910 research outputs found
Linear Complexity Lossy Compressor for Binary Redundant Memoryless Sources
A lossy compression algorithm for binary redundant memoryless sources is
presented. The proposed scheme is based on sparse graph codes. By introducing a
nonlinear function, redundant memoryless sequences can be compressed. We
propose a linear complexity compressor based on the extended belief
propagation, into which an inertia term is heuristically introduced, and show
that it has near-optimal performance for moderate block lengths.Comment: 4 pages, 1 figur
The Cavity Approach to Parallel Dynamics of Ising Spins on a Graph
We use the cavity method to study parallel dynamics of disordered Ising
models on a graph. In particular, we derive a set of recursive equations in
single site probabilities of paths propagating along the edges of the graph.
These equations are analogous to the cavity equations for equilibrium models
and are exact on a tree. On graphs with exclusively directed edges we find an
exact expression for the stationary distribution of the spins. We present the
phase diagrams for an Ising model on an asymmetric Bethe lattice and for a
neural network with Hebbian interactions on an asymmetric scale-free graph. For
graphs with a nonzero fraction of symmetric edges the equations can be solved
for a finite number of time steps. Theoretical predictions are confirmed by
simulation results. Using a heuristic method, the cavity equations are extended
to a set of equations that determine the marginals of the stationary
distribution of Ising models on graphs with a nonzero fraction of symmetric
edges. The results of this method are discussed and compared with simulations
A Mathematical Study of the One-Dimensional Keller and Rubinov Model for Liesegang Bands
Our purpose is to start understanding from a mathematical viewpoint experiments in which regularized structures with spatially distinct bands or rings of precipitated material are exhibited, with clearly visible scaling properties. Such patterns are known as Liesegang bands or rings. In this paper, we study a one-dimensional version of the Keller and Rubinow model and present conditions ensuring the existence of Liesegang bands
Synapse efficiency diverges due to synaptic pruning following over-growth
In the development of the brain, it is known that synapses are pruned
following over-growth. This pruning following over-growth seems to be a
universal phenomenon that occurs in almost all areas -- visual cortex, motor
area, association area, and so on. It has been shown numerically that the
synapse efficiency is increased by systematic deletion. We discuss the synapse
efficiency to evaluate the effect of pruning following over-growth, and
analytically show that the synapse efficiency diverges as O(log c) at the limit
where connecting rate c is extremely small. Under a fixed synapse number
criterion, the optimal connecting rate, which maximize memory performance,
exists.Comment: 15 pages, 16 figure
Self-Propelled Aero-GaN Based Liquid Marbles Exhibiting Pulsed Rotation on the Water Surface
We report on self-propelled rotating liquid marbles fabricated using droplets of alcoholic solution encapsulated in hollow microtetrapods of GaN with hydrophilic free ends of their arms and hydrophobic lateral walls. Apart from stationary rotation, elongated-spheroid-like liquid marbles were found, for the first time, to exhibit pulsed rotation on water surfaces characterized by a threshold speed of rotation, which increased with the weight of the liquid marble while the frequency of pulses proved to decrease. To throw light upon the unusual behavior of the developed self-propelled liquid marbles, we propose a model which takes into account skimming of the liquid marbles over the water surface similar to that inherent to flying water lily beetle and the so-called helicopter effect, causing a liquid marble to rise above the level of the water surface when rotating
Spatio-selection in Expanding Bacterial Colonies
Segregation of populations is a key question in evolution theory. One
important aspect is the relation between spatial organization and the
population's composition. Here we study a specific example -- sectors in
expanding bacterial colonies. Such sectors are spatially segregated
sub-populations of mutants. The sectors can be seen both in disk-shaped
colonies and in branching colonies. We study the sectors using two models we
have used in the past to study bacterial colonies -- a continuous
reaction-diffusion model with non-linear diffusion and a discrete
``Communicating Walkers'' model. We find that in expanding colonies, and
especially in branching colonies, segregation processes are more likely than in
a spatially static population. One such process is the establishment of stable
sub- population having neutral mutation. Another example is the maintenance of
wild-type population along side with sub-population of advantageous mutants.
Understanding such processes in bacterial colonies is an important subject by
itself, as well as a model system for similar processes in other spreading
populations
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