generalization in a multi state neural network the generalization ability of an extremely dilute feedback neural network with multi state neurons is studied by means of a deterministic noiseless parallel dynamics the overlap with any one of a macroscopic number of binary full activity concepts is determined when the network is trained with examples of variable activity according to a hebbian learning algorithm that favours stable symmetric mixture states explicit results about the phase diagram and the generalization error are obtained for a network with three state neurons which remain inactive below a threshold it is shown that the generalization ability can be considerably enhanced either by training the network with low activity examples or by means of a moderate increase in

structure of metastable states in the hopfield model an upper bound for the number of metastable states in the hopfield model is calculated as a function of the hamming fraction from an input pattern for all finite values of alpha the ratio of number of patterns to nodes the hamming fraction from the input pattern to the nearest metastable state is infinite when alpha 0 113 the bound also implies that there is a gap between a set of states close to the input pattern and another set centred around the hamming fraction 0 5 from it

onset of super retrieval phase and enhancement of the storage capacity in neural networks of nonmonotonic neurons analogue neural networks of associative memory with continuous time dynamics are studied for nonmonotonic transfer functions using the method of self consistent signal to noise analysis the hebb learning rule with unbiased random patterns is assumed for the synaptic couplings a novel phenomenon is found to occur as a result of a phase transition concerning the property of the local field distribution in retrieval states of the newly found phase which the authors refer to as the super retrieval phase noise in the local field vanishes and the memory retrieval without errors ensures even for an extensive number of memory patterns stored under the local learning rule the storage capacity is obtained as a function of the parameter representing the degree of nonmonotonicity of the transfer functions with the result that an enhancement of the storage capacity can also occur

enriched performance measure approach for reliability based design optimization an enriched performance measure approach is presented for reliability based design optimization to substantially improve computational efficiency when applied to large scale applications in the enriched performance measure approach four improvements are made over the original performance measure approach as a way to launch reliability based design optimization at a deterministic optimum design as a new enhanced hybrid mean value method as an efficient probabilistic feasibility check and as a fast reliability analysis under the condition of design closeness it is found that deterministic design optimization helps improve numerical efficiency by reducing some reliability based design optimization iterations in reliability based design optimization a computational burden on the feasibility check of constraints can be significantly reduced by using a mean value first order method and by carrying out the refined reliability analysis using the enhanced hybrid mean value method for e active and violated constraints the enhanced hybrid mean value method is developed to handle nonlinear and or nonmonotonic constraints in reliability analysis the fast reliability analysis method is proposed to efficiently evaluate probabilistic constraints under the condition of design closeness moreover two numerical examples are provided to compare the enriched performance measure approach to existing reliability based design optimization methods from a numerical efficiency and stability point of view

replica symmetric theory of nonlinear analogue neural networks on the basis of the theory of the naive mean field model of spin glasses analogue neural networks of the hopfield type are investigated in the saturation limit the saddle point equations for the order parameters describing retrieval and spin glass phases of the networks are obtained by means of a statistical mechanical analysis within the framework of the replica symmetric theory and are shown to undergo a modification to that of ags theory due to the absence of the onsager reaction term in the tap equation based on the equations the memory storage capacity of the networks is analysed as a function of the analogue gain beta a small increase in the critical storage capacity is found for finite values of beta compared with that of the ising model networks with corresponding inverse temperature although the qualitative nature of the phase diagram is unchanged

structural reliability optimization using an efficient safety index calculation procedure the objective of this paper is to conduct reliability based structural optimization in a multidisciplinary environment an efficient reliability analysis is developed by expanding the limit functions in terms of intermediate design variables the design constraints are approximated using multivariate splines in searching for the optimum the reduction in computational cost realized in safety index calculation and optimization are demonstrated through several structural problems this paper presents safety index computation analytical sensitivity analysis of reliability constraints and optimization using truss frame and plate examples

advanced probabilistic structural analysis method for implicit performance functions in probabilistic structural analysis the performance or response functions usually are implicitly defined and must be solved by numerical analysis methods such as finite elemen t methods in such cases the commonly used probabilistic analysis tool is the mean based second moment method which provides only the first two statistical moments this paper presents an advanced mean based method which is capable of establishing the full probability distributions to provide additional information for reliability design the method requires slightly more computations than the mean based second moment method but is highly efficient relative to the other alternative methods several examples are presented to demonstrate the method in particular the examples show that the new mean based method can be used to solve problems involving nonmonotonic functions that result in truncated distributions

outlier robust finite population estimation abstract outliers in sample data are a perennial problem for applied survey statisticians moreover it is a problem for which traditional sample survey theory offers no real solution beyond the sensible advice that such sample elements should not be weighted to their fullest extent in estimation sample outliers can be identified as of two basic types here we are concerned with the first type which may conveniently be termed representative outliers these are sample elements with values that have been correctly recorded and that cannot be assumed to be unique that is there is no good reason to assume there are no more similar outliers in the nonsampled part of the target population the remaining sample outliers which by default are termed nonrepresentative are sample elements whose data values are incorrect or unique in some sense methods for dealing with these nonrepresentative outliers lie basically within the scope of survey editing and imputation theory and are therefore not considered in

a probabilistic approach to parallel dynamics for the little hopfield model presents new results on a probabilistic approach to parallel dynamics of the little hopfield model the authors propose a truncated auxiliary dynamics method to control a feedback noise in this symmetrical neural network with full connection it allows them to propose an ansatz for derivation of the explicit recurrence relations for the main and residual noisy overlap evolution for arbitrary discrete moment t

bias calibrated estimation from sample surveys containing outliers we discuss the problem of estimating finite population parameters on the basis of a sample containing representative outliers we clarify the motivation for chambers s bias calibrated estimator of the population total and show that bias calibration is a key idea in constructing estimators of finite population parameters we then link the problem of estimating the population total to distribution function or quantile estimation and explore a methodology based on the use of chambers s estimator we also propose methodology based on the use of robust estimates and a bias calibrated form of the chambers and dunstan estimator of the population distribution function this proposal leads to a bias calibrated estimator of the population total which is an alternative to that of chambers we present a small simulation study to illustrate the utility of these estimators

the space of interactions in neural network models the typical fraction of the space of interactions between each pair of n ising spins which solve the problem of storing a given set of p random patterns as n bit spin configurations is considered the volume is calculated explicitly as a function of the storage ratio alpha p n of the value kappa 0 of the product of the spin and the magnetic field at each site and of the magnetisation m here m may vary between 0 no correlation and 1 completely correlated the capacity increases with the correlation between patterns from alpha 2 for correlated patterns with kappa 0 and tends to infinity as m tends to 1 the calculations use a saddle point method and the order parameters at the saddle point are assumed to be replica symmetric this solution is shown to be locally stable a local iterative learning algorithm for updating the interactions is given which will converge to a solution of given kappa provided such solutions exist

bifurcation analysis in an associative memory model we previously reported the chaos induced by the frustration of interaction in a nonmonotonic sequential associative memory model and showed the chaotic behaviors at absolute zero we have now analyzed bifurcation in a stochastic system namely a finite temperature model of the nonmonotonic sequential associative memory model we derived order parameter equations from the stochastic microscopic equations two parameter bifurcation diagrams obtained from those equations show the coexistence of attractors which do not appear at absolute zero and the disappearance of chaos due to the temperature effect

downweighting influential clusters in surveys certain clusters may be extremely influential on survey estimates and consequently contribute disproportionately to their variance we propose a general approach to estimation that downweights highly influential clusters with the amount of downweighting based on m estimation applied to the empirical influence of the clusters the method is motivated by a problem in census coverage estimation and we illustrate it by using data from the 1990 post enumeration survey pes in this context an objective prespecified methodology for handling influential observations is essential to avoid having to justify judgmental post hoc adjustment of weights in 1990 both extreme weights and large errors in the census led to extreme influence we estimated influence by taylor linearization of the survey estimator and we applied m estimators based on the t distribution and the huber function as predicted by theory the robust procedures greatly reduced the estimated variance of estimated coverage rates more so tha

noise induced order a new noise effect on chaos in one dimensional mappings is reported the transition from chaotic behavior to ordered behavior induced by external noise is observed in a certain class of one dimensional mappings this transition is clearly shown in terms of the lyapunov number entropy power spectrum and the nature of orbits

incorporating uncertainty in mechanical properties for finite element based evaluation of bone mechanics finite element fe models of bone developed from computed tomography ct scan data are used to evaluate stresses and strains load transfer and fixation of implants and potential for fracture the experimentally derived relationships used to transform ct scan data in hounsfield unit to modulus and strength contain substantial scatter the scatter in these relationships has potential to impact the results and conclusions of bone studies the objectives of this study were to develop a computationally efficient probabilistic fe based platform capable of incorporating uncertainty in bone property relationships and to apply the model to a representative analysis variability in stresses and fracture risk was predicted in five proximal femurs under stance loading conditions based on published variability in strength and modulus relationships derived in the proximal femur the probabilistic analysis predicted the distributions of stress and risk for the five femurs analyzed the 1 and 99 percentile bounds varied by an average of 17 3 mpa for stress and by 0 28 for risk in each femur the predicted variability in risk was greater than 50 of the mean risk calculated with obvious implications for clinical assessment results using the advanced mean value amv method required only seven analysis trials 1 h and differed by less than 2 when compared to a 1000 trial monte carlo simulation 400 h the probabilistic modeling platform developed has broad applicability to bone studies and can be similarly implemented to investigate other loading conditions structures sources of uncertainty or output measures of interest r 2007 elsevier ltd all rights reserved

reliability analysis of stiffened aircraft panels using adjusting mean value method with regard to real world engineering structures an adjusting mean value called the self adjusting mean value smv is proposed for improving the efficiency and robustness of a maximum performance

transient dynamics for sequence processing neural networks an exact solution of the transient dynamics for a sequential associative memory model is discussed through both the path integral method and the statistical neurodynamics although the path integral method has the ability to give an exact solution of the transient dynamics only stationary properties have been discussed for the sequential associative memory we have succeeded in deriving an exact macroscopic description of the transient dynamics by analysing the correlation of crosstalk noise surprisingly the order parameter equations of this exact solution are completely equivalent to those of the statistical neurodynamics which is an approximation theory that assumes crosstalk noise to obey the gaussian distribution in order to examine our theoretical findings we numerically obtain cumulants of the crosstalk noise we verify that the third and fourth order cumulants are equal to zero and that the crosstalk noise is normally distributed even in the non retrieval case we show that the results obtained by our theory agree with those obtained by computer simulations we have also found that the macroscopic unstable state completely coincides with the separatrix

curvilinear fatigue crack reliability analysis by stochastic boundary element method in this paper the stochastic boundary element method which combines the mixed boundary integral equations method explored in reference 1 with the first order reliability method is developed to study probabilistic fatigue crack growth due to the high degree of complexity and non linearity of the response direct differentiation coupied with the response surface method is employed to determine the response gradient three random processes the mode i and mode ii stress intensity factors and the crack direction angle are included in the expression of the response gradient the sensitivity of these random processes is determined using a first order response model an iteration scheme based on the hl rf method2 is applied to locate the most probable failure point on the limit state surface the accuracy and efficiency of the stochastic boundary element method are evaluated by comparing the cumulative distribution function of the fatigue life obtained with monte carlo simulation the reliability index and the corresponding probability of failure are calculated for a fatigue crack growth problem with randomness in the crack geometry defect geometry fatigue parameters and external loads the response sensitivity of each primary random variable at the design point is determined to show its role in the fatigue failure the variation of each primary random variable at the design point with the change of probability of failure is also presented in numerical examples

layered neural networks exact solutions for the dynamics of layered feedforward neural networks are presented these networks are expected to respond to an input by going through a sequence of preassigned states on the various layers the family of networks considered has a variety of interlayer couplings linear and non linear hebbian hebbian with gaussian synaptic noise and with various kinds of dilution in addition the authors also solve the problem of layered networks with the pseudoinverse projector matrix of couplings in all cases the solutions take the form of layer to layer recursions for the mean overlap with a random key pattern and for the width of the embedding field distribution the dynamics is governed by the fixed points of these recursions for all cases non trivial domains of attraction of the memory states are found and graphically displayed

outlier resistant alternatives to the ratio estimator abstract many techniques have been suggested to lower the impact of outliers on sample survey estimates outliers can be downweighted by winsorization that is by replacing extreme data points by a data dependent or a predetermined value before calculating estimates another approach is to reduce the weight of outliers from the inverse sampling fraction to 1 in the estimation of population characteristics in this article the problem of estimating the population mean using auxiliary information in the presence of outliers is considered a resistant version of the ratio estimator is introduced it is constructed with a m or a gm estimator of the slope of the regression model through the origin which is implicitly called on when considering the ratio estimator the asymptotic biases and asymptotic variances of the proposed alternatives to the ratio estimator are calculated with respect to the randomization of the sampling plan the selection of a resistant estimator is seen to involve a trade off betwee

some estimators of a population total from simple random samples containing large units abstract the problem considered is the estimation of the population total of some characteristic from a simple random sample containing a few large or extreme observations the effect of these large units in the sample is to distort the estimate of the population total it is therefore important to correct the weights for such units or deflate their values at the estimation stage once they have been sampled and identified as unusually large units in this paper three estimators that alter the usual sampling weights have been considered the efficiencies of these estimators have been worked out in terms of the ratio of the mean squared error of the usual estimator of the population total to the mean squared error of these estimators a numerical study of these estimators is also discussed

statistical mechanics of image restoration and error correcting codes we develop a statistical mechanical formulation for image restoration and error correcting codes these problems are shown to be equivalent to the ising spin glass with ferromagnetic bias under random external fields we prove that the quality of restoration decoding is maximized at a specific set of parameter values determined by the source and channel properties for image restoration in a mean field system a line of optimal performance is shown to exist in the parameter space these results are illustrated by solving exactly the infinite range model the solutions enable us to determine how precisely one should estimate unknown parameters monte carlo simulations are carried out to see how far the conclusions from the infinite range model are applicable to the more realistic two dimensional case in image restoration

learning of non monotonic rules by simple perceptrons in this paper we study the generalization ability of a simple perceptron which learns an unrealizable boolean function represented by a perceptron with a non monotonic transfer function of reversed wedge type this type of non monotonic perceptron is considered as a variant of multilayer perceptron and is parametrized by a single wedge parameter a reflecting the non monotonic nature of the target function a discontinuous transition from the poor generalization phase to the good generalization phase is observed in the learning curve for intermediate values of a we also find that asymptotic learning curves are classified into the following two categories depending on a for large a the learning curve obeys a power law with exponent 1 on the other hand a power law with exponent is obtained for small a although these two exponents are obtained from unstable replica symmetric solutions by using the replica method they are consistent with the results obtainable without using the replica method in a low dimensional version of this learning problem this suggests that our results are good approximations even if they are not exact