a constructive algorithm for binary neural networks the oil spot algorithm this paper presents a constructive training algorithm for supervised neural networks the algorithm relies on a topological approach based on the representation of the mapping of interest onto the binary hypercube of the input space it dynamically constructs a two layer neural network by involving successively binary examples a convenient treatment of real valued data is possible by means of a suitable real to binary codification in the case of target functions that have efficient halfspace union representations simulations show the constructed networks result optimized in terms of number of neurons

efficient modification scheme of stress strain tensor for wrinkled membranes a new modification scheme of the stress strain tensor for wrinkled membranes is presented on the basis of the tension field theory the scheme is applicable to finite element analysis of partly wrinkled membranes with arbitrary shapes derivation of the modification scheme rests on an introduction of the so called wrinkle strain and a simplification of the virtual work equation of wrinkled membranes because all of the modifications required to account for wrinkling are totally confined within the stress strain relations of membranes the scheme can be easily implemented with existing finite element codes furthermore the modified stress strain tensor automatically leads to the consistent tangent stiffness matrix where changes in both the wrinkling direction and the amount of wrinkliness are taken into account three numerical examples are treated to show the accuracy and effectiveness of the proposed modification scheme

large scale nonlinear deterministic and stochastic optimization formulations involving simulation of subsurface contamination once subsurface water supplies become contaminated designing cost effective and reliable remediation schemes becomes a difficult task the combination of finite element simulation of groundwater contaminant transport with nonlinear optimization is one approach to determine the best well selection and optimal fluid withdrawal and injection rates to contain and remove the contaminated water both deterministic and stochastic programming problems have been formulated and solved these tend to be large scale problems owing to the simulation component which serves as a portion of the constraint set the overall problem of combined groundwater process simulation and nonlinear optimization is discussed along with example problems because the contaminant transport simulation models give highly uncertain results quantifying their uncertainty and incorporating reliability into the remediation design results in a class of large stochastic nonlinear problems the reliability problem is beginning to be addressed and some strategies and formulations involving chance constraints and monte carlo methods are presented

the statistical mechanics of constructive algorithms the storage capacity of multilayer networks with overlapping receptive fields is studied for constructive algorithms using boolean perceptrons as their basic building block which have been investigated within a replica framework the assumption of weak coupling between subsequently constructed perceptrons is verified within a replica symmetric rs ansatz and shown to be negligible in most cases in comparison with correction due to replica symmetry breaking rsb in individual perceptrons the capacities of a tiling like and variants of the upstart algorithm are then calculated within rs and one step rsb with the quenched average taken over the individual units separately for networks with up to k 4000 and k 600 units respectively within this treatment the storage capacity seems to exhibit a power law behaviour in with an exponent n that may depend on the algorithm and the stability however due to finite size effects in k reliable estimates of n could not be extracted nevertheless the results strongly indicate that n should be strictly smaller than 1 within one step rsb whereas within rs the mitchison durbin bound is violated for finite k and n 1 may hold asymptotically

a method for globally minimizing concave functions over convex sets a method is described for globally minimizing concave functions over convex sets whose defining constraints may be nonlinear the algorithm generates linear programs whose solutions minimize the convex envelope of the original function over successively tighter polytopes enclosing the feasible region the algorithm does not involve cuts of the feasible region requires only simplex pivot operations and univariate search computations to be performed allows the objective function to be lower semicontinuous and nonseparable and is guaranteed to converge to the global solution computational aspects of the algorithm are discussed

carve a constructive algorithm for real valued examples a constructive neural network algorithm is presented for any consistent classification task on real valued training vectors the algorithm constructs a feedforward network with a single hidden layer of threshold units which implements the task the algorithm which we call carve extends the sequential learning algorithm of marchand et al 1990 from boolean inputs to the real valued input case and uses convex hull methods for the determination of the network weights the algorithm is an efficient training scheme for producing near minimal network solutions for arbitrary classification tasks the algorithm is applied to a number of benchmark problems including german and sejnowski s sonar data the monks problems and fisher s iris data a significant application of the constructive algorithm is in providing an initial network topology and initial weights for other neural network training schemes and this is demonstrated by application to backpropagation

inflating a flat toroidal membrane abstract a flat toroidal geometry composed of a stack of two flat annular membranes bonded together at the inner and outer boundaries equators is proposed the finite inflation mechanics of the composite membrane under uniform internal pressure is considered the membranes are assumed to be identical homogeneous and isotropic solids described by the gent hyperelastic model with a relaxed strain energy density function the variational inflation mechanics problem yields the governing equations and boundary conditions which are recast as a nonlinear two point boundary value problem in a suitable form for efficient computation the effects of the inflation pressure and material properties on the state of stretch and geometry of the inflated toroidal membrane are obtained which exhibit a number of desirable features the phenomenon of wrinkling instability is observed near the outer equator of the torus at low pressures in spite of a positive gaussian curvature which is exactly opposite to the behavior observed in a curved torus wrinkling at the inner equator at high pressure semi analytical expressions of the cauchy stress resultants are obtained which match well with the numerical computations further the limit point instability pressure of the toroidal membrane is shown to have a remarkable power law dependence on a geometric parameter of the uninflated flat torus and the material chain extensibility parameter involving two universal constants

capacity of the single layer perceptron and minimal trajectory training algorithms the entire set of binary vectors to be stored using a single layer perceptron can be divided into two groups one for which the output neuron state consistently equals one of the input neuron states and a second for which the output neuron state consistently negates the same input neuron the capacity of the single layer perceptron depends on the ratio between these two groups this dependence is examined via statistical mechanical methods producing the probability of obtaining a linearly separable solution for a random selection of input output relations for a given value of the above ratio this probability is extremely useful for designing recurrent neural network training algorithms these algorithms make use of the obtained results to select the most probable internal representations to be realized in such nets moreover the distribution of the linearly separable binary functions enables one to obtain a good estimate for the total number of linearly separable binary functions for a certain number of input neurons a task considered as a hard computational problem additional incentives for carrying out the calculation are understanding the capacity of simple nets for certain types of input output correlations and laying the foundations for analysing some constructive training algorithms such as the tiling and upstart algorithms all results show consistency with existing theoretical results

approximate mixed integer nonlinear programming methods for optimal aquifer remediation design an optimal aquifer remediation design model employing a nonlinear programming algorithm was developed to find the minimum cost design of a pump and treat aquifer remediation system the mixed integer nonlinear programming model includes the discontinuous fixed costs of system construction and installation as well as operation and maintenance the fixed cost terms in the objective function have been approximated by continuous functions of the decision variables using a polynomial penalty coefficient method resulting in a nonlinear programming formulation of an otherwise mixed integer nonlinear programming model results of applying the new polynomial penalty coefficient method to an example design problem show that a combined well field and treatment process model hat includes fixed costs has a significant impact on the design and cost of aquifer remediation systems reducing system costs by using fewer larger flow rate wells previous pump and treat design formulations have resulted in systems with numerous low flow rate wells due to the use of simplified cost functions that do not exhibit economies of scale or fixed costs the polynomial penalty coefficient method results were compared to two alternative approximate mixed integer nonlinear programming methods for solving optimal quifer remediation design problems the pseudo integer method and the exponential penalty coefficient method the polynomial penalty coefficient method obtains the same solutions and performs as well as or better than the exponential penalty coefficient method the polynomial penalty coefficient method almost always results in better less expensive designs and requires significantly less computer time than the pseudo integer method

construction algorithm for the parity machine abstract an algorithm for the training of a special multilayered feed forward neural network is presented the strategy is very similar to the well known tiling algorithm yet the resulting architecture is completely different neurons are added in one layer only the output of the network is given by the product of its k many hidden neurons which is for 1 units the result of the parity operation the capacity c of a network trained according to the algorithm is estimated for the storage of randomly defined classifications the asymptotic dependence is found to be c k ln k for k this is in agreement with recent analytic results for the algorithm independent storage capacity of a parity machine

multistate perceptrons learning rule and perceptron of maximal stability a new perceptron learning rule which works with multilayer neural networks made of multistate units is obtained and the corresponding convergence theorem is proved the definition of a perceptron of maximal stability is enlarged in order to include these new multistate perceptrons and a proof of the existence and uniqueness of such optimal solutions is outlined

numerical study of the wrinkling of a stretched thin sheet a thin sheet clamped at opposite ends and stretched develops wrinkles parallel to the direction of the applied tensile strain due to the hindered poisson lateral contraction at the clamps to study this phenomenon a variational model recently proposed by puntel deseri and fried is adopted the relevant energy functional includes bending and membranal contributions and is minimized subject to a constraint on the area of the mid surface of the sheet a fourth order partial differential equation is henceforth obtained and numerically implemented using b splines predictions are obtained concerning the number of wrinkles critical applied stretches and scaling relationships for wrinkle amplitude and wavelength both a linearized version of the boundary value problem based on the small slope approximation and a fully nonlinear one are considered their results are found to be in good agreement for the whole range of applied stretches taken into account comparisons with previous analytical results by puntel deseri and fried who used different boundary conditions and an ansatz on the deflection function are also provided the numerical results substantially confirm the validity of the analytical predictions the present work provides then an alternative numerical method for the study of wrinkling in thin sheets and supports the use of analytical and semi analytical solutions as viable options for specific geometries though further investigation particularly experimental is still needed extensive comparisons of the results with other studies available in the literature provide confirmation for the scaling laws and signal that predicted values of the critical stretches may only be accurate for higher length to width aspect ratios

a hierarchy of plate models derived from nonlinear elasticity by gamma convergence we derive a hierarchy of plate models from three dimensional nonlinear elasticity by convergence what distinguishes the different limit models is the scaling of the elastic energy per unit volume h where h is the thickness of the plate this is in turn related to the strength of the applied force h membrane theory derived earlier by le dret and raoult corresponds to 0 nonlinear bending theory to 2 von karman theory to 3 4 and linearized vk theory to 3 intermediate values of lead to certain theories with constraints a key ingredient in the proof is a generalization to higher derivatives of our rigidity result 29 which states that for maps v 0 1 3 3 the l2 distance of v from a single rotation is bounded by a multiple of the l2 distance from the set so 3 of all rotations

universal perceptron and dna like learning algorithm for binary neural networks lsbf and pbf implementations universal perceptron up a generalization of rosenblatt s perceptron is considered in this paper which is capable of implementing all boolean functions bfs in the classification of bfs there are 1 linearly separable boolean function lsbf class 2 parity boolean function pbf class and 3 non lsbf and non pbf class to implement these functions up takes different kinds of simple topological structures in which each contains at most one hidden layer along with the smallest possible number of hidden neurons inspired by the concept of dna sequences in biological systems a novel learning algorithm named dna like learning is developed which is able to quickly train a network with any prescribed bf the focus is on performing lsbf and pbf by a single layer perceptron slp with the new algorithm two criteria for lsbf and pbf are proposed respectively and a new measure for a bf named nonlinearly separable degree nlsd is introduced in the sense of this measure the pbf is the most complex one the new algorithm has many advantages including in particular fast running speed good robustness and no need of considering the convergence property for example the number of iterations and computations in implementing the basic 2 bit logic operations such as and or and xor by using the new algorithm is far smaller than the ones needed by using other existing algorithms such as error correction ec and backpropagation bp algorithms moreover the synaptic weights and threshold values derived from up can be directly used in designing of the template of cellular neural networks cnns which has been considered as a new spatial temporal sensory computing paradigm

new numerical method for two dimensional partially wrinkled membranes based on the introduction of a nonnegative adjustable parameter into poisson s ratio a new numerical method is proposed to solve numerically the partially wrinkled membrane problems with arbitrary complex shapes three fundamental issues in this new method are addressed first a nonnegative adjustable parameter is introduced into the constitutive law automatically representing unwrinkled taut and wrinkled states of a membrane second a parametric variational principle is developed for the new membrane model third by the variational principle the original membrane problem is converted to a nonlinear mathematical programming problem the variational principle and the mathematical programming formulation lay a foundation for efficient numerical analysis of wrinkled membrane structures using finite element discretization three typical examples are given to show the effectiveness of this method

analysis of pulled axisymmetric membranes with wrinkling the nonlinear behavior of an axisymmetric hyperelastic membrane subjected to pulling forces is analyzed the membrane is considered to be ideal in the sense that it cannot carry compressive stress resultants if the membrane has a positive initial gaussian curvature the pulling gives rise to wrinkles which form over parts of the surface the full nonlinear equations governing the membrane behavior in the doubly tense and in the wrinkled regions are formulated and then solved using a numerical integration procedure solutions for various examples are presented with hookean and neo hookean constitutive behavior these include a few examples of wrinkled membranes with positive initial gaussian curvatures and one example of a membrane with a negative initial gaussian curvature where no wrinkles are formed

synthesis of multivalued multithreshold functions for ccd implementation basic multivalued building blocks constructed using ccd charge coupled devices technology are presented they are used to realize simple threshold functions existing techniques for decomposition of multivalued multithreshold functions into simpler subfunctions are reviewed usage of the ccd technology in implementation of these subfunctions is discussed two new decomposition techniques are proposed their aim is to obtain realizations that are better suited to ccd technology in terms of the maximum number of thresholds per element and the generation of negative weights synthesis techniques based on the proposed decompositions are presented and compared although 4 valued logic functions are stressed the techniques are in principle applicable to functions of any radix

constructive neural networks as estimators of bayesian discriminant functions abstract of crucial importance to the successful use of artificial neural networks for pattern classification problems is how the appropriate network size can be automatically determined this issue is addressed by formulating the process as an automatic search in the space of functions that corresponds to a subclass of multilayer feedforward networks learning is thus a dynamic network construction process which involves adjusting both the network weights and the topology adding new hidden units corresponds to extracting higher level features from the original input features for reducing the residual classification errors it can be shown that the resultant network approximates a bayesian classifier that implements the bayesian decision rule for classification the empirical results of several pattern classification experiments are also reported

the solution of groundwater quality management problems with a nonconvex feasible region using a cutting plane optimization technique in groundwater quality management problems the concentration constraints have a nonlinear behavior which may be described either as a convex or a nonconvex function therefore the feasible region which is defined as the intersection of all of these constraints can be either a convex or a nonconvex set a review of existing optimization algorithms for the solution of the groundwater quality management problem indicates that the majority of them have an inability to determine a global optimum when nonconvexity occurs in an earlier paper that appeared in this journal karatzas and finder 1993 the outer approximation method a global optimization technique was presented for the solution of groundwater management problems with convex constraints the problem was formulated to minimize a concave objective function over a compact convex set of constraints in the present study the same concept is applied to problems with nonconvex constraints while the main concept of the current approach remains the same as that in our earlier study there is a significant difference in the determination of the cutting hyperplane the nonconvexity of the domain requires a special approach to insure that the introduction of the cutting hyperplane does not eliminate any part of the nonconvex feasible region in this work the theory of the developed algorithm is presented and subsequently applied to two groundwater quality problems in the first example a hypothetical aquifer is considered to illustrate the performance of the methodology in the second example a groundwater quality management problem in woburn massachusetts is solved results obtained are compared with those generated by minos 5 1

instability investigation on fluid loaded pre stretched cylindrical membranes this paper discusses the evaluation of instabilities on the quasi static equilibrium path of fluid loaded pre stretched cylindrical membranes and the switching to a secondary branch at a bifurcation point the membrane is represented by only the in plane stress components for which an incompressible isotropic hyperelastic material model is assumed the free inflation problem yields governing equations and boundary conditions which are discretized by finite differences and solved by a newton raphson method an incremental arclength cubic extrapolation method is used to find generalized equilibrium paths with different parametrizations limit points and bifurcation points are observed on the equilibrium path when fluid level is seen as the controlling parameter an eigen mode injection method is employed to switch to a secondary equilibrium branch at the bifurcation point a limit point with respect to fluid level is observed for a partially filled membrane when the aspect ratio length radius is high whereas for smaller aspect ratios the limit point with respect to fluid level is observed at over filling pre stretch is observed to have a stiffening effect in the pre limit zone and a softening effect in the post limit zone

equilibrium shapes of inflated inextensible membranes this paper proposes an effective method for directly determining the final equilibrium shapes of closed inextensible membranes subjected to internal pressures with reference to new high performance textile materials we assume that the mechanical response of a fabric membrane can be accurately represented by regarding it as a two state material in the active state the membrane is subject to tensile stresses and is virtually inextensible vice versa in the passive state it is unable to sustain any compressive stress so it contracts freely equilibrium of the membrane in the final configuration is enforced by recourse to the minimum total potential energy principle the lagrange multipliers method is used to solve the minimum problem by accounting for the aforesaid nonlinear constitutive law the set of governing equations is solved for the unknown coordinates of the equilibrium surface points closed form solutions are obtained for fully wrinkled cylindrical and axisymmetric membranes under homogeneous boundary conditions while a simple iterative procedure is used to numerically solve cases of axisymmetric membranes under various inhomogeneous boundary conditions the soundness of the proposed method is verified by comparing the results with solutions available in the literature

on the generalization ability of diluted perceptrons a linearly separable boolean function is teamed by a diluted perceptron with optimal stability a different level of dilution is allowed for teacher and student perceptron the learning algorithms used were the optimal annealed dilution and hebbian dilution the generalization ability i e the probability to recognize a pattern which has not been learned before is calculated in replica symmetry

remarks on a theory of elasticity for fluid films a theory of elastic fluid films that generalizes classical notions of capillarity is described for the purely mechanical problem restrictions on energy minimizing states are obtained these restrictions are in accord with the experimental findings of kwok et al 1994

enhancement of the outer approximation method for the solution of concentration constrained optimal design groundwater remediation problems 1 nonlinearity and nonconvexity are two major characteristics of groundwater quality management models the classical solutions of such problems require enormous computational effort without ensuring a global optimum to circumvent this problem the outer approximation method a global optimization technique was introduced to solve groundwater quality management problems characterized by a nonconvex objective function with minima at the boundary of the feasible region and constraints that have convex or nonconvex behavior in this paper a more sophisticated and computationally efficient approach for the case of the nonconvex constraints is presented to illustrate the efficacy and efficiency of this new approach a hypothetical and a field scale problem are considered

strip a strip based neural network growth algorithm for learning multiple valued functions we consider the problem of synthesizing multiple valued logic functions by neural networks a genetic algorithm ga which finds the longest strip in v spl sube k sup n is described a strip contains points located between two parallel hyperplanes repeated application of ga partitions the space v into certain number of strips each of them corresponding to a hidden unit we construct two neural networks based on these hidden units and show that they correctly compute the given but arbitrary multiple valued function preliminary experimental results are presented and discussed

a tree structured algorithm for reducing computation in networks with separable basis functions i describe a new algorithm for approximating continuous functions in high dimensional input spaces the algorithm builds a tree structured network of variable size which is determined both by the distribution of the input data and by the function to be approximated unlike other tree structured algorithms learning occurs through completely local mechanisms and the weights and structure are modified incrementally as data arrives efficient computation in the tree structure takes advantage of the potential for low order dependencies between the output and the individual dimensions of the input this algorithm is related to the ideas behind k d trees bentley 1975 cart breiman et al 1984 and mars friedman 1988 i present an example that predicts future values of the mackey glass differential delay equation

geometrical feature of the scaling behavior of the limit point pressure of inflated hyperelastic membranes the occurrence of the limit point instability is an intriguing phenomenon observed during stretching of hyperelastic membranes in toy rubber balloons this phenomenon may be experienced in the sudden reduction in the level of difficulty of blowing the balloon accompanied by its rapid inflation the present paper brings out a link between the geometry and strain hardening parameter of the membrane and the occurrence of the limit point instability inflation of membranes with different geometries and boundary conditions is considered and the corresponding limit point pressures are obtained for different strain hardening parameter values interestingly it is observed that the limit point pressure for the different geometries is inversely proportional to a geometric parameter of the uninflated membrane this dependence is shown analytically which can be extended to a general membrane geometry more surprisingly the proportionality constant has a power law dependence on the nondimensional material strain hardening parameter the constants involved in the power law relation are universal constants for a particular membrane geometry

storage capacity of a constructive learning algorithm upper and lower bounds for the typical storage capacity of a constructive algorithm the tilinglike learning algorithm for the parity machine biehl m and opper m 1991 phys rev a 44 6888 are determined in the asymptotic limit of large training set sizes the properties of a perceptron with threshold learning a training set of patterns having a biased distribution of targets needed as an intermediate step in the capacity calculation are determined analytically the lower bound for the capacity determined with a cavity method is proportional to the number of hidden units the upper bound obtained with the hypothesis of replica symmetry is close to the one predicted by mitchinson and durbin 1989 biol cybern 60 345

a primal method for the solution of the groundwater quality management problem a new algorithm for the solution of the groundwater quality management problem is presented the method assumes that most of the computational effort in such problems involves evaluation of the concentrations and their derivatives with respect to the pumping rates at the control points the methodology proposed herein is a combination of the cutting plane method and the primal method in this approach each line search moves from a feasible point towards the solution of a subproblem with linear constraints and the same objective function as the original problem sensitivity analysis is used to compute the derivative of a single concentration with respect to all the pumping rates by solving only one linear system at each time step the method has been tested with analytical convex problems and a model example a comparison of the algorithm s performance was conducted using minos 5 1 for the case of a linear cost function the method shows a computational growth rate almost linearly proportional to the number of decision variables

the modeling and numerical analysis of wrinkled membranes in this paper three fundamental issues regarding modeling and analysis of wrinkled membranes are addressed first a new membrane model with viable young s modulus and poisson s ratio is proposed which physically characterizes stress relaxation phenomena in membrane wrinkling and expresses taut wrinkled and slack states of a membrane in a systematic manner second a parametric variational principle is developed for the new membrane model third by the variational principle the original membrane problem is converted to a non linear complementarity problem in mathematical programming a parametric finite element discretization and a smoothing newton method are then used for numerical solution the proposed membrane model and numerical method are capable of delivering convergent results for membranes with a mixture of wrinkled and slack regions without iteration of membrane stresses three numerical examples are provided

a learning multiple valued logic network algebra algorithm and applications we propose a multiple valued logic mvl network with functional completeness and develop its learning capability the mvl network consists of layered arithmetic piecewise linear processors since the arithmetic operations of the network are basically a wired sum and a piecewise linear operation their implementations should be rather simple and straightforward furthermore the mvl network can be trained by the traditional backpropagation algorithm directly the algorithm trains the networks using examples and appears to be available for most mvl problems of interest

representation and generalization properties of class entropy networks using conditional class entropy cce as a cost function allows feedforward networks to fully exploit classification relevant information cce based networks arrange the data space into partitions which are assigned unambiguous symbols and are labeled by class information by this labeling mechanism the network can model the empirical data distribution at the local level region labeling evolves with the network training process which follows a plastic algorithm the paper proves several theoretical properties about the performance of cce based networks and considers both convergence during training and generalization ability at run time in addition analytical criteria and practical procedures are proposed to enhance the generalization performance of the trained networks experiments on artificial and real world domains confirm the accuracy of this class of networks and witness the validity of the described methods

a fuzzy approach to hierarchical multiobjective programming problems and its application to an industrial pollution control problem in this paper we focus on hierarchical multiobjective programming problems where multiple decision makers in a hierarchical organization have their own multiple objective functions and propose an interactive algorithm based on the dual decomposition method to obtain the satisfactory solution which reflects not only the hierarchical relationships between multiple decision makers but also their own preferences for their objective functions in the proposed algorithm assuming that each of the decision makers has fuzzy goals for his her objective functions corresponding membership functions are elicited from the decision makers in their subjective manner in order to deal with hierarchical multiobjective programming problems a new kind of pareto optimality concept in membership spaces is defined and the concept of decision powers of multiple decision makers in a hierarchical decision structure is introduced the proposed algorithm is applied to the industrial pollution control problem in osaka city in japan in order to show the efficiency of the proposed method

learning the unlearnable we present a local perceptron learning rule that either converges to a solution or establishes linear nonseparability we prove that when no solution exists the algorithm detects this in a finite time number of learning steps this time is polynomial in typical cases and exponential in the worst case when the set of patterns is nonstrictly linearly separable the algorithm is local and has no arbitrary parameters

on convergence properties of pocket algorithm the problem of finding optimal weights for a single threshold neuron starting from a general training set is considered among the variety of possible learning techniques the pocket algorithm has a proper convergence theorem which asserts its optimality however the original proof ensures the asymptotic achievement of an optimal weight vector only if the inputs in the training set are integer or rational this limitation is overcome in this paper by introducing a different approach that leads to the general result furthermore a modified version of the learning method considered called pocket algorithm with ratchet is shown to obtain an optimal configuration within a finite number of iterations independently of the given training set

an algorithm for building regularized piecewise linear discrimination surfaces the perceptron membrane the perceptron membrane is a new connectionist model that aims at solving discrimination classification problems with piecewise linear surfaces the discrimination surfaces of perceptron membranes are defined by the union of convex polyhedrons starting from only one convex polyhedron new facets and new polyhedrons are added during learning moreover the positions and orientations of the facets are continuously adapted according to the training examples considering each facet as a perceptron cell a geometric credit assignment provides a local training domain to each perceptron of the network this enables one to apply statistical theorems on the probability of good generalization for each unit on its learning domain and gives a reliable criterion for perceptron elimination using vapnik chervonenkis dimension furthermore a regularization procedure is implemented the model efficiency is demonstrated on well known problems such as the 2 spirals or waveforms

learning in feedforward layered networks the tiling algorithm the authors propose a new algorithm which builds a feedforward layered network in order to learn any boolean function of n boolean units the number of layers and the number of hidden units in each layer are not prescribed in advance they are outputs of the algorithm it is an algorithm for growth of the network which adds layers and units inside a layer at will until convergence the convergence is guaranteed and numerical tests of this strategy look promising

learning and generalization with minimerror a temperature dependent learning algorithm we study the numerical performances of minimerror a recently introduced learning algorithm for the perceptron that has analytically been shown to be optimal both on learning linearly and nonlinearly separable functions we present its implementation on learning linearly separable boolean functions numerical results are in excellent agreement with the theoretical predictions

a recurrent self organizing neural fuzzy inference network a recurrent self organizing neural fuzzy inference network rsonfin is proposed the rsonfin is inherently a recurrent multilayered connectionist network for realizing the basic elements and functions of dynamic fuzzy inference and may be considered to be constructed from a series of dynamic fuzzy rules the temporal relations embedded in the network are built by adding some feedback connections representing the memory elements to a feedforward neural fuzzy network each weight as well as node in the rsonfin has its own meaning and represents a special element in a fuzzy rule there are no hidden nodes initially in the rsonfin they are created online via concurrent structure identification and parameter identification the structure learning together with the parameter learning forms a fast learning algorithm for building a small yet powerful dynamic neural fuzzy network two major characteristics of the rsonfin can thus be seen 1 the recurrent property of the rsonfin makes it suitable for dealing with temporal problems and 2 no predetermination like the number of hidden nodes must be given since the rsonfin can find its optimal structure and parameters automatically and quickly moreover to reduce the number of fuzzy rules generated a flexible input partition method the aligned clustering based algorithm is proposed various simulations on temporal problems are done and performance comparisons with some existing recurrent networks are also made efficiency of the rsonfin is verified from these results

on the number of multilinear partitions and the computing capacity of multiple valued multiple threshold perceptrons we introduce the concept of multilinear partition of a point set v spl sub r sup n and the concept of multilinear separability of a function f v spl rarr k 0 k 1 based on well known relationships between linear partitions and minimal pairs we derive formulae for the number of multilinear partitions of a point set in general position and of the set k sup 2 the n k s perceptrons partition the input space v into s 1 regions with s parallel hyperplanes we obtain results on the capacity of a single n k s perceptron respectively for v spl sub r sup n in general position and for v k sup 2 finally we describe a fast polynomial time algorithm for counting the multilinear partitions of k sup 2

inflation of nonlinearly deformed annular elastic membranes abstract the inflation of an isotropic nonlinear elastic membrane by means of a volume independent hydrostatic pressure is studied in particular we consider annular membranes which on the inner boundary have been subjected to an axial twist and a displacement normal to the plane of the membrane with the outer boundary fixed a direct two dimensional approach is adopted and by introducing a relaxed strain energy function the occurrence of wrinkled solutions is considered the governing equations are found to reduce to a system of first order differential equations which are then solved numerically for a mooney rivlin material over a range of boundary value problems

groundwater management using numerical simulation and the outer approximation method for global optimization groundwater quantity management problems with fixed charges have been formulated in the past as mixed integer and linear programming problems in this paper a new methodology is presented where the fixed charges are incorporated into the objective function in an exponential form and the problem is solved as a concave minimization problem the principal difficulty in the minimization of a concave function over a linear or nonlinear set of constraints is that the local minima which are determined by the classical minimization algorithms may not be global in an effort to circumvent this problem the outer approximation method is introduced this method is applicable to the global minimization of a concave function over a compact set of constraints in the present work the outer approximation is applied to concave minimization problems over a convex compact set of constraints two applications of the method to groundwater management problems are presented herein and the results are compared with an existing solution obtained using a different optimization approach

a thermal perceptron learning rule the thermal perceptron is a simple extension to rosenblatt s perceptron learning rule for training individual linear threshold units it finds stable weights for nonseparable problems as well as separable ones experiments indicate that if a good initial setting for a temperature parameter to has been found then the thermal perceptron outperforms the pocket algorithm and methods based on gradient descent the learning rule stabilizes the weights learns over a fixed training period for separable problems it finds separating weights much more quickly than the usual rules

learning algorithms with optimal stability in neural networks to ensure large basins of attraction in spin glass like neural networks of two state elements xi imu or 1 the authors propose to study learning rules with optimal stability delta where delta is the largest number satisfying delta or sigma j jij xi jmu xi imu mu 1 p i 1 n where n is the number of neurons and p is the number of patterns they motivate this proposal and provide optimal stability learning rules for two different choices of normalisation for the synaptic matrix jij in addition numerical work is presented which gives the value of the optimal stability for random uncorrelated patterns

incremental stresses in loaded orthotropic circular membrane tubes i theory abstract starting from the equations of general elastic nonlinear membrane theory in intrinsic form the equations governing the incremental state of stress in an orthotropic circular membrane tube are derived and discussed the tube is initially subjected to uniform internal pressure and to longitudinal extension which lead to large homogeneous deformation then some changes in loading and or geometry are considered e g an additional load is applied the shape of the boundary is changed or a slit is formed in the membrane these changes are regarded as small perturbations on the initial homogeneous state of stress the general form as well as some simplified forms of the equations are presented leading finally to a set of two equations in terms of two scalar potential functions two different variational formulations for the problem are also presented each of which may serve as a basis for numerical treatment

a novel variational algorithmic formulation for wrinkling at finite strains based on energy minimization application to mesh adaption this paper is concerned with an efficient novel algorithmic formulation for wrinkling at finite strains in contrast to previously published numerical implementations the advocated method is fully variational more precisely the parameters describing wrinkles or slacks together with the unknown deformation mapping are computed jointly by minimizing the potential energy of the considered mechanical system furthermore the wrinkling criteria are naturally included within the presented variational framework the proposed method allows to employ three dimensional constitutive models without any additional modification i e a projection in plane stress space is not required analogously to the wrinkling parameters the non vanishing out of plane component of the strain tensor results conveniently from relaxing the respective helmholtz energy of the membrane the proposed framework is very general and does not rely on any assumption regarding the symmetry of the material i e arbitrary anisotropic hyperelastic models can be consistently taken into account the advantages associated with such a variational method are manifold for instance it opens up the possibility of applying standard optimization algorithms to the numerical implementation this is especially important for highly non linear or singular problems such as wrinkling on the other hand minimization principles provide a suitable basis for a posteriori error estimation and thus for adaptive finite element formulations as a prototype a variational error indicator leading to an efficient h adaption for wrinkling is briefly discussed the performance of the wrinkling approach is demonstrated by selected finite element analyses

anisotropic membrane wrinkling theory and analysis abstract a complete theory of wrinkling of anisotropic elastic membranes is presented based on the notion of relaxed energy function the theory is obtained as a particular case of a general theory of saturated elasticity it is shown that when any given hyperelastic constitutive law is supplemented with a saturation condition the right cauchy green strain tensor abides by an additive decomposition law governed by a normality rule for the case of wrinkling these results are implemented into a numerical procedure and examples are presented

a variational formulation for finite deformation wrinkling analysis of inelastic membranes this paper is concerned with a novel fully variational formulation for finite deformation analysis of inelastic membranes with wrinkling in contrast to conventional approaches every aspect of the physical problem derives from minimization of suitable energy functionals a variational formulation of finite strain plasticity theory which leads to a minimization problem for the constitutive updates serves as the starting point for the derivations in order to take into account the kinematics induced by wrinkles and slacks a relaxed version of the finite strain functional is postulated in effect the local incremental stress strain relations are established via differentiation of the relaxed energy functional with respect to the strains hence the presented formulation is fully analogous to that of hyperelasticity with the sole exception that the aforementioned functional depends on history variables and accordingly it is path dependent the advantages associated with the developed variational method are manifold from a practical point of view the possibility of applying standard optimization algorithms to solve the minimization problem describing inelastic membranes is remunerative from a mathematical point of view on the other hand the energy of the system induces some sort of natural metric representing an essential requirement for error estimation and thus for adaptive finite element methods the presented derivation of the model allows to consider possible material symmetries in the elastic as well as plastic response of the material as a prototype a von mises type model is implemented the efficiency and performance of the resulting algorithm are demonstrated by means of numerical examples

development of objective oriented groundwater models 2 robust experimental design 1 this paper continues the discussion in part 1 by considering the data collection strategy problem when the existing data are judged to be insufficient for constructing a reliable model designing an experiment for identifying a distributed parameter is very difficult because the identification of a more complex parameter structure requires more data moreover without knowing the sufficiency of a design finding an optimal design becomes meaningless these difficulties can be avoided if we turn to the construction of objective oriented models the identifiability of a distributed parameter as defined in this paper contains the reducibility of parameter structure sufficient conditions for this kind of identifiability are given when the structure error associated with a structure reduction is too large these conditions may not be satisfied no matter how much data are collected in this paper we formulate a new experimental design problem that consists of two objectives minimizing the cost and maximizing the information content with robustness and feasibility as constraints we develop an algorithm that can find a cost effective robust design for objective oriented parameter identification we also present a heuristic algorithm that can find a suboptimal design with less computational effort for real case studies the proposed methodology is used to design a pumping test for identifying a distributed hydraulic conductivity we verify the robustness of the obtained design by assuming that the true parameter may have continuous discrete random and fractured structures finally the presented procedure of constructing objective oriented models is described step by step

elastic surface substrate interactions a theory for three dimensional finite deformations of elastic solids with conforming elastic films attached to their bounding surfaces is described the gurtin murdoch theory incorporating elastic resistance of the film to strain is generalized to account for the effects of intrinsic flexural resistance this modification yields a model that can be used to describe equilibrium deformations in the presence of compressive surface stress fields an associated variational theory is given and material symmetry considerations are discussed the theory is illustrated by examples

a new interior point boundary projection method for solving nonlinear groundwater pollution control problems a new interior point algorithm for solving the groundwater pollution control design problem is presented the algorithm requires that the objective function is differentiable in the interior region for minimization problems with nonlinear constraints and a concave objective function the technique is shown to be similar to an active set gradient projection method where the tangent of the boundary between feasible and infeasible solutions is used to determine a search direction in this new method however the search direction is translated into the interior space of the feasible region this process allows progress to be made toward improving the objective function while remaining in the feasible space and ultimately converges to a stationary point although the solution technique was developed to solve a groundwater control formulation with a linear objective function and nonlinear constraints the method has been successfully applied to an unconstrained nonconcave nonconvex formulation and may be applicable to a wide variety of problems

constructive learning of recurrent neural networks limitations of recurrent cascade correlation and a simple solution it is often difficult to predict the optimal neural network size for a particular application constructive or destructive methods that add or subtract neurons layers connections etc might offer a solution to this problem we prove that one method recurrent cascade correlation due to its topology has fundamental limitations in representation and thus in its learning capabilities it cannot represent with monotone i e sigmoid and hard threshold activation functions certain finite state automata we give a preliminary approach on how to get around these limitations by devising a simple constructive training method that adds neurons during training while still preserving the powerful fully recurrent structure we illustrate this approach by simulations which learn many examples of regular grammars that the recurrent cascade correlation method is unable to learn

finite element analysis of dynamic response of wrinkling membranes a new iterative scheme for finite element analysis of wrinkling membranes originally devised for static analysis is extended for analyzing dynamic response of wrinkling membranes the scheme is found to be successfully implemented with an explicit total lagrangian finite element code based upon the central difference method the finite element implementation of the scheme is straightforward and only minor modifications are needed for existing membrane finite element codes in light of application for contact impact discussed are a couple of existing contact algorithms which are well suited for treating contact impact of wrinkling membranes with rigid bodies the validity of the scheme is demonstrated via a numerical simulation of an inflating automotive airbag made of orthotropic membranes under impulse pressure loading

differential equation for the amplitude of wrinkles introduction t he renewed interest in the phenomenonof wrinkling of membranes fueled by applications to the aerospace industry has spurred considerable activity on both the theoretical and computational aspectsof the subject althoughthe wrinklingphenomenonis known to be a case of shell buckling it seems unwise to utilize this knowledge in actual computations because treating the membrane as a shell with a vanishinglysmall thickness leads to the frustrating effects of numerical instability there exist on the other hand techniques based on themembrane theory alone that permit us to obtain with relative ease and numerical robustness not only the extent of thewrinkledzones but also the eldof directionsof thewrinkles 1i4 all that is needed therefore is a means for calculating the amplitude and wavelength of the wrinkles in an already known wrinkled domain in this note we derive an ordinary differential equation whose solution delivers such information for clarity of the presentation the equation is obtained under a number of simplifying assumptions mostly involving the smallness of the deformations however the method is straightforwardlyextendable to the general case our guiding principle has been to keep only those aspects of the model that are clearly determinant of the result while leaving all other aspects for future re nement we believe that this philosophy will serve to highlight the essential features rather than the technicalities of the proposedequation note that even under a geometrically andmaterially linear regime the resultingdifferentialequation is highly nonlinear the physical reason for this nonlinearityis to be foundin that becausewrinklingentailsno stress in thedirectionperpendicular to the wrinkles there exists a severe constraint between the wavelength and amplitude of the wrinkles this can be phrased intuitively as follows for a given amount of wrinkling strain the larger the number of wrinkles the smaller their amplitude to the best of our knowledge the only attempt in a direction similar to the one proposed herein is due to wong and pellegrino in their work these authors present a model basedmainly on the particular case of shearing of a rectangular panel their results are very valuable and will be used here as a benchmark for validation purposes

threshold induced phase transitions in perceptrons error rates of a boolean perceptron with threshold and either spherical or ising constraint on the weight vector are calculated for storing patterns from biased input and output distributions derived within a one step replica symmetry breaking rsb treatment for unbiased output distribution and non zero stability of the patterns we find a critical load p above which two solutions to the saddlepoint equations appear one with higher free energy and zero threshold and a dominant solution with non zero threshold we examine this second order phase transition and the dependence of p on the required pattern stability for both one step rsb and replica symmetry rs in the spherical case and for one step rsb in the ising case

three dimensional analysis of wrinkled membranes using modification scheme of stress strain tensor three dimensional finite element analysis using conventional membrane elements tends to be numerically unstable because of their lack of bending stiffness additionally membrane structures are highly susceptible to localized buckling posing further numerical difficulties in this paper a modified stress strain tensor recently proposed by the authors to account for membrane wrinkling is applied to three dimensional finite element analysis of membrane structures with the aim to overcome the preceding numerical difficulties it is found through numerical investigations that the use of the modified stress strain tensor renders the iterative solution process remarkably stable and enables one to obtain the converged solution for those problems that are difficult to solve using conventional membrane elements

neural network pruning with tukey kramer multiple comparison procedure reducing a neural network s complexity improves the ability of the network to generalize future examples like an overfitted regression function neural networks may miss their target because of the excessive degrees of freedom stored up in unnecessary parameters over the past decade the subject of pruning networks produced nonstatistical algorithms like skeletonization optimal brain damage and optimal brain surgeon as methods to remove connections with the least salience the method proposed here uses the bootstrap algorithm to estimate the distribution of the model parameter saliences statistical multiple comparison procedures are then used to make pruning decisions we show this method compares well with optimal brain surgeon in terms of ability to prune and the resulting network performance

tension field theory a general theory of the tension field is developed for application to the analysis of wrinkling in isotropic elastic membranes undergoing finite deformations the principal contribution is a partial differential equation describing a geometrical property of tension trajectories this is one of a system of two equations which describes the state of stress independently of the deformation this system is strongly elliptic at any stable solution whereas the deformation is described by a system of parabolic type controllable solutions i e those states that can be maintained in any isotropic elastic material by application of edge tractions and lateral pressure alone are obtained the general axisymmetric problem is solved implicitly and the theory is applied to the solution of two representative examples existing small strain theories are shown to correspond to a singular limit of the general theory at which the underlying system changes from elliptic to parabolic type

on the optimal design of multiple valued plas a description is given of the design and analysis of three types of multivalued plas programmable logic arrays type 1 plas realize functions directly in the form of the max of min of literal functions and constants in type 2 plas the body of the pla is binary and the output is encoded as a multiple valued logic value type 3 plas are the same as type 2 plas except for the use of 2 bit decoders and a permutation network on the input using the number of columns required to realize a given function as a measure to compare plas it is shown that type 3 plas are superior to type 2 which in turn are superior to type 1

function approximation fast convergence neural approach based on spectral analysis we propose a constructive approach to building single hidden layer neural networks for nonlinear function approximation using frequency domain analysis we introduce a spectrum based learning procedure that minimizes the difference between the spectrum of the training data and the spectrum of the network s estimates the network is built up incrementally during training and automatically determines the appropriate number of hidden units this technique achieves similar or better approximation with faster convergence times than traditional techniques such as backpropagation

a new computational framework for materials with different mechanical responses in tension and compression and its applications abstract materials possessing tension compression asymmetric behavior can be simulated by a bi modulus constitutive relation which assumes the materials have different moduli in tension and compression traditional iteration methods struggle for the convergence difficulty for such kind of constitutive model in this paper a new computational framework is established solution procedures under both small and finite deformations which have asymptotically quadratic rate of convergence have also been proposed and implemented in abaqus with umat numerical examples show that the proposed computational framework can be applied successfully to simulate the wrinkling analysis of thin plane membranes and explain some unusual cell mechanosensing phenomena