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Search Results: 1 - 10 of 200549 matches for " P. Tlusty "
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Remarks on Bootstrap Percolation in Metric Networks
T. Tlusty,J. -P. Eckmann
Physics , 2009, DOI: 10.1088/1751-8113/42/20/205004
Abstract: We examine bootstrap percolation in d-dimensional, directed metric graphs in the context of recent measurements of firing dynamics in 2D neuronal cultures. There are two regimes, depending on the graph size N. Large metric graphs are ignited by the occurrence of critical nuclei, which initially occupy an infinitesimal fraction, f_* -> 0, of the graph and then explode throughout a finite fraction. Smaller metric graphs are effectively random in the sense that their ignition requires the initial ignition of a finite, unlocalized fraction of the graph, f_* >0. The crossover between the two regimes is at a size N_* which scales exponentially with the connectivity range \lambda like_* \sim \exp\lambda^d. The neuronal cultures are finite metric graphs of size N \simeq 10^5-10^6, which, for the parameters of the experiment, is effectively random since N<< N_*. This explains the seeming contradiction in the observed finite f_* in these cultures. Finally, we discuss the dynamics of the firing front.
Screening by symmetry of long-range hydrodynamic interactions of polymers confined in sheets
Tsvi Tlusty
Physics , 2010, DOI: 10.1021/ma060251d
Abstract: Hydrodynamic forces may significantly affect the motion of polymers. In sheet-like cavities, such as the cell's cytoplasm and microfluidic channels, the hydrodynamic forces are long-range. It is therefore expected that that hydrodynamic interactions will dominate the motion of polymers in sheets and will be manifested by Zimm-like scaling. Quite the opposite, we note here that although the hydrodynamic forces are long-range their overall effect on the motion of polymers vanishes due to the symmetry of the two-dimensional flow. As a result, the predicted scaling of experimental observables such as the diffusion coefficient or the rotational diffusion time is Rouse-like, in accord with recent experiments. The effective screening validates the use of the non-interacting blobs picture for polymers confined in a sheet.
A relation between the multiplicity of the second eigenvalue of a graph Laplacian, Courant's nodal line theorem and the substantial dimension of tight polyhedral surfaces
Tsvi Tlusty
Physics , 2010,
Abstract: This note discusses a relation between the multiplicity m of the second eigenvalue {\lambda}2 of a Laplacian on a graph G, tight mappings of G and a discrete analogue of Courant's nodal line theorem. For a certain class of graphs, we show that the m-dimensional eigenspace of {\lambda}2 is tight and thus defines a tight mapping of G into an m-dimensional Euclidean space. The tightness of the mapping is shown to set Colin de Verdi\`ere's upper bound on the maximal {\lambda}2-multiplicity, where chr({\gamma}(G)) is the chromatic number and {\gamma}(G) is the genus of G.
Open charm hadron production via hadronic decays at STAR
David Tlusty
Physics , 2012, DOI: 10.1016/j.nuclphysa.2012.12.098
Abstract: Heavy quarks are a unique probe to study the medium produced in ultra-relativistic heavy ion collisions. The dominant process of charm quark production at RHIC is believed to be initial gluon fusion which can be calculated in the perturbative QCD. The upper limit of FONLL calculation seems to be in good agreement with charm cross section measurements at mid-rapidity in $p+p$ collisions at $\sqrt{s_{NN}}$ = 200 GeV provided by STAR. The same measurement in Au+Au collisions at equal energy reveals the number-of-binary-collisions scaling of charm cross section indicating that charm production is dominated by initial hard scatterings. In this article, we report the measurements of $D^{0}$, $D^{*}$ in $p+p$ at 0.6 GeV/$c < p_T < 6$ GeV/$c$ and $D^0$ in Au+Au collisions at 0.2 GeV/$c < p_T < 5$ GeV/$c$ via hadronic decays $D^{0}\rightarrow K^-\pi^+,\ D^{*+}\rightarrow D^0\pi^+\rightarrow K^-\pi^+\pi^+$ at mid-rapidity $|y|<1$. {abstract}
A rate-distortion scenario for the emergence and evolution of noisy molecular codes
Tsvi Tlusty
Mathematics , 2010, DOI: 10.1103/PhysRevLett.100.048101
Abstract: We discuss, in terms of rate-distortion theory, the fitness of molecular codes as the problem of designing an optimal information channel. The fitness is governed by an interplay between the cost and quality of the channel, which induces smoothness in the code. By incorporating this code fitness into population dynamics models, we suggest that the emergence and evolution of molecular codes may be explained by simple channel design considerations.
The physical language of molecular codes: A rate-distortion approach to the evolution and emergence of biological codes
Tsvi Tlusty
Mathematics , 2010, DOI: 10.1109/CISS.2009.5054834
Abstract: The function of the organism hinges on the performance of its information-processing networks, which convey information via molecular recognition. Many paths within these networks utilize molecular codebooks, such as the genetic code, to translate information written in one class of molecules into another molecular "language" . The present paper examines the emergence and evolution of molecular codes in terms of rate-distortion theory and reviews recent results of this approach. We discuss how the biological problem of maximizing the fitness of an organism by optimizing its molecular coding machinery is equivalent to the communication engineering problem of designing an optimal information channel. The fitness of a molecular code takes into account the interplay between the quality of the channel and the cost of resources which the organism needs to invest in its construction and maintenance. We analyze the dynamics of a population of organisms that compete according to the fitness of their codes. The model suggests a generic mechanism for the emergence of molecular codes as a phase transition in an information channel. This mechanism is put into biological context and demonstrated in a simple example.
A simple model for the evolution of molecular codes driven by the interplay of accuracy, diversity and cost
Tsvi Tlusty
Mathematics , 2010, DOI: 10.1088/1478-3975/5/1/016001
Abstract: Molecular codes translate information written in one type of molecules into another molecular language. We introduce a simple model that treats molecular codes as noisy information channels. An optimal code is a channel that conveys information accurately and efficiently while keeping down the impact of errors. The equipoise of the three conflicting needs, for minimal error-load, minimal cost of resources and maximal diversity of vocabulary, defines the fitness of the code. The model suggests a mechanism for the emergence of a code when evolution varies the parameters that control this equipoise and the mapping between the two molecular languages becomes non-random. This mechanism is demonstrated by a simple toy model that is formally equivalent to a mean-field Ising magnet.
A model for the emergence of the genetic code as a transition in a noisy information channel
Tsvi Tlusty
Mathematics , 2010, DOI: 10.1016/j.jtbi.2007.07.029
Abstract: The genetic code maps the sixty-four nucleotide triplets (codons) to twenty amino-acids. Some argue that the specific form of the code with its twenty amino-acids might be a 'frozen accident' because of the overwhelming effects of any further change. Others see it as a consequence of primordial biochemical pathways and their evolution. Here we examine a scenario in which evolution drives the emergence of a genetic code by selecting for an amino-acid map that minimizes the impact of errors. We treat the stochastic mapping of codons to amino-acids as a noisy information channel with a natural fitness measure. Organisms compete by the fitness of their codes and, as a result, a genetic code emerges at a supercritical transition in the noisy channel, when the mapping of codons to amino-acids becomes nonrandom. At the phase transition, a small expansion is valid and the emergent code is governed by smooth modes of the Laplacian of errors. These modes are in turn governed by the topology of the error-graph, in which codons are connected if they are likely to be confused. This topology sets an upper bound - which is related to the classical map-coloring problem - on the number of possible amino-acids. The suggested scenario is generic and may describe a mechanism for the formation of other error-prone biological codes, such as the recognition of DNA sites by proteins in the transcription regulatory network.
A colorful origin for the genetic code: Information theory, statistical mechanics and the emergence of molecular codes
Tsvi Tlusty
Mathematics , 2010, DOI: 10.1016/j.plrev.2010.06.002
Abstract: The genetic code maps the sixty-four nucleotide triplets (codons) to twenty amino-acids. While the biochemical details of this code were unraveled long ago, its origin is still obscure. We review information-theoretic approaches to the problem of the code's origin and discuss the results of a recent work that treats the code in terms of an evolving, error-prone information channel. Our model - which utilizes the rate-distortion theory of noisy communication channels - suggests that the genetic code originated as a result of the interplay of the three conflicting evolutionary forces: the needs for diverse amino-acids, for error-tolerance and for minimal cost of resources. The description of the code as an information channel allows us to mathematically identify the fitness of the code and locate its emergence at a second-order phase transition when the mapping of codons to amino-acids becomes nonrandom. The noise in the channel brings about an error-graph, in which edges connect codons that are likely to be confused. The emergence of the code is governed by the topology of the error-graph, which determines the lowest modes of the graph-Laplacian and is related to the map coloring problem.
Casting Polymer Nets to Optimize Noisy Molecular Codes
Tsvi Tlusty
Quantitative Biology , 2010, DOI: 10.1073/pnas.0710274105
Abstract: Life relies on the efficient performance of molecular codes, which relate symbols and meanings via error-prone molecular recognition. We describe how optimizing a code to withstand the impact of molecular recognition noise may be approximated by the statistics of a two-dimensional network made of polymers. The noisy code is defined by partitioning the space of symbols into regions according to their meanings. The "polymers" are the boundaries between these regions and their statistics defines the cost and the quality of the noisy code. When the parameters that control the cost-quality balance are varied, the polymer network undergoes a first-order transition, where the number of encoded meanings rises discontinuously. Effects of population dynamics on the evolution of molecular codes are discussed.
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