14,122 research outputs found
Probabilistic Models of Motor Production
N. Bernstein defined the ability of the central neural system (CNS) to control many degrees of freedom of a physical body with all its redundancy and flexibility as the main problem in motor control. He pointed at that man-made mechanisms usually have one, sometimes two degrees of freedom (DOF); when the number of DOF increases further, it becomes prohibitively hard to control them. The brain, however, seems to perform such control effortlessly. He suggested the way the brain might deal with it: when a motor skill is being acquired, the brain artificially limits the degrees of freedoms, leaving only one or two. As the skill level increases, the brain gradually "frees" the previously fixed DOF, applying control when needed and in directions which have to be corrected, eventually arriving to the control scheme where all the DOF are "free". This approach of reducing the dimensionality of motor control remains relevant even today.
One the possibles solutions of the Bernstetin's problem is the hypothesis of motor primitives (MPs) - small building blocks that constitute complex movements and facilitite motor learnirng and task completion. Just like in the visual system, having a homogenious hierarchical architecture built of similar computational elements may be beneficial.
Studying such a complicated object as brain, it is important to define at which level of details one works and which questions one aims to answer. David Marr suggested three levels of analysis: 1. computational, analysing which problem the system solves; 2. algorithmic, questioning which representation the system uses and which computations it performs; 3. implementational, finding how such computations are performed by neurons in the brain. In this thesis we stay at the first two levels, seeking for the basic representation of motor output.
In this work we present a new model of motor primitives that comprises multiple interacting latent dynamical systems, and give it a full Bayesian treatment. Modelling within the Bayesian framework, in my opinion, must become the new standard in hypothesis testing in neuroscience. Only the Bayesian framework gives us guarantees when dealing with the inevitable plethora of hidden variables and uncertainty.
The special type of coupling of dynamical systems we proposed, based on the Product of Experts, has many natural interpretations in the Bayesian framework. If the dynamical systems run in parallel, it yields Bayesian cue integration. If they are organized hierarchically due to serial coupling, we get hierarchical priors over the dynamics. If one of the dynamical systems represents sensory state, we arrive to the sensory-motor primitives. The compact representation that follows from the variational treatment allows learning of a motor primitives library. Learned separately, combined motion can be represented as a matrix of coupling values.
We performed a set of experiments to compare different models of motor primitives. In a series of 2-alternative forced choice (2AFC) experiments participants were discriminating natural and synthesised movements, thus running a graphics Turing test. When available, Bayesian model score predicted the naturalness of the perceived movements. For simple movements, like walking, Bayesian model comparison and psychophysics tests indicate that one dynamical system is sufficient to describe the data. For more complex movements, like walking and waving, motion can be better represented as a set of coupled dynamical systems. We also experimentally confirmed that Bayesian treatment of model learning on motion data is superior to the simple point estimate of latent parameters. Experiments with non-periodic movements show that they do not benefit from more complex latent dynamics, despite having high kinematic complexity.
By having a fully Bayesian models, we could quantitatively disentangle the influence of motion dynamics and pose on the perception of naturalness. We confirmed that rich and correct dynamics is more important than the kinematic representation.
There are numerous further directions of research. In the models we devised, for multiple parts, even though the latent dynamics was factorized on a set of interacting systems, the kinematic parts were completely independent. Thus, interaction between the kinematic parts could be mediated only by the latent dynamics interactions. A more flexible model would allow a dense interaction on the kinematic level too.
Another important problem relates to the representation of time in Markov chains. Discrete time Markov chains form an approximation to continuous dynamics. As time step is assumed to be fixed, we face with the problem of time step selection. Time is also not a explicit parameter in Markov chains. This also prohibits explicit optimization of time as parameter and reasoning (inference) about it. For example, in optimal control boundary conditions are usually set at exact time points, which is not an ecological scenario, where time is usually a parameter of optimization. Making time an explicit parameter in dynamics may alleviate this
Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling
Identifying a coupled dynamical system out of many plausible candidates, each
of which could serve as the underlying generator of some observed measurements,
is a profoundly ill posed problem that commonly arises when modelling real
world phenomena. In this review, we detail a set of statistical procedures for
inferring the structure of nonlinear coupled dynamical systems (structure
learning), which has proved useful in neuroscience research. A key focus here
is the comparison of competing models of (ie, hypotheses about) network
architectures and implicit coupling functions in terms of their Bayesian model
evidence. These methods are collectively referred to as dynamical casual
modelling (DCM). We focus on a relatively new approach that is proving
remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid
evaluation and comparison of models that differ in their network architecture.
We illustrate the usefulness of these techniques through modelling
neurovascular coupling (cellular pathways linking neuronal and vascular
systems), whose function is an active focus of research in neurobiology and the
imaging of coupled neuronal systems
Simultaneous Learning of Nonlinear Manifold and Dynamical Models for High-dimensional Time Series
The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.National Science Foundation (IIS 0308213, IIS 0329009, CNS 0202067
Stochastic collective dynamics of charged--particle beams in the stability regime
We introduce a description of the collective transverse dynamics of charged
(proton) beams in the stability regime by suitable classical stochastic
fluctuations. In this scheme, the collective beam dynamics is described by
time--reversal invariant diffusion processes deduced by stochastic variational
principles (Nelson processes). By general arguments, we show that the diffusion
coefficient, expressed in units of length, is given by ,
where is the number of particles in the beam and the Compton
wavelength of a single constituent. This diffusion coefficient represents an
effective unit of beam emittance. The hydrodynamic equations of the stochastic
dynamics can be easily recast in the form of a Schr\"odinger equation, with the
unit of emittance replacing the Planck action constant. This fact provides a
natural connection to the so--called ``quantum--like approaches'' to beam
dynamics. The transition probabilities associated to Nelson processes can be
exploited to model evolutions suitable to control the transverse beam dynamics.
In particular we show how to control, in the quadrupole approximation to the
beam--field interaction, both the focusing and the transverse oscillations of
the beam, either together or independently.Comment: 15 pages, 9 figure
Quantum Decoherence, Entropy and Thermalization in Strong Interactions at High Energy
Entropy is generated in high-multiplying events by a dynamical separation of
strongly interacting systems into partons and unobservable environment modes
(almost constant field configurations) due to confinement.Comment: 45 pages, 2 figure
Large deviations of lattice Hamiltonian dynamics coupled to stochastic thermostats
We discuss the Donsker-Varadhan theory of large deviations in the framework
of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We
derive a general formula for the Donsker-Varadhan large deviation functional
for dynamics which satisfy natural properties under time reversal. Next, we
discuss the characterization of the stationary state as the solution of a
variational principle and its relation to the minimum entropy production
principle. Finally, we compute the large deviation functional of the current in
the case of a harmonic chain thermostated by a Gaussian stochastic coupling.Comment: Revised version, published in Journal of Statistical Physic
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