pairings of automorphic distributions we present a pairing of automorphic distributions that applies in situations where a lie group acts with an open orbit on a product of generalized flag varieties the pairing gives meaning to an integral of products of automorphic distributions on these varieties this generalizes classical integral representations or rankin selberg integrals of l functions and gives new constructions and analytic continuations of automorphic l functions

genetic algorithm approach on multi criteria minimum spanning tree problem minimum spanning tree mst problem is of high importance in network optimization the multi criteria mst mc mst is a more realistic representation of the practical problem in the real world but it is difficult for the traditional network optimization technique to deal with in this paper a genetic algorithm ga approach is developed to deal with this problem without neglecting its network topology the proposed method adopts the prufer number as the tree encoding and applies the multiple criteria decision making mcdm technique and nondominated sorting technique to make the ga search give out all pareto optimal solutions either focused on the region near the ideal point or distributed all along the pareto frontier compared with the enumeration method of pareto optimal solution the numerical analysis shows the efficiency and effectiveness of the ga approach on the mc mst problem

monotonicity and the principle of optimality abstract this paper explores some of the theoretical and algorithmic implications of the fact that the monotonicity assumption does not ensure either the validity of the principle of optimality or the discovery of all optimal solutions in finite dynamic programs even though it is sufficient to ensure the validity of the functional equations a slightly stronger assumption is introduced to resolve these problems our analysis is illustrated with some extremely simple examples

the problem of the optimal biobjective spanning tree this paper studies the problem of finding the set of optimal spanning trees of a connected graph considering two cost functions defined on the set of edges this problem is np hard and the solution is described through an algorithm that builds the family of efficient trees this algorithm needs two procedures that solve the following uniobjective problems the construction of all the spanning trees of a connected graph and the construction of the whole set of minimum cost spanning trees the computational results obtained are shown in section 5

partial order bounding a new approach to evaluation in game tree search abstract in computer game playing the established method for constructing an evaluation function uses a scalar value computed as a weighted sum of features this paper advocates the use of partial order evaluation and describes an efficient new search method called partial order bounding pob previous tree search algorithms using a partial order evaluation have attempted to propagate partially ordered values through the search tree which leads to many problems in practice such as the complexity of backing up sets of incomparable evaluations pob compares partially ordered values only in the leaves of a game tree and backs up boolean values through the tree a closely related new algorithm linear extension partial order bounding le pob uses a standard scalar alpha beta search with values from a suitably chosen linear extension of the partial order evaluation as an application the effectiveness of partial order evaluation is shown in the case of modeling capturing races called semeai in the game of go

stability of basic steady states of networks in bounded domains in this article we study the problem of a network of curves in a planar domain with the normal velocity proportional to each curvature and fixed angle conditions at the points at which the curves intersect we introduce the evolution problem of networks identify two cases of basic steady states in bounded and smooth domains and study their stability in terms of the geometry of the boundary

a double bubble in a ternary system with inhibitory long range interaction the free energy of a ternary system with a self organization property includes an interface energy and a longer ranging inhibitory interaction energy in a planar domain if the two energies are properly balanced and two of the three constituents make up an equal but small fraction the free energy admits a local minimizer that is shaped like a perturbed double bubble most difficulties in the proof of this result are related to the triple junction phenomenon that the three constituents of the ternary system meet at a point two techniques are developed to deal with the triple junction first one defines restricted classes of perturbed double bubbles each perturbed double bubble in a restricted class is obtained from a standard double bubble by a special perturbation the two triple junction points of the standard double bubble can only move along the line connecting them in opposite directions and by the same distance the second technique is the use of the so called internal variables these variables derive from the more geometric quantities that describe perturbed double bubbles in restricted classes the advantage of the internal variables is that they are only subject to linear constraints and perturbed double bubbles in a restricted class represented by internal variables are elements of a hilbert space a local minimizer of the free energy in each restricted class is found as a fixed point of a nonlinear equation by a contraction mapping argument the second variation at the fixed point within its restricted class is positive this perturbed double bubble satisfies three of the four equations for critical points of the free energy the unsolved equation is the 120 degree angle condition at triple junction points then perform another minimization among the local minimizers from all restricted classes a minimum of minimizers emerges and solves all the equations for critical points

combinatorial algorithms for the minimum interval cost flow problem the aim of minimum the interval cost flow problem micfp is to find the least cost of the shipment of a commodity through a capacitated network in order to satisfy demands at certain nodes from available supplies at other nodes where there exists some vague in vector cost of problem interval cost is a common event in uncertainty environments where statistical data are applied moreover they almost play an essential role in fuzzy programming specially in the case of using their cuts in this paper a complete order on intervals is defined and efficient combinatorial algorithms for micfp are proposed digital simulation results show the performance of the proposed algorithms compared with real scenarios

a multicriteria pareto optimal path algorithm abstract in this paper we present an algorithm for finding in a multicriteria network pareto optimal paths one each for each efficient objective vector validation of the algorithm and two illustrative examples are included computational experience is also reported this algorithm is a generalization of an earlier one for the bicriterion case

searching game trees under a partial order abstract the problem of partial order game tree search arises from game playing situations where multiple conflicting and non commensurate criteria dictate the merit of a position of the game in partial order game trees the outcomes evaluated at the tip nodes are vectors where each dimension of the vector represents a distinct criterion of merit this leads to an interesting variant of the game tree searching problem where corresponding to every game playing strategy of a player several outcomes are possible depending on the individual priorities of the opponent in this paper we identify the necessary and sufficient conditions for a set of outcomes to be inferior to another set of outcomes for every strategy using an algebra called dominance algebra on sets of outcomes we describe a bottom up approach to find the non inferior sets of outcomes at the root node we also identify shallow and deep pruning conditions for partial order game trees and present a partial order search algorithm on lines similar to the pruning algorithm for conventional game trees

ranking function based solutions of fully fuzzified minimal cost flow problem the aim of minimal cost flow problem mcfp is to find the least transportation cost of a single commodity through a capacitated network this paper presents a model to deal with one particular group of such problems in which the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers for easier reference hereafter we refer to this group of problems as fully fuzzified mcfp to represent our model hukuhara s difference and approximated multiplication are used thereafter we sort fuzzy numbers by an order using a ranking function and show that it is a total order i e a reflexive anti symmetric transitive and complete binary relation utilizing the proposed ranking function we transform the fully fuzzified mcfp into three crisp problems solvable in polynomial time from this standpoint combinatorial algorithms are provided to solve the above mentioned problem and find the fuzzy optimal flow furthermore the proposed order is related to the importance weights of the center the left spread and the right spread of each fuzzy number thus this method is capable of handling the decision maker s risk taking by comparing some previous ranking function based works with our method the efficiency of the latter is revealed finally an application of our proposed method to petroleum industry is presented

shortest paths with ordinal weights abstract we investigate the single source single destination shortest path problem in directed acyclic graphs with ordinal weighted arc costs we define the concepts of ordinal dominance and efficiency for paths and their associated ordinal levels respectively further we show that the number of ordinally non dominated path vectors from the source node to every other node in the graph is polynomially bounded and we propose a polynomial time labeling algorithm for solving the problem of finding the set of ordinally non dominated path vectors from source to sink

a preference based approach to spanning trees and shortest paths problems comparison of solutions in combinatorial problems is often based on an additive cost function inducing a complete order on solutions we investigate here a generalization of the problem where preferences take the form of a quasi transitive binary relation defined on the solutions space we first propose preference based search algorithms for two classical combinatorial problems namely the preferred spanning trees problem a generalization of the minimum spanning tree problem and the preferred paths problem a generalization of the shortest path problem then we introduce a very useful axiom for preference relations called independence using this axiom we establish admissibility results concerning our preference based search algorithms finally we address the problem of dealing with non independent preference relations and provide different possible solutions for different particular problems e g lower approximation of the set of preferred solutions for multicriteria spanning trees problems or relaxation of the independence axiom for interval valued preferred path problems

shortest path problems with partial information models and algorithms for detecting dominance abstract in this work we focus on partial information models for the well known shortest path problem where we consider multiple instances of values for the parameters that determine the cost of each arc this allows coping with the uncertainty about the future the imprecision of data the arbitrariness of some options the evolving values of the decision makers dms and or the multiplicity of dms in group decision making this paper proves some results and presents detailed algorithms to identify the set of non dominated paths a concept from decision theory under partial information we first address problems with a finite set of instances then problems with a general eventually not discrete set of instances and finally we study a particular case of the latter which complies with a condition that may hold in some situations to deal with these partial information problems we propose a new use for existing multicriteria algorithms based on the ranking of shortest paths

on the rapid decay of cuspidal automorphic forms abstract many important analytic statements about automorphic forms such as the analytic continuation of certain l functions rely on the well known rapid decay of k finite cusp forms on siegel sets we extend this here to prove a more general decay statement along sets much larger than siegel sets and furthermore state and prove the decay for smooth but not necessarily k finite cusp forms we also state a general theorem about the convergence of rankin selberg integrals involving unipotent periods closing a gap in the literature on l functions these properties serve as the analytic basis miller and schmid 2009 15 of a new method to establish holomorphic continuations of langlands l functions in particular the exterior square l functions miller and schmid 2009 16 on g l n

on a multicriteria shortest path problem abstract multicriteria shortest path problems have not been treated intensively in the specialized literature despite their potential applications in fact a single objective function may not be sufficient to characterize a practical problem completely for instance in a road network several parameters as time cost distance etc can be assigned to each arc clearly the shortest path may be too expensive to be used nevertheless the decision maker must be able to choose some solution possibly not the best for all the criteria in this paper we present two algorithms for this problem one of them is an immediate generalization of the multiple labelling scheme algorithm of hansen for the bicriteria case based on this algorithm it is proved that any pair of nondominated paths can be connected by nondominated paths this result is the support of an algorithm that can be viewed as a variant of the simplex method used in continuous linear multiobjective programming a small example is presented for both algorithms

a parametric approach to solving bicriterion shortest path problems abstract in this paper a new algorithm is developed to solve bicriterion shortest path problems bsp this algorithm first relaxes the integrality conditions and solves a simple bicriterion network problem the bicriterion network problem is solved parametrically exploiting properties associated with adjacent basis trees those pareto optimal paths not obtained by solving the lp relaxation are obtained using a label correcting procedure computational results comparing the parametric approach to the label setting approach and the k th shortest path approach are also presented they indicate that the parametric approach is orders of magnitude faster than the k th shortest path approach for most problems tested for problems with a positive correlation between the two cost coefficients the parametric approach is seen to be significantly faster than the label setting approach

smooth cuspidal automorphic forms and integrable discrete series in this paper we construct smooth cuspidal automorphic forms related to integrable discrete series of a connected semisimple lie group with finite center for classical and adelic situation as an application of the theory of schwartz spaces for automorphic forms developed by casselman in the classical situation smooth cuspidal automorphic forms are constructed via an explicit continuous map from the frechet space of smooth vectors of a banach realization inside l 1 g of an integrable discrete series into the space of smooth vectors of a strong topological dual of an appropriate schwartz space

multiobjective a search with consistent heuristics the article describes and analyzes namoa an algorithm for multiobjective heuristic graph search problems the algorithm is presented as an extension of a an admissible scalar shortest path algorithm under consistent heuristics a is known to improve its efficiency with more informed heuristics and to be optimal over the class of admissible algorithms in terms of the set of expanded nodes and the number of node expansions equivalent beneficial properties are shown to prevail in the new algorithm

the solution and duality of imprecise network problems duality properties have been investigated by many researchers in the recent literature they are introduced in this paper for a fully fuzzified version of the minimal cost flow problem which is a basic model in network flow theory this model illustrates the least cost of the shipment of a commodity through a capacitated network in terms of the imprecisely known available supplies at certain nodes which should be transmitted to fulfil uncertain demands at other nodes first we review on the most valuable results on fuzzy duality concepts to facilitate the discussion of this paper by applying hukuhara s difference approximated and exact multiplication and wu s scalar production we exhibit the flow in network models then we use combinatorial algorithms on a reduced problem which is derived from fully fuzzified mcfp to acquire fuzzy optimal flows to give duality theorems we utilize a total order on fuzzy numbers due to the level of risk and realize optimality conditions for providing some efficient combinatorial algorithms finally we compare our results with the previous worthwhile works to demonstrate the efficiency and power of our scheme and the reasonability of our solutions in actual decision making problems

a numerical method for tracking curve networks moving with curvature motion abstract a finite difference method is proposed to track curves whose normal velocity is given by their curvature and which meet at different types of junctions the prototypical example is that of phase interfaces that meet at prescribed angles although eutectic junctions and interactions through nonlocal effects are also considered the method is based on a direct discretization of the underlying parabolic problem and boundary conditions a linear stability analysis is presented for our scheme as well as computational studies that confirm the second order convergence to smooth solutions after a singularity in the curve network where the solution is no longer smooth we demonstrate almost second order convergence a numerical study of singularity types is done for the case of networks that meet at prescribed angles at triple junctions finally different discretizations and methods for implicit time stepping are presented and compared

on three phase boundary motion and the singular limit of a vector valued ginzburg landau equation we present a formal asymptotic analysis which suggests a model for three phase boundary motion as a singular limit of a vector valued ginzburg landau equation we prove short time existence and uniqueness of solutions for this model that is for a system of three phase boundaries undergoing curvature motion with assigned angle conditions at the meeting point such models pertain to grain boundary motion in alloys the method we use based on linearization about the initial conditions applies to a wide class of parabolic systems we illustrate this further by its application to an eutectic solidification problem

optimality conditions in preference based spanning tree problems abstract spanning tree problems defined in a preference based environment are addressed in this approach optimality conditions for the minimum weight spanning tree problem mst are generalized for use with other more general preference orders the main goal of this paper is to determine which properties of the preference relations are sufficient to assure that the set of most preferred trees is the set of spanning trees verifying the optimality conditions finally algorithms for the construction of the set of spanning trees fulfilling the optimality conditions are designed improving the methods in previous papers