105,283 research outputs found
Noise-Induced Spatial Pattern Formation in Stochastic Reaction-Diffusion Systems
This paper is concerned with stochastic reaction-diffusion kinetics governed
by the reaction-diffusion master equation. Specifically, the primary goal of
this paper is to provide a mechanistic basis of Turing pattern formation that
is induced by intrinsic noise. To this end, we first derive an approximate
reaction-diffusion system by using linear noise approximation. We show that the
approximated system has a certain structure that is associated with a coupled
dynamic multi-agent system. This observation then helps us derive an efficient
computation tool to examine the spatial power spectrum of the intrinsic noise.
We numerically demonstrate that the result is quite effective to analyze
noise-induced Turing pattern. Finally, we illustrate the theoretical mechanism
behind the noise-induced pattern formation with a H2 norm interpretation of the
multi-agent system
Formal Modeling of Connectionism using Concurrency Theory, an Approach Based on Automata and Model Checking
This paper illustrates a framework for applying formal methods techniques, which are symbolic in nature, to specifying and verifying neural networks, which are sub-symbolic in nature. The paper describes a communicating automata [Bowman & Gomez, 2006] model of neural networks. We also implement the model using timed automata [Alur & Dill, 1994] and then undertake a verification of these models using the model checker Uppaal [Pettersson, 2000] in order to evaluate the performance of learning algorithms. This paper also presents discussion of a number of broad issues concerning cognitive neuroscience and the debate as to whether symbolic processing or connectionism is a suitable representation of cognitive systems. Additionally, the issue of integrating symbolic techniques, such as formal methods, with complex neural networks is discussed. We then argue that symbolic verifications may give theoretically well-founded ways to evaluate and justify neural learning systems in the field of both theoretical research and real world applications
PIN generation using EEG : a stability study
In a previous study, it has been shown that brain activity, i.e.
electroencephalogram (EEG) signals, can be used to generate personal
identification number (PIN). The method was based on brainâcomputer
interface (BCI) technology using a P300-based BCI approach and showed that
a single-channel EEG was sufficient to generate PIN without any error for
three subjects. The advantage of this method is obviously its better fraud
resistance compared to conventional methods of PIN generation such as
entering the numbers using a keypad. Here, we investigate the stability of these
EEG signals when used with a neural network classifier, i.e. to investigate the
changes in the performance of the method over time. Our results, based on
recording conducted over a period of three months, indicate that a single
channel is no longer sufficient and a multiple electrode configuration is
necessary to maintain acceptable performances. Alternatively, a recording
session to retrain the neural network classifier can be conducted on shorter
intervals, though practically this might not be viable
Guaranteed Control of Sampled Switched Systems using Semi-Lagrangian Schemes and One-Sided Lipschitz Constants
In this paper, we propose a new method for ensuring formally that a
controlled trajectory stay inside a given safety set S for a given duration T.
Using a finite gridding X of S, we first synthesize, for a subset of initial
nodes x of X , an admissible control for which the Euler-based approximate
trajectories lie in S at t [0,T]. We then give sufficient conditions
which ensure that the exact trajectories, under the same control, also lie in S
for t [0,T], when starting at initial points 'close' to nodes x. The
statement of such conditions relies on results giving estimates of the
deviation of Euler-based approximate trajectories, using one-sided Lipschitz
constants. We illustrate the interest of the method on several examples,
including a stochastic one
Age structure landscapes emerge from the equilibrium between aging and rejuvenation in bacterial populations.
The physiological asymmetry between daughters of a mother bacterium is produced by the inheritance of either old poles, carrying non-genetic damage, or newly synthesized poles. However, as bacteria display long-term growth stability leading to physiological immortality, there is controversy on whether asymmetry corresponds to aging. Here we show that deterministic age structure landscapes emerge from physiologically immortal bacterial lineages. Through single-cell microscopy and microfluidic techniques, we demonstrate that aging and rejuvenating bacterial lineages reach two distinct states of growth equilibria. These equilibria display stabilizing properties, which we quantified according to the compensatory trajectories of continuous lineages throughout generations. Finally, we show that the physiological asymmetry between aging and rejuvenating lineages produces complex age structure landscapes, resulting in a deterministic phenotypic heterogeneity that is neither an artifact of starvation nor a product of extrinsic damage. These findings indicate that physiological immortality and cellular aging can both be manifested in single celled organisms
Sparse sum-of-squares (SOS) optimization: A bridge between DSOS/SDSOS and SOS optimization for sparse polynomials
Optimization over non-negative polynomials is fundamental for nonlinear
systems analysis and control. We investigate the relation between three
tractable relaxations for optimizing over sparse non-negative polynomials:
sparse sum-of-squares (SSOS) optimization, diagonally dominant sum-of-squares
(DSOS) optimization, and scaled diagonally dominant sum-of-squares (SDSOS)
optimization. We prove that the set of SSOS polynomials, an inner approximation
of the cone of SOS polynomials, strictly contains the spaces of sparse
DSOS/SDSOS polynomials. When applicable, therefore, SSOS optimization is less
conservative than its DSOS/SDSOS counterparts. Numerical results for
large-scale sparse polynomial optimization problems demonstrate this fact, and
also that SSOS optimization can be faster than DSOS/SDSOS methods despite
requiring the solution of semidefinite programs instead of less expensive
linear/second-order cone programs.Comment: 9 pages, 3 figure
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