数学汇总学术速递[1.10]
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math数学汇总，共计102篇
【1】 QN Optimization with Hessian Sample
标题：基于黑森样本的QN优化
作者：Joy Azzam,Daniel Henderson,Benjamin Ong,Allan Struthers
摘要：This article explores how to effectively incorporate curvature information
generated using SIMD-parallel forward-mode Algorithmic Differentiation (AD)
into unconstrained Quasi-Newton (QN) minimization of a smooth objective
function, $f$. Specifically, forward-mode AD can be used to generate block
Hessian samples $Y=\nabla^2 f(x)\,S$ whenever the gradient is evaluated. Block
QN algorithms then update approximate inverse Hessians, $H_k \approx \nabla^2
f(x_k)$, with these Hessian samples. Whereas standard line-search based BFGS
algorithms carefully filter and correct secant-based approximate curvature
information to maintain positive definite approximations, our algorithms
directly incorporate Hessian samples to update indefinite inverse Hessian
approximations without filtering. The sampled directions supplement the
standard QN two-dimensional trust-region sub-problem to generate a moderate
dimensional subproblem which can exploit negative curvature. The resulting
quadratically-constrained quadratic program is solved accurately with a
generalized eigenvalue algorithm and the step advanced using standard trust
region step acceptance and radius adjustments. The article aims to avoid serial
bottlenecks, exploit accurate positive and negative curvature information, and
conduct a preliminary evaluation of selection strategies for $S$.
【2】 Recovery of wave speeds and density of mass across a heterogeneous smooth interface from acoustic and elastic wave reflection operators
标题：用声波和弹性波反射算子恢复非均匀光滑界面上的波速和质量密度
作者：Sombuddha Bhattacharyya,Maarten V. de Hoop,Vitaly Katsnelson,Gunther Uhlmann
备注：submitted for journal publication 10/21/2021; 42 pages
摘要：We revisit the problem of recovering wave speeds and density across a curved
interface from reflected wave amplitudes. Such amplitudes have been exploited
for decades in (exploration) seismology in this context. However, the analysis
in seismology has been based on linearization and mostly flat interfaces. Here,
we present a nonlinear analysis allowing curved interfaces, establish
uniqueness and provide a reconstruction, while making the notion of amplitude
precise through a procedure rooted in microlocal analysis.
【3】 Wavenumber-explicit hp-FEM analysis for Maxwell's equations with impedance boundary conditions
标题：阻抗边界条件下麦克斯韦方程的波数显式hp-FEM分析
作者：Jens M. Melenk,Stefan A. Sauter
备注：80 pages, 6 figures
摘要：The time-harmonic Maxwell equations at high wavenumber k in domains with an
analytic boundary and impedance boundary conditions are considered. A
wavenumber-explicit stability and regularity theory is developed that
decomposes the solution into a part with finite Sobolev regularity that is
controlled uniformly in k and an analytic part. Using this regularity,
quasi-optimality of the Galerkin discretization based on Nedelec elements of
order p on a mesh with mesh size h is shown under the k-explicit scale
resolution condition that a) kh/p is sufficient small and b) p/\ln k is bounded
from below.
【4】 Completeness of derived interleaving distances and sheaf quantization of non-smooth objects
标题：导出交织距离的完备性与非光滑物体的束量化
作者：Tomohiro Asano,Yuichi Ike
备注：33 pages, 1 figure, comments are welcome
摘要：We investigate sheaf-theoretic methods to deal with non-smooth objects in
symplectic geometry. We show the completeness of a derived category of sheaves
with respect to the interleaving-like distance and construct a sheaf
quantization of a hameomorphism. We also develop Lusternik-Schnirelmann theory
in the microlocal theory of sheaves. With these new tools, we prove an
Arnold-type theorem for the image of the zero-section under a hameomorphism by
a purely sheaf-theoretic method.
【5】 Summation formulae for quadrics
标题：二次曲面的求和公式
作者：Jayce R. Getz
摘要：We prove a Poisson summation formula for the zero locus of a quadratic form
in an even number of variables with no assumption on the support of the
functions involved. The key novelty in the formula is that all "boundary terms"
are given either by constants or sums over smaller quadrics related to the
original quadric. We also discuss the link with the classical problem of
estimating the number of solutions of a quadratic form in an even number of
variables. To prove the summation formula we compute (the Arthur truncated)
theta lift of the trivial representation of $\mathrm{SL}_2(\mathbb{A}_F)$. As
previously observed by Ginzburg, Rallis, and Soudry, this is an analogue for
orthogonal groups on vector spaces of even dimension of the global
Schr\"odinger representation of the metaplectic group.
【6】 The Inverse of the Incidence Matrix of a Unicyclic Graph
标题：单圈图的关联矩阵的逆
作者：Ryan Hessert,Sudipta Mallik
摘要：The vertex-edge incidence matrix of a (connected) unicyclic graph G is a
square matrix which is invertible if and only if the cycle of G is an odd
cycle. A combinatorial formula of the inverse of the incidence matrix of an odd
unicyclic graph was known. A combinatorial formula of the Moore-Penrose inverse
of the incidence matrix of an even unicyclic graph is presented solving an open
problem.
【7】 Incidence and Laplacian matrices of wheel graphs and their inverses
标题：轮图及其逆图的关联矩阵和拉普拉斯矩阵
作者：Jerad Ipsen,Sudipta Mallik
摘要：It has been an open problem to find the Moore-Penrose inverses of the
incidence, Laplacian, and signless Laplacian matrices of families of graphs
except trees and unicyclic graphs. Since the inverse formulas for an odd
unicyclic graph and an even unicyclic graph are quite different, we consider
wheel graphs as they are formed from odd or even cycles. In this article solve
the open problem for wheel graphs. This work has an interesting connection to
inverses of circulant matrices.
【8】 Coarse Geometry of Pure Mapping Class Groups of Infinite Graphs
标题：无限图的纯映射类群的粗几何
作者：George Domat,Hannah Hoganson,Sanghoon Kwak
备注：41 pages, 10 figures
摘要：We discuss the large-scale geometry of pure mapping class groups of locally
finite, infinite graphs, motivated from recent work by Algom-Kfir--Bestvina and
the work of Mann--Rafi on the large-scale geometry of mapping class groups of
infinite-type surfaces. Using the framework of Rosendal for coarse geometry of
non-locally compact groups, we classify when the pure mapping class group of a
locally finite, infinite graph is globally coarsely bounded (an analog of
compact) and when it is locally coarsely bounded (an analog of locally
compact). Our techniques also give lower bounds on the first integral
cohomology of the pure mapping class group for some graphs and show that some
of these groups have continuous actions on simplicial trees.
【9】 Exponential multiple mixing for commuting automorphisms of a nilmanifold
标题：零流形交换自同构的指数多重混合
作者：Timothée Bénard,Péter P. Varjú
备注：13 pages
摘要：Let $l\in \mathbb{N}_{\geq 1}$ and $\alpha : \mathbb{Z}^l\rightarrow
\text{Aut}(\mathscr{N})$ be an action of $\mathbb{Z}^l$ by automorphisms on a
compact nilmanifold $\mathscr{N}$. We assume the action of every $\alpha(z)$ is
ergodic for $z\in \mathbb{Z}^l\smallsetminus\{0\}$ and show that $\alpha$
satisfies exponential $n$-mixing for any integer $n\geq 2$. This extends
results of Gorodnik and Spatzier [Acta Math., 215 (2015)].
【10】 The Persistence Landscapes of Affine Fractals
标题：仿射分形的持久景观
作者：Michael J. Catanzaro,Lee Przybylski,Eric S. Weber
备注：32 pages, 5 figures. Comments welcome
摘要：We develop a method for calculating the persistence landscapes of affine
fractals using the parameters of the corresponding transformations. Given an
iterated function system of affine transformations that satisfies a certain
compatibility condition, we prove that there exists an affine transformation
acting on the space of persistence landscapes which intertwines the action of
the iterated function system. This latter affine transformation is a strict
contraction and its unique fixed point is the persistence landscape of the
affine fractal. We present several examples of the theory as well as confirm
the main results through simulations.
【11】 Multiplication and convolution topological algebras in spaces of $ω$-ultradifferentiable functions of Beurling type
标题：$ω$-超可微Beuring型函数空间中的乘法和卷积拓扑代数
作者：Angela A. Albanese,Claudio Mele
摘要：We determine multiplication and convolution topological algebras for classes
of $\omega$-ultradifferentiable functions of Beurling type. Hypocontinuous and
discontinuous mappings are investigated. It is also proved that the pre-dual
$\mathcal{O}_{C,\omega}(\mathbb{R}^N)$ of the space of convolutors of
$\mathcal{S}_\omega(\mathbb{R}^N)$ is a complete Montel space.
【12】 Standard Young tableaux and lattice paths
标题：标准Young画面和晶格路径
作者：Shaun V. Ault
备注：9 pages, 3 figures
摘要：Using lattice path counting arguments, we reproduce a well known formula for
the number of standard Young tableaux. We also produce an interesting new
formula for tableaux of height $\leq 3$ using the Fourier methods of Ault and
Kicey.
【13】 Machine-learning-based arc selection for constrained shortest path problems in column generation
标题：基于机器学习的列生成约束最短路径问题的圆弧选择
作者：Mouad Morabit,Guy Desaulniers,Andrea Lodi
摘要：Column generation is an iterative method used to solve a variety of
optimization problems. It decomposes the problem into two parts: a master
problem, and one or more pricing problems (PP). The total computing time taken
by the method is divided between these two parts. In routing or scheduling
applications, the problems are mostly defined on a network, and the PP is
usually an NP-hard shortest path problem with resource constraints. In this
work, we propose a new heuristic pricing algorithm based on machine learning.
By taking advantage of the data collected during previous executions, the
objective is to reduce the size of the network and accelerate the PP, keeping
only the arcs that have a high chance to be part of the linear relaxation
solution. The method has been applied to two specific problems: the vehicle and
crew scheduling problem in public transit and the vehicle routing problem with
time windows. Reductions in computational time of up to 40% can be obtained.
【14】 Semilinear Li & Yau inequalities
标题：半线性Li&Yau不等式
作者：Daniele Castorina,Giovanni Catino,Carlo Mantegazza
摘要：We derive an adaptation of Li & Yau estimates for positive solutions of
semilinear heat equations on Riemannian manifolds with nonnegative Ricci
tensor. We then apply these estimates to obtain a Harnack inequality and to
discuss monotonicity, convexity, decay estimates and triviality of ancient and
eternal solutions.
【15】 Singularity models in the three-dimensional Ricci flow
标题：三维Ricci流中的奇点模型
作者：S. Brendle
备注：This is survey paper which will appear in the KIAS Expositions
摘要：The Ricci flow is a natural evolution equation for Riemannian metrics on a
given manifold. The main goal is to understand singularity formation. In his
spectacular 2002 breakthrough, Perelman achieved a qualitative understanding of
singularity formation in dimension $3$. More precisely, Perelman showed that
every finite-time singularity to the Ricci flow in dimension $3$ is modeled on
an ancient $\kappa$-solution. Moreover, Perelman proved a structure theorem for
ancient $\kappa$-solutions in dimension $3$.
In this survey, we will discuss recent developments which have led to a
complete classification of all the singularity models in dimension $3$.
Moreover, we give an alternative proof of the classification of noncollapsed
steady gradient Ricci solitons in dimension $3$ (originally proved by the
author in 2012).
【16】 Four Blocks Cycles C(k,1,1,1) in Digraphs
标题：有向图中的四块圈C(k，1，1，1)
作者：Zahraa Mohsen
摘要：A four blocks cycle C(k1,k2,k3,k4) is an oriented cycle formed by the union
of four internally disjoint directed paths of lengths k1,k2,k3 and k4
respectively. El Mniny proved that if D is a digraph having a spanning out-tree
T with no subdivisions of C(k, 1, 1, 1), then the chromatic number of D is at
most 8^{3}k. In this paper, we will improve this bound to 18k.
【17】 Skew Dyck paths with catastrophes
标题：具有灾变的偏向Dyck路径
作者：Helmut Prodinger
摘要：Skew Dyck paths are like Dyck paths, but an additional south-west step
$(-1,-1)$ is allowed, provided that the path does not intersect itself. Lattice
paths with catastrophes can drop from any level to the origin in just one step.
We combine these two ideas. The analysis is strictly based on generating
functions, and the kernel method is used.
【18】 The Efficiency of the ANS Entropy Encoding
作者：Dmitry Kosolobov
备注：15 pages, 5 figures, 2 algorithms
摘要：The Asymmetric Numeral Systems (ANS) is a class of entropy encoders by Duda
that had an immense impact on the data compression, substituting arithmetic and
Huffman coding. The optimality of ANS was studied by Duda et al. but the
precise asymptotic behaviour of its redundancy (in comparison to the entropy)
was not completely understood. In this paper we establish an optimal bound on
the redundancy for the tabled ANS (tANS), the most popular ANS variant. Given a
sequence $a_1,\ldots,a_n$ of letters from an alphabet $\{0,\ldots,\sigma-1\}$
such that each letter $a$ occurs in it $f_a$ times and $n=2^r$, the tANS
encoder using Duda's ``precise initialization'' to fill tANS tables transforms
this sequence into a bit string of length (frequencies are not included in the
encoding size): $$ \sum\limits_{a\in
[0..\sigma)}f_a\cdot\log\frac{n}{f_a}+O(\sigma+r), $$ where $O(\sigma + r)$ can
be bounded by $\sigma\log e+r$. The $r$-bit term is an encoder artifact
indispensable to ANS; the rest incurs a redundancy of $O(\frac{\sigma}{n})$
bits per letter. We complement this bound by a series of examples showing that
an $\Omega(\sigma+r)$ redundancy is necessary when $\sigma > n/3$, where
$\Omega(\sigma + r)$ is at least $\frac{\sigma-1}{4}+r-2$. We argue that
similar examples exist for any methods that distribute letters in tANS tables
using only the knowledge about frequencies. Thus, we refute Duda's conjecture
that the redundancy is $O(\frac{\sigma}{n^2})$ bits per letter.
We also propose a new variant of range ANS (rANS), called rANS with fixed
accuracy, that is parameterized by $k \ge 1$. In this variant the integer
division, which is unavoidable in rANS, is performed only in cases when its
result belongs to $[2^k..2^{k+1})$. Hence, the division can be computed by
faster methods provided $k$ is small. We bound the redundancy for the rANS with
fixed accuracy $k$ by $\frac{n}{2^k-1}\log e+r$.
【19】 The automorphism groups of Artin groups of edge-separated CLTTF graphs
标题：边分离CLTTF图的Artin群的自同构群
作者：Byung Hee An,Youngjin Cho
备注：30 pages, 6 figures
摘要：We provide an explicit presentation of the automorphism group of an
edge-separated CLTTF Artin group.
【20】 On the Distance Spectra of Extended Double Stars
标题：关于扩展双星的距离谱
作者：Anuj Sakarda,Jerry Tan,Armaan Tipirneni
备注：13 pages, 13 figures, arXiv:1307.5931, arXiv:1606.07551, To be presented at JMM 2022
摘要：The distance matrix of a connected graph is defined as the matrix in which
the entries are the pairwise distances between vertices. The distance spectrum
of a graph is the set of eigenvalues of its distance matrix. A graph is said to
be determined by its distance spectrum if there does not exist a non-isomorphic
graph with the same spectrum. The question of which graphs are determined by
their spectrum has been raised in the past, but it remains largely unresolved.
In this paper, we prove that extended double stars are determined by their
distance spectra.
【21】 Cauchy, normal and correlations versus heavy tails
标题：柯西，正态和相关性与重尾
作者：Hui Xu,Joel Cohen,Richard Davis,Gennady Samorodnitsky
摘要：A surprising result of Pillai and Meng (2016) showed that a transformation
$\sum_{j=1}^n w_j X_j/Y_j$ of two iid centered normal random vectors,
$(X_1,\ldots, X_n)$ and $(Y_1,\ldots, Y_n)$, $n>1$, for any weights $0\leq
w_j\leq 1$, $ j=1,\ldots, n$, $\sum_{j=1}^n w_j=1$, has a Cauchy distribution
regardless of any correlations within the normal vectors. The correlations
appear to lose out in the competition with the heavy tails. To clarify how
extensive this phenomenon is, we analyze two other transformations of two iid
centered normal random vectors. These transformations are similar in spirit to
the transformation considered by Pillai and Meng (2016). One transformation
involves absolute values: $\sum_{j=1}^n w_j X_j/|Y_j|$. The second involves
randomly stopped Brownian motions: $\sum_{j=1}^n w_j X_j\bigl(Y_j^{-2}\bigr)$,
where $\bigl\{\bigl( X_1(t),\ldots, X_n(t)\bigr), \, t\geq 0\bigr\},\ n>1,$ is
a Brownian motion with positive variances; $(Y_1,\ldots, Y_n)$ is a centered
normal random vector with the same law as $( X_1(1),\ldots, X_n(1))$ and
independent of it; and $X(Y^{-2})$ is the value of the Brownian motion $X(t)$
evaluated at the random time $t=Y^{-2}$. All three transformations result in a
Cauchy distribution if the covariance matrix of the normal components is
diagonal, or if all the correlations implied by the covariance matrix equal 1.
However, while the transformation Pillai and Meng (2016) considered produces a
Cauchy distribution regardless of the normal covariance matrix. the
transformations we consider here do not always produce a Cauchy distribution.
The correlations between jointly normal random variables are not always
overwhelmed by the heaviness of the marginal tails. The mysteries of the
connections between normal and Cauchy laws remain to be understood.
【22】 TOWER-Complete Problems in Contraction-Free Substructural Logics
标题：无收缩子结构逻辑中的塔式完备性问题
作者：Hiromi Tanaka
备注：Draft
摘要：We investigate the computational complexity of a family of substructural
logics with exchange and weakening but without contraction. With the aid of the
techniques provided by Lazi\'c and Schmitz (2015), we show that the
deducibility problem for full Lambek calculus with exchange and weakening
($\mathbf{FL}_{\mathbf{ew}}$) is TOWER-complete, where TOWER is one of the
non-elementary complexity classes introduced by Schmitz (2016). The same
complexity result holds even for deducibility in BCK-logic, i.e., the
implicational fragment of $\mathbf{FL}_{\mathbf{ew}}$. We furthermore show the
TOWER-completeness of the provability problem for elementary affine logic,
which was proved to be decidable by Dal Lago and Martini (2004).
【23】 An efficient and easy-to-extend Matlab code of the Moving Morphable Component (MMC) method for three-dimensional topology optimization
标题：一种高效、易扩展的移动可变形分量(MMC)三维拓扑优化Matlab代码
作者：Zongliang Du,Tianchen Cui,Chang Liu,Weisheng Zhang,Yilin Guo,Xu Guo
摘要：Explicit topology optimization methods have received ever-increasing interest
in recent years. In particular, a 188-line Matlab code of the two-dimensional
(2D) Moving Morphable Component (MMC)-based topology optimization method was
released by Zhang et al. (Struct Multidiscip Optim 53(6):1243-1260, 2016). The
present work aims to propose an efficient and easy-to-extend 256-line Matlab
code of the MMC method for three-dimensional (3D) topology optimization
implementing some new numerical techniques. To be specific, by virtue of the
function aggregation technique, accurate sensitivity analysis, which is also
easy-to-extend to other problems, is achieved. Besides, based on an efficient
loading path identification algorithm, the degrees of freedoms (DOFs) not
belonging to the loading path are removed in finite element analysis (FEA),
which significantly accelerates the optimization process. As a result, compared
to the corresponding 188-line 2D code, the performance of the optimization
results, the computational efficiency of FEA, and the convergence rate and the
robustness of optimization process are greatly improved. For the sake of
completeness, a refined 218-line Matlab code implementing the 2D-MMC method is
also provided.
【24】 de Finetti-type theorems on quasi-local algebras and infinite Fermi tensor products
标题：关于拟局部代数和无限费米张量积的de Finetti型定理
作者：Vitonofrio Crismale,Stefano Rossi,Paola Zurlo
备注：31 pages
摘要：Local actions of $\mathbb{P}_\mathbb{N}$, the group of finite permutations on
$\mathbb{N}$, on quasi-local algebras are defined and proved to be
$\mathbb{P}_\mathbb{N}$-abelian. It turns out that invariant states under local
actions are automatically even, and extreme invariant states are strongly
clustering. Tail algebras of invariant states are shown to obey a form of the
Hewitt and Savage theorem, in that they coincide with the fixed-point von
Neumann algebra. Infinite graded tensor products of $C^*$-algebras, which
include the CAR algebra, are then addressed as particular examples of
quasi-local algebras acted upon $\mathbb{P}_\mathbb{N}$ in a natural way.
Extreme invariant states are characterized as infinite products of a single
even state, and a de Finetti theorem is established. Finally, infinite products
of factorial even states are shown to be factorial by applying a twisted
version of the tensor product commutation theorem, which is also derived here.
【25】 Hardy inequalities for magnetic $p$-Laplacians
标题：磁性$p$-Laplacian的Hardy不等式
作者：Cristian Cazacu,David Krejcirik,Ari Laptev
备注：20 pages
摘要：Improved Hardy inequalities for the $p$-Laplacian due to adding magnetic
fields are established, while other expected results are stated as conjectures.
Some general $L^p$ magnetic-free Hardy inequalities in the spirit of Allegretto
and Huang [Nonlinear Anal. 32 (1998)] are also considered.
【26】 Neighborly partitions and the numerators of Rogers-Ramanujan identities
标题：邻域划分与Rogers-Ramanujan恒等式的分子
作者：Zahraa Mohsen,Hussein Mourtada
摘要：We prove two partition identities which are dual to the Rogers-Ramanujan
identities. These identities are inspired by (and proved using) a
correspondence between three kinds of objects: a new type of partitions
(neighborly partitions), monomial ideals and some infinite graphs.
【27】 On The Decoding Error Weight of One or Two Deletion Channels
作者：Omer Sabary,Daniella Bar-Lev,Yotam Gershon,Alexander Yucovich,Eitan Yaakobi
备注：arXiv admin note: text overlap with arXiv:2001.05582
摘要：This paper tackles two problems that are relevant to coding for insertions
and deletions. These problems are motivated by several applications, among them
is reconstructing strands in DNA-based storage systems. Under this paradigm, a
word is transmitted over some fixed number of identical independent channels
and the goal of the decoder is to output the transmitted word or some close
approximation of it. The first part of this paper studies the deletion channel
that deletes a symbol with some fixed probability $p$, while focusing on two
instances of this channel. Since operating the maximum likelihood (ML) decoder
in this case is computationally unfeasible, we study a slightly degraded
version of this decoder for two channels and its expected normalized distance.
We identify the dominant error patterns and based on these observations, it is
derived that the expected normalized distance of the degraded ML decoder is
roughly $\frac{3q-1}{q-1}p^2$, when the transmitted word is any $q$-ary
sequence and $p$ is the channel's deletion probability. We also study the cases
when the transmitted word belongs to the Varshamov Tenengolts (VT) code or the
shifted VT code. Additionally, the insertion channel is studied as well as the
case of two insertion channels. These theoretical results are verified by
corresponding simulations. The second part of the paper studies optimal
decoding for a special case of the deletion channel, the $k$-deletion channel,
which deletes exactly $k$ symbols of the transmitted word uniformly at random.
In this part, the goal is to understand how an optimal decoder operates in
order to minimize the expected normalized distance. A full characterization of
an efficient optimal decoder for this setup, referred to as the maximum
likelihood* (ML*) decoder, is given for a channel that deletes one or two
symbols.
【28】 Triangles in intersecting families
标题：相交族中的三角形
作者：Dániel T. Nagy,Balázs Patkós
备注：7 pages
摘要：We prove the following the generalized Tur\'an type result. A collection
$\mathcal{T}$ of $r$ sets is an $r$-triangle if for every
$T_1,T_2,\dots,T_{r-1}\in \mathcal{T}$ we have
$\cap_{i=1}^{r-1}T_i\neq\emptyset$, but $\cap_{T\in \mathcal{T}}T$ is empty. A
family $\mathcal{F}$ of sets is $r$-wise intersecting if for any
$F_1,F_2,\dots,F_r\in \mathcal{F}$ we have $\cap_{i=1}^rF_i\neq \emptyset$ or
equivalently if $\mathcal{F}$ does not contain any $m$-triangle for
$m=2,3,\dots,r$. We prove that if $n\ge n_0(r,k)$, then the $r$-wise
intersecting family $\mathcal{F}\subseteq \binom{[n]}{k}$ containing the most
number of $(r+1)$-triangles is isomorphic to $\{F\in \binom{[n]}{k}:|F\cap
[r+1]|\ge r\}$.
【29】 Analytical calculation formulas for capacities of classical and classical-quantum channels
作者：Masahito Hayashi
摘要：We derive an analytical calculation formula for the channel capacity of a
classical channel without any iteration while its existing algorithms require
iterations and the number of iteration depends on the required precision level.
Hence, our formula is its first analytical formula without any iteration. We
apply the obtained formula to examples and see how the obtained formula works
in these examples. Then, we extend it to the channel capacity of a
classical-quantum (cq-) channel. Many existing studies proposed algorithms for
a cq-channel and all of them require iterations. Our extended analytical
algorithm have also no iteration and output the exactly optimum values.
【30】 Bregman divergence based em algorithm and its application to classical and quantum rate distortion theory
作者：Masahito Hayashi
摘要：We formulate em algorithm in the framework of Bregman divergence, which is a
general problem setting of information geometry. That is, we address the
minimization problem of the Bregman divergence between an exponential subfamily
and a mixture subfamily in a Bregman divergence system. Then, we show the
convergence and its speed under several conditions. We apply this algorithm to
rate distortion and its variants including the quantum setting, and show the
usefulness of our general algorithm.
【31】 Graded irreducible representations of Leavitt path algebras: a new type and complete classification
标题：Leavitt路代数的分次不可约表示：一种新的完全分类
作者：Lia Vas
摘要：We present a new class of graded irreducible representations of a Leavitt
path algebra. This class is new in the sense that its representation space is
not isomorphic to any of the existing simple Chen modules. The corresponding
graded simple modules complete the list of Chen modules which are graded,
creating an exhaustive class: the annihilator of any graded simple module is
equal to the annihilator of either a graded Chen module or a module of this new
type.
Our characterization of graded primitive ideals of a Leavitt path algebra in
terms of the properties of the underlying graph is the main tool for proving
the completeness of such classification. We also point out a problem with the
characterization of primitive ideals of a Leavitt path algebra in [K. M.
Rangaswamy, Theory of prime ideals of Leavitt path algebras over arbitrary
graphs, J. Algebra 375 (2013), 73 -- 90].
【32】 Indefinite least squares with a quadratic constraint
标题：带二次约束的不定最小二乘法
作者：Santiago Gonzalez Zerbo,Alejandra Maestripieri,Francisco Martínez Pería
备注：32 pages. Comments are welcomed!
摘要：An abstract indefinite least squares problem with a quadratic constraint is
considered. This is a quadratic programming problem with one quadratic equality
constraint, where neither the objective nor the constraint are convex
functions. Necessary and sufficient conditions are found for the existence of
solutions.
【33】 Linear pencils and quadratic programming problems with a quadratic constraint
标题：带二次约束的线性铅笔和二次规划问题
作者：Santiago Gonzalez Zerbo,Alejandra Maestripieri,Francisco Martínez Pería
备注：24 pages. Comments are welcomed!
摘要：Given bounded selfadjoint operators $A$ and $B$ acting on a Hilbert space
$\mathcal{H}$, consider the linear pencil $P(\lambda)=A+\lambda B$,
$\lambda\in\mathbb{R}$. The set of parameters $\lambda$ such that $P(\lambda)$
is a positive (semi)definite operator is characterized. These results are
applied to solving a quadratic programming problem with an equality quadratic
constraint (or a QP1EQC problem).
【34】 Bases for infinite dimensional simple $\mathfrak{osp}(1|2n)$-modules respecting the branching $\mathfrak{osp}(1|2n)\supset \mathfrak{gl}(n)$
作者：Asmus K. Bisbo,Joris Van der Jeugt
备注：31 pages
摘要：We study the effects of the branching $\mathfrak{osp}(1|2n)\supset
\mathfrak{gl}(n)$ on a particular class of simple infinite-dimensional
$\mathfrak{osp}(1|2n)$-modules $L(p)$ characterized by a positive integer $p$.
In the first part we use combinatorial methods such as Young tableaux and Young
subgroups to construct a new basis for $L(p)$ that respects this branching and
we express the basis elements explicitly in two distinct ways. First as
monomials of negative root vectors of $\mathfrak{gl}(n)$ acting on the
$\mathfrak{gl}(n)$-highest weight vectors in $L(p)$ and then as polynomials in
the generators of $\mathfrak{osp}(1|2n)$ acting on the
$\mathfrak{osp}(1|2n)$-lowest weight vector in $L(p)$. In the second part we
use extremal projectors and the theory of Mickelsson-Zhelobenko algebras to
give new explicit constructions of raising and lowering operators related to
the branching $\mathfrak{osp}(1|2n)\supset \mathfrak{gl}(n)$. We use the
raising operators to give new expressions for the elements of the
Gel'fand-Zetlin basis for $L(p)$ as monomials of operators from
$U(\mathfrak{osp}(1|2n))$ acting on the $\mathfrak{osp}(1|2n)$-lowest weight
vector in $L(p)$. We observe that the Gel'fand-Zetlin basis for $L(p)$ is
related to the basis constructed earlier in the paper by a triangular
transition matrix. We end the paper with a detailed example treating the case
$n=3$.
【35】 On some problems regarding distance-balanced graphs
标题：关于距离平衡图的几个问题
作者：Blas Fernandez,Ademir Hujdurovic
备注：16 pages
摘要：A graph $\Gamma$ is said to be distance-balanced if for any edge $uv$ of
$\Gamma$, the number of vertices closer to $u$ than to $v$ is equal to the
number of vertices closer to $v$ than to $u$, and it is called nicely
distance-balanced if in addition this number is independent of the chosen edge
$uv$. A graph $\Gamma$ is said to be strongly distance-balanced if for any edge
$uv$ of $\Gamma$ and any integer $k$, the number of vertices at distance $k$
from $u$ and at distance $k+1$ from $v$ is equal to the number of vertices at
distance $k+1$ from $u$ and at distance $k$ from $v$.
In this paper we answer an open problem posed by Kutnar and Miklavi\v{c}
[European J. Combin. 39 (2014), 57-67] by constructing several infinite
families of nonbipartite nicely distance-balanced graphs which are not strongly
distance-balanced. We disprove a conjecture regarding characterization of
strongly distance-balanced graphs posed by Balakrishnan et al. [European J.
Combin. 30 (2009), 1048-1053] by providing infinitely many counterexamples, and
answer an open question posed by Kutnar et al. in [Discrete Math. 306 (2006),
1881-1894] regarding existence of semisymmetric distance-balanced graphs which
are not strongly distance-balanced by providing an infinite family of such
examples. We also show that for a graph $\Gamma$ with $n$ vertices and $m$
edges it can be checked in $O(mn)$ time if $\Gamma$ is strongly-distance
balanced and in $O(m^2)$ time if $\Gamma$ is nicely distance-balanced.
【36】 An Adaptive Penalty Method for Inequality Constrained Minimization Problems
标题：不等式约束极小化问题的一种自适应惩罚方法
作者：Wietse M. Boon,Jan M. Nordbotten
备注：None
摘要：The primal-dual active set method is observed to be the limit of a sequence
of penalty formulations. Using this perspective, we propose a penalty method
that adaptively becomes the active set method as the residual of the iterate
decreases. The adaptive penalty method (APM) therewith combines the main
advantages of both methods, namely the ease of implementation of penalty
methods and the exact imposition of inequality constraints inherent to the
active set method. The scheme can be considered a quasi-Newton method in which
the Jacobian is approximated using a penalty parameter. This spatially varying
parameter is chosen at each iteration by solving an auxiliary problem.
【37】 Fano manifolds with Lefschetz defect 3
标题：Lefschetz亏数为3的Fano流形
作者：C. Casagrande,E. A. Romano,S. A. Secci
备注：30 pages, 2 figures
摘要：Let X be a smooth, complex Fano variety, and delta(X) its Lefschetz defect.
It is known that if delta(X) is at least 4, then X is isomorphic to a product
SxT, where dim T=dim X-2. In this paper we prove a structure theorem for the
case where delta(X)=3. We show that there exists a smooth Fano variety T with
dim T=dim X-2 such that X is obtained from T with two possible explicit
constructions; in both cases there is a P^2-bundle Z over T such that X is the
blow-up of Z along three pairwise disjoint smooth, irreducible, codimension 2
subvarieties. Then we apply the structure theorem to Fano 4-folds, to the case
where X has Picard number 5, and to Fano varieties having an elementary
divisorial contraction sending a divisor to a curve. In particular we complete
the classification of Fano 4-folds with delta(X)=3.
【38】 Non-linear heat equation on the Hyperbolic space: Global existence and finite-time Blow-up
标题：双曲空间上非线性热方程的整体存在性和有限时间爆破
作者：Debdip Ganguly,Debabrata Karmakar,Saikat Mazumdar
摘要：We consider the following Cauchy problem for the semi linear heat equation on
the hyperbolic space:
\begin{align}\label{abs:eqn} \left\{\begin{array}{ll}
\partial_{t}u=\Delta_{\mathbb{H}^{n}} u+ f(u, t) &\hbox{ in }~
\mathbb{H}^{n}\times (0, T),\\ \\ \quad u =u_{0} &\hbox{ in }~
\mathbb{H}^{n}\times \{0\}. \end{array}\right. \end{align}
We study Fujita phenomena for the non-negative initial data $u_0$ belonging
to $C(\mathbb{H}^{n}) \cap L^{\infty}(\mathbb{H}^{n})$ and for different
choices of $f$ of the form $f(u,t) = h(t)g(u).$ It is well-known that for power
nonlinearities in $u,$ the power weight $h(t) = t^q$ is sub-critical in the
sense that non-negative global solutions exist for small initial data. On the
other hand, it exhibits Fujita phenomena for the exponential weight $h(t) =
e^{\mu t},$ i.e. there exists a critical exponent $\mu^*$ such that if $\mu >
\mu^*$ then all non-negative solutions blow-up in finite time and if $\mu \leq
\mu^*$ there exists non-negative global solutions for small initial data. One
of the main objectives of this article is to find an appropriate nonlinearity
in $u$ so that the above mentioned Cauchy problem with the power weight $h(t) =
t^q$ does exhibit Fujita phenomena. In the remaining part of this article, we
study Fujita phenomena for exponential nonlinearity in $u.$ We further
generalize some of these results to Cartan-Hadamard manifolds.
【39】 An extension of an asymptotic result of Tricomi concerning a definite integral
标题：Tricomi关于定积分的一个渐近结果的推广
作者：R B Paris
备注：8 pages, 0 figures
摘要：We consider the expansion of an integral considered by F.G. Tricomi given by
\[\int_{-\infty}^\infty x e^{-x^2}(\frac{1}{2}+\frac{1}{2}\mbox{erf}\,x)^{m}
dx\] as $m\to\infty$. The procedure involves a suitable change of variable and
the inversion of the complementary error function $\mbox{erfc}\,x$. Numerical
results are presented to demonstrate the accuracy of the expansion.
A second part examines an extension of an integral arising in airfoil theory.
【40】 On the theory of generalized Ulrich modules
标题：关于广义Ulrich模的理论
作者：Cleto B. Miranda-Neto,Douglas S. Queiroz,Thyago S. Souza
备注：17 pages
摘要：In this paper we further develop the theory of generalized Ulrich modules
over Cohen-Macaulay local rings introduced in 2014 by Goto, Ozeki, Takahashi,
Watanabe and Yoshida. The term {\it generalized} refers to the fact that Ulrich
modules are taken with respect to a zero-dimensional ideal which is not
necessarily the maximal ideal, the latter situation corresponding to the
classical theory from the 80's; despite the apparent naivety of the idea, this
passage adds considerable depth to the theory and enlarges its horizon of
applications. First, we address the problem of when the Hom functor preserves
the Ulrich property, and in particular we study relations with semidualizing
modules. Second, we explore horizontal linkage of Ulrich modules, which we use
to provide a characterization of Gorensteiness. Finally, we investigate
connections between Ulrich modules and modules with minimal multiplicity,
including characterizations in terms of relative reduction numbers as well as
the Castelnuovo-Mumford regularity of certain blowup modules.
【41】 Model-Free Nonlinear Feedback Optimization
标题：无模型非线性反馈优化
作者：Zhiyu He,Saverio Bolognani,Jianping He,Florian Dörfler,Xinping Guan
摘要：Feedback optimization is a control paradigm that enables physical systems to
autonomously reach efficient operating points. Its central idea is to
interconnect optimization iterations in closed-loop with the physical plant.
Since iterative gradient-based methods are extensively used to achieve
optimality, feedback optimization controllers typically require the knowledge
of the steady-state sensitivity of the plant, which may not be easily
accessible in some applications. In contrast, in this paper we develop a
model-free feedback controller for efficient steady-state operation of general
dynamical systems. The proposed design consists in updating control inputs via
gradient estimates constructed from evaluations of the nonconvex objective at
the current input and at the measured output. We study the dynamic
interconnection of the proposed iterative controller with a stable nonlinear
discrete-time plant. For this setup, we characterize the optimality and the
stability of the closed-loop behavior as functions of the problem dimension,
the number of iterations, and the rate of convergence of the physical plant. To
handle general constraints that affect multiple inputs, we enhance the
controller with Frank-Wolfe type updates.
【42】 InRS: implementing the indicator function of NURBS-shaped planar domains
标题：INRS：实现NURBS形状平面域的指示器功能
作者：Alvise Sommarivaa,Marco Vianello
摘要：We provide an algorithm that implements the indicator function of
NURBS-shaped planar domains, tailored to the fast computation on huge point
clouds, together with the corresponding Matlab code.
【43】 Schrodinger equations with very singular potentials in Lipschitz domains
标题：Lipschitz域上具有非常奇异位势的薛定谔方程
作者：Moshe Marcus
备注：18 pages
摘要：Consider operators $L^{V}:=\Delta + V$ in a bounded Lipschitz domain $\Omega
\subset \mathbb{R}^N$. Assume that $V\in C^{1,1}(\Omega)$ and $V$ satisfies
$V(x) \leq \overline{a} \mathrm{dist}(x,\partial\Omega)^{-2}$ in $\Omega$ and a
second condition that guarantees the existence of a ground state $\Phi_V$. If,
for example, $V>0$ this condition reads $1
【44】 Asymptotic shape of isolated magnetic domains
标题：孤立磁畴的渐近形状
作者：Hans Knüpfer,Dominik Stantejsky
备注：27 pages, 2 figures
摘要：We investigate the energy of an isolated magnetized domain $\Omega \subset
\mathbb{R}^n$ for $n=2,3$. In non-dimensionalized variables, the energy given
by $$ \mathcal{E}(\Omega) \ = \ \int_{\mathbb{R}^n} |\nabla \chi_{\Omega}| \ dx
+ \int_{\mathbb{R}^n} |\nabla \Phi|^2 \ dx $$ penalizes the interfacial area of
the domain as well as the energy of the corresponding magnetostatic field.
Here, the magnetostatic potential $\Phi$ is determined by $\Delta \Phi =
\partial_1 \chi_\Omega$, corresponding to uniform magnetization within the
domain. We consider the macroscopic regime $|\Omega| \rightarrow \infty$, in
which we derive compactness and $\Gamma$-limit for the cross-section of the
anisotropically rescaled configuration. The limit energy is local and the
limiting shape of minimizers can be calculated.
【45】 The regulator dominates the rank
标题：监管者占主导地位
作者：Fabien Pazuki
摘要：After noticing that the regulator of a number field dominates the rank of its
group of units, we bound from below the regulator of the Mordell-Weil group of
elliptic curves over global function fields of characteristic $p\geq5$. The
lower bound is an increasing function of the rank and of the height.
【46】 Diffeomorphisms of discs
标题：圆盘的微分同态
作者：Oscar Randal-Williams
备注：Contributed to the Proceedings of the 2022 ICM
摘要：I describe what is currently known, for $d \geq 5$, about the rational
homotopy type of the group of diffeomorphisms of the $d$-disc relative to its
boundary, and the closely related group of homeomorphisms of $d$-dimensional
Euclidean space.
【47】 Proving some conjectures on Kekulé numbers for certain benzenoids by using Chebyshev polynomials
标题：用切比雪夫多项式证明某些苯类的Kekulé数猜想
作者：Guoce Xin,Yueming Zhong
备注：28 pages,3 figures, 1 table
摘要：In chemistry, Cyvin-Gutman enumerates Kekul\'{e} numbers for certain
benzenoids and record it as $A050446$ on OEIS. This number is exactly the two
variable array $T(n,m)$ defined by the recursion $T(n, m) = T(n, m-1) +
\sum^{\lfloor\frac{n-1}{2}\rfloor}_{k=0} T(2k, m-1)T(n-1-2k, m)$, where
$T(n,0)=T(0,m)=1$ for all nonnegative integers $m,n$. Interestingly, this
number also appeared in the context of weighted graphs, graph polytopes, magic
labellings, and unit primitive matrices, studied by different authors. Several
interesting conjectures were made on the OEIS. These conjectures are related to
both the row and column generating function of $T(n,m)$. In this paper, give
explicit formula of the column generating function, which is also the
generating function $F(n,x)$ studied by B\'{o}na, Ju, and Yoshida. We also get
trig function representations by using Chebyshev polynomials of the second
kind. This allows us to prove all these conjectures.
【48】 Not all nilpotent monoids are finitely related
标题：并非所有的幂零幺半群都是有限相关的
作者：Markus Steindl
摘要：A finite semigroup is finitely related (has finite degree) if its term
functions are determined by a finite set of finitary relations. For example, it
is known that all nilpotent semigroups are finitely related. A nilpotent monoid
is a nilpotent semigroup with adjoined identity. We show that every
$4$-nilpotent monoid is finitely related. We also give an example of a
$5$-nilpotent monoid that is not finitely related. This is the first known
example where adjoining an identity to a finitely related semigroup yields a
semigroup which is not finitely related. We also provide examples of finitely
related semigroups which have subsemigroups, homomorphic images, and in
particular Rees quotients, that are not finitely related.
【49】 The Green's function of the Lax-Wendroff and Beam-Warming schemes
标题：Lax-Wendroff和束温格式的格林函数
作者：Jean-François Coulombel
摘要：We prove a sharp uniform generalized Gaussian bound for the Green's function
of the Lax-Wendroff and Beam-Warming schemes. Our bound highlights the spatial
region that leads to the well-known (rather weak) instability of these schemes
in the maximum norm. We also recover uniform bounds in the maximum norm when
these schemes are applied to initial data of bounded variation.
【50】 Control problem for quadratic parabolic differential equations with sensor sets of finite volume or anisotropically decaying density
标题：具有有限体积或各向异性衰减传感器组的二次抛物型微分方程的控制问题
作者：Alexander Dicke,Albrecht Seelmann,Ivan Veselic
备注：35 pages
摘要：We prove observability and null-controllability for quadratic parabolic
differential equations. The sensor set is allowed to have finite volume if the
generator has trivial singular space $S$. In the case of generators with
singular space $S \neq \{ 0 \}$ the sensor set is permitted to decay in
directions determined by $S$. The proof is based on dissipation estimates for
the quadratic differential operator with respect to spectral projections of
partial harmonic oscillators and corresponding uncertainty relations.
【51】 Deligne-Beilinson cohomology of the universal K3 surface
标题：泛K3曲面的Deligne-Beilinson上同调
作者：Zhiyuan Li,Xun Zhang
备注：26 pages, any comments are welcome!
摘要：O'Grady's generalized Franchetta conjecture (GFC) is concerned with
codimension 2 algebraic cycles on universal polarized K3 surfaces. In
\cite{BL17}, this conjecture has been studied in the Betti cohomology groups.
Following a suggestion of Voisin, we investigate this problem in the
Deligne-Beilinson (DB) cohomology groups. In this paper, we develop the theory
of Deligne-Beilinson cohomology groups on separated (smooth) Deligne-Mumford
stacks. Using the automorphic cohomology group and Noether-Lefschetz theory, we
compute the 4-th DB-cohomology group of universal oriented polarized K3
surfaces with at worst an $A_1$-singularity and show that GFC for such family
holds in DB-cohomology. In particular, this confirms O'Grady's original
conjecture in DB cohomology.
【52】 The extent of saturation of induced ideals
标题：诱导理想的饱和程度
作者：Kenta Tsukuura
摘要：We construct a model with a saturated ideal $I$ over
$\mathcal{P}_{\kappa}\lambda$ and study the extent of saturation of $I$.
【53】 Concentration phenomena in Fitzhugh-Nagumo's equations: A mesoscopic approach
标题：Fitzhugh-Nagumo方程中的浓度现象：介观方法
作者：Alain Blaustein,Francis Filbet
摘要：We consider a spatially extended mesoscopic FitzHugh-Nagumo model with strong
local interactions and prove that its asymptotic limit converges towards the
classical nonlocal reaction-diffusion FitzHugh-Nagumo system. As the local
interactions strongly dominate, the weak solution to the mesoscopic equation
under consideration converges to the local equilibrium, which has the form of
Dirac distribution concentrated to an averaged membrane potential. Our approach
is based on techniques widely developed in kinetic theory (Wasserstein
distance, relative entropy method), where macroscopic quantities of the
mesoscopic model are compared with the solution to the nonlocal
reaction-diffusion system. This approach allows to make the rigorous link
between microscopic and reaction-diffusion models.
【54】 On M-O.Ore determinants
标题：关于M-O矿的决定因素
作者：Jean Fresnel,Michel Matignon
摘要：The existence of certain Fq-spaces of differential forms of the projective
line over a field K containing Fq leads us to prove an identity linking the
determinant of the Moore matrix of n indeterminates with the determinant of the
Moore matrix of the cofactors of its first row. These same spaces give an
interpretation of Elkies pairing in terms of residues of differential forms.
This pairing puts in duality the Fq-vector space of the roots of a Fq-linear
polynomial and that of the roots of its reversed polynomial.
【55】 A survey of Nevanlinna theory in the viewpoint of holomorphic forms
标题：从全纯形式看Nevanlinna理论
作者：Xianjing Dong,Shuangshuang Yang
摘要：This paper revisits the Nevanlinna theory for meromorphic functions on
$\mathbb C$ in the viewpoint of holomorphic forms. According to our
observation, Nevanlinna's functions can be formulated by a holomorphic form.
Applying this thought to Riemann surfaces, one then extends the definition of
Nevanlinna's functions using a holomorphic form $\mathscr S$. With the new
settings, an analogue of Nevanlinna theory on \emph{weak $\mathscr S$-exhausted
Riemann surfaces} is obtained, which is viewed as a generalization of the
classical Nevanlinna theory on $\mathbb C$ and $\mathbb D.$
【56】 Projective Embedding of Dynamical Systems: uniform mean field equations
标题：动力系统的射影嵌入：一致平均场方程
作者：Francesco Caravelli,Fabio L. Traversa,Michele Bonnin,Fabrizio Bonani
备注：45 pages; one column; 10 figures;
摘要：We study embeddings of continuous dynamical systems in larger dimensions via
projector operators. We call this technique PEDS, projective embedding of
dynamical systems, as the stable fixed point of the dynamics are recovered via
projection from the higher dimensional space. In this paper we provide a
general definition and prove that for a particular type of projector operator
of rank-1, the uniform mean field projector, the equations of motion become a
mean field approximation of the dynamical system. While in general the
embedding depends on a specified variable ordering, the same is not true for
the uniform mean field projector. In addition, we prove that the original
stable fixed points remain stable fixed points of the dynamics, saddle points
remain saddle, but unstable fixed points become saddles.
【57】 On the intersection ideal graph of semigroups
标题：关于半群的交理想图
作者：Barkha Baloda,Jitender Kumar
备注：2 figures. arXiv admin note: text overlap with arXiv:2110.14194
摘要：The intersection ideal graph $\Gamma(S)$ of a semigroup $S$ is a simple
undirected graph whose vertices are all nontrivial left ideals of $S$ and two
distinct left ideals $I, J$ are adjacent if and only if their intersection is
nontrivial. In this paper, we investigate the connectedness of $\Gamma(S)$. We
show that if $\Gamma(S)$ is connected then $diam(\Gamma(S)) \leq 2$. Further we
classify the semigroups such that the diameter of their intersection graph is
two. Other graph invariants, namely perfectness, planarity, girth, dominance
number, clique number, independence number etc. are also discussed. Finally, if
$S$ is union of $n$ minimal left ideals then we obtain the automorphism group
of $\Gamma(S)$.
【58】 Automorphisms of left Ideal relation graph over full matrix ring
标题：全矩阵环上左理想关系图的自同构
作者：Jitender Kumar,Barkha Baloda,Sanjeet Malhotra
摘要：The left-ideal relation graph on a ring $R$, denoted by
$\overrightarrow{\Gamma_{l-i}}(R)$, is a directed graph whose vertex set is all
the elements of $R$ and there is a directed edge from $x$ to a distinct $y$ if
and only if the left ideal generated by $x$, written as $[x]$, is properly
contained in the left ideal generated by $y$. In this paper, the automorphisms
of $\overrightarrow{\Gamma_{l-i}}(R)$ are characterized, where $R$ is the ring
of all $n \times n$ matrices over a finite field $F_q$. The undirected left
relation graph, denoted by $\Gamma_{l-i}(M_n(F_q))$, is the simple graph whose
vertices are all the elements of $R$ and two distinct vertices $x, y$ are
adjacent if and only if either $[x] \subset [y]$ or $[y] \subset [x]$ is
considered. Various graph theoretic properties of $\Gamma_{l-i}(M_n(F_q))$
including connectedness, girth, clique number, etc. are studied.
【59】 Existence and multiplicity of solutions to a Kirchhoff type elliptic system with Trudinger-Moser growth
标题：具有Trudinger-Moser增长的Kirchhoff型椭圆方程解的存在性和多解性
作者：Shengbing Deng,Xingliang Tian
摘要：This paper deals with the existence and multiplicity of solutions for a class
of Kirchhoff type elliptic system involving the Trudinger-Moser exponential
growth nonlinearities. We first study the existence of solutions for the
following system \begin{eqnarray*}
\left\{ \arraycolsep=1.5pt
\begin{array}{ll}
-\big(a_1+b_1\|u\|^{2(\theta_1-1)}\big)\Delta u= \lambda H_u(x,u,v)\ \ \ &\
\mbox{in}\ \ \ \Omega,\\[2mm]
-\big(a_2+b_2\|v\|^{2(\theta_2-1)}\big)\Delta v= \lambda H_v(x,u,v)\ \ \ &\
\mbox{in}\ \ \ \Omega,\\[2mm]
u=0, v=0\ \ \ \ &\ \mbox{on}\ \ \ \partial\Omega,
\end{array}
\right.
\end{eqnarray*} where $\Omega$ is a bounded domain in $\mathbb{R}^2$ with
smooth boundary,\ $\|u\|=\big(\int_{\Omega}|\nabla u|^2dx\big)^{1/2}$, $H_u$
and $H_v$ behave like $e^{\beta |s|^2}$ when $|s|\rightarrow \infty$ for some
$\beta>0$, $a_1,\ a_2>0$, $b_1,\ b_2> 0$, $\theta_1,\ \theta_2> 1$ and
$\lambda$ is a positive parameter. In the later part of the paper, we also
discuss a new multiplicity result for the above system with a positive
parameter induced by the nonlocal dependence. The Kirchhoff term and the lack
of compactness of the associated energy functional due to the Trudinger-Moser
embedding have to be overcome via some new techniques.
【60】 On a nonhomogeneous Kirchhoff type elliptic system with the singular Trudinger-Moser growth
标题：具有奇异Trudinger-Moser增长的非齐次Kirchhoff型椭圆组
作者：Shengbing Deng,Xingliang Tian
摘要：The aim of this paper is to study the multiplicity of solutions for the
following Kirchhoff type elliptic systems
\begin{eqnarray*}
\left\{ \arraycolsep=1.5pt
\begin{array}{ll}
-m\left(\sum^k_{j=1}\|u_j\|^2\right)\Delta
u_i=\frac{f_i(x,u_1,\ldots,u_k)}{|x|^\beta}+\varepsilon h_i(x),\ \ & \mbox{in}\
\ \Omega, \ \ i=1,\ldots,k ,\\[2mm]
u_1=u_2=\cdots=u_k=0,\ \ & \mbox{on}\ \ \partial\Omega,
\end{array}
\right.
\end{eqnarray*} where $\Omega$ is a bounded domain in $\mathbb{R}^2$
containing the origin with smooth boundary, $\beta\in [0,2)$, $m$ is a
Kirchhoff type function, $\|u_j\|^2=\int_\Omega|\nabla u_j|^2dx$, $f_i$ behaves
like $e^{\beta s^2}$ when $|s|\rightarrow \infty$ for some $\beta>0$, and there
is $C^1$ function $F: \Omega\times\mathbb{R}^k\to \mathbb{R}$ such that
$\left(\frac{\partial F}{\partial u_1},\ldots,\frac{\partial F}{\partial
u_k}\right)=\left(f_1,\ldots,f_k\right)$, $h_i\in
\left(\big(H^1_0(\Omega)\big)^*,\|\cdot\|_*\right)$. We establish sufficient
conditions for the multiplicity of solutions of the above system by using
variational methods with a suitable singular Trudinger-Moser inequality when
$\varepsilon>0$ is small.
【61】 Classical and quantum walks on paths associated with exceptional Krawtchouk polynomials
作者：Hiroshi Miki,Satoshi Tsujimoto,Luc Vinet
备注：22 pages, 4 figures
摘要：Classical and quantum walks on some finite paths are introduced. It is shown
that these walks have explicit solutions given in terms of exceptional
Krawtchouk polynomials and their properties are explored. In particular,
fractional revival is shown to take place in the corresponding quantum walks.
【62】 On f-Derangements and Decomposing Bipartite Graphs into Paths
标题：关于f-乱列与二部图的路分解
作者：Michael Plantholt,Hamidreza Habibi,Benjamin Mussell
摘要：Let $f: \{1, ..., n\} \rightarrow \{1, ..., n\}$ be a function (not
necessarily one-to-one). An $f-derangement$ is a permutation $ g:\{1,...,n\}
\rightarrow \{1,...,n\}$ such that $g(i) \neq f(i)$ for each $ i = 1, ..., n$.
When $f$ is itself a permutation, this is a standard derangement. We examine
properties of f-derangements, and show that when we fix the maximum number of
preimages for any item under $f$, the fraction of permutations that are
f-derangements tends to $ 1/e$ for large $n$, regardless of the choice of $f$.
We then use this result to analyze a heuristic method to decompose bipartite
graphs into paths of length 5
【63】 Asymptotic slopes and strong semistability on surfaces
标题：曲面上的渐近斜率与强半稳定性
作者：Mitra Koley,A. J. Parameswaran
备注：Comments welcome
摘要：In this article we study asymptotic slopes of strongly semistable vector
bundles on a smooth projective surface. A connection between asymptotic slopes
and strong restriction theorem of a strongly semistable vector bundle is shown.
We also give an equivalent criterion of strong semistability of a vector bundle
in terms of its asymptotic slopes under some assumptions on the surface and on
the bundle.
【64】 Prikry-type forcing and the set of possible cofinalities
标题：Prikry型强迫与可能余定集
作者：Kenta Tsukuura
摘要：It is known that the set of possible cofinalities $\mathrm{pcf}(A)$ has good
properties if $A$ is a progressive interval of regular cardinals. In this
paper, we give an interval of regular cardinals $A$ such that $\mathrm{pcf}(A)$
has no good properties in the presense of a measurable cardinal, or in generic
extensions by Prikry-type forcing.
【65】 Spatial integral of the solution to hyperbolic Anderson model with time-independent noise
标题：带时间无关噪声的双曲型Anderson模型解的空间积分
作者：Raluca M. Balan,Wangjun Yuan
备注：43 pages
摘要：In this article, we study the asymptotic behavior of the spatial integral of
the solution to the hyperbolic Anderson model in dimension $d\leq 2$, as the
domain of the integral gets large (for fixed time $t$). This equation is driven
by a spatially homogeneous Gaussian noise, whose covariance function is either
integrable, or is given by the Riesz kernel. The novelty is that the noise does
not depend on time, which means that It\^o's martingale theory for stochastic
integration cannot be used. Using a combination of Malliavin calculus with
Stein's method, we show that with proper normalization and centering, the
spatial integral of the solution converges to a standard normal distribution,
by estimating the speed of this convergence in the total variation distance. We
also prove the corresponding functional limit theorem for the spatial integral
process.
【66】 Stochastic Saddle Point Problems with Decision-Dependent Distributions
标题：决策相关分布的随机鞍点问题
作者：Killian Wood,Emiliano Dall'Anese
摘要：This paper focuses on stochastic saddle point problems with
decision-dependent distributions in both the static and time-varying settings.
These are problems whose objective is the expected value of a stochastic payoff
function, where random variables are drawn from a distribution induced by a
distributional map. For general distributional maps, the problem of finding
saddle points is in general computationally burdensome, even if the
distribution is known. To enable a tractable solution approach, we introduce
the notion of equilibrium points -- which are saddle points for the stationary
stochastic minimax problem that they induce -- and provide conditions for their
existence and uniqueness. We demonstrate that the distance between the two
classes of solutions is bounded provided that the objective has a
strongly-convex-strongly-concave payoff and Lipschitz continuous distributional
map. We develop deterministic and stochastic primal-dual algorithms and
demonstrate their convergence to the equilibrium point. In particular, by
modeling errors emerging from a stochastic gradient estimator as sub-Weibull
random variables, we provide error bounds in expectation and in high
probability that hold for each iteration; moreover, we show convergence to a
neighborhood in expectation and almost surely. Finally, we investigate a
condition on the distributional map -- which we call opposing mixture dominance
-- that ensures the objective is strongly-convex-strongly-concave. Under this
assumption, we show that primal-dual algorithms converge to the saddle points
in a similar fashion.
【67】 Electric Vehicle Routing Problem with Spatio-temporal Varying Electricity Price and Incentive-aware Customers
标题：具有时空变化电价和激励顾客的电动汽车路径问题
作者：Canqi Yao,Shibo Chen,Mauro Salazar,Zaiyue Yang
备注：Submitted to IEEE TSG. arXiv admin note: substantial text overlap with arXiv:2110.06441
摘要：This paper investigates the optimization problem of a fleet of electric
vehicles (EVs) serving a set of time-specified customers, where the operator
needs to optimize routing and charging problem jointly for each EV. In
particular, regarding to the spatio-temporal varying electricity price, we
consider incentive-aware customers and propose that the operator offers
monetary incentives to exchange time flexibility of customers. In this manner,
a win-win situation is achievable since time flexibility enables the fleet
operator to obtain a routing and charging schedule with lower cost, whilst the
customers receives monetary compensation. Specifically, we first devise a
bi-level model whereby the fleet operator optimizes the routing and charging
schedule jointly with a monetary incentive to reimburse the delivery time
flexibility experienced by the customers. At the same time, the customers
choose the optimal time flexibility by minimizing its own cost. Second, we
tackle the complexity resulting from the bi-level and nonlinear problem with an
equivalent transformation method. Eventually, we reformulate the problem as a
single-level optimization problem, which later is solved by proposed Benders
dual decomposition method holding a faster convergence rate than the
generalized Benders decomposition method. To evaluate the effectiveness of our
framework and proposed Benders dual decomposition algorithm, we carry out
extensive numerical experiments using VRP-REP data from Belgium.
【68】 Systems of equations over the group ring of Thompson's group $F$
标题：Thompson群的群环上的方程组$F$
作者：Victor Guba
备注：arXiv admin note: text overlap with arXiv:2101.01848
摘要：Let $R=K[G]$ be a group ring of a group $G$ over a field $K$. It is known
that if $G$ is amenable then $R$ satisfies the Ore condition: for any $a,b\in
R$ there exist $u,v\in R$ such that $au=bv$, where $u\ne0$ or $v\ne0$. It is
also true for amenable groups that a non-zero solution exists for any finite
system of linear equations over $R$, where the number of unknowns exceeds the
number of equations. Recently Bartholdi proved the converse. As a consequence
of this theorem, Kielak proved that R.\,Thompson's group $F$ is amenable if and
only if it satisfies the Ore condition. The amenability problem for $F$ is a
long-standing open question.
In this paper we prove that some equations or their systems have non-zero
solutions in the group rings of $F$. We improve some results by Donnelly
showing that there exist finite sets $Y\subset F$ with the property $|AY| <
\frac43|Y|$, where $A=\{x_0,x_1,x_2\}$. This implies some result on the systems
of equations. We show that for any element $b$ in the group ring of $F$, the
equation $(1-x_0)u=bv$ has a non-zero solution. The corresponding fact for
$1-x_1$ instead of $1-x_0$ remains open. We deduce that for any $m\ge1$ the
system $(1-x_0)u_0=(1-x_1)u_1=\cdots=(1-x_m)u_m$ has nonzero solutions in the
group ring of $F$. We also analyze the equation $(1-x_0)u=(1-x_1)v$ giving a
precise explicit description of all its solutions in $K[F]$. This is important
since to any group relation between $x_0$, $x_1$ in $F$ one can naturally
assign such a solution. So this can help to estimate the number of relations of
a given length between generators.
【69】 Local and Global Convergence of General Burer-Monteiro Tensor Optimizations
标题：广义布里-蒙泰罗张量优化问题的局部收敛性和全局收敛性
作者：Shuang Li,Qiuwei Li
摘要：Tensor optimization is crucial to massive machine learning and signal
processing tasks. In this paper, we consider tensor optimization with a convex
and well-conditioned objective function and reformulate it into a nonconvex
optimization using the Burer-Monteiro type parameterization. We analyze the
local convergence of applying vanilla gradient descent to the factored
formulation and establish a local regularity condition under mild assumptions.
We also provide a linear convergence analysis of the gradient descent algorithm
started in a neighborhood of the true tensor factors. Complementary to the
local analysis, this work also characterizes the global geometry of the best
rank-one tensor approximation problem and demonstrates that for orthogonally
decomposable tensors the problem has no spurious local minima and all saddle
points are strict except for the one at zero which is a third-order saddle
point.
【70】 Delay Alignment Modulation: Enabling Equalization-Free Single-Carrier Communication
作者：Haiquan Lu,Yong Zeng
备注：5 pages, 6 figures
摘要：This paper proposes a novel broadband transmission technology, termed delay
alignment modulation (DAM), which enables the low-complexity equalization-free
single-carrier communication, yet without suffering from inter-symbol
interference (ISI). The key idea of DAM is to deliberately introduce
appropriate delays for information-bearing symbols at the transmitter side, so
that after propagating over the time-dispersive channel, all multi-path signal
components will arrive at the receiver simultaneously and constructively. We
first show that by applying DAM for the basic multiple-input single-output
(MISO) communication system, an ISI-free additive white Gaussian noise (AWGN)
system can be obtained with the simple zero-forcing (ZF) beamforming.
Furthermore, the more general DAM scheme is studied with the ISI-maximal-ratio
transmission (MRT) and the ISI-minimum mean-square error (MMSE) beamforming.
Simulation results are provided to show that when the channel is sparse and/or
the antenna dimension is large, DAM not only resolves the notorious practical
issues suffered by orthogonal frequency-division multiplexing (OFDM) such as
high peak-to-average-power ratio (PAPR), severe out-of-band (OOB) emission, and
vulnerability to carrier frequency offset (CFO), with low complexity, but also
achieves higher spectral efficiency due to the saving of guard interval
overhead.
【71】 Perfect bases in representation theory: three mountains and their springs
标题：表征理论的完美基础：三座山及其泉水
作者：Joel Kamnitzer
备注：18 pages, ICM 2022 proceedings
摘要：In order to give a combinatorial descriptions of tensor product multiplicites
for semisimple groups, it is useful to find bases for representations which are
compatible with the actions of Chevalley generators of the Lie algebra. There
are three known examples of such bases, each of which flows from geometric or
algebraic mountain. Remarkably, each mountain gives the same combinatorial
shadow: the crystal B(infty) and the Mirkovic-Vilonen polytopes. In order to
distinguish between the three bases, we introduce measures supported on these
polytopes. We also report on the interaction of these bases with the cluster
structure on the coordinate ring of the maximal unipotent subgroup.
【72】 Asymptotic behaviour of non-radiative solution to the wave equations
标题：波动方程非辐射解的渐近行为
作者：Liang Li,Ruipeng Shen,Chenhui Wang,Lijuan Wei
备注：20 pages
摘要：In this work we consider weakly non-radiative solutions to both linear and
non-linear wave equations. We first characterize all weakly non-radiative free
waves, without the radial assumption. Then in dimension 3 we show that the
initial data of non-radiative solutions to a wide range of nonlinear wave
equations are similar to those of non-radiative free waves in term of
asymptotic behaviour.
【73】 Identities involving the tribonacci numbers squared via tiling with combs
标题：用梳子平铺的包含Tribonacci数平方的恒等式
作者：Michael A. Allen,Kenneth Edwards
备注：7 pages, 1 figure
摘要：The number of ways to tile an $n$-board (an $n\times1$ rectangular board)
with $(\frac12,\frac12;1)$-, $(\frac12,\frac12;2)$-, and
$(\frac12,\frac12;3)$-combs is $T_{n+2}^2$ where $T_n$ is the $n$th tribonacci
number. A $(\frac12,\frac12;m)$-comb is a tile composed of $m$ sub-tiles of
dimensions $\frac12\times1$ (with the shorter sides always horizontal)
separated by gaps of dimensions $\frac12\times1$. We use such tilings to obtain
quick combinatorial proofs of identities relating the tribonacci numbers
squared to one another, to other combinations of tribonacci numbers, and to the
Fibonacci, Narayana's cows, and Padovan numbers. Most of these identities
appear to be new.
【74】 An inequality regarding non-radiative linear waves via a geometric method
标题：关于无辐射线性波的一个几何不等式
作者：Liang Li,Ruipeng Shen,Chenhui Wang
备注：35 pages, 17 figures
摘要：In this work we consider the operator
\[
(\mathbf{T} G) (x)= \int_{\mathbb{S}^2} G(x\cdot \omega, \omega) d\omega,
\quad x\in \mathbb{R}^3, \; G\in L^2(\mathbb{R}\times \mathbb{S}^2).
\]
This is the adjoint operator of the Radon transform. We manage to give an
optimal $L^6$ decay estimate of $\mathbf{T} G$ near the infinity by a geometric
method, if the function $G$ is compactly supported. As an application we give
decay estimate of non-radiative solutions to the 3D linear wave equation in the
exterior region $\{(x,t)\in \mathbb{R}^3 \times \mathbb{R}: |x|>R+|t|\}$. This
kind of decay estimate is useful in the channel of energy method for wave
equations
【75】 Long time and large crowd dynamics of discrete Cucker-Smale alignment models
标题：离散Cucker-Smer线形模型的长时间大人群动力学
作者：Eitan Tadmor
摘要：We provide a bird's eye view on developments in analyzing the long time,
large crowd behavior of Cucker-Smale alignment dynamics. We consider a class of
(fully-)discrete models, paying particular attention to general alignment
protocols in which agents, with possibly time-dependent masses, are driven by a
large class of heavy-tailed communication kernels. The presence of
time-dependent masses allows, in particular, non-symmetric communication. While
revisiting known results in the literature, we also shed new light of various
aspects on the long time flocking/swarming behavior, driven by the decay of
energy fluctuations and heavy-tailed connectivity. We also discuss the large
crowd dynamics in terms of the hydrodynamic description of Euler alignment
models.
【76】 Regularity and uniqueness results for generated Jacobian equations
标题：生成的Jacobian方程的正则性和唯一性结果
作者：Cale Rankin
备注：ANU PhD thesis
摘要：This is a PhD thesis about generated Jacobian equations; our purpose is
twofold. First, we provide an introduction to these equations, whilst, at the
same time, collating some results scattered throughout the literature. The
other goal is to present the author's own results on these equations. These
results all concern solutions of generated Jacobian equations, usually paired
with the second boundary value problem. We prove strict convexity and $C^1$
differentiability results under optimal hypothesis in two dimensions, and the
same results in higher dimensions with some additional hypothesis. We also
consider uniqueness results for the second boundary value problem, and the
application of the uniqueness results to global regularity. We conclude with
notes on the parabolic generated Jacobian equation. The arXiv version contains
minor updates to the ANU open research repository version which is available
from the listed DOI.
【77】 The Stability of Generalized Ricci Solitons
标题：广义Ricci孤子的稳定性
作者：Kuan-Hui Lee
摘要：In this paper, I compute the second variation formula of the generalized
Einstein-Hilbert functional and prove that a Bismut-flat, Einstein manifold is
linearly stable under some curvature assumption. In the last part of the paper,
I prove that dynamical stability and the linear stability are equivalent on a
steady gradient generalized Ricci soliton $(g,H,f)$ which generalizes the
result done by Kr\"oncke, Haslhofer, Sesum, Raffero and Vezzoni.
【78】 Magnetic trajectories on 2-step nilmanifolds
标题：二阶零流形上的磁迹
作者：Gabriela P. Ovando,Mauro Subils
摘要：The aim of this work is the study of magnetic trajectories on nilmanifolds
but also of the associated magnetic fields. The magnetic equation is written
and the corresponding solutions are found for a family of Lorentz forces. The
existence question of magnetic fields is analyzed, obtaining non-existence
results. This is extended to prove the non-existence of uniform magnetic fields
under certain hypotheses. Finally some examples are computed in the Heisenberg
Lie groups $H_n$ for $n=3,5$, showing differences with the case of exact forms.
Interesting magnetic trajectories related to elliptic integrals appear in
$H_3$. The question of existence of closed or periodic magnetic trajectories
for every energy level on Lie groups or on compact quotients is treated.
【79】 Efficient Algebraic Two-Level Schwarz Preconditioner For Sparse Matrices
标题：稀疏矩阵的高效代数两级Schwarz预处理器
作者：Hussam Al Daas,Pierre Jolivet,Tyrone Rees
摘要：Domain decomposition methods are among the most efficient for solving sparse
linear systems of equations. Their effectiveness relies on a judiciously chosen
coarse space. Originally introduced and theoretically proved to be efficient
for self-adjoint operators, spectral coarse spaces have been proposed in the
past few years for indefinite and non-self-adjoint operators. This paper
presents a new spectral coarse space that can be constructed in a
fully-algebraic way unlike most existing spectral coarse spaces. We present
theoretical convergence result for Hermitian positive definite diagonally
dominant matrices. Numerical experiments and comparisons against
state-of-the-art preconditioners in the multigrid community show that the
resulting two-level Schwarz preconditioner is efficient especially for
non-self-adjoint operators. Furthermore, in this case, our proposed
preconditioner outperforms state-of-the-art preconditioners.
【80】 On Spectrum of Nonlinear Continuous Operators
标题：关于非线性连续算子的谱
作者：Kamal N. Soltanov
备注：22 p
摘要：This article proposed a new approach to the determination of the spectrum for
nonlinear continuous operators in the Banach spaces and using it investigated
the spectrum of some classes of operators. Here shows that in nonlinear
operators case is necessary to seek the spectrum of a given nonlinear operator
relatively to another nonlinear operator. Moreover, the order of nonlinearity
of examined operator and operator relatively to which seek the spectrum must be
identical. Here provided different examples relative to how one can find the
eigenvalue and also studied solvability problems.
【81】 A proof of the Graham Sloane conjecture
标题：格雷厄姆·斯隆猜想的一个证明
作者：Edinah K. Gnang,Michael Peretzian Williams
备注：arXiv admin note: text overlap with arXiv:2111.12812
摘要：We settle in the affirmative the Graham-Sloane conjecture.
【82】 Torsion and torsion-free classes from objects of finite type in Grothendieck categories
标题：Grothendieck范畴中有限型对象的挠类和无挠类
作者：Daniel Bravo,Sinem Odabaşı,Carlos E. Parra,Marco A. Pérez
备注：27 pages
摘要：In an arbitrary Grothendieck category, we find necessary and sufficient
conditions for the class of $\text{FP}_n$-injective objects to be a torsion
class. By doing so, we propose a notion of $n$-hereditary categories. We also
define and study the class of $\text{FP}_n$-flat objects in Grothendieck
categories with a generating set of small projective objects, and provide
several equivalent conditions for this class to be torsion-free. In the end, we
present several applications and examples of $n$-hereditary categories in the
contexts modules over a ring, chain complexes of modules and categories of
additive functors from an additive category to the category of abelian groups.
Concerning the latter setting, we find a characterization of when these functor
categories are $n$-hereditary in terms of the domain additive category.
【83】 Exploring the Steiner-Soddy Porism
标题：斯泰纳-索迪流浪主义探微
作者：Ronaldo Garcia,Liliana Gheorghe,Dan Reznik
备注：12 pages, 6 figures, 1 table
摘要：We explore properties and loci of a Poncelet family of polygons -- called
here Steiner-Soddy -- whose vertices are centers of circles in the Steiner
porism, including conserved quantities, loci, and its relationship to other
Poncelet families.
【84】 Almost order-weakly compact operators on Banach lattices
标题：Banach格上的几乎序弱紧算子
作者：Mina Matin,Mina Matin,Kazem Haghnejad Azar,Ali Ebadi
摘要：A continuous operator $T$ between two Banach lattices $E$ and $F$ is called
almost order-weakly compact, whenever for each almost order bounded subset $A$
of $E$, $T(A)$ is a relatively weakly compact subset of $F$. In Theorem 4, we
show that the positive operator $T$ from $E$ into Dedekind complete $F$ is
almost order-weakly compact if and only if $T(x_n) \xrightarrow{\|.\|}0$ in $F$
for each disjoint almost order bounded sequence $\{x_n\}$ in $E$. In this
manuscript, we study some properties of this class of operators and its
relationships with others known operators.
【85】 Isoperimetric 3- and 4-bubble results on $\mathbb{R}$ with density $|x|$
作者：Evan Alexander,Emily Burns,John Ross,Jesse Stovall,Zariah Whyte
备注：1 figure. arXiv admin note: text overlap with arXiv:2201.01808
摘要：We study the isoperimetric problem on $\mathbb{R}^1$ with a prescribed
density function $f(x) = |x|$. Under these conditions, we find that
isoperimetric $3$-bubble and $4$-bubble results satisfy a regular structure. As
our regions increase in size, the intervals that form them alternate
back-and-forth across the origin, with the smaller regions closer to the
origin. This expands on previously known observations about the single- and
double-bubble results on $\mathbb{R}$ with density $|x|^p$.
【86】 Pricing Bermudan options using regression trees/random forests
标题：使用回归树/随机森林为百慕大期权定价
作者：Zineb El Filali Ech-Chafiq,Pierre Henry-Labordere,Jérôme Lelong
摘要：The value of an American option is the maximized value of the discounted cash
flows from the option. At each time step, one needs to compare the immediate
exercise value with the continuation value and decide to exercise as soon as
the exercise value is strictly greater than the continuation value. We can
formulate this problem as a dynamic programming equation, where the main
difficulty comes from the computation of the conditional expectations
representing the continuation values at each time step. In (Longstaff and
Schwartz, 2001), these conditional expectations were estimated using
regressions on a finite-dimensional vector space (typically a polynomial
basis). In this paper, we follow the same algorithm; only the conditional
expectations are estimated using Regression trees or Random forests. We discuss
the convergence of the LS algorithm when the standard least squares regression
is replaced with regression trees. Finally, we expose some numerical results
with regression trees and random forests. The random forest algorithm gives
excellent results in high dimensions.
【87】 Quantifying unsharpness of observables in an outcome-independent way
作者：Arindam Mitra
备注：11 pages, 2 figures
摘要：Recently a very beautiful measure of the unsharpness (fuzziness) of the
observables is discussed in the paper [Phys. Rev. A 104, 052227 (2021)]. The
measure which is defined in this paper is constructed via uncertainty and does
not depend on the values of the outcomes. There exist several properties of a
set of observables (e.g., incompatibility, non-disturbance) that do not depend
on the values of the outcomes. Therefore, the approach in the above-said paper
is consistent with the above-mentioned fact and is able to measure the
intrinsic unsharpness of the observables. In this work, we also quantify the
unsharpness of observables in an outcome-independent way. But our approach is
different than the approach of the above-said paper. In this work, at first, we
construct a Luder's instrument-based unsharpness measure and provide a tight
upper bound of that measure. Then we prove the monotonicity of the above-said
measure under a class of fuzzifying processes (processes that make the
observables more fuzzy). This is consistent with the resource-theoretic
framework. Then we relate our approach to the approach of the above-said paper.
Next, we try to construct an instrument-independent unsharpness measure. In
particular, we define an instrument-independent unsharpness measure and provide
a tight upper bound of that measure and then we derive the condition for the
monotonicity of the measure under a class of fuzzifying processes and prove the
monotonicity for dichotomic qubit observables. Then we show that for an unknown
measurement, the value of these measures can be determined experimentally.
Finally, we present the idea of the resource theory of the sharpness of the
observables.
【88】 The spatial Functional Renormalization Group and Hadamard states on cosmological spacetimes
作者：Rudrajit Banerjee,Max Niedermaier
备注：59 pages, 1 figure
摘要：A spatial variant of the Functional Renormalization Group (FRG) is introduced
on (Lorentzian signature) globally hyperbolic spacetimes. Through its
perturbative expansion it is argued that such a FRG must inevitably be state
dependent and that it should be based on a Hadamard state. A concrete
implementation is presented for scalar quantum fields on flat
Friedmann-Lema\^{i}tre spacetimes. The universal ultraviolet behavior of
Hadamard states allows the flow to be matched to the one-loop renormalized flow
(where strict removal of the ultraviolet cutoff requires a tower of potentials,
one for each power of the Ricci scalar). The state-dependent infrared behavior
of the flow is investigated for States of Low Energy, which are Hadamard states
deemed to be viable vacua for a pre-inflationary period. A simple
time-dependent infrared fixed point equation (resembling that in Minkowski
space) arises for any scale factor, with analytically computable corrections
coding the non-perturbative ramifications of the Hadamard property in the
infrared.
【89】 Rethinking the ill-posedness of the spectral function reconstruction -- why is it fundamentally hard and how Artificial Neural Networks can help
作者：Shuzhe Shi,Lingxiao Wang,Kai Zhou
备注：29 pages, 6 figures
摘要：Reconstructing hadron spectral functions through Euclidean correlation
functions are of the important missions in lattice QCD calculations. However,
in a K\"allen--Lehmann(KL) spectral representation, the reconstruction is
observed to be ill-posed in practice. It is usually ascribed to the fewer
observation points compared to the number of points in the spectral function.
In this paper, by solving the eigenvalue problem of continuous KL convolution,
we show analytically that the ill-posedness of the inversion is fundamental and
it exists even for continuous correlation functions. We discussed how to
introduce regulators to alleviate the predicament, in which include the
Artificial Neural Networks(ANNs) representations recently proposed by the
Authors in [arXiv:2111.14760]. The uniqueness of solutions using ANNs
representations is manifested analytically and validated numerically.
Reconstructed spectral functions using different regularization schemes are
also demonstrated, together with their eigen-mode decomposition. We observe
that components with large eigenvalues can be reliably reconstructed by all
methods, whereas those with low eigenvalues need to be constrained by
regulators.
【90】 Solving formally the Auxiliary System of $O(N)$ Non Linear Sigma Model
作者：Dimitrios Katsinis
备注：5 pages
摘要：We show that the integrability of the $SO(N)/SO(N-1)$ Principal Chiral Model
(PCM) originates from the Pohlmeyer reduction of the $O(N)$ Non Linear Sigma
Model (NLSM). In particular, we show that the Lax pair of the PCM is related
upon redefinitions and identification of parameters to the zero curvature
condition, which is a consequence of the flatness of the enhanced space used in
the Pohlmeyer reduction. This identification provides the solution of the
auxiliary system that corresponds to an arbitrary NLSM/PCM solution.
【91】 Sparse PCA on fixed-rank matrices
标题：固定秩矩阵上的稀疏PCA
作者：Alberto Del Pia
备注：None
摘要：Sparse PCA is the optimization problem obtained from PCA by adding a sparsity
constraint on the principal components. Sparse PCA is NP-hard and hard to
approximate even in the single-component case. In this paper we settle the
computational complexity of sparse PCA with respect to the rank of the
covariance matrix. We show that, if the rank of the covariance matrix is a
fixed value, then there is an algorithm that solves sparse PCA to global
optimality, whose running time is polynomial in the number of features. We also
prove a similar result for the version of sparse PCA which requires the
principal components to have disjoint supports.
【92】 Power and Sample Size Calculations for Rerandomized Experiments
标题：随机试验的功率和样本量计算
作者：Zach Branson,Xinran Li,Peng Ding
备注：20 pages, 4 figures
摘要：Power is an important aspect of experimental design, because it allows
researchers to understand the chance of detecting causal effects if they exist.
It is common to specify a desired level of power, and then compute the sample
size necessary to obtain that level of power; thus, power calculations help
determine how experiments are conducted in practice. Power and sample size
calculations are readily available for completely randomized experiments;
however, there can be many benefits to using other experimental designs. For
example, in recent years it has been established that rerandomized designs,
where subjects are randomized until a prespecified level of covariate balance
is obtained, increase the precision of causal effect estimators. This work
establishes the statistical power of rerandomized treatment-control
experiments, thereby allowing for sample size calculators. Our theoretical
results also clarify how power and sample size are affected by treatment effect
heterogeneity, a quantity that is often ignored in power analyses. Via
simulation, we confirm our theoretical results and find that rerandomization
can lead to substantial sample size reductions; e.g., in many realistic
scenarios, rerandomization can lead to a 25% or even 50% reduction in sample
size for a fixed level of power, compared to complete randomization. Power and
sample size calculators based on our results are in the R package rerandPower
on CRAN.
【93】 Polynomial Dynamical Systems and Differentiation of Genus 4 Hyperelliptic Functions
标题：多项式动力系统与亏格4的超椭圆函数的微分
作者：E. Yu. Bunkova
摘要：We give an explicit solution to the problem of differentiation of
hyperelliptic functions in genus 4 case. We describe explicitly the polynomial
Lie algebras and polynomial dynamical systems connected to this problem.
【94】 General rogue wave solutions to the discrete nonlinear Schrödinger equation
作者：Yasuhiro Ohta,Bao-Feng Feng
备注：16 pages, 4 figures
摘要：In the present paper, we attempt to construct both the general rogue wave
solutions to the fully discrete nonlinear Schr\"odinger (fd-NLS) equation via
the KP-Toda reduction method. First, we deduce the general breather solution of
the fd-NLS equation starting from a pair of bilinear equations. We then derive
the general rogue wave solution by taking a limit to the breather solution.
【95】 Persistent Homology for Breast Tumor Classification using Mammogram Scans
标题：使用乳腺X线扫描实现乳腺肿瘤分类的持久同源性
作者：Aras Asaad,Dashti Ali,Taban Majeed,Rasber Rashid
备注：10 pages
摘要：An Important tool in the field topological data analysis is known as
persistent Homology (PH) which is used to encode abstract representation of the
homology of data at different resolutions in the form of persistence diagram
(PD). In this work we build more than one PD representation of a single image
based on a landmark selection method, known as local binary patterns, that
encode different types of local textures from images. We employed different PD
vectorizations using persistence landscapes, persistence images, persistence
binning (Betti Curve) and statistics. We tested the effectiveness of proposed
landmark based PH on two publicly available breast abnormality detection
datasets using mammogram scans. Sensitivity of landmark based PH obtained is
over 90% in both datasets for the detection of abnormal breast scans. Finally,
experimental results give new insights on using different types of PD
vectorizations which help in utilising PH in conjunction with machine learning
classifiers.
【96】 Well-Conditioned Linear Minimum Mean Square Error Estimation
作者：Edwin K. P. Chong
摘要：Computing linear minimum mean square error (LMMSE) filters is often ill
conditioned, suggesting that unconstrained minimization of the mean square
error is an inadequate principle for filter design. To address this, we first
develop a unifying framework for studying constrained LMMSE estimation
problems. Using this framework, we expose an important structural property of
all constrained LMMSE filters and show that they all involve an inherent
preconditioning step. This parameterizes all such filters only by their
preconditioners. Moreover, each filters is invariant to invertible linear
transformations of its preconditioner. We then clarify that merely constraining
the rank of the filters, leading to the well-known low-rank Wiener filter, does
not suitably address the problem of ill conditioning. Instead, we use a
constraint that explicitly requires solutions to be well conditioned in a
certain specific sense. We introduce two well-conditioned estimators and
evaluate their mean-squared-error performance. We show these two estimators
converge to the standard LMMSE filter as their truncated-power ratio converges
to zero, but more slowly than the low-rank Wiener filter in terms of scaling
law. This exposes the price for being well conditioned. We also show
quantitative results with historical VIX data to illustrate the performance of
our two well-conditioned estimators.
【97】 Schwarzian derivative, Painlevé XXV-Ermakov equation and Bäcklund transformations
作者：Sandra Carillo,Alexander Chichurin,Galina Filipuk,Federico Zullo
备注：21 pages
摘要：The role of Schwarzian derivative in the study of nonlinear ordinary
differential equations is revisited. Solutions and invariances admitted by
Painlev\'e XXV-Ermakov equation, Ermakov equation and third order linear
equation in a normal form are shown to be based on solutions of the Schwarzian
equation. Starting from the Riccati equation and the second order element of
the Riccati chian as the simplest examples of linearizable equations, by
introducing a suitable change of variables, it is shown how the Schwarzian
derivative represents a key tool in the construction of solutions. Two families
of B\"acklund transformations which link the linear and nonlinear equations
under investigation are obtained. Some examples with relevant applications are
given and discussed.
【98】 Invasion of cooperative parasites in moderately structured host populations
标题：合作寄生虫在中等结构宿主群体中的入侵
作者：Vianney Brouard,Cornelia Pokalyuk
摘要：Certain defense mechanisms of phages against the immune system of their
bacterial host rely on cooperation of phages. Motivated by this example we
analyse invasion probabilities of cooperative parasites in host populations
that are moderately structured. More precisely we assume that hosts are
arranged on the vertices of a configuration model and that offspring of
parasites move to nearest neighbours sites to infect new hosts. We consider
parasites that generate many offspring at reproduction, but do this (usually)
only when infecting a host simultaneously. In this regime we identify and
analyse the spatial scale of the population structure at which invasion of
parasites turns from being an unlikely to an highly probable event.
【99】 Quantum computing based on complex Clifford algebras
作者：Jaroslav Hrdina,Ales Navrat,Petr Vasik
摘要：We propose to represent both $n$--qubits and quantum gates acting on them as
elements in the complex Clifford algebra defined on a complex vector space of
dimension $2n.$ We demonstrate its functionality by performing quantum
computations with several well known examples of quantum gates. We also compare
our approach with representations that use real geometric algebras.
【100】 An Input-to-State Safety Approach to Anomaly-Resilient Parabolic PDEs: Application to Cyber-Physical Battery Modules
标题：异常弹性抛物型偏微分方程的输入到状态安全方法：在网络物理电池模块中的应用
作者：Tanushree Roy,Ashley Knichel,Satadru Dey
摘要：Distributed Parameter Cyber-Physical Systems (DPCPSs), modelled by Partial
Differential Equations (PDEs), are increasingly vulnerable to anomalies such as
physical faults as well as cyber-attacks. This motivates the need for
strategies towards anomaly-resilient control of these systems. Although anomaly
detection and diagnostics in PDE systems have received considerable attention
in existing literature, fault-tolerant or anomaly-resilient control for PDEs
remains relatively under-explored. However, given the vulnerabilities of these
systems against anomalies, it is essential that the control systems possess
resilience against these disruptions. In this context, we explore a Practical
Input-to-Safety (pISSf) based control design approach for a class of DPCPSs
modelled by linear Parabolic PDEs. Specifically, we develop a design framework
for anomaly-resilient control for this class of system with both safety and
stability guarantees based on control Lyapunov functional and control barrier
functional. To illustrate our methodology, we apply our strategy to design a
thermal-anomaly resilient boundary coolant control system for a cyber-physical
battery module. Several simulation studies are done to show the efficacy of our
method under anomalies such as mechanical battery degradation and cyber-attack
mediated overdischarge.
【101】 Persistent oscillations after quantum quenches in $d$ dimensions
作者：Gesualdo Delfino,Marianna Sorba
备注：None
摘要：We obtain analytical results for the time evolution of local observables in
systems undergoing quantum quenches in $d$ spatial dimensions. For homogeneous
systems we show that oscillations undamped in time occur when the state
produced by the quench includes single-quasiparticle modes and the observable
couples to those modes. In particular, a quench of the transverse field within
the ferromagnetic phase of the Ising model produces undamped oscillations of
the order parameter when $d>1$. For the more general case in which the quench
is performed only in a subregion of the whole $d$-dimensional space occupied by
the system, the time evolution occurs inside a light cone spreading away from
the boundary of the quenched region as time increases. The additional condition
for undamped oscillations is that the volume of the quenched region is
extensive in all dimensions.
【102】 Stream/block ciphers, difference equations and algebraic attacks
标题：流/挡路密码、差分方程和代数攻击
作者：Roberto La Scala,Sharwan K. Tiwari
备注：26 pages, to appear in Journal of Symbolic Computation
摘要：In this paper we model a class of stream and block ciphers as systems of
(ordinary) explicit difference equations over a finite field. We call this
class "difference ciphers" and we show that ciphers of application interest, as
for example systems of LFSRs with a combiner, Trivium and Keeloq, belong to the
class. By using Difference Algebra, that is, the formal theory of difference
equations, we can properly define and study important properties of these
ciphers, such as their invertibility and periodicity. We describe then general
cryptanalytic methods for difference ciphers that follow from these properties
and are useful to assess the security. We illustrate such algebraic attacks in
practice by means of the ciphers Bivium and Keeloq.
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