interval estimation of the risk difference in non compliance randomized trials with repeated binary measurements in a randomized clinical trial rct we often encounter non compliance with the treatment protocol for a subset of patients the intention to treat itt analysis is probably the most commonly used method in a rct with non compliance however the itt analysis estimates the programmatic effectiveness rather than the biological efficacy in this paper we focus attention on the latter index and consider use of the risk difference rd to measure the effect of a treatment based on a simple additive risk model proposed elsewhere we develop four asymptotic interval estimators of the rd for repeated binary measurements in a rct with non compliance we apply monte carlo simulation to evaluate and compare the finite sample performance of these interval estimators in a variety of situations we find that all interval estimators considered here can perform well with respect to the coverage probability we further find that the interval estimator using a tanh 1 x transformation is probably more precise than the others while the interval estimator derived from a randomization based approach may cause a slight loss of precision when the number of patients per treatment is large and the probability of compliance to an assigned treatment is high we find that all interval estimators discussed here are essentially equivalent finally we illustrate use of these interval estimators with data simulated from a trial of using macrophage colony stimulating factor to reduce febrile neutropenia incidence in acute myeloid leukaemia patients copyright 2006 john wiley sons ltd

typical kernel size and number of sparse random matrices over galois fields a statistical physics approach using methods of statistical physics we study the average number and kernel size of general sparse random matrices over gf q with a given connectivity profile in the thermodynamical limit of large matrices we introduce a mapping of gf q matrices onto spin systems using the representation of the cyclic group of order q as the q th complex roots of unity this representation facilitates the derivation of the average kernel size of random matrices using the replica approach under the replica symmetric ansatz resulting in saddle point equations for general connectivity distributions numerical solutions are then obtained for particular cases by population dynamics similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile we present numerical results for particular distributions

stratified analysis in randomized trials with noncompliance this article develops methods for stratified analyses of additive or multiplicative causal effect on binary outcomes in randomized trials with noncompliance the methods are based on a weighted estimating function for an unbiased estimating function under randomization in each stratum when known weights are used the derived estimator is a natural extension of the instrumental variable estimator for stratified analyses and test based confidence limits are solutions of a quadratic equation in the causal parameter optimal weights that maximize asymptotic efficiency incorporate variability in compliance aspects across strata an assessment based on asymptotic relative efficiency shows that a substantial enhancement in efficiency can be gained by using optimal weights instead of conventional ones which do not incorporate the variability in compliance aspects across strata application to a field trial for coronary heart disease is provided

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

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

finitely coordinated models for low temperature phases of amorphous systems we introduce models of heterogeneous systems with finite connectivity defined on random graphs to capture finite coordination effects on the low temperature behaviour of finite dimensional systems our models use a description in terms of small deviations of particle coordinates from a set of reference positions particularly appropriate for the description of low temperature phenomena a born von karman type expansion with random coefficients is used to model effects of frozen heterogeneities the key quantity appearing in the theoretical description is a full distribution of effective single site potentials which needs to be determined self consistently if microscopic interactions are harmonic the effective single site potentials turn out to be harmonic as well and the distribution of these single site potentials is equivalent to a distribution of localization lengths used earlier in the description of chemical gels for structural glasses characterized by frustration and anharmonicities in the microscopic interactions the distribution of single site potentials involves anharmonicities of all orders and both single well and double well potentials are observed the latter with a broad spectrum of barrier heights the appearance of glassy phases at low temperatures is marked by the appearance of asymmetries in the distribution of single site potentials as previously observed for fully connected systems double well potentials with a broad spectrum of barrier heights and asymmetries would give rise to the well known universal glassy low temperature anomalies when quantum effects are taken into account

continuous time random walk with correlated waiting times based on the langevin description of the continuous time random walk ctrw we consider a generalization of ctrw in which the waiting times between the subsequent jumps are correlated we discuss the cases of exponential and slowly decaying persistent power law correlations between the waiting times as two generic examples and obtain the corresponding mean squared displacements as functions of time in the case of exponential type correlations the sub diffusion at short times is slower than in the absence of correlations at long times the behavior of the mean squared displacement is the same as in uncorrelated ctrw for power law correlations we find subdiffusion characterized by the same exponent at all times which appears to be smaller than the one in uncorrelated ctrw interestingly in the limiting case of an extremely long power law correlations the sub diffusion exponent does not tend to zero but is bounded from below by the subdiffusion exponent corresponding to a short time behavior in the case of exponential correlations

antiferromagnetic potts model on the erdős renyi random graph we study the antiferromagnetic potts model on the poissonian erd s renyi random graph by identifying a suitable interpolation structure and an extended variational principle together with a positive temperature second moment analysis we prove the existence of a phase transition at a positive critical temperature upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution recovered in the framework of derrida ruelle probability cascades and from an entropy positivity argument

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

distributed order fractional diffusions on bounded domains fractional derivatives can be used to model time delays in a diffusion process when the order of the fractional derivative is distributed over the unit interval it is useful for modeling a mixture of delay sources this paper provides explicit strong solutions and stochastic analogues for distributed order time fractional diffusion equations on bounded domains with dirichlet boundary conditions

bounds on causal effects in randomized trials with noncompliance under monotonicity assumptions about covariates in randomized trials with nonrandom noncompliance the causal effects of a treatment among the entire population cannot be estimated in an unbiased manner therefore several authors have considered the bounds on the causal effects here we propose bounds by applying an idea of vanderweele biometrics 2008 64 702 706 who showed that the sign of the unmeasured confounding bias can be determined under monotonicity assumptions about covariates in the framework of observational studies in randomized trials with noncompliance by switching the treatment we show that the lower or upper bound on the expectation of the potential outcome becomes the expectation from the per protocol analysis under monotonicity assumptions similar to those of vanderweele in particular the monotonicity assumptions can yield both the lower and the upper bounds on causal effects when the monotonic relationship between the covariates and the treatment actually received depends on the treatment assigned the results are extended to cases of noncompliance by subjects not receiving any treatment although the monotonicity assumptions are not themselves identifiable they are nonetheless reasonable in some situations

bicolouring random hypergraphs we study the problem of bicolouring random hypergraphs both numerically and analytically we apply the zero temperature cavity method to find analytical results for the phase transitions dynamic and static in the one step replica symmetry breaking 1rsb approximation these points appear to be in agreement with the results of the numerical algorithm in the second part we implement and test the survey propagation algorithm for specific bicolouring instances in the so called hard sat phase

distributed order diffusion equations and multifractality models and solutions we study distributed order time fractional diffusion equations characterized by multifractal memory kernels in contrast to the simple power law kernel of common time fractional diffusion equations based on the physical approach to anomalous diffusion provided by the seminal scher montroll weiss continuous time random walk we analyze both natural and modified form distributed order time fractional diffusion equations and compare the two approaches the mean squared displacement is obtained and its limiting behavior analyzed we derive the connection between the wiener process described by the conventional langevin equation and the dynamics encoded by the distributed order time fractional diffusion equation in terms of a generalized subordination of time a detailed analysis of the multifractal properties of distributed order diffusion equations is provided

graph bipartitioning and spin glasses on a random network of fixed finite valence the authors study the problem of bipartitioning a random graph of fixed finite valence using a mean field replica symmetric theory of an ising ferromagnet with zero magnetisation constraint the thermodynamics is determined by the probability distribution of an auxiliary field the expression for the ground state energy agrees with that proposed by mezard and parisi 1986 using a cavity field method but their expression for the fraction of crazy spins is reinterpreted

minimizing unsatisfaction in colourful neighbourhoods colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods given a predetermined number of colours in the analytical framework of a tree approximation carried out at both zero and finite temperatures solutions obtained by population dynamics give rise to estimates of the threshold connectivity for the incomplete to complete transition which are consistent with those of existing algorithms the nature of the transition as well as the validity of the tree approximation are investigated

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

phase coexistence and finite size scaling in random combinatorial problems we study an exactly solvable version of the well known random boolean satisfiability sat problem the so called random xor sat problem rare events are shown to affect the combinatorial phase diagram leading to a coexistence of solvable and unsolvable instances of the combinatorial problem in a certain region of the parameters characterizing the model such instances differ by a non extensive quantity in the ground state energy of the associated diluted spin glass model we also show that the critical exponent controlling the size of the critical window where the probability of having solutions vanishes depends on the model parameters shedding light on the link between random hyper graph topology and universality classes in the case of random sat a similar behaviour was conjectured to be connected to the onset of computational intractability

statistical mechanics of the random k satisfiability model the random k satisfiability problem consisting in verifying the existence of an assignment of n boolean variables that satisfy a set of m ensuremath alpha n random logical clauses containing k variables each is studied using the replica symmetric framework of diluted disordered systems we present an exact iterative scheme for the replica symmetric functional order parameter together for the different cases of interest k 2 kg 3 and k ensuremath gg 1 the calculation of the number of solutions which allowed us phys rev lett 76 3881 1996 to predict a first order jump at the threshold where the boolean expressions become unsatisfiable with probability one is thoroughly displayed in the case k 2 the rigorously known critical value ensuremath alpha 1 of the number of clauses per boolean variable is recovered while for kg 3 we show that the system exhibits a replica symmetry breaking transition the annealed approximation is proven to be exact for large k

on the freezing of variables in random constraint satisfaction problems the set of solutions of random constraint satisfaction problems zero energy groundstates of mean field diluted spin glasses undergoes several structural phase transitions as the amount of constraints is increased this set first breaks down into a large number of well separated clusters at the freezing transition which is in general distinct from the clustering one some variables spins take the same value in all solutions of a given cluster in this paper we introduce and study a message passing procedure that allows to compute for generic constraint satisfaction problems the sizes of the rearrangements induced in response to the modification of a variable these sizes diverge at the freezing transition with a critical behavior which is also investigated in details we apply the generic formalism in particular to the random satisfiability of boolean formulas and to the coloring of random graphs the computation is first performed in random tree ensembles for which we underline a connection with percolation models and with the reconstruction problem of information theory the validity of these results for the original random ensembles is then discussed in the framework of the cavity method

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

frozen development in graph coloring we define the frozen development of coloring random graphs we identify two nodes in a graph as frozen if they are of the same color in all legal colorings and define the collapsed graph as the one in which all frozen pairs are merged this is analogous to studies of the development of a backbone or spine in sat the satisfiability problem we first describe in detail the algorithmic techniques used to study frozen development we present strong empirical evidence that freezing in 3 coloring is sudden a single edge typically causes the size of the graph to collapse in size by 28 we also use the frozen development to calculate unbiased estimates of probability of colorability in random graphs this applies even where this probability is infinitesimal such as 10 300 although our estimates might be subject to very high variance we investigate the links between frozen development and the solution cost of graph coloring in sat a discontinuity in the order parameter has been correlated with the hardness of sat instances and our data for coloring are suggestive of an asymptotic discontinuity the uncolorability threshold is known to give rise to hard test instances for graph coloring we present empirical evidence that the cost of coloring threshold graphs grows exponentially when using either a specialist coloring program or encoding into sat or even when using the best of both techniques hard instances seem to appear over an increasing range of graph connectivity as graph size increases we give theoretical and empirical evidence to show that the size of the smallest uncolorable subgraphs of threshold graphs becomes large as the number of nodes in graphs increases finally we discuss some of the issues involved in applying our work to the statistical mechanics analysis of coloring

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

statistical physics of regular low density parity check error correcting codes a variation of gallager error correcting codes is investigated using statistical mechanics in codes of this type a given message is encoded into a codeword that comprises boolean sums of message bits selected by two randomly constructed sparse matrices the similarity of these codes to ising spin systems with random interaction makes it possible to assess their typical performance by analytical methods developed in the study of disordered systems the typical case solutions obtained via the replica method are consistent with those obtained in simulations using belief propagation decoding we discuss the practical implications of the results obtained and suggest a computationally efficient construction for one of the more practical configurations

sample size calculations with compliance information in randomized clinical trials non compliance will lead to the loss of power in the standard intention to treat analysis and one should account for this in sample size calculations in this paper a new sample size formula for a binary outcome is proposed in which compliance information is considered the proposed method is based purely on the treatment randomization we compare it to the conventional sample size calculation method based on the two independent binomial distributions assumption we examine 3100 combinations of risks of control group baseline risks treatment effects risk differences compliances in the test treatment group and the control treatment group test sizes and powers we found that compared to the conventional method the proposed method gives similar sample sizes for baseline risks 0 4 0 6 larger sample sizes for baseline risks less than 0 4 and smaller sample sizes for baseline risks greater than 0 6 when the true risk difference is negative