State-space Perspective Research Articles

A transient high-dimensional geometry affords stable conjunctive subspaces for efficient action selection

Flexible action selection requires cognitive control mechanisms capable of mapping the same inputs to different output actions depending on the context. From a neural state-space perspective, this requires a control representation that separates similar input neural states by context. Additionally, for action selection to be robust and time-invariant, information must be stable in time, enabling efficient readout. Here, using EEG decoding methods, we investigate how the geometry and dynamics of control representations constrain flexible action selection in the human brain. Participants performed a context-dependent action selection task. A forced response procedure probed action selection different states in neural trajectories. The result shows that before successful responses, there is a transient expansion of representational dimensionality that separated conjunctive subspaces. Further, the dynamics stabilizes in the same time window, with entry into this stable, high-dimensional state predictive of individual trial performance. These results establish the neural geometry and dynamics the human brain needs for flexible control over behavior.

A Transient High-dimensional Geometry Affords Stable Conjunctive Subspaces for Efficient Action Selection.

Flexible action selection requires cognitive control mechanisms capable of mapping the same inputs to different output actions depending on the context. From a neural state-space perspective, this requires a control representation that separates similar input neural states by context. Additionally, for action selection to be robust and time-invariant, information must be stable in time, enabling efficient readout. Here, using EEG decoding methods, we investigate how the geometry and dynamics of control representations constrain flexible action selection in the human brain. Participants performed a context-dependent action selection task. A forced response procedure probed action selection different states in neural trajectories. The result shows that before successful responses, there is a transient expansion of representational dimensionality that separated conjunctive subspaces. Further, the dynamics stabilizes in the same time window, with entry into this stable, high-dimensional state predictive of individual trial performance. These results establish the neural geometry and dynamics the human brain needs for flexible control over behavior.

DOES CHINA’S IRON ORE FUTURES MARKET HAVE PRICE DISCOVERY FUNCTION? ANALYSIS BASED ON VECM AND STATE-SPACE PERSPECTIVE

As the world’s largest importer, trading of iron ore occupies a pivotal position in China’s international trade. In order to seek the decision power of deciding the price for iron ore, China’s Dalian Commodity Exchange (DCE) listed iron ore futures in October 2013,which has become the world’s largest iron ore financial derivatives trading market now. Based on VECM and state-space perspective, this paper aims to explore the price discovery function of iron ore futures on the DCE. Comprehensive analysis from the views of long-term equilibrium relationship, short-term information shocks and dynamic contribution share are made in this paper. The empirical results show that: firstly, from the perspective of cointegration test, there is a long-term equilibrium relationship between the futures prices in DCE and the spot prices; secondly, when facing with short-term information shocks, iron ore futures in DCE have an obviously price discovery function by the analysis of impulse response and variance decomposition; finally, by the way of state-space and Kalman filter algorithm, the long-term equilibrium relationship dynamic contribution for price discovery function of DCE's iron ore futures remains stable between 60% and 70% now.

Modeling Procedures.

Being concerned by the understanding of the mechanism underlying chronic degenerative diseases , we presented in the previous chapter the medical systems biology conceptual framework that we present for that purpose in this volume. More specifically, we argued there the clear advantages offered by a state-space perspective when applied to the systems-level description of the biomolecular machinery that regulates complex degenerative diseases. We also discussed the importance of the dynamical interplay between the risk factors and the network of interdependencies that characterizes the biochemical, cellular, and tissue-level biomolecular reactions that underlie the physiological processes in health and disease. As we pointed out in the previous chapter, the understanding of this interplay (articulated around cellular phenotypic plasticity properties, regulated by specific kinds of gene regulatory networks) is necessary if prevention is chosen as the human-health improvement strategy (potentially involving the modulation of the patient's lifestyle). In this chapter we provide the medical systems biology mathematical and computational modeling tools required for this task.

State-Space Geometry, Statistical Fluctuations, and Black Holes in String Theory

We study the state-space geometry of various extremal and nonextremal black holes in string theory. From the notion of the intrinsic geometry, we offer a state-space perspective to the black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic geometric meaning of the statistical fluctuations, local and global stability conditions, and long range statistical correlations. We provide a set of physical motivations pertaining to the extremal and nonextremal black holes, namely, the meaning of the chemical geometry and physics of correlation. We illustrate the state-space configurations for general charge extremal black holes. In sequel, we extend our analysis for various possible charge and anticharge nonextremal black holes. From the perspective of statistical fluctuation theory, we offer general remarks, future directions, and open issues towards the intrinsic geometric understanding of the vacuum fluctuations and black holes in string theory.

Identification and Control of Mechanical Systems

The control of vibrating systems is a significant issue in the design of aircraft, spacecraft, bridges and high-rise buildings. This 2001 book discusses the control of vibrating systems, integrating structural dynamics, vibration analysis, modern control and system identification. Integrating these subjects is an important feature in that engineers will need only one book, rather than several texts or courses, to solve vibration control problems. The book begins with a review of basic mathematics needed to understand subsequent material. Chapters then cover more recent and valuable developments in aerospace control and identification theory, including virtual passive control, observer and state-space identification, and data-based controller synthesis. Many practical issues and applications are addressed, with examples showing how various methods are applied to real systems. Some methods show the close integration of system identification and control theory from the state-space perspective, rather than from the traditional input-output model perspective of adaptive control. This text will be useful for advanced undergraduate and beginning graduate students in aerospace, mechanical and civil engineering, as well as for practising engineers.

Response and Discretization Methods for Axially Moving Materials

Through a convective acceleration component, the equations of motion for axially-moving materials are skew-symmetric in the state space formulation, so that the response problem is best analyzed within the broader context of continuous gyroscopic systems. With particular application to the prototypical traveling string and beam models, a modal analysis that associates degrees of freedom with the complex state eigenfunctions and their conjugates is presented. This procedure is well-suited for harmonic excitation sources, and in some instances, it is more convenient than previous methods which decompose the modal coordinates, eigenfunctions, and generalized forces into real and imaginary components. Also from the state space perspective, Rayleigh’s quotient for gyroscopic systems provides a variational method for determining the eigensolutions of axially-moving materials. Ritz discretization of the quotient can make effective use of the speed-adapting modes of the traveling string and beam models as they are rich in phase, as well as amplitude, content.