A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks

This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. One of the main results determines global asymptotic stability of the network from the diagonal stability of a "dissipativity matrix" which incorporates information about the passivity properties of the subsystems, the interconnection structure of the network, and the signs of the interconnection terms. This stability test encompasses the "secant criterion" for cyclic networks presented in our previous paper, and extends it to a general interconnection structure represented by a graph. A second main result allows one to accommodate state products. This extension makes the new stability criterion applicable to a broader class of models, even in the case of cyclic systems. The new stability test is illustrated on a mitogen activated protein kinase (MAPK) cascade model, and on a branched interconnection structure motivated by metabolic networks. Finally, another result addresses the robustness of stability in the presence of diffusion terms in a compartmental system made out of identical systems.Comment: See http://www.math.rutgers.edu/~sontag/PUBDIR/index.html for related (p)reprint

Λ(1520)\Lambda(1520) and Σ(1385)\Sigma(1385) in the nuclear medium

Recent studies of the $\Lambda(1520)$ resonance within chiral unitary theory with coupled channels find the resonance as a dynamically generated state from the interaction of the decuplet of baryons and the octet of mesons, essentially a quasibound state of $\pi \Sigma^*(1385)$ in this case, although the coupling of the $\Lambda(1520)$ to the $\bar{K}N$ and $\pi \Sigma$ makes this picture only approximate. The $\pi \Sigma^*(1385)$ decay channel of the $\Lambda(1520)$ is forbidden in free space for the nominal mass of the $\Sigma^*(1385)$, but the coupling of the $\pi$ to $ph$ components in the nuclear medium opens new decay channels of the $\Lambda(1520)$ in the nucleus and produces a much larger width. Together with medium modifications of the $\bar{K}N$ and $\pi \Sigma$ decay channels, the final width of the $\Lambda(1520)$ at nuclear matter density is more than five times bigger than the free one. We perform the calculations by dressing simultaneously the $\Lambda(1520)$ and the $\Sigma^*(1385)$ resonances, finding moderate changes in the mass but substantial ones in the width of both resonances.Comment: 20 pages, 6 figures; comparison made to data, new references and new (small) decay channel include

Regional Convergence and The Causal Impact of Migration on Regional Growth Rates

The standard growth theory predicts that allowing for labor mobility across regions would increase the speed of convergence in per capita income levels and that migration has a negative causal impact on regional growth rates. Although the empirical literature has uncovered some evidence for the former implication, the latter has not been verified empirically. This paper provides empirical evidence for the negative causal impact of migration on provincial growth rates in a developing country with a high level of internal migration that is characterized by unskilled labor exiting rural areas for urban centers. We utilize instrumental variables estimation method with an instrument unique to the country examined and also control for provincial fixed effects.Regional convergence; Regional growth; Internal migration; Fixed effects; IV estimation

On the probabilistic min spanning tree Problem

We study a probabilistic optimization model for min spanning tree, where any vertex vi of the input-graph G(V,E) has some presence probability pi in the final instance G′ ⊂ G that will effectively be optimized. Suppose that when this “real” instance G′ becomes known, a spanning tree T, called anticipatory or a priori spanning tree, has already been computed in G and one can run a quick algorithm (quicker than one that recomputes from scratch), called modification strategy, that modifies the anticipatory tree T in order to fit G ′. The goal is to compute an anticipatory spanning tree of G such that, its modification for any G ′ ⊆ G is optimal for G ′. This is what we call probabilistic min spanning tree problem. In this paper we study complexity and approximation of probabilistic min spanning tree in complete graphs under two distinct modification strategies leading to different complexity results for the problem. For the first of the strategies developed, we also study two natural subproblems of probabilistic min spanning tree, namely, the probabilistic metric min spanning tree and the probabilistic min spanning tree 1,2 that deal with metric complete graphs and complete graphs with edge-weights either 1, or 2, respectively

Two-scale convergence for locally-periodic microstructures and homogenization of plywood structures

The introduced notion of locally-periodic two-scale convergence allows to average a wider range of microstructures, compared to the periodic one. The compactness theorem for the locally-periodic two-scale convergence and the characterisation of the limit for a sequence bounded in $H^1(\Omega)$ are proven. The underlying analysis comprises the approximation of functions, which periodicity with respect to the fast variable depends on the slow variable, by locally-periodic functions, periodic in subdomains smaller than the considered domain, but larger than the size of microscopic structures. The developed theory is applied to derive macroscopic equations for a linear elasticity problem defined in domains with plywood structures.Comment: 22 pages, 4 figure

Supertwistors as Quarks of SU(2,2|4)

The GS superstring on AdS_5 x S^5 has a nonlinearly realized, spontaneously broken SU(2,2|4) symmetry. Here we introduce a two-dimensional model in which the unbroken SU(2,2|4) symmetry is linearly realized. The basic variables are supertwistors, which transform in the fundamental representation of this supergroup. The quantization of this supertwistor model leads to the complete oscillator construction of the unitary irreducible representations of the centrally extended SU(2,2|4). They include the states of d=4 SYM theory, massless and KK states of AdS_5 supergravity, and the descendants on AdS_5 of the standard massive string states, which form intermediate and long supermultiplets. We present examples of such multiplets and discuss possible states of solitonic and (p,q) strings.Comment: 12 pages, LaTeX, 1 EPS figur

The Easterbrook Theorem: An Application to Digital Markets

The rise of large firms in the digital economy, including Amazon, Apple, Facebook, and Google, has rekindled the debate about monopolization law. There are proposals to make finding liability easier against alleged digital monopolists by relaxing substantive standards; to flip burdens of proof; and to overturn broad swaths of existing Supreme Court precedent, and even to condemn a law review article. Frank Easterbrook’s seminal 1984 article, The Limits of Antitrust, theorizes that Type I error costs are greater than Type II error costs in the antitrust context, a proposition that has been woven deeply into antitrust law by the Supreme Court. We consider the implications of this assumption on the standard of proof. We find that, taking variants of the Easterbrook assumption as given, the optimal standard of proof is stronger than the preponderance of the evidence standard. Our conclusion is robust to how one specifies the preponderance of the evidence standard and stands in stark contrast to contemporary proposals to reduce or eliminate the burden of proof facing antitrust plaintiffs in digital markets