a determinant formula for a holonomic q difference system associated with jackson integrals of type bcn abstract a jackson integral of type bc n is a multisum generalization of the very well poised balanced 2 r 2 r basic hypergeometric series we state an explicit product formula for the determinant of a matrix with entries given by the bc n type jackson integrals in order to show this we treat the determinant as a solution of a holonomic q difference equation in particular we give the q difference equation explicitly as a two term recurrence relation which the determinant satisfies by introducing a set of new symmetric polynomials via the symplectic schur functions

rational function certification of multisum integral q identities the method of rational function certification for proving terminating hypergeometric identities is extended from single sums or integrals to multi integral sums and q integral sums

first order conditions for semidefinite representations of convex sets defined by rational or singular polynomials a set is called semidefinite representable or semidefinite programming sdp representable if it equals the projection of a higher dimensional set which is defined by some linear matrix inequality lmi this paper discusses the semidefinite representability conditions for convex sets of the form s mathcal d f x in mathcal d f x geq 0 here mathcal d x in mathbb r n g 1 x geq 0 ldots g m x geq 0 is a convex domain defined by some nice concave polynomials g i x they satisfy certain concavity certificates and f x is a polynomial or rational function when f x is concave over mathcal d we prove that s mathcal d f has some explicit semidefinite representations under certain conditions called preordering concavity or q module concavity which are based on the positivstellensatz certificates for the first order concavity criteria f u nabla f u t x u f x geq 0 quad forall x u in mathcal d when f x is a polynomial or rational function having singularities on the boundary of s mathcal d f a perspective transformation is introduced to find some explicit semidefinite representations for s mathcal d f under certain conditions in the special case n 2 if the laurent expansion of f x around one singular point has only two consecutive homogeneous parts we show that s mathcal d f always admits an explicitly constructible semidefinite representation

elliptic hypergeometric series on root systems abstract we derive a number of summation and transformation formulas for elliptic hypergeometric series on the root systems a n c n and d n in the special cases of classical and q series our approach leads to new elementary proofs of the corresponding identities

distributed delta 1 coloring in linear in delta time the distributed delta 1 coloring problem is one of the most fundamental and well studied problems in distributed algorithms starting with the work of cole and vishkin in 1986 a long line of gradually improving algorithms has been published the state of the art running time prior to our work is o delta log delta log n due to kuhn and wattenhofer proceedings of the 25 th annual acm symposium on principles of distributed computing denver co 2006 pp 7 15 linial proceedings of the 28 th annual ieee symposium on foundation of computer science los angeles ca 1987 pp 331 335 proved a lower bound of frac 1 2 log n for the problem and szegedy and vishwanathan proceedings of the 25th annual acm symposium on theory of computing san diego ca 1993 pp 201 207 provided a heuristic argument that shows that algorithms from a wide family of locally iterative algorithms are unlikely to achieve a running time smaller than theta delta log delta we present a de

deterministic distributed vertex coloring in polylogarithmic time consider an n vertex graph g v e of maximum degree and suppose that each vertex v v hosts a processor the processors are allowed to communicate only with their neighbors in g the communication is synchronous that is it proceeds in discrete rounds in the distributed vertex coloring problem the objective is to color g with 1 or slightly more than 1 colors using as few rounds of communication as possible the number of rounds of communication will be henceforth referred to as running time efficient randomized algorithms for this problem are known for more than twenty years alon et al 1986 luby 1986 specifically these algorithms produce a 1 coloring within o log n time with high probability on the other hand the best known deterministic algorithm that requires polylogarithmic time employs o 2 colors this algorithm was devised in a seminal focs 87 paper by linial 1987 its running time is o log n in the same article linial asked whether one can color with significantly less than 2 colors in deterministic polylogarithmic time by now this question of linial became one of the most central long standing open questions in this area in this article we answer this question in the affirmative and devise a deterministic algorithm that employs 1 o 1 colors and runs in polylogarithmic time specifically the running time of our algorithm is o f log log n for an arbitrarily slow growing function f 1 we can also produce an o 1 coloring in o log log n time for an arbitrarily small constant 0 and an o coloring in o e log n time for an arbitrarily small constant e 0 our results are in fact far more general than this in particular for a graph of arboricity a our algorithm produces an o a1 coloring for an arbitrarily small constant 0 in time o log a log n

distributed δ 1 coloring in sublogarithmic rounds we give a new randomized distributed algorithm for 1 coloring in the local model running in o log 2o log log n rounds in a graph of maximum degree this implies that the 1 coloring problem is easier than the maximal independent set problem and the maximal matching problem due to their lower bounds of min log n log log n log log log by kuhn moscibroda and wattenhofer podc 04 our algorithm also extends to list coloring where the palette of each node contains 1 colors we extend the set of distributed symmetry breaking techniques by performing a decomposition of graphs into dense and sparse parts

three term relations between interpolation polynomials for a bcn type basic hypergeometric series abstract we present an explicit expression for the q difference system of rank n 1 satisfied by a bc n type jackson integral q series as first order simultaneous q difference equations with a concrete basis for this purpose we introduce two types of symmetric laurent polynomials called the interpolation polynomials three term relations between the interpolation polynomials play an essential role in deriving the q difference system as an application we give another proof for the product formula of the q integral introduced by gustafson

alternative formulations of a combined trip generation trip distribution modal split and trip assignment model abstract the traditional four step model has been widely used in travel demand forecasting by considering trip generation trip distribution modal split and traffic assignment sequentially in a fixed order however this sequential approach suffers from the inconsistency among the level of service and flow values in each step of the procedure in the last two decades this problem has been addressed by many researchers who have sought to develop combined or integrated models that can consider travelers choice on different stages simultaneously and give consistent results in this paper alternative formulations including mathematical programming mp formulation and variational inequality vi formulations are provided for a combined travel demand model that integrates trip generation trip distribution modal split and traffic assignment using the random utility theory framework thus the proposed alternative formulations not only allow a systematic and consistent treatment of travel choice over different dimensions but also have behavioral richness qualitative properties of the formulations are also given to ensure the existence and uniqueness of the solution particularly the model is analyzed for a special but useful case where the probabilistic travel choices are assumed to be a hierarchical logit model furthermore a self adaptive goldstein levitin polyak glp projection algorithm is adopted for solving this special case

locality in distributed graph algorithms this paper concerns a number of algorithmic problems on graphs and how they may be solved in a distributed fashion the computational model is such that each node of the graph is occupied by a processor which has its own id processors are restricted to collecting data from others which are at a distance at most t away from them in t time units but are otherwise computationally unbounded this model focuses on the issue of locality in distributed processing namely to what extent a global solution to a computational problem can be obtained from locally available data three results are proved within this model a 3 coloring of an n cycle requires time omega log n this bound is tight by previous work of cole and vishkin any algorithm for coloring the d regular tree of radius r which runs for time at most 2r 3 requires at least omega sqrt d colors in an n vertex graph of largest degree delta an o delta 2 coloring may be found in time o log n

a bilateral extension of the q selberg integral a multi dimensional bilateral q series extending the q selberg integral is studied using concepts of truncation regularization and connection formulae following aomoto s method which involves regarding theq series as a solution of aq difference equation fixed by its asymptotic behavior an infinite product evaluation is obtained the q difference equation is derived applying the shifted symmetric polynomials introduced by knop and sahi as a special case of the infinite product formula askey evans s q selberg integral evaluation and its generalization by tarasov varchenko and stokman is reclaimed and an explanation in the context of aomoto s setting is thus provided 2010 mathematical subject classification primary 33d15 33d67 secondary 39a13

bgg reciprocity for current algebras abstract we study the category i gr of graded representations with finite dimensional graded pieces for the current algebra g c t where g is a simple lie algebra this category has many similarities with the category o of modules for g and in this paper we formulate and study an analogue of the famous bgg duality we recall the definition of the projective and simple objects in i gr which are indexed by dominant integral weights the role of the verma modules is played by a family of modules called the global weyl modules we show that in the case when g is of type s l 2 the projective module admits a flag in which the successive quotients are finite direct sums of global weyl modules the multiplicity with which a particular weyl module occurs in the flag is determined by the multiplicity of a jordan holder series for a closely associated family of modules called the local weyl modules we conjecture that the result remains true for arbitrary simple lie algebras we also prove some combinatorial product sum identities involving kostka polynomials which arise as a consequence of our theorem

rarefied elliptic hypergeometric functions abstract two exact evaluation formulae for multiple rarefied elliptic beta integrals related to the simplest lens space are proved they generalize evaluations of the type i and ii elliptic beta integrals attached to the root system c n in a special n 1 case the simplest p 0 limit is shown to lead to a new class of q hypergeometric identities symmetries of a rarefied elliptic analogue of the euler gauss hypergeometric function are described and the respective generalization of the hypergeometric equation is constructed some extensions of the latter function to c n and a n root systems and corresponding symmetry transformations are considered an application of the rarefied type ii c n elliptic hypergeometric function to some eigenvalue problems is briefly discussed

elliptic hypergeometry of supersymmetric dualities we give a full list of known mathcal n 1 supersymmetric quantum field theories related by the seiberg electric magnetic duality conjectures for su n sp 2n and g 2 gauge groups many of the presented dualities are new not considered earlier in the literature for all these theories we construct superconformal indices and express them in terms of elliptic hypergeometric integrals this gives a systematic extension of the related romelsberger and dolan osborn results equality of indices in dual theories leads to various identities for elliptic hypergeometric integrals about half of them were proven earlier and another half represents new challenging conjectures in particular we conjecture a dozen new elliptic beta integrals on root systems extending the univariate elliptic beta integral discovered by the first author

hyperbolic beta integrals abstract hyperbolic beta integrals are analogues of euler s beta integral in which the role of euler s gamma function is taken over by ruijsenaars hyperbolic gamma function they may be viewed as q q bibasic analogues of the beta integral in which the two bases q and q are interrelated by modular inversion and they entail q analogues of the beta integral for q 1 the integrals under consideration are the hyperbolic analogues of the ramanujan integral the askey wilson integral and the nassrallah rahman integral we show that the hyperbolic nassrallah rahman integral is a formal limit case of spiridonov s elliptic nassrallah rahman integral

some q beta and mellin barnes integrals on compact lie groups and lie algebras multidimensional generalizations of beta type integrals of bames ramanujan askey wilson and others are evaluated these integrals are analogues of the summation theorems for multilateral hypergeometric series associated to the simple lie algebras of classical type and type g2 many of these integrals can also be written as group integrals over a compact lie group or conjugation invariant integrals over the corresponding lie algebra

improved distributed algorithms for coloring interval graphs with application to multicoloring trees we give a distributed 1 epsilon approximation algorithm for the minimum vertex coloring problem on interval graphs which runs in the mathcal local model and operates in mathrm o frac 1 epsilon log n rounds if nodes are aware of their interval representations then the algorithm can be adapted to the mathcal congest model using the same number of rounds prior to this work only constant factor approximations using mathrm o log n rounds were known 12 linial s ring coloring lower bound implies that the dependency on log n cannot be improved we further prove that the dependency on frac 1 epsilon is also optimal

solving the combined modal split and traffic assignment problem with two types of transit impedance function abstract the gradient projection gp algorithm has been shown as a successful path based algorithm for solving various traffic assignment problems in this paper the gp algorithm is adapted for solving the combined modal split and traffic assignment cmsta problem which can be viewed as an elastic demand traffic equilibrium problem edtep with two modes using the excess demand formulation of edtep the cmsta problem is reformulated and solved by a modified gp algorithm numerical results based on a real bi modal network in the city of winnipeg canada are provided to demonstrate the efficiency and robustness of the modified path based gp algorithm for solving the cmsta problem in addition the cmsta problem is investigated with two types of impedance function for the transit mode and with different degrees of dispersion for the modal split function the computational results show the modified gp algorithm outperforms the classical evan s algorithm for both types of transit impedance function and it can be as efficient as the original gp algorithm for solving the traffic assignment problem with fixed demand

elliptic extension of gustafson s q integral of type g2 abstract the evaluation formula for an elliptic beta integral of type g 2 is proved the integral is expressed by a product of ruijsenaars elliptic gamma functions and the formula includes that of gustafson s q beta integral of type g 2 as a special limiting case as p 0 the elliptic beta integral of type b c 1 by van diejen and spiridonov is effectively used in the proof of the evaluation formula

an algorithmic proof theory for hypergeometric ordinary and q multisum integral identities it is shown that every proper hypergeometric multisum integral identity orq identity with a fixed number of summations and or integration signs possesses a short computer constructible proof we give a fast algorithm for finding such proofs most of the identities that involve the classical special functions of mathematical physics are readily reducible to the kind of identities treated here we give many examples of the method including computer generated proofs of identities of mehta dyson selberg hille hardy q saalschutz and others the prospect of using the method for proving multivariate identities that involve an arbitrary number of summations integrations is discussed

an algebraic approach to macdonald koornwinder polynomials rodrigues type formula and inner product identity we study macdonald koornwinder polynomials in the context of double affine hecke algebras nonsymmetric macdonald koornwinder polynomials are constructed by use of raising operators provided by a representation theory of the double affine hecke algebra associated with a2l 2 type affine root system this enables us to evaluate diagonal terms of scalar products of the nonsymmetric polynomials algebraically the macdonald koornwinder polynomials are expressed by linear combinations of the nonsymmetric counterparts we show a new proof of the inner product identity of the macdonald koornwinder polynomials without opdam cherednik s shift operators

distributed coloring algorithms for triangle free graphs vertex coloring is a central concept in graph theory and an important symmetry breaking primitive in distributed computing whereas degree graphs may require palettes of 1 colors in the worst case it is well known that the chromatic number of many natural graph classes can be much smaller in this paper we give new distributed algorithms to find k coloring in graphs of girth 4 triangle free graphs girth 5 and trees the parameter k can be at most 1 4 o 1 ln in triangle free graphs and at most 1 o 1 ln in girth 5 graphs and trees where o 1 is a function of specifically for sufficiently large we can find such a coloring in o k log n time moreover for any we can compute such colorings in roughly logarithmic time for triangle free and girth 5 graphs and in o log log log n time on trees as a byproduct our algorithm shows that the chromatic number of triangle free graphs is at most 4 o 1 ln which improves on jamall s recent bound of 67 o 1 ln finally we show that 1 coloring for triangle free graphs can be obtained in sublogarithmic time for any

some multidimensional integrals related to many body systems with the 1 r2 potential an n dimensional integral evaluated by k aomoto 1988 is shown to represent the density matrix for an impurity particle in the 1 r2 quantum many body problem on a line the value of the n dimensional integral representing the same density matrix in periodic boundary conditions is conjectured as too is the value of an n dimensional integral which represents a two point correlation function in the system also the partition function of a related classical hamiltonian is evaluated by formulating a conjecture which asserts that the sum of jacobians of a certain change of variables in n dimensions is a constant

transformations of elliptic hypergeometric integrals we prove a pair of transformations relating elliptic hypergeometric integrals of different dimensions corresponding to the root systems bc n and a n as a special case we recover some integral identities conjectured by van diejen and spiridonov for bc n we also consider their type ii integral their proof of that integral together with our transformation gives rise to pairs of adjoint integral operators a different proof gives rise to pairs of adjoint difference operators these allow us to construct a family of biorthogonal abelian functions generalizing the koornwinder polynomials and satisfying the analogues of the macdonald conjectures finally we discuss some transformations of type ii style integrals in particular we find that adding two parameters to the type ii integral gives an integral invariant under an appropriate action of the weyl group e 7

a generalization of weyl s denominator formulas for the classical groups abstract we give a generalization of weyl s denominator formulas for the classical groups we consider the matrices whose constituents are the characters of the respective classical groups in the restricted variables for each column of the matrices and show that the determinants of the matrices are equal to the powers of the fundamental alternating polynomials the original denominators of weyl s denominator formulas

a u n generalization of ramanujan s 1ψ1 summation abstract in this paper we derive a u n generalization of ramanujan s 1 1 summation directly from a recent u n multiple series refinement of the q binomial theorem we also obtain a new generalization of the macdonald identities for a 1 l

a generalization of the sears slater transformation and elliptic lagrange interpolation of type bcn abstract the connection formula for the jackson integral of type b c n is obtained in the form of a sears slater type expansion of a bilateral multiple basic hypergeometric series as a linear combination of several specific bilateral multiple series the coefficients of this expansion are expressed by certain elliptic lagrange interpolation functions analyzing basic properties of the elliptic lagrange interpolation functions an explicit determinant formula is provided for a fundamental solution matrix of the associated system of q difference equations

simultaneous estimation of the origin destination matrices and the parameters of a nested logit model in a combined network equilibrium model abstract this paper deals with the inverse problem of a type of traffic equilibrium models with combined modes this problem consists of obtaining a parametrization of the equilibrium model from a set of observations of the outputs for the model the inputs for the model are an origin destination o d trip matrix for the various alternatives that have been considered and a set of parameters for a nested logit model used as a demand model this model has been formulated by using a new approach called the calibration and demand adjustment model cdam based on bilevel programming which simultaneously estimates an o d matrix and the parameters for the nested logit model in this paper the cdam properties are studied and it is proved the cdam solution exists this paper develops a heuristic column paths hyperpaths generation algorithm for the cdam this algorithm iterates between the network equilibrium problem and that which is used to obtain a set of paths when equilibrium is attained and the cdam is restricted to the set of previously generated columns the so called restricted cdam the restricted cdam is formulated as a single level model under certain hypotheses and it furnishes a solution upon which to base a new estimation of the o d matrix and the vector of parameters the computational tests on the algorithm have been carried out using data from a multi modal network in madrid

q difference shift for a bcn type jackson integral arising from elementary symmetric polynomials we study a q difference equation of a bcn type jackson integral introduced by van diejen the bcn type jackson integral is a multiple q series generalized from a q analogue of selberg s integral the equation is characterized by some new symmetric polynomials defined via symplectic schur functions as an application we give another proof of a product formula for the bcn type jackson integral which is equivalent to the so called q macdonald morris identity for the root system bcn first obtained by gustafson

logit choice models for interactive attributes abstract in multi attribute decision making madm the choice of a decision maker dm is often the result of an interplay between the dm s unique attitude the utilities specific to the dm for the attributes and the degree of positive or negative interaction among the attributes based on this conglomeration of information we introduce a few choice models to give the probabilities for different possible choices of a dm more specifically the conventional multinomial logit mnl model is extended to consider the interaction among the attributes and also the dm s unique attitudinal character the usefulness of the proposed models is illustrated in a real world application

a new modified goldstein levitin polyakprojection method for variational inequality problems in this paper we first show that the adjustment parameter in the step size choice strategy of the modified goldstein levitin polyak projection method proposed by he et al for asymmetric strongly monotone variational inequality problems can be bounded away from zero by a positive constant under this observation we propose a new step size rule which seems to be more practical and robust than the original one we show that the new modified method is globally convergent under the same conditions and report some computational results to illustrate the method

macdonald s constant term conjectures for exceptional root systems we announce proofs of macdonald s constant term conjectures for the affine root systems s f 4 and s f 4 v we also give an algorithm for deciding the conjectures for the remaining root systems s e 6 s e 7 and s e 8 and prove that the constant term in question can indeed be expressed in closed form combined with previous work of zeilberger bressoud kadell and gustafson our results imply that macdonald s conjectures are true in form for any root system

a distributed 2 e approximation for vertex cover in o log δ e log log δ rounds we present a simple deterministic distributed 2 e approximation algorithm for minimum weight vertex cover which completes in o log elog log rounds where is the maximum degree in the graph for any e 0 that is at most o 1 for a constant e this implies a constant approximation in o log log log rounds which contradicts the lower bound of kmw10

classical discrete symplectic ensembles on the linear and exponential lattice skew orthogonal polynomials and correlation functions the eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalized to discrete settings involving either a linear or an exponential lattice the corresponding correlation functions can be expressed in terms of certain discrete and q skew orthogonal polynomials respectively we give a theory of both of these classes of polynomials and the correlation kernels determining the correlation functions in the cases in which the weights for the corresponding discrete unitary ensembles are classical crucial for this are certain difference operators which relate the relevant symmetric inner products to the skew symmetric ones and have a tridiagonal action on the corresponding discrete or q orthogonal polynomials

the locality of distributed symmetry breaking symmetry breaking problems are among the most well studied in the field of distributed computing and yet the most fundamental questions about their complexity remain open in this article we work in the local model where the input graph and underlying distributed network are identical and study the randomized complexity of four fundamental symmetry breaking problems on graphs computing miss maximal independent sets maximal matchings vertex colorings and ruling sets a small sample of our results includes the following an mis algorithm running in o log2 2o log log n time where is the maximum degree this is the first mis algorithm to improve on the 1986 algorithms of luby and alon babai and itai when log n l l 2 log n and comes close to the log log log lower bound of kuhn moscibroda and wattenhofer a maximal matching algorithm running in o log log 4log n time this is the first significant improvement to the 1986 algorithm of israeli and itai moreover its dependence on is nearly optimal a 1 coloring algorithm requiring o log 2o log log n time improving on an o log log n time algorithm of schneider and wattenhofer a method for reducing symmetry breaking problems in low arboricity degeneracy graphs to low degree graphs roughly speaking the arboricity or degeneracy of a graph bounds the density of any subgraph corollaries of this reduction include an o log n time maximal matching algorithm for graphs with arboricity up to 2 log n and an o log 2 3n time mis algorithm for graphs with arboricity up to 2 log n 1 3 each of our algorithms is based on a simple but powerful technique for reducing a randomized symmetry breaking task to a corresponding deterministic one on a poly log n size graph

the maximum capture problem with random utilities problem formulation and algorithms abstract a model for the optimal location of new facilities in a competitive market is introduced under the hypothesis that customers behavior can be modeled by random utility functions it means that the company that wished to locate uses a random utility model to forecast the market share of a location therefore the company cannot forecast the behavior of every customer in a deterministic fashion but is able to embed him by a probability distribution three formulations are proposed to compute upper bounds of the objective function and compared in a numerical simulation a branch and bound method is developed and tested on examples with up to 50 potential locations and a variable neighborhood search heuristic is proposed to solve larger instances

outer approximation and submodular cuts for maximum capture facility location problems with random utilities abstract we consider a family of competitive facility location problems in which a newcomer company enters the market and has to decide where to locate a set of new facilities so as to maximize its market share the multinomial logit model is used to estimate the captured customer demand we propose a first branch and cut approach for this family of difficult mixed integer non linear problems our approach combines two types of cutting planes that exploit particular properties of the objective function the first one are the outer approximation cuts and the second one are the submodular cuts the approach is computationally evaluated on three datasets from the recent literature the obtained results show that our new branch and cut drastically outperforms state of the art exact approaches both in terms of the computing times and in terms of the number of instances solved to optimality

exploring trust region method for the solution of logit based stochastic user equilibrium problem abstract in this research paper we explored using the trust region method to solve the logit based sue problem we proposed a modified trust region newton mtrn algorithm for this problem when solving the trust region sue subproblem we showed that applying the well known steihaug toint method is inappropriate since it may make the convergence rate of the major iteration very slow in the early stage of the computation to overcome this drawback a modified steihaug toint method was proposed we proved the convergence of our mtrn algorithm and showed its convergence rate is superlinear for the implication of our algorithm we proposed an important principle on how to select the basic route for each od pair we indicated that it is a crucial principle to accelerate the convergence rate of the minor iteration i e trust region subproblem solving iteration in this study other implication issues for the sue problem are also considered including the computation of the trial step and the strategy to ensure strict feasibility iteration point we compared the mtrn algorithm with the gradient projection gp algorithm on the sioux falls network some results of numerical analysis are also reported

properties of some families of hypergeometric orthogonal polynomials in several variables limiting cases are studied of the koornwinder macdonald multivariable generalization of the askey wilson polynomials we recover recently and not so recently introduced families of hypergeometric orthogonal polynomials in several variables consisting of multivariable wilson continuous hahn and jacobi type polynomials respectively for each class of polynomials we provide systems of difference or differential equations recurrence relations and expressions for the norms of the polynomials in terms of the norm of the constant polynomial

a comparison of linear reformulations for multinomial logit choice probabilities in facility location models abstract in the last decade several papers appeared on facility location problems that incorporate customer demand by the multinomial logit model three linear reformulations of the original non linear model have been proposed so far in this paper we discuss these models in terms of solvability we present empirical findings based on synthetic data

traffic assignment model with fuzzy level of travel demand an efficient algorithm based on quasi logit formulas abstract the place of fuzzy concepts in traffic assignment ta models has been studied in recent literature keeping fuzzy level of travel demand in mind we propose a new ta model in which the travel costs of links are depended on their congestion from the results of such fuzzy ta model network planners are able to estimate the number of travelers on network links by using zero one variables the proposed model is transformed into a crisp mixed integer problem with respect to path flow variables in order to produce the logit flows from this problem damberg et al algorithm is modified then the level of certainty is maximized and perceived travel delays are minimized for a fixed certainty degree the obtained solution which is named the fuzzy equilibrium flow satisfies a quasi logit formula similar to ordinary expression of the logit route choice model eventually we examine the quality of different path enumeration techniques in the proposed model

a simple parallel algorithm for the maximal independent set problem two basic design strategies are used to develop a very simple and fast parallel algorithms for the maximal independent set mis problem the first strategy consists of assigning identical copies o

an algorithm for the ranking of shortest paths an efficient computational implementation of a path deletion k shortest paths algorithm and a new algorithm for the same problem are presented in a path deletion k shortest paths algorithm a sequence g1 g2 gk of networks is is defined such that g1 is given network and its k th shortes path is trivially determined from the shortest path in gk in essence as soon as the shortest path in gk is determined it is excluded from gk in such a way that no new paths are formed and no more paths are deleted so far each gk two procedures are executed a shortest path algorithm and a path deletion algorithm in the presented computational implementation all the information resulting from the determination of the k th shortest path is carried throughout gk 1 gk 2 gk the new algorithm not only keeps this characteristics but also avoids the last k 1 executions of a shortest path algorithm which results in a suprising and very substantial reduction in the execution time in fact for randomly generated networks with 104 nodes and 105 arcs once the shortest the new algorithm computes the next 100 shortest paths in times of the order of 10 1 seconds to illustrate the efficiency of this algorithm comparative computational experiments are reported

inversions of integral operators and elliptic beta integrals on root systems we prove a novel type of inversion formula for elliptic hypergeometric integrals associated to a pair of root systems using the a c inversion formula to invert one of the known c type elliptic beta integrals we obtain a new elliptic beta integral for the root system of type a validity of this integral is established by a different method as well

the importance of the selberg integral it has been remarked that a fair measure of the impact of atle selberg s work is the number of mathematical terms that bear his name one of these is the selberg integral an n dimensional generalization of the euler beta integral we trace its sudden rise to prominence initiated by a question to selberg from enrico bombieri more than thirty years after its initial publication in quick succession the selberg integral was used to prove an outstanding conjecture in random matrix theory and cases of the macdonald conjectures it further initiated the study of q analogues which in turn enriched the macdonald conjectures we review these developments and proceed to exhibit the sustained prominence of the selberg integral as evidenced by its central role in random matrix theory calogero sutherland quantum many body systems knizhnik zamolodchikov equations and multivariable orthogonal polynomial theory

a branch and bound algorithm for the maximum capture problem with random utilities abstract the maximum capture problem with random utilities seeks to locate new facilities in a competitive market such that the captured demand of users is maximized assuming that each individual chooses among all available facilities according to the well know a random utility model namely the multinomial logit the problem is complex mostly due to its integer nonlinear objective function currently the most efficient approaches deal with this complexity by either using a nonlinear programing solver or reformulating the problem into a mixed integer linear programing milp model in this paper we show how the best milp reformulation available in the literature can be strengthened by using tighter coefficients in some inequalities we also introduce a new branch and bound algorithm based on a greedy approach for solving a relaxation of the original problem extensive computational experiments are presented benchmarking the proposed approach with other linear and non linear relaxations of the problem the computational experiments show that our proposed algorithm is competitive with all other methods as there is no method which outperforms the others in all instances we also show a large scale real instance of the problem which comes from an application in park and ride facility location where our proposed branch and bound algorithm was the most effective method for solving this type of problem

a determinant formula associated with the elliptic hypergeometric integrals of type bcn we establish a determinant formula for the bilinear form associated with the elliptic hypergeometric integrals of type bcn by studying the structure of q difference equations to be satisfied by them the determinant formula is proved by combining the q difference equations of the determinant and its asymptotic analysis along the singularities the elliptic interpolation functions of type bcn are essentially used in the study of the q difference equations we establish a determinant formula for the bilinear form associated with the elliptic hypergeometric integrals of type bcn by studying the structure of q difference equations to be satisfied by them the determinant formula is proved by combining the q difference equations of the determinant and its asymptotic analysis along the singularities the elliptic interpolation functions of type bcn are essentially used in the study of the q difference equations

askey wilson polynomials by means of a q selberg type integral abstract an integral representation of the askey wilson polynomials is presented in terms of a q selberg type integral our motivation consists in the study of q selberg type integrals from the viewpoint of de rham theory or holonomic systems

twisted strong macdonald theorems and adjoint orbits the strong macdonald theorems state that for l reductive and s an odd variable the cohomology algebras h l z z n and h l z s are freely generated and describe the cohomological s and z degrees of the generators the resulting identity for the z weighted euler characteristic is equivalent to macdonald s constant term identity for a finite root system we calculate h mathfrak p z n mathfrak p and h mathfrak p s for mathfrak p a standard parahoric in a twisted loop algebra giving strong macdonald theorems that take into account both a parabolic component and a possible diagram automorphism twist in particular we show that h mathfrak p z n mathfrak p contains a parabolic subalgebra of the coinvariant algebra of the fixed point subgroup of the weyl group of l and thus is no longer free we also prove a strong macdonald theorem for h mathfrak b s mathfrak n and h mathfrak b z n mathfrak n when mathfrak b and mathfrak n are iwahori and nilpotent subalgebras respectively of a twisted loop algebra for each strong macdonald theorem proved taking z weighted euler characteristics gives an identity equivalent to macdonald s constant term identity for the corresponding affine root system as part of the proof we study the regular adjoint orbits for the adjoint action of the twisted arc group associated to l proving an analogue of the kostant slice theorem

a multidimensional generalization of the barnes integral and the continuous hahn polynomial employing a multidimensional generalization of the beta integral of barnes we derive an expression of the continuous hahn polynomials motivation of the present work is to study such integrals from the viewpoint of a finite difference version of the de rham theory

symmetry breaking depending on the chromatic number or the neighborhood growth we deterministically compute a d 1 coloring and a maximal independent set mis in time o d 1 2 q 1 h log n for d 1 email protected email protected 1 i h where d j is defined as the maximal number of nodes within distance j for a node and d email protected 1 our greedy coloring and mis algorithms improve the state of the art algorithms running in o d log n for a large class of graphs i e graphs of moderate neighborhood growth with h 36 we also state and analyze a randomized coloring algorithm in terms of the chromatic number the run time and the used colors our algorithm runs in time o email protected log n for email protected email protected log 1 1 l o g nn and email protected o d log 1 1 l o g nn for graphs of polylogarithmic chromatic number the analysis reveals an exponential gap compared to the fastest d 1 coloring algorithm running in time o email protected logn the algorithm works without knowledge of g and uses less than d colors i e 1 1 o g d with high probability to the best of our knowledge this is the first distributed algorithm for such general graphs taking the chromatic number g into account we also improve on the state of the art deterministic computation of 2 c ruling sets

branching formula for macdonald koornwinder polynomials abstract we present an explicit branching formula for the six parameter macdonald koornwinder polynomials with hyperoctahedral symmetry

the q dixon anderson integral and multi dimensional 1 psi 1 summations the dixon anderson integral is a multi dimensional integral evaluation fundamental to the theory of the selberg integral the 11 summation is a bilateral generalization of the q binomial theorem it is shown that a q generalization of the dixon anderson integral due to evans and multi dimensional generalizations of the 11 summation due to milne and gustafson can be viewed as having a common origin in the theory of q difference equations as expounded by aomoto each is shown to be determined by a q difference equation of rank 1 and a certain asymptotic behavior in calculating the latter essential use is made of the concepts of truncation regularization and connection formulae