Tootfinder

$\ell_{1}^{2}-\eta\ell_{2}^{2}$ regularization for sparse recovery
Long Li, Liang Ding
https://arxiv.org/abs/2506.11372 https://arxiv…

$\ell_{1}^{2}-η\ell_{2}^{2}$ regularization for sparse recovery
This paper presents a regularization technique incorporating a non-convex and non-smooth term, $\ell_{1}^{2}-η\ell_{2}^{2}$, with parameters $0<η\leq 1$ designed to address ill-posed linear problems that yield sparse solutions. We explore the existence, stability, and convergence of the regularized solution, demonstrating that the $\ell_{1}^{2}-η\ell_{2}^{2}$ regularization is well-posed and results in sparse solutions. Under suitable source conditions, we establish a convergence rate of $\m…

Can LLMs Generate High-Quality Test Cases for Algorithm Problems? TestCase-Eval: A Systematic Evaluation of Fault Coverage and Exposure
Zheyuan Yang, Zexi Kuang, Xue Xia, Yilun Zhao
https://arxiv.org/abs/2506.12278

Can LLMs Generate High-Quality Test Cases for Algorithm Problems? TestCase-Eval: A Systematic Evaluation of Fault Coverage and Exposure
We introduce TestCase-Eval, a new benchmark for systematic evaluation of LLMs in test-case generation. TestCase-Eval includes 500 algorithm problems and 100,000 human-crafted solutions from the Codeforces platform. It focuses on two pivotal tasks: (1) Fault Coverage, which measures how well LLM-generated test sets probe diverse input scenarios and cover a wide range of potential failure modes. (2) Fault Exposure, which evaluates whether LLMs can craft a tailored test input that reveals a specif…

Optimal trace norms for Helmholtz problems
Benedikt Gr\"a{\ss}le
https://arxiv.org/abs/2506.11944 https://arxiv.org/pdf/2506.119…

Optimal trace norms for Helmholtz problems
The natural $H^1(Ω)$ energy norm for Helmholtz problems is weighted with the wavenumber modulus $σ$ and induces natural weighted norms on the trace spaces $H^{\pm1/2}(Γ)$ by minimial extension to $Ω\subset\mathbb R^n$. This paper presents a rigorous analysis for these trace norms with an explicit characterisation by weighted Sobolev-Slobodeckij norms and scaling estimates, highlighting their dependence on the geometry of the extension set $Ω\subset\mathbb R^n$ and the weight $σ$. The anal…

Regularization for time-dependent inverse problems: Geometry of Lebesgue-Bochner spaces and algorithms
Gesa Sarnighausen, Thorsten Hohage, Martin Burger, Andreas Hauptmann, Anne Wald
https://arxiv.org/abs/2506.11291

Regularization for time-dependent inverse problems: Geometry of Lebesgue-Bochner spaces and algorithms
We consider time-dependent inverse problems in a mathematical setting using Lebesgue-Bochner spaces. Such problems arise when one aims to recover a function from given observations where the function or the data depend on time. Lebesgue-Bochner spaces allow to easily incorporate the different nature of time and space. In this manuscript, we present two different regularization methods in Lebesgue Bochner spaces: 1. classical Tikhonov regularization in Banach spaces 2. variational regulari…

Greed is slow on sparse graphs of oriented valued constraints
Artem Kaznatcheev, Sofia Vazquez Alferez
https://arxiv.org/abs/2506.11662 https://

Greed is slow on sparse graphs of oriented valued constraints
Greedy local search is especially popular for solving valued constraint satisfaction problems (VCSPs). Since any method will be slow for some VCSPs, we ask: what is the simplest VCSP on which greedy local search is slow? We construct a VCSP on 6n Boolean variables for which greedy local search takes 7(2^n - 1) steps to find the unique peak. Our VCSP is simple in two ways. First, it is very sparse: its constraint graph has pathwidth 2 and maximum degree 3. This is the simplest VCSP on which some…

Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control
Larissa Fardigola, Kateryna Khalina
https://arxiv.org/abs/2506.10466

Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control
In the paper, the problems of approximate controllability are studied for the control system $w_t=Δw$, $w(0,x_2,t)=u(x_2,t)$, $x_1\in\mathbb R_+=(0,+\infty)$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u$ is a control belonging to a special subset of $L^\infty(\mathbb R\times (0,T))\cap L^2(\mathbb R\times (0,T))$. It is proved that each initial state belonging to $L^2(\mathbb R_+\times\mathbb R)$ is approximately controllable to an arbitrary end state belonging to $L^2(\mathbb R_+\times\mathbb R)…

Testing Suffixient Sets
Davide Cenzato, Francisco Olivares, Nicola Prezza
https://arxiv.org/abs/2506.08225 https://arxiv.org/pdf/2506…

Testing Suffixient Sets
Suffixient sets are a novel prefix array (PA) compression technique based on subsampling PA (rather than compressing the entire array like previous techniques used to do): by storing very few entries of PA (in fact, a compressed number of entries), one can prove that pattern matching via binary search is still possible provided that random access is available on the text. In this paper, we tackle the problems of determining whether a given subset of text positions is (1) a suffixient set or (2)…

There have been many instances documented, do a damn web search.
But forget that for a moment: What I’m doing is the same as what Netanyahu is doing? My opposing genocide is the same as a fucker perpetrating genocide?
Fuck you, Alfred.
Get some fucking perspective. https://mastodon.social/@amsz…

On one of Erd\H{o}s' Problems -- An Efficient Search for Benelux Pairs
Christian Hercher
https://arxiv.org/abs/2506.01099 https://

On one of Erdős' Problems -- An Efficient Search for Benelux Pairs
Erdős asked for positive integers $m

Sorting by pile shuffles on queue-like and stack-like piles can be hard
Kyle B. Treleaven
https://arxiv.org/abs/2506.05518 https://ar…

Sorting by pile shuffles on queue-like and stack-like piles can be hard
Inspired by a common technique for shuffling a deck of cards on a table without riffling, we continue the study of a prequel paper on the pile shuffle and its capabilities as a sorting device. We study two sort feasibility problems of general interest concerning pile shuffle, first introduced in the prequel. These problems are characterized by: (1) bounds on the number of sequential rounds of shuffle, and piles created in each round; (2) the use of a heterogeneous mixture of queue-like and stac…

Code-based $[3,1]$-avoiders in finite affine spaces $\mathrm{AG}(n,2)$
Benedek Kov\'acs
https://arxiv.org/abs/2505.24072 https://…

Code-based $[3,1]$-avoiders in finite affine spaces $\mathrm{AG}(n,2)$
The author, together with Nagy, studied the following problem on unavoidable intersections of given size in binary affine spaces. Given an $m$-element set $S\subseteq \mathbb{F}_2^n$, is there guaranteed to be a $[k,t]$-flat, that is, a $k$-dimensional affine subspace of $\mathbb{F}_2^n$ containing exactly $t$ points of $S$? Such problems can be viewed as generalizations of the cap set problem over the binary field. They conjectured that for every fixed pair $(k,t)$ with $k\ge 1$ and $0\le t\le…

Quadratic Segre indices
Felipe Espreafico, Stephen McKean, Sabrina Pauli
https://arxiv.org/abs/2506.01547 https://arxiv.org/pdf/2506.…

Quadratic Segre indices
We prove that the local Euler class of a line on a degree $2n-1$ hypersurface in projective $n+1$ space is given by a product of indices of Segre involutions. Segre involutions and their associated indices were first defined by Finashin and Kharlamov over the reals. Our result is valid over any field of characteristic not 2 and gives an infinite family of problems in enriched enumerative geometry with a shared geometric interpretation for the local type.

This https://arxiv.org/abs/2505.15992 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

On the Complexity of Finding Approximate LCS of Multiple Strings
Finding an Approximate Longest Common Substring (ALCS) within a given set $S=\{s_1,s_2,\ldots,s_m\}$ of $m \ge 2$ strings is a problem of particular importance in computational biology (e.g., identifying related mutations across multiple genetic sequences). In this paper, we study several ALCS problems that, for given integers $k$ and $t \le m$, require finding a longest string $u$ -- or a longest substring $u$ of any string in $S$ -- that lies within distance $k$ of at least one substring in $…

This https://arxiv.org/abs/2009.11945 has been replaced.
link: https://scholar.google.com/scholar?q=a

Some application of Grunsky coefficients in the theory of univalent functions
Let function $f$ be normalized, analytic and univalent in the unit disk ${\mathbb D}=\{z:|z|<1\}$ and $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$. Using a method based on Grusky coefficients we study several problems over that class of univalent functions: upper bounds of the special case of the generalised Zalcman conjecture $|a_2a_3-a_4|$, of the third logarithmic coefficient, and of the second Hankel determinant for the logarithmic coefficients.

This https://arxiv.org/abs/2403.03013 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

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…

Shape derivative approach to fractional overdetermined problems
Sidy M. Djitte, Ignace A. Minlend
https://arxiv.org/abs/2506.00268 https://

Shape derivative approach to fractional overdetermined problems
We use shape derivative approach to prove that balls are the only convex and $C^{1,1}$ regular domains in which the fractional overdetermined problem \begin{equation*} \left\{\begin{aligned} \Ds u&= λ_{s, p} u^{p-1}\quad\text{in}\quad\Om \\ u &= 0\quad \text{in}\quad\R^N\setminus \Om\\ u/d^s&=C_0\quad\text{on\;\; $\partialØ$} \end{aligned} \right. \end{equation*} admits a nontrivial solution for $p\in [1, 2]$ and where $λ_{s, p}= λ_{s, p}(Ø)$ is the best constant in the family of Subcritic…

This https://arxiv.org/abs/2506.00521 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convergence rates of regularized quasi-Newton methods without strong convexity
In this paper, we study convergence rates of the cubic regularized proximal quasi-Newton method (\csr) for solving non-smooth additive composite problems that satisfy the so-called Kurdyka-Łojasiewicz (KŁ) property with respect to some desingularization function $ϕ$ rather than strong convexity. After a number of iterations $k_0$, \csr\ exhibits non-asymptotic explicit super-linear convergence rates for any $k\geq k_0$. In particular, when $ϕ(t)=ct^{1/2}$, Cubic SR1 PQN has a convergence ra…

Counting the number of $\mathbb{Z}_{p}$-and $\mathbb{F}_{p}[t]$-fixed points of a discrete dynamical system with applications from arithmetic statistics, III
Brian Kintu
https://arxiv.org/abs/2505.24565

Counting the number of $\mathbb{Z}_{p}$-and $\mathbb{F}_{p}[t]$-fixed points of a discrete dynamical system with applications from arithmetic statistics, III
In this follow-up paper, we again inspect a surprising relationship between the set of fixed points of a polynomial map $φ_{d, c}$ defined by $φ_{d, c}(z) = z^d + c$ for all $c, z \in \mathcal{O}_{K}$ or $c, z \in \mathbb{Z}_{p}$ or $c, z \in \mathbb{F}_{p}[t]$ and the coefficient $c$, where $K$ is any number field (not necessarily real) of degree $n > 1$, $p>2$ is any prime integer, and $d>2$ is an integer. As in \cite{BK1,BK2} we again wish to study here counting problems that are inspired …

The Price of Being Partial: Complexity of Partial Generalized Dominating Set on Bounded-Treewidth Graphs
Jakob Greilhuber, D\'aniel Marx
https://arxiv.org/abs/2506.01645

The Price of Being Partial: Complexity of Partial Generalized Dominating Set on Bounded-Treewidth Graphs
The $(σ, ρ)$-domination framework introduced by Telle [Nord. J. Comput.'94] captures many classical graph problems. For fixed sets $σ, ρ$ of non-negative integers, a $(σ,ρ)$-set of a graph $G$ is a set $S$ such that for every $v\in V(G)$, we have (1) if $v \in S$, then $|N(v) \cap S| \in σ$, and (2) if $v \not\in S$, then $|N(v) \cap S| \in ρ$. We initiate the study of a natural partial variant of the problem, in which the constraints given by $σ, ρ$ need not be fu…