14,678 research outputs found

    Superconvergence of the Gradient Approximation for Weak Galerkin Finite Element Methods on Nonuniform Rectangular Partitions

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    This article presents a superconvergence for the gradient approximation of the second order elliptic equation discretized by the weak Galerkin finite element methods on nonuniform rectangular partitions. The result shows a convergence of O(hr){\cal O}(h^r), 1.5≀r≀21.5\leq r \leq 2, for the numerical gradient obtained from the lowest order weak Galerkin element consisting of piecewise linear and constant functions. For this numerical scheme, the optimal order of error estimate is O(h){\cal O}(h) for the gradient approximation. The superconvergence reveals a superior performance of the weak Galerkin finite element methods. Some computational results are included to numerically validate the superconvergence theory

    A Holomorphic Embedding Based Continuation Method for Identifying Multiple Power Flow Solutions

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    In this paper, we propose an efficient continuation method for locating multiple power flow solutions. We adopt the holomorphic embedding technique to represent solution curves as holomorphic functions in the complex plane. The holomorphicity, which provides global information of the curve at any regular point, enables large step sizes in the path-following procedure such that non-singular curve segments can be traversed with very few steps. When approaching singular points, we switch to the traditional predictor-corrector routine to pass through them and switch back afterward to the holomorphic embedding routine. We also propose a warm starter when switching to the predictor-corrector routine, i.e. a large initial step size based on the poles of the Pad\'{e} approximation of the derived holomorphic function, since these poles reveal the locations of singularities on the curve. Numerical analysis and experiments on many standard IEEE test cases are presented, along with the comparison to the full predictor-corrector routine, confirming the efficiency of the method.Comment: This paper has been submitted to IEEE Acces

    Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6d (2,0)(2,0) theories

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    The 6d (2,0)(2,0) theory has codimension-one symmetry defects associated to the outer-automorphism group of the underlying ADE Lie algebra. These symmetry defects give rise to twisted sectors of codimension-two defects that are either regular or irregular corresponding to simple or higher order poles of the Higgs field. In this paper, we perform a systematic study of twisted irregular codimension-two defects generalizing our earlier work in the untwisted case. In a class S setup, such twisted defects engineer 4d N=2{\mathcal N}=2 superconformal field theories of the Argyres-Douglas type whose flavor symmetries are (subgroups of) non-simply-laced Lie groups. We propose formulae for the conformal and flavor central charges of these twisted theories, accompanied by nontrivial consistency checks. We also identify the 2d chiral algebra (vertex operator algebra) of a subclass of these theories and determine their Higgs branch moduli space from the associated variety of the chiral algebra.Comment: 43 pages, 19 tables, 3 figure

    Equivariant resolution of singularities in characteristic 0

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    A new proof of equivariant resolution of singularities under a finite group action in characteristic 0 is provided. We assume we know how to resolve singularities without group action. We first prove equivariant resolution of toroidal singularities. Then we reduce the general case to the toroidal case.Comment: Latex2e in compatibility mod

    Learning from Others, Together: Brokerage, Closure and Team Performance

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    Scholarship on teams has focused on the relationship between a team's performance, however defined, and the network structure among team members. For example, Uzzi and Spiro (2005) find that the creative performance of Broadway musical teams depends heavily on the internal cohesion of team members and their past collaborative experience with individuals outside their immediate teams. In other words, team members' internal cohesion and external ties are crucial to the team's success. How, then, do they interact to produce positive performance outcomes? In our work, we separate the proximal causes of tie formation from the proximal determinants of outcomes to determine the mechanism behind this interaction. To examine this puzzle, we examine the performance of national soccer squads over time as a function of changing levels and configurations of brokerage and closure ties formed by players working for professional soccer clubs

    Classification of Argyres-Douglas theories from M5 branes

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    We obtain a large class of new 4d Argyres-Douglas theories by classifying irregular punctures for the 6d (2,0) superconformal theory of ADE type on a sphere. Along the way, we identify the connection between the Hitchin system and three-fold singularity descriptions of the same Argyres-Douglas theory. Other constructions such as taking degeneration limits of the irregular puncture, adding an extra regular puncture, and introducing outer-automorphism twists are also discussed. Later we investigate various features of these theories including their Coulomb branch spectrum and central charges.Comment: 35 pages, 9 tables, 6 figures. v2: minor correction

    Statistical Machine Translation by Generalized Parsing

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    Designers of statistical machine translation (SMT) systems have begun to employ tree-structured translation models. Systems involving tree-structured translation models tend to be complex. This article aims to reduce the conceptual complexity of such systems, in order to make them easier to design, implement, debug, use, study, understand, explain, modify, and improve. In service of this goal, the article extends the theory of semiring parsing to arrive at a novel abstract parsing algorithm with five functional parameters: a logic, a grammar, a semiring, a search strategy, and a termination condition. The article then shows that all the common algorithms that revolve around tree-structured translation models, including hierarchical alignment, inference for parameter estimation, translation, and structured evaluation, can be derived by generalizing two of these parameters -- the grammar and the logic. The article culminates with a recipe for using such generalized parsers to train, apply, and evaluate an SMT system that is driven by tree-structured translation models.Comment: 45 pages, with fixes for generating correct PDF forma

    Proof of a q-supercongruence conjectured by Guo and Schlosser

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    In this paper, we confirm the following conjecture of Guo and Schlosser: for any odd integer n>1n>1 and M=(n+1)/2M=(n+1)/2 or nβˆ’1n-1, βˆ‘k=0M[4kβˆ’1]q2[4kβˆ’1]2(qβˆ’2;q4)k4(q4;q4)k4q4k≑(2q+2qβˆ’1βˆ’1)[n]q24(mod[n]q24Ξ¦n(q2)), \sum_{k=0}^{M}[4k-1]_{q^2}[4k-1]^2\frac{(q^{-2};q^4)_k^4}{(q^4;q^4)_k^4}q^{4k}\equiv (2q+2q^{-1}-1)[n]_{q^2}^4\pmod{[n]_{q^2}^4\Phi_n(q^2)}, where [n]=[n]q=(1βˆ’qn)/(1βˆ’q),(a;q)0=1,(a;q)k=(1βˆ’a)(1βˆ’aq)β‹―(1βˆ’aqkβˆ’1)[n]=[n]_q=(1-q^n)/(1-q),(a;q)_0=1,(a;q)_k=(1-a)(1-aq)\cdots(1-aq^{k-1}) for kβ‰₯1k\geq 1 and Ξ¦n(q)\Phi_n(q) denotes the nn-th cyclotomic polynomial

    Interest-rate models: an extension to the usage in the energy market and pricing exotic energy derivatives.

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    In this thesis, we review various popular pricing models in the interest-rate market. Among these pricing models, we choose the LIBOR Market model (LMM) as the benchmark model. Based on market practice experience, we also develop a pricing model named the β€œMarket volatility model”. By pricing vanilla interest-rate options such as interest-rate caps and swaptions, we compare the performance of our Market volatility model to that of the LMM. It is proved that the Market Volatility model produce comparable results to the LMM, while its computing efficiency largely exceeds that of the LMM. Following the recent rapid development in the commodity market, in particular the energy market, we attempt to extend the use of our proposed Market volatility model from the interest-rate market to the energy market. We prove that the Market Volatility model is capable of pricing various energy derivative under the assumption of absence of the convenience yield. In addition, we propose a new type of exotic energy derivative which has a flexible option structure. This energy derivative is named as the Flex-Asian spread options (FASO). We give examples of different option structures within the FASO framework and use the Market volatility model to generate option prices and greeks for each structure. Although the Market volatility model can be used to price various energy derivatives based on oil/gas contracts, it is not compatible with the structure of one of the most advanced derivatives in the energy market, the storage option. We modify the existing pricing model for storage options and use our own 3D-binomial tree approach to price gas storage contracts. By doing these, we improve the performance of the traditional storage model

    Efficient coordinate-wise leading eigenvector computation

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    We develop and analyze efficient "coordinate-wise" methods for finding the leading eigenvector, where each step involves only a vector-vector product. We establish global convergence with overall runtime guarantees that are at least as good as Lanczos's method and dominate it for slowly decaying spectrum. Our methods are based on combining a shift-and-invert approach with coordinate-wise algorithms for linear regression
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