convergence properties of the softassign quadratic assignment algorithm the softassign quadratic assignment algorithm is a discrete time continuous state synchronous updating optimizing neural network while its effectiveness has been shown in the traveling salesman problem graph matching and graph partitioning in thousands of simulations its convergence properties have not been studied here we construct discrete time lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction which show convergence to a fixed point the combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization

alien attractors and memory annihilation of structured sets in hopfield networks this paper considers the encoding of structured sets into hopfield associative memories a structured set is a set of vectors with equal hamming distance h from one another and its centroid is an external vector that has distance h 2 from every vector of the set structured sets having centroids are not infrequent when such a set is encoded into a noiseless hopfield associative memory using a bipolar outer product connection matrix and the network operates with synchronous neuronal update the memory of all encoded vectors is annihilated even for sets with as few as three vectors in dimension n 5 four for n 5 in such self annihilating structured sets the centroid emerges as a stable attractor we call it an alien attractor for canonical structured sets self annihilation takes place only if h n 2 self annihilation does not occur and alien attractors do not emerge in dimensions less than five

rst invariant image watermarking algorithm with mathematical modeling and analysis of the watermarking processes in this paper a new rotation and scaling invariant image watermarking scheme is proposed based on rotation invariant feature and image normalization a mathematical model is established to approximate the image based on the mixture generalized gaussian distribution which can facilitate the analysis of the watermarking processes using maximum a posteriori probability based image segmentation the cover image is segmented into several homogeneous areas each region can be represented by a generalized gaussian distribution which is critical for the analysis of the watermarking processes mathematically the rotation invariant features are extracted from the segmented areas and are selected as reference points subregions centered at the feature points are used for watermark embedding and extraction image normalization is applied to the subregions to achieve scaling invariance meanwhile the watermark embedding and extraction schemes are analyzed mathematically based on the established mathematical model the watermark embedding strength is adjusted adaptively using the noise visibility function and the probability of error is analyzed mathematically the mathematical relationship between fidelity and robustness is established the experimental results show the effectiveness and accuracy of the proposed scheme

dynamical analysis of continuous higher order hopfield networks for combinatorial optimization in this letter the ability of higher order hopfield networks to solve combinatorial optimization problems is assessed by means of a rigorous analysis of their properties the stability of the continuous network is almost completely clarified 1 hyperbolic interior equilibria which are unfeasible are unstable 2 the state cannot escape from the unitary hypercube and 3 a lyapunov function exists numerical methods used to implement the continuous equation on a computer should be designed with the aim of preserving these favorable properties the case of nonhyperbolic fixed points which occur when the hessian of the target function is the null matrix requires further study we prove that these nonhyperbolic interior fixed points are unstable in networks with three neurons and order two the conjecture that interior equilibria are unstable in the general case is left open

a theoretical investigation into the performance of the hopfield model an analysis is made of the behavior of the hopfield model as a content addressable memory cam and as a method of solving the traveling salesman problem tsp the analysis is based on the geometry of the subspace set up by the degenerate eigenvalues of the connection matrix the dynamic equation is shown to be equivalent to a projection of the input vector onto this subspace in the case of content addressable memory it is shown that spurious fixed points can occur at any corner of the hypercube that is on or near the subspace spanned by the memory vectors analysed is why the network can frequently converge to an invalid solution when applied to the traveling salesman problem energy function with these expressions the network can be made robust and can reliably solve the traveling salesman problem with tour sizes of 50 cities or more

optimal hopfield network for combinatorial optimization with linear cost function an optimal hopfield network is presented for combinatorial optimization problems with linear cost function it is proved that a vertex of the network state hypercube is asymptotically stable if and only if it is an optimal solution to the problem that is one can always obtain an optimal solution whenever the network converges to a vertex in this sense this network can be called the optimal hopfield network it is also shown through simulations of assignment problems that this network obtains optimal or nearly optimal solutions more frequently than other familiar hopfield networks

accelerated cartesian expansions a fast method for computing of potentials of the form r ν for all real ν abstract the need to compute potentials of the form r for 1 occur in a variety of areas ranging from electromagnetics to biophysics to molecular dynamics to astrophysics etc for instance coulomb london lennard jones h bonds are of the form 1 5 6 and 12 10 respectively for a systems with n source observation points the cost of computing these potentials scales proportional to o n 2 methods to overcome this computational bottleneck have been a popular research topic for quite some time for instance the fast multipole method fmm and their cousins tree codes have revolutionized the computation of electrostatic potentials 1 these methods rely on a hierarchical decomposition of the computational domain i e construction of a regular oct tree decomposition and exploits the principle of divide and conquer to compute potentials at each observation point this paper presents two methods in the vein of fmm albeit based on cartesian tensors the salient features of the first are as follows i it relies on totally symmetric tensors and ii the errors are independent of the height of the tree the second method is presented specifically for 1 and relies on traceless totally symmetric cartesian tensors using the relationship between traceless cartesian tensors and spherical harmonics it will be shown that this technique has the same computational cost as the classical fmm generalization of the second method for 1 is trivial however one needs to use totally symmetric tensors instead finally in the whole computation scheme only the translation operator that used to traverse across the tree depends on convergence of the proposed method is proven for all r numerical results that validate the cost and accuracy are presented for several potential functions these include those typically encountered in the analysis of physical systems coulombic lennard jones lattice gas

image watermarking based on invariant regions of scale space representation this paper proposes a novel content based image watermarking method based on invariant regions of an image the invariant regions are self adaptive image patches that deform with geometric transformations three different invariant region detection methods based on the scale space representation of an image were considered for watermarking at each invariant region the watermark is embedded after geometric normalization according to the shape of the region by binding watermarking with invariant regions resilience against geometric transformations can be readily obtained experimental results show that the proposed method is robust against various image processing steps including geometric transformations cropping filtering and jpeg compression

a review of hopfield neural networks for solving mathematical programming problems the hopfield neural network hnn is one major neural network nn for solving optimization or mathematical programming mp problems the major advantage of hnn is in its structure can be realized on an electronic circuit possibly on a vlsi very large scale integration circuit for an on line solver with a parallel distributed process the structure of hnn utilizes three common methods penalty functions lagrange multipliers and primal and dual methods to construct an energy function when the function reaches a steady state an approximate solution of the problem is obtained under the classes of these methods we further organize hnns by three types of mp problems linear non linear and mixed integer the essentials of each method are also discussed in details some remarks for utilizing hnn and difficulties are then addressed for the benefit of successive investigations finally conclusions are drawn and directions for future study are provided

harmonic analysis of homogeneous networks we introduce a generalization of mutually inhibitory networks called homogeneous networks such networks have symmetric connection strength matrices that are circulant one dimensional case or block circulant with circulant blocks two dimensional case fourier harmonics provide universal eigenvectors and we apply them to several homogeneous examples k wta k cluster on center off surround and the assignment problem we also analyze one nonhomogeneous case the subset sum problem we present the results of 10000 trials on a 50 node k cluster problem and 100 trials on a 25 node subset sum problem

moment based image normalization with high noise tolerance in this paper the effects of noise with nonzero mean on existing moment based image normalization methods are studied several modifications to reduce noise sensitivity are presented and tested they involve nonlinear mapping and fractional and negative order moments

rotation and scale independent pattern recognition through optimization this paper presents a two dimensional pattern recognition paradigm which is independent of rotation and scale it uses a hopfield neural network with a configuration similar to that employed for the traveling salesman problem tsp enhancements to the original hopfield design are included which are based on the eigenvalues of the connection matrix and on modifications suggested by simulations the goal of the method is to determine the underlying linear transformation between a test image and an observed input pattern by minimizing the energy of a hopfield network this procedure is easy to implement and is well suited for sparse binary images e g skeletalized representations or the output from vertex detection algorithms in this work the effects of noise are studied both analytically and through monte carlo techniques yielding some useful performance guidelines and greatly increasing the utility of the method experiments show that this technique performs successfully on a variety of rotated and scaled images and is robust against additive noise

on the selection of optimal feature region set for robust digital image watermarking a novel feature region selection method for robust digital image watermarking is proposed in this paper this method aims to select a nonoverlapping feature region set which has the greatest robustness against various attacks and can preserve image quality as much as possible after watermarked it first performs a simulated attacking procedure using some predefined attacks to evaluate the robustness of every candidate feature region according to the evaluation results it then adopts a track with pruning procedure to search a minimal primary feature set which can resist the most predefined attacks in order to enhance its resistance to undefined attacks under the constraint of preserving image quality the primary feature set is then extended by adding into some auxiliary feature regions this work is formulated as a multidimensional knapsack problem and solved by a genetic algorithm based approach the experimental results for stirmark attacks on some benchmark images support our expectation that the primary feature set can resist all the predefined attacks and its extension can enhance the robustness against undefined attacks comparing with some well known feature based methods the proposed method exhibits better performance in robust digital watermarking

accelerating boundary integral equation method using a special purpose computer we present a new solution to accelerate the boundary integral equation method biem the calculation time of the biem is dominated by the evaluation of the layer potential in the boundary integral equation we performed this task using mdgrape 2 a special purpose computer designed for molecular dynamics simulations mdgrape 2 calculates pairwise interactions among particles e g atoms and ions using hardwired pipeline processors we combined this hardware with an iterative solver during the iteration process mdgrape 2 evaluates the layer potential the rest of the calculation is performed on a conventional pc connected to mdgrape 2 we applied this solution to the laplace and helmholtz equations in three dimensions numerical tests showed that biem is accelerated by a factor of 10 100 our rather naive solution has a calculation cost of o n2 niter where n is the number of unknowns and niter is the number of iterations copyright 2005 john wiley sons ltd

cluster based blind nonlinear channel estimation a cluster based maximum likelihood sequence estimator mlse for nonlinear channels was described which consists of a clustering network and an mlse implemented by the viterbi algorithm the cluster based mlse can be used for digital communication through nonlinear finite length channels because channel mapping estimation is used instead of channel estimation in the conventional mlse the clustering network of the cluster based mlse which estimates the channel mapping between the signal input vectors and the noiseless channel outputs is a supervised network and requires a training sequence we propose a blind channel mapping estimator to estimate the channel mapping without using the training sequence the blind channel mapping estimator has a clustering block and a mapping block the clustering block estimates the channel outputs which represent the channel mapping subject to an unknown permutation operation because no training sequence is utilized that permutation operation is resolved by the mapping block and therefore the channel mapping is obtained introducing the blind channel mapping estimator into the cluster based mlse a blind cluster based mlse for nonlinear channels can be done computer simulations of the blind channel mapping estimator and the blind mlse for nonlinear channels are presented

a feature based robust digital image watermarking scheme a robust digital image watermarking scheme that combines image feature extraction and image normalization is proposed the goal is to resist both geometric distortion and signal processing attacks we adopt a feature extraction method called mexican hat wavelet scale interaction the extracted feature points can survive a variety of attacks and be used as reference points for both watermark embedding and detection the normalized image of an image object is nearly invariant with respect to rotations as a result the watermark detection task can be much simplified when it is applied to the normalized image however because image normalization is sensitive to image local variation we apply image normalization to nonoverlapped image disks separately the disks are centered at the extracted feature points several copies of a 16 bit watermark sequence are embedded in the original image to improve the robustness of watermarks simulation results show that our scheme can survive low quality jpeg compression color reduction sharpening gaussian filtering median filtering row or column removal shearing rotation local warping cropping and linear geometric transformations

approximating maximum clique with a hopfield network in a graph a clique is a set of vertices such that every pair is connected by an edge max clique is the optimization problem of finding the largest clique in a given graph and is np hard even to approximate well several real world and theory problems can be modeled as max clique in this paper we efficiently approximate max clique in a special case of the hopfield network whose stable states are maximal cliques we present several energy descent optimizing dynamics both discrete deterministic and stochastic and continuous one of these emulates as special cases two well known greedy algorithms for approximating max clique we report on detailed empirical comparisons on random graphs and on harder ones mean field annealing an efficient approximation to simulated annealing and a stochastic dynamics are the narrow but clear winners all dynamics approximate much better than one which emulates a naive greedy heuristic

a hybrid neural network model for solving optimization problems a hybrid neural network model for solving optimization problems is proposed an energy function which contains the constraints and cost criteria of an optimization problem is derived and then the neural network is used to find the global minimum or maximum of the energy function which corresponds to a solution of the optimization problem the network contains two subnets a constraint network and a goal network the constraint network models the constraints of an optimization problem and computes the gradient updating value of each neuron such that the energy function monotonically converges to satisfy all constraints of the problem the goal network points out the direction of convergence for finding an optimal value for the cost criteria these two subnets ensure that the neural network finds feasible as well as optimal or near optimal solutions the traveling salesman problem and the hamiltonian cycle problem are used to demonstrate the method

a vorticity based method for incompressible unsteady viscous flows a novel approach is presented based on the integral form of the vorticity formulation in which the vorticity transport equation is solved by using the cell centred finite volume method while the velocities needed at the centre of each control volume are calculated by a modified biot savart formula in conjunction with a fast summation algorithm the vorticity and mass conservation in the flow are guaranteed during the calculation by virtue of the finite volume approach and the method of implementing the boundary conditions at the body surface as an example both the early stage development and long term evolution of the flow around an impulsively started circular cylinder are computed using the method the present results are compared with other numerical and experimental results for the same flow problem and show good agreement

a novel image watermarking scheme based on amplitude attack this paper presents a novel image watermark scheme based on the characteristics of amplitude attacks first of all the analysis of amplitude attacks is performed then the amplitude attacks are categorized into three types positive attack negative attack and random attack finally based on these attack types we design three corresponding detectors the detectors remove the unreliable discrete cosine transform dct coefficients in the attacked image so that only reliable coefficients are used for the extraction of the watermark embedded the experimental results indicate that the proposed technique improves robustness significantly without sacrificing the false alarm rate

rotation invariant watermark embedding based on scale adapted characteristic regions rotation invariance is one of the most challenging issues in robust image watermarking this paper presents two rotation invariant watermark embedding schemes in the non subsampled contourlet transform nsct domain based on the scale adapted local regions watermark synchronization is achieved using the scale space feature point based local characteristic regions the first method embeds a binary watermark sequence by partitioning the local regions in a rotation invariant pattern the second method embeds a binary watermark image in a content based manner and the watermark signal is adaptive to the orientation of the image both methods achieve rotation invariant embedding by only using the rotation normalizing angle thus no interpolation operation is performed extensive simulation results and comparisons show that the proposed schemes can efficiently resist both signal processing attacks and geometric attacks

a parallel version of the fast multipole method abstract this paper presents a parallel version of the fast multipole method fmm the fmm is a recently developed scheme for the evaluation of the potential and force fields in systems of particles whose interactions are coulombic or gravitational in nature the sequential method requires o n operations to obtain the fields due to n charges rather than the o n2 operations required by the direct calculation here we describe the modifications necessary for implementation of the method on parallel architectures and show that the expected time requirements grow as log n when using n processors numerical results are given for a shared memory machine the encore multimax 320

a parallel directional fast multipole method this paper introduces a parallel directional fast multipole method fmm for solving n body problems with highly oscillatory kernels with a focus on the helmholtz kernel in three dimensions this class of oscillatory kernels requires a more restrictive low rank criterion than that of the low frequency regime and thus effective parallelizations must adapt to the modified data dependencies we propose a simple partition at a fixed level of the octree and show that if the partitions are properly balanced between p processes the overall runtime is essentially mathcal o n log n p p by the structure of the low rank criterion we are able to avoid communication at the top of the octree we demonstrate the effectiveness of our parallelization on several challenging models

formulating and solving production planning problems production planning problems frequently involve the assignment of jobs or operations to machines the simplest model of this problem is the well known assignment problem ap however due to simplifying assumptions this model does not provide implementable solutions for many actual production planning problems extensions of the simple assignment model known as the generalized assignment problem gap and the multi resource generalized assignment problem mrgap have been developed to overcome this difficulty this paper presents an extension of the mrgap to allow splitting individual batches across multiple machines while considering the effect of setup times and setup costs the extension is important for many actual production planning problems including ones in the injection molding industry and in the metal cutting industry we formulate models which are logical extensions of previous models which ignored batch splitting for the problem we address we then give different formulations and suggest adaptations of a genetic algorithm ga and simulated annealing sa a systematic evaluation of these algorithms as well as a lagrangian relaxation lr approach is presented

fusion of color edge detection and color quantization for color image watermarking using principal axes analysis in the past few years many gray level image watermarking schemes have been proposed although the extension to the color case is rare and regularly accomplished by marking the image luminance or by processing each color channel separately this paper presents a new color image watermarking scheme that combines color edge detection and color quantization using principal axes analysis in three dimensional color space the watermark is hidden within the data by modifying a subset of carefully selected edge points to resist both geometric distortion and signal processing attacks experimental results show the robustness of the proposed scheme to resist common attacks

polyhedral combinatorics and neural networks the often disappointing performance of optimizing neural networks can be partly attributed to the rather ad hoc manner in which problems are mapped onto them for solution in this paper a rigorous mapping is described for quadratic 0 1 programming problems with linear equality and inequality constraints this being the most general class of problem such networks can solve the problem s constraints define a polyhedron p containing all the valid solution points and the mapping guarantees strict confinement of the network s state vector to p however forcing convergence to a 0 1 point within p is shown to be generally intractable rendering the hopfield and similar models inapplicable to the vast majority of problems a modification of the tabu learning technique is presented as a more coherent approach to general problem solving with neural networks when tested on a collection of knapsack problems the modified dynamics produced some very encouraging results

a lagrange multiplier and hopfield type barrier function method for the traveling salesman problem a lagrange multiplier and hopfield type barrier function method is proposed for approximating a solution of the traveling salesman problem the method is derived from applications of lagrange multipliers and a hopfield type barrier function and attempts to produce a solution of high quality by generating a minimum point of a barrier problem for a sequence of descending values of the barrier parameter for any given value of the barrier parameter the method searches for a minimum point of the barrier problem in a feasible descent direction which has a desired property that lower and upper bounds on variables are always satisfied automatically if the step length is a number between zero and one at each iteration the feasible descent direction is found by updating lagrange multipliers with a globally convergent iterative procedure for any given value of the barrier parameter the method converges to a stationary point of the barrier problem without any condition on the objective function theoretical and numerical results show that the method seems more effective and efficient than the softassign algorithm

fast multipole accelerated singular boundary method for the 3d helmholtz equation in low frequency regime this paper presents a fast multipole accelerated singular boundary method sbm to the solution of the large scale three dimensional helmholtz equation at low frequency by using a desingularization strategy to directly compute singular kernels in the strong form collocation discretization the sbm formulations are derived for the dirichlet and neumann problems a fast multipole method fmm is then introduced to expedite the solution process the cpu time and the memory requirement of the fmmsbm scheme are both reduced to o n where n is the number of boundary nodes numerical examples with up to one million unknowns have been tested on a desktop computer the results clearly illustrate that the proposed strategy appears very efficient and promising in solving large scale helmholtz problems

natural discriminant analysis using interactive potts models natural discriminant analysis based on interactive potts models is developed in this work a generative model composed of piece wise multivariate gaussian distributions is used to characterize the input space exploring the embedded clustering and mixing structures and developing proper internal representations of input parameters the maximization of a log likelihood function measuring the fitness of all input parameters to the generative model and the minimization of a design cost summing up square errors between posterior outputs and desired outputs constitutes a mathematical framework for discriminant analysis we apply a hybrid of the mean field annealing and the gradient descent methods to the optimization of this framework and obtain multiple sets of interactive dynamics which realize coupled potts models for discriminant analysis the new learning process is a whole process of component analysis clustering analysis and labeling analysis its major improvement compared to the radial basis function and the support vector machine is described by using some artificial examples and a real world application to breast cancer diagnosis

communications overlapping in fast multipole particle dynamics methods in molecular dynamics the fast multipole method fmm is an attractive alternative to ewald summation for calculating electrostatic interactions due to the operation counts however when applied to small particle systems and taken to many processors it has a high demand for interprocessor communication in a distributed memory environment this demand severely limits applicability of the fmm to systems with o 10 k atoms we present an algorithm that allows for fine grained overlap of communication and computation while not sacrificing synchronization and determinism in the equations of motion the method avoids contention in the communication subsystem making it feasible to use the fmm for smaller systems on larger numbers of processors our algorithm also facilitates application of multiple time stepping techniques within the fmm we present scaling at a reasonably high level of accuracy compared with optimized ewald methods

designing asymmetric hopfield type associative memory with higher order hamming stability the problem of optimal asymmetric hopfield type associative memory ham design based on perceptron type learning algorithms is considered it is found that most of the existing methods considered the design problem as either 1 finding optimal hyperplanes according to normal distance from the prototype vectors to the hyperplane surface or 2 obtaining weight matrix w w sub ij by solving a constraint optimization problem in this paper we show that since the state space of the ham consists of only bipolar patterns i e v v sub 1 v sub 2 v sub n sup t spl isin 1 1 sup n the basins of attraction around each prototype training vector should be expanded by using hamming distance measure for this reason in this paper the design problem is considered from a different point of view our idea is to systematically increase the size of the training set according to the desired basin of attraction around each prototype vector we name this concept the higher order hamming stability and show that conventional minimum overlap algorithm can be modified to incorporate this concept experimental results show that the recall capability as well as the number of spurious memories are all improved by using the proposed method moreover it is well known that setting all self connections w sub ii spl forall i to zero has the effect of reducing the number of spurious memories in state space from the experimental results we find that the basin width around each prototype vector can be enlarged by allowing nonzero diagonal elements on learning of the weight matrix w if the magnitude of w sub ii is small for all i then the condition w sub ii 0 spl forall i can be relaxed without seriously affecting the number of spurious memories in the state space therefore the method proposed in this paper can be used to increase the basin width around each prototype vector with the cost of slightly increasing the number of spurious memories in the state space

energy function analysis of dynamic programming neural networks all analytical examination of the energy function associated with a dynamic programming neural network is presented the analysis is carried out in two steps first the locations and numbers of the minimum states for different components of the energy function are investigated in the extreme cases a clearer insight into the energy function can be gained through the minimum states of different components secondly the locations of the minimum states of the energy function using different parameter values are derived it is shown that the minimum states can reside in regions which are regarded as valid solutions with certain conditions examples and simulation results are given to justify the validity of the theories developed

gradient projection network analog solver for linearly constrained nonlinear programming an analog approach is presented for solving nonlinear programming problems with linear constraint conditions the present method is based on transformation of variables with exponential functions which enables every trajectory to pass through an interior of feasible regions along a gradient direction projected onto the feasible space convergence of its trajectory to the solution of optimization problems is guaranteed and it is shown that the present scheme is an extension of the affine scaling method for linear programming to nonlinear programs under a slight modification of riemannian metric an analog electronic circuit is also presented that implements the proposed scheme in real time

an analysis of the elastic net approach to the traveling salesman problem this paper analyzes the elastic net approach durbin and willshaw 1987 to the traveling salesman problem of finding the shortest path through a set of cities the elastic net approach jointly minimizes the length of an arbitrary path in the plane and the distance between the path points and the cities the tradeoff between these two requirements is controlled by a scale parameter k a global minimum is found for large k and is then tracked to a small value in this paper we show that 1 in the small k limit the elastic path passes arbitrarily close to all the cities but that only one path point is attracted to each city 2 in the large k limit the net lies at the center of the set of cities and 3 at a critical value of k the energy function bifurcates we also show that this method can be interpreted in terms of extremizing a probability distribution controlled by k the minimum at a given k corresponds to the maximum a posteriori map bayesian estimate of the tour under a natural statistical interpretation the analysis presented in this paper gives us a better understanding of the behavior of the elastic net allows us to better choose the parameters for the optimization and suggests how to extend the underlying ideas to other domains

a decomposition of multidimensional point sets with applications to k nearest neighbors and n body potential fields we define the notion of a well separated pair decomposition of points in d dimensional space we then develop efficient sequential and parallel algorithms for computing such a decomposition we apply the resulting decomposition to the efficient computation of k nearest neighbors and n body potential fields

affine legendre moment invariants for image watermarking robust to geometric distortions geometric distortions are generally simple and effective attacks for many watermarking methods they can make detection and extraction of the embedded watermark difficult or even impossible by destroying the synchronization between the watermark reader and the embedded watermark in this paper we propose a new watermarking approach which allows watermark detection and extraction under affine transformation attacks the novelty of our approach stands on a set of affine invariants we derived from legendre moments watermark embedding and detection are directly performed on this set of invariants we also show how these moments can be exploited for estimating the geometric distortion parameters in order to permit watermark extraction experimental results show that the proposed watermarking scheme is robust to a wide range of attacks geometric distortion filtering compression and additive noise

statistical physics algorithms that converge in recent years there has been significant interest in adapting techniques from statistical physics in particular mean field theory to provide deterministic heuristic algorithms for obtaining app

traditional heuristic versus hopfield neural network approaches to a car sequencing problem this paper considers the problem of optimally sequencing different car models along an assembly line according to some contiguity constraints while ensuring that the demands for each of the models are satisfied this car sequencing problem csp is a practical np hard combinatorial optimisation problem the csp is formulated as a nonlinear integer programming problem and it is shown that exact solutions to the problem are difficult to obtain due to the indefinite quadratic form of the csp objective function two traditional heuristics steepest descent and simulated annealing are employed to solve the csp approximately several hopfield neural network hnn approaches are also presented the process of mapping an optimisation problem onto a hnn is demonstrated explicitly and modifications to the existing neural approaches are presented which guarantee feasibility of solutions further modifications are proposed to improve the solution quality by permitting escape from local minima in an attempt to locate the global optimum results from all solutions techniques are compared on a set of instances of the csp and conclusions drawn

linear and logarithmic capacities in associative neural networks a model of associate memory incorporating global linearity and pointwise nonlinearities in a state space of n dimensional binary vectors is considered attention is focused on the ability to store a prescribed set of state vectors as attractors within the model within the framework of such associative nets a specific strategy for information storage that utilizes the spectrum of a linear operator is considered in some detail comparisons are made between this spectral strategy and a prior scheme that utilizes the sum of kronecker outer products of the prescribed set of state vectors which are to function nominally as memories the storage capacity of the spectral strategy is linear in n the dimension of the state space under consideration whereas an asymptotic result of n 4 log n holds for the storage capacity of the outer product scheme computer simulated results show that the spectral strategy stores information more efficiently the preprocessing costs incurred in the two algorithms are estimated and recursive strategies are developed for their computation

a novel optimizing network architecture with applications we present a novel optimizing network architecture with applications in vision learning pattern recognition and combinatorial optimization this architecture is constructed by combining the following techniques 1 deterministic annealing 2 self amplification 3 algebraic transformations 4 clocked objectives and 5 softassign deterministic annealing in conjunction with self amplification avoids poor local minima and ensures that a vertex of the hypercube is reached algebraic transformations and clocked objectives help partition the relaxation into distinct phases the problems considered have doubly stochastic matrix constraints or minor variations thereof we introduce a new technique softassign which is used to satisfy this constraint experimental results on different problems are presented and discussed

fast electrostatic force calculation on parallel computer clusters the fast multipole method fmm and smooth particle mesh ewald spme are well known fast algorithms to evaluate long range electrostatic interactions in molecular dynamics and other fields fmm is a multi scale method which reduces the computation cost by approximating the potential due to a group of particles at a large distance using few multipole functions this algorithm scales like o n for n particles spme algorithm is an o nlnn method which is based on an interpolation of the fourier space part of the ewald sum and evaluating the resulting convolutions using fast fourier transform fft those algorithms suffer from relatively poor efficiency on large parallel machines especially for mid size problems around hundreds of thousands of atoms a variation of the fmm called pwa based on plane wave expansions is presented in this paper a new parallelization strategy for pwa which takes advantage of the specific form of this expansion is described its parallel efficiency is compared with spme through detail time measurements on two different computer clusters

a general weight matrix formulation using optimal control classical methods from optimal control theory are used in deriving general forms for neural network weights the network learning or application task is encoded in a performance index of a general structure consequently different instances of this performance index lead to special cases of weight rules including some well known forms comparisons are made with the outer product rule spectral methods and recurrent back propagation simulation results and comparisons are presented

feature based watermarking using watermark template match this paper presents a robust digital image watermarking scheme using feature point detection and watermark template match a scale interactive model based filter is used to extract the feature points of original image based on which a watermark template is constructed and embedded adaptively into the local region of these points watermark decision is made by computing the statistical correlation between the watermark and the embedded region because the proposed feature detection is robust against jpeg compression filtering noise addition and geometric distortions the proposed watermarking scheme can achieve good performance against these attacks and experimental results also demonstrate the superiority

robust watermarking against geometric attacks using partial calculation of radial moments and interval phase modulation this paper presents a new image watermarking scheme which is blind and robust against geometric attacks the proposed algorithm is based on the features of radial moments in this algorithm the radial moments were first computed and then the watermark was embedded into the differential phase of various blocks of the original image using a special type of psk modulation called interval phase modulation ipm in order to embed the watermark into the phase of moments a particular method namely the partial calculation of moments was utilized for computation the implementation results show the improvement in the robustness and quality of the watermarked images in comparison with other methods

random interactions in higher order neural networks recurrent networks of polynomial threshold elements with random symmetric interactions are studied precise asymptotic estimates are derived for the expected number of fixed points as a function of the margin of stability in particular it is shown that there is a critical range of margins of stability depending on the degree of polynomial interaction such that the expected number of fixed points with margins below the critical range grows exponentially with the number of nodes in the network while the expected number of fixed points with margins above the critical range decreases exponentially with the number of nodes in the network the random energy model is also briefly examined and links with higher order neural networks and higher order spin glass models are made explicit

quickly tracing detection for spread spectrum watermark based on effect estimation of the affine transform recently watermarking synchronization and spread spectrum watermarking schemes have become two interesting new focuses of study in this paper we propose a method based on the synchronization pre estimation in order to resist geometric attacks first we utilize the global features by testing them against translation rotation and scaling and present a simple method to estimate the geometric transform kernel of the two dimensional gray image maps applying some correlative barycenters to the original are produced that can accurately reflect the affine transform feature of the image furthermore unknown variables existing in the kernel of the transform are calculated secondly the watermark is directly embedded in the spatial domain watermarking tracing is well performed on the watermarked image instead of performing an inverse geometrical transform on it experimental results show that the proposed scheme can work well under several kinds of geometrical attacks

high order symmetrical hyperbolic wavelets this paper studies high order wavelets of the first order hyperbolic choi williams cw and nth order hyperbolic kernels for analyses of digital time series by using their second and higher order derivatives for time domain investigations normalisation constants of the second fourth sixth eighth and tenth order hyperbolic and cw wavelets are numerically given for frequency domain investigations wavelet parameters including band peak frequencies minimum numbers of sampling points scale limits scale resolutions and total number of scales are explicitly given and numerically estimated for the fourth order hyperbolic and cw wavelets parameter comparisons among the morlet wavelet hyperbolic and cw second and fourth order wavelets are also given detection of periodicity and chaos in the duffing oscillator is discussed

localized image watermarking based on feature points of scale space representation this paper proposes a novel method for content based watermarking based on feature points of an image at each feature point the watermark is embedded after scale normalization according to the local characteristic scale characteristic scale is the maximum scale of the scale space representation of an image at the feature point by binding watermarking with the local characteristics of an image resilience against affine transformations can be obtained easily experimental results show that the proposed method is robust against various image processing steps including affine transformations cropping filtering and jpeg compression