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

Bose-Einstein condensation and/or modulation of "displacements" in the two-state Bose-Hubbard model

Instabilities resulting in Bose-Einstein condensation and/or modulation of "displacements" in a system of quantum particles described by a two-state Bose-Hubbard model (with an allowance for the interaction between particle displacements on different lattice sites) are investigated. A possibility of modulation, which doubles the lattice constant, as well as the uniform displacement of particles from equilibrium positions are studied. Conditions for realization of the mentioned instabilities and phase transitions into the SF phase and into the "ordered" phase with frozen displacements are analyzed. The behaviour of order parameters is investigated and phase diagrams of the system are calculated both analytically (ground state) and numerically (at non-zero temperatures). It is revealed that the SF phase can appear as an intermediate one between the normal and "ordered" phases, while a supersolid phase is thermodynamically unstable and does not appear. The relation of the obtained results to the lattices with the double-well local potentials is discussed.Comment: 17 pages, 11 figure

Two-state Bose-Hubbard model in the hard-core boson limit

Phase transition into the phase with Bose-Einstein (BE) condensate in the two-band Bose-Hubbard model with the particle hopping in the excited band only is investigated. Instability connected with such a transition (which appears at excitation energies $\delta<\lvert t_0' \rvert$, where $\lvert t_0' \rvert$ is the particle hopping parameter) is considered. The re-entrant behaviour of spinodales is revealed in the hard-core boson limit in the region of positive values of chemical potential. It is found that the order of the phase transition undergoes a change in this case and becomes the first one; the re-entrant transition into the normal phase does not take place in reality. First order phase transitions also exist at negative values of $\delta$ (under the condition $\delta>\delta_{\mathrm{crit}}\approx-0.12\lvert t_0' \rvert$). At $\mu<0$ the phase transition mostly remains to be of the second order. The behaviour of the BE-condensate order parameter is analyzed, the $(\Theta,\mu)$ and $(\lvert t_0' \rvert,\mu)$ phase diagrams are built and localizations of tricritical points are established. The conditions are found at which the separation on the normal phase and the phase with the BE condensate takes place.Comment: 14 pages, 12 figure

Phase separation in lithium intercalated anatase: A theory

Lithium intercalated anatase used in Li-ion batteries has some special features: coexistence of Li-rich and Li-poor phases as well as two possible positions for Li ions in the oxygen tetrahedron. A theoretical description of the compound considering those peculiarities is presented. As shown by the performed symmetry analysis, the intercalation induced lattice deformation can be accompanied by the ordering of antiferroelectric type (internal piezoeffect). In the following step, a qualitative illustration of the phase separation in the lithiated anatase is given within the Landau expansion at the proper choice of coefficients. A microscopic model for description of the compound is also proposed which combines features of the Mitsui and Blume-Emery-Griffits models and utilizes the symmetry analysis results. Various ground state and temperature-dependent phase diagrams of the model are studied to find a set of model parameters corresponding to the lithiated anatase. A phase separation into the empty and half-filled phases in a wide temperature range has been found closely resembling the phase coexistence in the intercalated crystal. In the framework of the model, the two-position Li subsystem could have the ordering of ferro- or antiferroelectric types which, however, has not been yet observed by the experiment.Comment: 19 pages, Reported at the Conference "Statistical Physics: Modern Trends and Applications" dedicated to the 100-th anniversary of N.N. Bogolyubov (June 23--25, 2009 Lviv, Ukraine

Research and Development Workstation Environment: the new class of Current Research Information Systems

Against the backdrop of the development of modern technologies in the field of scientific research the new class of Current Research Information Systems (CRIS) and related intelligent information technologies has arisen. It was called - Research and Development Workstation Environment (RDWE) - the comprehensive problem-oriented information systems for scientific research and development lifecycle support. The given paper describes design and development fundamentals of the RDWE class systems. The RDWE class system's generalized information model is represented in the article as a three-tuple composite web service that include: a set of atomic web services, each of them can be designed and developed as a microservice or a desktop application, that allows them to be used as an independent software separately; a set of functions, the functional filling-up of the Research and Development Workstation Environment; a subset of atomic web services that are required to implement function of composite web service. In accordance with the fundamental information model of the RDWE class the system for supporting research in the field of ontology engineering - the automated building of applied ontology in an arbitrary domain area, scientific and technical creativity - the automated preparation of application documents for patenting inventions in Ukraine was developed. It was called - Personal Research Information System. A distinctive feature of such systems is the possibility of their problematic orientation to various types of scientific activities by combining on a variety of functional services and adding new ones within the cloud integrated environment. The main results of our work are focused on enhancing the effectiveness of the scientist's research and development lifecycle in the arbitrary domain area.Comment: In English, 13 pages, 1 figure, 1 table, added references in Russian. Published. Prepared for special issue (UkrPROG 2018 conference) of the scientific journal "Problems of programming" (Founder: National Academy of Sciences of Ukraine, Institute of Software Systems of NAS Ukraine

Інноваційний розвиток у логістиці та його зв’язок з логістичним управлінням і управлінням логістикою

У статті наведено авторську класифікацію та тлумачення основних видів (напрямів) інноваційного розвитку логістики. Установлено основні відмінності між процесами логістичного управління та управлінням логістикою, а також визначено їхній зв’язок з основними видами (напрямами) інноваційного логістичного розвитку. При цитуванні документа, використовуйте посилання http://essuir.sumdu.edu.ua/handle/123456789/30376В статье представлена авторская классификация и толкование основных видов (направлений) инновационного развития логистики. Установлены основные отличия между процессами логистического управления и управлением логистикой, а также определенна их связь с основными видами (направлениями) инновационного логистического развития. При цитировании документа, используйте ссылку http://essuir.sumdu.edu.ua/handle/123456789/30376In the article author’s classification and grounding of main kinds (directions) of innovative development in logistics have been revealed. Basic differences between processes of logistical management and management of logistics have been defined and their connection with main kinds (directions) of innovative development in logistics has been determined. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3037