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

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

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

BEARING CAPACITY OF T BEAM UNDER DIFFERENT PRESTRESS LEVELS: FULL-SCALE EXPERIMENT AND FEM ANALYSIS

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

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 $o(1)$-jointly differentially private (with probability at least $1-o(1)$); (2) it is an $o(\frac{1}{n})$-approximate Bayes Nash equilibrium for a $(1-o(1))$-fraction of agents to truthfully report their data, where $n$ is the number of agents; (3) the output could achieve an error of $o(1)$ to the underlying parameter; (4) it is individually rational for a $(1-o(1))$ fraction of agents in the mechanism ; (5) the payment budget required from the analyst to run the mechanism is $o(1)$. 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 $\ell_4$-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

O Simbolismo em Portugal e na China: Aproximações entre Camilo Pessanha e Dai Wangshu

Esta dissertação tem como objetivo estudar as semelhanças entre o simbolismo ocidental e a poesia clássica chinesa através do estudo dos poemas de Camilo Pessanha e Dai Wangshu. Para tal, a presente dissertação foi estruturada em três capítulos. O primeiro, foca-se na análise de quatro artigos sobre a cultura e a literatura chinesas da autoria de Pessanha, identificando as características da poesia clássica chinesa e apresentando em termos gerais o estilo próprio da corrente do Simbolismo. O segundo, incide sobre a poética específica de ambos os poetas, propondo-se uma análise das características de cada fase de Dai Wangshu. No terceiro capítulo, procede-se a uma análise da escrita simbolista nos dois poetas, elaborando-se um quadro das semelhanças entre os poemas de Camilo Pessanha e a poesia clássica chinesa, e entre a revolucionária carreira de Dai Wangshu e todas as transformações que o poeta acompanhou.This dissertation aims to study the similarities between Western symbolism and classical Chinese poetry through the study of the poems of Camilo Pessanha and Dai Wangshu. For this, this dissertation was structured in three chapters. The first focuses on the analysis of four articles about Chinese culture and literature written by Pessanha, identifying the characteristics of classical Chinese poetry and presenting in general terms the style of symbolism. The second, focuses on the specific poetics of both poets, proposing an analysis of the characteristics of each phase of Dai Wangshu. In the third chapter, an analysis of the symbolist writing in the two poets’ proceeds, elaborating a picture of the similarities between the poems of Camilo Pessanha and classical Chinese poetry, and between the revolutionary career of Dai Wangshu and all the transformations that accompanied the poet

Fair Division of Mixed Divisible and Indivisible Goods

We study the problem of fair division when the resources contain both divisible and indivisible goods. Classic fairness notions such as envy-freeness (EF) and envy-freeness up to one good (EF1) cannot be directly applied to the mixed goods setting. In this work, we propose a new fairness notion envy-freeness for mixed goods (EFM), which is a direct generalization of both EF and EF1 to the mixed goods setting. We prove that an EFM allocation always exists for any number of agents. We also propose efficient algorithms to compute an EFM allocation for two agents and for $n$ agents with piecewise linear valuations over the divisible goods. Finally, we relax the envy-free requirement, instead asking for $\epsilon$-envy-freeness for mixed goods ($\epsilon$-EFM), and present an algorithm that finds an $\epsilon$-EFM allocation in time polynomial in the number of agents, the number of indivisible goods, and $1/\epsilon$.Comment: Appears in the 34th AAAI Conference on Artificial Intelligence (AAAI), 202