vector coherent state constructions of u 3 symmetric tensors and their su 3 su 2 u 1 wigner coefficients generalized vector coherent state constructions of totally symmetric u 3 tensors are used to gain new expressions for the su 3 su 2 u 1 wigner coefficients for the coupling 1 1 20 3 3 these expressions show how the extremely simple formulas of le blanc and biedenharn involving a single 9 j coefficient arise as special cases of a general result that involves 12 j coefficients a simpler general result involving only 9 j coefficients and k normalization factors is derived in a way that can in principle be generalized to the generic coupling with multiplicity

on the projected bases for sp 4 u 2 and the orthogonalization problem the mutual expansion and overlaps of the projected smirnov tolstoy and szpikowski berej bases for the irreducible representations irreps of sp 4 restricted to u 2 are considered the equivalence relation connecting the overlaps of both st and sb bases after the definite substitution of parameters up to an elementary factor is presented the overlaps of the szpikowski berej basis states are rearranged to double sums restricted by the parameters characterizing the multiplicities of the repeating irreps of subgroup and thus representable in polynomial forms the regge type symmetry of these new expressions allows the proof of the earlier conjectured symmetry of the orthogonalization coefficients oc for the family of the biorthogonal bases of sp 4 u 2 su 4 su 2 su 2 and su n so n for two parametric irreps the structure of the orthogonalization coefficients for the szpikowski berej basis is also considered the symmetry of the b c abde functions as the conjectured numerator polynomials

self organised criticality in base pair breathing in dna with a defect abstract we analyse base pair breathing in a dna sequence of 12 base pairs with a defective base at its centre we use both all atom molecular dynamics md simulations and a system of stochastic differential equations sdes in both cases fourier analysis of the trajectories reveals self organised critical behaviour in the breathing of base pairs the fourier transforms fts of the inter base distances show power law behaviour with gradients close to 1 the scale invariant behaviour we have found provides evidence for the view that base pair breathing corresponds to the nucleation stage of large scale dna opening or melting and that this process is a second order phase transition although the random forces in our sde system were introduced as white noise fts of the displacements exhibit pink noise as do the displacements in the amber md simulations

dual bases and some coupling coefficients for su4 su2 su2 sun son and sp4 u2 general analytical expressions for isoscalar factors reduced wigner coefficients for the couplings p0 0q to 0 and p10 p20 to 0 in the chains su4 su2 su2 and sun son n 3 are derived by using the algebra of complementary groups and methods of analytical continuation a review of alternative approaches to the problem grounded on the concept of biorthogonal systems of non canonical bases is given it is demonstrated that the construction of dual bases polynomial and stretched or related ones is associated with the use of certain bilinear combinations of isoscalar factors and solutions of the boundary value problem for isoscalar factors overlaps are given for different non canonical basis states of the two parametric irreducible representations for the chains su4 su2 su2 sun son and sp4 u2 as well as the expansions of the projected basis states for sp4 u2 in terms of canonical basis states a new expression for some special su2 clebsch gordan coefficients is also given

bose realization for non canonical representations of the symplectic group sp 4 su 2 u 1 a new method is formulated for the construction of arbitrary unitary irreducible representations of the compact symplectic group sp 4 o 5 in orthonormal bases which are reduced with respect to the non canonical group chain sp 4 su 2 u 1 the method is based on a realization of the algebra of generators and basis states by means of a system of bose creation and annihilation operators as an illustration some series of representations with multiplicities equal to or less than three are given in explicit algebraic form

bose realization of the sp 4 su 2 u 1 tensor operators a realization of irreducible tensor operators under the non canonical reduction of the compact symplectic group sp 4 o 5 su 2 u 1 is developed in terms of a system of bose creation and annihilation operators the method of derivation of their matrix elements is presented and some concrete cases are explicitly computed as illustration

coherent state theory of the noncompact symplectic group an extended coherent state theory is presented for the noncompact sp 3 r group which reveals a simple relationship between the sp 3 r algebra and its contracted u 3 boson limit the relationship is used to derive a remarkably accurate analytic expression for sp 3 r matrix elements for the generic lowest weight representations the expression is shown to be exact whenever the states involved are multiplicity free with respect to the u 3 subalgebra it is further shown how exact matrix elements are easily calculated in general dyson and holstein primakoff type u 3 boson expansions are given

finding local optima of high dimensional functions using direct search methods this paper focuses on a subclass of box constrained non linear optimization problems we are particularly concerned with settings where gradient information is unreliable or too costly to calculate and the function evaluations themselves are very costly this encourages the use of derivative free optimization methods and especially a subclass of these referred to as direct search methods the thrust of our investigation is twofold first we implement and evaluate a number of traditional direct search methods according to the premise that they should be suitable as local optimizers when used in a metaheuristic framework second we introduce a new direct search method based on scatter search designed to remedy the lack of a good derivative free method for solving problems of high dimensions our new direct search method has convergence properties comparable to those of existing methods in addition to being able to solve larger problems more effectively

dynamical group of microscopic collective states iii coherent state representations in d dimensions the present series of papers deals with various realizations of the dynamical group spc 2d r of microscopic collective states for an a nucleon system in d 1 2 or 3 dimensions when these collective states are assumed to be invariant under the orthogonal group o n associated with the n a 1 relative jacobi vectors in this paper we further study the barut girardello representation proposed in the first two papers of the present series to show that it may be reformulated in terms of some coherent states by generalizing to spc 2d r a class of sp 2 r coherent states introduced by barut and girardello for such purpose our starting point is another coherent state representation namely the perelomov one previously considered by kramer we also propose a third new class of coherent states leading to holstein primakoff representation in a straightforward way we review various properties of these three classes of coherent states such as their reproducing kernel and measure explicit forms their gener

vector coherent state representation theory a vector coherent state theory is formulated as a natural extension of standard coherent state theory it is shown that the godement representations and the coherent state representations of the sp n r groups of rowe and of deenen and quesne are special cases of this more general theory

vector coherent state theory as a theory of induced representations a general definition is given of vector coherent state vcs representation theory it is shown that the theory is more general than suggested by previous applications and that it incorporates the standard theories of induced representations as special cases the associated k matrix theory is also given a fuller treatment than hitherto and shown to provide a rather general algorithm both for projecting vcs representations from larger representations in which they are embedded and for determining the hermitian form with respect to which an isometric equivalent representation is in fact isometric

noncommutative pfaffians and classification of states of five dimensional quasi spin noncommutative pfaffians associated with an orthogonal algebra on are some special elements of the universal enveloping algebra u on using pfaffians we construct the fourth quantum number which together with the naturally defined three quantum numbers allows to classify the states of a five dimensional quasi spin the pfaffians are treated as creation operators for the new quantum number

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

racah s method for general subalgebra chains coupling coefficients of so 5 in canonical and physical bases it is shown that the method of infinitesimal generators racah s method can be broadly and systematically formulated as a method applicable to the calculation of reduced coupling coefficients for a generic subalgebra chain g h provided the reduced matrix elements of the generators of g and the recoupling coefficients of h are known the calculation of so 5 so 4 reduced coupling coefficients is considered as an example and a procedure for transformation of reduced coupling coefficients between canonical and physical subalegebra chains is presented the problem of calculating coupling coefficients for generic irreps of so 5 reduced with respect to any of its subalgebra chains is completely resolved by this approach

deforming maps for lie group covariant creation and annihilation operators any deformation of a weyl or clifford algebra a can be realized through a deforming map i e a formal change of generators in a this is true in particular if a is covariant under a lie algebra g and its deformation is induced by some triangular deformation uhg of the hopf algebra ug we propose a systematic method to construct all the corresponding deforming maps together with the corresponding realizations of the action of uhg the method is then generalized and explicitly applied to the case that uhg is the quantum group uhsl 2 a preliminary study of the status of deforming maps at the representation level shows in particular that deformed fock representations induced by a compact uhg can be interpreted as standard undeformed fock representations describing particles with ordinary bose or fermi statistics

small random perturbations of dynamical systems and the definition of attractors the strange attractors plotted by computers and seen in physical experiments do not necessarily have an open basin of attraction in view of this we study a new definition of attractors based on ideas of conley we argue that the attractors observed in the presence of small random perturbations correspond to this new definition

iterated local search for the quadratic assignment problem iterated local search ils is a simple and powerful stochastic local search method this article presents and analyzes the application of ils to the quadratic assignment problem qap we justify the potential usefulness of an ils approach to this problem by an analysis of the qap search space however an analysis of the run time behavior of a basic ils algorithm reveals a stagnation behavior which strongly compromises its performance to avoid this stagnation behavior we enhance the ils algorithm using acceptance criteria that allow moves to worse local optima and we propose population based ils extensions an experimental evaluation of the enhanced ils algorithms shows their excellent performance when compared to other state of the art algorithms for the qap

deformations of the fermion realization of the sp 4 algebra and its subalgebras with a view towards future applications in nuclear physics the fermion realization of the compact symplectic sp 4 algebra and its q deformed versions are investigated three important reduction chains of the sp 4 algebra are explored in both the classical and deformed cases the deformed realizations are based on distinct deformations of the fermion creation and annihilation operators for the primary reduction the su 2 substructure can be interpreted as either the spin isospin or angular momentum algebra whereas for the other two reductions su 2 can be associated with pairing between fermions of the same type or pairing between two distinct fermion types each reduction provides for a complete classification of the basis states the deformed induced u 2 representations are reducible in the action spaces of sp 4 and are decomposed into irreducible representations

speeding up continuous grasp abstract continuous grasp c grasp is a stochastic local search metaheuristic for finding cost efficient solutions to continuous global optimization problems subject to box constraints hirsch et al 2007 like a greedy randomized adaptive search procedure grasp a c grasp is a multi start procedure where a starting solution for local improvement is constructed in a greedy randomized fashion in this paper we describe several improvements that speed up the original c grasp and make it more robust we compare the new c grasp with the original version as well as with other algorithms from the recent literature on a set of benchmark multimodal test functions whose global minima are known hart s sequential stopping rule 1998 is implemented and c grasp is shown to converge on all test problems

generalized q deformed symplectic sp 4 algebra for multi shell applications am ulti shell generalization of a fermion representation of the q deformed compact symplectic spq 4 algebra is introduced an analytic form for the action of two or more generators of the spq 4 symmetry on the basis states is determined and the result used to derive formulae for the overlap between number preserving states as well as for matrix elements of a model hamiltonian a second order operator in the generators of spq 4 is identified that is diagonal in the basis set and that reduces to the casimir invariant of the sp 4 algebra in the non deformed limit of the theory the results can be used in nuclear structure applications to calculate decay transition probabilities and to provide for a description of pairing and higher order interactions in systems with nucleons occupying more than a single j orbital

a double rotor coherent state construction of the wigner supermultiplet su 4 contains implies su 2 su 2 a double rotor vector coherent state construction of the su 4 3 su 2 x sup wigner supermultiplet leads to a simple matrix representation of this scheme matrix elements of the vector coherent state realizations of the group generators are given by very simple expressions in tem of ordinary spin s and isospin t wigner coefficients with intrinsic projection labels ks and kg the k mawix technique is used to effectively elevate these labels lo the status of good quantum numbers the kkt matrices bre given in analytic form for a number of impomt irreducible representations

screening and vertex operators for u n screening and vertex operators for u n are given in terms of generators of the group left action on the flag manifold u n 1 su n their matrix elements in a basis of holomorphic sections of a vector bundle are computed

a new generalization of vector coherent state theory for the so 5 u 2 proton neutron quasispin group the introduction of a set of intrinsic coordinates to give an explicit construction of the intrinsic states of vector coherent state theory has greatly simplified earlier attempts to generalize this theory to include operators lying outside the group algebra very explicit vector coherent state construction of such operators can now be given in terms of vector coupled combinations of intrinsic and collective operators when organized into tensors which induce specific shifts in irreducible representations these lead to the reduced wigner coefficients needed in practical calculations the so 5 u 2 proton neutron quasispin algebra is used as an example to give further simplifications of earlier results all wigner coefficients needed to give the n t dependence of matrix elements in the seniority scheme can now be given through a few terms expressed solely through angular momentum recoupling coefficients and the k matrix elements of vector coherent state theory

in and out forests on combinatorial landscapes abstract fitness landscape theory is a mathematical framework for numerical analysis of search algorithms on combinatorial optimization problems we study a representation of fitness landscape as a weighted directed graph we consider out forest and in forest structures in this graph and establish important relationships among the forest structures of a directed graph the spectral properties of the laplacian matrices and the numbers of local optima of the landscape these relationships provide a new approach for computing the numbers of local optima for various problem instances and neighborhood structures

self organized critical forest fire model a forest fire model is introduced which contains a lightning probability f this leads to a self organized critical state in the limit f ensuremath rightarrow 0 provided that the time scales of tree growth and burning down of forest clusters are separated we derive scaling laws and calculate all critical exponents the values of the critical exponents are confirmed by computer simulations for a two dimensional system we show that the forest density in the critical state assumes its minimum possible value i e that energy dissipation is maximum

on the q oscillator and the quantum algebra suq 1 1 the authors discuss some problems of the q deformed harmonic oscillator different q bosonisations of the quantum suq 1 1 algebra are given and the corresponding infinite dimensional representations of discrete series are analysed

a new physical basis for the irreducible representations of the orthogonal group so 5 in the quasi spin formalism new physical state vectors for the irs of the group so 5 are constructed in an analytical form the state vectors are labelled by the quantum numbers of the isospin its third component by the number of particles and by a fourth properly defined quantum number the previously constructed bases have been compared with the new construction from the same point of view two examples illustrate the new construction

investigating a hybrid simulated annealing and local search algorithm for constrained optimization constrained optimization problems cop often take place in many practical applications such as kinematics chemical process optimization power systems and so on these problems are challenging in terms of identifying feasible solutions when constraints are non linear and non convex therefore finding the location of the global optimum in the non convex cop is more difficult as compared to non convex bound constrained global optimization problems this paper proposes a hybrid simulated annealing method hsa for solving the general cop hsa has features that address both feasibility and optimality issues and here it is supported by a local search procedure feasible sequential quadratic programming fsqp we develop two versions of hsa the first version hsap incorporates penalty methods for constraint handling and the second one hsad eliminates the need for imposing penalties in the objective function by tracing feasible and infeasible solution sequences independently numerical experiments show that the second version is more reliable in the worst case performance

vector coherent state theory and its application to the orthogonal groups vector coherent state theory is developed and presented in a form that explicitly exhibits its general applicability to the ladder representations of all semisimple lie groups and their lie algebras it is shown that in a suitable basis the vector coherent state inner product can be inferred algebraically by k matrix theory and changed to a simpler bargmann inner product thereby facilitating the explicit calculation of the matrix representaions of lie algebras applications are made to the even and odd orthogonal lie algebras

random assignment problems abstract analysis of random instances of optimization problems provides valuable insights into the behavior and properties of problem s solutions feasible region and optimal values especially in large scale cases a class of problems that have been studied extensively in the literature using the methods of probabilistic analysis is represented by the assignment problems and many important problems in operations research and computer science can be formulated as assignment problems this paper presents an overview of the recent results and developments in the area of probabilistic assignment problems including the linear and multidimensional assignment problems quadratic assignment problem etc

partially coherent states of the real symplectic group in the present paper we introduce partially coherent states for the positive discrete series irreducible representations d n 2 1 n 2 of sp 2d r encountered in physical applications these states are characterized by both continuous and discrete labels the latter specify the row of the irreducible representation 1 2 d of the maximal compact subgroup u d while the former parametrize an element of the factor space sp 2d r h where h is the sp 2d r subgroup leaving the 1 2 d representation space invariant we consider three classes of partially coherent states respectively generalizing the perelomov and barut girardello coherent states as well as some recently introduced intermediate coherent states we prove that each family of partially coherent states forms an overcomplete set in the representation space of d n 2 1 n 2 and study its generating function properties we show that it leads to a representation of the sp 2d r generators in the form of differential operato

molecular modeling of proteins and mathematical prediction of protein structure this paper discusses the mathematical formulation of and solution attempts for the so called protein folding problem the static aspect is concerned with how to predict the folded native tertiary structure of a protein given its sequence of amino acids the dynamic aspect asks about the possible pathways to folding and unfolding including the stability of the folded protein from a mathematical point of view there are several main sides to the static problem the selection of an appropriate potential energy function the parameter identification by fitting to experimental data and the global optimization of the potential the dynamic problem entails in addition the solution of because of multiple time scales very stiff ordinary or stochastic differential equations molecular dynamics simulation or in case of constrained molecular dynamics of differential algebraic equations a theme connecting the static and dynamic aspect is the determination and formation of secondary structure motifs the present paper gives a self contained introduction to the necessary background from physics and chemistry and surveys some of the literature it also discusses the various mathematical problems arising some deficiencies of the current models and algorithms and possible past and future attacks to arrive at solutions to the protein folding problem

induced shift tensors in vector coherent state theory it is shown that the so called shift tensors of biedenharn and louck have a natural expression within the framework of vector coherent state vcs theory vcs theory was developed to give a systematic construction of the representations of lie groups and to derive the corresponding matrices representing the elements of their lie algebras in this paper there are explicit realizations of shift tensors within the framework of vcs theory for semisimple lie groups in terms of shift tensors for suitably defined subgroups

tensor operators for quantum groups and applications tensor operators are defined for hopf algebras if the hopf algebra is quasitriangular the properly defined tensor product of tensor operators is a tensor operator in one application the problem of defining invariant correlation functions for the uq sl 2 symmetric spin 1 2 heisenberg chain is considered in another application it is shown that suitably modified bosonic and fermionic q creation and annihilation operators are tensor operators of uq sl n