a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

tricriticality and the blume capel model a monte carlo study within the microcanonical ensemble the microcanonical partition function ensuremath omega ensuremath alpha n e of a three dimensional ferromagnetic simple cubic blume capel model is calculated for several coupling ratios ensuremath alpha close to and on the first order side of the tricritical point to this end a single monte carlo simulation of a suitably extended partition function for systems of l ifmmode times else texttimes fi l ifmmode times else texttimes fi l spins with l ensuremath in 8 10 12 14 18 was performed a finite system analog of the latent heat is introduced in order to define a tricritical point in finite systems as well an empirical scaling of its coordinates to the thermodynamic limit yields ensuremath alpha t 2 84479 ifmmode pm else textpm fi 0 00030 for the tricritical coupling ratio and k b t t j 1 4182 ifmmode pm else textpm fi 0 0055 for the tricritical transition temperature the results are compared with values obtained on fcc lattices

microcanonical finite size scaling in the microcanonical ensemble suitably defined observables show nonanalyticities and power law behavior even for finite systems for these observables a microcanonical finite size scaling theory is established and combined with the experimentally observed power law behavior scaling laws are obtained which relate exponents of the finite system and critical exponents of the infinite system to the system size dependence of the affiliated microcanonical observables

integral graphs and k τ regular sets abstract a subset of the vertex set of a graph g w v g is a k regular set if it induces a k regular subgraph of g and every vertex not in the subset has neighbors in it in this paper we deal with the existence of k regular sets associated with all distinct eigenvalues we show some families that have this property and we give some results concerning the existence of such sets considering restrictions on the symbol of circulant graphs

logarithmic corrections and finite size scaling in the two dimensional 4 state potts model we analyze the scaling and finite size scaling behavior of the two dimensional 4 state potts model we find new multiplicative logarithmic corrections for the susceptibility in addition to the already known ones for the specific heat we also find additive logarithmic corrections to scaling some of which are universal we have checked the theoretical predictions at criticality and off criticality by means of high precision monte carlo data

some rules on resistance distance with applications in this work some rules for resistance distances of a graph g are established let s be a set of vertices of g such that all vertices in s have the same neighborhood n in g s if s 2 3 4 simple formulae are derived to compute resistance distances between vertices in s in terms of the cardinality of n these show that resistance distances between vertices in s depend only on the cardinality of n and the induced subgraph g s one question arises naturally does this property hold for s with arbitrarily many vertices we answer this question by the following reduction principle resistance distances between vertices in s can be computed as in the subgraph obtained from g s n by deleting all the edges between vertices in n

a multiple imputation approach to cox regression with interval censored data we propose a general semiparametric method based on multiple imputation for cox regression with interval censored data the method consists of iterating the following two steps first from finite interval censored but not right censored data exact failure times are imputed using tanner and wei s poor man s or asymptotic normal data augmentation scheme based on the current estimates of the regression coefficient and the baseline survival curve second a standard statistical procedure for right censored data such as the cox partial likelihood method is applied to imputed data to update the estimates through simulation we demonstrate that the resulting estimate of the regression coefficient and its associated standard error provide a promising alternative to the nonparametric maximum likelihood estimate our proposal is easily implemented by taking advantage of existing computer programs for right censored data

25th order high temperature expansion results for three dimensional ising like systems on the simple cubic lattice 25th order high temperature series are computed for a general nearest neighbor three dimensional ising model with arbitrary potential on the simple cubic lattice in particular we consider three improved potentials characterized by suppressed leading scaling corrections critical exponents are extracted from high temperature series specialized to improved potentials obtaining gamma 1 2373 2 nu 0 63012 16 alpha 0 1096 5 eta 0 03639 15 beta 0 32653 10 delta 4 7893 8 moreover biased analyses of the 25th order series of the standard ising model provide the estimate delta 0 52 3 for the exponent associated with the leading scaling corrections by the same technique we study the small magnetization expansion of the helmholtz free energy the results are then applied to the construction of parametric representations of the critical equation of state using a systematic approach based on a global stationarity condition accurate estimates of several universal amplitude ratios are also presented

density of states of classical spin systems with continuous degrees of freedom in the last years different studies have revealed the usefulness of a microcanonical analysis of finite systems when dealing with phase transitions in this approach the quantities of interest are exclusively expressed as derivatives of the entropy s ln omega where omega is the density of states obviously the density of states has to be known with very high accuracy for this kind of analysis important progress has been achieved recently in the computation of the density of states of classical systems as new types of algorithms have been developed here we extend one of these methods originally formulated for systems with discrete degrees of freedom to systems with continuous degrees of freedom as an application we compute the density of states of the three dimensional xy model and demonstrate that critical quantities can directly be determined from the density of states of finite systems in cases where the degrees of freedom take continuous values

graphical designs and extremal combinatorics abstract a graphical design is a proper subset of vertices of a graph on which many eigenfunctions of the laplacian operator have mean value zero in this paper we show that extremal independent sets make extremal graphical designs that is a design on which the maximum possible number of eigenfunctions have mean value zero we then provide examples of such graphs and sets which arise naturally in extremal combinatorics we also show that sets which realize the isoperimetric constant of a graph make extremal graphical designs and provide examples for them as well we investigate the behavior of graphical designs under the operation of weak graph product in addition we present a family of extremal graphical designs for the hypercube graph

restricted mean survival time for interval censored data restricted mean survival time rmst evaluates the mean event free survival time up to a prespecified time point it has been used as an alternative measure of treatment effect owing to its model free structure and clinically meaningful interpretation of treatment benefit for right censored data in clinical trials another type of censoring called interval censoring may occur if subjects are examined at several discrete time points and the survival time falls into an interval rather than being exactly observed the missingness of exact observations under interval censored cases makes the nonparametric measure of treatment effect more challenging employing the linear smoothing technique to overcome the ambiguity we propose a new model free measure for the interval censored rmst as an alternative to the commonly used log rank test we further construct a hypothesis testing procedure to assess the survival difference between two groups simulation studies show that the bias of our proposed interval censored rmst estimator is negligible and the testing procedure delivers promising performance in detecting between group difference with regard to size and power under various configurations of survival curves the proposed method is illustrated by reanalyzing two real datasets containing interval censored observations

a survey of the theory of hypercube graphs abstract we present a comprehensive survey of the theory of hypercube graphs basic properties related to distance coloring domination and genus are reviewed the properties of the n cube defined by its subgraphs are considered next including thickness coarseness hamiltonian cycles and induced paths and cycles finally various embedding and packing problems are discussed including the determination of the cubical dimension of a given cubical graph

investigation of continuous time quantum walk via modules of bose mesner and terwilliger algebras the continuous time quantum walk on the underlying graphs of association schemes has been studied via the algebraic combinatorics structures of association schemes namely semi simple modules of their bose mesner and terwilliger algebras it is shown that the terwilliger algebra stratifies the graph into a d 1 disjoint union of strata which is different from the stratification based on distance except for distance regular graphs in underlying graphs of association schemes the probability amplitudes and average probabilities are given in terms of dual eigenvalues of association schemes such that the amplitudes of observing the continuous time quantum walk on all sites belonging to a given stratum are the same therefore there are at most d 1 different observing probabilities the importance of association scheme in continuous time quantum walk is shown by some worked out examples such as arbitrary finite group association schemes followed by symmetric sn dihedral d2m and cyclic groups at the end it is shown that the highest irreducible representations of terwilliger algebras pave the way to use the spectral distributions method of jafarizadeh and salimi 2005 preprint quant ph 0510174 in studying quantum walk on some rather important graphs called distance regular graphs

how many triangles and quadrilaterals are there in an n dimensional augmented cube abstract the augmented cube is an important variant of hypercube as interconnection topology of parallel computing in this paper we examine the numbers of short cycles in augmented cubes and prove that for n 3 there are 2 n n 1 triangles and 2 n 2 2 n 2 5 n 11 quadrilaterals in an n dimensional augmented cube this result shows that augmented cubes are promising interconnection networks with superior connectivity and fault tolerant capability

sensor networks with random links topology design for distributed consensus in a sensor network in practice the communication among sensors is subject to 1 errors that can cause failures of links among sensors at random times 2 costs and 3 constraints such as power data rate or communication since sensors and networks operate under scarce resources the paper studies the problem of designing the topology i e assigning the probabilities of reliable communication among sensors or of link failures to maximize the rate of convergence of average consensus when the link communication costs are taken into account and there is an overall communication budget constraint we model the network as a bernoulli random topology and establish necessary and sufficient conditions for mean square sense mss and almost sure a s convergence of average consensus when network links fail in particular a necessary and sufficient condition is for the algebraic connectivity of the mean graph topology to be strictly positive with these results we show that the topology design with random link failures link communication costs and a communication cost constraint is a constrained convex optimization problem that can be efficiently solved for large networks by semidefinite programming techniques simulations demonstrate that the optimal design improves significantly the convergence speed of the consensus algorithm and can achieve the performance of a non random network at a fraction of the communication cost

red bond exponents of the critical and the tricritical ising model in three dimensions using the wolff and geometric cluster algorithms and finite size scaling analysis we investigate the critical ising and the tricritical blume capel models with nearest neighbor interactions on the simple cubic lattice the sampling procedure involves the decomposition of the ising configuration into geometric clusters each of which consists of a set of nearest neighboring spins of the same sign connected with bond probability p these clusters include the well known kasteleyn fortuin clusters as a special case for p 1 exp 2k where k is the ising spin spin coupling along the critical line k kc the size distribution of geometric clusters is investigated as a function of p we observe that unlike in the case of two dimensional tricriticality the percolation threshold in both models lies at pc 1 exp 2kc further we determine the corresponding red bond exponents as yr 0 757 2 and 0 501 5 for the critical ising and the tricritical blume capel models respectively on this basis we conjecture yr 1 2 for the latter model

evaluation of effective resistances in pseudo distance regular resistor networks the effective resistance or two point resistance between two nodes of a resistor network is the potential difference that appears across them when a unit current source is applied between the nodes as terminals this concept arises in problems which deal with graphs as electrical networks including random walks distributed detection and estimation sensor networks distributed clock synchronization collaborative filtering clustering algorithms and etc in the previous paper jafarizadeh et al in j math phys 50 023302 2009 a recursive formula for evaluation of effective resistances on the so called distance regular networks was given based on the christoffel darboux identity in this paper we consider more general networks called pseudo distance regular networks or qd type networks where we use the stratification of these networks and show that the effective resistances between a given node say and all of the nodes belonging to the same stratum with respect to are the same then based on the spectral techniques for those s which satisfy l 1 alpha alpha l 1 beta beta l 1 is the pseudo inverse of the laplacian of the network an analytical formula for effective resistances r alpha beta m the equivalent resistance between terminals and so that belongs to the m th stratum with respect to is given in terms of the first and second orthogonal polynomials associated with the network from the fact that in distance regular networks l 1 alpha alpha l 1 beta beta is satisfied for all nodes of the network the effective resistances r alpha beta m for m 1 2 d d is diameter of the network which is the same as the number of strata are calculated directly by using the given formula

weighted kaplan meier statistics a class of distance tests for censored survival data a class of statistics based on the integrated weighted difference in kaplan meier estimators is introduced for the two sample censored data problem with positive weight functions these statistics are intuitive for and sensitive against the alternative of stochastic ordering the standard weighted log rank statistics are not always sensitive against this alternative particularly if the hazard functions cross qualitative comparisons are made between the weighted log rank statistics and these weighted kaplan meier wkm statistics a statement of null asymptotic distribution theory is given and the choice of weight function is discussed in some detail results from small sample simulation studies indicate that these statistics compare favorably with the log rank procedure even under the proportional hazards alternative and may perform better than it under the crossing hazards alternative

structure fault tolerance of hypercubes and folded hypercubes abstract let g be a graph and t be a certain connected subgraph of g the t structure connectivity g t resp t substructure connectivity s g t of g is the minimum number of a set of subgraphs f t 1 t 2 t m resp f t 1 t 2 t m such that t i is isomorphic to t resp t i is a connected subgraph of t for every 1 i m and f s removal will disconnect g let q n and f q n denote the n dimensional hypercube and folded hypercube respectively in 12 the q n t and s q n t were determined for t k 1 1 k 1 2 k 1 3 c 4 in this paper we generalize the above results by determining q n t and s q n t for t p k c 2 k k 1 4 where 3 k n we also determine f q n t and s f q n t for t p k c 2 k k 1 3 where n 7 and 2 k n

rank invariant tests for interval censored data under the grouped continuous model this paper creates rank invariant score tests for grouped or interval censored data this generalizes finkelstein 1986 biometrics 42 845 854 who derived score tests for interval censored data assuming proportional hazards we frame the problem as a linear rank test of a shift in location with a known error distribution we discuss adjustments to the test that may be required when the number of observation times is large we offer a graphical test of the assumption of the location shift model and discuss an alternative interpretation of the test using the logistic error when the location shift assumption does not hold

continuous phase transitions with a convex dip in the microcanonical entropy the appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition however a convex dip also shows up in some systems with a continuous transition as for example in the baxter wu model and in the four state potts model in two dimensions we demonstrate that the appearance of a convex dip in those cases can be traced back to a finite size effect the properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite size scaling theory for continuous phase transitions results obtained from numerical simulations corroborate the predictions of the scaling theory

monte carlo study of the triangular blume capel model under bond randomness the effects of bond randomness on the universality aspects of a two dimensional d 2 blume capel model embedded in the triangular lattice are discussed the system is studied numerically in both its first and second order phase transition regimes by a comprehensive finite size scaling analysis for a particularly suitable value of the disorder strength we find that our data for the second order phase transition emerging under random bonds from the second order regime of the pure model are compatible with the universality class of the two dimensional 2d random ising model furthermore we find evidence that the second order transition emerging under bond randomness from the first order regime of the pure model belongs again to the same universality class although the first finding reinforces the scenario of strong universality in the 2d ising model with quenched disorder the second is in difference from the critical behavior emerging under randomness in the cases of the ex first order transitions of the potts model finally our results verify previous renormalization group calculations on the blume capel model with disorder in the crystal field coupling

recursive calculation of effective resistances in distance regular networks based on bose mesner algebra and christoffel darboux identity recently jafarizadeh et al j phys a math theor 40 4949 2007 have given a method for calculation of effective resistance two point resistance on distance regular networks where the calculation was based on stratification introduced by jafarizadeh and salimi j phys a 39 1 2006 and stieltjes transform of the spectral distribution stieltjes function associated with the network also jafarizadeh et al j phys a math theor 40 4949 2007 have shown that effective resistances between a node and all nodes belonging to the same stratum with respect to r i belonging to the ith stratum with respect to are the same in this work an algorithm for recursive calculation of the effective resistances in an arbitrary distance regular resistor network is provided where the derivation of the algorithm is based on the bose mesner algebra stratification of the network spectral techniques and christoffel darboux identity it is shown that the effective resistance on a dista

some two vertex resistances of the three towers hanoi graph formed by a fractal graph the resistance distance between two vertices of a simple connected graph g is equal to the resistance between two equivalent points on an electrical network constructed to correspond to g with each edge being replaced by a unit resistor in this study we apply the principle of substitution to three towers hanoi graph to procure an equivalent network that enables us to only use the series and parallel principles and the delta wye transformation to acquire the some two vertex resistance distances of three towers hanoi graph

resistance distances in composite graphs the resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor let g h g h g h g h g h gh and g h be the join product composition direct product strong product corona and rooted product of two graphs g and h respectively in this paper formulae for resistance distances of these composite graphs are given in terms of parameters of the parent graphs and some properties are established explicit formulae are obtained for resistance distances of some classes of graphs including rook graphs diagonal mesh graphs and generalized double graphs

on first order phase transitions in microcanonical and canonical non extensive systems abstract two examples of microcanonical potts models two dimensional nearest neighbor and mean field are considered via exact enumeration of states and analytical asymptotic methods in the interval of energies corresponding to a first order phase transition both of these models exhibit a convex dip in the entropy vs energy plot and a region with negative specific heat within the dip it is observed that in the nearest neighbor model the dip flattens and disappears as the lattice size grows while in the mean field model the dip persists even in the limit of an infinite system if formal transitions from microcanonical to canonical ensembles and back are performed for an infinite but non extensive system the convex dip in the microcanonical entropy plot disappears

a two sample test for stochastic ordering with interval censored data a new class of asymptotically nonparametric two sample approximate tests for discrete interval censored data is proposed this class extends the family developed by pepe and fleming 1989 biometrics 45 497 507 for right censored data and is based on an integrated weighted difference in survival function estimates the tests are sensitive to the alternative of stochastic ordering and use turnbull s 1976 journal of the royal statistical society series b 38 290 295 estimator of the survival function the choice of appropriate weight functions is investigated simulation results indicate that for interval censored data the new procedure with an appropriate weight function can be more powerful than an omnibus likelihood ratio test and mantel s 1967 biometrics 23 65 78 test under a broad range of stochastically ordered alternatives for small sample sizes n 50 with moderate censoring 47 and 70 the size of the test is close to the nominal size

investigation of continuous time quantum walk on root lattice an and honeycomb lattice abstract the continuous time quantum walk ctqw on root lattice a n known as hexagonal lattice for n 2 and honeycomb one is investigated by using spectral distribution method to this aim some association schemes are constructed from abelian group z m n and two copies of finite hexagonal lattices such that their underlying graphs tend to root lattice a n and honeycomb one as the size of the underlying graphs grows to infinity the ctqw on these underlying graphs is investigated by using the spectral distribution method and stratification of the graphs based on terwilliger algebra where we get the required results for root lattice a n and honeycomb one from large enough underlying graphs moreover by using the stationary phase method the long time behavior of ctqw on infinite hexagonal lattice is approximated with finite ones for finite distances from the origin while for large distances the scaling behavior of the probability distribution is deduced also it is shown that the probability amplitudes at finite times possess the point group symmetry in the sense that two lattice points have the same probability amplitudes if and only if they belong to the same orbit stratum of the graph of the point group of the lattice apart from physical results it is shown that the bose mesner algebras of our constructed association schemes called n variable p polynomial can be generated by n commuting generators where raising flat and lowering operators as elements of terwilliger algebra are associated with each generator a system of n variable orthogonal polynomials which are special cases of generalized gegenbauer polynomials is constructed where the probability amplitudes are given by integrals over these polynomials or their linear combinations finally the supersymmetric structure of finite honeycomb lattices is revealed

nonconcave entropies in multifractals and the thermodynamic formalism we discuss a subtlety involved in the calculation of multifractal spectra when these are expressed as legendre fenchel transforms of functions analogous to free energy functions we show that the legendre fenchel transform of a free energy function yields the correct multifractal spectrum only when the latter is wholly concave if the spectrum has no definite concavity then the transform yields the concave envelope of the spectrum rather than the spectrum itself some mathematical and physical examples are given to illustrate this result which lies at the root of the nonequivalence of the microcanonical and canonical ensembles on a more positive note we also show that the impossibility of expressing nonconcave multifractal spectra through legendre fenchel transforms of free energies can be circumvented with the help of a generalized free energy function which relates to a recently introduced generalized canonical ensemble analogies with the calculation of rate functions in large deviation theory are finally discussed

applications of multiple imputation to the analysis of censored regression data the first part of the article reviews the data augmentation algorithm and presents two approximations to the data augmentation algorithm for the analysis of missing data problems the poor man s data augmentation algorithm and the asymptotic data augmentation algorithm these two algorithms are then implemented in the context of censored regression data to obtain semiparametric methodology the performances of the censored regression algorithms are examined in a simulation study it is found up to the precision of the study that the bias of both the poor man s and asymptotic data augmentation estimators as well as the buckley james estimator does not appear to differ from zero however with regard to mean squared error over a wide range of settings examined in this simulation study the two data augmentation estimators have a smaller mean squared error than does the buckley james estimator in addition associated with the two data augmentation estimators is a natural device for estimating the standard error of the estimated regression parameters it is shown how this device can be used to estimate the standard error of either data augmentation estimate of any parameter e g the correlation coefficient associated with the model in the simulation study the estimated standard error of the asymptotic data augmentation estimate of the regression parameter is found to be congruent with the monte carlo standard deviation of the corresponding parameter estimate the algorithms are illustrated using the updated stanford heart transplant data set

finite size behaviour of the microcanonical specific heat for models which exhibit a continuous phase transition in the thermodynamic limit a numerical study of small systems reveals a non monotonic behaviour of the microcanonical specific heat as a function of the system size this is in contrast to a treatment in the canonical ensemble where the maximum of the specific heat increases monotonically with the size of the system a phenomenological theory is developed which permits us to describe this peculiar behaviour of the microcanonical specific heat and allows in principle the determination of microcanonical critical exponents

the equivalent resistance of a 3 n cobweb network and its conjecture of an m n cobweb network we investigate the equivalent resistance of a 3 n cobweb network the difference equations of the model are constructed by network analysis and their general solution is obtained by matrix transformations it is found that the equivalent resistance can be expressed by the trigonometric function of k 7 which decreases with the increase of the order n by analyzing and comparing the equivalent resistances of the 1 n 2 n and 3 n cobweb networks a conjecture on the equivalent resistance of the m n cobweb network is proposed

bipanconnectivity of faulty hypercubes with minimum degree abstract in this paper we consider the conditionally faulty hypercube q n with n 2 where each vertex of q n is incident with at least m fault free edges 2 m n 1 we shall generalize the limitation m 2 in all previous results of edge bipancyclicity we also propose a new edge fault tolerant bipanconnectivity called k edge fault tolerant bipanconnectivity a bipartite graph is k edge fault tolerant bipanconnected if g f remains bipanconnected for any f e g with f k for every integer m under the same hypothesis we show that q n is n 2 edge fault tolerant edge bipancyclic and bipanconnected and the results are optimal with respect to the number of edge faults tolerated this not only improves some known results on edge bipancyclicity and bipanconnectivity of hypercubes but also simplifies the proof

transfer matrix for the restricted canonical and microcanonical ensembles the numerical transfer matrix for the partition function of discrete lattice models is generalized to allow the calculation of the density of states ensuremath omega e and the restricted density of states ensuremath omega e m given ensuremath omega e m the partition function is expressed as a polynomial in the variables x mathit e mathrm ensuremath beta mathit h and y mathit e mathrm ensuremath mathrm ensuremath beta these algorithms are illustrated with calculations for the ising model on finite square lattices the zeros of the partition function are examined in both the complex x and y planes finite size scaling analysis of the zeros leads to very accurate estimates for the critical temperature and critical exponents

estimation from relative measurements electrical analogy and large graphs we examine the problem of estimating vector valued variables from noisy measurements of the difference between certain pairs of them this problem which is naturally posed in terms of a measurement graph arises in applications such as sensor network localization time synchronization and motion consensus we obtain a characterization on the minimum possible covariance of the estimation error when an arbitrarily large number of measurements are available this covariance is shown to be equal to a matrix valued effective resistance in an infinite electrical network covariance in large finite graphs converges to this effective resistance as the size of the graphs increases this convergence result provides the formal justification for regarding large finite graphs as infinite graphs which can be exploited to determine scaling laws for the estimation error in large finite graphs furthermore these results indicate that in large networks estimation algorithms that use small subsets of all the available measurements can still obtain accurate estimates

position space renormalization group study of the spin 1 random semi infinite blume capel model abstract we study the spin 1 blume capel model under a random crystal field in the tridimensional semi infinite case this has been done by using the real space renormalization group approximation and specifically the migdal kadanoff technique interesting results are obtained which tell us that the randomness destroys the first order phase transitions and only those of the second order occur we give the list of nine fixed points and their topology describing the surface critical behavior five new types of phase diagram are found with a rich variety of phase transitions in accordance with the values of the bulk and surface probabilities and the ratios linking bulk and surface interactions

the bayesian bootstrap the bayesian bootstrap is the bayesian analogue of the bootstrap instead of simulating the sampling distribution of a statistic estimating a parameter the bayesian bootstrap simulates the posterior distribution of the parameter operationally and inferentially the methods are quite similar because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions neither method should be applied without some consideration of the reasonableness of these model assumptions in this sense neither method is a true bootstrap procedure yielding inferences unaided by external assumptions

a class of rank test procedures for censored survival data summary a class of linear rank statistics is proposed for the k sample problem with rightcensored survival data the class contains as special cases the log rank test mantel 1966 cox 1972 and a test essentially equivalent to peto peto s 1972 generalization of the wilcoxon test martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered and to derive expressions for asymptotic relative efficiencies under contiguous sequences of alternative hypotheses a class of distributions is presented which corresponds to the class of rank statistics in the sense that for each distribution there is a statistic with some optimal properties for detecting location alternatives from that distribution some monte carlo results are displayed which present small sample behaviour

extension of de bruijn graph and kautz graph abstract we introduce a method of division of vectors to extend the definitions of de bruijn graphs and kautz graphs basic properties of extended de bruijn graphs and extended kautz graphs are given and finally several new results on isomorphic factorization of those graphs are given

nonparametric comparison of two survival functions with dependent censoring via nonparametric multiple imputation when the event time of interest depends on the censoring time conventional two sample test methods such as the log rank and wilcoxon tests can produce an invalid test result we extend our previous work on estimation using auxiliary variables to adjust for dependent censoring via multiple imputation to the comparison of two survival distributions to conduct the imputation we use two working models to define a set of similar observations called the imputing risk set one model is for the event times and the other for the censoring times based on the imputing risk set a nonparametric multiple imputation method kaplan meier imputation is used to impute a future event or censoring time for each censored observation after imputation the conventional nonparametric two sample tests can be easily implemented on the augmented data sets simulation studies show that the sizes of the log rank and wilcoxon tests constructed on the imputed data sets are comparable to the nominal level and the powers are much higher compared with the tests based on the unimputed data in the presence of dependent censoring if either one of the two working models is correctly specified the method is illustrated using aids clinical trial data comparing zdv and placebo in which cd4 count is the time dependent auxiliary variable

efficient quantum circuits for continuous time quantum walks on composite graphs in this paper we investigate the simulation of continuous time quantum walks on specific classes of graphs for which it is possible to fast forward the time evolution operator to achieve constant time simulation complexity and to perform the simulation exactly i e while maintaining efficiency in particular we discuss two classes of composite graphs commuting graphs and cartesian product of graphs that contain classes of graphs which can be simulated in this fashion this allows us to identify new families of graphs that we can efficiently simulate in a quantum circuit framework providing practical and explicit means to explore quantum walk based algorithms in laboratories

smooth estimation of the survival function for interval censored data interval censored data arise naturally in large scale panel studies where subjects can only be followed periodically and the event of interest can only be observed in some time intervals to estimate the survival function the non parametric maximum likelihood estimator npmle is commonly used which is a step function having some large jumps however in many applications the underlying survival function can be reasonably assumed to be smooth and then the npmle does not efficiently use this information two smooth estimators have been proposed in the literature one is based on the kernel smoothing of the npmle another is the logspline density model however to our knowledge there is no finite sample study yet to assess their performance in the literature in this paper we first show by simulation that both smooth estimators improve over the npmle for smooth survival functions we then apply these estimators to compare two survival curves the test statistics based on the maximum difference between two survival functions kolmogorov smirnov test and on the integrated weighted difference of two survival functions iwdb test are investigated via the bootstrap from our simulation studies the iwdb test seems particularly promising for some stochastically ordered survival functions that do not satisfy the proportional hazards model the methods are illustrated by reanalysing the breast cosmesis study data set copyright 2000 john wiley sons ltd

nonparametric estimation for a form of doubly censored data with application to two problems in aids abstract in many epidemiologic studies of human immunodeficiency virus hiv disease interest focuses on the distribution of the length of the interval of time between two events two such problems are considered here estimation of the distribution of time or number of sexual contacts between infection of an individual an index case and transmission of hiv to their sexual partner and estimation of the distribution of time between infectiousness as a blood donor and the development of detectable antibody data regarding these two problems are available from certain partner studies and the hiv lookback study in both cases the statistical development is complicated by the fact that the times of both events are interval censored so that the length of time between the events is never observed exactly nonparametric methods for estimation of the interval length distribution are developed by casting the problem in terms of nonparametric estimation of a mixing distribution particular attention is paid to

scaling relations for logarithmic corrections multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical mechanical systems here a lee yang zero approach is used to systematically analyze the exponents of such logarithms and to propose scaling relations between them these proposed relations are then confronted with a variety of results from the literature

proper distance in edge colored hypercubes abstract an edge colored path is called properly colored if no two consecutive edges have the same color an edge colored graph is called properly connected if between every pair of vertices there is a properly colored path moreover the proper distance between vertices u and v is the length of the shortest properly colored path from u to v given a particular class of properly connected colorings of the hypercube we consider the proper distance between pairs of vertices in the hypercube

self consistent scaling theory for logarithmic correction exponents multiplicative logarithmic corrections frequently characterize critical behavior in statistical physics here a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific heat critical exponent vanishes also the theory is widened to encompass the correlation function the new relations are then confronted with results from the literature and some new predictions for logarithmic corrections in certain models are made

consistency of microcanonical and canonical finite size scaling typically in order to obtain finite size scaling laws for quantities in the microcanonical ensemble an assumption is taken as a starting point in this paper consistency of such a microcanonical finite size scaling assumption with its commonly accepted canonical counterpart is shown which puts microcanonical finite size scaling on a firmer footing

on the resistance diameter of hypercubes abstract the resistance distance among two vertices in some resistor networks has been widely considered by many physicists and mathematicians the resistance diameter of a graph is defined by the maximum resistance distance among all pairs of vertices in the graph the study of resistance diameter was initiated here it seems to be possible that the resistance diameter of a graph could play a significant role in analyzing the efficiency of the interconnection networks for wave or fluid like communication in order to improve the efficiency of wave or fluid like communication we need to minimize the resistance diameter of graphs the class of hypercubes is the most common multipurpose and efficient topological structure class of interconnection networks hypercube networks satisfy most requirements for the basic principles of network design the main result of this paper is to give a combinatorial formula for the resistance diameter of hypercubes in addition the minimum resistance distance among all pairs of vertices in hypercubes is also obtained these two results are deduced via the electrical network approach and the hitting time of random walks respectively

critical point finite size scaling in the microcanonical ensemble we develop a scaling theory for the finite size critical behavior of the microcanonical entropy density of states of a system with a critically divergent heat capacity the link between the microcanonical entropy and the canonical energy distribution is exploited to establish the former and corroborate its predicted scaling form in the case of the 3 d ising universality class we show that the scaling behavior emerges clearly when one accounts for the effects of the negative background constant contribution to the canonical critical specific heat we show that this same constant plays a significant role in determining the observed differences between the canonical and microcanonical specific heats of systems of finite size in the critical region s1063 651x 99 07510 8

computation of resistance distance and kirchhoff index of the two classes of silicate networks abstract the resistance distance between two vertices of a simple connected graph g is equal to the resistance between two equivalent points on an electrical network constructed so as to correspond to g with each edge being replaced by a unit resistor the kirchhoff index of g is the sum of resistance distances between all pairs of vertices in g in this paper the resistance distance between any two arbitrary vertices of a chain silicate network and a cyclic silicate network was procured by utilizing techniques from the theory of electrical networks i e the series and parallel principles the principle of elimination the star triangle transformation and the delta wye transformation two closed formulae for the kirchhoff index of the chain silicate network and the cyclic silicate network were obtained respectively

nonparametric rank based statistics and significance tests for fuzzy data nonparametric rank based statistics depending only on linear orderings of the observations are extended to fuzzy data the approach relies on the definition of a fuzzy partial order based on the necessity index of strict dominance between fuzzy numbers which is shown to contain in a well defined sense all the ordinal information present in the original data a concept of fuzzy set of linear extensions of a fuzzy partial order is introduced allowing the approximate computation of fuzzy statistics alpha cutwise using a markov chain monte carlo simulation approach the usual notions underlying significance tests are also extended leading to the concepts of fuzzy p value and graded rejection of the null hypothesis quantified by a degree of possibility and a degree of necessity at a given significance level this general approach is demonstrated in two special cases kendall s rank correlation coefficient and wilcoxon s two sample rank sum statistic

sample size determination for multiple comparison studies treating confidence interval width as random methods for optimal sample size determination are developed using four popular multiple comparison procedures scheffe s bonferroni s tukey s and dunnett s procedures where random samples of the same size n are to be selected from k 2 normal populations with common variance sigma2 and where primary interest concerns inferences about a family of l linear contrasts among the k population means for a simultaneous coverage probability of 1 alpha the optimal sample size is defined to be the smallest integer value n m such that simultaneously for all l confidence intervals the width of the lth confidence interval will be no greater than tolerance 2deltal l 1 2 l with tolerance probability at least 1 gamma treating the pooled sample variance s2p as a random variable using scheffe s procedure as an illustration comparisons are made to usual sample size methods that incorrectly ignore the stochastic nature of s2p the latter approach can lead to serious underestimation of required sample sizes and hence to unacceptably low values of the actually tolerance probability 1 gamma our approach guarantees a lower bound of 1 alpha gamma for the probability that the l confidence intervals will both cover the parametric functions of interest and also be sufficiently narrow recommendations are provided regarding the choices among the four multiple comparison procedures for sample size determination and inference making

critical exponents of the three dimensional blume capel model on a cellular automaton abstract the static critical exponents of the three dimensional blume capel model which has a tricritical point at d j 2 82 value are estimated for the standard and the cooling algorithms which improved from creutz cellular automaton the analyses of the data using the finite size scaling and power law relations reproduce their well established values in the d j 3 and d j 2 8 parameter region at standard and cooling algorithms respectively for the cooling algorithm at d j 2 8 value of single ion anisotropy parameter the static critical exponents are estimated as 0 31 1 6 0 32 and 0 87 these values are different from 0 31 1 25 0 12 and 0 64 universal values this case indicated that the bc model exhibits an ununiversal critical behavior at the d j 2 8 parameter value near the tricritical point d j 2 82 the simulations were carried out on a simple cubic lattice with periodic boundary conditions

critical phenomena at perfect and non perfect surfaces the effect of imperfections on surface critical properties is studied for ising models with nearest neighbour ferromagnetic couplings on simple cubic lattices in particular results of monte carlo simulations for flat perfect surfaces are compared to those for flat surfaces with random weak or strong interactions between neighbouring spins in the surface layer and for surfaces with steps of monoatomic height surface critical exponents at the ordinary transition in particular are found to be robust against these perturbations

calculating two point resistances in distance regular resistor networks an algorithm for the calculation of the resistance between two arbitrary nodes in an arbitrary distance regular resistor network is provided where the calculation is based on stratification introduced in jafarizadeh and salimi 2006 j phys a math gen 39 1 29 and the stieltjes transform of the spectral distribution stieltjes function associated with the network it is shown that the resistances between a node and all nodes belonging to the same stratum with respect to the r i belonging to the ith stratum with respect to the a re the same also the analytical formulae for two point resistances r i i 1 2 3 are given in terms of the size of the network and corresponding intersection numbers in particular the two point resistances in a strongly regular network are given in terms of its parameters v moreover the lower and upper bounds for two point resistances in strongly regular networks are discussed

the unicyclic graphs with maximum degree resistance distance for a connected graph with order n and size m the cyclomatic number number of independent cycles is equal to m n 1 the graphs with 1 are referred to the unicyclic graphs in this paper we characterized completely the unicyclic graphs with n vertices having maximum degree resistance distance

number of proper paths in edge colored hypercubes abstract given an integer 1 j n define the j coloring of a n dimensional hypercube h n to be the 2 coloring of the edges of h n in which all edges in dimension i 1 i j have color 1 and all other edges have color 2 cheng et al 2017 determined the number of distinct shortest properly colored paths between a pair of vertices for the 1 colored hypercubes it is natural to consider the number for j coloring j 2 in this note we determine the number of different shortest proper paths in j colored hypercubes for arbitrary j moreover we obtain a more general result

microcanonical finite size scaling in second order phase transitions with diverging specific heat a microcanonical finite size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so called quotients method to the microcanonical ensemble the ansatz is tested numerically in two models where the canonical specific heat diverges at criticality thus implying fisher renormalization of the critical exponents the three dimensional ferromagnetic ising model and the two dimensional four state potts model where large logarithmic corrections are known to occur in the canonical ensemble a recently proposed microcanonical cluster method allows simulating systems as large as l 1024 potts or l 128 ising the quotients method provides accurate determinations of the anomalous dimension ensuremath eta and of the fisher renormalized thermal ensuremath nu exponent while in the ising model the numerical agreement with our theoretical expectations is very good in the potts case we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data

resolving the order of phase transitions in monte carlo simulations the authors made a monte carlo simulation of the two dimensional potts model with q 3 4 and 5 to examine the question whether numerical methods can distinguish the order of a phase transition for the subtle cases that this model exemplifies they found that the finite size scaling test for susceptibilities has sufficient power for this purpose whereas the simple method of detecting metastability signals often fails

scaling corrections site percolation and ising model in three dimensions using finite size scaling techniques we obtain accurate results for critical quantities of the ising model and the site percolation in three dimensions we pay special attention to parametrizing the corrections to scaling which is necessary to bring the systematic errors below the statistical ones

universality of the ising and the s 1 model on archimedean lattices a monte carlo determination the ising models s 1 2 and s 1 are studied by efficient monte carlo schemes on the 3 4 6 4 and the 3 3 3 3 6 archimedean lattices the algorithms used a hybrid metropolis wolff algorithm and a parallel tempering protocol are briefly described and compared with the simple metropolis algorithm accurate monte carlo data are produced at the exact critical temperatures of the ising model for these lattices their finite size analysis provide with high accuracy all critical exponents which as expected are the same with the well known 2d ising model exact values a detailed finite size scaling analysis of our monte carlo data for the s 1 model on the same lattices provides very clear evidence that this model obeys also very well the 2d ising model critical exponents as a result we find that recent monte carlo simulations and attempts to define effective dimensionality for the s 1 model on these lattices are misleading accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two archimedean lattices

a two sample test with interval censored data via multiple imputation interval censored data arise naturally in large scale panel studies where subjects can only be followed periodically and the event of interest can only be recorded as having occurred between two examination times in this paper we consider the problem of comparing two interval censored samples we propose to impute exact failure times from interval censored observations to obtain right censored data then apply existing techniques such as harrington and fleming s g rho tests to imputed right censored data to appropriately account for variability a multiple imputation algorithm based on the approximate bayesian bootstrap abb is discussed through simulation studies we find that it performs well the advantage of our proposal is its simplicity to implement and adaptability to incorporate many existing two sample comparison techniques for right censored data the method is illustrated by reanalysing the breast cosmesis study data set

a multiple imputation approach to regression analysis for doubly censored data with application to aids studies sun liao and pagano 1999 proposed an interesting estimating equation approach to cox regression with doubly censored data here we point out that a modification of their proposal leads to a multiple imputation approach where the double censoring is reduced to single censoring by imputing for the censored initiating times for each imputed data set one can take advantage of many existing techniques and software for singly censored data under the general framework of multiple imputation the proposed method is simple to implement and can accommodate modeling issues such as model checking which has not been adequately discussed previously in the literature for doubly censored data here we illustrate our method with an application to a formal goodness of fit test and a graphical check for the proportional hazards model for doubly censored data we reanalyze a well known aids data set

restoration of macroscopic isotropy on d 1 simplex fractal conductor networks abstract restoration of macroscopic isotropy has been investigated in d 1 simplex fractal conductor networks via exact real space renormalization group transformations using some theorems of fixed point theory it has been shown very rigoroursly that the macroscopic conductivity becomes isotropic for large scales and anisotropy vanishes with a scaling exponent which is computed exactly for arbitrary values of d and decimation numbers b 2 3 4 and 5

distributed fault tolerant ring embedding and reconfiguration in hypercubes to embed a ring in a hypercube is to find a hamiltonian cycle through every node of the hypercube it is obvious that no 2 sup n node hamiltonian cycle exists in an n dimensional faulty hypercube which has at least one faulty node however if a hypercube has faulty links only and the number of faulty links is at most n 2 at least one 2 sup n node hamiltonian cycle can be found in this paper we propose a distributed ring embedding algorithm that can find a hamiltonian cycle in a fault free or faulty n dimensional hypercube q and the complexity is o n parallel steps the algorithm is based on the recursion property of the hypercube and the free link dimension concept in some cases even when the number of faulty links is larger than n 2 hamiltonian cycles may still exist we show that the largest possible number of faulty links that can be tolerated is 2 sup n 1 1 the performance and the constraints of the fault tolerant algorithm is also analyzed in detail in this paper furthermore a dynamic reconfiguration algorithm for an embedded ring is proposed and discussed due to the distributed nature of the algorithms they are useful for the simulation of ring based multiprocessors on mimd hypercube multiprocessors

nonparametric comparison of survival functions based on interval censored data with unequal censoring nonparametric comparison of survival functions is one of the most commonly required task in failure time studies such as clinical trials and for this many procedures have been developed under various situations this paper considers a situation that often occurs in practice but has not been discussed much the comparison based on interval censored data in the presence of unequal censoring that is one observes only interval censored data and the distributions of or the mechanisms behind censoring variables may depend on treatments and thus be different for the subjects in different treatment groups for the problem a test procedure is developed that takes into account the difference between the distributions of the censoring variables and the asymptotic normality of the test statistics is given for the assessment of the performance of the procedure a simulation study is conducted and suggests that it works well for practical situations an illustrative example is provided copyright 2017 john wiley sons ltd

data center interconnection networks are not hyperbolic topologies for data center interconnection networks have been proposed in the literature through various graph classes and operations a common trait to most existing designs is that they enhance the symmetric properties of the underlying graphs indeed symmetry is a desirable property for interconnection networks because it minimizes congestion problems and it allows each entity to run the same routing protocol however despite sharing similarities these topologies all come with their own routing protocol recently generic routing schemes have been introduced which can be implemented for any interconnection network the performances of such universal routing schemes are intimately related to the hyperbolicity of the topology roughly graph hyperbolicity is a metric parameter which measures how close is the shortest path metric of a graph from a tree metric the smaller the gap the better motivated by the good performances in practice of these new routing schemes we propose the first general study of the hyperbolicity of data center interconnection networks our findings are disappointingly negative we prove that the hyperbolicity of most data center interconnection topologies scales linearly with their diameter that is the worst case possible for hyperbolicity to obtain these results we introduce original connection between hyperbolicity and the properties of the endomorphism monoid of a graph in particular our results extend to all vertex and edge transitive graphs additional results are obtained for de bruijn and kautz graphs grid like graphs and networks from the so called cayley model

a measure of data collapse for scaling data collapse is a way of establishing scaling and extracting associated exponents in problems showing self similar or self affine characteristics as for example in equilibrium or non equilibrium phase transitions in critical phases in dynamics of complex systems and many others we propose a measure to quantify the nature of data collapse via a minimization of this measure the exponents and their error bars can be obtained the procedure is illustrated by considering finite size scaling near phase transitions and quite strikingly recovering the exact exponents

a semiparametric model for regression analysis of interval censored failure time data left right and interval censored response time data arise in a variety of settings including the analyses of data from laboratory animal carcinogenicity experiments clinical trials and longitudinal studies for such incomplete data the usual regression techniques such as the cox 1972 journal of the royal statistical society series b 34 187 220 proportional hazards model are inapplicable in this paper we present a method for regression analysis which accommodates interval censored data we present applications of this methodology to data sets from a study of breast cancer patients who were followed for cosmetic response to therapy a small animal tumorigenicity study and a clinical trial