14,678 research outputs found

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

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 ${\cal O}(h^r)$, $1.5\leq r \leq 2$, 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 ${\cal O}(h)$ 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

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 $(2,0)$ theories

The 6d $(2,0)$ 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 ${\mathcal N}=2$
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

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

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

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

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

In this paper, we confirm the following conjecture of Guo and Schlosser: for
any odd integer $n>1$ and $M=(n+1)/2$ or $n-1$, $\sum_{k=0}^{M}[4k-1]_{q^2}[4k-1]^2\frac{(q^{-2};q^4)_k^4}{(q^4;q^4)_k^4}q^{4k}\equiv
(2q+2q^{-1}-1)[n]_{q^2}^4\pmod{[n]_{q^2}^4\Phi_n(q^2)},$ where
$[n]=[n]_q=(1-q^n)/(1-q),(a;q)_0=1,(a;q)_k=(1-a)(1-aq)\cdots(1-aq^{k-1})$ for
$k\geq 1$ and $\Phi_n(q)$ denotes the $n$-th cyclotomic polynomial

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

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 βMarket volatility modelβ.
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

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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