Contraction analysis of switched Filippov systems via regularization

We study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems, we derive sufficient conditions for convergence of any two trajectories of the Filippov system between each other within some region of interest. We then apply these conditions to the study of different classes of Filippov systems including piecewise smooth (PWS) systems, piecewise affine (PWA) systems and relay feedback systems. We show that contrary to previous approaches, our conditions allow the system to be studied in metrics other than the Euclidean norm. The theoretical results are illustrated by numerical simulations on a set of representative examples that confirm their effectiveness and ease of application.Comment: Preprint submitted to Automatic

Testicular endocrine activity is upregulated by D-Aspartic acid in the green frog Rana esculenta

This study investigated the involvement of D-aspartic acid (D-Asp) in testicular steroidogenesis of the green frog Rana esculenta and its effect on stimulation of thumb pad morphology and glandular activity, a typical testosterone-dependent secondary sexual characteristic in this amphibian species. In the testis, D-Asp concentrations vary significantly during the reproductive cycle: they are low in pre- and post-reproductive periods, but reach peak levels in the reproductive period (140-236 nmol/g wet tissue). Moreover, the concentrations of D-Asp in the testis through the sexual cycle positively match the testosterone levels in the gonad and the plasma. The racemase activity evaluated during the cycle expresses its peak when D-Asp and testosterone levels are highest, that is, during the reproductive period, confirming the synthesis of D-Asp from L-Asp by an aspartate racemase. Short-term in vivo experiments consisting of a single injection of D-Asp (2.0 micro mol/g body weight) demonstrated that this amino acid accumulates significantly in the testis, and after 3 h its uptake is coupled with a testosterone increase in both testis and plasma. Moreover, within 18 h of amino acid administration, the D-Asp concentration in the testis decreased along with the testosterone titer to prestimulation levels. Other amino acids (L-Asp, D-Glu and L-Glu) used instead of D-Asp were ineffective, confirming that the significant increase in testicular testosterone was a specific feature of this amino acid. In long-term experiments, D-Asp had been administered chronically to frogs caught during the three phases of the reproductive cycle, inducing testosterone increase and 17beta-estradiol decrease in the gonad during the pre- and post-reproductive period, and vice versa during the reproductive period

A variation of Broyden Class methods using Householder adaptive transforms

In this work we introduce and study novel Quasi Newton minimization methods based on a Hessian approximation Broyden Class-\textit{type} updating scheme, where a suitable matrix $\tilde{B}_k$ is updated instead of the current Hessian approximation $B_k$. We identify conditions which imply the convergence of the algorithm and, if exact line search is chosen, its quadratic termination. By a remarkable connection between the projection operation and Krylov spaces, such conditions can be ensured using low complexity matrices $\tilde{B}_k$ obtained projecting $B_k$ onto algebras of matrices diagonalized by products of two or three Householder matrices adaptively chosen step by step. Extended experimental tests show that the introduction of the adaptive criterion, which theoretically guarantees the convergence, considerably improves the robustness of the minimization schemes when compared with a non-adaptive choice; moreover, they show that the proposed methods could be particularly suitable to solve large scale problems where $L$-$BFGS$ performs poorly

Matrix algebras in quasi-newtonian algorithms for optimal learning in multi-layer perceptrons

In this work the authors implement in a Multi-Layer Perceptron (MLP) environment a new class of quasi-newtonian (QN) methods. The algorithms proposed in the present paper use in the iterative scheme of a generalized BFGS-method a family of matrix algebras, recently introduced for displacement decompositions and for optimal preconditioning. This novel approach allows to construct methods having an O(n log_2 n) complexity. Numerical experiences compared with the performances of the best QN-algorithms known in the literature confirm the effectiveness of these new optimization techniques

Low complexity secant quasi-Newton minimization algorithms for nonconvex functions

In this work some interesting relations between results on basic optimization and algorithms for nonconvex functions (such as BFGS and secant methods) are pointed out. In particular, some innovative tools for improving our recent secant BFGS-type and LQN algorithms are described in detail

On the best least squares fit to a matrix and its applications

The best least squares fit L_A to a matrix A in a space L can be useful to improve the rate of convergence of the conjugate gradient method in solving systems Ax=b as well as to define low complexity quasi-Newton algorithms in unconstrained minimization. This is shown in the present paper with new important applications and ideas. Moreover, some theoretical results on the representation and on the computation of L_A are investigated

Adaptive matrix algebras in unconstrained minimization

In this paper we study adaptive L(k)QNmethods, involving special matrix algebras of low complexity, to solve general (non-structured) unconstrained minimization problems. These methods, which generalize the classical BFGS method, are based on an iterative formula which exploits, at each step, an ad hocchosen matrix algebra L(k). A global convergence result is obtained under suitable assumptions on f

Nonclassical Light in Interferometric Measurements

It is shown that the even and odd coherent light and other nonclassical states of light like superposition of coherent states with different phases may replace the squeezed light in interferometric gravitational wave detector to increase its sensitivity. (Contribution to the Second Workshop on Harmonic Oscillator, Cocoyoc, Mexico, March 1994)Comment: 8 pages,LATEX,preprint of Naples University, INFN-NA-IV-94/30,DSF-T-94/3

The Use of Methanol-Grown Yeast LI-70 in Feeds for Broilers

Abstract In 60-day feeding trials, broilers were fed commercial diets in which different amounts of methanol-grown yeast LI-70 replaced fish and soybean meal. In the first trial, all-mash diets containing up to 15% yeast produced growth rates and efficiencies of feed conversion almost equal to those of the soybean meal control and slightly below those of the fish meal control. In the second trial, pelleted diets containing up to 25% yeast were used. For yeast levels up to 15%, growth rates were faster than for the soybean meal control and slightly slower than for the fish meal control. Diets with more than 15% yeast lacked selenium. Diets containing 25% yeast as the sole source of protein but supplemented with .3 ppm selenium produced growth rates and efficiencies of feed conversion equal to those of the controls

Exon 3 of the NUMB Gene Emerged in the Chordate Lineage Coopting the NUMB Protein to the Regulation of MDM2

MDM2 regulates a variety of cellular processes through its dual protein:protein interaction and ubiquitin ligase activities. One major function of MDM2 is to bind and ubiquitinate P53, thereby regulating its proteasomal degradation. This function is in turn controlled by the cell fate determinant NUMB, which binds to and inhibits MDM2 via a short stretch of 11 amino acids, contained in its phosphotyrosine-binding (PTB) domain, encoded by exon 3 of the NUMB gene. The NUMB-MDM2-P53 circuitry is relevant to the specification of the stem cell fate and its subversion has been shown to be causal in breast cancer leading to the emergence of cancer stem cells. While extensive work on the evolutionary aspects of the MDM2/P53 circuitry has provided hints as to how these two proteins have evolved together to maintain conserved and linked functions, little is known about the evolution of the NUMB gene and, in particular, how it developed the ability to regulate MDM2 function. Here, we show that NUMB is a metazoan gene, which acquired exon 3 in the common ancestor of the Chordate lineage, first being present in the Cephalochordate and Tunicate subphyla, but absent in invertebrates. We provide experimental evidence showing that since its emergence, exon 3 conferred to the PTB domain of NUMB the ability to bind and to regulate MDM2 functions