We present a graph embedding space (i.e., a set of measures on graphs) for performing statistical analyses of networks. Key improvements over existing approaches include discovery of “motif hubs” (multiple overlappi...
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We present a graph embedding space (i.e., a set of measures on graphs) for performing statistical analyses of networks. Key improvements over existing approaches include discovery of “motif hubs” (multiple overlapping significant subgraphs), computational efficiency relative to subgraph census, and flexibility (the method is easily generalizable to weighted and signed graphs). The embedding space is based on scalars, functionals of the adjacency matrix representing the network. Scalars are global, involving all nodes; although they can be related to subgraph enumeration, there is not a one-to-one mapping between scalars and subgraphs. Improvements in network randomization and significance testing—we learn the distribution rather than assuming Gaussianity—are also presented. The resulting algorithm establishes a systematic approach to the identification of the most significant scalars and suggests machine-learning techniques for network classification.
The concept of a geometric phase (Berry’s phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum sys...
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The concept of a geometric phase (Berry’s phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry’s phases. Our results are demonstrated with a nonlinear two-level model.
Use of indocyanine green (ICG) in a pump-probe scheme for OCT is proposed. The study illustrates that ICG in protein solution shows unusual pump-probe imaging potential, indicating its usefulness as a contrast agent f...
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ISBN:
(纸本)1557527954
Use of indocyanine green (ICG) in a pump-probe scheme for OCT is proposed. The study illustrates that ICG in protein solution shows unusual pump-probe imaging potential, indicating its usefulness as a contrast agent for OCT.
We present a class of soliton solutions to a system of two coupled nonlinear Schrödinger equations, with an intrinsic domain wall (DW) which separates regions occupied by two different fields. The model describes...
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We present a class of soliton solutions to a system of two coupled nonlinear Schrödinger equations, with an intrinsic domain wall (DW) which separates regions occupied by two different fields. The model describes a binary mixture of two Bose-Einstein condensates (BECs) with interspecies repulsion. For the attractive or repulsive interactions inside each species, we find solutions which are bright or dark solitons in each component, while for the opposite signs of the intraspecies interaction, a bright-dark soliton pair is found (each time, with the intrinsic DW). These solutions can arise in the context of discrete lattices, and most of them can be supported in continuum settings by an external parabolic trap. The stability of the solitons with intrinsic DWs is examined, and the evolution of unstable ones is analyzed. We also briefly discuss the possibility of generating such families of solutions in the presence of linear coupling between the components, and an application of the model to bimodal light propagation in nonlinear optics.
We investigate fidelity for the quantum evolution of a Bose-Einstein condensate (BEC) and reveal its general property with a simple two-component BEC model. We find that, when the initial state is a coherent state, th...
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We investigate fidelity for the quantum evolution of a Bose-Einstein condensate (BEC) and reveal its general property with a simple two-component BEC model. We find that, when the initial state is a coherent state, the fidelity decays with time in the ways of exponential, Gaussian, and power law, depending on the initial location, the perturbation strength, as well as the underlying mean-field classical dynamics. In this case we find a clear correspondence between the fast quantum fidelity decay and the dynamical instability of the mean-field system. With the initial state prepared as a maximally entangled state, we find that the behavior of fidelity has no classical correspondence and observe an interesting behavior of the fidelity: periodic revival, where the period is inversely proportional to the number of bosons and the perturbation strength. An experimental observation of the fidelity decay is suggested.
Nucleon‐induced cross sections on magnesium isotopes, 24,25,26Mg, and silicon isotopes, 28,29,30Si, were evaluated for energies up to 3 GeV. Evaluation of nucleon‐scattering cross sections was performed by a consist...
Nucleon‐induced cross sections on magnesium isotopes, 24,25,26Mg, and silicon isotopes, 28,29,30Si, were evaluated for energies up to 3 GeV. Evaluation of nucleon‐scattering cross sections was performed by a consistent analysis of nuclear‐level structure and nucleon‐scattering data using a unified framework of a soft‐rotator model and coupled‐channel approach. The scattering cross sections for silicon isotopes were re‐analyzed based on two new considerations. First the silicon isotopes were assumed to be deformed nuclei having oblate shapes, second the more sophisticated form of optical‐potential energy dependence was used. The evaluation of the particle emissions was performed by using a nuclear‐model code system consisting of the GNASH code up to 150 MeV and the JQMD code above 150 MeV. The present results were compared with available experimental data and the LA 150 evaluation.
Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near 1.25∶1∶0.8 can approach the densest crystal packing (fcc) of spheres, with a packing frac...
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Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near 1.25∶1∶0.8 can approach the densest crystal packing (fcc) of spheres, with a packing fraction of 74%. We demonstrate that such dense packings are realizable. We introduce a novel way of determining packing density for a finite sample that minimizes surface effects. We have fabricated ellipsoids and show that, in a sphere, the radial packing fraction ϕ(r) can be obtained from V(h), the volume of added fluid to fill the sphere to height h. We also obtain ϕ(r) from a magnetic resonance imaging scan. The measurements of the overall density ϕavr, ϕ(r) and the core density ϕ0=0.74±0.005 agree with simulations.
The chemical mechanisms underlying the growth of cave formations such as stalactites are well known, yet no theory has yet been proposed which successfully accounts for the dynamic evolution of their shapes. Here we c...
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The chemical mechanisms underlying the growth of cave formations such as stalactites are well known, yet no theory has yet been proposed which successfully accounts for the dynamic evolution of their shapes. Here we consider the interplay of thin-film fluid dynamics, calcium carbonate chemistry, and CO2 transport in the cave to show that stalactites evolve according to a novel local geometric growth law which exhibits extreme amplification at the tip as a consequence of the locally-varying fluid layer thickness. Studies of this model show that a broad class of initial conditions is attracted to an ideal shape which is strikingly close to a statistical average of natural stalactites.
Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative an...
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Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit.
We prove the existence of solutions of the static Landau-Lifshitz equation with multi- direct effective field and with Dirichlet boundary condition,and establish the stability of the solution of Landau-Lifshitz equati...
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We prove the existence of solutions of the static Landau-Lifshitz equation with multi- direct effective field and with Dirichlet boundary condition,and establish the stability of the solution of Landau-Lifshitz equation with respect to time.
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