Existence of physical measures in some excitation–inhibition networks*

In this paper we present a rigorous analysis of a class of coupled dynamical systems in which two distinct types of components, one excitatory and the other inhibitory, interact with one another. These network models are finite in size but can be arbitrarily large. They are inspired by real biological networks, and possess features that are idealizations of those in biological systems. Individual components of the network are represented by simple, much studied dynamical systems. Complex dynamical patterns on the network level emerge as a result of the coupling among its constituent subsystems. Appealing to existing techniques in (nonuniform) hyperbolic theory, we study their Lyapunov exponents and entropy, and prove that large time network dynamics are governed by physical measures with the SRB property.

Can adults with cerebral palsy perform and benefit from ballistic strength training to improve walking outcomes? A mixed methods feasibility study

Background Power bursts of hips and ankle plantar flexors are prerequisites to walking propulsion. However, these power bursts are reduced during gait for persons with cerebral palsy (CP) and mainly in the ankle plantar flexors. Hence, task specific training, such as ballistic strength training, is suggested to increase muscle power in walking but not investigated in adults with CP. Therefore, the aim was to investigate if adults with CP could perform and benefit from ballistic strength training to improve walking, evaluated through physical measures and self-reported measures and interviews. Methods In this mixed methods feasibility study, eight ambulatory adults (aged 24–56) with spastic CP conducted ballistic strength training on a glideboard targeting the ankle plantarflexors two times a week for eight weeks. The feasibility of the training was assessed through objectives described by Orsmond and Cohn. Before and after the intervention, physical measures (6-Minute Walk Test and the eight-item High-level Mobility Assessment Tool) and self-reported measures (Patient Global Impression of Change, Numeric Pain Rating Scale, Fatigue Impact and Severity Self-Assessment, and Walk-12) were collected. After the intervention, semi-structured interviews explored experiences of this training. Results The participants experienced training the ankle plantar flexor as relevant but reported it took about four weeks to coordinate the exercises successfully. Although we observed no changes in the physical performance measures, most participants reported improvements; some felt steadier when standing, walking, and hopping. Conclusion This study demonstrated that ballistic strength training was feasible and suitable in adults with CP. However, guidance and a long (4 weeks) familiarization time were reported necessary to master the exercises. Most participants reported self-experienced improvements, although no physical performance measures improved. Thus, prolonged intervention may be required for perceived physical improvements to emerge. Also, other outcome measures sensitive to power output remains to be investigated.

GEOMETRICAL AND MEASURE-THEORETIC STRUCTURES OF MAPS WITH A MOSTLY EXPANDING CENTER

In this article we study physical measures for $\operatorname {C}^{1+\alpha }$ partially hyperbolic diffeomorphisms with a mostly expanding center. We show that every diffeomorphism with a mostly expanding center direction exhibits a geometrical-combinatorial structure, which we call skeleton, that determines the number, basins and supports of the physical measures. Furthermore, the skeleton allows us to describe how physical measures bifurcate as the diffeomorphism changes under $C^1$ topology. Moreover, for each diffeomorphism with a mostly expanding center, there exists a $C^1$ neighbourhood, such that diffeomorphism among a $C^1$ residual subset of this neighbourhood admits finitely many physical measures, whose basins have full volume. We also show that the physical measures for diffeomorphisms with a mostly expanding center satisfy exponential decay of correlation for any Hölder observes. In particular, we prove that every $C^2$ , partially hyperbolic, accessible diffeomorphism with 1-dimensional center and nonvanishing center exponent has exponential decay of correlations for Hölder functions.

Social measures of resilience: An investigation into community resilience by taking adaptive physical measures through social mediation during infrastructure disruption

This paper intends to break down a local case to grasp the possibility of adaptable measures by individuals and systems through the social exchange during infrastructure interruption on account of considerable precipitation. Finally, the extent of social resilience is assessed through the ‘5S’ framework. The assessment reveals the social capital and the incredible social conditions accomplished by the mix of the particular circumstance and differing interest packs are influencing the adaptable appraisals which can be considered as an important report to structure a strong framework by understanding the tangled social issues and multifaceted nature