600 research outputs found

    Connection between closeness of classical orbits and the factorization of radial Schr\"{o}dinger equation

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    It was shown that the Runge-Lenz vector for a hydrogen atom is equivalent to the raising and lowering operators derived from the factorization of radial Schr\"{o}dinger equation. Similar situation exists for an isotropic harmonic oscillator. It seems that there may exist intimate relation between the closeness of classical orbits and the factorization of radial Schr\"{o}dinger equation. Some discussion was made about the factorization of a 1D Schr\"{o}dinger equation.Comment: 14 pages, no figure

    ‘Double water exclusion’: a hypothesis refining the O-ring theory for the hot spots at protein interfaces

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    Motivation: The O-ring theory reveals that the binding hot spot at a protein interface is surrounded by a ring of residues that are energetically less important than the residues in the hot spot. As this ring of residues is served to occlude water molecules from the hot spot, the O-ring theory is also called ‘water exclusion’ hypothesis. We propose a ‘double water exclusion’ hypothesis to refine the O-ring theory by assuming the hot spot itself is water-free. To computationally model a water-free hot spot, we use a biclique pattern that is defined as two maximal groups of residues from two chains in a protein complex holding the property that every residue contacts with all residues in the other group


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    Insufficient prestress will cause cracks in the T beam, which will influence its stiffness and bearing capacity. This paper is devoted to studying the influence of prestress levels on the bearing capacity of T beam, and then judging its working state. A full-scale model experiment is carried out on the 13 meters prestressed concrete T beam. At the same time, a nonlinear finite element model is established and verified. The experimental results show the numerical simulation results are in good agreement with the experimental results. Finally, the finite element model is used to make a simulation of the bearing capacity of T beams under different prestress levels. The mathematical relationship between prestress levels and bearing capacity is obtained based on the results of the finite element model. The relationships between the mid-span deflection and load of the experimental beam are basically the same under different prestress levels, both including three stages: elastic stage, crack development stage and failure stage. With the increase of the prestress levels, the stiffness of the experimental beam before cracking is improved significantly

    Truthful Generalized Linear Models

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    In this paper we study estimating Generalized Linear Models (GLMs) in the case where the agents (individuals) are strategic or self-interested and they concern about their privacy when reporting data. Compared with the classical setting, here we aim to design mechanisms that can both incentivize most agents to truthfully report their data and preserve the privacy of individuals' reports, while their outputs should also close to the underlying parameter. In the first part of the paper, we consider the case where the covariates are sub-Gaussian and the responses are heavy-tailed where they only have the finite fourth moments. First, motivated by the stationary condition of the maximizer of the likelihood function, we derive a novel private and closed form estimator. Based on the estimator, we propose a mechanism which has the following properties via some appropriate design of the computation and payment scheme for several canonical models such as linear regression, logistic regression and Poisson regression: (1) the mechanism is o(1)o(1)-jointly differentially private (with probability at least 1−o(1)1-o(1)); (2) it is an o(1n)o(\frac{1}{n})-approximate Bayes Nash equilibrium for a (1−o(1))(1-o(1))-fraction of agents to truthfully report their data, where nn is the number of agents; (3) the output could achieve an error of o(1)o(1) to the underlying parameter; (4) it is individually rational for a (1−o(1))(1-o(1)) fraction of agents in the mechanism ; (5) the payment budget required from the analyst to run the mechanism is o(1)o(1). In the second part, we consider the linear regression model under more general setting where both covariates and responses are heavy-tailed and only have finite fourth moments. By using an ℓ4\ell_4-norm shrinkage operator, we propose a private estimator and payment scheme which have similar properties as in the sub-Gaussian case.Comment: To appear in The 18th Conference on Web and Internet Economics (WINE 2022

    Spatio-temporal Patterns and Driving Forces of Urban Land Expansion in China during the Economic Reform Era

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    High functional coherence in k-partite protein cliques of protein interaction networks

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    We introduce a new topological concept called k-partite protein cliques to study protein interaction (PPI) networks. In particular, we examine functional coherence of proteins in k-partite protein cliques. A k-partite protein clique is a k-partite maximal clique comprising two or more nonoverlapping protein subsets between any two of which full interactions are exhibited. In the detection of PPI&rsquo;s k-partite maximal cliques, we propose to transform PPI networks into induced K-partite graphs with proteins as vertices where edges only exist among the graph&rsquo;s partites. Then, we present a k-partite maximal clique mining (MaCMik) algorithm to enumerate k-partite maximal cliques from K-partite graphs. Our MaCMik algorithm is applied to a yeast PPI network. We observe that there does exist interesting and unusually high functional coherence in k-partite protein cliques&mdash;most proteins in k-partite protein cliques, especially those in the same partites, share the same functions. Therefore, the idea of k-partite protein cliques suggests a novel approach to characterizing PPI networks, and may help function prediction for unknown proteins.<br /