12,856 research outputs found
Coy v. Iowa: Reconciling a Defendant\u27s Right to Confrontation with a Child-Witness\u27 Interest in Avoiding Undue Psychological Trauma
Symmetry groupoids and patterns of synchrony in coupled cell networks
A coupled cell system is a network of dynamical systems, or “cells,” coupled together. Such systems
can be represented schematically by a directed graph whose nodes correspond to cells and whose
edges represent couplings. A symmetry of a coupled cell system is a permutation of the cells that
preserves all internal dynamics and all couplings. Symmetry can lead to patterns of synchronized
cells, rotating waves, multirhythms, and synchronized chaos. We ask whether symmetry is the only
mechanism that can create such states in a coupled cell system and show that it is not.
The key idea is to replace the symmetry group by the symmetry groupoid, which encodes information
about the input sets of cells. (The input set of a cell consists of that cell and all cells
connected to that cell.) The admissible vector fields for a given graph—the dynamical systems with
the corresponding internal dynamics and couplings—are precisely those that are equivariant under
the symmetry groupoid. A pattern of synchrony is “robust” if it arises for all admissible vector
fields. The first main result shows that robust patterns of synchrony (invariance of “polydiagonal”
subspaces under all admissible vector fields) are equivalent to the combinatorial condition that an
equivalence relation on cells is “balanced.” The second main result shows that admissible vector
fields restricted to polydiagonal subspaces are themselves admissible vector fields for a new coupled
cell network, the “quotient network.” The existence of quotient networks has surprising implications
for synchronous dynamics in coupled cell systems
Determination of antimicrobial susceptibilities on infected urines without isolation
A method is described for the quick determination of the susceptibilities of various unidentified bacteria contained in an aqueous physiological fluid sample, particularly urine, to one or more antibiotics. A bacterial adenosine triphosphate (ATP) assay is carried out after the elimination of non-bacterial ATP to determine whether an infection exists. If an infection does exist, a portion of the sample is further processed, including subjecting parts of the portion to one or more antibiotics. Growth of the bacteria in the parts are determined, again by an ATP assay, to determine whether the unidentified bacteria in the sample are susceptible to the antibiotic or antibiotics under test
Some Air Oxidation Products of DI-2-Ethylhexyl Sebacate
Author Institution: Department of Chemistry, The Ohio State University, Columbus 1
Excitation Thresholds for Nonlinear Localized Modes on Lattices
Breathers are spatially localized and time periodic solutions of extended
Hamiltonian dynamical systems. In this paper we study excitation thresholds for
(nonlinearly dynamically stable) ground state breather or standing wave
solutions for networks of coupled nonlinear oscillators and wave equations of
nonlinear Schr\"odinger (NLS) type. Excitation thresholds are rigorously
characterized by variational methods. The excitation threshold is related to
the optimal (best) constant in a class of discr ete interpolation inequalities
related to the Hamiltonian energy. We establish a precise connection among ,
the dimensionality of the lattice, , the degree of the nonlinearity
and the existence of an excitation threshold for discrete nonlinear
Schr\"odinger systems (DNLS).
We prove that if , then ground state standing waves exist if
and only if the total power is larger than some strictly positive threshold,
. This proves a conjecture of Flach, Kaldko& MacKay in
the context of DNLS. We also discuss upper and lower bounds for excitation
thresholds for ground states of coupled systems of NLS equations, which arise
in the modeling of pulse propagation in coupled arrays of optical fibers.Comment: To appear in Nonlinearit
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