11,748 research outputs found

    The Sampling-and-Learning Framework: A Statistical View of Evolutionary Algorithms

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    Evolutionary algorithms (EAs), a large class of general purpose optimization algorithms inspired from the natural phenomena, are widely used in various industrial optimizations and often show excellent performance. This paper presents an attempt towards revealing their general power from a statistical view of EAs. By summarizing a large range of EAs into the sampling-and-learning framework, we show that the framework directly admits a general analysis on the probable-absolute-approximate (PAA) query complexity. We particularly focus on the framework with the learning subroutine being restricted as a binary classification, which results in the sampling-and-classification (SAC) algorithms. With the help of the learning theory, we obtain a general upper bound on the PAA query complexity of SAC algorithms. We further compare SAC algorithms with the uniform search in different situations. Under the error-target independence condition, we show that SAC algorithms can achieve polynomial speedup to the uniform search, but not super-polynomial speedup. Under the one-side-error condition, we show that super-polynomial speedup can be achieved. This work only touches the surface of the framework. Its power under other conditions is still open

    ZOOpt: Toolbox for Derivative-Free Optimization

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    Recent advances of derivative-free optimization allow efficient approximating the global optimal solutions of sophisticated functions, such as functions with many local optima, non-differentiable and non-continuous functions. This article describes the ZOOpt (https://github.com/eyounx/ZOOpt) toolbox that provides efficient derivative-free solvers and are designed easy to use. ZOOpt provides a Python package for single-thread optimization, and a light-weighted distributed version with the help of the Julia language for Python described functions. ZOOpt toolbox particularly focuses on optimization problems in machine learning, addressing high-dimensional, noisy, and large-scale problems. The toolbox is being maintained toward ready-to-use tool in real-world machine learning tasks

    Kinematic Basis of Emergent Energetics of Complex Dynamics

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    Stochastic kinematic description of a complex dynamics is shown to dictate an energetic and thermodynamic structure. An energy function φ(x)\varphi(x) emerges as the limit of the generalized, nonequilibrium free energy of a Markovian dynamics with vanishing fluctuations. In terms of the φ\nabla\varphi and its orthogonal field γ(x)φ\gamma(x)\perp\nabla\varphi, a general vector field b(x)b(x) can be decomposed into D(x)φ+γ-D(x)\nabla\varphi+\gamma, where (ω(x)γ(x))=\nabla\cdot\big(\omega(x)\gamma(x)\big)= ωD(x)φ-\nabla\omega D(x)\nabla\varphi. The matrix D(x)D(x) and scalar ω(x)\omega(x), two additional characteristics to the b(x)b(x) alone, represent the local geometry and density of states intrinsic to the statistical motion in the state space at xx. φ(x)\varphi(x) and ω(x)\omega(x) are interpreted as the emergent energy and degeneracy of the motion, with an energy balance equation dφ(x(t))/dt=γD1γbD1bd\varphi(x(t))/dt=\gamma D^{-1}\gamma-bD^{-1}b, reflecting the geometrical Dφ2+γ2=b2\|D\nabla\varphi\|^2+\|\gamma\|^2=\|b\|^2. The partition function employed in statistical mechanics and J. W. Gibbs' method of ensemble change naturally arise; a fluctuation-dissipation theorem is established via the two leading-order asymptotics of entropy production as ϵ0\epsilon\to 0. The present theory provides a mathematical basis for P. W. Anderson's emergent behavior in the hierarchical structure of complexity science.Comment: 7 page

    The Face View of China and Foreign Countries under Cross-cultural Communication

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    “MianZi” is something that everyone is pursuing, it is the combination of “Lian” and “Mian”. It refers to the psychological feeling that is obtained from the comments of others on our speech and behavior. "Having face" is the psychological feeling when one person obtains affirmation and praise, and “losing face” is the psychological feeling of suffering criticism or negation. “Lian” and” Mian” are quite different in their meanings. Pure face is beautiful and fascinating. It is just like a ordinary man, even though he looks very average, but when he is with a little decoration, a little powder, he looks charming at once. But in many times, there are always some people who want to win others' approval so that they can win face for themselves, so they do not hesitate to use improper means to achieve their personal goals, such faces are disgusting and rebarbative. The concept of “face” embodies people's values and relates to social morality. It should play an active role in promoting the harmonious development and stability of our society

    Diquarks and the Semi-Leptonic Decay of Λb\Lambda_{b} in the Hybrid Scheme

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    In this work we use the heavy-quark-light-diquark picture to study the semileptonic decay ΛbΛc+l+νˉl\Lambda_b \to \Lambda_c+l+\bar{\nu}_l in the so-called hybrid scheme. Namely, we apply the heavy quark effective theory (HQET) for larger q2q^2 (corresponding to small recoil), which is the invariant mass square of l+νˉl+\bar\nu, whereas the perturbative QCD approach for smaller q2q^2 to calculate the form factors. The turning point where we require the form factors derived in the two approaches to be connected, is chosen near ρcut=1.1\rho_{cut}=1.1. It is noted that the kinematic parameter ρ\rho which is usually adopted in the perturbative QCD approach, is in fact exactly the same as the recoil factor ω=vv\omega=v\cdot v' used in HQET where vv, vv' are the four velocities of Λb\Lambda_b and Λc\Lambda_c respectively. We find that the final result is not much sensitive to the choice, so that it is relatively reliable. Moreover, we apply a proper numerical program within a small range around ρcut\rho_{cut} to make the connection sufficiently smooth and we parameterize the form factor by fitting the curve gained in the hybrid scheme. The expression and involved parameters can be compared with the ones gained by fitting the experimental data. In this scheme the end-point singularities do not appear at all. The calculated value is satisfactorily consistent with the data which is recently measured by the DELPHI collaboration within two standard deviations.Comment: 16 pages, including 4 figures, revtex
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