as well as the static data the numerical examples show that the coarse gradient langevin algorithms are much faster than the direct langevin algorithms but have similar acceptance rates

some asymptotic properties of duplication graphs duplication graphs are graphs that grow by duplication of existing vertices and are important models of biological networks including protein protein interaction networks and gene regulatory networks three models of graph growth are studied pure duplication growth and two two parameter models in which duplication forms one element of the growth dynamics a power law degree distribution is found to emerge in all three models however the parameter space of the latter two models is characterized by a range of parameter values for which duplication is the predominant mechanism of graph growth for parameter values that lie in this duplication dominated regime it is shown that the degree distribution either approaches zero asymptotically or approaches a nonzero power law degree distribution very slowly in either case the approach to the true asymptotic degree distribution is characterized by a dependence of the scaling exponent on properties of the initial degree distribution it is therefore conjectured that duplication dominated scale free networks may contain identifiable remnants of their early structure this feature is inherited from the idealized model of pure duplication growth for which the exact finite size degree distribution is found and its asymptotic properties studied

randomized obdd based graph algorithms abstract implicit graph algorithms deal with the characteristic function e of the edge set e of a graph g v e encoding the nodes by binary vectors e can be represented by an ordered binary decision diagram obdd which is a well known data structure for boolean functions obdd based graph algorithms solve graph optimization problems by mainly using functional operations and are a heuristic approach to cope with massive graphs these algorithms heavily rely on a compact representation of the underlying boolean functions which is why all previously known obdd based algorithms are deterministic since random functions are not compressible in general here the first randomized obdd based algorithms are presented where random functions with limited independence are used to overcome the large representation size on the theoretical part we investigate the size of obdds representing k wise independent random functions in addition we give a construction of almost k wise independent random functions by means of a random obdd generation and show an almost matching lower bound of the obdd size representing such random functions on the algorithmic part randomization often facilitates the design of simple algorithms which in the context of obdd based algorithms means a small number of functional operations and as few input variables of the used boolean functions as possible we present two randomized implicit algorithms a randomized minimum spanning tree algorithm and a maximal matching algorithm the matching algorithm needs o log 3 v functional operations in expectation and uses functions with at most 3 log v variables which is both better than the best known deterministic algorithms w r t functional operations and variables the algorithm may be of independent interest the experimental evaluation of the algorithms shows that they outperform known obdd based algorithms for the maximal matching problem and the minimum spanning tree problem

local computation lower and upper bounds the question of what can be computed and how efficiently is at the core of computer science not surprisingly in distributed systems and networking research an equally fundamental question is what can be computed in a distributed fashion more precisely if nodes of a network must base their decision on information in their local neighborhood only how well can they compute or approximate a global optimization problem in this paper we give the first polylogarithmic lower bound on such local computation for optimization problems including minimum vertex cover minimum connected dominating set maximum matching maximal independent set and maximal matching in addition we present a new distributed algorithm for solving general covering and packing linear programs for some problems this algorithm is tight with the lower bounds whereas for others it is a distributed approximation scheme together our lower and upper bounds establish the local computability and approximability of a large class of problems characterizing how much local information is required to solve these tasks

local approximation of the maximum cut in regular graphs abstract this paper is devoted to the distributed complexity of finding an approximation of the maximum cut maxcut in graphs a classical algorithm consists in letting each vertex choose its side of the cut uniformly at random this does not require any communication and achieves an approximation ratio of at least 1 2 in expectation when the graph is d regular and triangle free a slightly better approximation ratio can be achieved with a randomized algorithm running in a single round here we investigate the round complexity of deterministic distributed algorithms for maxcut in regular graphs we first prove that if g is d regular with d even and fixed no deterministic algorithm running in a constant number of rounds can achieve a constant approximation ratio we then give a simple one round deterministic algorithm achieving an approximation ratio of 1 d for d regular graphs when d is odd we show that this is best possible in several ways and in particular no deterministic algorithm with approximation ratio 1 d with 0 can run in a constant number of rounds we also prove results of a similar flavor for the maxdicut problem in regular oriented graphs where we want to maximize the number of arcs oriented from the left part to the right part of the cut

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

local edge colouring of yao like subgraphs of unit disk graphs the focus of the present paper is on providing a local deterministic algorithm for colouring the edges of yao like subgraphs of unit disk graphs these are geometric graphs such that for some positive integers l k the following property holds at each node v if we partition the unit circle centered at v into 2k equally sized wedges then each wedge can contain at most l points different from v we assume that the nodes are location aware i e they know their cartesian coordinates in the plane the algorithm presented is local in the sense that each node can receive information emanating only from nodes which are at most a constant depending on k and l but not on the size of the graph number of hops measured in the original underlying unit disk graph away from it and hence the algorithm terminates in a constant number of steps the number of colours used is 2kl 1 and this is optimal for local algorithms since the maximal degree is 2kl and a colouring with 2kl colours can only be constructed by a global algorithm thus showing that in this class of graphs the price for locality is only one additional colour

quantifying randomness in protein protein interaction networks of different species a random matrix approach abstract we analyze protein protein interaction networks for six different species under the framework of random matrix theory nearest neighbor spacing distribution of the eigenvalues of adjacency matrices of the largest connected part of these networks emulate universal gaussian orthogonal statistics of random matrix theory we demonstrate that spectral rigidity which quantifies long range correlations in eigenvalues for all protein protein interaction networks follow random matrix prediction up to certain ranges indicating randomness in interactions after this range deviation from the universality evinces underlying structural features in network

bit complexity of breaking and achieving symmetry in chains and rings we consider a failure free asynchronous message passing network with n links where the processors are arranged on a ring or a chain the processors are identically programmed but have distinct identities taken from 0 1 m 1 we investigate the communication costs of three well studied tasks consensus leader and maxf finding the maximum identity we show that in chain and ring topologies the message complexities of all three tasks are the same hence we study a finer measure of complexity the number of transmitted bits required to solve a task t denoted bitc t we prove several new lower bounds and some simple upper bounds that imply the following results for the two processors case bitc consensus e 2 and bitc leader e bitc maxf e 2log2 m o 1 where the gap between the lower and upper bounds is almost always 1 for a chain bitc consensus e n bitc leader e n p log m and bitc maxf e n log m for the ring topology we prove the lower bound of n log m for leader and hence maxf we consider also a chain where the intermediate processors have no identities we prove that bitc leader e n log m which is equal to n times the bit complexity of the problem for two processors for the specific case when the chain length is even we prove that bitc leader e n for both above settings in addition we show that for any algorithm solving maxf there exists an input for which every execution has the bit complexity n log m this is not the case for leader in our proofs we use both methods of distributed computing and of communication complexity theory establishing new links between the two areas

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

distributed δ 1 coloring in sublogarithmic rounds we give a new randomized distributed algorithm for 1 coloring in the local model running in o log 2o log log n rounds in a graph of maximum degree this implies that the 1 coloring problem is easier than the maximal independent set problem and the maximal matching problem due to their lower bounds of min log n log log n log log log by kuhn moscibroda and wattenhofer podc 04 our algorithm also extends to list coloring where the palette of each node contains 1 colors we extend the set of distributed symmetry breaking techniques by performing a decomposition of graphs into dense and sparse parts

optimal two stage algorithms for group testing problems group testing refers to the situation in which one is given a set of objects cal o an unknown subset cal p subseteq cal o and the task of determining cal p by asking queries of the type does cal p intersect cal q where cal q is a subset of cal o group testing is a basic search paradigm that occurs in a variety of situations such as quality control testing searching in storage systems multiple access communications and data compression among others group testing procedures have been recently applied in computational molecular biology where they are used for screening libraries of clones with hybridization probes and sequencing by hybridization motivated by particular features of group testing algorithms used in biological screening we study the efficiency of two stage group testing procedures our main result is the first optimal two stage algorithm that uses a number of tests of the same order as the information theoretic lower bound on the problem we also provide efficient algorithms for the case in which there is a bernoulli probability distribution on the possible sets cal p and an optimal algorithm for the case in which the outcome of tests may be unreliable because of the presence of inhibitory items in cal o our results depend on a combinatorial structure introduced in this paper we believe that it will prove useful in other contexts too

optimal bit complexity randomised distributed mis and maximal matching algorithms for anonymous rings we present and analyse las vegas distributed algorithms which compute a mis or a maximal matching for anonymous rings their bit complexity and time complexity are o logn with high probability these algorithms are optimal modulo a multiplicative constant beyond the complexity results the interest of this work stands in the description and the analysis of these algorithms which may be easily generalised furthermore these results show a separation between the complexity of the mis problem and of the maximal matching problem on the one hand and the colouring problem on the other colouring can be computed only in w logn rounds on rings with high probability while mis is shown to have a faster algorithm this is in contrast to other models in which mis is at least as hard as colouring

multilevel sequential importance sampling for rare event estimation the estimation of the probability of rare events is an important task in reliability and risk assessment we consider failure events that are expressed in terms of a limit state function which dep

the distributed bit complexity of the ring in moran and warmuth 1993 siam j comput 22 no 2 379 399 it was shown that computing any non constant function on a ring of n of processors requires n log bits and this bound is tight this model assumed that all the processors in the ring are identical anonymous i e all processors run the same program and the only parameter of the program is the input to the processor in a relaxed model the anonymity is broken by providing each processor with a distinct identity which becomes a second parameter of the program that is executed by all processors if the set of possible identities grows doubly exponentially in n then by a reduction to the anonymous case one can show that the lower bound holds as well in this paper we show that the lower bound of n log n bits for computing any non constant function holds even if the set of possible identities is very small that is of sizer n1 for any positive

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

constructions of generalized superimposed codes with applications to group testing and conflict resolution in multiple access channels in this paper we introduce a parameterized generalization of the well known superimposed codes we give algorithms for their construction and provide non existential results we apply our new combinatorial structures to the efficient solution of new group testing problems and access coordination issues in multiple access channels

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

sequential monte carlo samplers summary we propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space each distribution being known up to a normalizing constant these probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential monte carlo methods this methodology allows us to derive simple algorithms to make parallel markov chain monte carlo algorithms interact to perform global optimization and sequential bayesian estimation and to compute ratios of normalizing constants we illustrate these algorithms for various integration tasks arising in the context of bayesian inference

on the time and the bit complexity of distributed randomised anonymous ring colouring we present and analyse a very simple randomised distributed vertex colouring algorithm for ring graphs its time complexity is log 2n o logn on average and 2log 2n o logn with probability 1 o n 1 since each message contains one bit we deduce the same values for its bit complexity then we combine this algorithm with another and we obtain a 3 colouring algorithm for ring graphs thanks to an overlapping we obtain once more the same values for the time complexities on average and with probability 1 o n 1 the same results hold for the bit complexity these results are obtained using the mellin transform we establish lower bounds on average and with probability 1 o n 1 for the distributed randomised anonymous ring colouring problem we prove that our algorithms match these lower bounds modulo a negligible additive function negligible with respect to log 2n we assume that the ring is anonymous unique identities are not available to distinguish the processes we only assume that each vertex distinguishes between its neighbours furthermore we do not assume that the size or an upper bound on the size of the ring is known

lower bounds on communication complexity in distributed computer networks the main result of this paper is a general technique for determining lower bounds on the communication complexity of problems on various distributed computer networks this general technique is derived by simulating the general network by a linear array and then using a lower bound on the communication complexity of the problem on the linear array applications of this technique yield optimal bounds on the communication complexity of merging ranking uniqueness and triangle detection problems on a ring of processors nontrivial near optimal lower bounds on the communication complexity of distinctness merging and ranking on meshes and complete binary trees are also derived

a primal dual bicriteria distributed algorithm for capacitated vertex cover in this paper we consider the capacitated vertex cover problem which is the variant of vertex cover where each node is allowed to cover a limited number of edges we present an efficient deterministic distributed approximation algorithm for the problem our algorithm computes a 2 epsilon approximate solution which violates the capacity constraints by a factor of 4 epsilon in a polylogarithmic number of communication rounds on the other hand we also show that every efficient distributed approximation algorithm for this problem must violate the capacity constraints our result is achieved in two steps we first develop a 2 approximate sequential primal dual algorithm that violates the capacity constraints by a factor of 2 subsequently we present a distributed version of this algorithm we demonstrate that the sequential algorithm has an inherent need for synchronization which forces any naive distributed implementation to use a linear number of communication rounds the challenge in this step is therefore to achieve a reduction of the communication complexity to a polylogarithmic number of rounds without worsening the approximation guarantee

fully bayesian reconstructions from single photon emission computed tomography data abstract with suitably chosen priors bayesian models are useful in image reconstruction i consider reconstructions from single photon emission computerized tomography data using a gibbs pairwise difference prior a fully bayesian approach is presented where the prior parameters are considered drawn from hyperpriors the approach is problematical because the normalization constant in the prior is an intractable function of its parameters here the constant is estimated off line by reverse logistic regression markov chain monte carlo methods are used on simulated and real data to gain estimates of the posterior mean and pixelwise credibility bounds the resulting reconstructions are compared to those obtained by filtered back projection maximum likelihood em and the one step late solution to the fixed parameter posterior mode

markov random field models for high dimensional parameters in simulations of fluid flow in porous media we give an approach for using flow information from a system of wells to characterize hydrologic properties of an aquifer in particular we consider experiments where an impulse of tracer fluid is injected along with the water at the input wells and its concentration is recorded over time at the uptake wells we focus on characterizing the spatially varying permeability field which is a key attribute of the aquifer for determining flow paths and rates for a given flow experiment as is standard for estimation from such flow data we use complicated subsurface flow code that simulates the fluid flow through the aquifer for a particular well configuration and aquifer specification in particular the permeability field over a grid the solution to this ill posed problem requires that some regularity conditions be imposed on the permeability field typically this regularity is accomplished by specifying a stationary gaussian process model for the permeability field here we use an intrinsically stationary

a stochastic variational multiscale method for diffusion in heterogeneous random media a stochastic variational multiscale method with explicit subgrid modelling is provided for numerical solution of stochastic elliptic equations that arise while modelling diffusion in heterogeneous random media the exact solution of the governing equations is split into two components a coarse scale solution that can be captured on a coarse mesh and a subgrid solution a localized computational model for the subgrid solution is derived for a generalized trapezoidal time integration rule for the coarse scale solution the coarse scale solution is then obtained by solving a modified coarse formulation that takes into account the subgrid model the generalized polynomial chaos method combined with the finite element technique is used for the solution of equations resulting from the coarse formulation and subgrid models finally various numerical examples are considered for evaluating the method

network growth by copying we introduce a growing network model in which a new node attaches to a randomly selected node as well as to all ancestors of the target node this mechanism produces a sparse ultrasmall network where the average node degree grows logarithmically with network size while the network diameter equals 2 we determine basic geometrical network properties such as the size dependence of the number of links and the in and out degree distributions we also compare our predictions with real networks where the node degree also grows slowly with time the internet and the citation network of all physical review papers

bayesian calibration of computer models we consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models such models implemented as computer codes are often generic in the sense that by a suitable choice of some of the model s input parameters the code can be used to predict the behaviour of the system in a variety of specific applications however in any specific application the values of necessary parameters may be unknown in this case physical observations of the system in the specific context are used to learn about the unknown parameters the process of fitting the model to the observed data by adjusting the parameters is known as calibration calibration is typically effected by ad hoc fitting and after calibration the model is used with the fitted input values to predict the future behaviour of the system we present a bayesian calibration technique which improves on this traditional approach in two respects first the predictions allow for all sources of uncertainty including the remaining uncertainty over the fitted parameters second they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best fitting parameter values the method is illustrated by using data from a nuclear radiation release at tomsk and from a more complex simulated nuclear accident exercise

emergence of network structure in models of collective evolution and evolutionary dynamics we consider an evolving network of a fixed number of nodes the allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics namely by deleting and duplicating existing nodes and their edges the properties of the degree distribution in the stationary state is analysed by use of the fokker planck equation for a broad range of parameters exponential degree distributions are observed the mechanism responsible for this behaviour is illuminated by use of a simple mean field equation and reproduced by the fokker planck equation the latter is treated exactly except for an approximate treatment of the degree degree correlations in the limit of 0 mutations the degree distribution becomes a power law with exponent 1

on the construction of complex networks with optimal tsallis entropy abstract in this work we first formulate the tsallis entropy in the context of complex networks we then propose a network construction whose topology maximizes the tsallis entropy the growing network model has two main ingredients copy process and random attachment mechanism c r model we show that the resulting degree distribution exactly agrees with the required degree distribution that maximizes the tsallis entropy we also provide another example of network model using a combination of preferential and random attachment mechanisms p r model and compare it with the distribution of the tsallis entropy in this case we show that by adequately identifying the exponent factor q the degree distribution can also be written in the q exponential form taken together our findings suggest that both mechanisms copy process and preferential attachment play a key role for the realization of networks with maximum tsallis entropy finally we discuss the interpretation of q parameter of the tsallis entropy in the context of complex networks

bayesian inversion of geoelectrical resistivity data summary enormous quantities of geoelectrical data are produced daily and often used for large scale reservoir modelling to interpret these data requires reliable and efficient inversion methods which adequately incorporate prior information and use realistically complex modelling structures we use models based on random coloured polygonal graphs as a powerful and flexible modelling framework for the layered composition of the earth and we contrast our approach with earlier methods based on smooth gaussian fields we demonstrate how the reconstruction algorithm may be efficiently implemented through the use of multigrid metropolis coupled markov chain monte carlo methods and illustrate the method on a set of field data

on the relationship between continuous and discrete time quantum walk quantum walk is one of the main tools for quantum algorithms defined by analogy to classical random walk a quantum walk is a time homogeneous quantum process on a graph both random and quantum walks can be defined either in continuous or discrete time but whereas a continuous time random walk can be obtained as the limit of a sequence of discrete time random walks the two types of quantum walk appear fundamentally different owing to the need for extra degrees of freedom in the discrete time case

about randomised distributed graph colouring and graph partition algorithms we present and analyse a very simple randomised distributed vertex colouring algorithm for arbitrary graphs of size n that halts in time o logn with probability 1 o n 1 each message containing 1 bit its bit complexity per channel is o logn from this algorithm we deduce and analyse a randomised distributed vertex colouring algorithm for arbitrary graphs of maximum degree d and size n that uses at most d 1 colours and halts in time o logn with probability 1 o n 1 we also obtain a partition algorithm for arbitrary graphs of size n that builds a spanning forest in time o logn with probability 1 o n 1 we study some parameters such as the number the size and the radius of trees of the spanning forest

simple neural like p systems for maximal independent set selection membrane systems p systems are distributed computing models inspired by living cells where a collection of processors jointly achieves a computing task the problem of maximal independent set mis selection in a graph is to choose a set of nonadjacent nodes to which no further nodes can be added in this letter we design a class of simple neural like p systems to solve the mis selection problem efficiently in a distributed way this new class of systems possesses two features that are attractive for both distributed computing and membrane computing first the individual processors do not need any information about the overall size of the graph second they communicate using only one bit messages

deterministic distributed vertex coloring in polylogarithmic time consider an n vertex graph g v e of maximum degree and suppose that each vertex v v hosts a processor the processors are allowed to communicate only with their neighbors in g the communication is synchronous that is it proceeds in discrete rounds in the distributed vertex coloring problem the objective is to color g with 1 or slightly more than 1 colors using as few rounds of communication as possible the number of rounds of communication will be henceforth referred to as running time efficient randomized algorithms for this problem are known for more than twenty years alon et al 1986 luby 1986 specifically these algorithms produce a 1 coloring within o log n time with high probability on the other hand the best known deterministic algorithm that requires polylogarithmic time employs o 2 colors this algorithm was devised in a seminal focs 87 paper by linial 1987 its running time is o log n in the same article linial asked whether one can color with significantly less than 2 colors in deterministic polylogarithmic time by now this question of linial became one of the most central long standing open questions in this area in this article we answer this question in the affirmative and devise a deterministic algorithm that employs 1 o 1 colors and runs in polylogarithmic time specifically the running time of our algorithm is o f log log n for an arbitrarily slow growing function f 1 we can also produce an o 1 coloring in o log log n time for an arbitrarily small constant 0 and an o coloring in o e log n time for an arbitrarily small constant e 0 our results are in fact far more general than this in particular for a graph of arboricity a our algorithm produces an o a1 coloring for an arbitrarily small constant 0 in time o log a log n

on spanners and lightweight spanners of geometric graphs we consider the problem of computing spanners of euclidean and unit disk graphs embedded in the two dimensional euclidean plane we are particularly interested in spanners that possess useful properties such as planarity bounded degree and or light weight such spanners have been extensively studied in the area of computational geometry and have been used as the building block for constructing efficient and reliable wireless network communication topologies we study the above problem under two computational models the centralized and the distributed model in the distributed model we focus on algorithms that are local such algorithms are suitable for the relevant applications e g wireless computing under the centralized model we present an o n lg n time algorithm that computes a bounded degree plane spanner of a complete euclidean graph where n is the number of points in the graph both upper bounds on the degree and the stretch factor significantly improve the previous bounds we extend this algorithm to compute a bounded degree plane lightweight spanner of a complete euclidean graph under the distributed model we give the first local algorithm for computing a spanner of a unit disk graph that is of bounded degree and plane the upper bounds on the degree stretch factor and the locality of the algorithm dramatically improve the previous results as shown in the paper this algorithm can also be extended to compute a bounded degree plane lightweight spanner of a unit disk graph our algorithms rely on structural and geometric results that we develop in this paper

optimal lower bounds for some distributed algorithms for a complete network of processors abstract lower bounds for distributed algorithms for complete networks of processors i e networks where each pair of processors is connected by a communication line are discussed we first show an n log n lower bound for the number of messages required by any algorithm in a given class of distributed algorithms for such networks this class includes algorithms for problems like finding a leader or constructing a spanning tree we then show an n 2 lower bound for other problems like constructing a maximal matching or a hamiltonian circuit in proving the lower bounds we are counting the edges which carry messages during the executions of the algorithms ignoring the actual number of messages carried by each edge interestingly this number is shown to be of the same order of magnitude as the total number of messages needed by these algorithms the proofs of the lower bounds apply for synchronous networks and for arbitrarily long messages

the locality of distributed symmetry breaking symmetry breaking problems are among the most well studied in the field of distributed computing and yet the most fundamental questions about their complexity remain open in this article we work in the local model where the input graph and underlying distributed network are identical and study the randomized complexity of four fundamental symmetry breaking problems on graphs computing miss maximal independent sets maximal matchings vertex colorings and ruling sets a small sample of our results includes the following an mis algorithm running in o log2 2o log log n time where is the maximum degree this is the first mis algorithm to improve on the 1986 algorithms of luby and alon babai and itai when log n l l 2 log n and comes close to the log log log lower bound of kuhn moscibroda and wattenhofer a maximal matching algorithm running in o log log 4log n time this is the first significant improvement to the 1986 algorithm of israeli and itai moreover its dependence on is nearly optimal a 1 coloring algorithm requiring o log 2o log log n time improving on an o log log n time algorithm of schneider and wattenhofer a method for reducing symmetry breaking problems in low arboricity degeneracy graphs to low degree graphs roughly speaking the arboricity or degeneracy of a graph bounds the density of any subgraph corollaries of this reduction include an o log n time maximal matching algorithm for graphs with arboricity up to 2 log n and an o log 2 3n time mis algorithm for graphs with arboricity up to 2 log n 1 3 each of our algorithms is based on a simple but powerful technique for reducing a randomized symmetry breaking task to a corresponding deterministic one on a poly log n size graph

infinite order percolation and giant fluctuations in a protein interaction network we investigate a model protein interaction network whose links represent interactions between individual proteins this network evolves by the functional duplication of proteins supplemented by random link addition to account for mutations when link addition is dominant an infinite order percolation transition arises as a function of the addition rate in the opposite limit of high duplication rate the network exhibits giant structural fluctuations in different realizations for biologically relevant growth rates the node degree distribution has an algebraic tail with a peculiar rate dependence for the associated exponent

a simple asymmetric evolving random network we introduce a new oriented evolving graph model inspired by biological networks a node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes this leads to a statistical asymmetry between incoming and outgoing edges we show that the model exhibits a percolation transition and discuss its universality below the threshold the distribution of component sizes decreases algebraically with a continuously varying exponent depending on the average connectivity we prove that the transition is of infinite order by deriving the exact asymptotic formula for the size of the giant component close to the threshold we also present a thorough analysis of aging properties we compute local in time profiles for the components of finite size and for the giant component showing in particular that the giant component is always dense among the oldest nodes but invades only an exponentially small fraction of the young nodes close to the threshold

randomized distributed edge coloring via an extension of the chernoff hoeffding bounds certain types of routing scheduling and resource allocation problems in a distributed setting can be modeled as edge coloring problems we present fast and simple randomized algorithms for edge coloring a graph in the synchronous distributed point to point model of computation our algorithms compute an edge coloring of a graph g with n nodes and maximum degree delta with at most 1 6 delta o log 1 delta n colors with high probability arbitrarily close to 1 for any fixed delta 0 they run in polylogarithmic time the upper bound on the number of colors improves upon the 2 delta 1 coloring achievable by a simple reduction to vertex coloring to analyze the performance of our algorithms we introduce new techniques for proving upper bounds on the tail probabilities of certain random variables the chernoff hoeffding bounds are fundamental tools that are used very frequently in estimating tail probabilities however they assume stochastic independence among certain random variables which may not always hold our results extend the chernoff hoeffding bounds to certain types of random variables which are not stochastically independent we believe that these results are of independent interest and merit further study

a probabilistic graphical model approach to stochastic multiscale partial differential equations we develop a probabilistic graphical model based methodology to efficiently perform uncertainty quantification in the presence of both stochastic input and multiple scales both the stochastic input and model responses are treated as random variables in this framework their relationships are modeled by graphical models which give explicit factorization of a high dimensional joint probability distribution the hyperparameters in the probabilistic model are learned using sequential monte carlo smc method which is superior to standard markov chain monte carlo mcmc methods for multi modal distributions finally we make predictions from the probabilistic graphical model using the belief propagation algorithm numerical examples are presented to show the accuracy and efficiency of the predictive capability of the developed graphical model

the price of query rewriting in ontology based data access we give a solution to the succinctness problem for the size of first order rewritings of conjunctive queries in ontology based data access with ontology languages such as owl 2 ql linear datalog and sticky datalog we show that positive existential and nonrecursive datalog rewritings which do not use extra non logical symbols except for intensional predicates in the case of datalog rewritings suffer an exponential blowup in the worst case while first order rewritings can grow superpolynomially unless np p poly we also prove that nonrecursive datalog rewritings are in general exponentially more succinct than positive existential rewritings while first order rewritings can be superpolynomially more succinct than positive existential rewritings on the other hand we construct polynomial size positive existential and nonrecursive datalog rewritings under the assumption that any data instance contains two fixed constants

duplication divergence model of protein interaction network we investigate a very simple model describing the evolution of protein protein interaction networks via duplication and divergence the model exhibits a remarkably rich behavior depending on a single parameter the probability to retain a duplicated link during divergence when this parameter is large the network growth is not self averaging and an average node degree increases algebraically the lack of self averaging results in a great diversity of networks grown out of the same initial condition when less than a half of links are on average preserved after divergence the growth is self averaging the average degree increases very slowly or tends to a constant and a degree distribution has a power law tail the predicted degree distributions are in a very good agreement with the distributions observed in real protein networks

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

symmetry breaking depending on the chromatic number or the neighborhood growth we deterministically compute a d 1 coloring and a maximal independent set mis in time o d 1 2 q 1 h log n for d 1 email protected email protected 1 i h where d j is defined as the maximal number of nodes within distance j for a node and d email protected 1 our greedy coloring and mis algorithms improve the state of the art algorithms running in o d log n for a large class of graphs i e graphs of moderate neighborhood growth with h 36 we also state and analyze a randomized coloring algorithm in terms of the chromatic number the run time and the used colors our algorithm runs in time o email protected log n for email protected email protected log 1 1 l o g nn and email protected o d log 1 1 l o g nn for graphs of polylogarithmic chromatic number the analysis reveals an exponential gap compared to the fastest d 1 coloring algorithm running in time o email protected logn the algorithm works without knowledge of g and uses less than d colors i e 1 1 o g d with high probability to the best of our knowledge this is the first distributed algorithm for such general graphs taking the chromatic number g into account we also improve on the state of the art deterministic computation of 2 c ruling sets

lower bounds for local approximation in the study of deterministic distributed algorithms it is commonly assumed that each node has a unique o log n bit identifier we prove that for a general class of graph problems local algorithms constant time distributed algorithms do not need such identifiers a port numbering and orientation is sufficient our result holds for so called simple po checkable graph optimisation problems this includes many classical packing and covering problems such as vertex covers edge covers matchings independent sets dominating sets and edge dominating sets we focus on the case of bounded degree graphs and show that if a local algorithm finds a constant factor approximation of a simple po checkable graph problem with the help of unique identifiers then the same approximation ratio can be achieved on anonymous networks as a corollary of our result we derive a tight lower bound on the local approximability of the minimum edge dominating set problem by prior work there is a deterministic local algorithm that achieves the approximation factor of 4 1 2 in graphs of maximum degree this approximation ratio is known to be optimal in the port numbering model our main theorem implies that it is optimal also in the standard model in which each node has a unique identifier our main technical tool is an algebraic construction of homogeneously ordered graphs we say that a graph is r homogeneous if its nodes are linearly ordered so that an fraction of nodes have pairwise isomorphic radius r neighbourhoods we show that there exists a finite r homogeneous 2k regular graph of girth at least g for any