3,226 research outputs found
Instantaneous noise-based logic
We show two universal, Boolean, deterministic logic schemes based on binary
noise timefunctions that can be realized without time-averaging units. The
first scheme is based on a new bipolar random telegraph wave scheme and the
second one makes use of the recent noise-based logic which is conjectured to be
the brain's method of logic operations [Physics Letters A 373 (2009)
2338-2342]. Error propagation and error removal issues are also addressed.Comment: Accepted for publication in Fluctuation and Noise Letters (December
2010 issue
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Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations
We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated
Suppression of Decoherence and Disentanglement by the Exchange Interaction
Entangled qubit pairs can serve as a quantum memory or as a resource for
quantum communication. The utility of such pairs is measured by how long they
take to disentangle or decohere. To answer the question of whether qubit-qubit
interactions can prolong entanglement, we calculate the dissipative dynamics of
a pair of qubits coupled via the exchange interaction in the presence of random
telegraph noise and noise. We show that for maximally entangled (Bell)
states, the exchange interaction generally suppresses decoherence and
disentanglement. This suppression is more apparent for random telegraph noise
if the noise is non-Markovian, whereas for noise the exchange interaction
should be comparable in magnitude to strongest noise source. The entangled
singlet-triplet superposition state of 2 qubits ( Bell state) can
be protected by the interaction, while for the triplet-triplet state
( Bell state), it is less effective. Thus the former is more
suitable for encoding quantum information
Decision by sampling
We present a theory of decision by sampling (DbS) in which, in contrast with traditional models, there are no underlying psychoeconomic scales. Instead, we assume that an attribute’s subjective value is constructed from a series of binary, ordinal comparisons to a sample of attribute values drawn from memory and is its rank within the sample. We assume that the sample reflects both the immediate distribution of attribute values from the current decision’s context and also the background, real-world distribution of attribute values. DbS accounts for concave utility functions; losses looming larger than gains; hyperbolic temporal discounting; and the overestimation of small probabilities and the underestimation of large probabilities
Sub-Nyquist Sampling: Bridging Theory and Practice
Sampling theory encompasses all aspects related to the conversion of
continuous-time signals to discrete streams of numbers. The famous
Shannon-Nyquist theorem has become a landmark in the development of digital
signal processing. In modern applications, an increasingly number of functions
is being pushed forward to sophisticated software algorithms, leaving only
those delicate finely-tuned tasks for the circuit level.
In this paper, we review sampling strategies which target reduction of the
ADC rate below Nyquist. Our survey covers classic works from the early 50's of
the previous century through recent publications from the past several years.
The prime focus is bridging theory and practice, that is to pinpoint the
potential of sub-Nyquist strategies to emerge from the math to the hardware. In
that spirit, we integrate contemporary theoretical viewpoints, which study
signal modeling in a union of subspaces, together with a taste of practical
aspects, namely how the avant-garde modalities boil down to concrete signal
processing systems. Our hope is that this presentation style will attract the
interest of both researchers and engineers in the hope of promoting the
sub-Nyquist premise into practical applications, and encouraging further
research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin
On the asymmetric telegraph processes
We study the one-dimensional random motionX = X(t), t 0, which takes two different velocities with two different alternating intensities. The closed-form formulae for the density functions of X and for the moments of any order, as well as the distributions of the first passage times, are obtained. The limit behaviour of the moments is analysed under nonstandard Kac's scaling. © Applied Probability Trust 2014
Partial differential equations for self-organization in cellular and developmental biology
Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field
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