4,913 research outputs found
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
and in the nuclear medium
Recent studies of the 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 in this case, although the coupling
of the to the and makes this picture
only approximate. The decay channel of the
is forbidden in free space for the nominal mass of the , but
the coupling of the to components in the nuclear medium opens new
decay channels of the in the nucleus and produces a much larger
width. Together with medium modifications of the and
decay channels, the final width of the at nuclear matter
density is more than five times bigger than the free one. We perform the
calculations by dressing simultaneously the and the
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 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
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