budgeted matching and budgeted matroid intersection via the gasoline puzzle many polynomial time solvable combinatorial optimization problems become np hard if an additional complicating constraint is added to restrict the set of feasible solutions in this paper we consider two such problems namely maximum weight matching and maximum weight matroid intersection with one additional budget constraint we present the first polynomial time approximation schemes for these problems similarly to other approaches for related problems our schemes compute two solutions to the lagrangian relaxation of the problem and patch them together to obtain a near optimal solution however due to the richer combinatorial structure of the problems considered here standard patching techniques do not apply to circumvent this problem we crucially exploit the adjacency relations on the solution polytope and surprisingly the solution to an old combinatorial puzzle

age related alterations of relaxation processes and non markov effects in stochastic dynamics of r r intervals variability from human ecgs in this paper we consider the age related alterations of heart rate variability on the basis of the study of non markovian effects the age dynamics of relaxation processes is quantitatively described by means of local relaxation parameters calculated by the specific localization procedure we offer a quantitative informational measure of non markovity to evaluate the change of statistical effects of memory local relaxation parameters for young and elderly people differ by 3 3 times and quantitative measures of non markovity differ by 4 2 times the comparison of quantitative parameters allows to draw conclusions about the reduction of relaxation rate with ageing and the higher degree of the markovity of heart rate variability of elderly people

establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes stochastic fractal signals can be characterized by the hurst coefficient h which is related to the exponents of various power law statistics characteristic of these processes two techniques widely used to estimate h are spectral analysis and detrended fluctuation analysis dfa this paper examines the analytical link between these two measures and shows that they are related through an integral transform numerical simulations confirm this relationship for ideal synthesized fractal signals their performance as estimators of h is compared based on a mean square error criterion and found to be similar dfa measures are derived for physiological signals of heartbeat r ensuremath r intervals through the integral transform of a spectral density estimate these agree with directly calculated dfa estimates indicating that the relationship holds for signals with nonideal fractal properties it is concluded that dfa and spectral measures provide equivalent characterizations of stochastic signals with long term correlation

approximating minimum bounded degree spanning trees to within one of optimal in the minimum bounded degree spanning tree problem we are given an undirected graph g v e with a degree upper bound bv on each vertex v v and the task is to find a spanning tree of minimum cost that satisfies all the degree bounds let opt be the cost of an optimal solution to this problem in this article we present a polynomial time algorithm which returns a spanning tree t of cost at most opt and dt v bv 1 for all v where dt v denotes the degree of v in t this generalizes a result of furer and raghavachari 1994 to weighted graphs and settles a conjecture of goemans 2006 affirmatively the algorithm generalizes when each vertex v has a degree lower bound av and a degree upper bound bv and returns a spanning tree with cost at most opt and av 1 dt v bv 1 for all v v this is essentially the best possible the main technique used is an extension of the iterative rounding method introduced by jain 2001 for the design of approximation algorithms

statistical spectrum of the non markovity parameter for simple model systems the spectra of the non markovity parameter for three model systems are found an ideal gas weakly non ideal gas and a medium in hydrodynamic limits it is shown that the non markovian effects play the dominant role in all three above mentioned cases the effects of molecular memory are connected with the statistical appearance of intermolecular interactions in statistical systems

halin graphs and the travelling salesman problem a halin graphh t c is obtained by embedding a treet having no nodes of degree 2 in the plane and then adding a cyclec to join the leaves oft in such a way that the resulting graph is planar these graphs are edge minimal 3 connected hamiltonian and in general have large numbers of hamilton cycles we show that for arbitrary real edge costs the travelling salesman problem can be polynomially solved for such a graph and we give an explicit linear description of the travelling salesman polytope the convex hull of the incidence vectors of the hamilton cycles for such a graph

traveling salesman path problems in the traveling salesman path problem we are given a set of cities traveling costs between city pairs and fixed source and destination cities the objective is to find a minimum cost path from the source to destination visiting all cities exactly once in this paper we study polyhedral and combinatorial properties of a variant we call the traveling salesman walk problem in which the objective is to find a minimum cost walk from the source to destination visiting all cities at least once we first characterize traveling salesman walk perfect graphs graphs for which the convex hull of incidence vectors of traveling salesman walks can be described by linear inequalities we show these graphs have a description by way of forbidden minors and also characterize them constructively we also address the asymmetric traveling salesman path problem atspp and give a factor o sqrt n approximation algorithm for this problem

a lifting procedure for the asymmetric traveling salesman polytope and a large new class of facets given any family of valid inequalities for the asymmetric traveling salesman polytopep g defined on the complete digraphg we show that all members of are facet defining if the primitive members of usually a small subclass are based on this result we then introduce a general procedure for identifying new classes of facet inducing inequalities forp g by lifting inequalities that are facet inducing forp g whereg is some induced subgraph ofg unlike traditional lifting where the lifted coefficients are calculated one by one and their value depends on the lifting sequence our lifting procedure replaces nodes ofg with cliques ofg and uses closed form expressions for calculating the coefficients of the new arcs which are sequence independent we also introduce a new class of facet inducing inequalities the class of sd source destination inequalities which subsumes as special cases most known families of facet defining inequalities

fluctuation noise spectroscopy and a universal fitting function of amplitudes of random sequences abstract a universal fitting function has been recognized that makes use of the eigen coordinates method physica a 285 2000 547 to accurately describe the distribution of ordered amplitudes within random sequences taken from a diversity of sources it is shown that sequences with a discrete structure can be described in terms of specific distributions of relative frequencies with respect to the number of quantum levels an investigation of these quantum distributions leads to an increase in both sensitivity and selectivity when attempting the statistical detection of various predominant factors of the hidden signals the physical meaning of this new function is discussed and a proposal is made as the basis of a new fluctuation noise spectroscopy in which the recognized function can be used for the detection of small signals and or the forerunners of strong signals that are hidden within the random sequences analyzed

complex fractal dimensions describe the hierarchical structure of diffusion limited aggregate clusters we analyze large diffusion limited aggregates and uncover a ital discrete scaling invariance in their inner structure which can be quantified by the introduction of a set of ital complex fractal dimensions we provide a theoretical framework and prediction of their values based on renormalization group theory and a previous wavelet analysis copyright ital 1996 the american physical society

on the relationship between the biconnectivity augmentation and travelling salesman problems abstract a strategy for solving the traveling salesman problem is adapted to the problem of finding a biconnected subgraph of a weighted graph whose cost function satisfies the triangle inequality an approximation algorithm similar to christofides algorithm 5 for the traveling salesman problem is shown to possess the same worst case bound of 3 2 when applied to the biconnectivity augmentation problem a tight inequality is derived relating the cost of an optimal traveling salesman tour to the cost of an optimal biconnection

chain constrained spanning trees we consider the problem of finding a spanning tree satisfying a family of additional constraints several settings have been considered previously the most famous being the problem of finding a spanning tree with degree constraints since the problem is hard the goal is typically to find a spanning tree that violates the constraints as little as possible iterative rounding has become the tool of choice for constrained spanning tree problems however iterative rounding approaches are very hard to adapt to settings where an edge can be part of more than a constant number of constraints we consider a natural constrained spanning tree problem of this type namely where upper bounds are imposed on a family of cuts forming a chain our approach reduces the problem to a family of independent matroid intersection problems leading to a spanning tree that violates each constraint by a factor of at most 9 we also present strong hardness results among other implications these are the first to show in the setting of a basic constrained spanning tree problem a qualitative difference between what can be achieved when allowing multiplicative as opposed to additive constraint violations

solving optimization problems with diseconomies of scale via decoupling we present a new framework for solving optimization problems with a diseconomy of scale in such problems our goal is to minimize the cost of resources used to perform a certain task the cost of resources grows superlinearly as xq q 1 with the amount x of resources used we define a novel linear programming relaxation for such problems and then show that the integrality gap of the relaxation is aq where aq is the q th moment of the poisson random variable with parameter 1 using our framework we obtain approximation algorithms for the minimum energy efficient routing minimum degree balanced spanning tree load balancing on unrelated parallel machines and unrelated parallel machine scheduling with nonlinear functions of completion times problems our analysis relies on the decoupling inequality for nonnegative random variables the inequality states that ie1nxi q cq ie1nyi q where xi are independent nonnegative random variables yi are possibly dependent nonnegative random variables and each yi has the same distribution as xi the inequality was proved by de la pena in 1990 de la pena ibragimov and sharakhmetov showed that cq 2 for qi 1 2 and cq aq1 q for q 2 we show that the optimal constant is cqe aq1 q for any q 1 we then prove a more general inequality for every convex function v elv ie1nxi r elv p ie1n yi r and for every concave function el ie1n xi r el p ie1n yi r where p is a poisson random variable with parameter 1 independent of the random variables yi

symmetric inequalities and their composition for asymmetric travelling salesman polytopes the asymmetric travelling salesmanatspolytope atspv is the convex hull of incidence vectors of all hamiltonian circuits in a complete digraph with node set v this paper studies classes of valid symmetric inequalities ay a0 for ats polytopes with coefficients satisfying aij aji for all pair of cities i and j of particular interest are those inequalities derived from facet defining inequalities for symmetric travelling salesman polytopes stsps we show that known classes of stsp facet defining inequalities such as path wheelbarrow chain and ladder inequalities induce symmetric atsp facet defining inequalities for atspv with v 8 we show that there are precisely four types of stsp facet defining inequalities that do not induce atsp facets we propose a tree composition of symmetric inequalities and use it to generate a large new class of symmetric facet defining inequalities for ats polytopes subsuming all nonspanning clique tree inequalities a hamiltonian path approach is used for most of the polyhedral proofs in the paper

1 f α noise from self organized critical models with uniform driving using the well known olami feder christensen model as our paradigm we show how to modify uniform driven self organized critical models to generate 1 f ensuremath alpha noise this model can reproduce all the main features of 1 f ensuremath alpha noise 1 ensuremath alpha is close to one and does not depend on the dimension of the system 2 the 1 f ensuremath alpha behavior is found for very low frequencies 3 the spatial correlations do not obey a power law that proves that spatially extended systems based on activation deactivation processes do not have to be point driven to produce 1 f ensuremath alpha noise the essential ingredient is a local memory of the activation deactivation process

properties of isometric mappings abstract some relations between isometry and linearity are examined in particular generalizations of the mazur ulam theorem and open problems are discussed

the crown inequalities for the symmetric traveling salesman polytope we define a new family of valid inequalities for the symmetric traveling salesman polytope stspn that is the convex hull of the incidence vectors of all hamiltonian cycles of a complete graph with n nodes the smallest value of n for which the inequalities are defined is 8 we call these inequalities crown inequalities and we prove that they are facet inducing for stspn for n 8 we describe some extensions of the crown inequalities and we prove that they induce facets of stspn as well finally we discuss some issues on the possible applications of these inequalities in a polyhedral cutting plane algorithm

bounded cascade models as nonstationary multifractals we investigate a class of bounded random cascade models which are multiplicative by construction yet additive with respect to some but not all of their properties we assume the multiplicative weights go to unity as the cascade proceeds then the resulting field has upper and lower bounds two largely complementary multifractal statistical methods of analysis are used singular measures and structure functions yielding respectively the exponent hierarchies ital d sub ital q and ital h sub ital q we study in more detail a specific subclass of one dimensional models with weights 1 plus minus 1 minus 2 ital p ital r sub ital n minus 1 sup ital h at relative scale ital r sub ital n 2 sup minus ital n after ital n cascade steps the parameter ital h gt 0 regulates the degree of nonstationarity at ital h 0 stationarity prevails and singular ital p model cascades meneveau and sreenivasan phys rev lett 59 1424 1987 are retrieved our model has at once large scale stationarity and small scale nonstationarity with stationary increments due to the boundedness the ital d sub ital q all converge to unity with increasing ital n the rate of convergence is estimated and the results are discussed in terms of residual multifractality a spurious singularity spectrum due to finite size effects the structure function exponents are moremore interesting ital h sub ital q min l brace ital h 1 ital q r brace in the limit ital n r arrow infinity we further focus on the cases ital q 1 related to the fractal structure of the graph ital q 2 related to the energy spectrum and ital q 1 ital h the critical order beyond which our multiplicative and multiscaling bounded cascade model can be statistically distinguished from fractional brownian motion the corresponding additive and monoscaling model less

approximating min cost chain constrained spanning trees a reduction from weighted to unweighted problems we study the min cost chain constrained spanning tree mccst problem find a min cost spanning tree in a graph subject to degree constraints on a nested family of node sets we devise the first polytime algorithm that finds a spanning tree that i violates the degree constraints by at most a constant factor and ii whose cost is within a constant factor of the optimum previously only an algorithm for unweighted ccst was known olver and zenklusen in proceedings of the 16th ipco pp 324 335 2013 which satisfied i but did not yield any cost bounds this also yields the first result that obtains an o 1 factor for both the cost approximation and violation of degree constraints for any spanning tree problem with general degree bounds on node sets where an edge participates in a super constant number of degree constraints a notable feature of our algorithm is that we reduce mccst to unweighted ccst and then utilize olver and zenklusen in proceedings of the 16th ipco pp 324 335 2013 via a novel application of lagrangian duality to simplify the cost structure of the underlying problem and obtain a decomposition into certain uniform cost subproblems we show that this lagrangian relaxation based idea is in fact applicable more generally and for any cost minimization problem with packing side constraints yields a reduction from the weighted to the unweighted problem we believe that this reduction is of independent interest as another application of our technique we consider the k budgeted matroid basis problem where we build upon a recent rounding algorithm of bansal and nagarajan proceedings of ipco 2016 arxiv 1512 02254 2015 to obtain an improved n o k 1 5 epsilon time algorithm that returns a solution that satisfies any one of the budget constraints exactly and incurs a 1 epsilon violation of the other budget constraints

the traveling salesman problem on a graph and some related integer polyhedra given a graphg n e and a length functionl e the graphical traveling salesman problem is that of finding a minimum length cycle goingat least once through each node ofg this formulation has advantages over the traditional formulation where each node must be visited exactly once we give some facet inducing inequalities of the convex hull of the solutions to that problem in particular the so called comb inequalities of grotschel and padberg are generalized some related integer polyhedra are also investigated finally an efficient algorithm is given wheng is a series parallel graph

a matter of degree improved approximation algorithms for degree bounded minimum spanning trees in this paper we present a new bicriteria approximation algorithm for the degree bounded minimum spanning tree problem in this problem we are given an undirected graph a nonnegative cost function on the edges and a positive integer b and the goal is to find a minimum cost spanning tree t with maximum degree at most b in an n node graph our algorithm finds a spanning tree with maximum degree o b logn and cost o optb where optb is the minimum cost of any spanning tree whose maximum degree is at most b our algorithm uses ideas from lagrangean duality we show how a set of optimum lagrangean multipliers yields bounds on both the degree and the cost of the computed solution

regular and stochastic behavior of parkinsonian pathological tremor signals abstract regular and stochastic behavior in the time series of parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non markov stochastic processes and flicker noise spectroscopy we have developed a new method of analyzing and diagnosing parkinson s disease pd by taking into consideration discreteness fluctuations long and short range correlations regular and stochastic behavior markov and non markov effects and dynamic alternation of relaxation modes in the initial time signals the spectrum of the statistical non markovity parameter reflects markovity and non markovity in the initial time series of tremor the relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states the local time behavior of the initial time correlation function and the first point of the non markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series the obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a pd patient generally the method allows one to assess the efficacy of the medical treatment for a group of pd patients

additive guarantees for degree bounded directed network design we present polynomial time approximation algorithms for some degree bounded directed network design problems our main result is for intersecting supermodular connectivity requirements with degree bounds given a directed graph g v e with nonnegative edge costs a connectivity requirement specified by an intersecting supermodular function f and upper bounds a v b v v in v on in degrees and out degrees of vertices find a minimum cost f connected subgraph of g that satisfies the degree bounds we give a bicriteria approximation algorithm for this problem using the natural lp relaxation and show that our guarantee is the best possible relative to this lp relaxation we also obtain similar results for the more general class of crossing supermodular requirements in the absence of edge costs our result gives the first additive o 1 approximation guarantee for degree bounded intersecting crossing supermodular connectivity problems we also consider the minimum crossing spanning tree problem given an undirected edge weighted graph g edge subsets e i i 1 k and nonnegative integers b i i 1 k find a minimum cost spanning tree if it exists in g that contains at most b i edges from each set e i we obtain a r 1 additive approximation for this problem when each edge lies in at most r sets a special case of this problem is the degree bounded minimum spanning tree and our techniques give a substantially shorter proof of the recent 1 approximation of singh and lau in proceedings of the 40th annual acm symposium on theory of computing 2007 pp 661 670

possibility between earthquake and explosion seismogram differentiation by discrete stochastic non markov processes and local hurst exponent analysis the basic scientific point of this paper is to draw the attention of researchers to new possibilities of differentiation of similar signals having different nature one example of such kinds of signals is presented by seismograms containing recordings of earthquakes eq s and technogenic explosions te s eq s are among the most dramatic phenomena in nature we propose here a discrete stochastic model for possible solution of a problem of strong eq forecasting and differentiation of te s from the weak eq s theoretical analysis is performed by two independent methods by using statistical theory of discrete non markov stochastic processes phys rev e 62 6178 2000 and the local hurst exponent the following earth states have been considered among them before ib and during i strong eq during weak eq ii and during te iii and in a calm state of earth s core iv the estimation of states i ii and iii has been made on the particular examples of turkey 1999 eq s state iv has been taken as an example of earth s state before underground te time recordings of seismic signals of the first four dynamic orthogonal collective variables six various planes of phase portrait of four dimensional phase space of orthogonal variables and the local hurst exponent have been calculated for the dynamic analysis of states of systems i char21 iv the analysis of statistical properties of seismic time series i char21 iv has been realized with the help of a set of discrete time dependent functions time correlation function and first three memory functions their power spectra and the first three points in the statistical spectrum of non markovity parameters in all systems studied we have found a bizarre combination of the following spectral characteristics the fractal frequency spectra adjustable by phenomena of usual and restricted self organized criticality spectra of white and color noises and unusual alternation of markov and non markov effects of long range memory detected earlier j phys a 27 5363 1994 only for hydrodynamic systems our research demonstrates that discrete non markov stochastic processes and long range memory effects play a crucial role in the behavior of seismic systems i char21 iv the approaches permitting us to obtain an algorithm of strong eq forecasting and to differentiate te s from weak eq s have been developed

primal dual meets local search approximating msts with nonuniform degree bounds we present a new bicriteria approximation algorithm for the degree bounded minimum cost spanning tree mst problem given an undirected graph with nonnegative edge weights and a degree bound b find a spanning tree of maximum node degree b and minimum total edge cost our algorithm outputs a tree of maximum degree at most a constant times b and total edge cost at most a constant times that of a minimum cost degree b bounded spanning tree while our new algorithm is based on ideas from lagrangian relaxation as is our previous work siam j comput 31 2002 pp 1783 1793 it does not rely on computing a solution to a linear program instead it uses a repeated application of kruskal s mst algorithm interleaved with a combinatorial update of approximate lagrangian node multipliers maintained by the algorithm these updates cause subsequent repetitions of the spanning tree algorithm to run for longer and longer times leading to overall progress and a proof of the performance guarantee a second useful feature of our algorithm is that it can handle nonuniform degree bounds on the nodes given distinct bounds bv for every node v in v the output tree has degree at most o bv log v for every v in v as before the cost of the tree is at most a constant times that of a minimum cost tree obeying all degree bounds

stochastic dynamics of time correlation in complex systems with discrete time in this paper we present the concept of description of random processes in complex systems with discrete time it involves the description of kinetics of discrete processes by means of the chain of finite difference non markov equations for time correlation functions tcfs we have introduced the dynamic time dependent information shannon entropy s i t where i 0 1 2 3 ellipsis as an information measure of stochastic dynamics of time correlation i 0 and time memory i 1 2 3 ellipsis the set of functions s i t constitute the quantitative measure of time correlation disorder i 0 and time memory disorder i 1 2 3 ellipsis in complex system the theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states we examine two stochastic processes involving the creation and annihilation of time correlation or time memory in details we carry out the analysis of vectors dynamics employing finite difference equations for random variables and the evolution operator describing their natural motion the existence of tcf results in the construction of the set of projection operators by the usage of scalar product operation harnessing the infinite set of orthogonal dynamic random variables on a basis of gram shmidt orthogonalization procedure tends to creation of infinite chain of finite difference non markov kinetic equations for discrete tcfs and memory functions mfs the solution of the equations above thereof brings to the recurrence relations between the tcf and mf of senior and junior orders this offers new opportunities for detecting the frequency spectra of power of entropy function s i t for time correlation i 0 and time memory i 1 2 3 ellipsis the results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems application of this technique on the analysis of stochastic dynamics of rr intervals from human ecg s shows convincing evidence for a non markovian phenomemena associated with a peculiarities in short and long range scaling this method may be of use in distinguishing healthy from pathologic data sets based in differences in these non markovian properties

non markov stochastic dynamics of real epidemic process of respiratory infections abstract the study of social networks and especially of stochastic dynamics of diseases spread in human population has recently attracted considerable attention in statistical physics in this work we present a new statistical method of analyzing the spread of epidemic processes of grippe and acute respiratory track infections arti by means of the theory of discrete non markov stochastic processes we use the results of our last theory phys rev e 65 2002 046107 to study statistical memory effects long range correlation and discreteness in real data series describing the epidemic dynamics of human arti infections and grippe we have carried out the comparative analysis of the data of the two infections grippe and arti in one of the industrial districts of kazan one of the largest cities of russia the experimental data are analyzed by the power spectra of the initial time correlation function and the memory functions of junior orders the phase portraits of the four first dynamic variables the three first points of the statistical non markov parameter and the locally averaged kinetic and relaxation parameters the received results give an opportunity to provide a strict quantitative description of regular and stochastic components in epidemic dynamics of social networks taking into account their time discreteness and effects of statistical memory they also allow to reveal the degree of randomness and predictability of the real epidemic process in the specific social network

on the generalizations of the mazur ulam isometric theorem abstract this paper contains several generalizations of the mazur ulam isometric theorem in f spaces which are not assumed to be locally bounded let x and y be two real f spaces and let x be locally pseudoconvex or midpoint bounded assume that a operator t maps x onto y in a locally 1 2i isometric manner for all i 0 n then t is affine in addition we give the sufficient conditions of a mapping between two topological vector spaces being affine

implementing the dantzig fulkerson johnson algorithm for large traveling salesman problems dantzig fulkerson and johnson 1954 introduced the cutting plane method as a means of attacking the traveling salesman problem this method has been applied to broad classes of problems in combinatorial optimization and integer programming in this paper we discuss an implementation of dantzig et al s method that is suitable for tsp instances having 1 000 000 or more cities our aim is to use the study of the tsp as a step towards understanding the applicability and limits of the general cutting plane method in large scale applications

the quantified histograms detection of the hidden unsteadiness abstract for a given level of digitization a number of relative frequencies presented by a histogram constructed for a short sample defined as a segment of a random series related in a certain way to both the length of the sampling l and the number of decompositions k may form a set of some levels possessing a discrete spectrum this spectrum can be defined as a quantified histogram qh the structure of parameters of a certain qh can be analyzed via both the number of quantum levels nql and the proper collection of relative frequencies on every level these parameters form kind of specific fingerprints which characterizes statistical properties of the segment of random series treated in this way qhs allow us to introduce the concept of a standard noise sn which can be used as a noise ruler to compare random series of distinct nature this standard noise turns out to be very useful in the detection of both a hidden unsteadiness and superweak signals existing in random series in the capacity of an example of the application of this new method a comparison of statistically sensible distinctions between noises accompanying either earthquakes or technogenic explosions is given distinctions thus obtained called earthquake forerunner can be used for earthquakes forecasting

deeper local search for parameterized and approximation algorithms for maximum internal spanning tree the maximum internal spanning tree problem asks for a spanning tree of a given graph that has the maximum number of internal vertices among all spanning trees of this graph in its parameterized version we are interested in whether the graph has a spanning tree with at least k internal vertices fomin et al 2013 4 crafted a very ingenious reduction rule and showed that a simple application of this rule is sufficient to yield a 3k vertex kernel implying an o 8 k time parameterized algorithm using depth 2 local search knauer and spoerhase 2015 9 developed a 5 3 approximation algorithm for the optimization version we try deeper local search we conduct a thorough combinatorial analysis on the obtained spanning trees and explore their algorithmic consequences we first observe that from the spanning tree obtained by depth 3 local search one can easily find a reducible structure and apply the reduction rule of fomin et al this gives an improved kernel of 2k vertices and as a by product a deterministic algorithm running in time o 4 k we then go even deeper by considering the spanning tree obtained by depth 5 local search it is shown that the number of internal vertices of this spanning tree is at least 2 3 of the maximum number a spanning tree can have thereby delivering an improved approximation algorithm with ratio 1 5 for the problem

mappings of conservative distances in linear n normed spaces abstract the aim of this article is to generalize the mazur ulam theorem to the case of linear n normed spaces

equimodular and linearity in modular spaces abstract in this paper the concept of equimodular is introduced it contains several generalizations of mazur ulam s isometric theorem in modular spaces let x and y be two real modular spaces and x with 1 midpoint shrinking whose modular x satisfies the 2 condition assume that an operator t maps x onto y in an 2 ti equimodular manner for all i 0 n where ti is a null sequence of nonnegative reals with the property that t0 1 t1 1 2 and ti ti 1 2ti for i 2 then t is affine

violation of the scaling relation and non markovian nature of earthquake aftershocks abstract the statistical properties of earthquake aftershocks are studied the scaling relation for exponents of the omori law and the power law calm time distribution i e the interoccurrence time distribution which is valid if a sequence of aftershocks is a singular markovian process is carefully examined data analysis shows significant violation of the scaling relation implying the non markovian nature of aftershocks

on generalizations of network design problems with degree bounds iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems in this paper we extend the scope of the iterative relaxation method in two directions 1 by handling more complex degree constraints in the minimum spanning tree problem namely laminar crossing spanning tree and 2 by incorporating degree bounds in other combinatorial optimization problems such as matroid intersection and lattice polyhedra we give new or improved approximation algorithms hardness results and integrality gaps for these problems our main result is a 1 b o log n approximation algorithm for the minimum crossing spanning tree mcst problem with laminar degree constraints the laminar mcst problem is a natural generalization of the well studied bounded degree mst and is a special case of general crossing spanning tree we give an additive log c m hardness of approximation for general mcst even in the absence of costs c 0 is a fixed constant and m is the number of degree constraints this also leads to a multiplicative log c m hardness of approximation for the robust k median problem anthony et al in math oper res 35 79 101 2010 improving over the previously known factor 2 hardness we then consider the crossing contra polymatroid intersection problem and obtain a 2 2b 1 approximation algorithm where is the maximum element frequency this models for example the degree bounded spanning set intersection in two matroids finally we introduce the crossing latticep olyhedron problem and obtain a 1 b 2 1 approximation algorithm under certain condition this result provides a unified framework and common generalization of various problems studied previously such as degree bounded matroids

polynomial bounds for the grid minor theorem one of the key results in robertson and seymour s seminal work on graph minors is the grid minor theorem also called the excluded grid theorem the theorem states that for every grid h every graph whose treewidth is large enough relative to vv h v contains h as a minor this theorem has found many applications in graph theory and algorithms let f k denote the largest value such that every graph of treewidth k contains a grid minor of size f k f k the best previous quantitative bound due to recent work of kawarabayashi and kobayashi and leaf and seymour shows that f k e slog k log log k in contrast the best known upper bound implies that f k e o sk log k in this article we obtain the first polynomial relationship between treewidth and grid minor size by showing that f k e k for some fixed constant 0 and describe a randomized algorithm whose running time is polynomial in vv g v and k that with high probability finds a model of such a grid minor in g

dynamical shannon entropy and information tsallis entropy in complex systems abstract in this work we offer a new approach to the concept of the information entropy for the description of the dynamic behaviour of complex systems on the basis of the unification of the known information approach to the shannon entropy submitted in works of authors phys rev e 62 5 2000 6178 physica a 303 2002 427 and generalization of the boltzman gibbs entropy offered by tsallis braz j phys 29 1 1999 1 we have received a new representation of the dynamic information entropy here we present concrete applications of the received equations to the study of complex systems related to the electric signals of ecgs of healthy people and patients with myocardial infarction mi as an example various modifications of the non markovity parameter are also submitted they were received with the help of the new approach to the information entropy we have received detailed information about markov quasi markov and non markov characteristics of the rr interval fluctuations of the ecgs with the help of the chain of zwanzig mori s discrete kinetic equations and dynamical tsallis entropy

bounded degree minimum radius spanning trees in wireless sensor networks in this paper we study the problem of computing a spanning tree of a given undirected disk graph such that the radius of the tree is minimized subject to a given degree constraint d we first introduce an 8 4 bicriteria approximation algorithm for unit disk graphs which is a special case of disk graphs that computes a spanning tree such that the degree of any nodes in the tree is at most d 8 and its radius is at most email protected opt where opt is the minimum possible radius of any spanning tree with degree bound d we also introduce an a 2 bicriteria approximation algorithm for disk graphs that computes a spanning tree whose maximum node degree is at most d email protected and whose radius is bounded by email protected opt where a is a non constant value that depends on m and k with m being the number of distinct disk radii and k being the ratio of the largest and the smallest disk radius

data adaptive wavelets and multi scale singular spectrum analysis using multi scale ideas from wavelet analysis we extend singular spectrum analysis ssa to the study of nonstationary time series including the case where intermittency gives rise to the divergence of their variance the wavelet transform resembles a local fourier transform within a finite moving window whose width w proportional to the major period of interest is varied to explore a broad range of such periods ssa on the other hand relies on the construction of the lag correlation matrix c onm lagged copies of the time series over a fixed window width w to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components herew dm1t with1t as the time step the proposed multi scale ssa is a local ssa analysis within a moving window of widthm w n wheren is the length of the time series multi scale ssa variesw while keeping a fixed w m ratio and uses the eigenvectors of the corresponding lag correlation matrix c m as data adaptive wavelets successive eigenvectors of c m correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis multi scale ssa thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time frequency domain by a suitable localization of the signal s correlation matrix we present several examples of application to synthetic signals with fractal or power law behavior which mimic selected features of certain climatic or geophysical time series the method is applied next to the monthly values of the southern oscillation index soi for 1933 1996 the soi time series is widely believed to capture major features of the el nino southern oscillation enso in the tropical pacific our methodology highlights an abrupt periodicity shift in the soi near 1960 this abrupt shift between 5 and 3 years supports the devil s staircase scenario for the enso phenomenon preliminary results of this study were presented at the xxii general assembly of the european geophysical society vienna may 1997 and at the fall meeting of the american geophysical union san francisco december 1997 2000 elsevier science b v all rights reserved

stick slip statistics for two fractal surfaces a model for earthquakes abstract following the observations of the self similarity in various length scales in the roughness of the fractured solid surfaces we propose here a new model for the earthquake we demonstrate rigorously that the contact area distribution between two fractal surfaces follows a unique power law this is then utilised to show that the elastic energy releases for slips between two rough fractal surfaces indeed follow a guttenberg richter like power law

survivable network design with degree or order constraints we present algorithmic and hardness results for network design problems with degree or order constraints the first problem we consider is the survivable network design problem with degree constraints on vertices the objective is to find a minimum cost subgraph which satisfies connectivity requirements between vertices and also degree upper bounds b v on the vertices this includes the well studied minimum bounded degree spanning tree problem as a special case our main result is a 2 2b v 3 approximation algorithm for the edge connectivity survivable network design problem with degree constraints where the cost of the returned solution is at most twice the cost of an optimum solution satisfying the degree bounds and the degree of each vertex v is at most 2b v 3 this implies the first constant factor bicriteria approximation algorithms for many degree constrained network design problems including the minimum bounded degree steiner forest problem our results also extend to directed graphs and provide the first constant factor bicriteria approximation algorithms for the minimum bounded degree arborescence problem and the minimum bounded degree strongly k edge connected subgraph problem in contrast we show that the vertex connectivity survivable network design problem with degree constraints is hard to approximate even when the cost of every edge is zero a striking aspect of our algorithmic result is its simplicity it is based on the iterative relaxation method which is an extension of jain s iterative rounding method this provides an elegant and unifying algorithmic framework for a broad range of network design problems we also study the problem of finding a minimum cost lambda edge connected subgraph with at least k vertices which we call the k lambda subgraph problem this generalizes some well studied classical problems such as the k mst and the minimum cost lambda edge connected subgraph problems we give a polylogarithmic approximation for the k 2 subgraph problem however by relating it to the densest k subgraph problem we provide evidence that the k lambda subgraph problem might be hard to approximate for arbitrary lambda

approximate multi matroid intersection via iterative refinement we introduce a new iterative rounding technique to round a point in a matroid polytope subject to further matroid constraints this technique returns an independent set in one matroid with limited violations of the constraints of the other matroids in addition to the classical steps of iterative relaxation approaches we iteratively refine involved matroid constraints this leads to more restrictive constraint systems whose structure can be exploited to prove the existence of constraints that can be dropped hence throughout the iterations we both tighten constraints and later relax them by dropping constraints under certain conditions due to the refinement step we can deal with considerably more general constraint classes than existing iterative relaxation and rounding methods which typically involve a single matroid polytope with additional simple cardinality constraints that do not overlap too much we show that our rounding method combined with an application of a matroid intersection algorithm yields the first 2 approximation for finding a maximum weight common independent set in 3 matroids moreover our 2 approximation is lp based and settles the integrality gap for the natural relaxation of the problem prior to our work no upper bound better than 3 was known for the integrality gap which followed from the greedy algorithm we also discuss various other applications of our techniques including an extension that allows us to handle a mixture of matroid and knapsack constraints

order picking in a rectangular warehouse a solvable case of the traveling salesman problem this paper addresses the problem of order picking in a rectangular warehouse that contains crossovers only at the ends of aisles an algorithm is presented for picking an order in minimum time the computational effort required is linear in the number of aisles the procedure has been implemented on a microcomputer a 50 aisle problem requires only about 1 minute to solve

universal approach to overcoming nonstationarity unsteadiness and non markovity of stochastic processes in complex systems abstract in the present paper we suggest a new universal approach to study complex systems by microscopic mesoscopic and macroscopic methods we discuss new possibilities of extracting information on nonstationarity unsteadiness and non markovity of discrete stochastic processes in complex systems we consider statistical properties of the fast intermediate and slow components of the investigated processes in complex systems within the framework of microscopic mesoscopic and macroscopic approaches separately among them theoretical analysis is carried out by means of local noisy time dependent parameters and the conception of a quasi brownian particle qbp mesoscopic approach as well as the use of wavelet transformation of the initial row time series as a concrete example we examine the seismic time series data for strong and weak earthquakes in turkey 1998 1999 in detail as well as technogenic explosions we propose a new possible solution to the problem of forecasting strong earthquakes besides we have found out that an unexpected restoration of the first two local noisy parameters in weak earthquakes and technogenic explosions is determined by exponential law in this paper we have also carried out the comparison and have discussed the received time dependence of the local parameters for various seismic phenomena

applications of statistical physics to economic and financial topics abstract problems in economy and finance have started to attract the interest of statistical physicists fundamental problems pertain to the existence or not of long medium short range power law correlations in economic systems as well as to the presence of financial cycles methods like the extended detrended fluctuation analysis and the multi affine analysis are recalled emphasizing their value in sorting out correlation ranges and predictability among spectacular results the possibility of crash predictions is indicated the well known financial analyst technique the so called moving average is shown to raise questions about fractional brownian motion properties finally the m k zipf method and the i variability diagram technique are presented for sorting out short range correlations analogies with other fields of modern applied statistical physics are also presented in view of some universal openess

relaxation and phase space singularities in time series of human magnetoencephalograms as indicator of photosensitive epilepsy to analyze the crucial role of fluctuation and relaxation effects for the function of the human brain we studied some statistical quantifiers that support the information characteristics of neuromagnetic brain responses magnetoencephalogram meg the signals to a flickering stimulus of different color combinations have been obtained from a group of control subjects which is then contrasted with those of a patient suffering photosensitive epilepsy pse we found that the existence of the specific stratification of the phase clouds and the concomitant relaxation singularities of the corresponding nonequilibrium dynamics of the chaotic behavior of the signals in separate areas in a patient provide likely indicators for the zones which are responsible for the appearance of pse