Sparse Stabilization and Control of Alignment Models

From a mathematical point of view self-organization can be described as patterns to which certain dynamical systems modeling social dynamics tend spontaneously to be attracted. In this paper we explore situations beyond self-organization, in particular how to externally control such dynamical systems in order to eventually enforce pattern formation also in those situations where this wished phenomenon does not result from spontaneous convergence. Our focus is on dynamical systems of Cucker-Smale type, modeling consensus emergence, and we question the existence of stabilization and optimal control strategies which require the minimal amount of external intervention for nevertheless inducing consensus in a group of interacting agents. We provide a variational criterion to explicitly design feedback controls that are componentwise sparse, i.e. with at most one nonzero component at every instant of time. Controls sharing this sparsity feature are very realistic and convenient for practical issues. Moreover, the maximally sparse ones are instantaneously optimal in terms of the decay rate of a suitably designed Lyapunov functional, measuring the distance from consensus. As a consequence we provide a mathematical justification to the general principle according to which "sparse is better" in the sense that a policy maker, who is not allowed to predict future developments, should always consider more favorable to intervene with stronger action on the fewest possible instantaneous optimal leaders rather than trying to control more agents with minor strength in order to achieve group consensus. We then establish local and global sparse controllability properties to consensus and, finally, we analyze the sparsity of solutions of the finite time optimal control problem where the minimization criterion is a combination of the distance from consensus and of the l1-norm of the control.Comment: 33 pages, 5 figure

Mean-field sparse Jurdjevic-Quinn control

International audienceWe consider nonlinear transport equations with non-local velocity, describing the time-evolution of a measure, which in practice may represent the density of a crowd. Such equations often appear by taking the mean-field limit of finite-dimensional systems modelling collective dynamics. We first give a sense to dissipativity of these mean-field equations in terms of Lie derivatives of a Lyapunov function depending on the measure. Then, we address the problem of controlling such equations by means of a time-varying bounded control action localized on a time-varying control subset with bounded Lebesgue measure (sparsity space constraint). Finite-dimensional versions are given by control-affine systems, which can be stabilized by the well known Jurdjevic–Quinn procedure. In this paper, assuming that the uncontrolled dynamics are dissipative, we develop an approach in the spirit of the classical Jurdjevic–Quinn theorem, showing how to steer the system to an invariant sublevel of the Lyapunov function. The control function and the control domain are designed in terms of the Lie derivatives of the Lyapunov function, and enjoy sparsity properties in the sense that the control support is small. Finally, we show that our result applies to a large class of kinetic equations modelling multi-agent dynamics

Comparison between three glass fiber post cementation techniques

The aim of this experimental study was to compare the traditional cement systems with those of the latest generation, to assess if indeed these could represent of viable substitutes in the cementation of indirect restorations, and in the specific case of endodontic posts

Identification of muscle innervation zones using linear electrode arrays: a fundamental step to measure fibers conduction velocity

Fiber conduction velocity (CV) is a parameter correlated to the physiological membrane properties of the skeletal muscle fibers. Changes in muscle fiber CV are correlated to the gradation of force and fatigue, and can be measured by means of surface electromyography EMG (sEMG). sEMG measurement of CV during muscle contractions requires the correct identification of the skeletal muscle innervation zone (IZ). In superficial muscles, IZ location can be detected using linear electrode arrays and visually identified as the point of inversion of the detected motor unit action potential (MUAP) propagation. In the present work, we present a method for the effective and fast detection of the IZ location, through the following procedures: (1) identification of the target superficial muscle considering the muscle fiber architecture; (2) electrode array selection based on interelectrode distance and number of electrodes; (3) subject training to perform submaximal isometric contractions of the target muscle/s; (4) electrode array positioning along the muscle surface to investigate the IZ position during the contractions by visual identification of MUAP patterns

Hyperthermia Enhances CD95-Ligand Gene Expression in T Lymphocytes

AbstractHyperthermia represents an interesting therapeutic strategy for the treatment of tumors. Moreover, it is able to regulate several aspects of the immune response. Fas (APO-1/CD95) and its ligand (FasL) are cell surface proteins whose interaction activates apoptosis of Fas-expressing targets. In T cells, the Fas-Fas-L system regulates activation-induced cell death, is implicated in diseases in which lymphocyte homeostasis is compromised, and plays an important role during cytotoxic and regulatory actions mediated by these cells. In this study we describe the effect of hyperthermia on activation of the fas-L gene in T lymphocytes. We show that hyperthermic treatment enhances Fas-L-mediated cytotoxicity, fas-L mRNA expression, and fas-L promoter activity in activated T cell lines. Our data indicate that hyperthermia enhances the transcriptional activity of AP-1 and NF-κB in activated T cells, and this correlates with an increased expression/nuclear translocation of these transcription factors. Moreover, we found that heat shock factor-1 is a transactivator of fas-L promoter in activated T cells, and the overexpression of a dominant negative form of heat shock factor-1 may attenuate the effect of hyperthermia on fas-L promoter activity. Furthermore, overexpression of dominant negative mutants of protein kinase Cε (PKCε) and PKCθ partially inhibited the promoter activation and, more importantly, could significantly reduce the enhancement mediated by hyperthermia, indicating that modulation of PKC activity may play an important role in this regulation. These results add novel information on the immunomodulatory action of heat, in particular in the context of its possible use as an adjuvant therapeutic strategy to consider for the treatment of cancer

Relationship between Isometric Muscle Force and Fractal Dimension of Surface Electromyogram

The relationship between fractal dimension of the surface electromyogram (sEMG) and the intensity of muscle contraction is still controversial in simulated and experimental conditions. To support the use of fractal analysis to investigate myoelectric fatigue, it is crucial to establish the interdependence between fractal dimension and muscle contraction intensity. We analyzed the behavior of fractal dimension, conduction velocity, mean frequency, and average rectified value in twenty-eight volunteers at nine levels of isometric force. sEMG was obtained using bidimensional arrays in the biceps brachii muscle. The values of fractal dimension and mean frequency increased with force unless a plateau was reached at 30% maximal voluntary contraction. Overall, our findings suggest that, above a certain level of force, the use of fractal dimension to evaluate the myoelectric manifestations of fatigue may be considered, regardless of muscle contraction intensity