It’s about time: Linking dynamical systems with human neuroimaging to understand the brain

Most human neuroscience research to date has focused on statistical approaches that describe stationary patterns of localized neural activity or blood flow. While these patterns are often interpreted in light of dynamic, information-processing concepts, the static, local and inferential nature of the statistical approach makes it challenging to directly link neuroimaging results to plausible underlying neural mechanisms. Here, we argue that dynamical systems theory provides the crucial mechanistic framework for characterizing both the brain’s time-varying quality and its partial stability in the face of perturbations, and hence, that this perspective can have a profound impact on the interpretation of human neuroimaging results and their relationship with behavior. After briefly reviewing some key terminology, we identify three key ways in which neuroimaging analyses can embrace a dynamical systems perspective: by shifting from a local to a more global perspective; by focusing on dynamics instead of static snapshots of neural activity; and by embracing modeling approaches that map neural dynamics using “forward” models. Through this approach, we envisage ample opportunities for neuroimaging researchers to enrich their understanding of the dynamic neural mechanisms that support a wide array of brain functions, both in health and in the setting of psychopathology.

Pt-Free Metal Nanocatalysts for the Oxygen Reduction Reaction Combining Experiment and Theory: An Overview

The design and manufacture of highly efficient nanocatalysts for the oxygen reduction reaction (ORR) is key to achieve the massive use of proton exchange membrane fuel cells. Up to date, Pt nanocatalysts are widely used for the ORR, but they have various disadvantages such as high cost, limited activity and partial stability. Therefore, different strategies have been implemented to eliminate or reduce the use of Pt in the nanocatalysts for the ORR. Among these, Pt-free metal nanocatalysts have received considerable relevance due to their good catalytic activity and slightly lower cost with respect to Pt. Consequently, nowadays, there are outstanding advances in the design of novel Pt-free metal nanocatalysts for the ORR. In this direction, combining experimental findings and theoretical insights is a low-cost methodology—in terms of both computational cost and laboratory resources—for the design of Pt-free metal nanocatalysts for the ORR in acid media. Therefore, coupled experimental and theoretical investigations are revised and discussed in detail in this review article.

Partial stability of linear systems with respect to a given component of the phase vector

A new geometric approach to the study of the partial stability of linear systems is proposed, which is based on the application of the geometric theory of linear operators. Using the theory of conjugate spaces and conjugate linear operators, bases are constructed in which the system under study takes the canonical form. A cyclic subspace with respect to the conjugate linear operator is considered. A basis is constructed for the dual space of a linear operator, in which its matrix takes the canonical form. This basis corresponds to the dual basis of the original linear space. Then, in a pair of bases of dual spaces the system under study takes the simplest form. The geometric properties of the system are realized using a non-singular linear transformation in the space of a part of the components of the system’s phase vector. This allows us to decompose the system under study in order to obtain necessary and sufficient conditions for the partial stability of the linear system. In an equivalent system, an independent subsystem is distinguished, whose nature of stability determines the behavior of the investigated component of the original system’s phase vector. The relationship between the partial stability of the system and the existence of an invariant subspace of a linear operator characterizing the dynamics of the system is established. The canonical form of the resulting subsystem makes it easy to exclude auxiliary variables and write an equation equivalent to this system. The application of the obtained results to the solution of the problem of partial stability for linear systems with constant coefficients belonging to the classes of ordinary differential equations, discrete systems and systems with deviating argument is shown. An example of a linear system of differential equations is given to illustrate the result obtained.

Practical partial stability of time-varying systems

<p style='text-indent:20px;'>In this paper we investigate the practical asymptotic and exponential partial stability of time-varying nonlinear systems. We derive some sufficient conditions that guarantee practical partial stability of perturbed systems using Lyapunov's theory where a converse theorem is presented. Therefore, we generalize some works which are already made in the literature. Furthermore, we present some illustrative examples to verify the effectiveness of the proposed methods.</p>

The Use of Partial Stability in the Analysis of Interconnected Systems

In this paper, we develop sufficient conditions for uniform asymptotic stability of interconnected dynamical systems that are not in cascade form. We show that the stability analysis of a two-subsystem interconnection can be reduced to ensuring the stability of the first nonisolated subsystem with respect to its own state vector (partial stability) and the stability of the isolated second subsystem. In addition, based on the above results, we provide a control design framework for nonlinear systems where the control objective reduces to stabilization of only a part of the system state while guaranteeing the stability for the entire state of the system. We validate the efficacy of the proposed control framework via simulations and experiments using the wheeled mobile robot platform.

The ADI-3: A Revised Neighborhood Risk Index of the Social Determinants of Health Over Time and Place

Since its development, Singh’s 2003 Area Deprivation Index (ADI) has been routinely used by researchers to measure a global construct of neighborhood socioeconomic deprivation and how living in neighborhoods of different levels of deprivation affects individuals’ health. We tested the ADI’s dimensionality and the stability of its performance across time and place. Factor analysis findings illuminated three distinct dimensions, the ADI-3, consisting of neighborhood financial strength, economic hardship and inequality, and educational attainment. The prior-assumed unidimensional ADI measure fails standard tests of construct validity. Findings from multigroup structural equation modeling across 2009 and 2017 and between New York and Minnesota suggest that the ADI performs with only partial stability across time and place. In order to most precisely understand the complex role of neighborhood socioeconomic position in health, public health researchers must integrate construct-valid and regionally- and temporally-relevant measures.