sufficient second order optimality conditions for semilinear control problems with pointwise state constraints second order sufficient optimality conditions are established for the optimal control of semilinear elliptic and parabolic equations with pointwise constraints on the control and the state in contrast to former publications on this subject the cone of critical directions is the smallest possible in the sense that the second order sufficient conditions are the closest to the associated necessary ones the theory is developed for elliptic distributed controls in domains up to dimension three moreover problems of elliptic boundary control and parabolic distributed control are discussed in spatial domains of dimension two and one respectively

optimal control problem for an ecosystem with two competing preys and one predator abstract this work is devoted to the optimal control problem for an ecosystem composed of one predator and two competing preys and our goal is to maximize the total density of the three populations we first investigate the existence and uniqueness of the positive strong solution for the controlled system and find an optimal solution under given initial conditions then we establish the first order necessary optimality condition and point out that the optimal control has a bang bang form moreover the second order necessary and sufficient optimality conditions are established

local linearization filters for non linear continuous discrete state space models with multiplicative noise in this paper the local linearization method for the approximate computation of the prediction and filtering estimates of continuous discrete state space models is extended to the general case of non linear non autonomous models with multiplicative noise the approximate prediction and filter estimates are obtained by applying the optimal linear filter to the piecewise linear state space model that emerges from a local linearization of both the non linear state equation and the non linear measurement equation in addition the solutions of the differential equations that describe the evolution of the first two conditional moments between observations are obtained and an algorithm for their numerical computation is also given the performance of the ll filters is illustrated by mean of numerical experiments

blowup for fractional nls abstract we consider fractional nls with focusing power type nonlinearity i t u s u u 2 u t x r r n where 1 2 s 1 and 0 for s n 2 and 0 2 s n 2 s for s n 2 we prove a general criterion for blowup of radial solutions in r n with n 2 for l 2 supercritical and l 2 critical powers 2 s n in addition we study the case of fractional nls posed on a bounded star shaped domain r n in any dimension n 1 and subject to exterior dirichlet conditions in this setting we prove a general blowup result without imposing any symmetry assumption on u t x for the blowup proof in r n we derive a localized virial estimate for fractional nls in r n which uses balakrishnan s formula for the fractional laplacian s from semigroup theory in the setting of bounded domains we use a pohozaev type estimate for the fractional laplacian to prove blowup

second order optimality conditions for semilinear elliptic control problems with finitely many state constraints this paper deals with necessary and sufficient optimality conditions for control problems governed by semilinear elliptic partial differential equations with finitely many equality and inequality state constraints some recent results on this topic for optimal control problems based upon results for abstract optimization problems are compared with some new results using methods adapted to the control problems meanwhile the lagrangian formulation is followed to provide the optimality conditions in the first case the lagrangian and hamiltonian functions are used in the second statement finally we prove the equivalence of both formulations

recursive noise adaptive kalman filtering by variational bayesian approximations this article considers the application of variational bayesian methods to joint recursive estimation of the dynamic state and the time varying measurement noise parameters in linear state space models the proposed adaptive kalman filtering method is based on forming a separable variational approximation to the joint posterior distribution of states and noise parameters on each time step separately the result is a recursive algorithm where on each step the state is estimated with kalman filter and the sufficient statistics of the noise variances are estimated with a fixed point iteration the performance of the algorithm is demonstrated with simulated data

bbb l 2 sufficient conditions for end constrained optimal control problems with inputs in a polyhedron an hbox bbb l 2 local optimality sufficiency theorem is proved for a class of structured infinite dimensional nonconvex programs with constraints of the form u in omega and h u 0 where omega is a set of lebesgue measurable essentially bounded vector valued functions u cdot 0 1 rightarrow hbox bbb r m with range in a polyhedron u and h is a smooth map of the space of essentially bounded functions u cdot into bbb r k the sufficiency theorem is based on formal counterparts of the finite dimensional karush kuhn tucker sufficient conditions in a cartesian product of polyhedra a strengthened variant of pontryagin s necessary condition and structure and continuity conditions on the first and second differentials of the objective function and equality constraint functions the new sufficient conditions are directly applicable to nonconvex continuous time bolza optimal control problems with control quadratic hamiltonians unqualified affine inequality constraints on vector valued control inputs and equality constraints on the terminal state vector or equivalent isoperimetric constraints on integrals of functions depending on the state and control variables

state space analysis of granger geweke causality measures with application to fmri the recent interest in the dynamics of networks and the advent across a range of applications of measuring modalities that operate on different temporal scales have put the spotlight on some significant gaps in the theory of multivariate time series fundamental to the description of network dynamics is the direction of interaction between nodes accompanied by a measure of the strength of such interactions granger causality and its associated frequency domain strength measures gems due to geweke provide a framework for the formulation and analysis of these issues in pursuing this setup three significant unresolved issues emerge first computing gems involves computing submodels of vector time series models for which reliable methods do not exist second the impact of filtering on gems has never been definitively established third the impact of downsampling on gems has never been established in this work using state space methods we resolve all these issues and illustrate the results with some simulations our analysis is motivated by some problems in fmri brain imaging to which we apply it but it is of general applicability

optimal control problems with partially polyhedric constraints this paper discusses a class of state constrained optimal control problems for which it is possible to formulate second order necessary or sufficient conditions for local optimality or quadratic growth that do not involve all curvature terms for the constraints this kind of result is classical in the case of polyhedric control constraints our theory of optimization problems with partially polyhedric constraints allows to extend these results to the case when the control constraints are polyhedric in the presence of state constraints satisfying some specific hypotheses the analysis is based on the assumption that some strict semilinearized qualification condition is satisfied we apply the theory to some optimal control problems of elliptic equations with state and control constraints

gaussian filters for nonlinear filtering problems we develop and analyze real time and accurate filters for nonlinear filtering problems based on the gaussian distributions we present the systematic formulation of gaussian filters and develop efficient and accurate numerical integration of the optimal filter we also discuss the mixed gaussian filters in which the conditional probability density is approximated by the sum of gaussian distributions a new update rule of weights for gaussian sum filters is proposed our numerical tests demonstrate that new filters significantly improve the extended kalman filter with no additional cost and the new gaussian sum filter has a nearly optimal performance

stability of standing waves for the fractional schrodinger choquard equation abstract in this paper we consider the stability of standing waves for the fractional schrodinger choquard equation with an l 2 critical nonlinearity by using the profile decomposition of bounded sequences in h s and variational methods we prove that the standing waves are orbitally stable we extend the study of bhattarai for a single equation bhattarai 2017 to the l 2 critical case

a legendre galerkin spectral method for optimal control problems governed by stokes equations in this paper we study the legendre galerkin spectral approximation of distributed optimal control problems governed by stokes equations we show that the discretized control problems satisfy the well known babuska brezzi conditions by choosing an appropriate pair of discretization spaces for the velocity and the pressure constructing suitable base functions of the discretization spaces leads to sparse coefficient matrices we first derive a priori error estimates in both h 1 and l 2 norms for the legendre galerkin approximation of the unconstrained control problems then both a priori and a posteriori error estimates are obtained for control problems with the constraints of an integral type thanks to the higher regularity of the optimal control finally some illustrative numerical examples are presented to demonstrate the error estimates

second order analysis for strong solutions in the optimal control of parabolic equations in this paper we provide a second order analysis for strong solutions in the optimal control of parabolic equations we consider the case of box constraints on the control and final integral constraints on the state in contrast to sufficient conditions assuring quadratic growth in the weak sense i e when the cost increases at least quadratically for admissible controls uniformly near to the nominal one see e g 16 26 our main result provides a sufficient condition for quadratic growth of the cost for admissible controls whose associated states are uniformly near to the state of the nominal one as a consequence of our results for qualified problems with a strictly convex and quadratic hamiltonian we prove that both notions of quadratic growth coincide

robustly estimating the flow direction of information in complex physical systems we propose a new measure phase slope index to estimate the direction of information flux in multivariate time series this measure a is insensitive to mixtures of independent sources b gives meaningful results even if the phase spectrum is not linear and c properly weights contributions from different frequencies these properties are shown in extended simulations and contrasted to granger causality which yields highly significant false detections for mixtures of independent sources an application to electroencephalography data eyes closed condition reveals a clear front to back information flow

nonparametric filtering for stochastic nonlinear oscillations this paper proposes a method of nonparametric filtering for stochastic nonlinear oscillations with particular interest in their derivative estimation based on a second order ordinary differential equation a stochastic oscillation is modeled by a two variate stochastic differential equation without specifying the function form of the drift function where the first variable is assumed to be observable but not the other given the discrete time series with observation error the proposed method enables us to estimate the values of the drift function and its derivatives including those of the unobservable variable according to the results of numerical experiments to compare estimation accuracy with a parametric method the proposed method shows better performance in the estimation of nonlinear models

a state space model of the hemodynamic approach nonlinear filtering of bold signals in this paper a new procedure is presented which allows the estimation of the states and parameters of the hemodynamic approach from blood oxygenation level dependent bold responses the proposed method constitutes an alternative to the recently proposed friston neuroimage 16 2002 513 method and has some advantages over it the procedure is based on recent groundbreaking time series analysis techniques that have been in this case adopted to characterize hemodynamic responses in functional magnetic resonance imaging fmri this work represents a fundamental improvement over existing approaches to system identification using nonlinear hemodynamic models and is important for three reasons first our model includes physiological noise previous models have been based upon ordinary differential equations that only allow for noise or error to enter at the level of observation secondly by using the innovation method and the local linearization filter not only the parameters but also the underlying states of the system generating responses can be estimated these states can include things like a flow inducing signal triggered by neuronal activation de oxyhemoglobine cerebral blood flow and volume finally radial basis functions have been introduced as a parametric model to represent arbitrary temporal input sequences in the hemodynamic approach which could be essential to understanding those brain areas indirectly related to the stimulus hence thirdly by inferring about the radial basis parameters we are able to perform a blind deconvolution which permits both the reconstruction of the dynamics of the most likely hemodynamic states and also to implicitly reconstruct the underlying synaptic dynamics induced experimentally which caused these states variations from this study we conclude that in spite of the utility of the standard discrete convolution approach used in statistical parametric maps spm nonlinear bold phenomena and unspecific input temporal sequences must be included in the fmri analysis

second order sufficient optimality conditions for some state constrained control problems of semilinear elliptic equations this paper deals with a class of optimal control problems governed by elliptic equations with nonlinear boundary condition the case of boundary control is studied pointwise constraints on the control and certain equality and set constraints on the state are considered second order sufficient conditions for local optimality of controls are established

optimal control of navier stokes equations by oseen approximation a non standard sequential quadratic programming type iterational process based on oseen s approximation is proposed and analyzed to solve an optimal control problem for the steady state navier stokes equations further numerical approximation by a finite element method and sample computational experiments are presented too

augmented lagrangian sqp methods for nonlinear optimalcontrol problems of tracking type an augmented lagrangian method with second order update is developed and its relationship to the sequential quadratic programming method is described the rate of convergence proof depends on a second order sufficient optimality condition which is shown to be satisfied for a class of nonlinear optimal control problems of tracking type numerical examples are included which demonstrate the globalizing effect of the augmented lagrangian method

nonlinear small data scattering for the generalized korteweg de vries equation abstract we study the longtime stability of small solutions to the ivp for the generalized korteweg de vries equation we obtain a lower bound for the degrees of nonlinearity of the perturbation which guarantees that the small solutions of the nonlinear problem behave asymptotically like the solutions of the associated linear problem this behavior allows us to establish a nonlinear scattering result for small perturbations with these degrees for a class of small data we improve the value of this lower bound the new crucial ingrediants in our proofs are the l p decay estimates of the half derivative of the airy kernel

first and second order optimality conditions for a class of optimal control problems with quasilinear elliptic equations a class of optimal control problems for quasilinear elliptic equations is considered where the coefficients of the elliptic differential operator depend on the state function first and second order optimality conditions are discussed for an associated control constrained optimal control problem main emphasis is laid on second order sufficient optimality conditions to this aim the regularity of the solutions to the state equation and its linearization is studied in detail and the pontryagin maximum principle is derived one of the main difficulties is the nonmonotone character of the state equation

on finite time blow up for the mass critical hartree equations we consider the fractional schrodinger equations with focusing hartree type nonlinearities when the energy is negative we show that the solution blows up in a finite time for this purpose based on glassey s argument we obtain a virial type inequality

optimal control strategies for a new ecosystem governed by reaction diffusion equations abstract an optimal control problem for a new ecosystem described by reaction diffusion equations is studied in this contribution different from the classical prey predator law the phenomenon that the growth of predator population gradually reduces due to the after effects of prey population is ubiquitous in the real world such as allelopathy phenomenon in planktonic ecosystems to model this relationship between predator and prey populations together with diffusion behaviors a novel model with general holling type functional response is presented after that the existence and uniqueness of the global positive strong solution to the ecosystem is obtained by the method of semigroups of operators on this basis an optimal control problem of the ecosystem is considered the existence of optimal control strategy is proved by using minimal sequence then the first order necessary optimality condition is obtained and the corresponding optimal control is found to be of on off form furthermore the second order necessary condition for optimal control and sufficient condition for local optimal control are all established finally a numerical example is offered to demonstrate the applications of the results obtained in this work

a method to produce evolving functional connectivity maps during the course of an fmri experiment using wavelet based time varying granger causality functional magnetic resonance imaging fmri is widely used to identify neural correlates of cognitive tasks however the analysis of functional connectivity is crucial to understanding neural dynamics although many studies of cerebral circuitry have revealed adaptative behavior which can change during the course of the experiment most of contemporary connectivity studies are based on correlational analysis or structural equations analysis assuming a time invariant connectivity structure in this paper a novel method of continuous time varying connectivity analysis is proposed based on the wavelet expansion of functions and vector autoregressive model wavelet dynamic vector autoregressive dvar the model also allows identification of the direction of information flow between brain areas extending the granger causality concept to locally stationary processes simulation results show a good performance of this approach even using short time intervals the application of this new approach is illustrated with fmri data from a simple ab motor task experiment

bayesian estimation of dynamical systems an application to fmri this paper presents a method for estimating the conditional or posterior distribution of the parameters of deterministic dynamical systems the procedure conforms to an em implementation of a gauss newton search for the maximum of the conditional or posterior density the inclusion of priors in the estimation procedure ensures robust and rapid convergence and the resulting conditional densities enable bayesian inference about the model parameters the method is demonstrated using an input state output model of the hemodynamic coupling between experimentally designed causes or factors in fmri studies and the ensuing bold response this example represents a generalization of current fmri analysis models that accommodates nonlinearities and in which the parameters have an explicit physical interpretation second the approach extends classical inference based on the likelihood of the data given a null hypothesis about the parameters to more plausible inferences about the parameters of the model given the data this inference provides for confidence intervals based on the conditional density 2002 elsevier science usa

dynamic modeling of neuronal responses in fmri using cubature kalman filtering this paper presents a new approach to inverting fitting models of coupled dynamical systems based on state of the art cubature kalman filtering crucially this inversion furnishes posterior estimates of both the hidden states and parameters of a system including any unknown exogenous input because the underlying generative model is formulated in continuous time with a discrete observation process it can be applied to a wide variety of models specified with either ordinary or stochastic differential equations these are an important class of models that are particularly appropriate for biological time series where the underlying system is specified in terms of kinetics or dynamics i e dynamic causal models we provide comparative evaluations with generalized bayesian filtering dynamic expectation maximization and demonstrate marked improvements in accuracy and computational efficiency we compare the schemes using a series of difficult nonlinear toy examples and conclude with a special focus on hemodynamic models of evoked brain responses in fmri our scheme promises to provide a significant advance in characterizing the functional architectures of distributed neuronal systems even in the absence of known exogenous experimental input e g resting state fmri studies and spontaneous fluctuations in electrophysiological studies importantly unlike current bayesian filters e g dem our scheme provides estimates of time varying parameters which we will exploit in future work on the adaptation and enabling of connections in the brain

second order optimality conditions in sets of sf l infty functions with range in a polyhedron formal extensions of the general second order necessary conditions and sufficient conditions for local optimality in a polyhedral convex set u subset bbb r m are established for sf l infty local optimality and sf l 2 local optimality in the infinite dimensional nonpolyhedral convex set omega of sf l infty functions u cdot 0 1 rightarrow u a more refined analysis for nonconvex cost functions with specially structured differentials yields optimality conditions that apply to an important class of constrained input bolza optimal control problems the gap between the necessary conditions and sufficient conditions in this setting is uncharacteristically small for infinite dimensional problems in the control problem context the sf l infty local optimality conditions and sf l 2 local optimality conditions entail a mild strengthening of a pointwise strict complementarity condition and variants of the legendre clebsch condition and the pontryagin minimum principle in related recent studies similar second order sufficient conditions for the special case u 0 infty are the key hypotheses in corresponding local convergence theories for iterative constrained minimization algorithms

a connectivity based method for defining regions of interest in fmri data in this paper we describe a new methodology for defining brain regions of interset rois in functional magnetic resonance imaging fmri data the rois are defined based on their functional connectivity to other rois i e rois are defined as sets of voxels with similar connectivity patterns to other rois the method relies on 1 a spatially regularized canonical correlation analysis for identifying maximally correlated signals which are not due to correlated noise 2 a test for merging rois which have similar connectivity patterns to the other rois and 3 a graph cuts optimization for assigning voxels to rois since our method is fully connectivity based the extracted rois and their corresponding time signals are ideally suited for a subsequent brain connectivity analysis

sharp threshold of blow up and scattering for the fractional hartree equation abstract we consider the fractional hartree equation in the l 2 supercritical case and find a sharp threshold of the scattering versus blow up dichotomy for radial data if m u 0 s s c s c e u 0 m q s s c s c e q and m u 0 s s c s c u 0 h s 2 m q s s c s c q h s 2 then the solution u t is globally well posed and scatters if m u 0 s s c s c e u 0 m q s s c s c e q and m u 0 s s c s c u 0 h s 2 m q s s c s c q h s 2 the solution u t blows up in finite time this condition is sharp in the sense that the solitary wave solution e i t q x is global but not scattering which satisfies the equality in the above conditions here q is the ground state solution for the fractional hartree equation

dispersion of small amplitude solutions of the generalized korteweg de vries equation abstract we study the long time behavior of small solutions of the initial value problem for the generalized korteweg de vries equation t u x 3 u x f u 0 gkdv u x 0 g x for the case where f w w s with s 1 4 23 57 3 8625 our results imply that if g l11 g l22 is sufficiently small then sup r 1 t 1 3 u t l in particular the solution tends to zero in the supremum norm the proofs make use of duhamel s formula and dispersion estimates for the linear propagator as well as chain and leibniz rules for fractional derivatives of compositions d f u lp and products d fg lp 0

wavelets and functional magnetic resonance imaging of the human brain the discrete wavelet transform dwt is widely used for multiresolution analysis and decorrelation or whitening of nonstationary time series and spatial processes wavelets are naturally appropriate for analysis of biological data such as functional magnetic resonance images of the human brain which often demonstrate scale invariant or fractal properties we provide a brief formal introduction to key properties of the dwt and review the growing literature on its application to fmri we focus on three applications in particular i wavelet coefficient resampling or wavestrapping of 1 d time series 2 to 3 d spatial maps and 4 d spatiotemporal processes ii wavelet based estimators for signal and noise parameters of time series regression models assuming the errors are fractional gaussian noise fgn and iii wavelet shrinkage in frequentist and bayesian frameworks to support multiresolution hypothesis testing on spatially extended statistic maps we conclude that the wavelet domain is a rich source of new concepts and techniques to enhance the power of statistical analysis of human fmri data

characterization of local quadratic growth for strong minima in the optimal control of semi linear elliptic equations in this article we consider an optimal control problem of a semi linear elliptic equation with bound constraints on the control our aim is to characterize local quadratic growth for the cost function j in the sense of strong solutions this means that the function j growths quadratically over all feasible controls whose associated state is close enough to the nominal one in the uniform topology the study of strong solutions classical in the calculus of variations seems to be new in the context of pde optimization our analysis based on a decomposition result for the variation of the cost combines pontryagin s principle and second order conditions while these two ingredients are known we use them in such a way that we do not need to assume that the hessian of lagrangian of the problem is a legendre form or that it is uniformly positive on an extended set of critical directions

remarks on damped fractional schrodinger equation with pure power nonlinearity we investigate the initial value problem for a semi linear fractional damped schrodinger equation global existence and scattering are proved depending on the size of the damping coefficient

remarks on the inhomogeneous fractional nonlinear schrodinger equation using a sharp gagliardo nirenberg type inequality well posedness issues of the initial value problem for a fractional inhomogeneous schrodinger equation are investigated

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

simulation of stochastic differential equations through the local linearization method a comparative study a new local linearization ll scheme for the numerical integration of nonautonomous multidimensional stochastic differential equations sdes with additive noise is introduced the numerical scheme is based on the local linearization of the sde s drift coefficient by means of a truncated ito taylor expansion a comparative study with the other ll schemes is presented which shows some advantanges of the new scheme over other ones

pontryagin s principle for state constrained boundary control problems of semilinear parabolic equations this paper deals with state constrained optimal control problems governed by semilinear parabolic equations we establish a minimum principle of pontryagin s type to deal with the state constraints we introduce a penalty problem by using ekeland s principle the key tool for the proof is the use of a special kind of spike perturbations distributed in the domain where the controls are defined conditions for normality of optimality conditions are given

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

dem a variational treatment of dynamic systems this paper presents a variational treatment of dynamic models that furnishes time dependent conditional densities on the path or trajectory of a system s states and the time independent densities of its parameters these are obtained by maximising a variational action with respect to conditional densities under a fixed form assumption about their form the action or path integral of free energy represents a lower bound on the model s log evidence or marginal likelihood required for model selection and averaging this approach rests on formulating the optimisation dynamically in generalised coordinates of motion the resulting scheme can be used for online bayesian inversion of nonlinear dynamic causal models and is shown to outperform existing approaches such as kalman and particle filtering furthermore it provides for dual and triple inferences on a system s states parameters and hyperparameters using exactly the same principles we refer to this approach as dynamic expectation maximisation dem

new developments in state estimation for nonlinear systems based on an interpolation formula accurate state estimators for nonlinear systems can be derived the estimators do not require derivative information which makes them simple to implement

second order necessary and sufficient optimality conditions for optimization problems and applications to control theory this paper deals with a class of nonlinear optimization problems in a function space where the solution is restricted by pointwise upper and lower bounds and by finitely many equality and inequality constraints of functional type second order necessary and sufficient optimality conditions are established where the cone of critical directions is arbitrarily close to the form which is expected from the optimization in finite dimensional spaces the results are applied to some optimal control problems for ordinary and partial differential equations

global voxel and cluster tests by theory and permutation for a difference between two groups of structural mr images of the brain the authors describe almost entirely automated procedures for estimation of global voxel and cluster level statistics to test the null hypothesis of zero neuroanatomical difference between two groups of structural magnetic resonance imaging mri data theoretical distributions under the null hypothesis are available for 1 global tissue class volumes 2 standardized linear model analysis of variance anova and ancova coefficients estimated at each voxel and 3 an area of spatially connected clusters generated by applying an arbitrary threshold to a two dimensional 2 d map of normal statistics at voxel level the authors describe novel methods for economically ascertaining probability distributions under the null hypothesis with fewer assumptions by permutation of the observed data nominal type i error control by permutation testing is generally excellent whereas theoretical distributions may be over conservative permutation has the additional advantage that it can be used to test any statistic of interest such as the sum of suprathreshold voxel statistics in a cluster or cluster mass regardless of its theoretical tractability under the null hypothesis these issues are illustrated by application to mri data acquired from 18 adolescents with hyperkinetic disorder and 16 control subjects matched for age and gender

spatio temporal granger causality a new framework that physiological oscillations of various frequencies are present in fmri signals is the rule not the exception herein we propose a novel theoretical framework spatio temporal granger causality which allows us to more reliably and precisely estimate the granger causality from experimental datasets possessing time varying properties caused by physiological oscillations within this framework granger causality is redefined as a global index measuring the directed information flow between two time series with time varying properties both theoretical analyses and numerical examples demonstrate that granger causality is a monotonically increasing function of the temporal resolution used in the estimation this is consistent with the general principle of coarse graining which causes information loss by smoothing out very fine scale details in time and space our results confirm that the granger causality at the finer spatio temporal scales considerably outperforms the traditional approach in terms of an improved consistency between two resting state scans of the same subject to optimally estimate the granger causality the proposed theoretical framework is implemented through a combination of several approaches such as dividing the optimal time window and estimating the parameters at the fine temporal and spatial scales taken together our approach provides a novel and robust framework for estimating the granger causality from fmri eeg and other related data

nonlinear estimation of the bold signal signal variations in functional magnetic resonance imaging experiments essentially reflect the vascular system response to increased demand for oxygen caused by neuronal activity termed the blood oxygenation level dependent bold effect the most comprehensive model to date of the bold signal is formulated as a mixed continuous discrete time system of nonlinear stochastic differential equations previous approaches to the analysis of this system have been based on linearised approximations of the dynamics which are limited in their ability to capture the inherent nonlinearities in the physiological system in this paper we present a nonlinear filtering method for simultaneous estimation of the hidden physiological states and the system parameters based on an iterative coordinate descent framework state estimates of the cerebral blood flow cerebral blood volume and deoxyhaemoglobin content are determined using a particle filter demonstrated via simulation to be accurate robust and efficient in comparison to linearisation based techniques the adaptive state and parameter estimation algorithm generates physiologically reasonable parameter estimates for experimental fmri data it is anticipated that signal processing techniques for modelling and estimation will become increasingly important in fmri analyses as limitations of linear and linearised modelling are reached

cubature kalman filters in this paper we present a new nonlinear filter for high dimensional state estimation which we have named the cubature kalman filter ckf the heart of the ckf is a spherical radial cubature rule which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear bayesian filter specifically we derive a third degree spherical radial cubature rule that provides a set of cubature points scaling linearly with the state vector dimension the ckf may therefore provide a systematic solution for high dimensional nonlinear filtering problems the paper also includes the derivation of a square root version of the ckf for improved numerical stability the ckf is tested experimentally in two nonlinear state estimation problems in the first problem the proposed cubature rule is used to compute the second order statistics of a nonlinearly transformed gaussian random variable the second problem addresses the use of the ckf for tracking a maneuvering aircraft the results of both experiments demonstrate the improved performance of the ckf over conventional nonlinear filters

stability of standing waves for the fractional schrodinger hartree equation abstract in this paper we consider the stability of standing waves for the fractional schrodinger hartree equation by using the profile decomposition theory and variational methods we firstly obtain the best constant of a generalized gagliardo nirenberg inequality and then prove that the standing waves are orbitally stable

global existence of small solutions to nonlinear evolution equations abstract we study the global existence and asymptotic behaviour of small solutions of a large class of nonlinear partial differential equations if the nonlinear terms are of high degree the solutions will be asymptotic to solutions of the linear equation

second order analysis for bang bang control problems of pdes in this paper we derive some sufficient second order optimality conditions for control problems of partial differential equations pdes when the cost functional does not involve the usual quadratic term for the control or higher nonlinearities for it though not always in this situation the optimal control is typically bang bang two different control problems are studied the second differs from the first in the presence of the l 1 norm of the control this term leads to optimal controls that are sparse and usually take only three different values we call them bang bang bang controls though the proofs are detailed in the case of a semilinear elliptic state equation the approach can be extended to parabolic control problems some hints are provided in the last section to extend the results

energy concentration of the focusing energy critical fnls abstract we consider the fractional nonlinear schrodinger equation fnls with non local dispersion and focusing energy critical hartree type nonlinearity x 2 u 2 u we consider the energy concentration phenomena of radial blowup solutions near the maximal existence time we use the concentration compactness approach of 19 for confined case and kinetic energy trapping approach of 21 for unconfined case