qaplib a quadratic assignment problem library abstract after a short introduction into quadratic assignment problems we give a library of problem instances for the quadratic assignment problem the examples are listed y authors in alphabetical order

random copolymers and the morita approximation polymer adsorption and polymer localization we analyse directed walk models of random copolymer adsorption and localization ideally we would like t os olve thequenched problem but it appears to be intractable even for simple directed models the annealed approximation is solvable but is inadequate in the strong interaction regime fo rt he adsorption problem and gives a qualitatively incorrect phase diagram for the localization problem in this paper we treat these directed models using an approximation suggested by morita 1964 j math phys 5 1401 5 in which the proportion of each comonomer is fixed we find that the morita approximation leads to behaviour that is closer to that of the quenched average model and this is particularly interesting in the localization problem where the phase diagram is a tl east qualitatively very similar to that of the quenched average problem we also show that the phase boundaries in the morita approximation are bounds on the locations of the phase boundaries of the quenched model

hierarchical pinning models quadratic maps and quenched disorder we consider a hierarchical model of polymer pinning in presence of quenched disorder introduced by derrida et al j stat phys 66 1189 1213 1992 which can be re interpreted as an infinite dimensional dynamical system with random initial condition the disorder it is defined through a recurrence relation for the law of a random variable r n n 1 2 which in absence of disorder i e when the initial condition is degenerate reduces to a particular case of the well known logistic map the large n limit of the sequence of random variables 2 n log r n a non random quantity which is naturally interpreted as a free energy plays a central role in our analysis the model depends on a parameter 0 1 related to the geometry of the hierarchical lattice and has a phase transition in the sense that the free energy is positive if the expectation of r 0 is larger than a certain threshold value and it is zero otherwise it was conjectured in derrida et al j stat phys 66 1189 1213 1992 that disorder is relevant respectively irrelevant or marginally relevant if 1 2 1 2 we find the correct scaling form for weak disorder of the critical point shift

study of the iterations of a mapping associated to a spin glass model we study the iterations of the mapping mathcal n f s frac f s 2 f 0 2 s f 0 2 with the constraintsf 1 1 f s ansn an 0 and find that except iff s s n f s approaches either 0 or 1 for s 1 ask

robust comparative statics of risk changes the standard method for establishing the comparative statics of risk changes in optimization problems has been confined to comparing unique interior solutions relying on strong assumptions about payoff functions and decision variables we propose a simple and intuitive approach that hinges on considerably weaker assumptions merging insights from the monotone comparative statics literature with insights from the risk apportionment literature we show that the ranking of simple lottery pairs is all that is needed for establishing the comparative statics of risk changes we use this approach to analyze the comparative statics of nth degree stochastic dominance shifts in a general setting with one and with multiple decision variables and we show how these results can be applied to generalize the classical theories of precautionary saving self protection and others this paper was accepted by james smith decision analysis

path comparisons for a priori and time adaptive decisions in stochastic time varying networks abstract travel times in congested transportation networks are time varying quantities that can at best be known a priori probabilistically in such networks the arc weights travel times are represented by random variables whose probability distribution functions vary with time these networks are referred to herein as stochastic time varying or stv networks the determination of least time routes in stv networks is more difficult than in deterministic networks in part because for a given departure time more than one path may exist between an origin and destination each with a positive probability of having the least travel time in this paper measures for comparing time varying random path travel times over a time period are given for both a priori optimization and time adaptive choices where a driver may react to revealed arrival times at intermediate nodes the resulting measures are central to the development of methodologies for determining optimal paths in stv networks

pinning and wetting transition for 1 1 dimensional fields with laplacian interaction we consider a random field 1 n as a model for a linear chain attracted to the defect line 0 that is the x axis the free law of the field is specified by the density exp iv i with respect to the lebesgue measure on n where is the discrete laplacian and we allow for a very large class of potentials v the interaction with the defect line is introduced by giving the field a reward 0 each time it touches the x axis we call this model the pinning model we consider a second model the wetting model in which in addition to the pinning reward the field is also constrained to stay nonnegative we show that both models undergo a phase transition as the intensity of the pinning reward varies both in the pinning a p and in the wetting a w case there exists a critical value ca such that when ca the field touches the defect line a positive fraction of times localization while this does not happen for ca delocalization the two critical values are nontrivial and distinct 0 cp cw and they are the only nonanalyticity points of the respective free energies for the pinning model the transition is of second order hence the field at cp is delocalized on the other hand the transition in the wetting model is of first order and for cw the field is localized the core of our approach is a markov renewal theory description of the field

differential migdal kadanoff renormalization group for disordered systems phase transitions in quenched random systems are studied within the migdal kadanoff approximation exact differential recursion relations for the distribution of coupling are derived the q state potts model with random ferromagnetic couplings is studied in two and three dimensions in three dimensions there is a non perturbative random fixed point which exists when the specific heat exponent is either positive or slightly negative if the specific heat exponent is slightly negative a multicritical point separates strong and weak disorder regimes the analytic results are confirmed by numerical simulations of the recursion relations

the migdal kadanoff approximation optimisation generalisation ising model in external fields and the migdal kadanoff hierarchies the simplest migdal kadanoff approximation is optimised on hypercubic lattices generalisation is made to all regular lattices leading to recursion relations continuous in lattice coordination one variety of these relations shows universality whilst another variety shows duality on planar lattices the ising model in external fields both normal and staggered is investigated phase diagrams and exponents are found under a complete treatment of the ambiguity in the handling of external fields by bond moving finally the underlying exactly solved family of hierarchical lattices is considered it is shown that these lattices exhibit a complete breakdown in the concept of universality

the parameter space investigation method of multiple objective nonlinear programming a computational investigation in this paper we study the parameter space investigation method of i m sobol and r b statnikov the method is a random hitting procedure for solving the kinds of small but difficult multiple objective nonlinear programming problems often encountered in engineering design and optimal control sobol and statnikov have argued the effectiveness of their approach and its application possibilities in this paper we computationally test the parameter space investigation method to examine the extent to which claims about their method can be substantiated

dominance relations among standardized variables this paper examines stochastic dominance relations among discrete random variables defined on a common integer domain while these restrictions are minimal they lead both to new theoretical results and to simpler proofs of existing one the new results obtained for dominance criteria of any degree generalize an ssd result of rothschild stiglitz to describe how for any dominance criterion a dominated variable is equal in distribution to a dominated variable plus perturbation terms if the variables are comparable under fsd the perturbations are downward shift terms while under ssd tsd all but two three of the perturbations are zero mean disturbance terms noise under ssd the remaining perturbations are shift terms and under tsd noise and shift terms however under either ssd or tsd these remaining terms are identically zero if the variables to be compared have equal means the paper also finds new proofs of well known results relating dominance criteria to preferences

risk vulnerability and the tempering effect of background risk we examine in this paper a new natural restriction on utility functions namely that adding an unfair background risk to wealth makes risk averse individuals behave in a more risk averse way with respect to any other independent risk this concept is called risk vulnerability it is equivalent to the condition that an undesirable risk can never be made desirable by the presence of an independent unfair risk moreover under risk vulnerability adding an unfair background risk reduces the demand for risky assets risk vulnerability generalizes the concept of properness individually undesirable independent risks are always jointly undesirable introduced by pratt and zeckhauser 1987 it implies that the two first derivatives of the utility function are concave transformations of the original utility function under decreasing absolute risk aversion a sufficient condition for risk vulnerability is local properness i e r r r where r is the arrow pratt coefficient of absolute risk aversion

valid inequalities and restrictions for stochastic programming problems with first order stochastic dominance constraints stochastic dominance relations are well studied in statistics decision theory and economics recently there has been significant interest in introducing dominance relations into stochastic optimization problems as constraints in the discrete case stochastic optimization models involving second order stochastic dominance constraints can be solved by linear programming however problems involving first order stochastic dominance constraints are potentially hard due to the non convexity of the associated feasible regions in this paper we consider a mixed 0 1 linear programming formulation of a discrete first order constrained optimization model and present a relaxation based on second order constraints we derive some valid inequalities and restrictions by employing the probabilistic structure of the problem we also generate cuts that are valid inequalities for the disjunctive relaxations arising from the underlying combinatorial structure of the problem by applying the lift and project procedure we describe three heuristic algorithms to construct feasible solutions based on conditional second order constraints variable fixing and conditional value at risk finally we present numerical results for several instances of a real world portfolio optimization problem

oscillatory critical amplitudes in hierarchical models we study the oscillatory critical amplitudes of theq states potts model on a diamond hierarchical lattice we consider an example of the generic case finite critical index as well as the degenerate case essential singularity in both cases we compare the magnitude of the oscillations with geometrical characteristics of the julia set of zeroes of the partition function

locally self similar phase diagram of the disordered potts model on the hierarchical lattice we study the critical behavior of the random q state potts model in the large q limit on the diamond hierarchical lattice with an effective dimensionality d eff 2 by varying the temperature and the strength of the frustration the system has a phase transition line between the paramagnetic and the ferromagnetic phases which is controlled by four different fixed points according to our renormalization group study the phase boundary in the vicinity of the multicritical point is self similar it is well represented by a logarithmic spiral we expect an infinite number of reentrances in the thermodynamic limit consequently one cannot define standard thermodynamic phases in this region

variational characterization of the critical curve for pinning of random polymers in this paper we look at the pinning of a directed polymer by a one dimensional linear interface carrying random charges there are two phases localized and delocalized depending on the inverse temperature and on the disorder bias using quenched and annealed large deviation principles for the empirical process of words drawn from a random letter sequence according to a random renewal process birkner greven and den hollander 6 we derive variational formulas for the quenched respectively annealed critical curve separating the two phases these variational formulas are used to obtain a necessary and sufficient criterion stated in terms of relative entropies for the two critical curves to be different at a given inverse temperature a property referred to as relevance of the disorder this criterion in turn is used to show that the regimes of relevant and irrelevant disorder are separated by a unique inverse critical temperature subsequently upper and lower bounds are derived for the inverse critical temperature from which sufficient conditions under which it is strictly positive respectively finite are obtained the former condition is believed to be necessary as well a problem that we will address in a forthcoming paper random pinning has been studied extensively in the literature the present paper opens up a window with a variational view our variational formulas for the quenched and the annealed critical curve are new and provide valuable insight into the nature of the phase transition our results on the inverse critical temperature drawn from these variational formulas are not new but they offer an alternative approach that is flexible enough to be extended to other models of random polymers with disorder

istmo an interval reference point based method for stochastic multiobjective programming problems in this paper we present an interactive algorithm istmo for stochastic multiobjective problems with continuous random variables this method combines the concept of probability efficiency for stochastic problems with the reference point philosophy for deterministic multiobjective problems the decision maker expresses her his references by dividing the variation range of each objective into intervals and by setting the desired probability for each objective to achieve values belonging to each interval these intervals may also be redefined during the process this interactive procedure helps the decision maker to understand the stochastic nature of the problem to discover the risk level s he is willing to assume for each objective and to learn about the trade offs among the objectives

one sided local large deviation and renewal theorems in the case of infinite mean if s n n 0 is an integer valued random walk such that s n a n converges in distribution to a stable law of index 0 1 as n then gnedenko s local limit theorem provides a useful estimate for p s n r for values of r such that r a n is bounded the main point of this paper is to show that under certain circumstances there is another estimate which is valid when r a n in other words to establish a large deviation local limit theorem we also give an asymptotic bound for p s n r which is valid under weaker assumptions this last result is then used in establishing some local versions of generalized renewal theorems

on the irrelevant disorder regime of pinning models recent results have lead to substantial progress in understanding the role of disorder in the de localization transition of polymer pinning models notably there is an understanding of the crucial issue of disorder relevance and irrelevance that albeit still partial is now rigorous in this work we exploit interpolation and replica coupling methods to get sharper results on the irrelevant disorder regime of pinning models in particular we compute in this regime the first order term in the expansion of the free energy close to criticality and this term coincides with the first order of the formal ex pansion obtained by field theory methods we also show that the quenched and the quenched averaged correlation length exponents coincide while in general they are ex pected to be different interpolation and replica coupling methods in this class of models naturally lead to studying the behavior of the intersection of certain renewal sequences and one of the main tools in this work is precisely renewal theory and the study of these intersection renewals 2000 mathematics subject classification 60k35 60k05 82b41 82b44

marginal relevance of disorder for pinning models the effect of disorder on pinning and wetting models has attracted much attention in theoretical physics in particular it has been predicted on the basis of the harris criterion that disorder is relevant annealed and quenched model have different critical points and critical exponents if the return probability exponent alpha a positive number that characterizes the model is larger than 1 2 weak disorder has been predicted to be irrelevant i e coinciding critical points and exponents if alpha 1 2 recent mathematical work has put these predictions on firm grounds in renormalization group terms the case alpha 1 2 is a marginal case and there is no agreement in the literature as to whether one should expect disorder relevance or irrelevance at marginality the question is particularly intriguing also because the case alpha 1 2 includes the classical models of two dimensional wetting of a rough substrate of pinning of directed polymers on a defect line in dimension 3 1 or 1 1 and of pinning of an heteropolymer by a point potential in three dimensional space here we prove disorder relevance both for the general alpha 1 2 pinning model and for the hierarchical version of the model proposed by b derrida v hakim and j vannimenus jsp 1992 in the sense that we prove a shift of the quenched critical point with respect to the annealed one in both cases we work with gaussian disorder and we show that the shift is at least of order exp 1 beta 4 for beta small if beta is the standard deviation of the disorder

analytic methods for obstruction to integrability in discrete dynamical systems a unique analytic continuation result is proven for solutions of a relatively general class of difference equations by using techniques of generalized borel summability this continuation allows for painleve property methods to be extended to difference equations it is shown that the painleve property pp induces under relatively general assumptions a dichotomy within first order difference equations all equations with pp can be solved in closed form on the contrary absence of pp implies under some further assumptions that the local conserved quantities are strictly local in the sense that they develop singularity barriers on the boundary of some compact set the technique produces analytic formulas to describe fractal sets originating in polynomial iterations 2004 wiley periodicals inc

a strongly polynomial algorithm for the transportation problem for the linear transportation problem withm supply nodes n demand nodes andk feasible arcs we describe an algorithm which runs in time proportional tom logm k n logn assuming w l o g m n the algorithm uses excess scaling the complexity bound is a slight improvement over the bound achieved by an application of a min cost flow algorithm of orlin to the transportation problem

the effect of disorder on polymer depinning transitions we consider a polymer with monomer locations modeled by the trajectory of a markov chain in the presence of a potential that interacts with the polymer when it visits a particular site 0 we assume that probability of an excursion of length n is given by n c varphi n for some 1 3 2 at high temperature the quenched and annealed curves differ significantly only in a very small neighborhood of the critical point the size of this neighborhood scales as beta 1 2c 3 where is the inverse temperature for c 0 for sufficiently high temperature the quenched and annealed curves are within a factor of 1 epsilon for all u near the critical point in particular the quenched and annealed critical points are equal for c 3 2 the regime depends on the slowly varying function varphi

the continuum disordered pinning model any renewal processes on mathbb n 0 with a polynomial tail with exponent alpha in 0 1 has a non trivial scaling limit known as the alpha stable regenerative set in this paper we consider gibbs transformations of such renewal processes in an i i d random environment called disordered pinning models we show that for alpha in left frac 1 2 1 right these models have a universal scaling limit which we call the continuum disordered pinning model cdpm this is a random closed subset of mathbb r in a white noise random environment with subtle features any fixed a s property of the alpha stable regenerative set e g its hausdorff dimension is also an a s property of the cdpm for almost every realization of the environment nonetheless the law of the cdpm is singular with respect to the law of the alpha stable regenerative set for almost every realization of the environment the existence of a disordered continuum model such as the cdpm is a manifestation of disorder relevance for pinning models with alpha in left frac 1 2 1 right

an algorithm for isotonic regression for two or more independent variables algorithms for solving the isotonic regression problem in more than one dimension are difficult to implement because of the large number of lower sets present or because they involve search techniques which require a significant amount of checking and readjustment here a new algorithm for solving this problem based on a simple iterative technique is proposed and shown to converge to the correct solution

a sampling based method for generating nondominated solutions in stochastic momp problems chapters 4 and 6 presented methods for incorporating risk in the project selection optimization problem this chapter presents a method for generating nondominated solutions for stochastic multiobjective mathematical programming problems that is applicable to both continuous and zero one variables the method is based on the assumption that the objective function coefficients are random variables with probability distributions that are known or can be approximated the method results in solutions that are nondominated in terms of the expected value of each objective and the probability that each objective meets or exceeds a specified target value a method for generating a set of such solutions is presented and illustrated with examples the method presented here is more general in that it allows for any probability distribution it makes no behavioral assumptions about the decision maker it can accommodate integer zero one or real valued variables and it can accommodate linear or nonlinear constraints and objective functions

estimates on path delocalization for copolymers at selective interfaces starting from the simple symmetric random walk s n n we introduce a new process whose path measure is weighted by a factor exp open image in new window with h 0 w n n a typical realization of an iid process and n a positive integer we are looking for results in the large n limit this factor favors s n 0 if w n h 0 and s n 0 if w n h 0 the process can be interpreted as a model for a random heterogeneous polymer in the proximity of an interface separating two selective solvents it has been shown 6 that this model undergoes a de localization transition more precisely there exists a continuous increasing function h c such that if h h c then the model is localized while it is delocalized if h h c however localization and delocalization were not given in terms of path properties but in a free energy sense later on it has been shown that free energy localization does indeed correspond to a strong form of path localization 3 on the other hand only weak results on the delocalized regime have been known so far

a numerical approach to copolymers at selective interfaces we consider a model of a random copolymer at a selective interface which undergoes a localization delocalization transition in spite of the several rigorous results available for this model the theoretical characterization of the phase transition has re mained elusive and there is still no agreement about several important issues for example the behavior of the polymer near the phase transition line from a rigorous viewpoint non coinciding upper and lower bounds on the critical line are known in this paper we combine numerical computations with rigorous arguments to get to a better understanding of the phase diagram our main results include various numerical observations that suggest that the critical line lies strictly in between the two bounds a rigorous statistical test based on concentration inequalities and super additivity for determining whether a given point of the phase diagram is in the localized phase this is applied in particular to show that with a very low level of error the lower bound does not coincide with the critical line an analysis of the precise asymptotic behavior of the partition function in the de localized phase with particular attention to the effect of rare atypical stretches in the disorder sequence and on whether or not in the delocalized regime the polymer path has a brownian scaling a new proof of the lower bound on the critical line this proof relies on a characteri zation of the localized regime which is more appealing for interpreting the numerical data

solution approaches for the multiobjective stochastic programming abstract we survey in this paper various solution approaches for multiobjective stochastic problems where random variables can be in both objectives and constraints parameters once a problem requires a stochastic formulation a first step consists in transforming the problem into its deterministic formulation we propose to classify and evaluate such transformations with regards to the many proposed concepts of efficiency the paper addresses also some applications of the multiobjective stochastic programming models

non coincidence of quenched and annealed connective constants on the supercritical planar percolation cluster in this paper we study the abundance of self avoiding paths of a given length on a supercritical percolation cluster on mathbb z d more precisely we count z n the number of self avoiding paths of length n on the infinite cluster starting from the origin which we condition to be in the cluster we are interested in estimating the upper growth rate of z n limsup n rightarrow infty z n 1 n which we call the connective constant of the dilute lattice after proving that this connective constant is a s non random we focus on the two dimensional case and show that for every percolation parameter p in 1 2 1 almost surely z n grows exponentially slower than its expected value in other words we prove that limsup n rightarrow infty z n 1 n lim n rightarrow infty mathbb e z n 1 n where the expectation is taken with respect to the percolation process this result can be considered as a first mathematical attempt to understand the influence of disorder for self avoiding walks on a quenched dilute lattice our method which combines change of measure and coarse graining arguments does not rely on the specifics of percolation on mathbb z 2 so our result can be extended to a large family of two dimensional models including general self avoiding walks in a random environment

first order dominance stronger characterization and a bivariate checking algorithm how to determine whether one distribution first order dominates another is a fundamental problem that has many applications in economics finance probability theory and statistics nevertheless little is known about how to efficiently check first order dominance for finite multivariate distributions utilizing that this problem can be formulated as a transportation problem with a special structure we provide a stronger characterization of multivariate first order dominance and develop a linear time complexity checking algorithm for the bivariate case we illustrate the use of the checking algorithm when numerically assessing first order dominance among continuous bivariate distributions

concavity and efficient points of discrete distributions in probabilistic programming we consider stochastic programming problems with probabilistic constraints involving integer valued random variables the concept of a p efficient point of a probability distribution is used to derive various equivalent problem formulations next we introduce the concept of r concave discrete probability distributions and analyse its relevance for problems under consideration these notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables the results are illustrated with numerical examples

stochastic orderings of convex concave type on an arbitrary grid several new classes of discrete stochastic orderings are introduced for comparing discrete random variables that are valued in an arbitrary ordered finite grid of nonnegative points these order relations correspond to particular cases of integral stochastic orderings which are generated by different classes of functions of convex concave type defined on the grid they are natural extensions from equidistant to arbitrary grids of various orderings familiar in the literature the main question addressed in the paper is how an extension of the grid of points can affect such stochastic orderings it will be shown that a crucial factor is the location of the additional point that is inserted in the grid

optimization with multivariate stochastic dominance constraints we consider stochastic optimization problems where risk aversion is expressed by a stochastic ordering constraint the constraint requires that a random vector depending on our decisions stochastically dominates a given benchmark random vector we identify a suitable multivariate stochastic order and describe its generator in terms of von neumann morgenstern utility functions we develop necessary and sufficient conditions of optimality and duality relations for optimization problems with this constraint assuming convexity we show that the lagrange multipliers corresponding to dominance constraints are elements of the generator of this order thus refining and generalizing earlier results for optimization under univariate stochastic dominance constraints furthermore we obtain necessary conditions of optimality for non convex problems under additional smoothness assumptions

analog computation through high dimensional physical chaotic neuro dynamics conventional von neumann computers have difficulty in solving complex and ill posed real world problems however living organisms often face such problems in real life and must quickly obtain suitable solutions through physical dynamical and collective computations involving vast assemblies of neurons these highly parallel computations through high dimensional dynamics computation through dynamics are completely different from the numerical computations on von neumann computers computation through algorithms in this paper we explore a novel computational mechanism with high dimensional physical chaotic neuro dynamics we physically constructed two hardware prototypes using analog chaotic neuron integrated circuits these systems combine analog computations with chaotic neuro dynamics and digital computation through algorithms we used quadratic assignment problems qaps as benchmarks the first prototype utilizes an analog chaotic neural network with 800 dimensional dynamics an external algorithm constructs a solution for a qap using the internal dynamics of the network in the second system 300 dimensional analog chaotic neuro dynamics drive a tabu search algorithm we demonstrate experimentally that both systems efficiently solve qaps through physical chaotic dynamics we also qualitatively analyze the underlying mechanism of the highly parallel and collective analog computations by observing global and local dynamics furthermore we introduce spatial and temporal mutual information to quantitatively evaluate the system dynamics the experimental results confirm the validity and efficiency of the proposed computational paradigm with the physical analog chaotic neuro dynamics

stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems abstract in this work we deal with obtaining efficient solutions for stochastic multiobjective programming problems in general these solutions are obtained in two stages in one of them the stochastic problem is transformed into its equivalent deterministic problem and in the other one some of the existing generating techniques in multiobjective programming are applied to obtain efficient solutions which involves transforming the multiobjective problem into a problem with only one objective function our aim is to determine whether the order in which these two transformations are carried out influences in any way the efficient solution obtained our results show that depending on the type of stochastic criterion followed and the statistical characteristics of the initial problem the order can have an influence on the final set of efficient solutions obtained for a given problem

fractal structure of zeros in hierarchical models we consider an ising and aq state potts model on a diamond hierarchical lattice we give pictures of the distribution of zeros of the partition function in the complex plane of temperatures for several choices ofq these zeros are just the julia set corresponding to the renormalization group transformation

local utility and multivariate risk aversion we revisit machina s local utility as a tool to analyze attitudes to multivariate risks we show that for nonexpected utility maximizers choosing between multivariate prospects aversion to multivariate mean preserving increases in risk is equivalent to the concavity of the local utility functions thereby generalizing machina s result machina m 1982 expected utility analysis without the independence axiom econometrica 50 277 323 to analyze comparative risk attitudes within the multivariate extension of rank dependent expected utility of galichon and henry galichon a henry m 2012 dual theory of choice with multivariate risks j econom theory 147 1501 1516 we extend quiggin s monotone mean and utility preserving increases in risk and show that the useful characterization given in landsberger and meilijson landsberger m meilijson i 1994 comonotone allocations bickel lehmann dispersion and the arrow pratt measure of risk aversion ann oper res 52 97 106 still holds in the multivariat

a replica coupling approach to disordered pinning models we consider a renewal process 0 1 on the integers where the law of i i 1 has a power like tail p i i 1 n n 1 l n with 0 and l slowly varying we then assign a random n dependent reward penalty to the occurrence of the event that the site n belongs to in such generality this class of problems includes among others 1 d dimensional models of pinning of directed polymers on a one dimensional random defect 1 1 dimensional models of wetting of disordered substrates and the poland scheraga model of dna denaturation by varying the average of the reward the system undergoes a transition from a localized phase where occupies a finite fraction of mathbb n to a delocalized phase where the density of vanishes in absence of disorder i e if the reward is independent of n the transition is of first order for 1 and of higher order for 1 2 11 in physical terms disorder is relevant in this situation in agreement with the heuristic harris criterion on the other hand for 0 1 2 it has been proven recently by k alexander 2 that if disorder is sufficiently weak critical exponents are not modified by randomness disorder is irrelevant in this work generalizing techniques which in the framework of spin glasses are known as replica coupling and interpolation we give a new simpler proof of the main results of 2 moreover we partially justify a small disorder expansion worked out in 9 for 1 2 showing that it provides a free energy upper bound which improves the annealed one

remarks on disorder and aperiodicity in a model for interacting polymers abstract we present a comparative study of the effects of random and aperiodically distributed interactions on the critical behavior of a model for two interacting polymers on a diamond hierarchical lattice the problem is formulated in terms of exact renormalization group rg recursion relations in the disordered case it is possible to develop a perturbative treatment in order to obtain the fixed points of the moments associated with the random distribution of interactions fully uncorrelated disorder may become relevant driving the system away from a homogeneous fixed point layered disorder may lead to a breakdown of the perturbative treatment in the case of aperiodic interactions we also show some examples of relevance and irrelevance of geometric fluctuations and further investigate the models by resorting to an independent transfer matrix tm analysis which fully corroborates the scaling results

on efficient sets in vector maximum problems a brief survey the notion of efficient nondominated noninferior pareto optimal functional efficient set to a vectormaximum problem vmp has been analysed and developed in several directions during the last 30 years starting with the basic notion of efficiency given by pareto 1896 formal descriptions of the efficient properly efficient locally proper efficient weak or strong efficient set have been developed beginning in the 50th of this century based on these notions various characteristics and properties of the efficient set have been studied whereas the feasible set x and the functions zk x k 1 k constituting the vector valued criterion z x of vmp have various properties e g convexity of x concavity of zk x for all k differentiability etc based on such properties the structure of the efficient set and the existence of efficient solutions have been analysed a part of the corresponding publications are rather of a pure theoretical character others try to develope theories serving as the basis for working out methods for determining the efficient set or for interactive methods determining some compromise solutions duality theories for more or less general cases have been developed and various aspects of stability of vmp have been investigated a brief survey is given

adsorption of a random heteropolymer at a potential well revisited location of transition point and design of sequences the adsorption of an ideal heteropolymer loop at a potential point well is investigated within the framework of standard random matrix theory on the basis of a semi analytical semi numerical approach a histogram of transition points for the ensemble of quenched heteropolymer structures with bimodal symmetric distribution of types of chain links is constructed it is shown that the sequences having transition points in the tail of the histogram display correlations between nearest neighbour monomers

log periodic critical amplitudes a perturbative approach log periodic amplitudes appear in the critical behavior of a large class of systems in particular when a discrete scale invariance is present here we show how to compute these critical amplitudes perturbatively when they originate from a renormalization map which is close to a monomial in this case the log periodic amplitudes of the subdominant corrections to the leading critical behavior can also be calculated

a novel chaotic search for quadratic assignment problems abstract we propose a novel method for solving the quadratic assignment problems first we realize the conventional tabu search on a neural network and modify it to a chaotic version our novel method includes both effects of chaotic dynamics and tabu search we compare the performance of the novel chaotic search with the conventional tabu search and an exponential tabu search whose memory effect for tabu forbidding previous moves decays exponentially we show that the exponential tabu search has higher performance than the conventional tabu search and further that the novel method with a chaotic neural network exhibits the best performance we also propose a controlling method of the chaotic neural network for realizing easy and robust applications of our method then better performance can be realized without manual parameter setting for various problems

a class of utility functions containing all the common utility functions this paper presents a class of utility functions class a that contains all of the utility functions commonly used for mathematical modeling the class consisting of those utility functions whose derivatives alternate in sign a simple representation via mixtures of exponential utilities is provided for this class which is both mathematically convenient and conducive to functional operations a connection with laplace transforms and the resultant implications for preference relations aggregation and utility assessment are discussed

distributional efficiency in multiobjective stochastic linear programming several concepts of distributional efficiency are proposed for the multiobjective stochastic linear programming mslp problem in contexts where the probability distribution of random parameters is known and the decision maker dm has an unknown multi attribute utility function belonging to a given glass u we present a general efficient set the u admissible solutions and two subsets the u unanimous and u advocated solutions the latter being particularly relevant to the case of a single dm we show how advocated solutions can be generated and or tested when u is the class of non decreasing additive concave functions

optimization with stochastic preferences based on a general class of scalarization functions it is of crucial importance to develop risk averse models for multicriteria decision making under uncertainty a major stream of the related literature studies optimization problems that feature multivariate stochastic benchmarking constraints these problems typically involve a univariate stochastic preference relation often based on stochastic dominance or a coherent risk measure such as conditional value at risk which is then extended to allow the comparison of random vectors by the use of a family of scalarization functions all scalarized versions of the vector of the uncertain outcomes of a decision are required to be preferable to the corresponding scalarizations of the benchmark outcomes while this line of research has been dedicated almost entirely to linear scalarizations the corresponding deterministic literature uses a wide variety of scalarization functions that among other advantages offer a high degree of modeling flexibility in this paper we aim to incorporate these scalarizations i

influence of spatial correlation for directed polymers in this paper we study a model of a brownian polymer in x d introduced by rovira and tindel j funct anal 222 2005 178 201 our investigation focuses mainly on the effect of strong spatial correlation in the environment in that model in terms of free energy fluctuation exponent and volume exponent in particular we prove that under some assumptions very strong disorder and superdiffusivity hold at all temperatures when d 3 and provide a novel approach to petermann s superdiffusivity result in dimension one superdiffusivity of directed polymers in random environment 2000 ph d thesis we also derive results for a brownian model of pinning in a nonrandom potential with power law decay at infinity

on the localization transition of random copolymers near selective interfaces in this note we consider the de localization transition for random directed 1 1 dimensional copolymers in the proximity of an interface separating selective solvents we derive a rigorous lower bound on the free energy this yields a substantial improvement on the bounds from below on the critical line that were known so far our result implies that the critical curve does not lie below the critical curve set forth by monthus eur phys j b 13 111 130 2000 on the base of a renormalization group analysis we discuss this result in the light of the rigorous and non rigorous approaches present in the literature and by making an analogy with a particular asymptotics of a disordered wetting model we propose a simplified framework in which the question of identifying the critical curve as well as understanding the nature of the transition may be approached

high temperature scaling limit for directed polymers on a hierarchical lattice with bond disorder diamond lattices are sequences of recursively defined graphs that provide a network of directed pathways between two fixed root nodes a and b the construction recipe for diamond graphs depends on a branching number b in mathbb n and a segmenting number s in mathbb n for which a larger value of the ratio s b intuitively corresponds to more opportunities for intersections between two randomly chosen paths by attaching i i d random variables to the bonds of the graphs we construct a random gibbs measure on the set of directed paths by assigning each path an energy through summing the random variables along the path for the case b s we propose a scaling regime in which the temperature grows along with the number of hierarchical layers of the graphs and the partition function the normalization factor of the gibbs measure appears to converge in law we prove that all of the positive integer moments of the partition function converge in this limiting regime the motivation of this work is to prove a functional limit theorem that is analogous to a previous result obtained in the b s case

positive dependence upper sets and multidimensional partitions let u be an upper set contained in the finite discrete lattice l 1 d1 1 dp representations for u are obtained and shown to correspond to certain multidimensional partitions of integers it is shown that for p 3 the number of possible upper sets in l is prod t 0 d3 1 left d1 d2 t atop d1 right big left d1 t atop d1 right various other representation and enumeration results are obtained for related settings considered are a variety of applications to multivariate positive dependence and various notions in statistics and reliability theory

dominance conditions for multivariate utility functions stochastic dominance conditions are given for n variate utility functions when k variate risk aversion is assumed for k 1 2 n these conditions are expressed through a comparison of distribution functions as in the well known univariate case and through a comparison of random variables defined on the same probability space

critical points of quadratic renormalizations of random variables and phase transitions of disordered polymer models on diamond lattices we study the wetting transition and the directed polymer delocalization transition on diamond hierarchical lattices these two phase transitions with frozen disorder correspond to the critical points of quadratic renormalizations of the partition function these exact renormalizations on diamond lattices can also be considered as approximate migdal kadanoff renormalizations for hypercubic lattices in terms of the rescaled partition function z z z typ we find that the critical point corresponds to a fixed point distribution with a power law tail p c z phi ln z z 1 mu as z infinity up to some subleading logarithmic correction phi ln z so that all moments z n with n mu diverge for the wetting transition the first moment diverges z infinity case 0 mu 1 and the critical temperature is strictly below the annealed temperature t c t ann for the directed polymer case the second moment diverges z 2 infinity case 1 mu 2 and the critical temperature is strictly below the exactly known transition temperature t2 of the second moment we then consider the correlation length exponent nu the linearized renormalization around the fixed point distribution coincides with the transfer matrix describing a directed polymer on the cayley tree but the random weights determined by the fixed point distribution p c z are broadly distributed this induces some changes in the traveling wave solutions with respect to the usual case of more narrow distributions

a survey for the quadratic assignment problem the quadratic assignment problem qap one of the most difficult problems in the np hard class models many real life problems in several areas such as facilities location parallel and distributed computing and combinatorial data analysis combinatorial optimization problems such as the traveling salesman problem maximal clique and graph partitioning can be formulated as a qap in this paper we present some of the most important qap formulations and classify them according to their mathematical sources we also present a discussion on the theoretical resources used to define lower bounds for exact and heuristic algorithms we then give a detailed discussion of the progress made in both exact and heuristic solution methods including those formulated according to metaheuristic strategies finally we analyze the contributions brought about by the study of different approaches

elicitation of multiattribute value functions through high dimensional model representations monotonicity and interactions abstract this work addresses the early phases of the elicitation of multiattribute value functions proposing a practical method for assessing interactions and monotonicity we exploit the link between multiattribute value functions and the theory of high dimensional model representations the resulting elicitation method does not state any a priori assumption on an individual s preference structure we test the approach via an experiment in a riskless context in which subjects are asked to evaluate mobile phone packages that differ on three attributes

copolymers at selective interfaces new bounds on the phase diagram we investigate the phase diagram of disordered copolymers at the interface between two selective solvents and in particular its weak coupling behavior encoded in the slope mc of the critical line at the origin we focus on the directed walk case which has turned out to be in spite of the apparent simplicity extremely challenging in mathematical terms the partition function of such a model does not depend on all the details of the markov chain that models the polymer but only on the time elapsed between successive returns to zero and on whether the walk is in the upper or lower half plane between such returns this observation leads to a natural generalization of the model in terms of arbitrary laws of return times the most interesting case being the one of return times with power law tails with exponent 1 1 2 in the case of the symmetric random walk the main results we present here are

scenarios and policy aggregation in optimization under uncertainty a common approach in coping with multiperiod optimization problems under uncertainty where statistical information is not really enough to support a stochastic programming model has been to set up and analyze a number of scenarios the aim then is to identify trends and essential features on which a robust decision policy can be based this paper develops for the first time a rigorous algorithmic procedure for determining such a policy in response to any weighting of the scenarios the scenarios are bundled at various levels to reflect the availability of information and iterative adjustments are made to the decision policy to adapt to this structure and remove the dependence on hindsight

combinatorial benders cuts for mixed integer linear programming mixed integer programs mips involving logical implications modeled through big m coefficients are notoriously among the hardest to solve in this paper we propose and analyze computationally an automatic problem reformulation of quite general applicability aimed at removing the model dependency on the big m coefficients our solution scheme defines a master integer linear problem ilp with no continuous variables which contains combinatorial information on the feasible integer variable combinations that can be distilled from the original mip model the master solutions are sent to a slave linear program lp which validates them and possibly returns combinatorial inequalities to be added to the current master ilp the inequalities are associated to minimal or irreducible infeasible subsystems of a certain linear system and can be separated efficiently in case the master solution is integer the overall solution mechanism closely resembles the benders one but the cuts we produce are purely co

decision making with incomplete information abstract decision situations with incomplete information are characterized by a decision maker without a precisely defined stable preference structure by probability distributions not known completely or by an inexact evaluation of consequences within the paper a general framework for decision making with incomplete information is presented which shows how to solve problems from descriptive as well as prescriptive decision theory based on this framework an overview of existing methods which are particularly suitable for handling incomplete information is given

hierarchical lattices some examples with a comparison of intrinsic dimension and connectivity and ising model exponents the recently recognised class of hierarchical lattices is examined through a number of examples definitions of length intrinsic dimension and connectivity are made and used to discuss variations of exponents calculated on the ising model generalisations of regular lattice results are found for exponents at discontinuity fixed points and in 1 epsilon dimensions

an exactly solvable continuous time derrida retaux model to study the depinning transition in the limit of strong disorder derrida and retaux j stat phys 156 2 26 290 2014 introduced a discrete time max type recursive model it is believed that for a large class of recursive models including derrida and retaux model there is a highly non trivial phase transition in this article we present a continuous time version of derrida and retaux model built on a yule tree which yields an exactly solvable model belonging to this universality class the integrability of this model allows us to study in details the phase transition near criticality and can be used to confirm the infinite order phase transition predicted by physicists we also study the scaling limit of this model at criticality which we believe to be universal

diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice we construct critical percolation clusters on the diamond hierarchical lattice and show that the scaling limit is a graph directed random recursive fractal a dirichlet form can be constructed on the limit set and we consider the properties of the associated laplace operator and diffusion process in particular we contrast and compare the behaviour of the high frequency asymptotics of the spectrum and the short time behaviour of the on diagonal heat kernel for the percolation clusters and for the underlying lattice in this setting a number of features of the lattice are inherited by the critical cluster

strange an interactive method for multi objective linear programming under uncertainty abstract in the field of investment planning within a time horizon problems typically involve multiple objectives and basic data are uncertain in a large number of cases these decision problems can be written as linear programming problems in which time dependent uncertainties affect the coefficients and the right hand side of constraints given the possibility of defining plausible scenarios on basic data discrete sets of such coefficients are given each with its subjective probability of occurrence the corresponding structure is then characteristic for multi objective stochastic linear programming moslp in the paper an interactive procedure is described to obtain a best compromise for such a moslp problem this algorithm called strange extends the stem method to take the random aspects into account it involves in particular the concepts of stochastic programming with recourse in its interactive steps the efficiency projection techniques are used to provide the decision maker with detailed graphical information on efficient solution families as an illustration of the successive steps a didactic example is solved in some detail and the results of a case study in energy planning are given

directed polymers with random interaction an exactly solvable case we propose a model for two d 1 dimensional directed polymers subjected to a mutual function interaction with a random coupling constant and present an exact renormalization group study for this system the exact function evaluated through an e 1 d expansion for second and third moments of the partition function exhibits the marginal relevance of the disorder at d 1 and the presence of a phase transition from a weak to strong disorder regime for d 1 the length scale exponent for the critical point is 2 e 1 we give details of the renormalization we show that higher moments do not require any new interaction and hence the function remains the same for all moments the method is extended to multicritical systems involving an m chain interaction the corresponding disorder induced phase transition for d d m 1 m 1 has the critical exponent v m 2d m 1 2 1 for both the cases an essential singularity appears for the length scale right at the upper critical dimension d m we also discuss the strainge behavior of an annealed system with more than two chains with pairwise random interactions among each other

multiattribute utility satisfying a preference for combining good with bad an important challenge in multiattribute decision analysis is the choice of an appropriate functional form for the utility function we show that if a decision maker prefers more of any attribute to less and prefers to combine good lotteries with bad as opposed to combining good with good and bad with bad her utility function should be a weighted average a mixture of multiattribute exponential utilities mixex utility in the single attribute case mixex utility satisfies properties typically thought to be desirable and encompasses most utility functions commonly used in decision analysis in the multiattribute case mixex utility implies aversion to any multivariate risk risk aversion with respect to any attribute decreases as that attribute increases under certain restrictions such risk aversion also decreases as any other attribute increases and a multivariate one switch property is satisfied one of the strengths of mixex utility is its ability to represent cases where utility independence does not hold but mixex utility can be consistent with mutual utility independence and take on a multilinear form an example illustrates the fitting of mixex utility to preference assessments

a real space renormalisation group approach to electrical and noise properties of percolation clusters the migdal kadanoff renormalisation scheme which becomes exact on hierarchical lattices is used to investigate electrical properties of 2d and 3d percolation clusters the author studies in detail the frequency dependence of the conductivity and the loss angle and the amplification of resistance flicker noise this type of noise exhibits critical amplification with its own exponents x and y which are related to the exponent b recently defined by rammal et al 1985

critical behavior of spin and polymer models with aperiodic interactions we review and extend some recent investigations of the effects of aperiodic interactions on the critical behavior of ferromagnetic q state potts models by considering suitable diamond or necklace hierarchical lattices and assuming a distribution of interactions according to a class of two letter substitution rules the problem can be formulated in terms of recursion relations in parameter space the analysis of stability of the fixed points leads to an exact criterion to gauge the relevance of geometric fluctuations for irrelevant fluctuations the critical behavior remains unchanged with respect to the uniform systems for relevant fluctuations there appears a two cycle of saddle point character in parameter space a scaling analysis supported by direct numerical thermodynamic calculations shows the existence of novel critical universality classes associated with relevant geometric fluctuations also we show that similar qualitative results are displayed by a simple model of two directed polymers on a diamond hierarchical structure with aperiodic bond interactions

portfolio selection problems with random fuzzy variable returns this paper considers several portfolio selection problems including probabilistic future returns with ambiguous expected returns assumed as random fuzzy variables random fuzzy portfolio selection problems are formulated as nonlinear programming problems based on both stochastic and fuzzy programming approaches since there is no efficient solution method to solve these problems directly main problems are transformed into equivalent deterministic quadratic programming problems using probabilistic chance constraints possibility measure and fuzzy goals and their efficient solution methods to find a global optimal solution of each problem is constructed furthermore numerical examples of portfolio selection problems are provided to illustrate our proposed models and solution methods compared with several previous basic models and to show that our proposed model is a versatile model to be applicable to various unexpected conditions

a compromise solution for the multiobjective stochastic linear programming under partial uncertainty abstract this paper solves the multiobjective stochastic linear program with partially known probability we address the case where the probability distribution is defined by crisp inequalities we propose a chance constrained approach and a compromise programming approach to transform the multiobjective stochastic linear program with linear partial information on probability distribution into its equivalent uniobjective problem the resulting program is then solved using the modified l shaped method we illustrate our results by an example

an interactive fuzzy satisficing method for multiobjective stochastic linear programming problems through an expectation model abstract for decision making problems involving uncertainty both stochastic programming as an optimization method based on the theory of probability and fuzzy programming representing the ambiguity by fuzzy concept have been developing in various ways in this paper we focus on multiobjective linear programming problems with random variable coefficients in objective functions and or constraints for such problems as a fusion of these two approaches after incorporating fuzzy goals of the decision maker for the objective functions we propose an interactive fuzzy satisficing method for the expectation model to derive a satisficing solution for the decision maker an illustrative numerical example is provided to demonstrate the feasibility of the proposed method

functional anova ultramodularity and monotonicity applications in multiattribute utility theory abstract utility function properties as monotonicity and concavity play a fundamental role in reflecting a decision maker s preference structure these properties are usually characterized via partial derivatives however elicitation methods do not necessarily lead to twice differentiable utility functions furthermore while in a single attribute context concavity fully reflects risk aversion in multiattribute problems such correspondence is not one to one we show that tsetlin and winkler s multivariate risk attitudes imply ultramodularity of the utility function we demonstrate that geometric properties of a multivariate utility function can be successfully studied by utilizing an integral function expansion functional anova the necessary and sufficient conditions under which monotonicity and or ultramodularity of single attribute functions imply the monotonicity and or ultramodularity of the corresponding multiattribute function under additive preferential and mutual utility independence are then established without reliance on the utility function differentiability we also investigate the relationship between the presence of interactions among the attributes of a multiattribute utility function and the decision maker s multivariate risk attitudes

oscillatory critical amplitudes in hierarchical models and the harris function of branching processes oscillatory critical amplitudes have been repeatedly observed in hierarchical models and in the cases that have been taken into consideration these oscillations are so small to be hardly detectable hierarchical models are tightly related to iteration of maps and in fact very similar phenomena have been repeatedly reported in many fields of mathematics like combinatorial evaluations and discrete branching processes it is precisely in the context of branching processes with bounded off spring that t harris in 1948 first set forth the possibility that the logarithm of the moment generating function of the rescaled population size in the super critical regime does not grow near infinity as a power but it has an oscillatory prefactor the harris function these oscillations have been observed numerically only much later and while the origin is clearly tied to the discrete character of the iteration the amplitude size is not so well understood the purpose of this note is to reconsider the issue for hierarchical models and in what is arguably the most elementary setting the pinning model that actually just boils down to iteration of polynomial maps and notably quadratic maps in this note we show that the oscillatory critical amplitude for pinning models and the harris function coincide moreover we make explicit the link between these oscillatory functions and the geometry of the julia set of the map making thus rigorous and quantitative some ideas set forth in derrida et al commun math phys 94 115 132 1984

hierarchical pinning model with site disorder disorder is marginally relevant we study a hierarchical disordered pinning model with site disorder for which like in the bond disordered case derrida et al in j stat phys 66 1189 1213 1992 and giacomin et al in probab theor rel fields 2009 arxiv 0711 4649 math pr there exists a value of a parameter b which enters in the definition of the hierarchical lattice that separates an irrelevant disorder regime and a relevant disorder regime we show that for such a value of b the critical point of the disordered system is different from the critical point of the annealed version of the model the proof goes beyond the technique used in giacomin et al probab theor rel fields 2009 arxiv 0711 4649 math pr and it takes explicitly advantage of the inhomogeneous character of the green function of the model

renormalisation group study of a disordered model we study the potts model on a diamond hierarchical lattice with random interactions using weak disorder expansions we calculate analytically the position and the exponents of the random fixed point which appears when the specific heat exponent ap of the pure system becomes positive at ap 0 we find how the logarithmic singularity is modified by the disorder lastly we suggest that this model should present griffiths like singularities

quadratic assignment problems abstract this paper surveys quadratic assignment problems qap at first several applications of this problem class are described and mathematical formulations of qaps are given then some exact solution methods and good heuristics are outlined their computational behaviour is illustrated by numerical results further recent results on the asymptotic probabilistic behaviour of qaps are outlined

threshold boolean form for joint probabilistic constraints with random technology matrix we develop a new modeling and solution method for stochastic programming problems that include a joint probabilistic constraint in which the multirow random technology matrix is discretely distributed we binarize the probability distribution of the random variables in such a way that we can extract a threshold partially defined boolean function pdbf representing the probabilistic constraint we then construct a tight threshold boolean minorant for the pdbf any separating structure of the tight threshold boolean minorant defines sufficient conditions for the satisfaction of the probabilistic constraint and takes the form of a system of linear constraints we use the separating structure to derive three new deterministic formulations for the studied stochastic problem and we derive a set of strengthening valid inequalities a crucial feature of the new integer formulations is that the number of integer variables does not depend on the number of scenarios used to represent uncertainty the computational study based on instances of the stochastic capital rationing problem shows that the mixed integer linear programming formulations are orders of magnitude faster to solve than the mixed integer nonlinear programming formulation the method integrating the valid inequalities in a branch and bound algorithm has the best performance