56,919 research outputs found

    Application of Information Theory in Nuclear Liquid Gas Phase Transition

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    Information entropy and Zipf's law in the field of information theory have been used for studying the disassembly of nuclei in the framework of the isospin dependent lattice gas model and molecular dynamical model. We found that the information entropy in the event space is maximum at the phase transition point and the mass of the cluster show exactly inversely to its rank, i.e. Zipf's law appears. Both novel criteria are useful in searching the nuclear liquid gas phase transition experimentally and theoretically.Comment: 5 pages, 5 figure

    Angoricity and compactivity describe the jamming transition in soft particulate matter

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    The application of concepts from equilibrium statistical mechanics to out-of-equilibrium systems has a long history of describing diverse systems ranging from glasses to granular materials. For dissipative jammed systems-- particulate grains or droplets-- a key concept is to replace the energy ensemble describing conservative systems by the volume-stress ensemble. Here, we test the applicability of the volume-stress ensemble to describe the jamming transition by comparing the jammed configurations obtained by dynamics with those averaged over the ensemble as a probe of ergodicity. Agreement between both methods suggests the idea of "thermalization" at a given angoricity and compactivity. We elucidate the thermodynamic order of the jamming transition by showing the absence of critical fluctuations in static observables like pressure and volume. The approach allows to calculate observables such as the entropy, volume, pressure, coordination number and distribution of forces to characterize the scaling laws near the jamming transition from a statistical mechanics viewpoint.Comment: 27 pages, 13 figure

    Entropy-scaling search of massive biological data

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    Many datasets exhibit a well-defined structure that can be exploited to design faster search tools, but it is not always clear when such acceleration is possible. Here, we introduce a framework for similarity search based on characterizing a dataset's entropy and fractal dimension. We prove that searching scales in time with metric entropy (number of covering hyperspheres), if the fractal dimension of the dataset is low, and scales in space with the sum of metric entropy and information-theoretic entropy (randomness of the data). Using these ideas, we present accelerated versions of standard tools, with no loss in specificity and little loss in sensitivity, for use in three domains---high-throughput drug screening (Ammolite, 150x speedup), metagenomics (MICA, 3.5x speedup of DIAMOND [3,700x BLASTX]), and protein structure search (esFragBag, 10x speedup of FragBag). Our framework can be used to achieve "compressive omics," and the general theory can be readily applied to data science problems outside of biology.Comment: Including supplement: 41 pages, 6 figures, 4 tables, 1 bo

    Edwards thermodynamics of the jamming transition for frictionless packings: ergodicity test and role of angoricity and compactivity

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    This paper illustrates how the tools of equilibrium statistical mechanics can help to explain a far-from-equilibrium problem: the jamming transition in frictionless granular materials. Edwards ideas consist of proposing a statistical ensemble of volume and stress fluctuations through the thermodynamic notion of entropy, compactivity, X, and angoricity, A (two temperature-like variables). We find that Edwards thermodynamics is able to describe the jamming transition (J-point). Using the ensemble formalism we elucidate the following: (i)We test the combined volume-stress ensemble by comparing the statistical properties of jammed configurations obtained by dynamics with those averaged over the ensemble of minima in the potential energy landscape as a test of ergodicity. Agreement between both methods supports the idea of "thermalization" at a given angoricity and compactivity. (ii) A microcanonical ensemble analysis supports the idea of maximum entropy principle for grains. (iii) The intensive variables describe the approach to jamming through a series of scaling relations as A {\to} 0+ and X {\to} 0-. Due to the force-volume coupling, the jamming transition can be probed thermodynamically by a "jamming temperature" TJ comprised of contributions from A and X. (iv) The thermodynamic framework reveals the order of the jamming phase transition by showing the absence of critical fluctuations at jamming in observables like pressure and volume. (v) Finally, we elaborate on a comparison with relevant studies showing a breakdown of equiprobability of microstates.Comment: 22pages, 24 figure

    Multi-Qubit Systems: Highly Entangled States and Entanglement Distribution

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    A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multi-qubits states. In particular, our present results are compared with those recently reported by Brown et al. [J. Phys. A: Math. Gen. 38 (2005) 1119]. The statistical distribution of entanglement values for the aforementioned multi-qubit systems is also explored.Comment: 24 pages, 3 figure

    Universality of Entanglement and Quantum Computation Complexity

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    We study the universality of scaling of entanglement in Shor's factoring algorithm and in adiabatic quantum algorithms across a quantum phase transition for both the NP-complete Exact Cover problem as well as the Grover's problem. The analytic result for Shor's algorithm shows a linear scaling of the entropy in terms of the number of qubits, therefore difficulting the possibility of an efficient classical simulation protocol. A similar result is obtained numerically for the quantum adiabatic evolution Exact Cover algorithm, which also shows universality of the quantum phase transition the system evolves nearby. On the other hand, entanglement in Grover's adiabatic algorithm remains a bounded quantity even at the critical point. A classification of scaling of entanglement appears as a natural grading of the computational complexity of simulating quantum phase transitions.Comment: 30 pages, 17 figures, accepted for publication in PR

    Multi-Scale CLEAN deconvolution of radio synthesis images

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    Radio synthesis imaging is dependent upon deconvolution algorithms to counteract the sparse sampling of the Fourier plane. These deconvolution algorithms find an estimate of the true sky brightness from the necessarily incomplete sampled visibility data. The most widely used radio synthesis deconvolution method is the CLEAN algorithm of Hogbom. This algorithm works extremely well for collections of point sources and surprisingly well for extended objects. However, the performance for extended objects can be improved by adopting a multi-scale approach. We describe and demonstrate a conceptually simple and algorithmically straightforward extension to CLEAN that models the sky brightness by the summation of components of emission having different size scales. While previous multiscale algorithms work sequentially on decreasing scale sizes, our algorithm works simultaneously on a range of specified scales. Applications to both real and simulated data sets are given.Comment: Submitted to IEEE Special Issue on Signal Processin
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