non self adjoint zakharov shabat operator with a potential of the finite asymptotic values i direct spectral and scattering problems the zakharov and shabat equation for the scattering problem is studied the estimates analytical properties and asymptotic expansions of the jost solution are presented for a general class of the potentials q x not vanishing at infinity the existence of the similarity transformation is also shown for q x vanishing at infinity the continuous part of the spectrum doubly degenerates however nonvanishing finite asymptotic values of q x dissolve the degeneracy completely the expansion theorem is given in c 0 2 r and for a class of q x we prove that the zakharov and shabat equation yields a non self adjoint spectral operator in the hilbert space in the sense of dunford and schwartz

two component kp hierarchy and the classical boussinesq equation it has been shown that solutions to the kp equation and other equations in the kp hierarchy take a wronskian form the authors extend these ideas to two component wronskians and the hirota equations 1986 which they satisfy by a reduction procedure they show how dependence on some of the variables can be removed and look in detail at the classical boussinesq equation and its modifications and show how these equations fit into the two component kp hierarchy

a binless correlation measure reduces the variability of memory reactivation estimates summary the standard procedure for measuring correlations between pairs of spike trains is to count the numbers of spikes occurring within a specified set of time intervals partitioning the continuous time line into discrete bins of width w seconds one then computes the pearson correlation between pairs of the bin occupancy vectors this method introduces a form of quantization noise similar to that in analog to digital signal processing devices due to the arbitrary positioning of bin boundaries relative to pairs of spikes small changes in bin width and small uniform shifts in bin boundaries typically produce large variations in the apparent correlation an alternative method of determining a correlation between pairs of spike trains was recently introduced rather than discretize the data in time the original spike trains are convolved with a gaussian kernel with parameter chosen to give an effective width matching the bin width w 12 calculating the pearson correlation of the resulting smooth functions gives an estimate of the correlation between the spike trains matching that given by the bin based procedure without introducing the significant variability of the bin based estimate measures of memory reactivation based on the partial correlations between ensembles of pairwise spike train correlations are biased downwards by the quantization noise present in the pairwise correlation estimates using a binless method to measure pairwise correlation we find that the partial correlation or explained variance of rat hippocampal maze activity and post maze sleep taking into account pre maze sleep correlations increases significantly over estimates made with the standard bin based procedure copyright 2007 john wiley sons ltd

a measure of multivariate phase synchrony using hyperdimensional geometry phase synchrony has been used to investigate the dynamics of subsystems that make up a complex system current measures of phase synchrony are mostly bivariate focusing on the synchrony between pairs of time series bivariate measures do not necessarily lead to a complete picture of the global interactions within a complex system current multivariate synchrony measures are based on either averaging all possible pairwise synchrony values or eigendecomposition of the pairwise bivariate synchrony matrix these approaches are sensitive to the accuracy of the bivariate synchrony indices computationally complex and indirect ways of quantifying the multivariate synchrony recently we had proposed a method to compute the multivariate phase synchrony using a hyperdimensional coordinate system this method referred to as hyperspherical phase synchrony hps has been found to be dependent on the ordering of the phase differences in this paper we propose a more general hyperspherical coordinate system along with a new higher dimensional manifold representation to eliminate the dependency on the ordering of the signals phases this new framework referred to as hyper torus synchrony hts is shown to be equivalent to the root mean square of a sufficient set of squared phase locking values whose phase differences contain information about all oscillators in the network the statistical properties of hts are given analytically and its performance is evaluated thoroughly for both synthetic and real signals

effect of reference scheme on power and phase of the local field potential brain signals are often analyzed in the spectral domain where the power spectral density psd and phase differences and consistency can reveal important information about the network however for proper interpretation it is important to know whether these measures depend on stimulus behavioral conditions or the reference scheme used to analyze data we recorded local field potential lfp from an array of microelectrodes chronically implanted in area v1 of monkeys under different stimulus behavioral conditions and computed psd slopes coherence and phase difference between lfps as a function of frequency and interelectrode distance while using four reference schemes single wire average bipolar and current source density psd slopes were dependent on reference scheme at low frequencies below 200i hz but became invariant at higher frequencies average phase differences between sites also depended critically on referencing switching from 0 degrees for single wire to 180 degrees for average reference results were consistent across different stimulus behavioral conditions we were able to account for these results based on the coherence profile across sites and properties of the spectral estimator our results show that using different reference schemes can have drastic effects on phase differences and psd slopes and therefore must be interpreted carefully to gain insights about network properties

finite rank constraints on linear flows and the davey stewartson equation finite rank constraints for the right derivatives of certain automorphisms solving the heat equation imply the davey stewartson system solutions comprising wronskian and grammian determinants are found and the real reductions for the davey stewartson i and davey stewartson ii are considered

simultaneous confidence bands for linear regression and smoothing suppose we observe y i f x i varepsilon i i 1 ldots n we wish to find approximate 1 alpha simultaneous confidence regions for f x x in mathscr x our regions will be centered around linear estimates hat f x of nonparametric or nonparametric f x there is a large amount of previous work on this subject substantial restrictions have been usually placed on some or all of the dimensionality of x the class of functions f that can be considered the class of linear estimates hat f and the region mathscr x the method we present is an approximation to the tube formula dn can be used for multidimensional x and a wide class of linear estimates by considering the effect of bias we are able to relax assumptions on the class of functions f which are considered simultaneous and numerical computations are used to illustrate the performance

a direct method for dromion solutions of the davey stewartson equations and their asymptotic properties a new direct approach to determining a class of solutions including the dromion solutions of the davey stewartson equations is presented the form of solution obtained allows a detailed asymptotic analysis of the dromion solutions and compact expression for the phase shifts and changes of amplitude as a result of interaction of the dromions to be determined a class of solutions describing dromion scattering is discussed and computer plots of the interactions of such solutions are presented

a tighter variant of jensen s lower bound for stochastic programs and separable approximations to recourse functions abstract in this paper we propose a new method to compute lower bounds on the optimal objective value of a stochastic program and show how this method can be used to construct separable approximations to the recourse functions we show that our method yields tighter lower bounds than jensen s lower bound and it requires a reasonable amount of computational effort even for large problems the fundamental idea behind our method is to relax certain constraints by associating dual multipliers with them this yields a smaller stochastic program that is easier to solve we particularly focus on the special case where we relax all but one of the constraints in this case the recourse functions of the smaller stochastic program are one dimensional functions we use these one dimensional recourse functions to construct separable approximations to the original recourse functions computational experiments indicate that our lower bounds can significantly improve jensen s lower bound and our recourse function approximations can provide good solutions

stochastic network interdiction using limited assets an interdictor attempts to destroy parts of a capacitated network through which an adversary will subsequently maximize flow we formulate and solve a stochastic version of the interdictor s problem minimize the expected maximum flow through the network when interdiction successes are binary random variables extensions are made to handle uncertain arc capacities and other realistic variations these two stage stochastic integer programs have applications to interdicting illegal drugs and to reducing the effectiveness of a military force moving materiel troops information etc through a network in wartime two equivalent model formulations allow jensen s inequality to be used to compute both lower and upper bounds on the objective and these bounds are improved within a sequential approximation algorithm successful computational results are reported on networks with over 100 nodes 80 interdictable arcs and 180 total arcs

realizability of point processes there are various situations in which it is natural to ask whether a given collection of k functions j r 1 r j j 1 k defined on a set x are the first k correlation functions of a point process on x here we describe some necessary and sufficient conditions on the j s for this to be true our primary examples are x d x d and x an arbitrary finite set in particular we extend a result by ambartzumian and sukiasian showing realizability at sufficiently small densities 1 r typically if any realizing process exists there will be many even an uncountable number in this case we prove when x is a finite set the existence of a realizing gibbs measure with k body potentials which maximizes the entropy among all realizing measures we also investigate in detail a simple example in which a uniform density and translation invariant 2 are specified on there is a gap between our best upper bound on possible values of and the largest for which realizability can be established

bounding multi stage stochastic programs from above the purpose of this paper is to present general approaches for bounding some multi stage stochastic programs from above the results are based on restricting the solution set such that the remaining multi stage stochastic program is easy to solve an example where the methods can be applied is presented

a piecewise linear upper bound on the network recourse function we consider the optimal value of a pure minimum cost network flow problem as a function of supply demand and arc capacities we present a new piecewise linear upper bound on this function which is called the network recourse function the bound is compared to the standard madansky bound and is shown computationally to be a little weaker but much faster to find the amount of work is linear in the number of stochastic variables not exponential as is the case for the madansky bound therefore the reduction in work increases as the number of stochastic variables increases computational results are presented

assessing neuronal coherence with single unit multi unit and local field potentials the purpose of this study was to obtain a better understanding of neuronal responses to correlated input in particular focusing on the aspect of synchronization of neuronal activity the first aim was to obtain an analytical expression for the coherence between the output spike train and correlated input and for the coherence between output spike trains of neurons with correlated input for poisson neurons we could derive that the peak of the coherence between the correlated input and multi unit activity increases proportionally with the square root of the number of neurons in the multi unit recording the coherence between two typical multi unit recordings 2 to 10 single units with partially correlated input increases proportionally with the number of units in the multi unit recordings the second aim of this study was to investigate to what extent the amplitude and signal to noise ratio of the coherence between input and output varied for single unit versus multi unit activity and how they are affected by the duration of the recording the same problem was addressed for the coherence between two single unit spike series and between two multi unit spike series the analytical results for the poisson neuron and numerical simulations for the conductance based leaky integrate and fire neuron and for the conductance based hodgkin huxley neuron show that the expectation value of the coherence function does not increase for a longer duration of the recording the only effect of a longer duration of the spike recording is a reduction of the noise in the coherence function the results of analytical derivations and computer simulations for model neurons show that the coherence for multi unit activity is larger than that for single unit activity this is in agreement with the results of experimental data obtained from monkey visual cortex v4 finally we show that multitaper techniques greatly contribute to a more accurate estimate of the coherence by reducing the bias and variance in the coherence estimate

single commodity network design with random edge capacities this paper examines the single commodity network design problem with stochastic edge capacities we characterize the structures of the optimal designs and compare with the deterministic counterparts we do this partly to understand what constitutes robust network designs but also to construct a heuristic for the stochastic problem leading to optimality gaps of about 10 in our view that is a rather good result for problems that otherwise cannot be solved at all

a note on the phase locking value and its properties we investigate the properties of the phase locking value plv and the phase lag index pli as metrics for quantifying interactions in bivariate local field potential lfp electroencephalography eeg and magnetoencephalography meg data in particular we describe the relationship between nonparametric estimates of plv and pli and the parameters of two distributions that can both be used to model phase interactions the first of these is the von mises distribution for which the sample plv is a maximum likelihood estimator the second is the relative phase distribution associated with bivariate circularly symmetric complex gaussian data we derive an explicit expression for the plv for this distribution and show that it is a function of the cross correlation between the two signals we compare the bias and variance of the sample plv and the plv computed from the cross correlation we also show that both the von mises and gaussian models are suitable for representing relative phase in application to lfp data from a visually cued motor study in macaque we then compare results using the two different plv estimators and conclude that for this data the sample plv provides equivalent information to the cross correlation of the two complex time series

solving the kp hierarchy by gauge transformations we show that it is convenient to use gauge transformations sometimes called explicit backlund transformations to generate new solutions for the kp hierarchy two particular kinds of gauge transformation operators constructed out of the initial wave functions are of fundamental importance in this approach through such gauge transformations a very simple formula for the tau function is obtained encompassing and unifying all kinds of existing solutions the corresponding free fermion representation and baker functions for the new function can also be constructed

second order lower bounds on the expectation of a convex function we develop a class of lower bounds on the expectation of a convex function the bounds utilize the first two moments of the underlying random variable whose support is contained in a bounded interval or hyperrectangle our bounds have applications to stochastic programs whose random parameters are known only through limited moment information computational results are presented for two stage stochastic linear programs

learning algorithms for separable approximations of discrete stochastic optimization problems we propose the use of sequences of separable piecewise linear approximations for solving nondifferentiable stochastic optimization problems the approximations are constructed adaptively using a combination of stochastic subgradient information and possibly sample information on the objective function itself we prove the convergence of several versions of such methods when the objective function is separable and has integer break points and we illustrate their behavior on numerical examples we then demonstrate the performance on nonseparable problems that arise in the context of two stage stochastic programming problems and demonstrate that these techniques provide near optimal solutions with a very fast rate of convergence compared with other solution techniques

the pairwise phase consistency a bias free measure of rhythmic neuronal synchronization oscillatory activity is a widespread phenomenon in nervous systems and has been implicated in numerous functions signals that are generated by two separate neuronal sources often demonstrate a consistent phase relationship in a particular frequency band i e they demonstrate rhythmic neuronal synchronization this consistency is conventionally measured by the plv phase locking value or the spectral coherence measure both statistical measures suffer from significant bias in that their sample estimates overestimate the population statistics for finite sample sizes this is a significant problem in the neurosciences where statistical comparisons are often made between conditions with a different number of trials or between neurons with a different number of spikes we introduce a new circular statistic the ppc pairwise phase consistency we demonstrate that the sample estimate of the ppc is a bias free and consistent estimator of its corresponding population parameter we show both analytically and by means of numerical simulations that the population statistic of the ppc is equivalent to the population statistic of the squared plv the variance and mean squared error of the ppc and plv are compared finally we demonstrate the practical relevance of the method in actual neuronal data recorded from the orbitofrontal cortex of rats that engage in a two odour discrimination task we find a strong increase in rhythmic synchronization of spikes relative to the local field potential as measured by the ppc for a wide range of low frequencies including the theta band during the anticipation of sucrose delivery in comparison to the anticipation of quinine delivery

the dirac equation and integrable systems of kp type the propagator for the 2d heat equation in an arbitrary linear space is shown to give solutions of the two component kadomtsev petviashvilii kp equations also called davey stewartson system this propagator is subject to the klein gordon equation and its right derivatives are required to be of rank one that imply that it can be expressed in terms of solutions of the dirac equation large families of solutions of the two component kadomtsev petviashvilii equations are constructed in terms of solutions of the heat and dirac equations particular attention is paid to the real reductions of the davey stewartson type recovering in this way the line solitons and the multidromion solutions moreover new solutions to the davey stewartson i are presented as massive deformations of the dromion

the dependence of spike field coherence on expected intensity the coherence between neural spike trains and local field potential recordings called spike field coherence is of key importance in many neuroscience studies in this work aside from questions of estimator performance we demonstrate that theoretical spike field coherence for a broad class of spiking models depends on the expected rate of spiking this rate dependence confounds the phase locking of spike events to field potential oscillations with overall neuron activity and is demonstrated analytically for a large class of stochastic models and in simulation finally the relationship between the spike field coherence and the intensity field coherence is detailed analytically this latter quantity is independent of neuron firing rate and under commonly found conditions is proportional to the probability that a neuron spikes at a specific phase of field oscillation hence intensity field coherence is a rate independent measure and a candidate on which to base the appropriate statistical inference of spike field synchrony

an arc exchange decomposition method for multistage dynamic networks with random arc capacities abstract multistage dynamic networks with random arc capacities mdnrac have been successfully used for modeling various resource allocation problems in the transportation area however solving these problems is generally computationally intensive and there is still a need to develop more efficient solution approaches in this paper we propose a new heuristic approach that solves the mdnrac problem by decomposing the network at each stage into a series of subproblems with tree structures each subproblem can be solved efficiently the main advantage is that this approach provides an efficient computational device to handle the large scale problem instances with fairly good solution quality we show that the objective value obtained from this decomposition approach is an upper bound for that of the mdnrac problem numerical results demonstrate that our proposed approach works very well

an improved index of phase synchronization for electrophysiological data in the presence of volume conduction noise and sample size bias phase synchronization is a manifestation of interaction between neuronal groups measurable from lfp eeg or meg signals however volume conduction can cause the coherence and the phase locking value to spuriously increase it has been shown that the imaginary component of the coherency imc cannot be spuriously increased by volume conduction of independent sources recently it was proposed that the phase lag index pli which estimates to what extent the phase leads and lags between signals from two sensors are nonequiprobable improves on the imc compared to imc pli has the advantage of being less influenced by phase delays however sensitivity to volume conduction and noise and capacity to detect changes in phase synchronization is hindered by the discontinuity of the pli as small perturbations turn phase lags into leads and vice versa to solve this problem we introduce a related index namely the weighted phase lag index wpli differently from pli in wpli the contribution of the observed phase leads and lags is weighted by the magnitude of the imaginary component of the cross spectrum we demonstrate two advantages of the wpli over the pli in terms of reduced sensitivity to additional uncorrelated noise sources and increased statistical power to detect changes in phase synchronization another factor that can affect phase synchronization indices is sample size bias we show that when directly estimated both pli and the magnitude of the imc have typically positively biased estimators to solve this problem we develop an unbiased estimator of the squared pli and a debiased estimator of the squared wpli

a biased look at phase locking brief critical review and proposed remedy a number of popular measures of dependence between pairs of bandlimited signals rely on analytic phase a common misconception is that the dependence revealed by these measures must be specific to the spectral range of the filtered input signals implicitly or explicitly obtaining analytic phase involves normalizing the signal by its own envelope which is a nonlinear operation that introduces broad spectral leakage we review how this generates bias and complicates the interpretation of commonly used measures of phase locking a specific example of this effect may create spurious phase locking as a consequence of nonzero circular mean in the phase of input signals which can be viewed as spectral leakage to 0 hz corrections for this problem which recenter or uniformize the distribution of phase may fail when the amplitudes of the compared signals are correlated to address the more general problem of spectral bias a novel measure of phase locking is proposed the amplitude weighted phase locking value this measure is closely related to coherence but it removes ambiguities of interpretation that detract from the latter

phase coupling estimation from multivariate phase statistics coupled oscillators are prevalent throughout the physical world dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real world systems and are compelling models of neural systems however these formulations usually deal with the forward problem simulating a system from known coupling parameters here we provide a solution to the inverse problem determining the coupling parameters from measurements starting from the dynamic equations of a system of symmetrically coupled phase oscillators given by a nonlinear langevin equation we derive the corresponding equilibrium distribution this formulation leads us to the maximum entropy distribution that captures pairwise phase relationships to solve the inverse problem for this distribution we derive a closed form solution for estimating the phase coupling parameters from observed phase statistics through simulations we show that the algorithm performs well in high dimensions d 100 and in cases with limited data as few as 100 samples per dimension in addition we derive a regularized solution to the estimation and show that the resulting procedure improves performance when only a limited amount of data is available because the distribution serves as the unique maximum entropy solution for pairwise phase statistics phase coupling estimation can be broadly applied in any situation where phase measurements are made under the physical interpretation the model may be used for inferring coupling relationships within cortical networks

dependence of neuronal correlations on filter characteristics and marginal spike train statistics correlated neural activity has been observed at various signal levels e g spike count membrane potential local field potential eeg fmri bold most of these signals can be considered as superpositions of spike trains filtered by components of the neural system synapses membranes and the measurement process it is largely unknown how the spike train correlation structure is altered by this filtering and what the consequences for the dynamics of the system and for the interpretation of measured correlations are in this study we focus on linearly filtered spike trains and particularly consider correlations caused by overlapping presynaptic neuron populations we demonstrate that correlation functions and statistical second order measures like the variance the covariance and the correlation coefficient generally exhibit a complex dependence on the filter properties and the statistics of the presynaptic spike trains we point out that both contributions can play a significant role in modulating the interaction strength between neurons or neuron populations in many applications the coherence allows a filter independent quantification of correlated activity in different network models we discuss the estimation of network connectivity from the high frequency coherence of simultaneous intracellular recordings of pairs of neurons

solving slp recourse problems with arbitrary multivariate distributions the dependent case bounding the expectation of a convex function of a multivariate random variable is of great importance for solving stochastic linear programming problems slp with recourse the classic bounds are those of jensen and edmundson madansky whereby jensen s inequality is available in the independent as well as in the dependent case in contrast with the edmundson madansky e m inequality madansky a 1959 bounds on the expectation of a convex function of multivariate random variable ann math statist 30 743 746 which is valid only in the independent case this paper presents a straightforward extension of the e m inequality for the dependent case yielding a discrete distribution that is extremal with respect to a partial ordering of a set of distribution functions further we prove that the bounds for the expectation behave monotonically by applying the obtained inequality to smaller and smaller subintervals as this requires the evaluation of conditional probabilities and expectations we replace the given distribution by a discrete one resulting from sampling and determine the sampling size that keeps the statistical error negligible finally we conclude with the application to slp recourse problems and state some computational results illustrating the effort for solving recourse problems

joint analysis of spikes and local field potentials using copula recent technological advances which allow for simultaneous recording of spikes and local field potentials lfps at multiple sites in a given cortical area or across different areas have greatly increased our understanding of signal processing in brain circuits joint analysis of simultaneously collected spike and lfp signals is an important step to explicate how the brain orchestrates information processing in this contribution we present a novel statistical framework based on gaussian copula to jointly model spikes and lfp in our approach we use copula to link separate marginal regression models to construct a joint regression model in which the binary valued spike train data are modeled using generalized linear model glm and the continuous valued lfp data are modeled using linear regression model parameters can be efficiently estimated via maximum likelihood in particular we show that our model offers a means to statistically detect directional influence between spikes and lfp akin to granger causality measure and that we are able to assess its statistical significance by conducting a wald test through extensive simulations we also show that our method is able to reliably recover the true model used to generate the data to demonstrate the effectiveness of our approach in real setting we further apply the method to a mixed neural dataset consisting of spikes and lfp simultaneously recorded from the visual cortex of a monkey performing a contour detection task

sampling properties of the spectrum and coherency of sequences of action potentials the spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes this article begins with a review of these quantities their interpretation and how they may be estimated a discussion of how to assess the statistical significance of features in these measures is included in addition new work is presented that builds on the framework established in the review section this work investigates how the estimates and their error bars are modified by finite sample sizes finite sample corrections are derived based on a doubly stochastic inhomogeneous poisson process model in which the rate functions are drawn from a low variance gaussian process it is found that in contrast to continuous processes the variance of the estimators cannot be reduced by smoothing beyond a scale set by the number of point events in the interval alternatively the degrees of freedom of the estimators can be thought of as bounded from above by the expected number of point events in the interval further new work describing and illustrating a method for detecting the presence of a line in a point process spectrum is also presented corresponding to the detection of a periodic modulation of the underlying rate this work demonstrates that a known statistical test applicable to continuous processes applies with little modification to point process spectra and is of utility in studying a point process driven by a continuous stimulus although the material discussed is of general applicability to point processes attention will be confined to sequences of neuronal action potentials spike trains the motivation for this work

the darboux system finite rank constraints and darboux transformations the exponential solutions of the darboux equations for conjugate nets is considered it is shown that rank one constraints over the right derivatives of invertible operators on an arbitrary linear space give solutions of the darboux system which can be understood as a vectorial darboux transformation of the exponential background the method is extended further to obtain vectorial darboux transformations of the darboux system

energy exchange of interacting coherent structures in multidimensions abstract the formalism recently developed by fokas and the author for the solution of the initial boundary value problem for the davey stewartson equation is used to study the time evolution of the multidromion solution showing in particular that interacting coherent structures in multidimensions not only exhibit a two dimensional phase shift but also change amplitude and exchange energy several examples of physically relevant boundary conditions which generate other kinds of explicit finite energy solutions are also presented

restricted recourse bounds for stochastic linear programming we consider the problem of bounding the expected value of a linear program lp containing random coefficients with applications to solving two stage stochastic programs an upper bound for minimizations is derived from a restriction of an equivalent penalty based formulation of the primal stochastic lp and a lower bound is obtained from a restriction of a reformulation of the dual our restricted recourse bounds are more general and more easily computed than most other bounds because random coefficients may appear anywhere in the lp neither independence nor boundedness of the coefficients is needed and the bound is computed by solving a single lp or nonlinear program analytical examples demonstrate that the new bounds can be stronger than complementary jensen bounds an upper bound is complementary to a lower bound and vice versa in computational work we apply the bounds to a two stage stochastic program for semiconductor manufacturing with uncertain demand and production rates

sublinear upper bounds for stochastic programs with recourse separable sublinear functions are used to provide upper bounds on the recourse function of a stochastic program the resulting problem s objective involves the inf convolution of convex functions a dual of this problem is formulated to obtain an implementable procedure to calculate the bound function evaluations for the resulting convex program only require a small number of single integrations in contrast with previous upper bounds that require a number of function evaluations that grows exponentially in the number of random variables the sublinear bound can often be used when other suggested upper bounds are intractable computational results indicate that the sublinear approximation provides good efficient bounds on the stochastic program objective value

a jackknife approach to quantifying single trial correlation between covariance based metrics undefined on a single trial basis the quantification of covariance between neuronal activities functional connectivity requires the observation of correlated changes and therefore multiple observations the strength of such neuronal correlations may itself undergo moment by moment fluctuations which might e g lead to fluctuations in single trial metrics such as reaction time rt or may co fluctuate with the correlation between activity in other brain areas yet quantifying the relation between moment by moment co fluctuations in neuronal correlations is precluded by the fact that neuronal correlations are not defined per single observation the proposed solution quantifies this relation by first calculating neuronal correlations for all leave one out subsamples i e the jackknife replications of all observations and then correlating these values because the correlation is calculated between jackknife replications we address this approach as jackknife correlation jc first we demonstrate the equivalence of jc to conventional correlation for simulated paired data that are defined per observation and therefore allow the calculation of conventional correlation while the jc recovers the conventional correlation precisely alternative approaches like sorting and binning result in detrimental effects of the analysis parameters we then explore the case of relating two spectral correlation metrics like coherence that require multiple observation epochs where the only viable alternative analysis approaches are based on some form of epoch subdivision which results in reduced spectral resolution and poor spectral estimators we show that jc outperforms these approaches particularly for short epoch lengths without sacrificing any spectral resolution finally we note that the jc can be applied to relate fluctuations in any smooth metric that is not defined on single observations

a dynamic network flow problem with uncertain arc capacities formulation and problem structure we consider a dynamic network flow problem where the arc capacities are random variables this gives a multistage stochastic linear program we describe the randomness using a multi scenario approach because of the multilayered structure there are several ways to decompose the linear program we classify different decomposition schemes and we develop a scheme calledcompath decomposition which is derived from path decomposition for network flows we give a polynomial time algorithm to find a cheapest compath that can solve the subproblems resulting from compath decomposition finally compath decomposition is extended to multicommodity flow problems

the full infinite dimensional moment problem on semi algebraic sets of generalized functions we consider a generic basic semi algebraic subset s of the space of generalized functions that is a set given by not necessarily countably many polynomial constraints we derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on s namely to be the moment sequence of a finite measure concentrated on s our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi algebraic sets of rd in this way we determine realizability conditions that can be more easily verified than the well known haviland type conditions our result completely characterizes the support of the realizing measure in terms of its moments as concrete examples of semi algebraic sets of generalized functions we consider the set of all radon measures and the set of all the measures having bounded radon nikodym density w r t the lebesgue measure