28,711 research outputs found
An intrinsic homotopy for intersecting algebraic varieties
Recently we developed a diagonal homotopy method to compute a numerical
representation of all positive dimensional components in the intersection of
two irreducible algebraic sets. In this paper, we rewrite this diagonal
homotopy in intrinsic coordinates, which reduces the number of variables,
typically in half. This has the potential to save a significant amount of
computation, especially in the iterative solving portion of the homotopy path
tracker. There numerical experiments all show a speedup of about a factor two
Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities
We study the formation of long-lived states near avoided resonance crossings
in open systems. For three different optical microcavities (rectangle, ellipse,
and semi-stadium) we provide numerical evidence that these states are localized
along periodic rays, resembling scarred states in closed systems. Our results
shed light on the morphology of long-lived states in open mesoscopic systems.Comment: 4 pages, 5 figures (in reduced quality), to appear in Phys. Rev. Let
A Dissociation of Attention and Awareness in Phase-sensitive but Not Phase-insensitive Visual Channels
The elements most vivid in our conscious awareness are the ones to which we direct our attention. Scientific study confirms the impression of a close bond between selective attention and visual awareness, yet the nature of this association remains elusive. Using visual afterimages as an index, we investigate neural processing of stimuli as they enter awareness and as they become the object of attention. We find evidence of response enhancement accompanying both attention and awareness, both in the phase-sensitive neural channels characteristic of early processing stages and in the phase-insensitive channels typical of higher cortical areas. The effects of attention and awareness on phase-insensitive responses are positively correlated, but in the same experiments, we observe no correlation between the effects on phase-sensitive responses. This indicates independent signatures of attention and awareness in early visual areas yet a convergence of their effects at more advanced processing stages
Is intra-abdominal hypertension a missing factor that drives multiple organ dysfunction syndrome?
In a recent issue of Critical Care, Cheng and colleagues conducted a rabbit model study that demonstrated that intra-abdominal hypertension (IAH) may damage both gut anatomy and function. With only 6 hours of IAH at 25 mmHg, these authors observed an 80% reduction in mucosal blood flow, an exponential increase in mucosal permeability, and erosion and necrosis of the jejunal villi. Such dramatic findings should remind all caring for the critically ill that IAH may severely damage the normal gut barrier functions and thus may be reasonably expected to facilitate bacterial and mediator translocation. The potential contribution of IAH as a confounding factor in the efficacy of selective decontamination of the digestive tract should be considered
Systems level circuit model of C. elegans undulatory locomotion: mathematical modeling and molecular genetics
To establish the relationship between locomotory behavior and dynamics of
neural circuits in the nematode C. elegans we combined molecular and
theoretical approaches. In particular, we quantitatively analyzed the motion of
C. elegans with defective synaptic GABA and acetylcholine transmission,
defective muscle calcium signaling, and defective muscles and cuticle
structures, and compared the data with our systems level circuit model. The
major experimental findings are: (i) anterior-to-posterior gradients of body
bending flex for almost all strains both for forward and backward motion, and
for neuronal mutants, also analogous weak gradients of undulatory frequency,
(ii) existence of some form of neuromuscular (stretch receptor) feedback, (iii)
invariance of neuromuscular wavelength, (iv) biphasic dependence of frequency
on synaptic signaling, and (v) decrease of frequency with increase of the
muscle time constant. Based on (i) we hypothesize that the Central Pattern
Generator (CPG) is located in the head both for forward and backward motion.
Points (i) and (ii) are the starting assumptions for our theoretical model,
whose dynamical patterns are qualitatively insensitive to the details of the
CPG design if stretch receptor feedback is sufficiently strong and slow. The
model reveals that stretch receptor coupling in the body wall is critical for
generation of the neuromuscular wave. Our model agrees with our behavioral
data(iii), (iv), and (v), and with other pertinent published data, e.g., that
frequency is an increasing function of muscle gap-junction coupling.Comment: Neural control of C. elegans motion with genetic perturbation
Spatial properties of entangled photon pairs generated in nonlinear layered structures
A spatial quantum model of spontaneous parametric down-conversion in
nonlinear layered structures is developed expanding the interacting vectorial
fields into monochromatic plane waves. A two-photon spectral amplitude
depending on the signal- and idler-field frequencies and propagation directions
is used to derive transverse profiles of the emitted fields as well as their
spatial correlations. Intensity spatial profiles and their spatial correlations
are mainly determined by the positions of transmission peaks formed in these
structures with photonic bands. A method for geometry optimization of the
structures with respect to efficiency of the nonlinear process is suggested.
Several structures composed of GaN/AlN layers are analyzed as typical examples.
They allow the generation of photon pairs correlated in several emission
directions. Photon-pair generation rates increasing better than the second
power of the number of layers can be reached. Also structures efficiently
generated photon pairs showing anti-bunching and anti-coalescence can be
obtained. Three reasons for splitting the correlated area in photonic-band-gap
structures are revealed: zig-zag movement of photons inside the structure,
spatial symmetry and polarization-dependent properties. Also spectral splitting
can be observed in these structures.Comment: 13 pages, 17 figure
Impact of nuclear vibrations on van der Waals and Casimir interactions at zero and finite temperature
Van der Waals (vdW) and Casimir interactions depend crucially on material
properties and geometry, especially at molecular scales, and temperature can
produce noticeable relative shifts in interaction characteristics. Despite
this, common treatments of these interactions ignore electromagnetic
retardation, atomism, or contributions of collective mechanical vibrations
(phonons) to the infrared response, which can interplay with temperature in
nontrivial ways. We present a theoretical framework for computing
electromagnetic interactions among molecular structures, accounting for their
geometry, electronic delocalization, short-range interatomic correlations,
dissipation, and phonons at atomic scales, along with long-range
electromagnetic interactions among themselves or in the vicinity of continuous
macroscopic bodies. We find that in carbon allotropes, particularly fullerenes,
carbyne wires, and graphene sheets, phonons can couple strongly with long-range
electromagnetic fields, especially at mesoscopic scales (nanometers), to create
delocalized phonon polaritons that significantly modify the infrared molecular
response. These polaritons especially depend on the molecular dimensionality
and dissipation, and in turn affect the vdW interaction free energies of these
bodies above a macroscopic gold surface, producing nonmonotonic power laws and
nontrivial temperature variations at nanometer separations that are within the
reach of current Casimir force experiments.Comment: 11 pages, 4 figures (3 single-column, 1 double-column), 2 appendice
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