Tootfinder

Some direct and inverse problems for the Restricted Signed sumset in set of integers
Mohan, Raj Kumar Mistri, Ram Krishna Pandey
https://arxiv.org/abs/2403.03625

Some direct and inverse problems for the Restricted Signed sumset in set of integers
Given a positive integer $h$ and a nonempty finite set of integers $A=\{a_{1},a_{2},\ldots,a_{k}\}$, the restricted $h$-fold signed sumset of $A$, denoted by $h^{\wedge}_{\pm}A$, is defined as $$h^{\wedge}_{\pm}A=\left\lbrace \sum_{i=1}^{k} λ_{i} a_{i}: λ_{i} \in \left\lbrace -1, 0, 1\right\rbrace \ \text{for} \ i= 1, 2, \ldots, k \ \text{and} \ \sum_{i=1}^{k} \left| λ_{i} \right| =h\right\rbrace.$$ The direct problem associated with this sumset is to find the optimal lower bound o…

This https://arxiv.org/abs/2404.19718 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Roman Domination on Graphings
We study a variant of domination, called Roman domination, where we must assign to each vertex one of the labels 0, 1, or 2 and require that every vertex with label 0 has a neighbour with label 2. We study the problem of finding a low-cost Roman dominating function on Lebesgue-measurable graphings, that is, on infinite graphs whose vertices are the points of a probability space. We provide a framework to tackle optimisation problems in the measurable combinatorial setting. In particular, we ful…

Inner Functions and Laminations
Oleg Ivrii, Mariusz Urba\'nski
https://arxiv.org/abs/2405.02878 https://arxiv.org/pdf/2405.02878<…

Inner Functions and Laminations
In this paper, we study orbit counting problems for inner functions using geodesic and horocyclic flows on Riemann surface laminations. For a one component inner function of finite Lyapunov exponent with $F(0) = 0$, other than $z \to z^d$, we show that the number of pre-images of a point $z \in \mathbb{D} \setminus \{ 0\}$ that lie in a ball of hyperbolic radius $R$ centered at the origin satisfies $$ \mathcal{N}(z, R) \, \sim \, \frac{1}{2} \log \frac{1}{|z|} \cdot \frac{1}{\int_{\pa…

Been having problems with 2 local #PHP projects on my Mac closing the connection when using PHP-FPM. Finally after almost 1 year (since Sonoma apparently) I found the solution:
https://<…

PHP pg_connect() does not return in PHP-FPM after MacOS Sonoma Upgrade
I have wasted a lot of time on this and I'm stumped. Anyone have some insight or work arounds? Thanks in advance for your attention... My PHP/PostgreSQL/NGINX app has been running on MacOS using PH...

Configurations in the Euclidean space related to the 3D genome reconstruction problem from partially phased data
Annachiara Korchmaros
https://arxiv.org/abs/2403.00407

Configurations in the Euclidean space related to the 3D genome reconstruction problem from partially phased data
A motivation for studying the following problems comes from applications to Biology; see \cite{cifuentes20233d}. In the $3$-dimensional Euclidean space ${\bf{E}}^3$, fix six pairwise distinct points \begin{equation*} \label{eqA} \begin{array}{ccc} A=(a_1,a_2,a_3), & B=(b_1,b_2,b_3), & C=(c_1,c_2,c_3), \\ D=(d_1,d_2,d_3), & E=(e_1,e_2,e_3), & F=(f_1,f_2,f_3) \end{array} \end{equation*} together with two further points $X^*=(x_1^*,x_2^*,x_3^*)$ and $Y^*=(y_1^*,y_2^*,y_3^*)$ in $\mathbf{E}^3$. We …

Problems and results on determinants involving Legendre symbols
Zhi-Wei Sun
https://arxiv.org/abs/2405.03626 https://arxiv.org/pdf/24…

Problems and results on determinants involving Legendre symbols
In this paper we investigate determinants whose entries are linear combinations of Legendre symbols. After a review of known results, we present some new results and pose many conjectures for further research. For example, we conjecture that $$\det\left[x+\left(\frac{j-k}p\right)+\left(\frac jp\right)-\left(\frac kp\right)\right]_{0\le j,k\le (p-1)/2}=4$$ for any prime $p\equiv3\pmod4$, where $(\frac{\cdot}p)$ denotes the Legendre symbol.

This https://arxiv.org/abs/2402.15861 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

MATHWELL: Generating Educational Math Word Problems at Scale
Math word problems are critical K-8 educational tools, but writing them is time-consuming and requires domain expertise. We suggest that language models can support K-8 math education by automatically generating problems at scale. To be educational, generated problems must be 1) solvable, 2) accurate, and 3) appropriate. Existing datasets are unlabeled for these criteria, making them ill-suited for training problem generators. We introduce MATHWELL, a Llama-2 (70B) model iteratively finetuned t…

The clique chromatic number of sparse random graphs
Manuel Fernandez V, Lutz Warnke
https://arxiv.org/abs/2403.03013 https://arxiv.or…

The clique chromatic number of sparse random graphs
The clique chromatic number of a graph is the smallest number of colors in a vertex coloring so that no maximal clique is monochromatic. In this paper, we determine the order of magnitude of the clique chromatic number of the random graph G_{n,p} for most edge-probabilities p in the range n^{-2/5} \ll p \ll 1. This resolves open problems and questions of Lichev, Mitsche and Warnke as well as Alon and Krievelevich. One major proof difficulty stems from high-degree vertices, which prevent maxim…

This https://arxiv.org/abs/2402.01275 has been replaced.
link: https://scholar.google.com/scholar?q=a

Parametric-Task MAP-Elites
Optimizing a set of functions simultaneously by leveraging their similarity is called multi-task optimization. Current black-box multi-task algorithms only solve a finite set of tasks, even when the tasks originate from a continuous space. In this paper, we introduce Parametric-Task MAP-Elites (PT-ME), a new black-box algorithm for continuous multi-task optimization problems. This algorithm (1) solves a new task at each iteration, effectively covering the continuous space, and (2) exploits a ne…

Problems and results on determinants involving Legendre symbols
Zhi-Wei Sun
https://arxiv.org/abs/2405.03626 https://arxiv.org/pdf/24…

Problems and results on determinants involving Legendre symbols
In this paper we investigate determinants whose entries are linear combinations of Legendre symbols. After a review of known results, we present some new results and pose many conjectures for further research. For example, we conjecture that $$\det\left[x+\left(\frac{j-k}p\right)+\left(\frac jp\right)-\left(\frac kp\right)\right]_{0\le j,k\le (p-1)/2}=4$$ for any prime $p\equiv3\pmod4$, where $(\frac{\cdot}p)$ denotes the Legendre symbol.

Bounds and Limiting Minimizers for a Family of Interaction Energies
Cameron Davies
https://arxiv.org/abs/2404.02322 https://arxiv.org…

Bounds and Limiting Minimizers for a Family of Interaction Energies
We study a two parameter family of energy minimization problems for interaction energies $\mathcal{E}_{α,β}$ with attractive-repulsive potential $W_{α,β}$. We develop a concavity principle, which allows us to provide a lower bound on $\mathcal{E}_{α,β}$ if there exist $β_0<β<β_1$ with minimizers of $\mathcal{E}_{α,β_0}$ and $\mathcal{E}_{α,β_1}$ known. In addition to this, we also derive new conclusions about the limiting behaviour of $\mathcal{E}_{α,β}$ for $β\approx 2.$ Finall…

The least primary factor of the multiplicative group
Greg Martin, Chau Nguyen
https://arxiv.org/abs/2403.02548 https://arxiv.org/pdf/…

The least primary factor of the multiplicative group
Let $S(n)$ denote the least primary factor in the primary decomposition of the multiplicative group $M_n = (\Bbb Z/n\Bbb Z)^\times$. We give an asymptotic formula, with order of magnitude $x/(\log x)^{1/2}$, for the counting function of those integers $n$ for which $S(n) \ne 2$. We also give an asymptotic formula, for any prime power $q$, for the counting function of those integers $n$ for which $S(n) = q$. This group-theoretic problem can be reduced to problems of counting integers with restri…

This https://arxiv.org/abs/2402.15861 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

MATHWELL: Generating Educational Math Word Problems at Scale
Math word problems are critical K-8 educational tools, but writing them is time-consuming and requires domain expertise. We suggest that language models can support K-8 math education by automatically generating problems at scale. To be educational, generated problems must be 1) solvable, 2) accurate, and 3) appropriate. Existing datasets are unlabeled for these criteria, making them ill-suited for training problem generators. We introduce MATHWELL, a Llama-2 (70B) model iteratively finetuned t…

This https://arxiv.org/abs/2306.05599 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On optimal exponent pairs
We quantify the set of known exponent pairs $(k, \ell)$ and develop a framework to compute the optimal exponent pair for an arbitrary objective function. Applying this methodology, we make progress on several open problems, including bounds of the Riemann zeta-function $ζ(s)$ in the critical strip, estimates of the moments of $ζ(1/2 + it)$ and the generalised Dirichlet divisor problem.

This https://arxiv.org/abs/2311.09253 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

The Perception-Robustness Tradeoff in Deterministic Image Restoration
We study the behavior of deterministic methods for solving inverse problems in imaging. These methods are commonly designed to achieve two goals: (1) attaining high perceptual quality, and (2) generating reconstructions that are consistent with the measurements. We provide a rigorous proof that the better a predictor satisfies these two requirements, the larger its Lipschitz constant must be, regardless of the nature of the degradation involved. In particular, to approach perfect perceptual qua…

It’s 4/11 for North Americans, which is excuse enough to share this post:
“The 411 on 4.1.1”
https://adrianroselli.com/2022/12/the-411-on-4-1-1.html
WCAG 2.1/2.2 obsoleting SC 4.1.1 Parsing has made a lot of people frowny, but the more I dig the more …

The 411 on 4.1.1
There is a non-zero chance that WCAG Success Criterion 4.1.1 Parsing will go away in WCAG 2.2. This isn’t a problem for users, regardless of the problems it may pose for the WCAG process, ACT rules, automated testing tools, or ossified testing processes. The joke here is using an antique…

This https://arxiv.org/abs/2306.05599 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On optimal exponent pairs
We quantify the set of known exponent pairs $(k, \ell)$ and develop a framework to compute the optimal exponent pair for an arbitrary objective function. Applying this methodology, we make progress on several open problems, including bounds of the Riemann zeta-function $ζ(s)$ in the critical strip, estimates of the moments of $ζ(1/2 + it)$ and the generalised Dirichlet divisor problem.

An Interpretable Power System Transient Stability Assessment Method with Expert Guiding Neural-Regression-Tree
Hanxuan Wang, Na Lu, Zixuan Wang, Jiacheng Liu, Jun Liu
https://arxiv.org/abs/2404.02555

An Interpretable Power System Transient Stability Assessment Method with Expert Guiding Neural-Regression-Tree
Deep learning based transient stability assessment (TSA) has achieved great success, yet the lack of interpretability hinders its industrial application. Although a great number of studies have tried to explore the interpretability of network solutions, many problems still remain unsolved: (1) the difference between the widely accepted power system knowledge and the generated interpretive rules is large, (2) the probability characteristics of the neural network have not been fully considered du…

Existence, uniqueness, and regularity of solutions to nonlinear and non-smooth parabolic obstacle problems
Durandard Th\'eo, Strulovici Bruno
https://arxiv.org/abs/2404.01498 …

Existence, uniqueness, and regularity of solutions to nonlinear and non-smooth parabolic obstacle problems
We establish the existence, uniqueness, and $W^{1,2,p}$-regularity of solutions to fully nonlinear parabolic obstacle problems when the obstacle is the pointwise supremum of arbitrary functions in $W^{1,2,p}$ and the operator is only assumed to be measurable in the state and time variables. The results hold for a large class of non-smooth obstacles, including all convex obstacles. Applied to stopping problems, they imply that the decision maker never stops at a convex kink of the stopping payof…

This https://arxiv.org/abs/2403.00407 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Configurations in the Euclidean space related to the 3D genome reconstruction problem from partially phased data
A motivation for studying the following problems comes from applications to Biology; see \cite{cifuentes20233d}. In the $3$-dimensional Euclidean space ${\bf{E}}^3$, fix six pairwise distinct points \begin{equation*} \label{eqA} \begin{array}{ccc} A=(a_1,a_2,a_3), & B=(b_1,b_2,b_3), & C=(c_1,c_2,c_3), \\ D=(d_1,d_2,d_3), & E=(e_1,e_2,e_3), & F=(f_1,f_2,f_3) \end{array} \end{equation*} together with two further points $X^*=(x_1^*,x_2^*,x_3^*)$ and $Y^*=(y_1^*,y_2^*,y_3^*)$ in $\mathbf{E}^3$. We …

Clique-free t-matchings in degree-bounded graphs
Katarzyna Paluch, Mateusz Wasylkiewicz
https://arxiv.org/abs/2405.00429 https://arxi…

Clique-free t-matchings in degree-bounded graphs
We consider problems of finding a maximum size/weight $t$-matching without forbidden subgraphs in an undirected graph $G$ with the maximum degree bounded by $t+1$, where $t$ is an integer greater than $2$. Depending on the variant forbidden subgraphs denote certain subsets of $t$-regular complete partite subgraphs of $G$. A graph is complete partite if there exists a partition of its vertex set such that every pair of vertices from different sets is connected by an edge and vertices from the sa…

A Unified Algorithmic Framework for Dynamic Assortment Optimization under MNL Choice
Shuo Sun (Max), Rajan Udwani (Max), Zuo-Jun (Max), Shen
https://arxiv.org/abs/2404.03604

A Unified Algorithmic Framework for Dynamic Assortment Optimization under MNL Choice
We consider assortment and inventory planning problems with dynamic stockout-based substitution effects and no replenishment. We consider two settings: 1. Customers can see all available products when they arrive, which is commonly seen in physical stores. 2. The seller can choose to offer a subset of available products to each customer, which is typical on online platforms. Both settings are known to be computationally challenging, and the current approximation algorithms for the two settings …

Extended Galerkin neural network approximation of singular variational problems with error control
Mark Ainsworth, Justin Dong
https://arxiv.org/abs/2405.00815

Extended Galerkin neural network approximation of singular variational problems with error control
We present extended Galerkin neural networks (xGNN), a variational framework for approximating general boundary value problems (BVPs) with error control. The main contributions of this work are (1) a rigorous theory guiding the construction of new weighted least squares variational formulations suitable for use in neural network approximation of general BVPs (2) an ``extended'' feedforward network architecture which incorporates and is even capable of learning singular solution structures, thus…

Mean-field theory of 1 1D $\mathbb{Z}_2$ lattice gauge theory with matter
Matja\v{z} Kebri\v{c}, Ulrich Schollw\"ock, Fabian Grusdt
https://arxiv.org/abs/2404.02890

Mean-field theory of 1+1D $\mathbb{Z}_2$ lattice gauge theory with matter
Lattice gauge theories (LGTs) provide valuable insights into problems in strongly correlated many-body systems. Confinement which arises when matter is coupled to gauge fields is just one of the open problems, where LGT formalism can explain the underlying mechanism. However, coupling gauge fields to dynamical charges complicates the theoretical and experimental treatment of the problem. Developing a simplified mean-field theory is thus one of the ways to gain new insights into these complicate…

MorphText: Deep Morphology Regularized Arbitrary-shape Scene Text Detection
Chengpei Xu, Wenjing Jia, Ruomei Wang, Xiaonan Luo, Xiangjian He
https://arxiv.org/abs/2404.17151 https://arxiv.org/pdf/2404.17151
arXiv:2404.17151v1 Announce Type: new
Abstract: Bottom-up text detection methods play an important role in arbitrary-shape scene text detection but there are two restrictions preventing them from achieving their great potential, i.e., 1) the accumulation of false text segment detections, which affects subsequent processing, and 2) the difficulty of building reliable connections between text segments. Targeting these two problems, we propose a novel approach, named ``MorphText", to capture the regularity of texts by embedding deep morphology for arbitrary-shape text detection. Towards this end, two deep morphological modules are designed to regularize text segments and determine the linkage between them. First, a Deep Morphological Opening (DMOP) module is constructed to remove false text segment detections generated in the feature extraction process. Then, a Deep Morphological Closing (DMCL) module is proposed to allow text instances of various shapes to stretch their morphology along their most significant orientation while deriving their connections. Extensive experiments conducted on four challenging benchmark datasets (CTW1500, Total-Text, MSRA-TD500 and ICDAR2017) demonstrate that our proposed MorphText outperforms both top-down and bottom-up state-of-the-art arbitrary-shape scene text detection approaches.

Getting closer and closer to the point where I'll start a git tree[1] with fixes and reverts for #Linux #kernel regressions in the latest stable series, as from here it seems quite a few of the known problems could quickly be solved by a revert or applying fixes already queued[2]/still under review[3].…

Sparse Linear Regression and Lattice Problems
Aparna Gupte, Neekon Vafa, Vinod Vaikuntanathan
https://arxiv.org/abs/2402.14645 https://

Sparse Linear Regression and Lattice Problems
Sparse linear regression (SLR) is a well-studied problem in statistics where one is given a design matrix $X\in\mathbb{R}^{m\times n}$ and a response vector $y=Xθ^*+w$ for a $k$-sparse vector $θ^*$ (that is, $\|θ^*\|_0\leq k$) and small, arbitrary noise $w$, and the goal is to find a $k$-sparse $\widehatθ \in \mathbb{R}^n$ that minimizes the mean squared prediction error $\frac{1}{m}\|X\widehatθ-Xθ^*\|^2_2$. While $\ell_1$-relaxation methods such as basis pursuit, Lass…

The Real Story Behind NPR’s Current Problems
https://slate.com/business/2024/04/npr-diversity-public-broadcasting-radio.html
See our guidelines for 2024 election coverage

Algorithmic Analysis of Termination Problems for Nondeterministic Quantum Programs
Jianling Fu, Hui Jiang, Ming Xu, Yuxin Deng, Zhi-Bin Li
https://arxiv.org/abs/2402.15827

Algorithmic Analysis of Termination Problems for Nondeterministic Quantum Programs
We consider the two categories of termination problems of quantum programs with nondeterminism: 1) Is an input of a program terminating with probability one under all schedulers? If not, how can a scheduler be synthesized to evidence the nontermination? 2) Are all inputs terminating with probability one under their respective schedulers? If yes, a further question asks whether there is a scheduler that forces all inputs to be terminating with probability one together with how to synthesize it; …

Semantic Information Theory in a feedback-control Kuramoto Model
Damian R Sowinski, Adam Frank, Gourab Ghoshal
https://arxiv.org/abs/2404.02221 https://

Semantic Information Theory in a feedback-control Kuramoto Model
Semantic Information Theory (SIT) offers a new approach to evaluating the information architecture of complex systems. In this study we describe the steps required to {\it operationalize} SIT via its application to dynamical problems. Our road map has four steps: (1) separating the dynamical system into agent-environment sub-systems; (2) choosing an appropriate coarse graining and quantifying correlations; (3) identifying a measure of viability; (4) implementing a scrambling protocol and measur…

This https://arxiv.org/abs/2307.09444 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDC_…

No distributed quantum advantage for approximate graph coloring
We give an almost complete characterization of the hardness of $c$-coloring $χ$-chromatic graphs with distributed algorithms, for a wide range of models of distributed computing. In particular, we show that these problems do not admit any distributed quantum advantage. To do that: 1) We give a new distributed algorithm that finds a $c$-coloring in $χ$-chromatic graphs in $\tilde{\mathcal{O}}(n^{\frac{1}α})$ rounds, with $α= \bigl\lfloor\frac{c-1}{χ- 1}\bigr\rfloor$. 2) We prove that any di…

Algorithms for Halfplane Coverage and Related Problems
Haitao Wang, Jie Xue
https://arxiv.org/abs/2402.16323 https://arxiv.org/pdf/24…

Algorithms for Halfplane Coverage and Related Problems
Given in the plane a set of points and a set of halfplanes, we consider the problem of computing a smallest subset of halfplanes whose union covers all points. In this paper, we present an $O(n^{4/3}\log^{5/3}n\log^{O(1)}\log n)$-time algorithm for the problem, where $n$ is the total number of all points and halfplanes. This improves the previously best algorithm of $n^{10/3}2^{O(\log^*n)}$ time by roughly a quadratic factor. For the special case where all halfplanes are lower ones, our algorit…

On the non-existence of oscillation numbers in Sturm-Liouville theory
Angelo B. Mingarelli
https://arxiv.org/abs/2404.19575 https://a…

On the non-existence of oscillation numbers in Sturm-Liouville theory
We prove an old conjecture that relates the existence of non-real eigenvalues of Sturm-Liouville Dirichlet problems on a finite interval to the non-existence of oscillation numbers of its real eigenfunctions, [[6], p.104, Problems 3 and 5]. This extends to the general case, a previous result in [1], [2] where it was shown that the presence of even one pair of non-real eigenvalues implies the non-existence of a positive eigenfunction (or ground state). We also provide estimates on the Haupt and …

This https://arxiv.org/abs/2402.15861 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

MATHWELL: Generating Educational Math Word Problems at Scale
Math word problems are critical K-8 educational tools, but writing them is time-consuming and requires domain expertise. We suggest that language models can support K-8 math education by automatically generating problems at scale. To be educational, generated problems must be 1) solvable, 2) accurate, and 3) appropriate. Existing datasets are unlabeled for these criteria, making them ill-suited for training problem generators. We introduce MATHWELL, a Llama-2 (70B) model iteratively finetuned t…

This https://arxiv.org/abs/2003.13055 has been replaced.
link: https://scholar.google.com/scholar?q=a

The spanning method and the Lehmer totient problem
In this paper we introduce and develop the notion of spanning of integers along functions $f:\mathbb{N}\longrightarrow \mathbb{R}$. We apply this method to a class of problems requiring to determine if the equations of the form $tf(n)=n-k$ has a solution $n\in \mathbb{N}$ for a fixed $k\in \mathbb{N}$ and some $t\in \mathbb{N}$. In particular, we show that \begin{align} \# \{n\leq s~|~tφ(n)+1=n,~\mathbf{for~some}~t\in \mathbb{N}\}\geq \frac{s}{2\log s}\prod \limits_{p | \lfloor s\rfl…

Shaving Logs via Large Sieve Inequality: Faster Algorithms for Sparse Convolution and More
Ce Jin, Yinzhan Xu
https://arxiv.org/abs/2403.20326 https://

Shaving Logs via Large Sieve Inequality: Faster Algorithms for Sparse Convolution and More
In sparse convolution-type problems, a common technique is to hash the input integers modulo a random prime $p\in [Q/2,Q]$ for some parameter $Q$, which reduces the range of the input integers while preserving their additive structure. However, this hash family suffers from two drawbacks, which led to bottlenecks in many state-of-the-art algorithms: (1) The collision probability of two elements from $[N]$ is $O(\frac{\log N}{Q})$ rather than $O(\frac{1}{Q})$; (2) It is difficult to derandomize …

Roman Domination on Graphings
Adrian Rettich
https://arxiv.org/abs/2404.19718 https://arxiv.org/pdf/2404.19718

Roman Domination on Graphings
We study a variant of domination, called Roman domination, where we must assign to each vertex one of the labels 0, 1, or 2 and require that every vertex with label 0 has a neighbour with label 2. We study the problem of finding a low-cost Roman dominating function on Lebesgue-measurable graphings, that is, on infinite graphs whose vertices are the points of a probability space. We provide a framework to tackle optimisation problems in the measurable combinatorial setting. In particular, we ful…

Parameter Selection by GCV and a $\chi^2$ test within Iterative Methods for $\ell_1$-regularized Inverse Problems
Brian Sweeney, Rosemary Renaut, Malena Espa\~nol
https://arxiv.org/abs/2404.19156

Parameter Selection by GCV and a $χ^2$ test within Iterative Methods for $\ell_1$-regularized Inverse Problems
$\ell_1$ regularization is used to preserve edges or enforce sparsity in a solution to an inverse problem. We investigate the Split Bregman and the Majorization-Minimization iterative methods that turn this non-smooth minimization problem into a sequence of steps that include solving an $\ell_2$-regularized minimization problem. We consider selecting the regularization parameter in the inner generalized Tikhonov regularization problems that occur at each iteration in these $\ell_1$ iterative me…

The instance s-h.social has just come to my attention. What problems are there with it? Well....
1. It still runs Mastodon v4.2.3
2. It is overrun by spammers
3. The admin appears to be absent
4. I don't think I need to say any more
#Fediblock #MastoAdmin

This https://arxiv.org/abs/2404.10404 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCR_…

Sisu: Decentralized Trustless Bridge For Full Ethereum Node
In this paper, we present a detailed approach and implementation to prove Ethereum full node using recursive SNARK, distributed general GKR and Groth16. Our protocol's name is Sisu whose architecture is based on distributed Virgo in zkBridge with some major improvements. Besides proving signature aggregation, we provide solutions to 2 hard problems in proving Ethereum full node: 1) any public key is valid under previous beacon state and 2) all public keys are pairwise distinct. Our solution doe…

This https://arxiv.org/abs/2310.03755 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCE_…

Physics Informed Neural Network Code for 2D Transient Problems (PINN-2DT) Compatible with Google Colab
We present an open-source Physics Informed Neural Network environment for simulations of transient phenomena on two-dimensional rectangular domains, with the following features: (1) it is compatible with Google Colab which allows automatic execution on cloud environment; (2) it supports two dimensional time-dependent PDEs; (3) it provides simple interface for definition of the residual loss, boundary condition and initial loss, together with their weights; (4) it support Neumann and Dirichlet b…

Simplex slicing: an asymptotically-sharp lower bound
Colin Tang
https://arxiv.org/abs/2403.13224 https://arxiv.org/pdf/2403.13224

Simplex slicing: an asymptotically-sharp lower bound
We show that for the regular n-simplex, the 1-codimensional central slice that's parallel to a facet will achieve the minimum area (up to a 1-o(1) factor) among all 1-codimensional central slices, thus improving the previous best known lower bound (Brzezinski 2013) by a factor of $\frac{2\sqrt{3}}{e} \approx 1.27$. In addition to the standard technique of interpreting geometric problems as problems about probability distributions and standard Fourier-analytic techniques, we rely on a new idea, …

This https://arxiv.org/abs/2401.09773 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCV_…

SEINE: Structure Encoding and Interaction Network for Nuclei Instance Segmentation
Nuclei instance segmentation in histopathological images is of great importance for biological analysis and cancer diagnosis but remains challenging for two reasons. (1) Similar visual presentation of intranuclear and extranuclear regions of chromophobe nuclei often causes under-segmentation, and (2) current methods lack the exploration of nuclei structure, resulting in fragmented instance predictions. To address these problems, this paper proposes a structure encoding and interaction network, …

Using Large Language Models for Natural Language Processing Tasks in Requirements Engineering: A Systematic Guideline
Andreas Vogelsang, Jannik Fischbach
https://arxiv.org/abs/2402.13823

Using Large Language Models for Natural Language Processing Tasks in Requirements Engineering: A Systematic Guideline
To use Large Language Models (LLMs) in a targeted way for NLP problems in RE, we require both (1) basic knowledge about the inner workings of LLMs and (2) a guideline on how to select and systematically utilize or repurpose LLMs for NLP4RE tasks. This chapter establishes the required knowledge and introduces the fundamentals of LLMs in the first part. In the second part, we present a detailed guideline for students, researchers, and practitioners on using LLMs for their purposes.

Algorithmic Analysis of Termination Problems for Nondeterministic Quantum Programs
Jianling Fu, Hui Jiang, Ming Xu, Yuxin Deng, Zhi-Bin Li
https://arxiv.org/abs/2402.15827

Algorithmic Analysis of Termination Problems for Nondeterministic Quantum Programs
We consider the two categories of termination problems of quantum programs with nondeterminism: 1) Is an input of a program terminating with probability one under all schedulers? If not, how can a scheduler be synthesized to evidence the nontermination? 2) Are all inputs terminating with probability one under their respective schedulers? If yes, a further question asks whether there is a scheduler that forces all inputs to be terminating with probability one together with how to synthesize it; …

Large Sieve Inequalities for periods of Maass forms
Dimitrios Lekkas, Marios Voskou
https://arxiv.org/abs/2405.01056 https://arxiv.or…

Large Sieve Inequalities for periods of Maass forms
For $Γ$ a Fuchsian Group of the first kind, we obtain large sieve inequalities with weights the hyperbolic periods of Maass forms of even weight. This is inspired by work of Chamizo, who proved a large sieve inequality with weights values of Maass forms of weight $0$. The motivation is applications in counting problems in $Γ_1 \backslash Γ/ Γ_2$, where $Γ_1$, $Γ_2$ are hyperbolic subgroups of $Γ$.

This https://arxiv.org/abs/2404.13336 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Modeling Seismic Wave Propagation in TTI Media Using Residual Perfectly Matched Layer
The perfectly matched layer(PML) is commonly used in wave propagation, radiation and diffraction problems in unbounded space domains. A new implementation scheme of PML is presented. The PML formulation is pre-defined, and the wave field absorption is achieved by calculating the residual between the PML equation and original equation through backward induction. Two forms of the Residual PML (RPML) are presented: RPML-1, which defines the residual as the difference between the original and PML e…

A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems
Erik Burman, Rebecca Durst, Miguel A. Fern\'andez, Johnny Guzm\'an, Sijing Liu
https://arxiv.org/abs/2404.01599

A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems
We consider a parabolic-parabolic interface problem and construct a loosely coupled prediction-correction scheme based on the Robin-Robin splitting method analyzed in [J. Numer. Math., 31(1):59--77, 2023]. We show that the errors of the correction step converge at $\mathcal O((Δt)^2)$, under suitable convergence rate assumptions on the discrete time derivative of the prediction step, where $Δt$ stands for the time-step length. Numerical results are shown to support our analysis and the assump…

Analytic pseudo-rotations II
Pierre Berger
https://arxiv.org/abs/2402.15303 https://arxiv.org/pdf/2402.15303

Analytic pseudo-rotations II
We construct analytic surface symplectomorphisms with unstable elliptic fixed points; this solves a problem of Birkhoff (1927). More precisely, we construct analytic symplectomorphisms of the sphere and of the disk which are transitive, with respectively only 2 and 1 periodic points. This also solves problems of proposed by Herman (1998), Fayad-Katok (2004) and Fayad-Krikorian (2018). To establish these results, we introduce a principle that enables to realize, by an analytic symplectomorphism,…

Cowboys release LB Leighton Vander Esch, WR Michael Gallup https://www.yardbarker.com/nfl/articles/cowboys_release_lb_leighton_vander_esch_wr_michael_gallup/s1_17049_40116211

Cowboys release LB Leighton Vander Esch, WR Michael Gallup
The Dallas Cowboys released linebacker Leighton Vander Esch and receiver Michael Gallup on Friday. The Cowboys said Vander Esch was released with a failed physical designation. According to reports, the move frees up $2.14 million in salary cap space. Vander Esch missed the final 12 games of the 2023 season with a neck injury and has long had problems with his neck. The Cowboys said Gallup will be listed as a post-June 1 cut. The move reportedly saves Dallas $9.5 million. Vander Esch, a first-r…

Extremal problems in BMO and VMO involving the Garsia norm
Konstantin M. Dyakonov
https://arxiv.org/abs/2404.05565 https://arxiv.org/…

Extremal problems in BMO and VMO involving the Garsia norm
Given an $L^2$ function $f$ on the unit circle $\mathbb T$, we put $$Φ_f(z):=\mathcal P(|f|^2)(z)-|\mathcal Pf(z)|^2,\qquad z\in\mathbb D,$$ where $\mathbb D$ is the open unit disk and $\mathcal P$ is the Poisson integral operator. The Garsia norm $\|f\|_G$ is then defined as $\sup_{z\in\mathbb D}\left(Φ_f(z)\right)^{1/2}$, and the space ${\rm BMO}$ is formed by the functions $f\in L^2$ with $\|f\|_G<\infty$. If $\|f\|^2_G=Φ_f(z_0)$ for some …

This https://arxiv.org/abs/2312.13588 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A few new oddtown and eventown problems
Given a vector $α= (α_1, \ldots, α_k) \in \mathbb{F}_2^k$, we say a collection of subsets $\mathcal{F}$ satisfies $α$-intersection pattern modulo $2$ if all $i$-wise intersections consisting of $i$ distinct sets from $\mathcal{F}$ have size $α_i \pmod{2}$. In this language, the classical oddtown and eventown problems correspond to vectors $α=(1,0)$ and $α=(0,0)$ respectively. In this paper, we determine the largest such set families of subsets on a $n$-element set with $α$-intersection …

A Faster Algorithm for Pigeonhole Equal Sums
Ce Jin, Hongxun Wu
https://arxiv.org/abs/2403.19117 https://arxiv.org/pdf/2403.19117

A Faster Algorithm for Pigeonhole Equal Sums
An important area of research in exact algorithms is to solve Subset-Sum-type problems faster than meet-in-middle. In this paper we study Pigeonhole Equal Sums, a total search problem proposed by Papadimitriou (1994): given $n$ positive integers $w_1,\dots,w_n$ of total sum $\sum_{i=1}^n w_i < 2^n-1$, the task is to find two distinct subsets $A, B \subseteq [n]$ such that $\sum_{i\in A}w_i=\sum_{i\in B}w_i$. Similar to the status of the Subset Sum problem, the best known algorithm for Pigeonh…

A symmetric function approach to polynomial regression
Hans-Christian Herbig, Daniel Herden, Christopher Seaton
https://arxiv.org/abs/2402.11717 https://…

A symmetric function approach to polynomial regression
We give an explicit solution formula for the polynomial regression problem in terms of Schur polynomials and Vandermonde determinants. We thereby generalize the work of Chang, Deng, and Floater to the case of model functions of the form $\sum _{i=1}^{n} a_{i} x^{d_{i}}$ for some integer exponents $d_{1} >d_{2} >\dotsc >d_{n} \geq 0$ and phrase the results using Schur polynomials. Even though the solution circumvents the well-known problems with the forward stability of the normal equation, it i…

This https://arxiv.org/abs/2211.02277 has been replaced.
link: https://scholar.google.com/scholar?q=a

Discretized sum-product type problems: Energy variants and Applications
In this paper, we provide estimates for the additive discretized energy of \[\sum_{c\in C} |\{(a_1, a_2, b_1, b_2)\in A^2\times B^2: |(a_1 +cb_1) - (a_2 + cb_2)|\le δ\}|_δ,\] that depend on non-concentration conditions of the sets. Our proof follows the Guth-Katz-Zahl approach (2021) with appropriate changes along the way clarifying and optimizing many of the steps. Several applications will also be discussed.

This https://arxiv.org/abs/2401.07152 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Inference for Synthetic Controls via Refined Placebo Tests
The synthetic control method is often applied to problems with one treated unit and a small number of control units. A common inferential task in this setting is to test null hypotheses regarding the average treatment effect on the treated. Inference procedures that are justified asymptotically are often unsatisfactory due to (1) small sample sizes that render large-sample approximation fragile and (2) simplification of the estimation procedure that is implemented in practice. An alternative is…

This https://arxiv.org/abs/2311.12672 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Neumann-Poincaré operators and self-adjoint transmission problems
We discuss the self-adjointness in $L^2$-setting of the operators acting as $-\nabla\cdot h\nabla$, with piecewise constant functions $h$ having a jump along a Lipschitz hypersurface $Σ$, without explicit assumptions on the sign of $h$. We establish a number of sufficient conditions for the self-adjointness of the operator with $H^s$-regularity for suitable $s\in[1,\frac{3}{2}]$, in terms of the jump value and the regularity and geometric properties of $Σ$. An important intermediate step is a…

This https://arxiv.org/abs/2404.10404 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCR_…

Sisu: Decentralized Trustless Bridge For Full Ethereum Node
In this paper, we present a detailed approach and implementation to prove Ethereum full node using recursive SNARK, distributed general GKR and Groth16. Our protocol's name is Sisu whose architecture is based on distributed Virgo in zkBridge with some major improvements. Besides proving signature aggregation, we provide solutions to 2 hard problems in proving Ethereum full node: 1) any public key is valid under previous beacon state and 2) all public keys are pairwise distinct. Our solution doe…

This https://arxiv.org/abs/2305.02925 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDM_…

Maximum values of the Sombor-index-like graph invariants of trees and connected graphs
A set of novel vertex-degree-based invariants was introduced by Gutman, denoted by \newline $SO_1, SO_2, \ldots,SO_6$. These invariants were constructed through geometric reasoning based on a new graph invariant framework. Motivated by proposed open problems in [Z. Tang, Q. Li, H. Deng, \textit{Trees with Extremal Values of the Sombor-Index-Like Graph Invariants}, MATCH Commun. Math. Comput. Chem. \textbf{90} (2023) 203-222], we have found the maximum values of $SO_5$ and $SO_6$ in the set of m…

This https://arxiv.org/abs/2204.10161 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the nodal set of solutions to some sublinear equations without homogeneity
We investigate the structure of the nodal set of solutions to an unstable Alt-Phillips type problem \[ -Δu = λ_+(u^+)^{p-1}-λ_-(u^-)^{q-1} \] where $1 \le p0$, $λ_- \ge 0$. The equation is characterized by the sublinear inhomogeneous character of the right hand-side, which makes difficult to adapt in a standard way classical tools from free-boundary problems, such as monotonicity formulas and blow-up arguments. Our main results are: the local behavior of solutions close to the…

This https://arxiv.org/abs/2305.08650 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Uniqueness of optimal plans for multi-marginal mass transport problems via a reduction argument
For a family of probability spaces $\{(X_k,\mathcal{B}_{X_k},μ_k)\}_{k=1}^N$ and a cost function $c: X_1\times\cdots\times X_N\to \mathbb{R}$ we consider the Monge-Kantorovich problem \begin{align*}\tag{MK}\label{MONKANT} \inf_{λ\inΠ(μ_1,\ldots,μ_N)}\int_{\prod_{k=1}^N X_k}c\,dλ. \end{align*} Then for each ordered subset $\mathcal{P}=\{i_1,\ldots,i_p\}\subsetneq\{1,...,N\}$ with $p\geq 2$ we create a new cost function $c_\mathcal{P}$ corresponding to the original cost function $c$ defined…

This https://arxiv.org/abs/2401.12084 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Temporal Aggregation for the Synthetic Control Method
The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit with panel data. Two challenges arise with higher frequency data (e.g., monthly versus yearly): (1) achieving excellent pre-treatment fit is typically more challenging; and (2) overfitting to noise is more likely. Aggregating data over time can mitigate these problems but can also destroy important signal. In this paper, we bound the bias for SCM with disaggregated and aggregated o…

Exact and Approximate High-Multiplicity Scheduling on Identical Machines
Klaus Jansen, Kai Kahler, Esther Zwanger
https://arxiv.org/abs/2404.17274 https://…

Exact and Approximate High-Multiplicity Scheduling on Identical Machines
Goemans and Rothvoss (SODA'14) gave a framework for solving problems in time $enc(P)^{2^{O(N)}}enc(Q)^{O(1)}$ that can be described as finding a point in $\text{int.cone}(P\cap\mathbb{Z}^N)\cap Q$, where $P,Q\subset\mathbb{R}^N$ are (bounded) polyhedra. This framework can be used to solve various scheduling problems, but the encoding length $enc(P)$ usually involves large parameters like the makespan. We describe three tools to improve the framework by Goemans and Rothvoss: Problem-specific pre…

This https://arxiv.org/abs/2402.02525 has been replaced.
link: https://scholar.google.com/scholar?q=a

A note on vertex Turán problems in the Kneser cube
The Kneser cube $Kn_n$ has vertex set $2^{[n]}$ and two vertices $F,F'$ are joined by an edge if and only if $F\cap F'=\emptyset$. For a fixed graph $G$, we are interested in the most number $vex(n,G)$ of vertices of $Kn_n$ that span a $G$-free subgraph in $Kn_n$. We show that the asymptotics of $vex(n,G)$ is $(1+o(1))2^{n-1}$ for bipartite $G$ and $(1-o(1))2^n$ for graphs with chromatic number at least 3. We also obtain results on the order of magnitude of $2^{n-1}-vex(n,G)$ and $2^n-vex(n,G)$…

Simple algorithms to test and learn local Hamiltonians
Francisco Escudero Guti\'errez
https://arxiv.org/abs/2404.06282 https://ar…

Simple algorithms to test and learn local Hamiltonians
We consider the problems of testing and learning an $n$-qubit $k$-local Hamiltonian from queries to its evolution operator with respect the 2-norm of the Pauli spectrum, or equivalently, the normalized Frobenius norm. For testing whether a Hamiltonian is $ε_1$-close to $k$-local or $ε_2$-far from $k$-local, we show that $O(1/(ε_2-ε_1)^{8})$ queries suffice. This solves two questions posed in a recent work by Bluhm, Caro and Oufkir. For learning up to error $ε$, we show that $\exp(O(k^2+k\l…

Quantum Speedup for Some Geometric 3SUM-Hard Problems and Beyond
J. Mark Keil, Fraser McLeod, Debajyoti Mondal
https://arxiv.org/abs/2404.04535 https://

Quantum Speedup for Some Geometric 3SUM-Hard Problems and Beyond
The classical 3SUM conjecture states that the class of 3SUM-hard problems does not admit a truly subquadratic $O(n^{2-δ})$-time algorithm, where $δ>0$, in classical computing. The geometric 3SUM-hard problems have widely been studied in computational geometry and recently, these problems have been examined under the quantum computing model. For example, Ambainis and Larka [TQC'20] designed a quantum algorithm that can solve many geometric 3SUM-hard problems in $O(n^{1+o(1)})$-time, whereas Bu…

Sisu: Decentralized Trustless Bridge For Full Ethereum Node
Billy Pham, Huy Nguyen
https://arxiv.org/abs/2404.10404 https://arxiv.org…

Sisu: Decentralized Trustless Bridge For Full Ethereum Node
In this paper, we present a detailed approach and implementation to prove Ethereum full node using recursive SNARK, distributed general GKR and Groth16. Our protocol's name is Sisu whose architecture is based on distributed Virgo in zkBridge with some major improvements. Besides proving signature aggregation, we provide solutions to 2 hard problems in proving Ethereum full node: 1) any public key is valid under previous beacon state and 2) all public keys are pairwise distinct. Our solution doe…

TRIPs-Py: Techniques for Regularization of Inverse Problems in Python
Mirjeta Pasha, Silvia Gazzola, Connor Sanderford, Ugochukwu O. Ugwu
https://arxiv.org/abs/2402.17603

TRIPs-Py: Techniques for Regularization of Inverse Problems in Python
In this paper, we describe TRIPs-Py, a new Python package of linear discrete inverse problems solvers and test problems. The goal of the package is two-fold: 1) to provide tools for solving small and large-scale inverse problems, and 2) to introduce test problems arising from a wide range of applications. The solvers available in TRIPs-Py include direct regularization methods (such as truncated singular value decomposition and Tikhonov) and iterative regularization techniques (such as Krylov su…

Spatially sparse optimization problems in fractional order Sobolev spaces
Anna Lentz, Daniel Wachsmuth
https://arxiv.org/abs/2402.14417 https://

Spatially sparse optimization problems in fractional order Sobolev spaces
We investigate time-dependent optimization problems in fractional Sobolev spaces with the sparsity promoting $L^p$-pseudo norm for $0

Numerical Discretization Methods for Linear Quadratic Control Problems with Time Delays
Zhanhao Zhang, Steen H{\o}rsholt, John Bagterp J{\o}rgensen
https://arxiv.org/abs/2404.08440

Numerical Discretization Methods for Linear Quadratic Control Problems with Time Delays
This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We describe the weight matrices of the LQ-OCPs as differential equations systems, allowing us to derive the discrete equivalent of the continuous-time LQ-OCPs. Three numerical methods are introduced for solving proposed differential equations systems: 1) the ordinary differential equation (ODE) method, 2) the matrix exponential method, and 3) the …

This https://arxiv.org/abs/2401.07152 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Inference for Synthetic Controls via Refined Placebo Tests
The synthetic control method is often applied to problems with one treated unit and a small number of control units. A common inferential task in this setting is to test null hypotheses regarding the average treatment effect on the treated. Inference procedures that are justified asymptotically are often unsatisfactory due to (1) small sample sizes that render large-sample approximation fragile and (2) simplification of the estimation procedure that is implemented in practice. An alternative is…

This https://arxiv.org/abs/2308.13428 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the arithmetic of the join rings over finite fields
Given a collection $\{ G_i\}_{i=1}^d$ of finite groups and a ring $R$, we have previously introduced and studied certain foundational properties of the join ring $\mathcal{J}_{G_1, G_2, \ldots, G_d}(R)$. This ring bridges two extreme worlds: matrix rings $M_n(R)$ on one end, and group rings $R[G]$ on the other. The construction of this ring was motivated by various problems in graph theory, network theory, nonlinear dynamics, and neuroscience. In this paper, we continue our investigations of th…

Simple algorithms to test and learn local Hamiltonians
Francisco Escudero Guti\'errez
https://arxiv.org/abs/2404.06282 https://ar…

Simple algorithms to test and learn local Hamiltonians
We consider the problems of testing and learning an $n$-qubit $k$-local Hamiltonian from queries to its evolution operator with respect the 2-norm of the Pauli spectrum, or equivalently, the normalized Frobenius norm. For testing whether a Hamiltonian is $ε_1$-close to $k$-local or $ε_2$-far from $k$-local, we show that $O(1/(ε_2-ε_1)^{8})$ queries suffice. This solves two questions posed in a recent work by Bluhm, Caro and Oufkir. For learning up to error $ε$, we show that $\exp(O(k^2+k\l…

Improving the Bit Complexity of Communication for Distributed Convex Optimization
Mehrdad Ghadiri, Yin Tat Lee, Swati Padmanabhan, William Swartworth, David Woodruff, Guanghao Ye
https://arxiv.org/abs/2403.19146

Improving the Bit Complexity of Communication for Distributed Convex Optimization
We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression, $p$-norm regression (for $1\leq p\leq 2$), linear programming, minimizing the sum of finitely many convex nonsmooth functions with varying supports, and low rank approximation; for a number of these fundamental problems our bounds are nearly optimal, as proven by …

This https://arxiv.org/abs/2301.03420 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Criticality in Sperner's Lemma
We answer a question posed by T. Gallai in 1969 concerning criticality in Sperner's lemma, listed as Problem 9.14 in the collection of Jensen and Toft [Graph coloring problems, John Wiley & Sons, Inc., New York, 1995]. Sperner's lemma states that if a labelling of the vertices of a triangulation of the $d$-simplex $Δ^d$ with labels $1, 2, \ldots, d+1$ has the property that (i) each vertex of $Δ^d$ receives a distinct label, and (ii) any vertex lying in a face of $Δ^d$ has the same label as…

This https://arxiv.org/abs/2309.03029 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multiplicity and symmetry breaking for supercritical elliptic problems in exterior domains
We deal with the following semilinear equation in exterior domains \[-Δu + u = a(x)|u|^{p-2}u,\qquad u\in H^1_0({A_R}), \] where ${A_R} := \{x\in\mathbb{R}^N:\, |x|>{R}\}$, $N\ge 3$, $R>0$. Assuming that the weight $a$ is positive and satisfies some symmetry and monotonicity properties, we exhibit a positive solution having the same features as $a$, for values of $p>2$ in a suitable range that includes exponents greater than the standard Sobolev critical one. In the special…

This https://arxiv.org/abs/2402.15303 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Analytic pseudo-rotations II: a principle for spheres, disks and annuli
We construct analytic surface symplectomorphisms with unstable elliptic fixed points; this solves a problem of Birkhoff (1927). More precisely, we construct analytic symplectomorphisms of the sphere and of the disk which are transitive, with respectively only 2 and 1 periodic points. This also solves problems of proposed by Herman (1998), Fayad-Katok (2004) and Fayad-Krikorian (2018). To establish these results, we introduce a principle that enables to realize, by an analytic symplectomorphism,…

This https://arxiv.org/abs/2308.07004 has been replaced.
link: https://scholar.google.com/scholar?q=a

$(1-ε)$-Approximation of Knapsack in Nearly Quadratic Time
Knapsack is one of the most fundamental problems in theoretical computer science. In the $(1 - ε)$-approximation setting, although there is a fine-grained lower bound of $(n + 1 / ε) ^ {2 - o(1)}$ based on the $(\min, +)$-convolution hypothesis ([K{ü}nnemann, Paturi and Stefan Schneider, ICALP 2017] and [Cygan, Mucha, Wegrzycki and Wlodarczyk, 2017]), the best algorithm is randomized and runs in $\tilde O\left(n + (\frac{1}ε)^{11/5}/2^{Ω(\sqrt{\log(1/ε)})}\right)$ time [Deng, Jin and Mao,…

This https://arxiv.org/abs/2206.13635 has been replaced.
link: https://scholar.google.com/scholar?q=a

Coloring hypergraphs with excluded minors
Hadwiger's conjecture, among the most famous open problems in graph theory, states that every graph that does not contain $K_t$ as a minor is properly $(t-1)$-colorable. The purpose of this work is to demonstrate that a natural extension of Hadwiger's problem to hypergraph coloring exists, and to derive some first partial results and applications. Generalizing ordinary graph minors to hypergraphs, we say that a hypergraph $H_1$ is a minor of a hypergraph $H_2$, if a hypergraph isomorphic to $H_…

This https://arxiv.org/abs/2310.17777 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A unified treatment of tractability for approximation problems defined on Hilbert spaces
A large literature specifies conditions under which the information complexity for a sequence of numerical problems defined for dimensions $1, 2, \ldots$ grows at a moderate rate, i.e., the sequence of problems is tractable. Here, we focus on the situation where the space of available information consists of all linear functionals and the problems are defined as linear operator mappings between Hilbert spaces. We unify the proofs of known tractability results and generalize a number of existing…

This https://arxiv.org/abs/2309.03029 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multiplicity and symmetry breaking for supercritical elliptic problems in exterior domains
We deal with the following semilinear equation in exterior domains \[-Δu + u = a(x)|u|^{p-2}u,\qquad u\in H^1_0({A_R}), \] where ${A_R} := \{x\in\mathbb{R}^N:\, |x|>{R}\}$, $N\ge 3$, $R>0$. Assuming that the weight $a$ is positive and satisfies some symmetry and monotonicity properties, we exhibit a positive solution having the same features as $a$, for values of $p>2$ in a suitable range that includes exponents greater than the standard Sobolev critical one. In the special…

This https://arxiv.org/abs/2308.07004 has been replaced.
link: https://scholar.google.com/scholar?q=a

$(1-ε)$-Approximation of Knapsack in Nearly Quadratic Time
Knapsack is one of the most fundamental problems in theoretical computer science. In the $(1 - ε)$-approximation setting, although there is a fine-grained lower bound of $(n + 1 / ε) ^ {2 - o(1)}$ based on the $(\min, +)$-convolution hypothesis ([K{ü}nnemann, Paturi and Stefan Schneider, ICALP 2017] and [Cygan, Mucha, Wegrzycki and Wlodarczyk, 2017]), the best algorithm is randomized and runs in $\tilde O\left(n + (\frac{1}ε)^{11/5}/2^{Ω(\sqrt{\log(1/ε)})}\right)$ time [Deng, Jin and Mao,…

This https://arxiv.org/abs/2402.15303 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Analytic pseudo-rotations II: a principle for spheres, disks and annuli
We construct analytic surface symplectomorphisms with unstable elliptic fixed points; this solves a problem of Birkhoff (1927). More precisely, we construct analytic symplectomorphisms of the sphere and of the disk which are transitive, with respectively only 2 and 1 periodic points. This also solves problems of proposed by Herman (1998), Fayad-Katok (2004) and Fayad-Krikorian (2018). To establish these results, we introduce a principle that enables to realize, by an analytic symplectomorphism,…

This https://arxiv.org/abs/2306.01073 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCG_…

Improved Algorithms for Distance Selection and Related Problems
In this paper, we propose new techniques for solving geometric optimization problems involving interpoint distances of a point set in the plane. Given a set $P$ of $n$ points in the plane and an integer $1 \leq k \leq \binom{n}{2}$, the distance selection problem is to find the $k$-th smallest interpoint distance among all pairs of points of $P$. The previously best deterministic algorithm solves the problem in $O(n^{4/3} \log^2 n)$ time [Katz and Sharir, SIAM J. Comput. 1997 and SoCG 1993]. In…

This https://arxiv.org/abs/2308.05887 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A search-free $O(1/k^{3/2})$ homotopy inexact proximal-Newton extragradient algorithm for monotone variational inequalities
We present and study the iteration-complexity of a relative-error inexact proximal-Newton extragradient algorithm for solving smooth monotone variational inequality problems in real Hilbert spaces. We removed a search procedure from Monteiro and Svaiter (2012) by introducing a novel approach based on homotopy, which requires the resolution (at each iteration) of a single strongly monotone linear variational inequality. For a given tolerance $ρ>0$, our main algorithm exhibits pointwise $O\left(…

This https://arxiv.org/abs/2308.07004 has been replaced.
link: https://scholar.google.com/scholar?q=a

$(1-ε)$-Approximation of Knapsack in Nearly Quadratic Time
Knapsack is one of the most fundamental problems in theoretical computer science. In the $(1 - ε)$-approximation setting, although there is a fine-grained lower bound of $(n + 1 / ε) ^ {2 - o(1)}$ based on the $(\min, +)$-convolution hypothesis ([K{ü}nnemann, Paturi and Stefan Schneider, ICALP 2017] and [Cygan, Mucha, Wegrzycki and Wlodarczyk, 2017]), the best algorithm is randomized and runs in $\tilde O\left(n + (\frac{1}ε)^{11/5}/2^{Ω(\sqrt{\log(1/ε)})}\right)$ time [Deng, Jin and Mao,…

This https://arxiv.org/abs/2308.05887 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A search-free $O(1/k^{3/2})$ homotopy inexact proximal-Newton extragradient algorithm for monotone variational inequalities
We present and study the iteration-complexity of a relative-error inexact proximal-Newton extragradient algorithm for solving smooth monotone variational inequality problems in real Hilbert spaces. We removed a search procedure from Monteiro and Svaiter (2012) by introducing a novel approach based on homotopy, which requires the resolution (at each iteration) of a single strongly monotone linear variational inequality. For a given tolerance $ρ>0$, our main algorithm exhibits pointwise $O\left(…

Families of Equiangular Lines and Lattices
Jacques Martinet
https://arxiv.org/abs/2403.09446 https://arxiv.org/pdf/2403.09446<…

Families of Equiangular Lines and Lattices
We construct Euclidean lattices whose sets of minimal vectors support some large equiangular families of lines, using notably reduction modulo~$2$ of lattices. %as considered in \cite{Ma1} and \cite{Ma2}. We also consider some related problems, and answer a question raised by Greaves ([G], Subsection~1.3.2).

$C^{1,\alpha}$ regularity of variational problems with a convexity constraint
Ling Wang, Bin Zhou
https://arxiv.org/abs/2403.04235 https://

$C^{1,α}$ regularity of variational problems with a convexity constraint
In this paper, we establish the interior $C^{1,α}$ regularity of minimizers of a class of functionals with a convexity constraint, which includes the principal-agent problems studied by Figalli-Kim-McCann (\textit{J. Econom. Theory} \textbf{146} (2011), no. 2, 454-478). The $C^{1,1}$ regularity was previously proved by Caffarelli-Lions in an unpublished note when the cost is quadratic, and recently extended to the case where the cost is uniformly convex with respect to a general preference fun…

This https://arxiv.org/abs/2108.10256 has been replaced.
link: https://scholar.google.com/scholar?q=a

Eremenko's conjecture, wandering Lakes of Wada, and maverick points
We develop a general technique for realising full closed subsets of the complex plane as wandering sets of entire functions. Using this construction, we solve a number of open problems. (1) We construct a counterexample to Eremenko's conjecture, a central problem in transcendental dynamics that asks whether every connected component of the set of escaping points of a transcendental entire function is unbounded. (2) We prove that there is a transcendental entire function for which infinitely…

Optimal complexity solution of space-time finite element systems for state-based parabolic distributed optimal control problems
Richard L\"oscher, Michael Reichelt, Olaf Steinbach
https://arxiv.org/abs/2404.10350

Optimal complexity solution of space-time finite element systems for state-based parabolic distributed optimal control problems
We consider a distributed optimal control problem subject to a parabolic evolution equation as constraint. The control will be considered in the energy norm of the anisotropic Sobolev space $[H_{0;,0}^{1,1/2}(Q)]^\ast$, such that the state equation of the partial differential equation defines an isomorphism onto $H^{1,1/2}_{0;0,}(Q)$. Thus, we can eliminate the control from the tracking type functional to be minimized, to derive the optimality system in order to determine the state. Since the a…

Canonical labelling of Latin squares in average-case polynomial time
Michael J. Gill, Adam Mammoliti, Ian M. Wanless
https://arxiv.org/abs/2402.06205 https…

Canonical labelling of Latin squares in average-case polynomial time
A Latin square of order $n$ is an $n\times n$ matrix in which each row and column contains each of $n$ symbols exactly once. For $ε>0$, we show that with high probability a uniformly random Latin square of order $n$ has no proper subsquare of order larger than $n^{1/2}\log^{1/2+ε}n$. Using this fact we present a canonical labelling algorithm for Latin squares of order $n$ that runs in average time bounded by a polynomial in $n$. The algorithm can be used to solve isomorphism problems for ma…

Optimal complexity solution of space-time finite element systems for state-based parabolic distributed optimal control problems
Richard L\"oscher, Michael Reichelt, Olaf Steinbach
https://arxiv.org/abs/2404.10350

Optimal complexity solution of space-time finite element systems for state-based parabolic distributed optimal control problems
We consider a distributed optimal control problem subject to a parabolic evolution equation as constraint. The control will be considered in the energy norm of the anisotropic Sobolev space $[H_{0;,0}^{1,1/2}(Q)]^\ast$, such that the state equation of the partial differential equation defines an isomorphism onto $H^{1,1/2}_{0;0,}(Q)$. Thus, we can eliminate the control from the tracking type functional to be minimized, to derive the optimality system in order to determine the state. Since the a…

POD Suboptimal Control of Evolution Problems: Theory and Applications
Stefan Banholzer, Dennis Beermann, Luca Mechelli, Stefan Volkwein
https://arxiv.org/abs/2404.07015

POD Suboptimal Control of Evolution Problems: Theory and Applications
The work is organized as follows. First an introduction is given in Chapter 1. In Chapter 2 we introduce the POD method in finite and infinite-dimensional Hilbert spaces and discuss various applications. Chapter 3 is devoted to to POD-based Galerkin schemes for evolution problems. Mainly, we study linear problems taking different discretization methods into account. We provide a certified a-priori and a-posteriori error analysis. Furthermore, the numerical realizations are explained and illustr…

On systems of fractional nonlinear partial differential equations
Ravshan Ashurov, Oqila Mukhiddinova
https://arxiv.org/abs/2403.11638 https://

On systems of fractional nonlinear partial differential equations
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the equation does not depend on the solution of the problem and 2) it depends on the solution, but at the same time satisfies the classical Lipschitz condition with respect to this variable and an additional condition which guarantees a global existence of the solutio…

Quadratic Point Estimate Method for Probabilistic Moments Computation
Minhyeok Ko, Konstantinos G. Papakonstantinou
https://arxiv.org/abs/2403.13203 https:…

Quadratic Point Estimate Method for Probabilistic Moments Computation
This paper presents in detail the originally developed Quadratic Point Estimate Method (QPEM), aimed at efficiently and accurately computing the first four output moments of probabilistic distributions, using 2n^2+1 sample (or sigma) points, with n, the number of input random variables. The proposed QPEM particularly offers an effective, superior, and practical alternative to existing sampling and quadrature methods for low- and moderately-high-dimensional problems. Detailed theoretical derivat…

Directed Buy-at-Bulk Spanners
Elena Grigorescu, Nithish Kumar, Young-San Lin
https://arxiv.org/abs/2404.05172 https://arxiv.org/pdf/2…

Directed Buy-at-Bulk Spanners
We present a framework that unifies directed buy-at-bulk network design and directed spanner problems, namely, \emph{buy-at-bulk spanners}. The goal is to find a minimum-cost routing solution for network design problems that capture economies at scale, while satisfying demands and distance constraints for terminal pairs. A more restricted version of this problem was shown to be $O(2^{{\log^{1-\ep} n}})$-hard to approximate, where $n$ is the number of vertices, under a standard complexity assump…

Domain-Independent Dynamic Programming and Constraint Programming Approaches for Assembly Line Balancing Problems with Setups
Jiachen Zhang, J. Christopher Beck
https://arxiv.org/abs/2403.06780

Domain-Independent Dynamic Programming and Constraint Programming Approaches for Assembly Line Balancing Problems with Setups
We propose domain-independent dynamic programming (DIDP) and constraint programming (CP) models to exactly solve type-1 and type-2 assembly line balancing problem with sequence-dependent setup times (SUALBP). The goal is to assign tasks to assembly stations and to sequence these tasks within each station, while satisfying precedence relations specified between a subset of task pairs. Each task has a given processing time and a setup time dependent on the previous task on the station to which th…

Directed Buy-at-Bulk Spanners
Elena Grigorescu, Nithish Kumar, Young-San Lin
https://arxiv.org/abs/2404.05172 https://arxiv.org/pdf/2…

Directed Buy-at-Bulk Spanners
We present a framework that unifies directed buy-at-bulk network design and directed spanner problems, namely, \emph{buy-at-bulk spanners}. The goal is to find a minimum-cost routing solution for network design problems that capture economies at scale, while satisfying demands and distance constraints for terminal pairs. A more restricted version of this problem was shown to be $O(2^{{\log^{1-\ep} n}})$-hard to approximate, where $n$ is the number of vertices, under a standard complexity assump…