control design of uncertain quantum systems with fuzzy estimators an approach of control design using fuzzy estimators fes is proposed for quantum systems with uncertainties two types of quantum control problems are considered 1 control of a pure state quantum system in the presence of uncertainties and 2 control design of quantum systems with initial mixed states and uncertainties for the first type of tasks a partial feedback control scheme with an fe is presented to design controllers in this scheme an fe is trained to estimate the quantum state for feedback control of a quantum system and controlled projective measurement is used to assist in controlling the system for the second type of quantum control tasks a probabilistic fuzzy estimator pfe is trained to estimate the quantum state for control design of a quantum system with an initial mixed state and a corresponding control algorithm is proposed to design a control law that drives the system from the mixed state to a target pure state two examples of two spin 1 2 systems are also presented and analyzed to demonstrate the process of control design and potential applications of the proposed approach

averaged controllability of parameter dependent conservative semigroups abstract we consider the problem of averaged controllability for parameter depending either in a discrete or continuous fashion control systems the aim being to find a control independent of the unknown parameters so that the average of the states is controlled we do it in the context of conservative models both in an abstract setting and also analysing the specific examples of the wave and schrodinger equations our first result is of perturbative nature assuming the averaging probability measure to be a small parameter dependent perturbation in a sense that we make precise of an atomic measure given by a dirac mass corresponding to a specific realisation of the system we show that the averaged controllability property is achieved whenever the system corresponding to the support of the dirac is controllable similar tools can be employed to obtain averaged versions of the so called ingham inequalities particular attention is devoted to the 1d wave equation in which the time periodicity of solutions can be exploited to obtain more precise results provided the parameters involved satisfy diophantine conditions ensuring the lack of resonances

further results on sampled data design for robust control of a single qubit this paper presents further results on the robust control method for qubit systems in dong et al 2013 based on the properties of an antisymmetric system an alternative method is presented to analyse and exclude singularity intervals in the proof of partial original results for the case of amplitude damping decoherence a larger sampling period is presented when the upper bound of the probability of failure is small enough for the case of phase damping decoherence a larger sampling period is given when the lower bound of the target coherence is large enough furthermore we provide improved sampling periods for amplitude damping decoherence and phase damping decoherence without the above prior constraints

labeling of ambiguous subvoxel fibre bundle configurations in high angular resolution diffusion mri whereas high angular resolution reconstruction methods for diffusion mri can estimate multiple dominant fibre orientations within a single imaging voxel they are fundamentally limited in certain cases of complex subvoxel fibre structures resulting in ambiguous local orientation distribution functions in this article we address the important problem of disambiguating such complex subvoxel fibre tract configurations with the purpose of improving the performance of fibre tractography we do so by extending a curve inference method to distinguish between the cases of curving and fanning fibre bundles using differential geometric estimates in a local neighbourhood the key benefit of this method is the inference of curves instead of only fibre orientations to model the underlying fibre bundles this in turn allows distinct fibre geometries that contain nearly identical sets of fibre orientations at a voxel to be distinguished from one another experimental results demonstrate the ability of the method to successfully label voxels into one of the above categories and improve the performance of a fibre tracking algorithm

free endpoint optimal control of inhomogeneous bilinear ensemble systems optimal control of bilinear systems has been a well studied subject in the areas of mathematical and computational optimal control however effective methods for solving emerging optimal control problems involving an ensemble of deterministic or stochastic bilinear systems are underdeveloped these burgeoning problems arise in diverse applications from quantum control and molecular imaging to neuroscience in this work we develop an iterative method to find optimal controls for an inhomogeneous bilinear ensemble system with free endpoint conditions the central idea is to represent the bilinear ensemble system at each iteration as a time varying linear ensemble system and then solve it in an iterative manner we analyze convergence of the iterative procedure and discuss optimality of the convergent solutions the method is directly applicable to solve the same class of optimal control problems involving a stochastic bilinear ensemble system driven by independent additive noise processes we demonstrate the robustness and applicability of the developed iterative method through practical control designs in neuroscience and quantum control

ensemble control of bloch equations in this article we study a class of control problems which involves controlling a continuum of dynamical systems with different values of parameters characterizing the system dynamics by using the same control signal we call such problems control of ensembles the motivation for looking into these problems comes from the manipulation of an ensemble of nuclear spins in nuclear magnetic resonance nmr spectroscopy and imaging mri with dispersions in natural frequencies and the strengths of the applied radio frequency rf field from the standpoint of mathematical control theory the challenge is to simultaneously steer a continuum of systems between points of interest with the same control input this raises some new and unexplored questions about controllability of such systems we show that controllability of an ensemble can be understood by the study of the algebra of polynomials defined by the noncommuting vector fields that govern the system dynamics a systematic study of these systems has immediate applications to broad areas of control of ensembles of quantum systems as arising in coherent spectroscopy and quantum information processing the new mathematical structures appearing in such problems are excellent motivation for new developments in control theory

a method for solving exact controllability problems governed by closed quantum spin systems the liouville von neumann master equation models closed quantum spin systems that arise in nuclear magnetic resonance applications in this paper an efficient and robust computational framework to solve exact controllability problems governed by the liouville von neumann master equation is presented the proposed control framework is based on a new optimisation formulation of exact controllability quantum spin problems that allows the application of efficient computational techniques this formulation results in an optimality system with four differential equations and an optimality condition the differential equations are approximated with an appropriate modified crank nicholson scheme and the resulting discretised optimality system is solved with a matrix free krylov newton scheme combined with a cascadic nonlinear conjugate gradient initialisation results of numerical experiments demonstrate the ability of the proposed framework to solve quantum spin exact controllability control problems

distributed control for identical dynamically coupled systems a decomposition approach we consider the problem of designing distributed controllers for a class of systems which can be obtained from the interconnection of a number of identical subsystems if the state space matrices of these systems satisfy a certain structural property then it is possible to derive a procedure for designing a distributed controller which has the same interconnection pattern as the plant this procedure is basically a multiobjective optimization under linear matrix inequality constraints with system norms as performance indices the explicit expressions for computing these controllers are given for both h infin or h 2 performance and both for static state feedback and dynamic output feedback in discrete time at the end of the paper two application examples illustrate the effectiveness of the approach

direct estimation of the fiber orientation density function from diffusion weighted mri data using spherical deconvolution diffusion weighted magnetic resonance imaging can provide information related to the arrangement of white matter fibers the diffusion tensor is the model most commonly used to derive the orientation of the fibers within a voxel however this model has been shown to fail in regions containing several fiber populations with distinct orientations a number of alternative models have been suggested such as multiple tensor fitting q space and q ball imaging however each of these has inherent limitations in this study we propose a novel method for estimating the fiber orientation distribution directly from high angular resolution diffusion weighted mr data without the need for prior assumptions regarding the number of fiber populations present we assume that all white matter fiber bundles in the brain share identical diffusion characteristics thus implicitly assigning any differences in diffusion anisotropy to partial volume effects the diffusion weighted signal attenuation measured over the surface of a sphere can then be expressed as the convolution over the sphere of a response function the diffusion weighted attenuation profile for a typical fiber bundle with the fiber orientation density function odf the fiber odf the distribution of fiber orientations within the voxel can therefore be obtained using spherical deconvolution the properties of the technique are demonstrated using simulations and on data acquired from a volunteer using a standard 1 5 t clinical scanner the technique can recover the fiber odf in regions of multiple fiber crossing and holds promise for applications such as tractography

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

ensemble observability of linear systems we address the observability problem for ensembles that are described by probability distributions the problem is to reconstruct a probability distribution of the initial state from the time evolution of the probability distribution of the output under a classical finite dimensional linear system we present two solutions to this problem one based on formulating the problem as an inverse problem and the other one based on reconstructing all the moments of the distribution the first approach leads us to a connection between the reconstruction problem and mathematical tomography problems in the second approach we use the framework of tensor systems to describe the dynamics of the moments which leads to a more systems theoretic treatment of the reconstruction problem furthermore we show that both frameworks are inherently related the appeal of having two dual viewpoints the first being more geometric and the second one being more systems theoretic is illuminated in several examples of theoretical or practical importance

minimum time frictionless atom cooling in harmonic traps frictionless atom cooling in harmonic traps is formulated as a time optimal control problem and a synthesis of optimal controlled trajectories is obtained

time optimal simultaneous control of two level quantum systems in this paper we solve the problem of simultaneously driving in minimum time to arbitrary final conditions n two level quantum systems subject to independent controls the solution of this problem is obtained via an explicit description of the reachable set of the associated control system on s u 2 the treatment generalizes previous results on the time optimal control of two level quantum systems and suggests that similar techniques could be used to solve the minimum time control problem for a larger class of right invariant systems on lie groups

penalty function with memory for discrete optimization via simulation with stochastic constraints we consider a discrete optimization via simulation dovs problem with stochastic constraints on secondary performance measures in which both objective and secondary performance measures need to be estimated by stochastic simulation to solve the problem we develop a new method called the penalty function with memory pfm it is similar to an existing penalty type method which consists of a penalty parameter and a measure of violation of constraints in a sense that it converts a dovs problem with constraints into a series of unconstrained problems however pfm uses a different penalty parameter called a penalty sequence determined by the past history of feasibility checks on a solution specifically assuming a minimization problem a penalty sequence diverges to infinity for any infeasible solution but converges to zero for any feasible solution under certain conditions as a result a dovs algorithm combined with pfm performs well even when an optimal feasible solution is a boundary solution with o

uniform ensemble controllability for one parameter families of time invariant linear systems abstract in this paper we derive necessary as well as sufficient conditions for approximate controllability of parameter dependent linear systems in the supremum norm using tools from complex approximation theory we prove the existence of parameter independent open loop controls that steer the zero initial state of an ensemble of linear systems uniformly to a prescribed family of terminal states new necessary conditions for uniform ensemble controllability of single input systems are derived our results extend earlier ones of li for ensemble controllability of linear systems

control and synchronization of neuron ensembles synchronization of oscillations is a phenomenon prevalent in natural social and engineering systems controlling synchronization of oscillating systems is motivated by a wide range of applications from surgical treatment of neurological diseases to the design of neurocomputers in this paper we study the control of an ensemble of uncoupled neuron oscillators described by phase models we examine controllability of such a neuron ensemble for various phase models and furthermore study the related optimal control problems in particular by employing pontryagin s maximum principle we analytically derive optimal controls for spiking single and two neuron systems and analyze the applicability of the latter to an ensemble system finally we present a robust computational method for optimal control of spiking neurons based on pseudospectral approximations the methodology developed here is universal to the control of general nonlinear phase oscillators

controllability of a quantum particle in a moving potential well we consider a nonrelativistic charged particle in a 1d moving potential well this quantum system is subject to a control which is the acceleration of the well it is represented by a wave function solution of a schrodinger equation the position of the well together with its velocity we prove the following controllability result for this bilinear control system given 0 close enough to an eigenstate and f close enough to another eigenstate the wave function can be moved exactly from 0 to f in finite time moreover we can control the position and the velocity of the well our proof uses moment theory a nash moser implicit function theorem the return method and expansion to the second order

growth of sobolev norms and controllability of the schrodinger equation in this paper we obtain a stabilization result for both linear and nonlinear schrodinger equations under generic assumptions on the potential then we consider the schrodinger equations with a potential which has a random time dependent amplitude we show that if the distribution of the amplitude is sufficiently non degenerate then any trajectory of the system is almost surely non bounded in sobolev spaces

geometric optimal control of the contrast imaging problem in nuclear magnetic resonance the objective of this article is to introduce the tools to analyze the contrast imaging problem in nuclear magnetic resonance optimal trajectories can be selected among extremal solutions of the pontryagin maximum principle applied to this mayer type optimal problem such trajectories are associated to the question of extremizing the transfer time hence the optimal problem is reduced to the analysis of the hamiltonian dynamics related to singular extremals and their optimality status this is illustrated by using the examples of cerebrospinal fluid water and grey white matter of cerebrum

probabilistic diffusion tractography with multiple fibre orientations what can we gain we present a direct extension of probabilistic diffusion tractography to the case of multiple fibre orientations using automatic relevance determination we are able to perform online selection of the number of fibre orientations supported by the data at each voxel simplifying the problem of tracking in a multi orientation field we then apply the identical probabilistic algorithm to tractography in the multi and single fibre cases in a number of example systems which have previously been tracked successfully or unsuccessfully with single fibre tractography we show that multi fibre tractography offers significant advantages in sensitivity when tracking non dominant fibre populations but does not dramatically change tractography results for the dominant pathways

on discontinuous continuity equation and impulsive ensemble control abstract the note is devoted to a class of singular ensemble control problems we consider the continuity equation driven by a control affine vector field subject to the constraint on the l 1 norm of the input function since no geometric constraints on control are imposed solutions to the continuity equation can potentially tend somehow to discontinuous measure valued functions we elaborate a representation of such discontinuous generalized solutions through an ordinary control equation being a time reparameterization of the characteristic ordinary differential equation ode of the original continuity equation by virtue of standard results from impulsive control theory of odes we perform a constructive formula for generalized solutions in terms of a measure differential equation finally we state an optimal impulsive control problem for the singular continuity equation and prove the existence of its solution the obtained results can be useful for modeling and analysis of impulsive control problems with uncertain initial data

local controllability of a one dimensional beam equation we prove that the beam equation with clamped ends is locally controllable in a h 5 epsilon times h 3 epsilon 0 1 mathbb r neighborhood of a particular trajectory of the free system with epsilon 0 and with control functions in h 1 0 0 t mathbb r ball marsden and slemrod already proved that this equation is not controllable in h 2 0 times l 2 0 1 mathbb r with control functions in l r text loc mathbb r mathbb r r 1 this article justifies that their negative result is due to a choice of functional spaces which does not allow controllability our proof uses moment theory and the nash moser theorem

a novel tensor distribution model for the diffusion weighted mr signal diffusion mri is a non invasive imaging technique that allows the measurement of water molecule diffusion through tissue in vivo the directional features of water diffusion allow one to infer the connectivity patterns prevalent in tissue and possibly track changes in this connectivity over time for various clinical applications in this paper we present a novel statistical model for diffusion weighted mr signal attenuation which postulates that the water molecule diffusion can be characterized by a continuous mixture of diffusion tensors an interesting observation is that this continuous mixture and the mr signal attenuation are related through the laplace transform of a probability distribution over symmetric positive definite matrices we then show that when the mixing distribution is a wishart distribution the resulting closed form of the laplace transform leads to a rigaut type asymptotic fractal expression which has been phenomenologically used in the past to explain the mr signal decay but never with a rigorous mathematical justification until now our model not only includes the traditional diffusion tensor model as a special instance in the limiting case but also can be adjusted to describe complex tissue structure involving multiple fiber populations using this new model in conjunction with a spherical deconvolution approach we present an efficient scheme for estimating the water molecule displacement probability functions on a voxel by voxel basis experimental results on both simulations and real data are presented to demonstrate the robustness and accuracy of the proposed algorithms

averaged control we analyze the problem of controlling parameter dependent systems we introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter first we consider the problem of controllability for linear finite dimensional systems and show that a necessary and sufficient condition for averaged controllability is an averaged rank condition in the spirit of the classical rank condition for linear control systems but involving averaged momenta of any order of the matrices generating the dynamics and representing the control action we also describe some open problems and directions of possible research in particular on the average controllability of evolution partial differential equations in this context we analyze also the averaged version of a classical optimal control problem for a parameter dependent elliptic equation and derive the corresponding optimality system

a two step strategy for stabilizing control of quantum systems with uncertainties as a matter of course designed control laws are to be acted on actual systems however most designed control laws are proven to be effective when performed on ideal models of the systems as opposed to the actual systems themselves one fundamental problem is how to ensure the satisfactory performance of the designed control laws when they are performed on actual systems focusing on the state stabilization of quantum systems a two step strategy is proposed to solve this problem a feedback strategy and the open loop control technique of dynamical decoupling are combined therein to deal with the inevitable differences between an actual system and its model by taking advantage of the distinct quantum characteristics the measurement induced state transfer and the tensor product structure with the structure characterizing the coupling between a quantum system and its environment specifically in the first step a measurement based feedback control strategy is selected according to a model of the actual system in the second step by identifying the differences between the actual system and the established model as decoherence noise a specific control procedure is designed through dynamical decoupling this procedure allows the realization of the chosen control strategy so as to deal with the differences

robust controllability assessment via semi definite programming abstract this paper presents a new framework for systematic assessment of the controllability of uncertain linear time invariant lti systems the objective is to evaluate controllability of an uncertain system with norm bounded perturbation over the entire uncertain region the method is based on a singular value minimization problem over the entire complex plane to solve the problem first a necessary and sufficient condition is proposed to avert the difficulties of griding over the complex plane and to verify the controllability of directed and undirected networks in a single step secondly the results are utilized to formulate the problem as two lyapunov based linear matrix inequalities lmis for undirected networks and four lmis for directed ones the proposed approach is subsequently extended to evaluate the maximum guaranteed distance to uncontrollability of a system through a quasi convex optimization problem whose solution is guaranteed to be globally optimal by duality analogous results are established for robust observability of directed and undirected networks the proposed framework is implemented efficiently using lmi tools and provides a fast and reliable tool for the assessment of robust controllability and by duality robust observability it is also extendable to robust control system design problems such as control node selection for uncertain systems

on the phase reduction and response dynamics of neural oscillator populations weundertake a probabilistic analysis of the response of repetitively firing neural populations to simple pulselike stimuli recalling and extending results from the literature we compute phase response curves prcs valid near bifurcations to periodic firing for hindmarsh rose hodgkin huxley fitzhugh nagumo and morris lecar models encompassing the four generic codimension one bifurcations phase density equations are then used to analyze the role of the bifurcation and the resulting prc in responses to stimuli in particular we explore the interplay among stimulus duration baseline firing frequency and population level response patterns we interpret the results in terms of the signal processing measure of gain and discuss further applications and experimentally testable predictions

a moment based approach to ensemble controllability of linear systems abstract in this paper we introduce a new perspective on the l 2 ensemble controllability problem of linear time invariant systems using an l 2 framework the reformulation results from focussing on the controllability of the ensemble s moments which evolve under a linear system defined on the space of square summable sequences for a specific class of ensembles a necessary and sufficient condition can be stated in terms of truncations of infinite kalman matrices we illustrate the analysis in this framework on several examples which highlight the possibility of using elementary structural arguments in proving or disproving the controllability of an ensemble s moments as well as essential differences to the uniform ensemble controllability property which is mostly considered in the literature

joint reconstruction of white matter pathways from longitudinal diffusion mri data with anatomical priors we consider the problem of reconstructing white matter pathways in a longitudinal study where diffusion weighted and t1 weighted mr images have been acquired at multiple time points for the same subject we propose a method for joint reconstruction of a subject s pathways at all time points given the subject s entire set of longitudinal data we apply a method for unbiased within subject registration to generate a within subject template from the t1 weighted images of the subject at all time points we follow a global probabilistic tractography approach where the unknown pathway is represented in the space of this within subject template and propagated to the native space of the diffusion weighted images at all time points to compute its posterior probability given the images this ensures spatial correspondence of the reconstructed pathway among time points which in turn allows longitudinal changes in diffusion measures to be estimated consistently along the pathway we evaluate the reliability of the proposed method on data from healthy controls scanned twice within a month where no changes in white matter microstructure are expected between scans we evaluate the sensitivity of the method on data from huntington s disease patients scanned repeatedly over the course of several months where changes are expected between scans we show that reconstructing white matter pathways jointly using the data from all time points leads to improved reliability and sensitivity when compared to reconstructing the pathways at each time point independently

ensemble control of finite dimensional time varying linear systems in this article we investigate the problem of simultaneously steering an uncountable family of finite dimensional time varying linear systems with the same control signal this class of control problems motivates further research in the new subject of control theory called ensemble control a notion coming from the study of complex spin dynamics in nuclear magnetic resonance spectroscopy and imaging we derive the necessary and sufficient controllability conditions and an accompanying analytical optimal control law for an ensemble of finite dimensional time varying linear systems we show that ensemble controllability is in connection with singular values of the operator characterizing the system dynamics in addition the problem of optimal ensemble control of harmonic oscillators is studied to demonstrate the controllability results we show that the optimal solutions are pertinent to the study of time frequency limited signals and prolate spheroidal wave functions a systematic study of ensemble control systems has immediate applications to dynamical systems with parameter uncertainty as well as to wide ranging areas such as neuroscience and quantum control the work in ensemble control will foster further developments in mathematical control and systems theory

stabilization of an arbitrary profile for an ensemble of half spin systems we consider the feedback stabilization of a variable profile for an ensemble of non interacting half spins described by the bloch equations we propose an explicit feedback law that stabilizes asymptotically the system around a given arbitrary target profile the convergence proof is done when the target profile is entirely in the south hemisphere or in the north hemisphere of the bloch sphere the convergence holds for initial conditions in a h1 neighbourhood of this target profile this convergence is shown for the weak h1 topology the proof relies on an adaptation of the lasalle invariance principle to infinite dimensional systems numerical simulations illustrate the efficiency of these feedback laws even for initial conditions far from the target profile

controllability issues for continuous spectrum systems and ensemble controllability of bloch equations we study the controllability of the bloch equation for an ensemble of non interactinghalf spins inastaticmagneticfield withdispersioninthelarmorfrequency this system may be seen as a prototype for infinite dimensional bilinear systems with continuous spectrum whose controllability is not well understood we provide several mathematical answers with discrimination between approximate and exact controlla bility and between finite time or infinite time controllability this system is not exactly controllable in finite time t with bounded controls in l 2 0 t but it is approximately controllable in l in finite time with unbounded controls in l 0 moreover we propose explicit controls realizing the asymptotic exact controllability to a uniform state of spin 1 2o r 1 2

stabilization for an ensemble of half spin systems feedback stabilization of an ensemble of non interacting half spins described by the bloch equations is considered this system may be seen as an interesting example for infinite dimensional systems with continuous spectra we propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin 1 2 or 1 2 the proof of the convergence is done locally around the equilibrium in the h 1 topology this local convergence is shown to be a weak asymptotic convergence for the h 1 topology and thus a strong convergence for the c 0 topology the proof relies on an adaptation of the lasalle invariance principle to infinite dimensional systems numerical simulations illustrate the efficiency of these feedback laws even for initial conditions far from the equilibrium

anatomical mapping of functional activation in stereotactic coordinate space numerous applications have been reported for the stereotactic mapping of focal changes in cerebral blood flow during sensory and cognitive activation as measured with positron emission tomography pet subtraction images since these images lack significant anatomical information analysis of these kinds of data has been restricted to an automated search for peaks in the pet subtraction dataset and localization of the peak coordinates within a standardized stereotactic atlas this method is designed to identify isolated foci with dimensions smaller than the image resolution details of activation patterns that may extend over finite distances following the underlying anatomical structures will not be apparent we describe the combined mapping into stereotactic coordinate space of magnetic resonance imaging mri and pet information from each of a set of subjects such that the major features of the activation pattern particularly extended tracts of increased blood flow can be immediately assessed within their true anatomical context as opposed to that presumed using a standard atlas alone near areas of high anatomical variability e g central sulcus or of sharp curvature e g frontal and temporal poles this information can be essential to the localization of a focus to the correct gyrus or for the rejection of extracerebral peaks it also allows for the removal from further analysis of data from cognitively normal subjects with abnormal anatomy such as enlarged ventricles in patients with neuropathology e g alzheimer s disease arteriovenous malformation stroke or neoplasm the use of correlated mri is mandatory for correct localization of functional activation

tract based morphometry for white matter group analysis we introduce an automatic method that we call tract based morphometry or tbm for measurement and analysis of diffusion mri data along white matter fiber tracts using subject specific tractography bundle segmentations we generate an arc length parameterization of the bundle with point correspondences across all fibers and all subjects allowing tract based measurement and analysis in this paper we present a quantitative comparison of fiber coordinate systems from the literature and we introduce an improved optimal match method that reduces spatial distortion and improves intra and inter subject variability of fa measurements we propose a method for generating arc length correspondences across hemispheres enabling a tbm study of interhemispheric diffusion asymmetries in the arcuate fasciculus af and cingulum bundle cb the results of this study demonstrate that tbm can detect differences that may not be found by measuring means of scalar invariants in entire tracts such as the mean diffusivity md differences found in af we report tbm results of higher fractional anisotropy fa in the left hemisphere in af caused primarily by lower 3 the smallest eigenvalue of the diffusion tensor in the left af and higher left hemisphere fa in cb related to higher 1 the largest eigenvalue of the diffusion tensor in the left cb by mapping the significance levels onto the tractography trajectories for each structure we demonstrate the anatomical locations of the interhemispheric differences the tbm approach brings analysis of dti data into the clinically and neuroanatomically relevant framework of the tract anatomy

ensemble control of linear systems with parameter uncertainties abstractin this paper we study the optimal control problem for a class of four dimensional linear systems based on quaternionic and fourier analysis when the control is unconstrained the optimal ensemble controller for this linear ensemble control systems is given in terms of prolate spheroidal wave functions for the constrained convex optimisation problem of such systems the quadratic programming is presented to obtain the optimal control laws simulations are given to verity the effectiveness of the proposed theory

dt mri fiber tracking a shortest paths approach we derive a new fiber tracking algorithm for dt mri that parts with the locally ldquogreedyrdquo paradigm intrinsic to conventional tracking algorithms we demonstrate the ability to precisely reconstruct a diverse range of fiber trajectories in authentic and computer generated dt mri data for which well known conventional tracking algorithms are shown to fail our approach is to pose fiber tracking as a problem in computing shortest paths in a weighted digraph voxels serve as vertices and edges are included between neighboring voxels we assign probabilities weights to edges using a bayesian framework higher probabilities are assigned to edges that are aligned with fiber trajectories in their close proximity we compute optimal paths of maximum probability using computationally scalable shortest path algorithms the salient features of our approach are global optimality unlike conventional tracking algorithms local errors do not accumulate and one ldquowrong turnrdquo does not spell disaster a target point is specified a priori precise reconstruction is demonstrated for extremely low signal to noise ratio impartiality to which of two endpoints is used as a seed and faster computation times than conventional all paths tracking we can use our new tracking algorithm in either a single path tracking mode deterministic tracking or an all paths tracking mode probabilistic tracking

sampled observability and state estimation of linear discrete ensembles we consider the problem of reconstructing the initial states of a finite group of structurally identical linear systems in the situation that output measurements of the individual systems are received at discrete time steps and in an anonymized manner while we do know all output measurements of the individual systems in the group we do not know which output measurement corresponds to which system this state estimation problem addresses the essence of state estimation problems for populations in which the output measurements of the individual systems are given only as statistics we adopt a measure theoretical approach in which the group is modelled by an lti system describing the structure of the individual systems and an initial state which is expressed by a discrete measure in this framework we derive a geometric characterization for the state estimation to admit a unique solution which combined with a result on the observability of linear systems under irregular sampling yields a sufficient condition for the sampled observability of discrete ensembles as a supplement to our theoretical findings we provide illustrations by means of simulation examples furthermore we consider the practical state estimation problem under noisy output measurements

singular trajectories and the contrast imaging problem in nuclear magnetic resonance in this article the contrast imaging problem in nuclear magnetic resonance is modeled as a mayer problem in optimal control whose solutions can be parameterized using pontryagin s maximum principle and analyzed using geometric optimal control in particular the optimal problem can be mainly reduced to the analysis of the hamiltonian dynamics describing the singular trajectories and encoding their optimality status

ensemble observability of bloch equations with unknown population density abstract we introduce in the paper a novel observability problem for a large population in the limit a continuum ensemble of nonholonomic control systems with unknown population density we address the problem by focussing on a prototype namely the ensemble of bloch equations which is known for its use of describing the evolution of the bulk magnetization of a collective of non interacting nuclear spins in a static field modulated by a radio frequency rf field the dynamics of the equations are structurally identical but show variations in larmor dispersion and rf inhomogeneity we assume that the initial state of any individual system i e individual bloch equation is unknown and moreover the population density of these individual systems is also unknown furthermore we assume that at any time there is only one scalar measurement output at our disposal the measurement output integrates a certain observation function common to all individual systems over the continuum ensemble the observability problem we pose in the paper is thus the following whether one is able to use the common control input i e the rf field and the single measurement output to estimate both the initial states of the individual systems and the population density amongst other things we establish a sufficient condition for the ensemble system to be observable we show that if the common observation function is any harmonic homogeneous polynomial of positive degree then the ensemble system is observable the proof of the result utilizes tools from representation theory of lie algebras although the results established in the paper are for the specific ensemble of bloch equations the approach developed along the analysis can be generalized to investigate observability of other ensemble systems with single integrated measurement outputs

around the eakin sathaye theorem abstract we present a generalisation of the eakin sathaye theorem on reductions to the case of complete and so of joint reductions in the sense of rees applications are given generalisations are also indicated for work of lipman eakin sathaye and sally vasconcelos that fed into or resulted from the original version of the eakin sathaye theorem finally the result is reinterpreted as a multiplicative normalisation theorem

structural decomposition for quantum two level systems an input output model of a two level quantum system in the heisenberg picture is of bilinear form with constant system matrices which allows the introduction of the concepts of controllability and observability in analogy with those of quantum linear systems by means of the notions of controllability and observability coordinate transformations which are rotation matrices can be constructed explicitly that transform an input output model to a new one the new input output model enables us to investigate many interesting properties of the two level quantum system such as steady state solutions to the lindblad master equation quantum decoherence free df subspaces quantum non demolition qnd variables and the realization of quantum back action evading bae measurements the physical system in wang and wiseman 2001 is re studied to illustrate the results presented in this paper

control in the spaces of ensembles of points we study the controlled dynamics of the ensembles of points of a riemannian manifold m parameterized ensemble of points of m is the image of a continuous map gamma theta to m where the

a characterization of von neumann rings in terms of linear systems abstract a new characterization of commutative von neumann regular rings is given in terms of linear control systems having locally a brunovsky canonical form the problem of enumerating reachable systems over certain von neumann regular ring is solved extending classical results over fields

borel fixed ideals and reduction number abstract the aim of this paper is to study the relationship between the reduction number and borel fixed ideals in all characteristics especially it is shown that r r i r r i lex where i lex denotes the unique lex segment ideal whose hilbert function is equal to that of i this solves a recent question by conca

improved optimization for the robust and accurate linear registration and motion correction of brain images linear registration and motion correction are important components of structural and functional brain image analysis most modern methods optimize some intensity based cost function to determine the best registration to date little attention has been focused on the optimization method itself even though the success of most registration methods hinges on the quality of this optimization this paper examines the optimization process in detail and demonstrates that the commonly used multiresolution local optimization methods can and do get trapped in local minima to address this problem two approaches are taken 1 to apodize the cost function and 2 to employ a novel hybrid global local optimization method this new optimization method is specifically designed for registering whole brain images it substantially reduces the likelihood of producing misregistrations due to being trapped by local minima the increased robustness of the method compared to other commonly used methods is demonstrated by a consistency test in addition the accuracy of the registration is demonstrated by a series of experiments with motion correction these motion correction experiments also investigate how the results are affected by different cost functions and interpolation methods

optimal ensemble control of stochastic time varying linear systems abstract we consider the optimal guidance of an ensemble of independent structurally identical finite dimensional stochastic linear systems with variation in system parameters between initial and target states of interest by applying a common control function without the use of feedback our exploration of such ensemble control systems is motivated by practical control design problems in which variation in system parameters and stochastic effects must be compensated for when state feedback is unavailable such as in pulse design for nuclear magnetic resonance spectroscopy and imaging in this paper we extend the notion of ensemble control to stochastic linear systems with additive noise and jumps which we model using white gaussian noise and poisson counters respectively and investigate the optimal steering problem in our main result we prove that the minimum norm solution to a fredholm integral equation of the first kind provides the optimal control that simultaneously minimizes the mean square error mse and the error in the mean of the terminal state the optimal controls are generated numerically for several example ensemble control problems and monte carlo simulations are used to illustrate their performance this work has immediate applications to the control of dynamical systems with parameter dispersion or uncertainty that are subject to additive noise which are of interest in quantum control neuroscience and sensorless robotic manipulation

asymptotic ensemble stabilizability of the bloch equation in this paper we are concerned with the stabilizability to an equilibrium point of an ensemble of non interacting half spins we assume that the spins are immersed in a static magnetic field with dispersion in the larmor frequency and are controlled by a time varying transverse field our goal is to steer the whole ensemble to the uniform down position two cases are addressed for a finite ensemble of spins we provide a control function in feedback form that asymptotically stabilizes the ensemble in the down position generically with respect to the initial condition for an ensemble containing a countable number of spins we construct a sequence of control functions such that the sequence of the corresponding solutions pointwise converges asymptotically in time to the target state generically with respect to the initial conditions the control functions proposed are uniformly bounded and continuous

notes on sliding mode control of two level quantum systems in dong d and petersen i r 2012 sliding mode control of two level quantum systems automatica 48 725 735 a sliding mode control approach has been proposed for two level quantum systems to deal with bounded uncertainties in the system hamiltonian this paper further extends these results in two directions one extension is to consider the effect of uncertainties during the process of driving the system s state back to the sliding mode domain from outside and we propose two approaches to accomplish this control task the other extension generalizes the previous design approach to consider uncertainties described as perturbations in the free hamiltonian

improved tractography using asymmetric fibre orientation distributions diffusion mri allows us to make inferences on the structural organisation of the brain by mapping water diffusion to white matter microstructure however such a mapping is generally ill defined for instance diffusion measurements are antipodally symmetric diffusion along x and x are equal whereas the distribution of fibre orientations within a voxel is generally not symmetric therefore different sub voxel patterns such as crossing fanning or sharp bending cannot be distinguished by fitting a voxel wise model to the signal however asymmetric fibre patterns can potentially be distinguished once spatial information from neighbouring voxels is taken into account we propose a neighbourhood constrained spherical deconvolution approach that is capable of inferring asymmetric fibre orientation distributions a fods importantly we further design and implement a tractography algorithm that utilises the estimated a fods since the commonly used streamline tractography paradigm cannot directly take advantage of the new information we assess performance using ultra high resolution histology data where we can compare true orientation distributions against sub voxel fibre patterns estimated from down sampled data finally we explore the benefits of a fods based tractography using in vivo data by evaluating agreement of tractography predictions with connectivity estimates made using different in vivo modalities the proposed approach can reliably estimate complex fibre patterns such as sharp bending and fanning which voxel wise approaches cannot estimate moreover histology based and in vivo results show that the new framework allows more accurate tractography and reconstruction of maps quantifying symmetric and asymmetric fibre complexity

controllability for distributed bilinear systems this paper studies controllability of systems of the form dw dt mathcal a w p t mathcal b w where mathcal a is the infinitesimal generator of a c 0 semigroup of bounded linear operators e mathcal a t on a banach space x mathcal b x to x is a c 1 map and p in l 1 0 t mathbb r is a control the paper i gives conditions for elements of x to be accessible from a given initial state w 0 and ii shows that controllability to a full neighborhood in x of w 0 is impossible for dim x infty examples of hyperbolic partial differential equations are provided

on controllability of diagonal systems with one dimensional input space abstract this paper deals with diagonal systems on a hilbert state space with a one dimensional input space and a possibly unbounded control operator a priori it is not assumed that the input operator is admissible necessary and sufficient conditions for different notions of controllability such as null controllability exact controllability and approximate controllability are presented these conditions which are given in terms of the eigenvalues of the diagonal operator and in terms of the control operator are linked with the theory of interpolation in hardy spaces

a bayesian framework for global tractography we readdress the diffusion tractography problem in a global and probabilistic manner instead of tracking through local orientations we parameterise the connexions between brain regions at a global level and then infer on global and local parameters simultaneously in a bayesian framework this approach offers a number of important benefits the global nature of the tractography reduces sensitivity to local noise and modelling errors by constraining tractography to ensure a connexion is found and then inferring on the exact location of the connexion we increase the robustness of connectivity based parcellations allowing parcellations of connexions that were previously invisible to tractography the bayesian framework allows a direct comparison of the evidence for connecting and non connecting models to test whether the connexion is supported by the data crucially by explicit parameterisation of the connexion between brain regions we infer on a parameter that is shared with models of functional connectivity this model is a first step toward the joint inference on functional and anatomical connectivity

on the controllability of quantum transport in an electronic nanostructure we investigate the controllability of quantum electrons trapped in a two dimensional device typically a metal oxide semiconductor mos field effect transistor the problem is modeled by the schrodinger equation in a bounded domain coupled to the poisson equation for the electrical potential the controller acts on the system through the boundary condition on the potential on a part of the boundary modeling the gate we prove that generically with respect to the shape of the domain and boundary conditions on the gate the device is controllable we also consider control properties of a more realistic nonlinear version of the device taking into account the self consistent electrostatic poisson potential

the k hbox p problem on tensor products of lie groups and time optimal control of n quantum bits with a bounded field we use properties of sub riemannian k hbox p problems and the optimal synthesis on su 2 to solve the time optimal control of n noninteracting two level quantum systems qubits controlled in parallel with a control field bounded in l 2 norm every qubit is controlled independently but the total energy of the controls used is bounded for this system we describe the reachable set at every time moreover we compute the diameter that is the worst case minimum time the mathematical problem is motivated by the control of two level systems with different resonance frequencies where the control fields are obtained from a single signal having bounded energy

ensemble control of time invariant linear systems with linear parameter variation in this paper we study the control of a class of time invariant linear ensemble systems whose natural dynamics are linear in the system parameter this class of ensemble control systems arises from practical engineering and physical applications such as transport of quantum particles and control of uncertain harmonic systems we establish explicit algebraic criteria to examine controllability of such ensemble systems our derivation is based on the notion of polynomial approximation where the elements of the reachable set of the ensemble system are represented in polynomials of the system parameter and used to approximate the desired state of interest in addition we highlight the role of the spectra of the system matrices play in the determination of ensemble controllability finally illustrative examples and numerical simulations for optimal control of this class of linear ensemble systems are presented to demonstrate the theoretical results

analysis of quantum linear systems response to multi photon states the purpose of this paper is to present a mathematical framework for analyzing the response of quantum linear systems driven by multi photon states both the factorizable namely no correlation among the photons in the channel and unfactorizable multi photon states are treated pulse information of a multi photon input state is represented in terms of tensor and the response of quantum linear systems to multi photon input states is characterized by tensor operations analytic forms of output correlation functions and output states are derived the proposed framework is applicable no matter whether the underlying quantum dynamic system is passive or active examples from the physics literature are used to illustrate the results presented

local controllability and non controllability for a 1d wave equation with bilinear control abstract we consider a linear wave equation on the interval 0 1 with bilinear control and neumann boundary conditions we study the controllability of this nonlinear control system locally around a constant reference trajectory we prove that the following results hold generically for every t 2 this system is locally controllable in h 3 h 2 in time t with controls in l 2 0 t r for t 2 this system is locally controllable up to codimension one in h 3 h 2 in time t with controls in l 2 0 t r the reachable set is locally a non flat submanifold of h 3 h 2 with codimension one for every t 2 this system is not locally controllable more precisely the reachable set with controls in l 2 0 t r is contained in a non flat submanifold of h 3 h 2 with infinite codimension the proof of these results relies on the inverse mapping theorem and second order expansions

bootstrap white matter tractography boot trac white matter tractography is a noninvasive method for estimating and visualizing the white matter connectivity patterns in the human brain using diffusion tensor imaging dti data sources of experimental noise may induce errors in the measured fiber directions which will reduce the accuracy of the estimated white matter trajectories in this study a statistical nonparametric bootstrap method is described for estimating the dispersion and other errors in white matter tractography results prior studies have derived models of tractography error using the signal to noise ratio snr and diffusion anisotropy of the dti data tractography errors measured using bootstrap methods were generally consistent with an analytic model of tractography error except in areas where branching was evident white matter tractography with bootstrap resampling is also applied to estimate the probabilities of connection between brain regions the approach was used to generate probabilistic connectivity maps between the cerebral peduncles and specific cortical regions