topological bf theories in 3 and 4 dimensions in this paper we discuss topological bf theories in 3 and 4 dimensions observables are associated to ordinary knots and links in 3 dimensions and to 2 knots in 4 dimensions the vacuum expectation values of such observables give a wide range of invariants here we consider mainly the 3 dimensional case where these invariants include alexander polynomials homfly polynomials and kontsevich integrals

strongly stable equilibrium points of n person noncooperative games we introduce a concept of a strongly stable nash equilibrium point of an n person noncooperative game in normal form roughly speaking an equilibrium point is strongly stable if it changes continuously and uniquely against any small perturbation to payoffs of players we establish a necessary and sufficient condition for an equilibrium point to be strongly stable by the karush kuhn tuckcr optimality condition for nonlinear programs an equilibrium point is shown to correspond to a zero point of a certain pc1 mapping then our condition is stated in terms of the local nonsingularity of the jacobian matrix of this mapping our proof is based on the degree theory of mappings finally we give an example of a 3 person game with two nonquasi strong equilibrium points only one of which is strongly stable

combinatorial formulas for vassiliev invariants from chern simons gauge theory we analyze the perturbative series expansion of the vacuum expectation value of a wilson loop in chern simons gauge theory in the temporal gauge from the analysis emerges the notion of the kernel of a vassiliev invariant the kernel of a vassiliev invariant of order n is not a knot invariant since it depends on the regular knot projection chosen but it differs from a vassiliev invariant by terms that vanish on knots with n singular crossings we conjecture that vassiliev invariants can be reconstructed from their kernels we present the general form of the kernel of a vassiliev invariant and we describe the reconstruction of the full primitive vassiliev invariants at orders two three and four at orders two and three we recover known combinatorial expressions for these invariants at order four we present new combinatorial expressions for the two primitive vassiliev invariants present at this order

primitive vassiliev invariants and factorization in chern simons perturbation theory the general structure of the perturbative expansion of the vacuum expectation value of a wilson line operator in chern simons gauge field theory is analyzed the expansion is organized according to the independent group structures that appear at each order it is shown that the analysis is greatly simplified if the group factors are chosen in a certain way that we call canonical this enables us to show that the logarithm of a polynomial knot invariant can be written in terms of primitive vassiliev invariants only

uniqueness and differentiability of solutions of parametric nonlinear complementarity problems we derive conditions for the local uniqueness of solutions of nonlinear complementarity problems ncp we then prove the existence continuity and directional differentiability of a locally unique parametric solution of the parametric ncp under stronger assumptions in the absence of degeneracy this parametric solution is also shown to be continuously differentiable

an invariant of regular isotopy this paper studies a two variable laurent polynomial invariant of regular isotopy for classical unoriented knots and links this invariant is denoted lk for a link k and it satisfies the axioms 1 regularly isotopic links receive the same polynomial 2 lo0 1 3 l al l a l 4 l small diagrams indicate otherwise identical parts of larger diagrams regular isotopy is the equivalence relation generated by the reidemeister moves of type ii and type iii invariants of ambient isotopy are obtained from l by writhe normalization

explicit computation of the drinfeld associator in the case of the fundamental representation of gl n we solve the regularized knizhnik zamolodchikov equation and find an explicit expression for the drinfeld associator we restrict ourselves to the case of the fundamental representation of gl n several tests of the results are presented it can be explicitly seen that components of this solution for the associator coincide with certain components of the wzw conformal block for primary fields we introduce the symmetrized version of the drinfeld associator by dropping the odd terms the symmetrized associator gives the same knot invariants but has a simpler structure and is fully characterized by one symmetric function which we call the drinfeld prepotential

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

error analysis of maximum likelihood estimates of physical parameters from one or more dispersive waves measurement of physical parameters from one or more dispersive waves propagating in a band of frequencies across a linear array of receivers is considered the waves propagate according to a known physical model having real valued parameters and have spatially uncorrelated white gaussian noise added to them the objective of the measurement is to estimate a specified subset of the physical parameters the remaining physical parameters are externally provided and have known error statistics existing maximum likelihood ml estimation and cramer rao cr bounds theory describes the measurement under the assumption of correct values for the externally provided parameters a review of this theory is presented for completeness then a bounding estimate on the total error on the estimated parameters is derived which takes into account both the cr bounds and errors in the externally provided parameters suggestions for the application of the theory to practical problems are provided a criterion is derived for determining whether additional unwanted nuisance parameters should be included in the estimate to improve the total error on the desired parameters

application of degree theory in stability of the complementarity problem in this paper we study the behavior of a solution of the complementarity problem when the problem is perturbed the basic result is that if the degree of a certain function is nonzero then the problem is stable we show that several well known conditions for the existence of a solution to the problem also imply stability of the problem we also show that in the nondegenerate case there are simple conditions that ensure stability

a solution condition for complementarity problems with an application to spatial price equilibrium a sufficient condition is developed for the existence of solutions to complementarity problems which is applicable to all continuous functions in addition it is shown to imply a number of simpler conditions including the well known coerciveness condition finally this condition is applied to an existence problem in spatial price equilibrium where it is shown to yield not only a more general result but also a simpler method of proof

the jones polynomial for fluid knots from helicity in this paper we prove that under ideal conditions the helicity of fluid knots such as vortex filaments or magnetic flux tubes provides a fundamentally new topological means by which we may associate a topological invariant the jones polynomial that is much stronger than prior interpretations in terms of gauss linking numbers our proof is based on an extension of the kauffman bracket polynomial for unoriented knots explicit calculations of the jones polynomial for the left and right handed trefoil knots and for the whitehead link via the figure of eight knot are presented for illustration this novel approach establishes a topological foundation of classical field theory in general and of mathematical fluid dynamics in particular by opening up new directions of work both in theory and applications

exponentiated beta distributions beta distributions are usually defined on the unit interval 0 1 for wider applicability we introduce six exponentiated beta distributions and derive several of their properties including the moment generating function expectation variance skewness kurtosis shannon entropy and the renyi entropy

stable pseudomonotone variational inequality in reflexive banach spaces stability of a generalized variational inequality with either the mapping or the set perturbed is discussed in reflexive banach spaces provided that the mappings are pseudomonotone in the sense of karamardian as a byproduct generalized variational inequality having nonempty and bounded set is proved to be equivalent to the strictly feasibility

the chern simons theory and knot polynomials the chern simons gauge theory is studied using a functional integral quantization this leads to a differential equation for expectations of wilson lines the solution of this differential equation is shown to be simply related to the two variable jones polynomial of the corresponding link in the case where the gauge group issu n a similar equation has been used before to get the jones polynomial from a braid representation of the link the main novelty of our approach is that we get the jones polynomial from a plat representation of the link

a direct derivation of polynomial invariants from perturbative chern simons gauge theory there have been several methods to show that the expectation values of wilson loop operators in the su n chern simons gauge theory satisfy the homfly skein relation we shall give another method from the perturbative method of the su n chern simons gauge theory in the light cone gauge which is more direct than already known methods

the connected components of the set of r0 matrices abstract a matrix m is an r0 matrix if it satisfies a nondegeneracy property that is often assumed for the linear complementarity problem this property can be verified from the incidence structure of a polytope defined by m it is shown that a 3 x 3 matrix in r0 can be perturbed within r0 so that the associated polytope is one of seven types each corresponding to a different component of r0

knot theory and the heuristics of functional integration abstract this paper is an exposition of the relationship between the heuristics of witten s functional integral and the theory of knots and links in three dimensional space

a homological characterization of q matrices a real square matrix m is said to be a q matrix if the linear complementarity problem q m has a solution for every vector q there is as yet no characterization of q matrices which makes it easy to determine whether or not a given matrix is q ideas from topology in particular degreetheory have previously been used to obtain sufficient conditions for when a matrix is q in this paper we will apply some other ideas from topology to give a homological characterization of q matrices continuing to borrow from topology we define the nerve of a matrix which along with our characterization leads to an algorithm for checking whether or not a matrix is q this algorithm has smaller bounds on its worst case time complexity than previous methods

the degree of an exact order matrix the classes of exact order k matrices for any positive integer k were defined and studied by mohan parthasarathy and sridhar mohan s r t parthasarathy r sridhar 1994 the linear complementarity problem with exact order matrices math oper res 19 618 644 here we prove results on the linear complementarity problem lcpq m for m belonging to the class of exact order k k 3 using the concepts of degree theory our main result in this paper consists in proving that a matrix m rn n of exact order k for any positive integer n k 3 belongs to the class q if and only if the degree of m is either 1 or 1 also a complete characterization of exact order 2 matrices is presented in terms of their inverse structure

a relation between the kauffman and the homfly polynomials for torus knots polynomial invariants corresponding to the fundamental representation of the gauge group so n are computed for arbitrary torus knots in the framework of chern simons gauge theory making use of knot operators as a result a formula that relates the kauffman and the homfly polynomials for torus knots is presented

applications of degree theory to linear complementarity problems in this paper we consider two applications of degree theory to linear complementarity problems in the first application we study the stability of an lcp at a solution point specifically we prove the stability of an lcp corresponding to a p0 matrix at an isolated solution using a recent degree formula due to stewart 1991 we strengthen a stability result of gowda and pang 1992 in the second application we use the same degree formula of stewart to describe the number of solutions of lcpm q when m is a negative almost n matrix this analysis leads to a lipschitzian characterization of the solution map i q solm q corresponding to a nondegenerate negative matrix

maximum likelihood localization of multiple sources by alternating projection an algorithm referred to as apm for computing the maximum likelihood estimator of the locations of simple sources in passive sensor arrays is presented the algorithm is equally applicable to the case of coherent signals and to the case of a single snapshot the algorithm is iterative the maximum of the likelihood function is computed by successive approximations the convergence of the algorithm to the global maximum is demonstrated for a variety of scenarios the key to this global convergence is the initialization scheme

on solution stability of the linear complementarity problem in the paper 5 c d ha introduced the notion of stability of a linear complementarity problem at a solution point and established several sufficient conditions for stability to hold in the present paper we derive some new stability results which significantly improve ha s results included in these new results are i a complete characterization of the stability condition under a nonsingularity assumption and ii further characterizations of solution stability in the case of a linear complementarity problem with a fully semimonotone matrix

error bars for sonic slowness measurements semblance provides a quality indicator for beam former array processing methods such as slowness time coherence stc and dispersive stc dstc semblance does not indicate the slowness variance because the array design the processing time bandwidth parameters and the signal spectral content are not taken into account for the classical case of a single propagating wave with added gaussian noise semblance is distributed according to the noncentral beta distribution this distribution is parameterized by the number of receivers m the processing time bandwidth product bt and signal to noise ratio given m and bt the measured semblance can be inverted to give a high quality estimate of the signal to noise ratio the cramer rao lower bounds on slowness variance for the classical case of signals in added gaussian noise depend on the array dimensions the signal power spectrum and the signal to noise ratio estimates of the cramer rao bounds can be calculated from the estimated signal to noise ratio an

local indices for degenerate variational inequalities we provide an index formula for solutions of variational inequality problems defined by a continuously differentiable function f over a convex set m represented by a finite number of inequality constraints our index formula can be applied when the solutions are nonsingular and possibly degenerate as long as they also satisfy the injective normal map inm property which is implied by strong stability we show that when the inm property holds the degeneracy in a solution can be removed by perturbing the function f slightly i e the index of a degenerate solution is equal to the index of a nondegenerate solution of a slightly perturbed variational inequality problem we further show that our definition of the index is equivalent to the topological index of the normal map at the zero corresponding to the solution as an application of our index formula we provide a global index theorem for variational inequalities which holds even when the solutions are degenerate

robust stochastic resonance for simple threshold neurons simulation and theoretical results show that memoryless threshold neurons benefit from small amounts of almost all types of additive noise and so produce the stochastic resonance or sr effect input output mutual information measures the performance of such threshold systems that use subthreshold signals the sr result holds for all possible noise probability density functions with finite variance the only constraint is that the noise mean must fall outside a forbidden threshold related interval that the user can control a new theorem shows that this condition is also necessary a corollary and simulations show that the sr effect occurs for right sided beta and weibull noise as well these sr results further hold for the entire uncountably infinite class of alpha stable probability density functions alpha stable noise densities have infinite variance and infinite higher order moments and often model impulsive noise environments the stable noise densities include the special case of symmetric bell curve densities with thick tails such as the cauchy probability density the sr result for alpha stable noise densities shows that the sr effect in threshold and thresholdlike systems is robust against occasional or even frequent violent fluctuations in noise regression analysis reveals both an exponential relationship for the optimal noise dispersion as a function of the alpha bell curve tail thickness and an approximate linear relationship for the sr maximal mutual information as a function of the alpha bell curve tail thickness

structural and stability properties of p 0 nonlinear complementarity problems we consider p0 nonlinear complementarity problems and study the connectedness and stability of the solutions by applying degree theory and the mountain pass theorem to a smooth reformulation of the complementarity problem we show that the solution set is connected and bounded if a bounded isolated component of the solution set exists and that a solution is locally unique if and only if it is globally unique furthermore we prove that a solution is stable in ha s sense if and only if it is globally unique while the complementarity problem is stable if and only if the solution set is bounded

vassiliev knot invariants and chern simons perturbation theory to all orders at any order the perturbative expansion of the expectation values of wilson lines in chern simons theory gives certain integral expressions we show that they all lead to knot invariants moreover these are finite type invariants whose order coincides with the order in the perturbative expansion together they combine to give a universal vassiliev invariant

stability analysis of variational inequalities and nonlinear complementarity problems via the mixed linear complementarity problem and degree theory this paper is concerned with the mixed linear complementarity problem and the role it and its variants play in the stability analysis of the nonlinear complementarity problem and the karush kuhn tucker system of a variational inequality problem under a nonsingular assumption the mixed linear complementarity problem can be converted to the standard problem in this case the rich theory of the latter can be directly applied to the former in this work we employ degree theory to derive some sufficient conditions for the existence of a solution to the mixed linear complementarity problem in the absence of the nonsingularity property next we extend this existence theory to the mixed nonlinear complementarity problem and establish a main stability result under a certain degree theoretic assumption concerning the linearized problem we then specialize this stability result and its consequences to the parametric variational inequality problem under the assumption of a unique set of multipliers finally we

stability of the linear complementarity problem at a solution point in this paper we study the behavior of a solution of the linear complementarity problem when data are perturbed we give characterizations of strong stability of the linear complementarity problem at a solution in the case of stability we give sufficient and necessary conditions

a bifurcation analysis of the nonlinear parametric programming problem the structure of solutions to the nonlinear parametric programming problem with a one dimensional parameter is analyzed in terms of the bifurcation behavior of the curves of critical points and the persistence of minima along these curves changes in the structure of the solution occur at singularities of a nonlinear system of equations motivated by the fritz john first order necessary conditions it has been shown that these singularities may be completely partitioned into seven distinct classes based upon the violation of one or more of the following a complementarity condition a constraint qualification and the nonsingularity of the hessian of the lagrangian on a tangent space to apply classical bifurcation techniques to these singularities a further subdivision of each case is necessary the structure of curves of critical points near singularities of lowest zero codimension within each case is analyzed as well as the persistence of minima along curves emanating from these singularities bifurcation behavior is also investigated or discussed for many of the subcases giving rise to a codimension one singularity

an index formula for degenerate lcps a degree formula for the topological index of an isolated possibly degenerate solution of a linear complementary problem is derived this is used to answer affirmatively a recent conjecture of broyden regarding the parities of degenerate solutions

bifurcation problems in nonlinear parametric programming the nonlinear parametric programming problem is reformulated as a closed system of nonlinear equations so that numerical continuation and bifurcation techniques can be used to investigate the dependence of the optimal solution on the system parameters this system which is motivated by the fritz john first order necessary conditions contains all fritz john and all karush kuhn tucker points as well as local minima and maxima saddle points feasible and nonfeasible critical points necessary and sufficient conditions for a singularity to occur in this system are characterized in terms of the loss of a complementarity condition the linear dependence of the gradients of the active constraints and the singularity of the hessian of the lagrangian on a tangent space any singularity can be placed in one of seven distinct classes depending upon which subset of these three conditions hold true at a solution for problems with one parameter we analyze simple and multiple bifurcation of critical points from a singularity arising from the loss of the complementarity condition and then develop a set of conditions which guarantees the unique persistence of a minimum through this singularity

kontsevich integral for vassiliev invariants from chern simons perturbation theory in the light cone gauge we analyze the structure of the perturbative series expansion of chern simons gauge theory in the light cone gauge after introducing a regularization prescription that entails the consideration of framed knots we present the general form of the vacuum expectation value of a wilson loop the resulting expression turns out to give the same framing dependence as the one obtained using nonperturbative methods and perturbative methods in covariant gauges it also contains the kontsevich integral for vassiliev invariants of framed knots

on the self linking of knots this note describes a subcomplex f of the de rham complex of parametrized knot space which is combinatorial over a number of universal anomaly integrals the self linking integrals of guadaguini martellini and mintchev perturbative aspects of chern simons field theory phys lett b 227 111 1989 and bar natan perturbative aspects of the chern simons topological quantum field theory ph d thesis princeton university 1991 also on the vassiliev knot invariants to appear in topology are seen to represent the first nontrivial element in h0 f occurring at level 4 and are anomaly free however already at the next level an anomalous term is possible