Perturbation theory and singular perturbations for input-to-state multistable systems on manifolds

We consider the notion of Input-to-State Multistability, which generalizes ISS to nonlinear systems evolving on Riemannian manifolds and possessing a finite number of compact, globally attractive, invariant sets, which in addition satisfy a specific condition of acyclicity. We prove that a parameterized family of dynamical systems whose solutions converge to those of a limiting system inherits such Input-to-State Multistability property from the limiting system in a semi-global practical fashion. A similar result is also established for singular perturbation models whose boundary-layer subsystem is uniformly asymptotically stable and whose reduced subsystem is Input-to-State Multistable. Known results in the theory of perturbations, singular perturbations, averaging, and highly oscillatory control systems, are here generalized to the multistable setting by replacing the classical asymptotic stability requirement of a single invariant set with attractivity and acyclicity of a decomposable invariant one

Input-to-state stability for cascade systems with multiple invariant sets

In a recent paper Angeli and Efimov (2015), the notion of Input-to-State Stability (ISS) has been generalized for systems with decomposable invariant sets and evolving on Riemannian manifolds. In this work, we analyze the cascade interconnection of such ISS systems and we characterize the finest possible decomposition of its invariant set for three different scenarios: 1. the driving system exhibits multistability (convergence to fixed points only); 2. the driving system exhibits multi-almost periodicity (convergence to fixed points as well as periodic and almost-periodic orbits) and the driven system is assumed to be incremental ISS; 3. the driving system exhibits multiperiodicity (convergence to fixed points and periodic orbits) whereas the driven system is ISS in the sense of Angeli and Efimov (2015). Furthermore, we provide marginal results on the backward/forward asymptotic behavior of incremental ISS systems and on the response of a contractive system under asymptotically almost-periodic forcing. Three examples illustrate the potentiality of the proposed framework

Halogen bonding enhances nonlinear optical response in poled supramolecular polymers

We demonstrate that halogen bonding strongly enhances the nonlinear optical response of poled supramolecular polymer systems. We compare three nonlinear optical chromophores with similar electronic structures but different bond-donating units, and show that both the type and the strength of the noncovalent interaction between the chromophores and the polymer matrix play their own distinctive roles in the optical nonlinearity of the systems

On the detectability of non-trivial topologies

We explore the main physical processes which potentially affect the topological signal in the Cosmic Microwave Background (CMB) for a range of toroidal universes. We consider specifically reionisation, the integrated Sachs-Wolfe (ISW) effect, the size of the causal horizon, topological defects and primordial gravitational waves. We use three estimators: the information content, the S/N statistic and the Bayesian evidence. While reionisation has nearly no effect on the estimators, we show that taking into account the ISW strongly decreases our ability to detect the topological signal. We also study the impact of varying the relevant cosmological parameters within the 2 sigma ranges allowed by present data. We find that only Omega_Lambda, which influences both ISW and the size of the causal horizon, significantly alters the detection for all three estimators considered here.Comment: 11 pages, 9 figure

Induction of resistance or enhancement to a transplantable murine plasmacytoma by transfer of non-immune leucocytes.

Newborn mice have a lower spontaneous resistance to the growth of a syngeneic plasmacytoma (MOPC-460) as compared to adult mice. The transfer of different leucocyte populations from non-immunized adult donors to newborn mice influence in a dual way the resistance to MOPC-460 growth, depending on the number of cells transferred. The transfer of a low number of neutrophils, thymus or spleen cells enhances the MOPC-460 takes. Higher numbers of neutrophils, thymus or bone marrow cells induce an effective protenction. By contrast, macrophages over a dose of 1 X 10(4) constantly produce a reduction of tumour growth

Eigenvalue Ratio Estimators for the Number of Dynamic Factors

In this paper we introduce three dynamic eigenvalue ratio estimators for the number of dynamic factors. Two of them, the Dynamic Eigenvalue Ratio (DER) and the Dynamic Growth Ratio (DGR) are dynamic counterparts of the eigenvalue ratio estimators (ER and GR) proposed by Ahn and Horenstein (2013). The third, the Dynamic eigenvalue Difference Ratio (DDR), is a new one but closely related to the test statistic proposed by Onatsky (2009). The advantage of such estimators is that they do not require preliminary determination of discretionary parameters. Finally, a static counterpart of the latter estimator, called eigenvalue Difference Ratio estimator (DR), is also proposed. We prove consistency of such estimators and evaluate their performance under simulation. We conclude that both DDR and DR are valid alternatives to existing criteria. Application to real data gives new insights on the number of factors driving the US economy