time dependent critical properties of ising models by damage spreading abstract we use the method of damage spreading to study the time t taken for a spin at a distance r to be damaged for the first time in ising models with heat bath dynamics we report time dependent scaling exponents d t 2 0 1d 2 52 2d 2 26 3d and 2 0 4d if we assume that t r dt we also analyze our data assuming various forms of logarithmic corrections and we find that d t 2 25 or less 2d and 2 0 3d we argue that it is extremely plausible that d t is equal to z the dynamic critical exponent and thus our estimate of z in two dimensions is higher than the consensus value of 2 14 but we find good agreement in one three and four dimensions with the exact and expected values

higher differentiability for solutions of nonhomogeneous elliptic obstacle problems abstract this paper focuses on weak solutions to the following variational inequality a x d u d u d x f p 2 f d u d x for all a w w 1 p w a e in where the vector field a satisfies some growth and ellipticity conditions we derive that the higher differentiability property of the weak solution u is related to the regularity of the assigned obstacle and the nonhomogeneous term f under a suitable integer or fractional differentiability assumption on a x with respect to x

cluster distribution of damage spreading in 3d ising model abstract examination of damage spreading offers analogies to thermodynamic properties of ising models a coniglio l de arcangelis h j herrmann and n jan europhys lett 8 1989 315 we compare the size distribution of coniglio klein ising clusters with the distribution of cluster sizes in damage systems in the case of metropolis glauber dynamics and by distinguishing and damage the critical exponents of damage clusters and ising clusters are very close at t c away from t c no relationship between damage spreading and the ising system can be found

nonlinear gradient estimates for parabolic problems with irregular obstacles abstract we establish the natural calderon zygmund theory for solutions to parabolic variational inequalities satisfying an irregular obstacle constraint and involving degenerate singular operators in divergence form of general type and proving that the spatial gradient of solutions is as integrable as both the spatial gradient of the obstacles and the inhomogeneous terms under the assumption that the involved nonlinearities have small a bmo semi norm in the spatial variables while they are allowed to be merely measurable in the time variable

monte carlo simulation of the shape space model of immunology abstract the shape space model of de boer segel and perelson for the immune system is studied with a probabilistic updating rule by monte carlo simulation a suitable mathematical form is chosen for the probability of increase of b cell concentration depending on the concentration around the mirror image site the results obtained agree reasonably with the results obtained by deterministic cellular automata

the parameterized complexity of sequence alignment and consensus the longest common subsequence problem is examined from the point of view of parameterized computational complexity there are several different ways in which parameters enter the problem such as the number of sequences to be analyzed the length of the common subsequence and the size of the alphabet lower bounds on the complexity of this basic problem imply lower bounds on a number of other sequence alignment and consensus problems at issue in the theory of parameterized complexity is whether a problem which takes input x k can be solved in time f k n where is independent of k termed fixed parameter tractability it can be argued that this is the appropriate asymptotic model of feasible computability for problems for which a small range of parameter values cover important applications a situation which certainly holds for many problems in biological sequence analysis our main results show that 1 the longest common subsequence lcs parameterized by the number of sequences to be analyzed is hard for w t for all t 2 the lcs problem problem parameterized by the length of the common subsequence belongs to w p and is hard for w 2 3 the lcs problem parameterized both by the number of sequences and the length of the common subsequence is complete for w 1 all of the above results are obtained for unrestricted alphabet sizes for alphabets of a fixed size problems 2 and 3 are fixed parameter tractable we conjecture that 1 remains hard

comparative study of damage spreading in the ising model using heat bath glauber and metropolis dynamics we study the time evolution of two configurations of the ising model submitted to heat bath hb glauber g and two types of metropolis m and tilde m dynamics analyzing the damage spreading on a square lattice we find that the damages produced by the dynamics g and m are greater than those resulting from hb and tilde m dynamics we also observe that only for zero magnetic field the damages of the dynamics g and m seem to be numerically equivalent

damage spreading and dynamic stability of kinetic ising models we investigate how the time evolution of different kinetic ising models depends on the initial conditions of the dynamics to this end we consider the simultaneous evolution of two identical systems subjected to the same thermal noise we derive a master equation for the time evolution of a joint probability distribution of the two systems this equation is then solved within an effective field approach by analysing the fixed points of the master equation and their stability we identify regular and chaotic phases

on the singular set in the navier stokes equations we consider suitably weak solutions u p to the incompressible navier stokes equations and under various assumptions on u obtain estimates for the size of its singular set one of our results improves a well known theorem of caffarelli kohn and nirenberg

regularity results for nonlinear parabolic obstacle problems with subquadratic growth abstract in 26 it was shown that the spatial gradient of the solution u to the parabolic obstacle problem with superquadratic growth is local holder continuous provided the obstacle is regular enough in this paper we extend this regularity result to the subquadratic case this means we establish the local holder continuity of the spatial gradient of the solution u to the parabolic obstacle problem with subquadratic growth more precisely we prove that d u c loc 0 2 for some 0 1 provided the coefficients and the obstacle are regular enough moreover we use the local holder continuity to prove the local lipschitz continuity of the solution u i e u c loc 0 1 1 2

mixing heat bath and glauber dynamics damage spreading in the ising model the authors study damage spreading in the ising model on a square lattice by a monte carlo approach using a general f dynamics 0 or f or 1 which reproduces for f 0 the well known heat bath dynamics and for f 1 glauber dynamics they find for initially small damage a critical value fc 0 50 or 0 03 as the threshold for damage spreading for fc f or 1 the damage is non zero only for tc t t0 f where tc is the usual critical temperature and t0 f rises with f like t0 f tc infinity f fc alpha alpha 0 83 or 0 08 for tc or t the damage d t f seems to satisfy the scaling relation d t f approximately mod 1n f fc mod 1t 1 tc t f fc alpha

a local field type model for immunological systems time evolution in real and shape spaces abstract we introduce a new model for the interaction of immunological cells that takes into account their location in real space each one of the model cells mimics the real b cells in the sense that they detect antigens and they are also capable of reproducing themselves we perform computer simulations for the simplest cases the main differences between the results obtained within this model and those obtained through the usual models which do not consider a real space concern the final stationary states in mean field calculations not only the system as a whole but also each individual cell population reach an equilibrium state in the present approach the entire system reaches a stationary state but the individual populations present strong fluctuations at least for the explored range of parameters we exhibit that in spite of the simplicity of the present model interesting real space effects can take place

damage spreading in the kawasaki ising model abstract we observe no phase transition in the damage spreading probability at the curie point of the 2d ising model with nearest neighbor spin exchange dynamics furthermore we report values of the growth exponent z close to unity implying speed of light transmission of information and values of the exponents describing the scaling behavior of the damage mass with time and distance close to two finally we discuss the spreading of damage in a one dimensional system

computing similarity between rna structures the primary structure of a ribonucleic acid rna molecule is a sequence of nucleotides bases over the four letter alphabet a c g u the secondary or tertiary structure of an rna is a set of base pairs nucleotide pairs which forms bonds between au and cg for secondary structures these bonds have been traditionally assumed to be one to one and non crossing this paper considers a notion of similarity between two rna molecule structures taking into account the primary the secondary and the tertiary structures we show that for tertiary structures it is max snp hard for both minimization and maximization versions we show a stronger result for the maximization version where it cannot be approximated within ratio 2logn in polynomial time unless npdtime 2polylogn we then present an algorithm that can be used for practical application our algorithm will produce an optimal solution for the case where at least one of the rna involved is of a secondary structure we also show an approximation algorithm

effective analysis of damage spreading in ising models using large lattices and different methods of simulation and analysis the kinetic critical exponent z for damage spreading is shown to be consistent with z 2 in two to five dimensions without the logarithmic problems seen in some earlier work

computer simulation of immunological cellular automata the tsallis model abstract a modification of the model of de boer van der laan and hogeweg is discussed where a condition favorable to the growth of antibody cells lets not only that cell type grow but with equal probability also one of its neighbors in immunological shape space

computing the similarity of two sequences with nested arc annotations we present exact algorithms for the np complete longest common subsequence problem for sequences with nested arc annotations a problem occurring in structure comparison of rna given two sequences of length at most n and nested arc structure one of our algorithms determines if existent in o 3 31k1 k2 n time an arc preserving subsequence of both sequences which can be obtained by deleting together with corresponding arcs k1 letters from the first and k2 letters from the second sequence a second algorithm shows that in case of a four letter alphabet we can find a length l arc annotated subsequence in o 12l l n time this means that the problem is fixed parameter tractable when parameterized by the number of deletions as well as when parameterized by the subsequence length our findings complement known approximation results which give a quadratic time factor 2 approximation for the general and polynomial time approximation schemes for restricted versions of the problem in addition we obtain further fixed parameter tractability results for these restricted versions

local kinetic energy and singularities of the incompressible navier stokes equations abstract we study the partial regularity problem of the incompressible navier stokes equations a reverse holder inequality of velocity gradient with increasing support is obtained under the condition that a scaled functional corresponding the local kinetic energy is uniformly bounded as an application we give a new bound for the hausdorff dimension and the minkowski dimension of singular set when weak solutions v belong to l 0 t l 3 w r 3 where l 3 w r 3 denotes the standard weak lebesgue space

calderon zygmund theory for nonlinear elliptic problems with irregular obstacles abstract we consider a nonhomogeneous elliptic problem with an irregular obstacle involving a discontinuous nonlinearity over an irregular domain in divergence form of p laplacian type to establish the global calderon zygmund estimate by proving that the gradient of the weak solution is as integrable as both the gradient of the obstacle and the nonhomogeneous term under the bmo smallness of the nonlinearity and sufficient flatness of the boundary in the reifenberg sense

damage spreading in random field systems we investigate how a quenched random field influences the damage spreading transition in kinetic ising models to this end we generalize a recent master equation approach and derive an effective field theory for damage spreading in random field systems this theory is applied to the glauber ising model with a bimodal random field distribution we find that the random field influences the spreading transition by two different mechanisms with opposite effects first the random field favours the same particular direction of the spin variable at each site in both systems which reduces the damage second the random field suppresses the magnetization which in turn tends to increase the damage the competition between these two effects leads to a rich behaviour

time evolution of damage in the ising model the time evolution of the damage in the ising model with the heat bath and glauber dynamics has been investigated with the damage spreading method the damage density d t and the average distance r t of damaged sites from the origin have been measured numerically from the simulational data the scaling forms have been established as d t tx r t t1z and d t r t df and the corresponding exponents x z and df have been estimated

new methods for 3 sat decision and worst case analysis abstract we prove the worst case upper bound 1 5045 n for the time complexity of 3 sat decision where n is the number of variables in the input formula introducing new methods for the analysis as well as new algorithmic techniques we add new 2 and 3 clauses called blocked clauses generalizing the extension rule of extended resolution our methods for estimating the size of trees lead to a refined measure of formula complexity of 3 clause sets and can be applied also to arbitrary trees

dynamical properties of the two and three dimensional ising models by damage spreading the method of damage spreading is used to measure the dynamic exponent z for both the two and three dimensional ising models with heat bath dynamics the authors also measure a new exponent alpha describing the rate at which a damage cloud grows they report values of z 2 24 or 0 04 and alpha 0 77 or 0 11 in two dimensions and z 2 202 or 0 03 and alpha 0 92 or 0 10 in three dimensions

scaling properties of the damage cloud in the 3d ising model the authors show that in the three dimensional ising model at the critical temperature the fractal dimension of the touching damage determined by the box counting method asymptotically converges to the expected value df d beta v in contrast the finite size scaling analysis indicates for the touching damage an effective fractal dimension whose value is 20 smaller the expected df is however recovered again when instead of the system size l the quantity l ln l is used as a scaling variable this behaviour could be explained by the recently discovered dynamical multiscaling

high dimensional simulation of the shape space model for the immune system abstract for the reactions among the antibodies of the immune system fighting against a foreign antigen the recent model of de boer segel and perelson introduced a cellular automata approximation for the interaction of different types of b cells bone marrow derived lymphocytes in contrast to most physics models here each lattice site interacts mainly with its mirror image with respect to the lattice center in the opposite part of the lattice we simplify their model and then generalize it to include more than one or two shape space parameters thus instead of simulating a chain or square lattice we simulate a d dimensional hypercubic lattice with dimension d up to 10 in particular we check for the concentration of b cells and the stability against localized perturbations damage spreading

damage spreading and critical exponents for model a ising dynamics using damage spreading and heat bath dynamics we study the ising model in 2 and 3 dimensions with non conservative dynamics our algorithm differs in some important points from previous ones which makes it rather efficient we give estimates for the exponent z which seem to be the most precise published so far 2 172 0 006 for d 2 2 032 0 004 for d 3 we also give precise estimates of the exponent introduced by janssen et al z phys b 73 1989 539 and of analogous but in principle independent exponents we find surprisingly that some of the latter agree with and give an explanation for this

damage spreading in the q2r ising model abstract we find evidence of metastability in the spreading of damage in the q2r cellular automaton approximation for a 2d ising system which is first equilibrated with a standard metropolis simulation a subsequent study of both single site and whole line damage spreading in metropolis q2r systems as well as in pure q2r systems shows a logarithmic dependence of the damage spreading threshold on time and saturation effects in single site damage suggest a transition in the damage spreading threshold at low initial energy values examination of the magnetization as a function of energy in pure q2r shows extremely long relaxation times for p

time dependent thermodynamic properties of the ising model from damage spreading the relationship between damage spreading and static thermodynamic properties in the ising model developed by coniglioet al is here extended to include time dependent thermodynamic quantities we exploit this new result to measure the time dependent spin correlation function from damage spreading in the ising model with heat bath and glauber dynamics until now only static thermodynamic quantities have been correctly determined from damage spreading and even then only with heat bath dynamics we also show that there are significant differences between the kinetics of damage spreading as found in heat bath and glauber dynamics

the three dimensional ising model in a temperature gradient abstract the critical temperature t c and the correlation length exponent for the three dimensional ising model is determined via the gradient method by numerical studies of systems of size up to 360 3 we determine the correlation length exponent 0 62 0 01 in comparison to the best estimates ranging from 0 624 to 0 630