A Vexing Question in Motor Control: The Degrees of Freedom Problem

The human “marionette” is extremely complex and multi-articulated: anatomical redundancy (in terms of Degrees of Freedom: DoFs), kinematic redundancy (movements can have different trajectories, velocities, and accelerations and yet achieve the same goal, according to the principle of Motor Equivalence), and neurophysiological redundancy (many more muscles than DoFs and multiple motor units for each muscle). Although it is quite obvious that such abundance is not noxious at all because, in contrast, it is instrumental for motor learning, allowing the nervous system to “explore” the space of feasible actions before settling on an elegant and possibly optimal solution, the crucial question then boils down to figure out how the nervous system “chooses/selects/recruits/modulates” task-dependent subsets of countless assemblies of DoFs as functional motor synergies. Despite this daunting conceptual riddle, human purposive behavior in daily life activities is a proof of concept that solutions can be found easily and quickly by the embodied brain of the human cognitive agent. The point of view suggested in this essay is to frame the question above in the old-fashioned but still seminal observation by Marr and Poggio that cognitive agents should be regarded as Generalized Information Processing Systems (GIPS) and should be investigated according to three nearly independent but complementary levels of analysis: 1) the computational level, 2) the algorithmic level, and 3) the implementation level. In this framework, we attempt to discriminate as well as aggregate the different hypotheses and solutions proposed so far: the optimal control hypothesis, the muscle synergy hypothesis, the equilibrium point hypothesis, or the uncontrolled manifold hypothesis, to mention the most popular ones. The proposed GIPS follows the strategy of factoring out shaping and timing by adopting a force-field based approach (the Passive Motion Paradigm) that is inspired by the Equilibrium Point Hypothesis, extended in such a way to represent covert as well overt actions. In particular, it is shown how this approach can explain spatio-temporal invariances and, at the same time, solve the Degrees of Freedom Problem.

Power Generation Control of Renewable Energy Based Hybrid Deregulated Power System

This work presents the power generation control of a two-area, hybrid, deregulated power system integrated with renewable energy sources (RES). The incorporation of appropriate system non-linearities and RES into the power system makes it complex, but more practical. The hybrid deregulated power system with RES is a complex nonlinear system that regularly exposes the major issue of system dynamic control due to insufficient damping under varying loading circumstances. The generation-demand equilibrium point of the power system varies following a contingency; hence, it becomes difficult to maintain the appropriate equilibrium point via traditional control approaches. To solve this problem, novel control approaches, along with rapid-acting energy storage devices (ESD), are immediate need for advanced power systems. As a result, various secondary controllers are inspected for improvements in system dynamics. A performance comparison infers the cascaded ID-PD controller as the optimum one. The secondary controller gains are successfully optimized by the powerful satin bowerbird optimization (SBO) technique. Additionally, the impact of a super-conducting-magnetic-energy-storage (SMES) device in system dynamics and control of developed power system is analyzed in this study. A sensitivity evaluation (SE) infers that SBO-optimized cascaded ID-PD controller gains are strong enough for alterations in load perturbations, system loading, inertial constant (H), solar irradiance and the DISCO involvement matrix (DIM).

Characterization and Evolution of a Digital Economy Ecosystem Based on an Interspecies Competition Model

This paper provides an in-depth study and analysis of the characterization of the digital economy ecosystem and the mechanism of eye-flowering through the method of interspecies competition. The evolutionary game model of symbiotic decision-making in the entrepreneurial ecosystem is constructed, the evolutionary process of symbiotic decision-making of subjects is analyzed through mathematical derivation, and the symbiotic decision-making process of subjects is simulated through computer simulation to answer how the subjects of the entrepreneurial ecosystem make symbiotic decisions and explore the mechanism of symbiotic formation of the entrepreneurial ecosystem. Then, based on the ecological perspective, the symbiotic evolution model of entrepreneurial ecosystem subjects is constructed from the subject level, the equilibrium point of the evolution of entrepreneurial ecosystem subjects, the stability conditions, and the relationship between the equilibrium point and the symbiosis model are analyzed, and the symbiotic evolution paths of entrepreneurial ecosystem subjects under different symbiosis modes, initial population size, maximum size, and natural growth rate are presented with simulation experiments, respectively. The main characteristics and manifestations of the dynamic evolution of the platform ecosystem are analyzed, and the key competitive factors that determine the dynamic evolution of the platform ecosystem are depicted. Then, according to the inherent characteristic laws of the platform ecosystem, the complex network approach is applied to construct a dynamic evolution model with originality and wide applicability for the change of bilateral user scale. Based on the dynamic evolution process, the relationship between model parameters and business performance is explored, and the trajectory of bilateral user size change over time and the range of parameters are derived by numerical calculation. Finally, using Monte Carlo simulation methods, the dynamic evolution model is used to predict the future operating conditions of platform enterprises, providing a valuation basis for investors to make investment decisions and helping platform managers to formulate business strategies.

New Robust Projection to Latent Structure

In many actual nonlinear systems, especially near the equilibrium point, linearity is the primary feature and nonlinearity is the secondary feature. For the system that deviates from the equilibrium point, the secondary nonlinearity or local structure feature can also be regarded as the small uncertainty part, just as the nonlinearity can be used to represent the uncertainty of a system (Wang et al. 2019). So this chapter also focuses on how to deal with the nonlinearity in PLS series method, but starts from an different view, i.e., robust PLS. Here the system nonlinearity is considered as uncertainty and a new robust $$\mathrm{L}_1$$ L 1 -PLS is proposed.

Global dynamics for a class of reaction–diffusion multigroup SIR epidemic models with time fractional-order derivatives

This paper investigates the global dynamics for a class of multigroup SIR epidemic model with time fractional-order derivatives and reaction–diffusion. The fractional order considered in this paper is in (0; 1], which the propagation speed of this process is slower than Brownian motion leading to anomalous subdiffusion. Furthermore, the generalized incidence function is considered so that the data itself can flexibly determine the functional form of incidence rates in practice. Firstly, the existence, nonnegativity, and ultimate boundedness of the solution for the proposed system are studied. Moreover, the basic reproduction number R0 is calculated and shown as a threshold: the disease-free equilibrium point of the proposed system is globally asymptotically stable when R0 ≤ 1, while when R0 > 1, the proposed system is uniformly persistent, and the endemic equilibrium point is globally asymptotically stable. Finally, the theoretical results are verified by numerical simulation.

Dynamics of COVID-19 Epidemic Model with Asymptomatic Infection, Quarantine, Protection and Vaccination

We discuss the dynamics of new COVID-19 epidemic model by considering asymptomatic infections and the policies such as quarantine, protection (adherence to health protocols), and vaccination. The proposed model contains nine subpopulations: susceptible (S), exposed (E), symptomatic infected (I), asymptomatic infected (A), recovered (R), death (D), protected (P), quarantined (Q), and vaccinated (V ). We first show the non-negativity and boundedness of solutions. The equilibrium points, basic reproduction number, and stability of equilibrium points, both locally and globally, are also investigated analytically. The proposed model has disease-free equilibrium point and endemic equilibrium point. The disease-free equilibrium point always exists and is globally asymptotically stable if basic reproduction number is less than one. The endemic equilibrium point exists uniquely and is globally asymptotically stable if the basic reproduction number is greater than one. These properties have been confirmed by numerical simulations using the fourth order Runge-Kutta method. Numerical simulations show that the disease transmission rate of asymptomatic infection, quarantine rates, protection rate, and vaccination rates affect the basic reproduction number and hence also influence the stability of equilibrium points.

Take Action: Give A Hope to Minimize Inequality!

From equality to inequality, the equilibrium point fluctuates all the time. How to balance and minimize the negative impact of inequality on the individual’s socioeconomic, educational, psychological, and overall health is critical. Even it is of extremely difficult to realize the real equality, it is still worthwhile to take action to minimize the inequality.

Evaluation of the Number of Visits to Chinese Medical Institutions Using a Logistic Differential Equation Model

In this study, we established a two-dimensional logistic differential equation model to study the number of visits in Chinese PHCIs and hospitals based on the behavior of patients. We determine the model's equilibrium points and analyze their stability and then use China medical services data to fit the unknown parameters of the model. Finally, the sensitivity of model parameters is evaluated to determine the parameters that are susceptible to influence the system. The results indicate that the system corresponds to the zero-equilibrium point, the boundary equilibrium point, and the positive equilibrium point under different parameter conditions. We found that, in order to substantially increase visits to PHCIs, efforts should be made to improve PHCI comprehensive capacity and maximum service capacity.

An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of Newborns

This paper analyses an SIRS epidemic model with the vaccination of susceptible individuals and treatment of infectious ones. Both actions are governed by a designed control system whose inputs are the subpopulations of the epidemic model. In addition, the vaccination of a proportion of newborns is considered. The control reproduction number Rc of the controlled epidemic model is calculated, and its influence in the existence and stability of equilibrium points is studied. If such a number is smaller than a threshold value Rc, then the model has a unique equilibrium point: the so-called disease-free equilibrium point at which there are not infectious individuals. Furthermore, such an equilibrium point is locally and globally asymptotically stable. On the contrary, if Rc>Rc, then the model has two equilibrium points: the referred disease-free one, which is unstable, and an endemic one at which there are infectious individuals. The proposed control strategy provides several free-design parameters that influence both values Rc and Rc. Then, such parameters can be appropriately adjusted for guaranteeing the non-existence of the endemic equilibrium point and, in this way, eradicating the persistence of the infectious disease.

Stability Analysis of SEIL Tuberculosis Epidemic Model with Logistic Growth in Susceptible Compartment

This article discusses modifications to the SEIL model that involve logistical growth. This model is used to describe the dynamics of the spread of tuberculosis disease in the population. The existence of the model's equilibrium points and its local stability depends on the basic reproduction number. If the basic reproduction number is less than unity, then there is one equilibrium point that is locally asymptotically stable. The equilibrium point is a disease-free equilibrium point. If the basic reproduction number ranges from one to three, then there are two equilibrium points. The two equilibrium points are disease-free equilibrium and endemic equilibrium points. Furthermore, for this case, the endemic equilibrium point is locally asymptotically stable.