5,312 research outputs found
Bifurcation of hyperbolic planforms
Motivated by a model for the perception of textures by the visual cortex in
primates, we analyse the bifurcation of periodic patterns for nonlinear
equations describing the state of a system defined on the space of structure
tensors, when these equations are further invariant with respect to the
isometries of this space. We show that the problem reduces to a bifurcation
problem in the hyperbolic plane D (Poincar\'e disc). We make use of the concept
of periodic lattice in D to further reduce the problem to one on a compact
Riemann surface D/T, where T is a cocompact, torsion-free Fuchsian group. The
knowledge of the symmetry group of this surface allows to carry out the
machinery of equivariant bifurcation theory. Solutions which generically
bifurcate are called "H-planforms", by analogy with the "planforms" introduced
for pattern formation in Euclidean space. This concept is applied to the case
of an octagonal periodic pattern, where we are able to classify all possible
H-planforms satisfying the hypotheses of the Equivariant Branching Lemma. These
patterns are however not straightforward to compute, even numerically, and in
the last section we describe a method for computation illustrated with a
selection of images of octagonal H-planforms.Comment: 26 pages, 11 figure
Reversibility in Massive Concurrent Systems
Reversing a (forward) computation history means undoing the history. In
concurrent systems, undoing the history is not performed in a deterministic way
but in a causally consistent fashion, where states that are reached during a
backward computation are states that could have been reached during the
computation history by just performing independent actions in a different
order.Comment: Presented at MeCBIC 201
New Coordinates for de Sitter Space and de Sitter Radiation
We introduce a simple coordinate system covering half of de Sitter space. The
new coordinates have several attractive properties: the time direction is a
Killing vector, the metric is smooth at the horizon, and constant-time slices
are just flat Euclidean space. We demonstrate the usefulness of the coordinates
by calculating the rate at which particles tunnel across the horizon. When
self-gravitation is taken into account, the resulting tunneling rate is only
approximately thermal. The effective temperature decreases through the emission
of radiation.Comment: LaTeX, 10 pages; v2. references added; v3. minor sign errors fixed,
reference added, journal versio
A Multi-Scale Network Model of Brightness Perception
A neural network model of brightness perception is developed to account for a wide variety of difficult data, including the classical phenomenon of Mach bands and nonlinear contrast effects associated with sinusoidal luminance waves. The model builds upon previous work by Grossberg and colleagues on filling-in models that predict brightness perception through the interaction of boundary and feature signals. Model equations are presented and computer simulations illustrate the model's potential.Air Force Office of Scientific Research (F49620-92-J-0334); Northeast Consortium for Engineering Education (NCEE-A303-21-93); Office of Naval Research (N00014-91-J-4100); German BMFT grant (413-5839-01 IN 101 C/1); CNPq and NUTES/UFRJ, Brazi
Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving
We derive efficient algorithms for coarse approximation of algebraic
hypersurfaces, useful for estimating the distance between an input polynomial
zero set and a given query point. Our methods work best on sparse polynomials
of high degree (in any number of variables) but are nevertheless completely
general. The underlying ideas, which we take the time to describe in an
elementary way, come from tropical geometry. We thus reduce a hard algebraic
problem to high-precision linear optimization, proving new upper and lower
complexity estimates along the way.Comment: 15 pages, 9 figures. Submitted to a conference proceeding
Detecting and Estimating Signals over Noisy and Unreliable Synapses: Information-Theoretic Analysis
The temporal precision with which neurons respond to synaptic inputs has a direct bearing on the nature of the neural code. A characterization of the neuronal noise sources associated with different sub-cellular components (synapse, dendrite, soma, axon, and so on) is needed to understand the relationship between noise and information transfer. Here we study the effect of the unreliable, probabilistic nature of synaptic transmission on information transfer in the absence of interaction among presynaptic inputs. We derive theoretical lower bounds on the capacity of a simple model of a cortical synapse under two different paradigms. In signal estimation, the signal is assumed to be encoded in the mean firing rate of the presynaptic neuron, and the objective is to estimate the continuous input signal from the postsynaptic voltage. In signal detection, the input is binary, and the presence or absence of a presynaptic action potential is to be detected from the postsynaptic voltage. The efficacy of information transfer in synaptic transmission is characterized by deriving optimal strategies under these two paradigms. On the basis of parameter values derived from neocortex, we find that single cortical synapses cannot transmit information reliably, but redundancy obtained using a small number of multiple synapses leads to a significant improvement in the information capacity of synaptic transmission
Stokesian jellyfish: Viscous locomotion of bilayer vesicles
Motivated by recent advances in vesicle engineering, we consider
theoretically the locomotion of shape-changing bilayer vesicles at low Reynolds
number. By modulating their volume and membrane composition, the vesicles can
be made to change shape quasi-statically in thermal equilibrium. When the
control parameters are tuned appropriately to yield periodic shape changes
which are not time-reversible, the result is a net swimming motion over one
cycle of shape deformation. For two classical vesicle models (spontaneous
curvature and bilayer coupling), we determine numerically the sequence of
vesicle shapes through an enthalpy minimization, as well as the fluid-body
interactions by solving a boundary integral formulation of the Stokes
equations. For both models, net locomotion can be obtained either by
continuously modulating fore-aft asymmetric vesicle shapes, or by crossing a
continuous shape-transition region and alternating between fore-aft asymmetric
and fore-aft symmetric shapes. The obtained hydrodynamic efficiencies are
similar to that of other low Reynolds number biological swimmers, and suggest
that shape-changing vesicles might provide an alternative to flagella-based
synthetic microswimmers
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