some experiments with simulated annealing for coloring graphs abstract methods of thermodynamical simulation have been used for several famous combinatorial optimization problems for graph coloring i e partition of the node set into as few independent sets as possible we describe a method of simulation such an approach is combined with other techniques for graph coloring experiments on random graphs show evidence that this combination gives better results than anyone of the original non combined methods

wandering domains for composition of entire functions abstract c bishop in 10 theorem 17 1 constructs an example of an entire function f in class b with at least two grand orbits of oscillating wandering domains in this paper we show that his example has exactly two such orbits that is f has no unexpected wandering domains we apply this result to the classical problem of relating the julia sets of composite functions with the julia set of its members more precisely we show the existence of two entire maps f and g in class b such that the fatou set of f g has a wandering domain while all fatou components of f or g are preperiodic this complements a result of a singh in 22 theorem 4 and results of w bergweiler and a hinkkanen in 6 related to this problem

frame potential for finite dimensional banach spaces abstract we define the frame potential for a schauder frame on a finite dimensional banach space as the square of the 2 summing norm of the frame operator as is the case for frames for hilbert spaces we prove that the frame potential can be used to characterize finite unit norm tight frames funtfs for finite dimensional banach spaces we prove the existence of funtfs for a variety of spaces and in particular that every n dimensional complex banach space with a 1 unconditional basis has a funtf of n vectors for every n n however many interesting results on funtfs and sums of rank one projections for hilbert spaces remain unknown for banach spaces and we conclude the paper with multiple open questions

mechanisms for local search abstract local search methods for combinatorial optimization make a series of steps at each stage improving the current solution by moving to a neighbouring solution this is usually done by considering the neighbouring solutions one at a time and moving to the first one which gives an improvement a first improving method in this paper we consider whether there are circumstances in which some other strategy will have better performance in exploring this question we begin by giving a theoretical treatment of a simple model with random objective values at each solution point we carry out some experiments on the travelling salesman problem and the quadratic assignment problem using varying values of a spread parameter k the value of k corresponds to the number of improving solutions looked at before making a move we also make some conjectures relating the overall performance of the local search method to the average number of solutions which are evaluated before a local minimum is reached

optimal tight frames and quantum measurement tight frames and rank one quantum measurements are shown to be intimately related in fact the family of normalized tight frames for the space in which a quantum mechanical system lies is precisely the family of rank one generalized quantum measurements on that space using this relationship frame theoretical analogs of various quantum mechanical concepts and results are developed the analog of a least squares quantum measurement is a tight frame that is closest in a least squares sense to a given set of vectors the least squares tight frame is found for both the case in which the scaling of the frame is specified constrained least squares frame clsf and the case in which the scaling is chosen to minimize the least squares error unconstrained least squares frame ulsf the well known canonical frame is shown to be proportional to the ulsf and to coincide with the clsf with a certain scaling

permutable entire functions and multiply connected wandering domains abstract let f and g be permutable transcendental entire functions we use a recent analysis of the dynamical behavior in multiply connected wandering domains to make progress on the long standing conjecture that the julia sets of f and g are equal in particular we show that j f j g provided that neither f nor g has a simply connected wandering domain in the fast escaping set

nonuniform sampling and reconstruction in shift invariant spaces this article discusses modern techniques for nonuniform sampling and reconstruction of functions in shift invariant spaces it is a survey as well as a research paper and provides a unified framework for uniform and nonuniform sampling and reconstruction in shift invariant subspaces by bringing together wavelet theory frame theory reproducing kernel hilbert spaces approximation theory amalgam spaces and sampling inspired by applications taken from communication astronomy and medicine the following aspects will be emphasized a the sampling problem is well defined within the setting of shift invariant spaces b the general theory works in arbitrary dimension and for a broad class of generators c the reconstruction of a function from any sufficiently dense nonuniform sampling set is obtained by efficient iterative algorithms these algorithms converge geometrically and are robust in the presence of noise d to model the natural decay conditions of real signals and images the sampling theory is developed in weighted l p spaces

the quadratic three dimensional assignment problem exact and approximate solution methods abstract this paper reports on algorithm development for solving the quadratic three dimensional assignment problem q3ap the q3ap arises for example in the implementation of a hybrid arq automatic repeat request scheme for enriching diversity among multiple packet re transmissions by optimizing the mapping of data bits to modulation symbols typical practical problem sizes would be 8 16 32 and 64 we present an exact solution method based upon a reformulation linearization technique that is one of the best available for solving the quadratic assignment problem qap our current exact algorithm is useful for q3ap instances of size 13 or smaller we also investigate four stochastic local search algorithms that provide optimum or near optimum solutions for large and difficult qap instances and adapt them for solving the q3ap the results of our experiments make it possible to get good solutions to signal mapping problems of size 8 and 16

lyapunov exponents and related concepts for entire functions let f be an entire function and denote by f the spherical derivative of f and by f n the n th iterate of f for an open set u intersecting the julia set j f we consider how fast sup z in u f n z and int u f n z 2 dx dy tend to infty we also study the growth rate of the sequence f n z for z in j f

experimental analysis of simulated annealing based algorithms for the layout problem abstract in this paper results from an experimental analysis involving the 2 way and 3 way exchange algorithms a modified penalty algorithm the simulated annealing algorithm and a hybrid simulated annealing algorithm are presented the hybrid simulated annealing algorithm uses the modified penalty algorithm to generate an initial solution and then improves it using simulated annealing it is tested on single row layout problems with facilities of unequal area and multi row layout problems with facilities of equal area the algorithm produced solutions better than those previously reported in the literature for two of the larger single row problems and five multi row layout problems for all the other single row problems and eight of ten multi row layout test problems it produced the best known solutions the hybrid simulated annealing algorithm appears to produce better quality solutions than the simulated annealing and tabu navigation algorithms but requires more computation time than simulated annealing

shrinking and boundedly complete schauder frames in frechet spaces abstract we study schauder frames in frechet spaces and their duals as well as perturbation results we define shrinking and boundedly complete schauder frames on a locally convex space study the duality of these two concepts and their relation with the reflexivity of the space we characterize when an unconditional schauder frame is shrinking or boundedly complete in terms of properties of the space several examples of concrete schauder frames in function spaces are also presented

an extreme point algorithm for a local minimum solution to the quadratic assignment problem abstract in this paper the network structure of basic solutions to the quadratic assignment problem qap is revisited the concept of a relative local star minimum is introduced results characterizing a relative local star minimum are obtained then an extreme point algorithm for qap is proposed

annular itineraries for entire functions in order to analyse the way in which the size of the iterates of a transcendental entire function f can behave we introduce the concept of the annular itinerary of a point z this is the sequence of non negative integers s 0 s 1 defined by f n z a s n r for n 0 where a 0 r z z r and a n r z m n 1 r z m n r n 1 here m r is the maximum modulus of f on z z r and r 0 is so large that m r r for r r we consider the different types of annular itineraries that can occur for any transcendental entire function f and show that it is always possible to find points with various types of prescribed annular itineraries the proofs use two new annuli covering results that are of wider interest

a minimax assignment problem in treelike communication networks abstract a given system of communication centres c 1 c 2 c n has to be embedded into a given undirected network n the centres exchange messages at given rates per time unit through a selected routing pattern if there is no direct connection between c i and c j the messages sent from c i to c j pass through several intermediate centres the messages exchanged between c i and c j may be sent along a single path or they may be split into several parts each part being sent along its own path the goal is to find an embedding of the centres into the network and a routing pattern which minimizes the maximum intermediate traffic over all centres the paper deals mainly with the single path model the complexity of the problem is fully discussed drawing a sharp borderline between np complete and polynomially solvable cases in case that n is a tree a branch and bound algorithm is described and numerical results for random test data are reported and discussed

global optimality conditions and optimization methods for quadratic assignment problems abstract in this paper some global optimality conditions for general quadratic 0 1 programming problems with linear equality constraints are discussed and then some global optimality conditions for quadratic assignment problems qap are presented a local optimization method for qap is derived according to the necessary global optimality conditions a global optimization method for qap is presented by combining the sufficient global optimality conditions the local optimization method and some auxiliary functions some numerical examples are given to illustrate the efficiency of the given optimization methods

heuristics for biquadratic assignment problems and their computational comparison abstract the biquadratic assignment problem biqap is a generalization of the quadratic assignment problem qap as for any hard optimization problem also for biqap a reasonable effort to cope with the problem is trying to derive heuristics which solve it suboptimally and which possibly yield a good trade off between the solution quality and the time and memory requirements in this paper we describe several heuristics for biqaps in particular pair exchange algorithms improvement methods and variants of simulated annealing and taboo search we implement these heuristics as c codes and analyze their performances

an asymptotical study of combinatorial optimization problems by means of statistical mechanics the analogy between combinatorial optimization and statistical mechanics has proven to be a fruitful object of study simulated annealing a metaheuristic for combinatorial optimization problems is based on this analogy in this paper we show how a statistical mechanics formalism can be utilized to analyze the asymptotic behavior of combinatorial optimization problems with sum objective function and provide an alternative proof for the following result under a certain combinatorial condition and some natural probabilistic assumptions on the coefficients of the problem the ratio between the optimal solution and an arbitrary feasible solution tends to one almost surely as the size of the problem tends to infinity so that the problem of optimization becomes trivial in some sense whereas this result can also be proven by purely probabilistic techniques the above approach allows one to understand why the assumed combinatorial condition is essential for such a type of asymptotic behavior

an improved annealing scheme for the qap abstract recently there has been some interest in the use of simulated annealing to obtain good solutions to a number of combinatorial problems this paper reports on the use of this method applied to the quadratic assignment problem i e the assignment of inter communicating objects to locations to minimize the total cost of communication between them the result is a much improved annealing scheme for this problem which performs well on a range of examples finding improved solutions for several of the largest problems available in the literature and requiring only modest amounts of computational effort

the asymptotic behaviour of quadratic sum assignment problems a statistical mechanics approach abstract in this paper we apply the statistical mechanics formalism to study quadratic sum assignment problems qsap this formalism allows us to exhibit in the limit of large problems the asymptotic behaviour of the optimal value of the cost function the conclusions of the study are confirmed by the results of metropolis computer simulations

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

a heuristic for quadratic boolean programs with applications to quadratic assignment problems abstract a heuristic for quadratic boolean programs is presented computational tests with quadratic assignment problems qap showed that it finds very good suboptimal solutions in moderate time and behaves computationally stable in the appendix a fortran program for qap is listed which improves an earlier code published by burkard and derigs

intelligent local search strategies for solving facility layout problems with the quadratic assignment problem formulation abstract in this paper we implement a tabu search heuristic a probabilistic tabu search heuristic a simulated annealing heuristic and a hybrid tabu search heuristic to solve facility layout problems with the quadratic assignment problem formulation classical problems are used as a benchmark for performance comparison extensive computational experiments were conducted and the results were statistically analyzed to observe the behavior of each heuristic and to discriminate the performance of each heuristic the computational results strongly support the competitiveness of intelligent heuristics for the design of facilities the hybrid tabu search heuristic combining the advantages from both tabu search and simulated annealing can generally outperform their parent algorithms

a thermodynamically motivated simulation procedure for combinatorial optimization problems abstract exchange algorithms are an important class of heuristics for hard combinatorial optimization problems as e g salesman problems or quadratic assignment problems in kirkpatrick s and cerny s exchange algorithms for the travelling salesman problem and placement problem they propose to perform an exchange not only if the objective function value decreases by this exchange but also in certain cases if the objective function value increases an exchange increasing the objective function value is performed stochastically depending on the size of the increment computational tests with quadratic assignment problems revealed an excellent behaviour in such an approach suboptimal solutions differing 1 2 from the best known solutions are obtained by a simple program in short time by starting this program several times with different starting values all known minimal objective function values were reached thus this approach is well suited also for smaller computers and leads in short time to acceptable solutions

a convex form of the quadratic assignment problem abstract the standard quadratic assignment problem suffers from the non convex form of the objective function in this paper we show how the objective function may be made convex and how the convexity properties might be useful in solving the original problem convexity leads to a sufficient condition for any current solution to be optimal a property not available for the non convex form if a current solution is not optimal the convexity leads to easily computable bounds on the loss of optimality

multiply connected wandering domains of entire functions the dynamical behaviour of a transcendental entire function in any periodic component of the fatou set is well understood here we study the dynamical behaviour of a transcendental entire function f in any multiply connected wandering domain u of f by introducing a certain positive harmonic function h in u related to harmonic measure we are able to give the first detailed description of this dynamical behaviour using this new technique we show that for sufficiently large n the image domains u n f n u contain large annuli c n and that the union of these annuli acts as an absorbing set for the iterates of f in u moreover f behaves like a monomial within each of these annuli and the orbits of points in u settle in the long term at particular levels within the annuli determined by the function h we also discuss the proximity of partial u n and partial c n for large n and the connectivity properties of the components of u n setminus overline c n these properties are deduced from new results about the behaviour of entire functions that omit certain values in an annulus

on the lyapunov spectrum for rational maps we study the dimension spectrum for lyapunov exponents for rational maps on the riemann sphere

algodesk an experimental comparison of eight evolutionary heuristics applied to the quadratic assignment problem abstract this work compares the effectiveness of eight evolutionary heuristic algorithms applied to the quadratic assignment problem qap reputedly one of the most difficult combinatorial optimization problems qap is merely used as a carrier for the comparison we do not attempt to compare any heuristics with solving algorithms specific for it results are given both with respect to the best result achieved by each algorithm in a limited time span and to its speed of convergence to that result

perturbing misiurewicz parameters in the exponential family in one dimensional real and complex dynamics a map whose post singular or post critical set is bounded and uniformly repelling is often called a misiurewicz map in results hitherto perturbing a misiurewicz map is likely to give a non hyperbolic map as per jakobson s theorem for unimodal interval maps this is despite genericity of hyperbolic parameters at least in the interval setting we show the contrary holds in the complex exponential family z mapsto lambda exp z misiurewicz maps are lebesgue density points for hyperbolic parameters as a by product we also show that lyapunov exponents almost never exist for exponential misiurewicz maps the lower lyapunov exponent is almost everywhere the upper lyapunov exponent is non negative and depends on the choice of metric

simulated annealing for the qap optimal tradeoff between simulation time and solution quality abstract this paper reports on the optimization of solution quality for a simulated annealing algorithm applied to the quadratic assignment problem the optimization is performed by varying two of the parameters in the algorithm the size of the ensemble i e the number of simulations and the length of each simulation the variation is performed in such a way that the algorithm always uses the same amount of time for a given problem size it is found that the simulation length is indeed optimizable but also that a rather broad spectrum of values produce a near optimal solution quality generally it seems that the optimal simulation length is rather short compared to results found for other optimization problems

computing lower bounds for the quadratic assignment problem with an interior point algorithm for linear programming an example of the quadratic assignment problem qap is the facility location problem in which n facilities are assigned at minimum cost to n sites between each pair of facilities there is a given amount of flow contributing a cost equal to the product of the flow and the distance between sites to which the facilities are assigned proving optimality of qaps has been limited to instances having fewer than 20 facilities largely because known lower bounds are weak we compute lower bounds for a wide range of qaps using a linear programming based lower bound studied by z drezner 1995 on the majority of qaps tested a new best known lower bound is computed on 87 of the instances we produced the best known lower bound on several instances including some having more the 20 facilities the lower bound is tight the linear programs which can be large even for small qaps are solved with an interior point code that uses a preconditioned conjugate gradient algorithm to compute the interior point directions attempts to solve these instances using the cplex primal simplex algorithm as well as the cplex barrier primal dual interior point method were successful only for the smallest instances

recent advances in the solution of quadratic assignment problems the quadratic assignment problem qap is notoriously difficult for exact solution methods in the past few years a number of long open qaps including those posed by steinberg 1961 nugent et al 1968 and krarup 1972 were solved to optimality for the first time the solution of these problems has utilized both new algorithms and novel computing structures we describe these developments as well as recent work which is likely to result in the solution of even more difficult instances

parseval p frames and the feichtinger conjecture abstract in this paper we give a precise characterization of parseval p frames by the known clarkson s inequality for l p as a direct application we show that every tight p frame g j j 1 for l p with frame bound b 0 and inf j g j c 0 can be decomposed into b c p standard q riesz basic sequences and we show that the estimate b c p is optimal moreover we prove the existence of a p frame which is not equivalent to any parsevel p frame for l p and a parseval p frame which is not a schauder frame sequence for the space or its dual space while we obtain that every p frame can become a pseudo framing with l q coefficients for the dual space

on shrinking and boundedly complete schauder frames of banach spaces this paper studies schauder frames in banach spaces a concept which is a natural generalization of frames in hilbert spaces and schauder bases in banach spaces the associated minimal and maximal spaces are introduced as are shrinking and boundedly complete schauder frames our main results extend the classical duality theorems on bases to the situation of schauder frames in particular we will generalize james results on shrinking and boundedly complete bases to frames secondly we will extend his characterization of the reflexivity of spaces with unconditional bases to spaces with unconditional frames

a universal reflexive space for the class of uniformly convex banach spaces we show that there exists a separable reflexive banach space into which every separable uniformly convex banach space isomorphically embeds this solves problems raised by j bourgain b in 1980 and by w b johnson in 1977 jo we also give intrinsic characterizations of separable reflexive banach spaces which embed into a reflexive space with a block q hilbertian and or a block p besselian finite dimensional decomposition

eremenko points and the structure of the escaping set much recent work on the iterates of a transcendental entire function f has been motivated by eremenko s conjecture that all the components of the escaping set i f are unbounded we prove several general results about the topological structure of i f including the fact that if i f is disconnected then it contains uncountably many pairwise disjoint unbounded continua all of which are subsets of ar f the core of the fast escaping set we also show that for some r 0 the set ar f is connected and has the structure of an infinite spider s web or it contains uncountably many unbounded connected f sets there are analogous results for the intersections of these sets with the julia set when multiply connected wandering domains are not present but very different results when such wandering domains are present in proving these we obtain the unexpected result that some types of multiply connected wandering domains have complementary components with no interior indeed uncountably many

an efficient implementation of the robust tabu search heuristic for sparse quadratic assignment problems abstract we propose and develop an efficient implementation of the robust tabu search heuristic for sparse quadratic assignment problems the traditional implementation of the heuristic applicable to all quadratic assignment problems is of o n 2 complexity per iteration for problems of size n using multiple priority queues to determine the next best move instead of scanning all possible moves and using adjacency lists to minimize the operations needed to determine the cost of moves we reduce the asymptotic n complexity per iteration to o n log n for practical sized problems the complexity is o n

coefficient quantization for frames in banach spaces let ei be a fundamental system of a banach space we consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients we will concentrate on systems which are possibly redundant our model for this situation will be frames in banach spaces

balancing hydraulic turbine runners a quadratic assignment problem abstract hydraulic turbine runners are used in electricity generation these consist of a cylinder around which are welded at regular spacings a number of blades whose weights differ slightly it is desired to locate the blades around the cylinder in order to minimize the distance between the center of mass of the blades and the geometric center of the cylinder the problem can be formulated as a quadratic assignment problem it is solved by adapting an interchange algorithm devised by or for the travelling salesman problem computational results are reported

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