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Human embryonic stem cells (ESC) are undifferentiated and are endowed with the capacities of self renewal and pluripotential differentiation. Adult stem cells renew their own tissue, but whether they can trans-differentiate to other tissues is still controversial. To understand the genetic program that underlies the pluripotency of stem cells, we compared the transcription profile of ESC with that of progenitor/stem cells of human hematopoietic and keratinocytic origins, along with their mature cells to be viewed as snapshots along tissue differentiation. ESC gene profile show higher complexity with significantly more highly expressed genes than adult cells. We hypothesize that ESC use a strategy of expressing genes that represent various differentiation pathways and selection of only a few for continuous expression upon differentiation to a particular target. Such a strategy may be necessary for the pluripotency of ESC. The progenitors of either hematopoietic or keratinocytic cells also follow the same design principle. Using advanced clustering, we show that many of the ESC expressed genes are turned off in the progenitors/stem cells followed by a further downregulation in adult tissues. Concomitantly, genes specific to the target tissue are upregulated towards matured cells of skin or blood.
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arxiv:q-bio/0409015
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We describe an new algorithm for visualizing an alignment of biological sequences according to a probabilistic model of evolution. The resulting data array is readily interpreted by the human eye and amenable to digital image techniques. We present examples using mRNA sequences from mouse and rat: three cytochromes, Rattus norvegicus Cyp2a1, Cyp2a2, (Medline: 90212624) and Mus musculus Cyp2a12 (Medline: 93249380); and two zinc finger proteins, Mus musculus zfp111 and zfp235 (Medline: 22683274). The underlying evolutionary model is derived from one proposed by Thorne, Kishino, and Felsenstein and improved by Hein and others. The demonstration implementation aligns two sequences using time and memory quadratic in the mean sequence length. The algorithm is extensible, after Hein, to multiple sequences. We mention a basic method to reduce time and memory demands.
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arxiv:q-bio/0409035
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It is proposed that the co-expression of statistically significant motifs among the sequences of a proteome is a phylogenetic trait. From the co-expression matrix of such motifs in a group of prokaryotic proteomes a suitable definition of a phylogenetic distance is introduced and the corresponding distance matrix between proteomes is constructed. From the distance matrix a phylogenetic tree is inferred, following a standard procedure. It compares well with a reference tree deduced from a distance matrix obtained from the alignment of ribosomal RNA sequences. Our results are consistent with the hypothesis that biological evolution manifests itself with a modulation of basic correlations between shared peptides of short length, present in protein sequences. Moreover, the simple procedure we propose reconfirms that it is possible, sampling entire proteomes, to average the effects of lateral gene transfer and infer reasonable phylogenies.
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arxiv:q-bio/0410011
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Background: Elucidating gene regulatory networks is crucial for understanding normal cell physiology and complex pathologic phenotypes. Existing computational methods for the genome-wide ``reverse engineering'' of such networks have been successful only for lower eukaryotes with simple genomes. Here we present ARACNE, a novel algorithm, using microarray expression profiles, specifically designed to scale up to the complexity of regulatory networks in mammalian cells, yet general enough to address a wider range of network deconvolution problems. This method uses an information theoretic approach to eliminate the majority of indirect interactions inferred by co-expression methods. Results: We prove that ARACNE reconstructs the network exactly (asymptotically) if the effect of loops in the network topology is negligible, and we show that the algorithm works well in practice, even in the presence of numerous loops and complex topologies. We assess ARACNE's ability to reconstruct transcriptional regulatory networks using both a realistic synthetic dataset and a microarray dataset from human B cells. On synthetic datasets ARACNE achieves very low error rates and outperforms established methods, such as Relevance Networks and Bayesian Networks. Application to the deconvolution of genetic networks in human B cells demonstrates ARACNE's ability to infer validated transcriptional targets of the c MYC proto-oncogene. We also study the effects of mis estimation of mutual information on network reconstruction, and show that algorithms based on mutual information ranking are more resilient to estimation errors.
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arxiv:q-bio/0410037
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Recently, several theoretical and experimental studies have been undertaken to probe the effect of stochasticity on gene expression (GE). In experiments, the GE response to an inducing signal in a cell, measured by the amount of mRNAs/proteins synthesized, is found to be either graded or binary. The latter type of response gives rise to a bimodal distribution in protein levels in an ensemble of cells. One possible origin of binary response is cellular bistability achieved through positive feedback or autoregulation. In this paper, we study a simple, stochastic model of GE and show that the origin of binary response lies exclusively in stochasticity. The transitions between the active and inactive states of the gene are random in nature. Graded and binary responses occur in the model depending on the relative stability of the activated and deactivated gene states with respect to that of mRNAs/proteins.The theoretical results on binary response provide a good description of the ``all-or-none'' phenomenon observed in an eukaryotic system.
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arxiv:q-bio/0411012
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An oscillation with a period of around 500 kb in guanine and cytosine content (GC%) is observed in the DNA sequence of human chromosome 21. This oscillation is localized in the rightmost one-eighth region of the chromosome, from 43.5 Mb to 46.5 Mb. Five cycles of oscillation are observed in this region with six GC-rich peaks and five GC-poor valleys. The GC-poor valleys comprise regions with low density of CpG islands and, alternating between the two DNA strands, low gene density regions. Consequently, the long-range oscillation of GC% result in spacing patterns of both CpG island density, and to a lesser extent, gene densities.
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arxiv:q-bio/0411015
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The study of gene regulation and expression is often discussed in quantitative terms. In particular, the expression of genes is regularly characterized with respect to how much, how fast, when and where. Whether discussing the level of gene expression in a bacterium or its precise location within a developing embryo, the natural language for these experiments is that of numbers. Such quantitative data demands quantitative models. We review a class of models ("thermodynamic models") which exploit statistical mechanics to compute the probability that RNA polymerase is at the appropriate promoter. This provides a mathematically precise elaboration of the idea that activators are agents of recruitment which increase the probability that RNA polymerase will be found at the promoter of interest. We discuss a framework which describes the interactions of repressors, activators, helper molecules and RNA polymerase using the concept of effective concentrations, expressed in terms of a function we call the "regulation factor". This analysis culminates in an expression for the probability of RNA polymerase binding at the promoter of interest as a function of the number of regulatory proteins in the cell. In a companion paper [1], these ideas are applied to several case studies which illustrate the use of the general formalism.
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arxiv:q-bio/0412010
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Single molecule FRET (fluorescence resonance energy transfer) is a powerful technique for detecting real-time conformational changes and molecular interactions during biological reactions. In this review, we examine different techniques of extending observation times via immobilization and illustrate how useful biological information can be obtained from single molecule FRET time trajectories with or without absolute distance information.
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arxiv:q-bio/0412013
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We study a master equation system modelling a population dynamics problem in a lattice. The problem is the calculation of the minimum size of a refuge that can protect a population from hostile external conditions, the so called critical patch size problem. We analize both cases in which the particles are considered fermions and bosons and show using exact analitical methods that, while the Fermi-Dirac statistics leads to certain extinction for any refuge size, the Bose-Eistein statistics allows survival even for the minimal refuge.
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arxiv:q-bio/0412049
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By starting from the four DNA bases order in the Boolean lattice, a novel Lie Algebra of the genetic code is proposed. Here, the principal partitions of the genetic code table were obtained as equivalent classes of quotient subspaces of the genetic code vector space over the Galois field of the four DNA bases. The new algebraic structure shows strong connections among algebraic relationships, codon assignment and physicochemical properties of amino acids. Moreover, a distance function defined between codons in the Lie algebra was demonstrated to have a linear behavior respect to physical variables such as the mean of amino acids energy in proteins. It was also noticed that the distance between wild type and mutant codons approach smaller values in mutational variants of four genes, i.e, human phenylalanine hydroxylase, human beta-globin, HIV-1 protease and HIV-1 reverse transcriptase. These results strongly suggest that deterministic rules in genetic code origin must be involved.
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arxiv:q-bio/0501036
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This third part of the lecture series deals with the question: Who will pay for your retirement? For Western Europe the answer may be ``nobody'', but for Algeria the demography looks more promising.
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arxiv:q-bio/0503015
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In biology experiments, oligonucleotide microarrays are contacted with a solution of long nucleic acid (NA) targets. The hybridized probes thus carry long tails. When the surface density of the oligonucleotide probes is high enough, the progress of hybridization leads to the formation of a polyelectrolyte brush due to mutual crowding of the NA tails. The free energy penalty associated with the brush modifies both the hybridization isotherms and the rate equations: the attainable hybridization is lowered significantly as is the hybridization rate. While the equilibrium hybridization fraction, $x_{eq}$, is low, the hybridization follows a Langmuir type isotherm, $x_{eq}/(1-x_{eq}) = c_t K$ where $c_t$ is the target concentration and $K$ is the equilibrium constant smaller than its bulk value by a factor $(n/N)^{2/5}$ due to wall effects where $n$ and $N$ denote the number of bases in the probe and the target. At higher $x_{eq}$, when the brush is formed, the leading correction is $x_{eq}/(1-x_{eq}) = c_t K \exp [ - const' (x_{eq}^{2/3} - x_B^{2/3})]$ where $x_B$ corresponds to the onset of the brush regime. The denaturation rate constant in the two regimes are identical. However, the hybridization rate constant in the brush regime is lower, the leading correction being $\exp [- const' (x^{2/3} - x_B^{2/3})]$.
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arxiv:q-bio/0504002
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We propose to model the dynamics of metabolic networks from a systems biology point of view by four dynamical structure elements: potential function, transverse matrix, degradation matrix, and stochastic force. These four elements are balanced to determine the network dynamics, which gives arise to a special stochastic differential equation supplemented by a relationship between the stochastic force and the degradation matrix. Important network behaviors can be obtained from the potential function without explicitly solving for the time-dependent solution. The existence of such a potential function suggests a global optimization principle, and the existence stochastic force corresponds natural to the hierarchical structure in metabolic networks. We provide theoretical evidences to justify our proposal by discussing its connections to others large-scale biochemical systems approaches, such as the network thermodynamics theory, biochemical systems theory, metabolic control analysis, and flux balance analysis. Experimental data displaying stochasticity are also pointed out.
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arxiv:q-bio/0504003
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Metabolic networks are known to be scale free but the evolutionary origin of this structural property is not clearly understood. One way of studying the dynamical process is to compare the metabolic networks of species that have arisen at different points in evolution and hence are related to each other to varying extents. We have compared the reaction sets of each metabolite across and within 15 groups of species. For a given pair of species and a given metabolite, the number $\Delta k$ of reactions of the metabolite that appear in the metabolic network of only one species and not the other is a measure of the distance between the two networks. While $\Delta k$ is small within groups of related species and large across groups, we find its probability distribution to be $\sim (\Delta k)^{-\gamma'}$ where $\gamma'$ is a universal exponent that is the same within and across groups. This exponent equals, upto statistical uncertainties, the exponent $\gamma$ in the scale free degree distribution $\sim k^{-\gamma}$. We argue that this, as well as our finding that $\Delta k$ is approximately linearly correlated with the degree $k$ of the metabolite, is evidence of a `proportionate change' process in evolution. We also discuss some molecular mechanisms that might be responsible for such an evolutionary process.
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arxiv:q-bio/0504015
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The Fitzhugh-Nagumo equations have been used as a caricature of the Hodgkin-Huxley equations of neuron firing to better understand the essential dynamics of the interaction of the membrane potential and the restoring force and to capture, qualitatively, the general properties of an excitable membrane. Even though its simplicity allows very valuable insight to be gained, the accuracy of reproducing real experimental results is limited. In this paper, we utilize a modified version of the Fitzhugh-Nagumo equations to model the spatial propagation of neuron firing; we assume that this propagation is (at least, partially) caused by the cross-diffusion connection between the potential and recovery variables. We show that the cross-diffusion version of the model, besides giving rise to the typical fast traveling wave solution exhibited in the original diffusion Fitzhugh-Nagumo equations, also gives rise to a slow traveling wave solution. We analyze all possible traveling wave solutions of the Fitzhugh-Nagumo equations with this cross-diffusion term and show that there exists a threshold of the cross-diffusion coefficient (the maximum value for a given speed of propagation), which bounds the area where normal impulse propagation is possible.
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arxiv:q-bio/0505031
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This article describes the application of recently introduced complex networks concepts and methods to the characterization and analysis of cortical bone structure. Three-dimensional reconstructions of the system of channels underlying bone structure are obtained by using histological and computer graphics methods and then represented in terms of complex networks. Confluences of two or more channels are represented as nodes, while the interconnecting channels are expressed as edges. The hierarchical backbone (the tree with maximum depth) of such a network is obtained and understood to correspond to the main structure underlying the channel system. The remainder of the network is shown to correspond to geographical communities, suggesting that the bone channel structure involves a number of regular communities appended along the hierarchical backbone. It is shown that such additional edges play a crucial role in enhancing the network resilience and in reducing the shortest paths in both topology and geometry.The recently introduced concept of fractal dimension of a network (cond-mat/0503078) is then correlated with the resilience of the several components of the bone channel structure to obstruction and failure, with important implications for the understanding of the organization and robustness of cortical bone structure.
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arxiv:q-bio/0506019
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Our paper computationally explores the extinction dynamics of an animal species effected by a sudden spike in mortality due to an extreme event. In our study, the animal species has a 2-year life cycle and is endowed with a high survival probability under normal circumstances. Our proposed approach does not involve any restraining assumptions concerning environmental variables or predator-prey relationships. Rather it is based on the simple premise that if observed on an year-to-year basis, the population size will be noted to either have gone up or come down as compared to last year. The conceptualization is borrowed from the theory of asset pricing in stochastic finance. Our results indicate that an extreme event with a maximum shock size (i.e. the maximum number of immediate mortalities that may be caused by an extreme event) exceeding two-thirds the size of the pristine population can potentially drive any animal species with a 2-year life cycle to extinction for any fecundity level.
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arxiv:q-bio/0506035
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The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional form contains important clues as to underlying evolutionary processes that have shaped the network. Generally, the functional form for the degree distribution has been determined in an ad-hoc fashion, with clear power-law like behaviour often only extending over a limited range of connectivities. Here we apply formal model selection techniques to decide which probability distribution best describes the degree distributions of protein interaction networks. Contrary to previous studies this well defined approach suggests that the degree distribution of many molecular networks is often better described by distributions other than the popular power-law distribution. This, in turn, suggests that simple, if elegant, models may not necessarily help in the quantitative understanding of complex biological processes.\
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arxiv:q-bio/0507005
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This paper has been withdrawn by the author.
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arxiv:q-bio/0507008
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Sporulation in Bacillus subtilis serves as a paradigm for the development of two different cell types (mother cell and prespore) from a single cell. The mechanism by which the two different developmental programs are initiated has been much studied but is not well understood. With the help of existing and new experimental results, a mathematical model has been developed that reproduces all published in vitro experiments and makes new predictions about the properties of the system in vivo.
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arxiv:q-bio/0507015
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The systematic study of large-scale networks has unveiled the ubiquitous presence of connectivity patterns characterized by large scale heterogeneities and unbounded statistical fluctuations. These features affect dramatically the behavior of the diffusion processes occurring on networks, determining the ensuing statistical properties of their evolution pattern and dynamics. In this paper, we investigate the role of the large scale properties of the airline transportation network in determining the global evolution of emerging disease. We present a stochastic computational framework for the forecast of global epidemics that considers the complete world-wide air travel infrastructure complemented with census population data. We address two basic issues in global epidemic modeling: i) We study the role of the large scale properties of the airline transportation network in determining the global diffusion pattern of emerging diseases; ii) We evaluate the reliability of forecasts and outbreak scenarios with respect to the intrinsic stochasticity of disease transmission and traffic flows. In order to address these issues we define a set of novel quantitative measures able to characterize the level of heterogeneity and predictability of the epidemic pattern. These measures may be used for the analysis of containment policies and epidemic risk assessment.
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arxiv:q-bio/0507029
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A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions which are optimal in an appropriate sense. In graph-theoretic language, the problems can be recast in terms of maximal sign-consistent subgraphs. The theoretical results include polynomial-time approximation algorithms as well as constant-ratio inapproximability results. One of the algorithms, which has a worst-case guarantee of 87.9 percent from optimality, is based on the semidefinite programming relaxation approach of Goemans-Williamson. The algorithm was implemented and tested on a Drosophila segmentation network and an Epidermal Growth Factor Receptor pathway model, and it was found to perform close to optimally.
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arxiv:q-bio/0509040
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SELEX (Systematic Evolution of Ligands by Exponential Enrichment) is an experimental procedure that allows extracting, from an initially random pool of DNA, those oligomers with high affinity for a given DNA-binding protein. We address what is a suitable experimental and computational procedure to infer parameters of transcription factor-DNA interaction from SELEX experiments. To answer this, we use a biophysical model of transcription factor-DNA interactions to quantitatively model SELEX. We show that a standard procedure is unsuitable for obtaining accurate interaction parameters. However, we theoretically show that a modified experiment in which chemical potential is fixed through different rounds of the experiment allows robust generation of an appropriate data set. Based on our quantitative model, we propose a novel bioinformatic method of data analysis for such modified experiment and apply it to extract the interaction parameters for a mammalian transcription factor CTF/NFI. From a practical point of view, our method results in a significantly improved false positive/false negative trade-off, as compared to both the standard information theory based method and a widely used empirically formulated procedure.
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arxiv:q-bio/0512001
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Fuzzy cognitive mapping was used to understand the wants and desires of local people before resettlement. Variables that the affected people think will increase their welfare during and after dam construction were determined. Simulations were done with their cumulative social cognitive map to determine which policy options would most increase their welfare. The construction of roads, job opportunities, advance payment of condemnation value, and schools are central variables that had the most effect on increasing people's income and welfare. The synergistic effects of variables demonstrated that the implementation of different policies not only add cumulatively to the people's welfare but also have an increased effect.
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arxiv:q-bio/0601032
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In the process of translation, ribosomes read the genetic code on an mRNA and assemble the corresponding polypeptide chain. The ribosomes perform discrete directed motion which is well modeled by a totally asymmetric simple exclusion process (TASEP) with open boundaries. Using Monte Carlo simulations and a simple mean-field theory, we discuss the effect of one or two ``bottlenecks'' (i.e., slow codons) on the production rate of the final protein. Confirming and extending previous work by Chou and Lakatos, we find that the location and spacing of the slow codons can affect the production rate quite dramatically. In particular, we observe a novel ``edge'' effect, i.e., an interaction of a single slow codon with the system boundary. We focus in detail on ribosome density profiles and provide a simple explanation for the length scale which controls the range of these interactions.
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arxiv:q-bio/0602024
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We have developed a quantitative model for the creation of cytoplasmic Ca2+ gradients near the inner surface of the plasma membrane (PM). In particular we simulated the refilling of the sarcoplasmic reticulum (SR) via PM-SR junctions during asynchronous [Ca2+] oscillations in smooth muscle cells of the rabbit inferior vena cava. We have combined confocal microscopy data on the [Ca2+] oscillations, force transduction data from cell contraction studies and electron microscopic images to build a basis for computational simulations that model the transport of calcium ions from Na+/Ca2+ exchangers (NCX) on the PM to sarcoplasmic/endoplasmic reticulum Ca2+ ATPase (SERCA) pumps on the SR as a three-dimensional random walk through the PM-SR junctional cytoplasmic spaces. Electron microscopic ultrastructural images of the smooth muscle cells were elaborated with software algorithms to produce a very clear and dimensionally accurate picture of the PM-SR junctions. From this study, we conclude that it is plausible and possible for enough Ca2+ to pass through the PM-SR junctions to replete the SR during the regenerative Ca2+ release, which underlies agonist induced asynchronous Ca2+ oscillations in vascular smooth muscle.
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arxiv:q-bio/0603001
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The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as N^{(D+1)/D} in D-dimensional hypercubic lattices and as N ln N in fully-connected graphs. It is shown that the surface of the interface between mutants and non-mutants is crucial in predicting the dynamics of the system. Network topology has a significant effect on the equilibrium fitness of a simple population model incorporating multiple mutations and sexual reproduction. Includes supplementary information.
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arxiv:q-bio/0604009
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I study the spreading of infectious diseases on heterogeneous populations. I represent the population structure by a contact-graph where vertices represent agents and edges represent disease transmission channels among them. The population heterogeneity is taken into account by the agent's subdivision in types and the mixing matrix among them. I introduce a type-network representation for the mixing matrix allowing an intuitive understanding of the mixing patterns and the analytical calculations. Using an iterative approach I obtain recursive equations for the probability distribution of the outbreak size as a function of time. I demonstrate that the expected outbreak size and its progression in time are determined by the largest eigenvalue of the reproductive number matrix and the characteristic distance between agents on the contact-graph. Finally, I discuss the impact of intervention strategies to halt epidemic outbreaks. This work provides both a qualitative understanding and tools to obtain quantitative predictions for the spreading dynamics on heterogeneous populations.
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arxiv:q-bio/0605001
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The exploration of the structural topology and the organizing principles of genome-based large-scale metabolic networks is essential for studying possible relations between structure and functionality of metabolic networks. Topological analysis of graph models has often been applied to study the structural characteristics of complex metabolic networks.In this work, metabolic networks of 75 organisms were investigated from a topological point of view. Network decomposition of three microbes (Escherichia coli, Aeropyrum pernix and Saccharomyces cerevisiae) shows that almost all of the sub-networks exhibit a highly modularized bow-tie topological pattern similar to that of the global metabolic networks. Moreover, these small bow-ties are hierarchically nested into larger ones and collectively integrated into a large metabolic network, and important features of this modularity are not observed in the random shuffled network. In addition, such a bow-tie pattern appears to be present in certain chemically isolated functional modules and spatially separated modules including carbohydrate metabolism, cytosol and mitochondrion respectively. The highly modularized bow-tie pattern is present at different levels and scales, and in different chemical and spatial modules of metabolic networks, which is likely the result of the evolutionary process rather than a random accident. Identification and analysis of such a pattern is helpful for understanding the design principles and facilitate the modelling of metabolic networks.
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arxiv:q-bio/0605003
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Some species of purple bacteria as, e.g., Rhodobacter sphaeroides contain the protein PufX. Concurrently, the light harvesting complexes 1 (LH1) form dimers of open rings. In mutants without PufX, the LH1s are closed rings and photosynthesis breaks down, because the ubiquinone exchange at the reaction center is blocked. Thus, PufX is regarded essential for quinone exchange. In contrast to this view, which implicitly treats the LH1s as obstacles to photosynthesis, we propose that the primary purpose of PufX is to improve the efficiency of light harvesting by inducing the LH1 dimerization. Calculations with a dipole model, which compare the photosynthetic efficiency of various configurations of monomeric and dimeric core complexes, show that the dimer can absorb photons directly into the RC about 30% more efficient, when related to the number of bacteriochlorophylls, but that the performance of the more sophisticated dimeric LH1 antenna degrades faster with structural perturbations. The calculations predict an optimal orientation of the reaction centers relative to the LH1 dimer, which agrees well with the experimentally found configuration. For the increased required rigidity of the dimer additional modifications of the LH1 subunits are necessary, which would lead to the observed ubiquinone blockage, when PufX is missing.
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arxiv:q-bio/0605023
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Scientists investigate the dynamics of complex systems with quantitative models, employing them to synthesize knowledge, to explain observations, and to forecast future system behavior. Complete specification of systems is impossible, so models must be simplified abstractions. Thus, the art of modeling involves deciding which system elements to include and determining how they should be represented. We view modeling as search through a space of candidate models that is guided by model objectives, theoretical knowledge, and empirical data. In this contribution, we introduce a method for representing process-based models that facilitates the discovery of models that explain observed behavior. This representation casts dynamic systems as interacting sets of processes that act on entities. Using this approach, a modeler first encodes relevant ecological knowledge into a library of generic entities and processes, then instantiates these theoretical components, and finally assembles candidate models from these elements. We illustrate this methodology with a model of the Ross Sea ecosystem.
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arxiv:q-bio/0605025
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A dynamical theory for the evolution of the genetic code is presented, which accounts for its universality and optimality. The central concept is that a variety of collective, but non-Darwinian, mechanisms likely to be present in early communal life generically lead to refinement and selection of innovation-sharing protocols, such as the genetic code. Our proposal is illustrated using a simplified computer model, and placed within the context of a sequence of transitions that early life may have made, prior to the emergence of vertical descent.
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arxiv:q-bio/0605036
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We describe an asymptotic approach to gated ionic models of single-cell cardiac excitability. It has a form essentially different from the Tikhonov fast-slow form assumed in standard asymptotic reductions of excitable systems. This is of interest since the standard approaches have been previously found inadequate to describe phenomena such as the dissipation of cardiac wave fronts and the shape of action potential at repolarization. The proposed asymptotic description overcomes these deficiencies by allowing, among other non-Tikhonov features, that a dynamical variable may change its character from fast to slow within a single solution. The general asymptotic approach is best demonstrated on an example which should be both simple and generic. The classical model of Purkinje fibers (Noble, 1962) has the simplest functional form of all cardiac models but according to the current understanding it assigns a physiologically incorrect role to the Na current. This leads us to suggest an ``Archetypal Model'' with the simplicity of the Noble model but with a structure more typical to contemporary cardiac models. We demonstrate that the Archetypal Model admits a complete asymptotic solution in quadratures. To validate our asymptotic approach, we proceed to consider an exactly solvable ``caricature'' of the Archetypal Model and demonstrate that the asymptotic of its exact solution coincides with the solutions obtained by substituting the ``caricature'' right-hand sides into the asymptotic solution of the generic Archetypal Model. This is necessary, because, unlike in standard asymptotic descriptions, no general results exist which can guarantee the proximity of the non-Tikhonov asymptotic solutions to the solutions of the corresponding detailed ionic model.
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arxiv:q-bio/0607047
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In this work we develop a theory of interaction of randomly patterned surfaces as a generic prototype model of protein-protein interactions. The theory predicts that pairs of randomly superimposed identical (homodimeric) random patterns have always twice as large magnitude of the energy fluctuations with respect to their mutual orientation, as compared with pairs of different (heterodimeric) random patterns. The amplitude of the energy fluctuations is proportional to the square of the average pattern density, to the square of the amplitude of the potential and its characteristic length, and scales linearly with the area of surfaces. The greater dispersion of interaction energies in the ensemble of homodimers implies that strongly attractive complexes of random surfaces are much more likely to be homodimers, rather than heterodimers. Our findings suggest a plausible physical reason for the anomalously high fraction of homodimers observed in real protein interaction networks.
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arxiv:q-bio/0607050
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When bacteria are grown on a mixture of two growth-limiting substrates, they exhibit a rich spectrum of substrate consumption patterns including diauxic growth, simultaneous consumption, and bistable growth. In previous work, we showed that a minimal model accounting only for enzyme induction and dilution captures all the substrate consumption patterns. Here, we construct the bifurcation diagram of the minimal model. The bifurcation diagram explains several general properties of mixed-substrate growth. (1) In almost all cases of diauxic growth, the "preferred" substrate is the one that, by itself, supports a higher specific growth rate. In the literature, this property is often attributed to optimality of regulatory mechanisms. Here, we show that the minimal model, which contains only induction, displays the property under fairly general conditions. This suggests that the higher growth rate of the preferred substrate is an intrinsic property of the induction and dilution kinetics.(2) The model explains the phenotypes of various mutants containing lesions in the regions encoding for the operator, repressor, and peripheral enzymes. A particularly striking phenotype is the "reversal of the diauxie" in which the wild-type and mutant strains consume the very same two substrates in opposite order. This phenotype is difficult to explain in terms of molecular mechanisms, but it turns out to be a natural consequence of the model. We show furthermore that the model is robust. The key property of the model, namely, the competitive dynamics of the enzymes, is preserved even if the model is modified to account for various regulatory mechanisms. Finally, the model has important implications for size regulation in development, since it suggests that protein dilution is one mechanism for coupling patterning and growth.
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arxiv:q-bio/0608021
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Knowledge regarding the kinetics of metastatic tumor formation, as related to the growth of the primary tumor, represents a fundamental issue in cancer biology. Using an in vivo mammalian model, we show here that one can obtain useful information from the frequency distribution of the sizes of metastatic colonies in distant organs after serial sectioning and image reconstruction. To explain the experimental findings, we constructed a biophysical model based on the respective growth patterns of the primary tumor and metastases and a stochastic process of metastatic colony formation. Heterogeneous distributions of various biological parameters were considered. We found that the elementary assumption of exponential forms of growth for the primary tumor and metastatic colonies predicts a linear relation on a log-log plot of a metastatic colony size distribution, which was consistent with the experimental results. Furthermore, the slope of the curve signifies the ratio of growth rates of the primary and the metastases. Non-exponential (Gompertzian and logistic) tumor growth patterns were also incorporated into the theory to explain possible deviation from the log-log linear relation. The observed metastasis-free probability also supported the assumption of a time-dependent Poisson process. With this approach, we determined the mechanistic parameters governing the process of metastatogenesis in the lungs for two murine tumor cell lines (KHT and MCaK). Since biological parameters specified in the model could be obtained in the laboratory, a workable metastatic "assay" may be established for various malignancies and in turn contribute in formulating rational treatment regimens for subclinical metastases.
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arxiv:q-bio/0608024
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We are looking at local protein interaction networks from the perspective of directed, labeled graphs with quantitative values for monotonic changes in concentrations. These systems can be used to perform stability analysis for a stable attractor, given initial values. They can also show re-configuration of whole system states by dynamic insertion of links, given specific patterns of input. The latter issue seems particularly relevant for the concept of multistability in cellular memory. We attempt to show that this level of analysis is well-suited for a number of relevant biological subsystems, such as transactivation in cardiac myocytes or G-protein coupling to adrenergic receptors. In particular, we analyse the 'motif' of an "overflow gate" as a concentration-dependent system reconfiguration.
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arxiv:q-bio/0609014
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In stochastic dynamical systems, different concepts of stability can be obtained in different limits. A particularly interesting example is evolutionary game theory, which is traditionally based on infinite populations, where strict Nash equilibria correspond to stable fixed points that are always evolutionarily stable. However, in finite populations stochastic effects can drive the system away from strict Nash equilibria, which gives rise to a new concept for evolutionary stability. The conventional and the new stability concepts may apparently contradict each other leading to conflicting predictions in large yet finite populations. We show that the two concepts can be derived from the frequency dependent Moran process in different limits. Our results help to determine the appropriate stability concept in large finite populations. The general validity of our findings is demonstrated showing that the same results are valid employing vastly different co-evolutionary processes.
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arxiv:q-bio/0609021
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The clustering of B cell receptor (BCR) molecules and the formation of the protein segregation structure known as the immunological synapse appears to precede antigen (Ag) uptake by B cells. The mature B cell synapse is characterized by a central cluster of BCR/Ag molecular complexes surrounded by a ring of LFA-1/ICAM-1 complexes. Recent experimental evidence shows receptor clustering in B cells can occur via mechanical or signaling-driven processes. An alternative mechanism of diffusion and affinity-dependent binding has been proposed to explain synapse formation in the absence of signaling-driven processes. In this work, we investigated the biophysical mechanisms that drive immunological synapse formation in B cells across the physiological range of BCR affinity (KA~10^6-10^10 M-1) through computational modeling. Our computational approach is based on stochastic simulation of diffusion and reaction events with a clearly defined mapping between probabilistic parameters of our model and their physical equivalents. We show that a diffusion-and-binding mechanism is sufficient to drive synapse formation only at low BCR affinity and for a relatively stiff B cell membrane that undergoes little deformation. We thus predict the need for alternative mechanisms: a difference in the mechanical properties of BCR/Ag and LFA-1/ICAM-1 bonds and/or signaling driven processes.
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arxiv:q-bio/0609026
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This paper proposes a new mathematical approach to characterize native protein structures based on the discrete differential geometry of tetrahedron tiles. In the approach, local structure of proteins is classified into finite types according to shape. And one would obtain a number sequence representation of protein structures automatically. As a result, it would become possible to quantify structural preference of amino-acids objectively. And one could use the wide variety of sequence alignment programs to study protein structures since the number sequence has no internal structure. The programs and this paper with clear figures are available from http://www.genocript.com.
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arxiv:q-bio/0610017
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A recently proposed model of non-autocatalytic reactions in dipeptide reactions leading to spontaneous symmetry breaking and homochirality is examined. The model is governed by activation, polymerization, epimerization and depolymerization of amino acids. Symmetry breaking is primarily a consequence of the fact that the rates of reactions involving homodimers and heterodimers are different, i.e., stereoselective, and on the fact that epimerization can only occur on the N-terminal residue and not on the Cterminal residue. This corresponds to an auto-inductive cyclic process that works only in one sense. It is argued that epimerization mimics both autocatalytic behavior as well as mutual antagonism - both of which were known to be crucial for producing full homochirality.
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arxiv:q-bio/0610051
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Using an example of physical interactions between proteins, we study how perturbations propagate in interconnected networks whose equilibrium state is governed by the law of mass action. We introduce a comprehensive matrix formalism which predicts the response of this equilibrium to small changes in total concentrations of individual molecules, and explain it using a heuristic analogy to a current flow in a network of resistors. Our main conclusion is that on average changes in free concentrations exponentially decay with the distance from the source of perturbation. We then study how this decay is influenced by such factors as the topology of a network, binding strength, and correlations between concentrations of neighboring nodes. An exact analytic expression for the decay constant is obtained for the case of uniform interactions on the Bethe lattice. Our general findings are illustrated using a real biological network of protein-protein interactions in baker's yeast with experimentally determined protein concentrations.
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arxiv:q-bio/0611026
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This work presents a mathematical model that establishes an interesting connection between nucleotide frequencies in human single-stranded DNA and the famous Fibonacci's numbers. The model relies on two assumptions. First, Chargaff's second parity rule should be valid, and, second, the nucleotide frequencies should approach limit values when the number of bases is sufficiently large. Under these two hypotheses, it is possible to predict the human nucleotide frequencies with accuracy. It is noteworthy, that the predicted values are solutions of an optimization problem, which is commonplace in many nature's phenomena.
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arxiv:q-bio/0611041
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We build a simple model for feedback systems involving small RNA (sRNA) molecules based on the iron metabolism system in the bacterium E. coli, and compare it with the corresponding system in H. pylori which uses purely transcriptional regulation. This reveals several unique features of sRNA based regulation that could be exploited by cells. Firstly, we show that sRNA regulation can maintain a smaller turnover of target mRNAs than transcriptional regulation, without sacrificing the speed of response to external shocks. Secondly, we propose that a single sRNA can prioritize the usage of different target mRNAs. This suggests that sRNA regulation would be more common in more complex systems which need to co-regulate many mRNAs efficiently.
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arxiv:q-bio/0611069
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The sensory-triggered activity of a neuron is typically characterized in terms of a tuning curve, which describes the neuron's average response as a function of a parameter that characterizes a physical stimulus. What determines the shapes of tuning curves in a neuronal population? Previous theoretical studies and related experiments suggest that many response characteristics of sensory neurons are optimal for encoding stimulus-related information. This notion, however, does not explain the two general types of tuning profiles that are commonly observed: unimodal and monotonic. Here, I quantify the efficacy of a set of tuning curves according to the possible downstream motor responses that can be constructed from them. Curves that are optimal in this sense may have monotonic or non-monotonic profiles, where the proportion of monotonic curves and the optimal tuning curve width depend on the general properties of the target downstream functions. This dependence explains intriguing features of visual cells that are sensitive to binocular disparity and of neurons tuned to echo delay in bats. The numerical results suggest that optimal sensory tuning curves are shaped not only by stimulus statistics and signal-to-noise properties, but also according to their impact on downstream neural circuits and, ultimately, on behavior.
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arxiv:q-bio/0612036
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Since the 1960s I proposed that we could understand and replicate the highest level of intelligence seen in the brain, by building ever more capable and general systems for adaptive dynamic programming (ADP), which is like reinforcement learning but based on approximating the Bellman equation and allowing the controller to know its utility function. Growing empirical evidence on the brain supports this approach. Adaptive critic systems now meet tough engineering challenges and provide a kind of first-generation model of the brain. Lewis, Prokhorov and myself have early second-generation work. Mammal brains possess three core capabilities, creativity/imagination and ways to manage spatial and temporal complexity, even beyond the second generation. This paper reviews previous progress, and describes new tools and approaches to overcome the spatial complexity gap.
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arxiv:q-bio/0612045
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In this paper, we investigate the emergence of a ratio-dependent predator-prey system with Michaelis-Menten-type functional response and reaction-diffusion. We derive the conditions for Hopf, Turing and Wave bifurcation on a spatial domain. Furthermore, we present a theoretical analysis of evolutionary processes that involves organisms distribution and their interaction of spatially distributed population with local diffusion. The results of numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripelike or spotted or coexistence of both. Our study shows that the spatially extended model has not only more complex dynamic patterns in the space, but also chaos and spiral waves. It may help us better understand the dynamics of an aquatic community in a real marine environment.
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arxiv:q-bio/0701012
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We study the Susceptible-Infected-Recovered model of epidemics in the vicinity of the threshold infectivity. We derive the distribution of total outbreak size in the limit of large population size $N$. This is accomplished by mapping the problem to the first passage time of a random walker subject to a drift that increases linearly with time. We recover the scaling results of Ben-Naim and Krapivsky that the effective maximal size of the outbreak scales as $N^{2/3}$, with the average scaling as $N^{1/3}$, with an explicit form for the scaling function.
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arxiv:q-bio/0701024
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Most primates live in social groups which survival and stability depend on individuals' abilities to create strong social relationships with other group members. The existence of those groups requires to identify individuals and to assign to each of them a social status. Individual recognition can be achieved through vocalizations but also through faces. In humans, an efficient system for the processing of own species faces exists. This specialization is achieved through experience with faces of conspecifics during development and leads to the loss of ability to process faces from other primate species. We hypothesize that a similar mechanism exists in social primates. We investigated face processing in one Old World species (genus Macaca) and in one New World species (genus Cebus). Our results show the same advantage for own species face recognition for all tested subjects. This work suggests in all species tested the existence of a common trait inherited from the primate ancestor: an efficient system to identify individual faces of own species only.
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arxiv:q-bio/0702020
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The mechanism of propulsion of host bacteria under the action of actin gel networks is examined by means of a continuum model of the dynamics of F-actin concentration. The model includes the elasticity of the network, its attachment to the host and the polymerization at the interface with it. A formula for the cruise velocity is derived wherefrom the contributions of elasticity and polymerization are made explicit. The velocity is proportional to the size of the active portion of the gel, and in turn it elongates its shape. It is shown how a finite latency time is needed for the onset of motion: the related threshold condition is explicitly given. It is numerically found that at steady state the velocity has a pulsating behavior, with sudden decelerations and subsequent recoveries: this unveils the dominant role of the elastic forces in propulsion.
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arxiv:q-bio/0702061
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We construct an individual-based kinematic model of rolling migratory locust swarms. The model incorporates social interactions, gravity, wind, and the effect of the impenetrable boundary formed by the ground. We study the model using numerical simulations and tools from statistical mechanics, namely the notion of H-stability. For a free-space swarm (no wind and gravity), as the number of locusts increases, it approaches a crystalline lattice of fixed density if it is H-stable, and in contrast becomes ever more dense if it is catastrophic. Numerical simulations suggest that whether or not a swarm rolls depends on the statistical mechanical properties of the corresponding free-space swarm. For a swarm that is H-stable in free space, gravity causes the group to land and form a crystalline lattice. Wind, in turn, smears the swarm out along the ground until all individuals are stationary. In contrast, for a swarm that is catastrophic in free space, gravity causes the group to land and form a bubble-like shape. In the presence of wind, the swarm migrates with a rolling motion similar to natural locust swarms. The rolling structure is similar to that observed by biologists, and includes a takeoff zone, a landing zone, and a stationary zone where grounded locusts can rest and feed.
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arxiv:q-bio/0703016
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In this Supporting Information, we provide background information on our model of the in vitro Kai system and the calculations that we have performed. We will closely follow the outline of the main text.
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arxiv:q-bio/0703042
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In this paper a quantum mechanical description of the assembly/disassembly process for microtubules is proposed. We introduce creation and annihilation operators that raise or lower the microtubule length by a tubulin layer. Following that, the Hamiltonian and corresponding equations of motion are derived that describe the dynamics of microtubules. These Heisenberg-type equations are then transformed to semi-classical equations using the method of coherent structures. The latter equations are very similar to the phenomenological equations that describe dynamic instability of microtubules in a tubulin solution.
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arxiv:q-bio/0703050
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At the Institute in Physical-Technical Problems experiments on sonoluminescence was started by our group at the beginning of 1998. The study was focused at properties of the SBSL, and the aim was to find more optimum conditions for a search for some recently predicted rare effects in SBSL- process.
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arxiv:quant-ph/0001040
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The method of multidimensional SUSY Quantum Mechanics is applied to the investigation of supersymmetrical N-particle systems on a line for the case of separable center-of-mass motion. New decompositions of the superhamiltonian into block-diagonal form with elementary matrix components are constructed. Matrices of coefficients of these minimal blocks are shown to coincide with matrices of irreducible representations of permutations group S_N, which correspond to the Young tableaux (N-M,1^M). The connections with known generalizations of N-particle Calogero and Sutherland models are established.
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arxiv:quant-ph/0001063
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The physical model of a nonrelativistic quantized Schrodinger's electron (SE) is offered. The behaviour of the SE well spread elementary electric charge had been understood by means of two independent and different in a frequency and size motions. The description of this resultant motion may be done by substitution of the classical Wiener continuous integral with the quantized Feynmam continuous integral. There are possibility to show by means of the existent not only formal but substantial analogy between the quadratic differential wave equation in partial derivatives of Schrodinger and quadratic differential particle equation in partial derivatives of Hamilton-Jacoby that the addition of a kinetic energy of the stochastic harmonic oscillation of some quantized micro particles to the kinetic energy of classical motion of the same micro particles formally determines their wave behaviour.It turns out the stochastic motion of the quantized micro particles powerfully to break up the smooth thin line of the classical motion of the same micro particle in many broad cylindrically spread path. The SE participate in stochastically roughly determined circumferences within different flats and with different radii, with centres which are successively arranjed over short and very disorderly orientated lines. Therefore the quantized motion of some micro particle cannot be descripted by smooth thin well contured (focused) line, describing the classical motion of the macro particle.
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arxiv:quant-ph/0001078
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The relativistic angular momentum is introduced as an extension of the non-relativistic analysis of allowed states in the phase space for a quantum particle. The paper shows the conceptual basis of the approach. An interesting feature of the present point of view is that the indistinguishability of identical particles and the Pauli principle are found as corollaries.
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arxiv:quant-ph/0001098
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We propose an implementation for quantum logic and computing using trapped atomic spins of two different species, interacting via direct magnetic spin-spin interaction. In this scheme, the spins (electronic or nuclear) of distantly spaced trapped neutral atoms serve as the qubit arrays for quantum information processing and storage, and the controlled interaction between two spins, as required for universal quantum computing, is implemented in a three step process that involves state swapping with a movable auxiliary spin.
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arxiv:quant-ph/0002029
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We examine security of a protocol on cryptographic key distribution via classical noise proposed by Yuen and Kim (Phys. Lett. A 241 135 (1998)). Theoretical and experimental analysis in terms of the secure key distribution rate shows that secure key distribution is possible even if the eavesdropper could receive more photons than the legitimate receiver, as long as the signal-to-noise-ratio (SNR) of the receiver is better than -9dB of the eavesdropper's SNR. Secure key distribution was demonstrated at the maximum rate of 0.04 bit per sender's bit and transmission rate of 2 Mb/s in the experiment employing conventional fiber optics. The present protocol has advantages of the efficient key distribution and the simple implementation over other quantum key distribution protocols. However, careful design and management are necessary to keep the security of the crypto-system.
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arxiv:quant-ph/0002044
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The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for both cases, this operator can be used in finding complete sets of wave functions of a generalized harmonic oscillator system from the well-known sets of the simple harmonic oscillator. Exact invariants of the time-dependent systems can also be obtained from the constant Hamiltonians of unit mass and frequency by making use of this unitary transformation. The geometric phases for the wave functions of a generalized harmonic oscillator with an inverse-square potential are given.
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arxiv:quant-ph/0002065
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We derive a sufficient condition for a set of pure states, each entangled in two remote $N$-dimensional systems, to be transformable to $k$-dimensional-subspace equivalent entangled states ($k\leq N$) by same local operations and classical communication. If $k=N$, the condition is also necessary. This condition reveals the function of the relative marginal density operators of the entangled states in the entanglement manipulation without sufficient information of the initial states.
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arxiv:quant-ph/0002068
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Off-resonant effects are a significant source of error in quantum computation. This paper presents a group theoretic proof that off-resonant transitions to the higher levels of a multilevel qubit can be completely prevented in principle. This result can be generalized to prevent unwanted transitions due to qubit-qubit interactions. A simple scheme exploiting dynamic pulse control techniques is presented that can cancel transitions to higher states to arbitrary accuracy.
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arxiv:quant-ph/0003034
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We consider a special kind of mixed states -- a {\it Werner derivative}, which is the state transformed by nonlocal unitary -- local or nonlocal -- operations from a Werner state. We show the followings. (i) The amount of entanglement of Werner derivatives cannot exceed that of the original Werner state. (ii) Although it is generally possible to increase the entanglement of a single copy of a Werner derivative by LQCC, the maximal possible entanglement cannot exceed the entanglement of the original Werner state. The extractable entanglement of Werner derivatives is limited by the entanglement of the original Werner state.
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arxiv:quant-ph/0003058
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Bedard has argued that the 'minimalist' interpretation of Bohm's theory "do[es] not make sense", essentially because one cannot account for bonding properties in terms of particles cofigurations alone. I argue that while this point is correct, the minimalist interpretation never sought to provide such an explanation (nor is it incumbant upon this interpretation to do so).
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arxiv:quant-ph/0003102
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We give a detailed description of the entanglement purification protocol which generates maximally entangled states with high efficiencies from realistic Gaussian continuous variable entangled states. The physical implementation of this protocol is extensively analyzed using high finesse cavities and cavity enhanced cross Kerr nonlinearities. In particular, we take into account many imperfections in the experimental scheme and calculate their influences. Quantitative requirements are given for the relevant experimental parameters.
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arxiv:quant-ph/0003116
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Phase diagrams of the micromaser system are mapped out in terms of the physical parameters at hand like the atom cavity transit time, the atom-photon frequency detuning, the number of thermal photons and the probability for a pump atom to be in its excited state. Critical fluctuations are studied in terms of correlation measurements on atoms having passed through the micromaser or on the microcavity photons themselves. At sufficiently large values of the detuning we find a ``twinkling'' mode of the micromaser system. Detailed properties of the trapping states are also presented.
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arxiv:quant-ph/0003133
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We show that at least the quasi-exactly solvable eigenvalues of the Schr\"odinger equation with the potential $V(x) = -(\zeta \cosh 2x -iM)^2$ as well as the periodic potential $V(x) = (\zeta \cos 2\theta -iM)^2$ are real for the PT-invariant non-Hermitian potentials in case the parameter $M$ is any odd integer. We further show that the norm as well as the weight functions for the corresponding weak orthogonal polynomials are also real.
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arxiv:quant-ph/0004019
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Call a spectrum of Hamiltonian sparse if each eigenvalue can be quickly restored with accuracy $\epsilon$ from its rough approximation in within $\epsilon_1$ by means of some classical algorithm. It is shown how a behavior of system with sparse spectrum up to time $T=\frac{1-\rho}{14\epsilon}$ can be predicted with fidelity $\rho$ on quantum computer in time $t=\frac{4}{(1-\rho)\epsilon_1}$ plus the time of classical algorithm. The quantum knowledge of Hamiltonian $H$ eigenvalues is considered as a wizard Hamiltonian $W_H$ which action on any eigenvector of $H$ gives the corresponding eigenvalue. Speedup of evolution for systems with sparse spectrum is possible because for such systems wizard Hamiltonians can be quickly simulated on a quantum computer. This simulation, generalizing Shor trick, is a part of presented algorithm. In general case the action of wizard Hamiltonian cannot be simulated in time smaller than the dimension of main space which is exponential of the size of quantum system. For an arbitrary system (even for classical) its behavior cannot be predicted on quantum computer even for one step ahead. This method can be used also for restoration of a state of an arbitrary primary system in time instant $-T$ in the past with the same fidelity which requires the same time.
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arxiv:quant-ph/0004021
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The paper is devoted to the mathematical foundation of the quantum tomography using the theory of square-integrable representations of unimodular Lie groups.
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arxiv:quant-ph/0004026
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The role of probability in quantum mechanics is reviewed, with a discussion of the ``orthodox'' versus the statistical interpretive frameworks, and of a number of related issues. After a brief summary of sources of unease with quantum mechanics, a survey is given of attempts either to give a new interpretive framework assuming quantum mechanics is exact, or to modify quantum mechanics assuming it is a very accurate approximation to a more fundamental theory. This survey focuses particularly on the issues of whether probabilities in quantum mechanics are postulated or emergent.
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arxiv:quant-ph/0004077
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The Einstein-Podolsky-Rosen nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is resolved if the quantum correlations are calculated directly from local quantities which preserve the phase information in the quantum system. We assume strict locality for the probability amplitudes instead of local realism for the outcomes, and calculate an amplitude correlation function.Then the experimentally observed correlation of outcomes is calculated from the square of the amplitude correlation function. Locality of amplitudes implies that the measurement on one particle does not collapse the companion particle to a definite state. Apart from resolving the EPR puzzle, this approach shows that the physical interpretation of apparently `nonlocal' effects like quantum teleportation and entanglement swapping are different from what is usually assumed. Bell type measurements do not change distant states. Yet the correlations are correctly reproduced, when measured, if complex probability amplitudes are treated as the basic local quantities. As examples we discuss the quantum correlations of two-particle maximally entangled states and the three-particle GHZ entangled state.
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arxiv:quant-ph/0005103
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We present detailed discussions of cooling and trapping mechanisms for an atom in an optical trap inside an optical cavity, as relevant to recent experiments. The interference pattern of cavity QED and trapping fields in space makes the trapping wells distinguishable from one another. This adds considerable flexibility to creating effective trapping and cooling conditions and to detection possibilities. Friction and diffusion coefficients are calculated in and beyond the low excitation limit and full 3-D simulations of the quasiclassical motion of a Cs atom are performed.
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arxiv:quant-ph/0005133
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We show in this Comment that the interpretation of experimental data as well as the theory presented in Atat\"ure et al. [Phys. Rev. Lett. 84, 618 (2000)] are incorrect and discuss why such a scheme cannot be used to "recover" high-visibility quantum interference.
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arxiv:quant-ph/0006003
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The buildup process of the probability density inside the quantum well of a double-barrier resonant structure is studied by considering the analytic solution of the time dependent Schr\"{o}dinger equation with the initial condition of a cutoff plane wave. For one level systems at resonance condition we show that the buildup of the probability density obeys a simple charging up law, $| \Psi (\tau) / \phi | =1-e^{-\tau /\tau_0},$ where $\phi$ is the stationary wave function and the transient time constant $\tau_0$ is exactly two lifetimes. We illustrate that the above formula holds both for symmetrical and asymmetrical potential profiles with typical parameters, and even for incidence at different resonance energies. Theoretical evidence of a crossover to non-exponential buildup is also discussed.
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arxiv:quant-ph/0006052
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Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem and characterize the set of effectively different states (which cannot be related by local transformations). Thus we generalize earlier results obtained for the simplest 2 x 2 system, which lead to a stratification of the 6D set of N=4 pure states. We define the concept of absolutely separable states, for which all globally equivalent states are separable.
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arxiv:quant-ph/0006068
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A quantum key distribution scheme whose security depends on the features of pre- and post-selected quantum states is described.
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arxiv:quant-ph/0006086
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A generalization of the quantum XOR-gate is presented which operates in arbitrary dimensional Hilbert spaces. Together with one-particle Fourier transforms this gate is capable of performing a variety of tasks which are important for quantum information processing in arbitrary dimensional Hilbert spaces. Among these tasks are the preparation of Bell states, quantum teleportation and quantum state purification. A physical realization of this generalized XOR-gate is proposed which is based on non-linear optical elements.
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arxiv:quant-ph/0008022
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We report an experimental confirmation of the power-law relationship between the critical anisotropy parameter and ion number for the linear-to-zigzag phase transition in an ionic crystal. Our experiment uses laser cooled calcium ions confined in a linear radio-frequency trap. Measurements for up to 10 ions are in good agreement with theoretical and numeric predictions. Implications on an upper limit to the size of data registers in ion trap quantum computers are discussed.
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arxiv:quant-ph/0008045
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Although the conditions for performing arbitrary unitary operations to simulate the dynamics of a closed quantum system are well understood, the same is not true of the more general class of quantum operations (also known as superoperators) corresponding to the dynamics of open quantum systems. We propose a framework for the generation of Markovian quantum dynamics and study the resources needed for universality. For the case of a single qubit, we show that a single nonunitary process is necessary and sufficient to generate all unital Markovian quantum dynamics, whereas a set of processes parametrized by one continuous parameter is needed in general. We also obtain preliminary results for the unital case in higher dimensions.
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arxiv:quant-ph/0008070
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We experimentally demonstrate and systematically study the stimulated revival (echo) of motional wave packet oscillations. For this purpose, we prepare wave packets in an optical lattice by non-adiabatically shifting the potential and stimulate their reoccurence by a second shift after a variable time delay. This technique, analogous to spin echoes, enables one even in the presence of strong dephasing to determine the coherence time of the wave packets. We find that for strongly bound atoms it is comparable to the cooling time and much longer than the inverse of the photon scattering rate.
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arxiv:quant-ph/0008083
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We show that in parametrically driven systems and, more generally, in systems in coherent states, off-resonant pumping can cause a transition from a continuum energy spectrum of the system to a discrete one, and result in quantum revivals of the initial state. The mechanism responsible for quantum revivals in the present case is different from that in the non-linear wavepacket dynamics of systems such as Rydberg atoms. We interpret the reported phenomena as an optical analog of Bloch oscillations realized in Fock space and propose a feasible scheme for inducing Bloch oscillations in trapped ions.
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arxiv:quant-ph/0008106
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We consider the time development of the density matrix for a system coupled to a thermal bath, in models that go beyond the standard two-level systems through addition of an energy excitation degree of freedom and through the possibility of the replacement of the spin algebra by a more complex algebra. We find conditions under which increasing the coupling to the bath above a certain level decreases the rate of entropy production, and in which the limiting behavior is a dissipationless sinusoidal oscillation that could be interpreted as the synchronization of many modes of the uncoupled system.
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arxiv:quant-ph/0008133
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A general proof of the security against eavesdropping of a previously introduced protocol for two-party quantum key distribution based on entanglement swapping [Phys. Rev. A {\bf 61}, 052312 (2000)] is provided. In addition, the protocol is extended to permit multiparty quantum key distribution and secret sharing of classical information.
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arxiv:quant-ph/0009025
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We give a new algorithm for generating Greechie diagrams with arbitrary chosen number of atoms or blocks (with 2,3,4,... atoms) and provide a computer program for generating the diagrams. The results show that the previous algorithm does not produce every diagram and that it is at least 100,000 times slower. We also provide an algorithm and programs for checking of Greechie diagram passage by equations defining varieties of orthomodular lattices and give examples from Hilbert lattices. At the end we discuss some additional characteristics of Greechie diagrams.
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arxiv:quant-ph/0009039
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Recently, Zhang, Li, and Guo have proposed a particular eavesdropping attack [Phys. Rev. A {\bf 63}, 036301 (2001), quant-ph/0009042] which shows that my quantum key distribution protocol based on entanglement swapping [Phys. Rev. A {\bf 61}, 052312 (2000), quant-ph/9911025] is insecure. However, security against this attack can be attained with a simple modification. In addition, a simpler version of the protocol using four qubits is introduced.
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arxiv:quant-ph/0009051
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A theoretical framework is presented allowing the treatment of quantum messages with components of variable length. To this aim a many-letter space, similiar to the Fock space, is constructed, generalizing the standard quantum information theory of block messages of fixed length. In the many-letter space a length operator can be defined measuring the length of a quantum message, whose eigenspaces are the block Hilbert spaces used in the standard theory.
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arxiv:quant-ph/0009052
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We show that universally covariant cloning is not optimal for achieving joint measurements of noncommuting observables with minimum added noise. For such a purpose a cloning transformation that is covariant with respect to a restricted transformation group is needed.
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arxiv:quant-ph/0009080
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Recent work has extended Bell's theorem by quantifying the amount of communication required to simulate entangled quantum systems with classical information. The general scenario is that a bipartite measurement is given from a set of possibilities and the goal is to find a classical scheme that reproduces exactly the correlations that arise when an actual quantum system is measured. Previous results have shown that, using local hidden variables, a finite amount of communication suffices to simulate the correlations for a Bell state. We extend this in a number of ways. First, we show that, when the communication is merely required to be finite {\em on average}, Bell states can be simulated {\em without} any local hidden variables. More generally, we show that arbitrary positive operator valued measurements on systems of $n$ Bell states can be simulated with $O(n 2^n)$ bits of communication on average (again, without local hidden variables). On the other hand, when the communication is required to be {\em absolutely bounded}, we show that a finite number of bits of local hidden variables is insufficent to simulate a Bell state. This latter result is based on an analysis of the non-deterministic communication complexity of the NOT-EQUAL function, which is constant in the quantum model and logarithmic in the classical model.
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arxiv:quant-ph/0009088
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A new cryptographic tool, anonymous quantum key technique, is introduced that leads to unconditionally secure key distribution and encryption schemes that can be readily implemented experimentally in a realistic environment. If quantum memory is available, the technique would have many features of public-key cryptography; an identification protocol that does not require a shared secret key is provided as an illustration. The possibility is also indicated for obtaining unconditionally secure quantum bit commitment protocols with this technique.
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arxiv:quant-ph/0009113
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We propose dissociation of cold diatomic molecules as a source of atom pairs with highly correlated (entangled) positions and momenta, approximating the original quantum state introduced by Einstein, Podolsky and Rosen (EPR) [Phys. Rev. 47, 777 (1935)]. Wavepacket teleportation is shown to be achievable by its collision with one of the EPR correlated atoms and manipulation of the other atom in the pair.
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arxiv:quant-ph/0009121
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The representation of numbers by tensor product states of composite quantum systems is examined. Consideration is limited to k-ary representations of length L and arithmetic modulo k^{L}. An abstract representation on an L fold tensor product Hilbert space H^{arith} of number states and operators for the basic arithmetic operations is described. Unitary maps onto a physical parameter based tensor product space H^{phy} are defined and the relations between these two spaces and the dependence of algorithm dynamics on the unitary maps is discussed. The important condition of efficient implementation by physically realizable Hamiltonians of the basic arithmetic operations is also discussed.
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arxiv:quant-ph/0009124
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We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous variable quadrature phase amplitude (``position'' and ``momentum'') measurements, by way of a violation of a Bell inequality. For any quantum state, this contradiction is lost for situations where the quadrature phase amplitude results are always macroscopically distinct. We show that for optical realisations of this experiment, where one uses homodyne detection techniques to perform the quadrature phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors. The high efficiencies of such detectors may open a way for a loophole-free test of local hidden variable theories.
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arxiv:quant-ph/0010024
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We show that the modern quantum mechanics, and particularly the theory of decoherence, allows for formulating a sort of a physical metatheory of consciousness. Particularly, the analysis of the necessary conditions for the occurrence of decoherence, along with the hypothesis that consciousness bears (more-or-less) well definable physical origin, leads to a wider physical picture naturally involving consciousness. This can be considered as a sort of a psycho-physical parallelism, but on rather wide scales bearing some cosmological relevance.
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arxiv:quant-ph/0010042
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We report a quantum teleportation experiment in which nonlinear interactions are used for the Bell state measurements. The experimental results demonstrate the working principle of irreversibly teleporting an unknown arbitrary quantum state from one system to another distant system by disassembling into and then later reconstructing from purely classical information and nonclassical EPR correlations. The distinct feature of this experiment is that \emph{all} four Bell states can be distinguished in the Bell state measurement. Teleportation of a quantum state can thus occur with certainty in principle.
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arxiv:quant-ph/0010046
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We study the collective Raman cooling of a polarized trapped Fermi gas in the Festina Lente regime, when the heating effects associated with photon reabsorptions are suppressed. We predict that by adjusting the spontaneous Raman emission rates and using appropriately designed anharmonic traps, temperatures of the order of 2.7% of the Fermi temperature can be achieved in 3D.
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arxiv:quant-ph/0010067
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See quant-ph/0101012
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arxiv:quant-ph/0010083
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We study separability properties in a 5-dimensional set of states of quantum systems composed of three subsystems of equal but arbitrary finite Hilbert space dimension d. These are the states, which can be written as linear combinations of permutation operators, or, equivalently, commute with unitaries of the form UxUxU. We compute explicitly the following subsets and their extreme points: (1) triseparable states, which are convex combinations of triple tensor products, (2) biseparable states, which are separable for a twofold partition of the system, and (3) states with positive partial transpose with respect to such a partition. Tripartite entanglement is investigated in terms of the relative entropy of tripartite entanglement and of the trace norm.
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arxiv:quant-ph/0010096
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To account for the phenomenon of quantum decoherence of a macroscopic object, such as the localization and disappearance of interference, we invoke the adiabatic quantum entanglement between its collective states(such as that of the center-of-mass (C.M)) and its inner states based on our recent investigation. Under the adiabatic limit that motion of C.M dose not excite the transition of inner states, it is shown that the wave function of the macroscopic object can be written as an entangled state with correlation between adiabatic inner states and quasi-classical motion configurations of the C.M. Since the adiabatic inner states are factorized with respect to each parts composing the macroscopic object, this adiabatic separation can induce the quantum decoherence. This observation thus provides us with a possible solution to the Schroedinger cat paradox
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arxiv:quant-ph/0010102
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Using the leading vector method, we show that any vector $h\in(C^2)^{\otimes l}$ can be decomposed as a sum of at most (and at least in the generic case) $2^l-l$ product vectors using local bitwise unitary transformations. The method is based on representing the vectors by chains of appropriate simplicial complex. This generalizes the Scmidt decomposition of pure states of a 2-bit register to registers of arbitrary length $l$.
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arxiv:quant-ph/0010104
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We show that spatial entanglement of two twin images obtained by parametric down-conversion is complete, i.e. concerns both amplitude and phase. This is realised through a homodyne detection of these images which allows for measurement of the field quadrature components. EPR correlations are shown to exist between symmetrical pixels of the two images. The best possible correlation is obtained by adjusting the phase of the local oscillator field (LO) in the area of maximal amplification. The results for quadrature components hold unchanged even in absence of any input image i.e. for pure parametric fluorescence. In this case they are not related to intensity and phase fluctuations.
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arxiv:quant-ph/0010108
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