Moving constraints as stabilizing controls in classical mechanics

The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms which are linear or quadratic w.r.t.time derivatives of the control functions. After reviewing the basic equations, we explain the significance of the quadratic terms, related to geodesics orthogonal to a given foliation. We then study the problem of stabilization of the system to a given point, by means of oscillating controls. This problem is first reduced to the weak stability for a related convex-valued differential inclusion, then studied by Lyapunov functions methods. In the last sections, we illustrate the results by means of various mechanical examples.Comment: 52 pages, 4 figure

Perturbations and chaos in quantum maps

The local density of states (LDOS) is a distribution that characterizes the effect of perturbations on quantum systems. Recently, it was proposed a semiclassical theory for the LDOS of chaotic billiards and maps. This theory predicts that the LDOS is a Breit-Wigner distribution independent of the perturbation strength and also gives a semiclassical expression for the LDOS witdth. Here, we test the validity of such an approximation in quantum maps varying the degree of chaoticity, the region in phase space where the perturbation is applying and the intensity of the perturbation. We show that for highly chaotic maps or strong perturbations the semiclassical theory of the LDOS is accurate to describe the quantum distribution. Moreover, the width of the LDOS is also well represented for its semiclassical expression in the case of mixed classical dynamics.Comment: 9 pages, 11 figures. Accepted for publication in Phys. Rev.

The economic crisis of spanish football: current state and ways of solving

The article is devoted to the economic component of football in Spain. It reveals the main causes of the difficult financial situation which the majority of Spanish clubs face. The article considers the main anti-crisis solutions to the problems of the economy of professional football in Spain

The economic crisis of spanish football: current state and ways of solving

The article is devoted to the economic component of football in Spain. It reveals the main causes of the difficult financial situation which the majority of Spanish clubs face. The article considers the main anti-crisis solutions to the problems of the economy of professional football in Spain

Structural Balance via Gradient Flows over Signed Graphs

Structural balance is a classic property of signed graphs satisfying Heider's seminal axioms. Mathematical sociologists have studied balance theory since its inception in the 1940s. Recent research has focused on the development of dynamic models explaining the emergence of structural balance. In this paper, we introduce a novel class of parsimonious dynamic models for structural balance based on an interpersonal influence process. Our proposed models are gradient flows of an energy function, called the dissonance function, which captures the cognitive dissonance arising from violations of Heider's axioms. Thus, we build a new connection with the literature on energy landscape minimization. This gradient flow characterization allows us to study the transient and asymptotic behaviors of our model. We provide mathematical and numerical results describing the critical points of the dissonance function

Saccades and smooth pursuit eye movements in central vertigo

In order to analyze the diagnostic efficiency of saccadic and pursuit eye movements compared to findings from brain magnetic resonance imaging in patients with central vertigo, 108 patients were selected from 580 dizzy patients as cases of suspected central origin; the saccadic and pursuit eye movements were evaluated by electronystagmography and findings were compared to information from magnetic resonance imaging. The study of oculomotor movements in patients suspected of having a central lesion revealed a 83.3% sensitivity and 21.2% specificity. Restricting consideration to severe alterations in eye movements as indicative of a central origin, this test gives a 71.4% sensitivity and 50.0% specificity. In conclusion, the study of alterations in oculomotor movements, in patients with suspected central lesions, proved to be a test with good sensitivity also compared with results of magnetic resonance imaging

Momentum and energy preserving integrators for nonholonomic dynamics

In this paper, we propose a geometric integrator for nonholonomic mechanical systems. It can be applied to discrete Lagrangian systems specified through a discrete Lagrangian defined on QxQ, where Q is the configuration manifold, and a (generally nonintegrable) distribution in TQ. In the proposed method, a discretization of the constraints is not required. We show that the method preserves the discrete nonholonomic momentum map, and also that the nonholonomic constraints are preserved in average. We study in particular the case where Q has a Lie group structure and the discrete Lagrangian and/or nonholonomic constraints have various invariance properties, and show that the method is also energy-preserving in some important cases.Comment: 18 pages, 6 figures; v2: example and figures added, minor correction to example 2; v3: added section on nonholonomic Stoermer-Verlet metho

Exercise prescription to improve clinical practice on cancer patients suffering chemotherapy-induced peripheral neuropathy undergoing treatment: a systematic review

This document aims to summarize and analyze systematically the current body of evidence about the effects of specific exercise proto- cols on physical function, balance control and quality of life in patients with peripheral neuropathy (PNP) induced by chemotherapy. Methods: Systematic Review, Literature survey Specific terms were identified for the literature research in MEDLINE, Scopus, Bandolier, PEDro, and Web of Science. Only studies pub- lished in peer-reviewed journals written in English language were considered. Four manuscripts were classified as eligible with 88 total participants, with an average of 57.1 years old. Quality appraisal classified two studies as high quality investigations while two with low quality. Results were summarized in the following domains: \u201cCIPN symptoms\u201d, \u201cStatic balance control\u201d, \u201cDynamic balance control\u201d, \u201cQuali- ty of life and Physical function\u201d. Results Specific exercise protocols were able to counteract common symptoms of chemotherapy-induced peripheral neuropathy (CIPN) during chemotherapy treatments. Significant improvements were detected on postural control. Additionally, patients\u2019 quality of life and inde- pendence were found ameliorated after exercise sessions, together with reductions on altered sensations and in other peripheral neu- ropathy symptoms. Combined exercise protocols including endurance, strength and sensorimotor training showed larger improvements. Conclusions Exercise prescriptions for cancer patients undergoing chemotherapy with CIPN symptoms should be recommended since these exercise interventions appeared as feasible and have been demonstrated as useful tools to counteract some common side effects of chemother- apeutic agents