Tootfinder

Restricted (2 1)-TQFTs supported by thickened and solid tori
Du\v{s}an {\DJ}or{\dj}evi\'c, Danica Kosanovi\'c, Jovana Nikoli\'c, Zoran Petri\'c
https://arxiv.org/abs/2505.21373

Restricted (2+1)-TQFTs supported by thickened and solid tori
A faithful $(1+1)$ TQFT has recently been constructed, but the existence of a faithful $(2+1)$ TQFT remains an open question, that subsumes the hard problem of linearity of mapping class groups of surfaces. To circumvent the latter problem we construct a subcategory of the category of 3-cobordisms, containing disjoint unions of tori and simplest cobordisms between them. On this we define TQFTs that are able to distinguish pairs of torus bundles and lens spaces, previously shown not to be distin…

On the Erd\H{o}s-Ko-Rado problem of flags with type $\{1, n-3 \}$ of finite sets
Philipp Heering
https://arxiv.org/abs/2506.20556 https://

On the Erdős-Ko-Rado problem of flags with type $\{1, n-3 \}$ of finite sets
A flag of a finite set $S$ is a set $f$ of non-empty, proper subsets of $S$, such that $X\subseteq Y$ or $Y\subseteq X$ for all $X,Y\in f$. Two flags $f_1$ and $f_2$ of $S$ are opposite if $X_1\cap X_2=\emptyset$, or $X_1\cup X_2=S$ for all $X_1\in f_1$ and $X_2\in f_2$. The set $\{|X| \mid X\in f \}$ is the type of a flag $f$. A set of pairwise non-opposite flags is an Erdős-Ko-Rado set. In 2022 Metsch posed the problem of determining the maximum size of all Erdős-Ko-Rado sets of f…

Weil jetzt sehr viel Empörung unter meinem Post zur Ablehnung der SPD zum Familiennachzug entsteht: Die Abgeordneten konnten nicht anders. Sonst wäre die Koalition geplatzt. Alternative? AfD mit Union? Hm.
Das eigentliche Problem hat zwei Teile:
1. Das Ergebnis der Wahl = keine progressive Mehrheit.
2. Die Prioritäten der SPD in der Koalitionsverhandlung. Eine Katastrophe. (Auch für die SPD.)
Einmal verhandelt, muss die Fraktion so abstimmen - oder Klingbeil stürzen.…

This https://arxiv.org/abs/1512.03127 has been replaced.
link: https://scholar.google.com/scholar?q=a

Flexible constraint satisfiability and a problem in semigroup theory
We examine some flexible notions of constraint satisfaction, observing some relationships between model theoretic notions of universal Horn class membership and robust satisfiability. We show the \texttt{NP}-completeness of $2$-robust monotone 1-in-3 3SAT in order to give very small examples of finite algebras with \texttt{NP}-hard variety membership problem. In particular we give a $3$-element algebra with this property, and solve a widely stated problem by showing that the $6$-element Brandt …

Arithmetic properties and zeros of the Bergman kernel on a class of quotient domains
Luke D. Edholm, Vikram T. Mathew
https://arxiv.org/abs/2505.20489 http…

Arithmetic properties and zeros of the Bergman kernel on a class of quotient domains
An effective formula for the Bergman kernel on $\mathbb{H}_γ = \{|z_1|^γ< |z_2| < 1 \}$ is obtained for rational $γ= \frac{m}{n} >1$. The formula depends on arithmetic properties of $γ$, which uncovers new symmetries and clarifies previous results. The formulas are then used to study the Lu Qi-Keng problem. We produce sequences of rationals $γ_j \searrow 1$, where each $\mathbb{H}_{γ_j}$ has a Bergman kernel with zeros (while $\mathbb{H}_1$ is known to have a zero-free…

The final solution of the Hitchhiker's problem #5
Matja\v{z} Omladi\v{c}, Martin Vuk, Alja\v{z} Zalar
https://arxiv.org/abs/2506.20672 https://

The final solution of the Hitchhiker's problem #5
A recent survey, nicknamed "Hitchhiker's Guide", J.J. Arias-Garcıa, R. Mesiar, and B. De Baets, A hitchhiker's guide to quasi-copulas, Fuzzy Sets and Systems 393 (2020) 1-28, has raised the rating of quasi-copula problems in the dependence modeling community in spite of the lack of statistical interpretation of quasi-copulas. In our previous work (arXiv:2410.19339, accepted in Fuzzy Sets and Systems), we addressed the question of extreme values of the mass distribution associated with multivar…

Once upon a time the French had a real problem with the 1%. THEY SOLVED IT.

On the convergence of critical points on real algebraic sets and applications to optimization
Saugata Basu, Ali Mohammad-Nezhad
https://arxiv.org/abs/2506.20565

On the convergence of critical points on real algebraic sets and applications to optimization
Let $F \in \R[X_1,\ldots,X_n]$ and the zero set $V=\zero(\mathcal{P},\R^n)$, where $\mathcal{P}:=\{P_1,\ldots,P_s\} \subset \R[X_1,\ldots,X_n]$ is a finite set of polynomials. We investigate existence of critical points of $F$ on an infinitesimal perturbation $V_ξ = \zero(\{P_1-ξ_1.\ldots,P_s-ξ_s\},\R^n)$. Our motivation is to understand the limiting behavior of central paths in polynomial optimization, which is an important problem in the theory of interior point methods for polynomial opti…

Replaced article(s) found for cs.CE. https://arxiv.org/list/cs.CE/new
[1/1]:
- Solving Inverse Problem for Multi-armed Bandits via Convex Optimization
Hao Zhu, Joschka Boedecker

All-Pairs Shortest Paths with Few Weights per Node
Amir Abboud, Nick Fischer, Ce Jin, Virginia Vassilevska Williams, Zoe Xi
https://arxiv.org/abs/2506.20017

All-Pairs Shortest Paths with Few Weights per Node
We study the central All-Pairs Shortest Paths (APSP) problem under the restriction that there are at most $d$ distinct weights on the outgoing edges from every node. For $d=n$ this is the classical (unrestricted) APSP problem that is hypothesized to require cubic time $n^{3-o(1)}$, and at the other extreme, for $d=1$, it is equivalent to the Node-Weighted APSP problem. We present new algorithms that achieve the following results: 1. Node-Weighted APSP can be solved in time $\tilde{O}(n^{(3+ω…

Guarding Offices with Maximum Dispersion
S\'andor P. Fekete, Kai Kobbe, Dominik Krupke, Joseph S. B. Mitchell, Christian Rieck, Christian Scheffer
https://arxiv.org/abs/2506.21307

Guarding Offices with Maximum Dispersion
We investigate the Dispersive Art Gallery Problem with vertex guards and rectangular visibility ($r$-visibility) for a class of orthogonal polygons that reflect the properties of real-world floor plans: these office-like polygons consist of rectangular rooms and corridors. In the dispersive variant of the Art Gallery Problem, the objective is not to minimize the number of guards but to maximize the minimum geodesic $L_1$-distance between any two guards, called the dispersion distance. Our mai…

Replaced article(s) found for quant-ph. https://arxiv.org/list/quant-ph/new
[1/2]:
- Possible consequences for physics of the negative resolution of Tsirelson's problem
Ad\'an Cabello, Marco T\'ulio Quintino, Matthias Kleinmann

Falls ihr übrigens das Problem habt, dass ihr das mit Firefox nicht drucken könnt, nur anzeigen (scheint so zu sein), dann empfehle ich euch die Tastenkombination Umschalt Command 4 auf MacOS. Die macht einen Screenshot, den ihr dann ausdrucken und einscannen könnt.
Folgt mir für mehr Digitalisierungstipps.

Finite groups with nearly half as many cyclic subgroups as elements
Vaibhav Chhajer, Sumana Hatui, Palash Sharma
https://arxiv.org/abs/2506.21163 https://

Finite groups with nearly half as many cyclic subgroups as elements
Suppose $C(G)$ denotes the set of all cyclic subgroups of a finite group $G$, and $\mathcal{O}_{2}(G)$ denotes the number of elements of order $2$ in $G$. In [Marius T., Finite groups with a certain number of cyclic subgroups. The American Mathematical Monthly 122.3 (2015): 275-276], an open problem was asked to classify the groups $G$ with $|C(G)|=|G|-r$, where $2 \leq r \leq |G|-1$. In this article, first we show that there are infinitely many groups $G$ with $&#…

Replaced article(s) found for stat.ML. https://arxiv.org/list/stat.ML/new
[1/1]:
- High-dimensional Contextual Bandit Problem without Sparsity
Junpei Komiyama, Masaaki Imaizumi

Making Graphs Irregular through Irregularising Walks
Julien Bensmail, Romain Bourneuf, Paul Colinot, Samuel Humeau, Timoth\'ee Martinod
https://arxiv.org/abs/2506.21254

Making Graphs Irregular through Irregularising Walks
The 1-2-3 Conjecture, introduced by Karoński, Łuczak, and Thomason in 2004, was recently solved by Keusch. This implies that, for any connected graph $G$ different from $K_2$, we can turn $G$ into a locally irregular multigraph $M(G)$, i.e., in which no two adjacent vertices have the same degree, by replacing some of its edges with at most three parallel edges. In this work, we introduce and study a restriction of this problem under the additional constraint that edges added to $G$ to reach $…

A Flavor of SO(10) Unification with a Spinor Higgs
Juanca Carrasco-Martinez, Lawrence J. Hall, Keisuke Harigaya, Kevin Langhoff
https://arxiv.org/abs/2506.20708

A Flavor of SO(10) Unification with a Spinor Higgs
We investigate Higgs Parity Unification-a realization of $SO(10)$ grand unification based on the Higgs Parity mechanism in which the Standard Model (SM) Higgs resides in a spinor representation. The theory has an intermediate left-right symmetric stage where the $SU(2)_R$ symmetry breaking scale is fixed by the vanishing of the SM Higgs quartic coupling. The strong $CP$ problem is solved by parity. Gauge coupling unification successfully predicts $α_s(M_Z)$ to within 1%. The spinor Higgs natur…

I get mixed feelings when I can create a small reproduction project for an issue caused by a single version bump in a third party dependency. It's nice to know it's not my code, but a fix-release is also out of my control
Today's problem; The compiler in #Kotlin 2.1.20. I've even managed to boil it down to a 1 line change where "2.1.10" works, and "2.1.20" o…

A Taylor-Hood finite element method for the surface Stokes problem without penalization
Alan Demlow, Michael Neilan
https://arxiv.org/abs/2506.20419 https:…

A Taylor-Hood finite element method for the surface Stokes problem without penalization
Finite element approximation of the velocity-pressure formulation of the surfaces Stokes equations is challenging because it is typically not possible to enforce both tangentiality and $H^1$ conformity of the velocity field. Most previous works concerning finite element methods (FEMs) for these equations thus have weakly enforced one of these two constraints by penalization or a Lagrange multiplier formulation. Recently in [A tangential and penalty-free finite element method for the surface Sto…

A Framework for Building Data Structures from Communication Protocols
Alexandr Andoni, Shunhua Jiang, Omri Weinstein
https://arxiv.org/abs/2506.20761 https…

A Framework for Building Data Structures from Communication Protocols
We present a general framework for designing efficient data structures for high-dimensional pattern-matching problems ($\exists \;? i\in[n], f(x_i,y)=1$) through communication models in which $f(x,y)$ admits sublinear communication protocols with exponentially-small error. Specifically, we reduce the data structure problem to the Unambiguous Arthur-Merlin (UAM) communication complexity of $f(x,y)$ under product distributions. We apply our framework to the Partial Match problem (a.k.a, matchin…

Quantum k-SAT Related Hypergraph Problems
Simon-Luca Kremer, Dorian Rudolph, Sevag Gharibian
https://arxiv.org/abs/2506.17066 https://

Quantum k-SAT Related Hypergraph Problems
The Quantum k-SAT problem is the quantum generalization of the k-SAT problem. It is the problem whether a given local Hamiltonian is frustration-free. Frustration-free means that the ground state of the k-local Hamiltonian minimizes the energy of every local interaction term simultaneously. This is a central question in quantum physics and a canonical QMA_1-complete problem. The Quantum k-SAT problem is not as well studied as the classical k-SAT problem in terms of special tractable cases, appr…

Just got a small space heater and damn it’s so much more comfortable here now
As a @… fan I’d prefer if my AC/heat pump supported heating mode, but welp it was already installed when I moved here so an electric heater will do it for the 2 days a year it’s actually cold enough for that to be useful here. Getting all that heat from the bedroom to the living room would be a problem anyway.
And I didn’t even need to make a fire hazard in order to use it since a 20A outlet was already around due to the coffee thingy, yay!
It’s been on for just around 40mins and it’s already sooo much better in here (the temp sensor is not on the side the heater is pointing to (the sofa) so it’ll take a while for it to reflect the change specially since this is a big room (kitchen dinner living), but just pointing the heater to where I’m at is enough to make it a comfortable temperature (and probably even way too hot in a bit)).
I’ve been wanting this for a while, but it never felt worth it bc we don’t really have many cold days here. Tho this year we got some more I think and today was specially cold (9~11°C) so I decided to just do it. Extra points bc it was available on fucking iFood of all places so it arrived less than an hour after I ordered it lmao.

Bosonized theory of de Haas-van Alphen quantum oscillation in Fermi liquids
Yuxuan Wang
https://arxiv.org/abs/2506.20735 https://arxi…

Bosonized theory of de Haas-van Alphen quantum oscillation in Fermi liquids
The de Haas-van Alphen effect (dHvA) of a 2d Fermi liquid remains poorly understood, due to the $\sim\mathcal{O}(1)$ contribution to the oscillations of grand potential from the oscillatory part of the fermionic self energy, which has no known closed-form solution. In this work, we solve this problem via coadjoint-orbit bosonization of the Fermi surface. Compared with the fermionic formalism, the issue of the oscillatory self energy is circumvented. As an effective field theory, Landau paramete…

This https://arxiv.org/abs/2406.11369 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCG_…

Approximation Algorithms for Smallest Intersecting Balls
We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in computational geometry and machine learning, including smallest enclosing ball, polytope distance, intersection radius, $\ell_1$-loss support vector machine, $\ell_1$-loss support vector data description, and so on. Leveraging our novel framework for solving zero…

Adaptive Supergeo Design: A Scalable Framework for Geographic Marketing Experiments
Charles Shaw
https://arxiv.org/abs/2506.20499 https://

Adaptive Supergeo Design: A Scalable Framework for Geographic Marketing Experiments
Geographic experiments are a gold-standard for measuring incremental return on ad spend (iROAS) at scale, yet their design is challenging: the unit count is small, heterogeneity is large, and the optimal Supergeo partitioning problem is NP-hard. We introduce Adaptive Supergeo Design (ASD), a two-stage framework that renders Supergeo designs practical for thousands of markets. A bespoke graph-neural network first learns geo-embeddings and proposes a concise candidate set of 'supergeos'; a CP-SAT…

A Nonlinear Nonlocal Problem for the Caputo Fractional Subdiffusion Equation
Ravshan Ashurov, Rajapboy Saparboyev, Navbahor Nuraliyeva
https://arxiv.org/abs/2506.19516

A Nonlinear Nonlocal Problem for the Caputo Fractional Subdiffusion Equation
In this paper, we study a time-fractional subdiffusion equation with a nonlinear nonlocal initial condition involving the unknown solution at the final time. The considered problem is formulated using the Caputo fractional derivative of order \(0 < α< 1\), along with homogeneous Dirichlet boundary conditions. The nonlocal initial condition is of the form \( u(x,0) = g(x, u(x,T)) \), where \(g\) is a nonlinear function satisfying a Lipschitz condition. The main challenge arises from the implici…

Replaced article(s) found for cs.SC. https://arxiv.org/list/cs.SC/new
[1/1]:
- A matrix criterion and algorithmic approach for the Peterson hit problem: Part I
Dang Vo Phuc

Hybrid Deep Learning and Signal Processing for Arabic Dialect Recognition in Low-Resource Settings
Ghazal Al-Shwayyat, Omer Nezih Gerek
https://arxiv.org/abs/2506.21386

Hybrid Deep Learning and Signal Processing for Arabic Dialect Recognition in Low-Resource Settings
Arabic dialect recognition presents a significant challenge in speech technology due to the linguistic diversity of Arabic and the scarcity of large annotated datasets, particularly for underrepresented dialects. This research investigates hybrid modeling strategies that integrate classical signal processing techniques with deep learning architectures to address this problem in low-resource scenarios. Two hybrid models were developed and evaluated: (1) Mel-Frequency Cepstral Coefficients (MFCC)…

On the Maximization of Real Sequences
Assal\'e Adj\'e
https://arxiv.org/abs/2506.18409 https://arxiv.org/pdf/2506.18409

On the Maximization of Real Sequences
In this paper, we study a maximization problem on real sequences. More precisely, for a given sequence, we are interesting in computing the supremum of the sequence and an index for which the associated term is maximal. We propose a general methodology to solve this maximization problem. The method is based on upper approximations constructed from pairs of eventually decreasing sequences of strictly increasing continuous functions on $[0,1]$ and of scalars in $(0,1)$. Then, we can associate int…

Another essential thread from @… ...
https://mamot.fr/@pluralistic/114733317506784669
pluralistic@mamot.fr - A major problem with letting billionaires decide how your country is run is that they will back whichever psycho promises the lowest taxes and least regulation, no matter how completely batshit and unfit that person is:
https://www.hamiltonnolan.com/p/nations-are-people
--
If you'd like an essay-formatted version of this thread to read or share, here's a link to it on pluralistic.net, my surveillance-free, ad-free, tracker-free blog:
https://pluralistic.net/2025/06/23/billionaires-eh/#galen-weston-is-a-rat
1/

Self-Interacting Dark-Matter Spikes and the Final-Parsec Problem: Bayesian constraints from the NANOGrav 15-Year Gravitational-Wave Background
Shreyas Tiruvaskar, Chris Gordon
https://arxiv.org/abs/2506.18153

Self-Interacting Dark-Matter Spikes and the Final-Parsec Problem: Bayesian constraints from the NANOGrav 15-Year Gravitational-Wave Background
A self-interacting dark-matter (SIDM) density spike around merging supermassive black holes (SMBHs) may be able to supply the dynamical friction needed to shrink binaries from $\sim 1\, \mathrm{pc}$ to $\sim 10^{-2} \,\mathrm{pc}$, thereby resolving the long-standing ``final-parsec problem.'' Embedding the binary-halo system in a cosmological population model, we evolve the inspiral under the combined influence of gravitational-wave (GW) emission and SIDM drag, compute the resulting nanohertz G…

Finite energy foliations in the restricted three-body problem
Lei Liu, Pedro A. S. Salom\~ao
https://arxiv.org/abs/2506.17867 https://

Finite energy foliations in the restricted three-body problem
This paper is about using pseudo-holomorphic curves to study the circular planar restricted three-body problem. The main result states that for mass ratios sufficiently close to $\frac{1}{2}$ and energies slightly above the first Lagrange value, the flow on the regularized component $\mathbb R P^3 \# \mathbb R P^3$ of the energy surface admits a finite energy foliation with three binding orbits, namely two retrograde orbits around the primaries and the Lyapunov orbit in the neck region about th…

Stable Minima of ReLU Neural Networks Suffer from the Curse of Dimensionality: The Neural Shattering Phenomenon
Tongtong Liang, Dan Qiao, Yu-Xiang Wang, Rahul Parhi
https://arxiv.org/abs/2506.20779

Stable Minima of ReLU Neural Networks Suffer from the Curse of Dimensionality: The Neural Shattering Phenomenon
We study the implicit bias of flatness / low (loss) curvature and its effects on generalization in two-layer overparameterized ReLU networks with multivariate inputs -- a problem well motivated by the minima stability and edge-of-stability phenomena in gradient-descent training. Existing work either requires interpolation or focuses only on univariate inputs. This paper presents new and somewhat surprising theoretical results for multivariate inputs. On two natural settings (1) generalization g…

Every tech oligarch wants to build an Everything App - because they now have the power to do so, but also because they're completely out of ideas.
This week's issue of my newsletter tackles the rise of the "data-driven" Nothing Manager responsible for building Everything, with the "power" of #GenAI.

The Everything App is a symptom of Nothing Management (part 1)
Leaders who surrender their point of view inevitably arrive at the same conclusion: we must solve every problem for every user. This approach demolishes the possibility of real impact.

Low-order finite element complex with application to a fourth-order elliptic singular perturbation problem
Xuewei Cui, Xuehai Huang
https://arxiv.org/abs/2506.20240

Low-order finite element complex with application to a fourth-order elliptic singular perturbation problem
A low-order nonconforming finite element discretization of a smooth de Rham complex starting from the $H^2$ space in three dimensions is proposed, involving an $H^2$-nonconforming finite element space, a new tangentially continuous $H^1$-nonconforming vector-valued finite element space, the lowest-order Raviart-Thomas space, and piecewise constant functions. While nonconforming for the smooth complex, the discretization conforms to the classical de Rham complex. It is applied to develop a decou…

from my link log —
Elementary functions NOT following the IEEE 754 floating-point standard.
http://www.hlsl.co.uk/blog/2020/1/29/ieee754-is-not-followed
saved 2025-02-11

Elementary Functions and NOT Following the IEEE 754 Floating-Point Standard — TRYING TO FIND THE OBVIOUS
The IEEE-754 Standard for floating-point numbers was introduced initially in 1985 to solve the problem of diverse floating point implementations prevent code being portable and increase stability across platforms. It has been widely adopted and revised over the last 30 years and if you have dealt

This https://arxiv.org/abs/1907.13457 has been replaced.
link: https://scholar.google.com/scholar?q=a

Universal Entanglement and an Information-Complete Quantum Theory
The most challenging problem of modern physics is how to reconcile quantum theory and general relativity, namely, to find a consistent quantum theory in which gravity is quantized. This Progress Report focuses on such a tentative theory called the information-complete quantum theory (ICQT), in which (1) spacetime (gravity) as a physical quantum system plays a central role for formulating the theory, and (2) there are no any classical systems and concepts. Here universal spacetime-matter entangl…

Weird $\mathbb R$-Factorizable Groups
Evgenii Reznichenko, Ol'ga Sipacheva
https://arxiv.org/abs/2506.18733 https://arxiv.org/pdf…

Weird $\mathbb R$-Factorizable Groups
The problem of the existence of non-pseudo-$\aleph_1$-compact $\mathbb R$-factorizable groups is studied. It is proved that any such group is submetrizable and has weight larger than $ω_1$. Closely related results concerning the $\mathbb R$-factorizability of products of topological groups and spaces are also obtained (a product $X\times Y$ of topological spaces is said to be $\mathbb R$-factorizable if any continuous function $X\times Y\to \mathbb R$ factors through a product of maps from $X$…

Replaced article(s) found for math.HO. https://arxiv.org/list/math.HO/new
[1/1]:
- An old number theory problem related to the Legendre symbol
Wenpeng Zhang

End-to-End Learning of Probabilistic Constellation Shaping through Importance Sampling
Shrinivas Chimmalgi, Laurent Schmalen, Vahid Aref
https://arxiv.org/abs/2506.16098

End-to-End Learning of Probabilistic Constellation Shaping through Importance Sampling
Probabilistic constellation shaping enables easy rate adaption and has been proven to reduce the gap to Shannon capacity. Constellation point probabilities are optimized to maximize either the mutual information or the bit-wise mutual information. The optimization problem is however challenging even for simple channel models. While autoencoder-based machine learning has been applied successfully to solve this problem [1], it requires manual computation of additional terms for the gradient which…

The Optimality of a Nested Generalized Pairwise Group Testing Procedure
Yaakov Malinovsky, Viktor Skorniakov
https://arxiv.org/abs/2506.15797 https://

The Optimality of a Nested Generalized Pairwise Group Testing Procedure
We study the problem of identifying defective units in a finite population of \( n \) units, where each unit \( i \) is independently defective with known probability \( p_i \). This setting is referred to as the \emph{Generalized Group Testing Problem}. A testing procedure is called optimal if it minimizes the expected number of tests. It has been conjectured that, when all probabilities \( p_i \) lie within the interval \( \left[1 - \frac{1}{\sqrt{2}},\, \frac{3 - \sqrt{5}}{2} \right] \), the…

A progressive (#Mamdani) has a chance of winning the #NYCMayoralRace D primary, so of course billionaires are going to throw money at the problem. But rather than propping up someone more reasonable, they're picking the scummiest, most corrupt piece of shit in the race (

Replaced article(s) found for math.CV. https://arxiv.org/list/math.CV/new
[1/1]:
- On the Commuting Problem of Toeplitz Operators on the Harmonic Bergman Space
H. Iqtaish, I. Louhichi, A. Yousef

Unstable $1$-semiadditivity as classifying Goodwillie towers
Connor Malin
https://arxiv.org/abs/2506.11245 https://arxiv.org/pdf/2506…

Unstable $1$-semiadditivity as classifying Goodwillie towers
A stable $\infty$-category is $1$-semiadditive if all norms for finite group actions are equivalences. In the presence of $1$-semiadditivity, Goodwillie calculus simplifies drastically. We introduce two unstable analogs of $1$-semiadditivity for an $\infty$-category $C$ and study their relation to the Goodwillie calculus of functors $C \rightarrow \s(C)$. We demonstrate these qualities are complete obstructions to the problem of endowing $\partial_\ast F$ with either a right module or a divided…

Pattern formation and film rupture in a two-dimensional thermocapillary thin-film model of the B\'enard-Marangoni problem
Stefano B\"ohmer, Bastian Hilder, Jonas Jansen
https://arxiv.org/abs/2506.19795

Pattern formation and film rupture in a two-dimensional thermocapillary thin-film model of the Bénard-Marangoni problem
We study two-dimensional, stationary square and hexagonal patterns in the thermocapillary deformational thin-film model for the fluid height $h$\begin{equation*} \partial_t h+\nabla\cdot\left(h^3\left(\nablaΔh-g\nabla h\right)+M\frac{h^2}{(1+h)^2}\nabla h\right)=0,\quad t>0,\quad x\in\mathbb{R}^2, \end{equation*} that can be formally derived from the Bénard-Marangoni problem via a long-wave approximation. Using a linear stability analysis, we show that the flat surface profile correspondi…

${\sf QMA}={\sf QMA}_1$ with an infinite counter
Stacey Jeffery, Freek Witteveen
https://arxiv.org/abs/2506.15551 https://arxiv.org/p…

${\sf QMA}={\sf QMA}_1$ with an infinite counter
A long-standing open problem in quantum complexity theory is whether ${\sf QMA}$, the quantum analogue of ${\sf NP}$, is equal to ${\sf QMA}_1$, its one-sided error variant. We show that ${\sf QMA}={\sf QMA}^{\infty}= {\sf QMA}_1^{\infty}$, where ${\sf QMA}_1^\infty$ is like ${\sf QMA}_1$, but the verifier has an infinite register, as part of their witness system, in which they can efficiently perform a shift (increment) operation. We call this register an ``infinite counter'', and compare it t…

Fast and Accurate Reconstruction of Voronoi Generators in Large Tessellations
Carlos M Hernandez-Suarez
https://arxiv.org/abs/2506.19076 https://

Fast and Accurate Reconstruction of Voronoi Generators in Large Tessellations
A Voronoi diagram partitions the plane into convex cells, each containing the points closest to a single generator. Given such a tessellation, the inverse Voronoi problem seeks the generator set \( S \) that produced it. Our algorithm selects a single interior cell with \( k \) edges and solves a compact, consistent linear system with \( 2(k+1) \) unknowns and \( 4k \) scalar equations to recover that cell's generator together with the \( k \) generators of its neighbors in one step. The remain…

Quasi-Monte Carlo with one categorical variable
Valerie N. P. Ho, Art B. Owen, Zexin Pan
https://arxiv.org/abs/2506.16582 https://arx…

Quasi-Monte Carlo with one categorical variable
We study randomized quasi-Monte Carlo (RQMC) estimation of a multivariate integral where one of the variables takes only a finite number of values. This problem arises when the variable of integration is drawn from a mixture distribution as is common in importance sampling and also arises in some recent work on transport maps. We find that when integration error decreases at an RQMC rate that it is then beneficial to oversample the smallest mixture components instead of using a proportional all…

Oh, boo, am I irrationally angry about genocide?
Do gently fuck off. https://autistics.life/@VulcanTourist/114659503436582815

Meeting a Challenge raised by Ekhad and Zeilberger related to Stern's Triangle
Jinlong Tang, Guoce Xin
https://arxiv.org/abs/2506.13375 https://…

Meeting a Challenge raised by Ekhad and Zeilberger related to Stern's Triangle
This paper resolves an open problem raised by Ekhad and Zeilberger for computing $ω(10000)$, which is related to Stern's triangle. While $ν(n)$, defined as the sum of squared coefficients in $\prod_{i=0}^{n-1} (1 + x^{2^i} + x^{2^{i+1}})$, admits a rational generating function, the analogous function $ω(n)$ for $\prod_{i=0}^{n-1} (1 + x^{2^i+1} + x^{2^{i+1}+1})$ presents substantial computational difficulties due to its complex structure. We develop a method integrating constant term techn…

Topological slow entropy, sequence entropy, and generalized $[T,T^{-1}]$ systems
Nicanor Carrasco-Vargas
https://arxiv.org/abs/2506.17932 https://

Topological slow entropy, sequence entropy, and generalized $[T,T^{-1}]$ systems
We consider topological dynamical systems given by skew products $S\rtimes_τ T$, where $S\colon Y\to Y$ is a subshift, $τ\colon Y\to\mathbb{Z}$ is a continuous cocycle, and $T$ is an arbitrary invertible topological system. For fixed $(Y,S,τ)$ it may happen that all systems of the form $S\rtimes_τT$ have the same topological entropy, and thus it arises the problem of distinguishing two such systems. We show that if $T_1$ and $T_2$ are invertible topological dynamical systems with differen…

A Two-Operator Calculus for Arithmetic-Progression Paths in the Collatz Graph
Sebastian Angermund
https://arxiv.org/abs/2506.19115 https://

A Two-Operator Calculus for Arithmetic-Progression Paths in the Collatz Graph
A recast of the standard residue-class analysis of the 3x+1 (Collatz) map in terms of two elementary operators on arithmetic progressions. The resulting calculus (i) splits any progression into its even and odd subsequences in a single step, (ii) gives a closed formula for every set of seeds that realises a prescribed parity word, (iii) yields a one line affine invariant that forbids trajectories consisting of infinitely many odd moves, and (iv) reduces the non-trivial-cycle problem to a pair o…

The Word Problem for Products of Symmetric Groups
Hans U. Simon
https://arxiv.org/abs/2506.13655 https://arxiv.org/pdf/2506.13655

The Word Problem for Products of Symmetric Groups
The word problem for products of symmetric groups (WPPSG) is a well-known NP-complete problem. An input instance of this problem consists of ``specification sets'' $X_1,\ldots,X_m \seq \{1,\ldots,n\}$ and a permutation $τ$ on $\{1,\ldots,n\}$. The sets $X_1,\ldots,X_m$ specify a subset of the symmetric group $\cS_n$ and the question is whether the given permutation $τ$ is a member of this subset. We discuss three subproblems of WPPSG and show that they can be solved efficiently. The subproble…

Why AI can't possibly make you more productive; long
#AI and "productivity", some thoughts:
Productivity is a concept that isn't entirely meaningless outside the context of capitalism, but it's a concept that is heavily inflected in a capitalist context. In many uses today it effectively means "how much you can satisfy and/or exceed your boss' expectations." This is not really what it should mean: even in an anarchist utopia, people would care about things like how many shirts they can produce in a week, although in an "I'd like to voluntarily help more people" way rather than an "I need to meet this quota to earn my survival" way. But let's roll with this definition for a second, because it's almost certainly what your boss means when they say "productivity", and understanding that word in a different (even if truer) sense is therefore inherently dangerous.
Accepting "productivity" to mean "satisfying your boss' expectations," I will now claim: the use of generative AI cannot increase your productivity.
Before I dive in, it's imperative to note that the big generative models which most people think of as constituting "AI" today are evil. They are 1: pouring fuel on our burning planet, 2: psychologically strip-mining a class of data laborers who are exploited for their precarity, 3: enclosing, exploiting, and polluting the digital commons, and 4: stealing labor from broad classes of people many of whom are otherwise glad to give that labor away for free provided they get a simple acknowledgement in return. Any of these four "ethical issues" should be enough *alone* to cause everyone to simply not use the technology. These ethical issues are the reason that I do not use generative AI right now, except for in extremely extenuating circumstances. These issues are also convincing for a wide range of people I talk to, from experts to those with no computer science background. So before I launch into a critique of the effectiveness of generative AI, I want to emphasize that such a critique should be entirely unnecessary.
But back to my thesis: generative AI cannot increase your productivity, where "productivity" has been defined as "how much you can satisfy and/or exceed your boss' expectations."
Why? In fact, what the fuck? Every AI booster I've met has claimed the opposite. They've given me personal examples of time saved by using generative AI. Some of them even truly believe this. Sometimes I even believe they saved time without horribly compromising on quality (and often, your boss doesn't care about quality anyways if the lack of quality is hard to measure of doesn't seem likely to impact short-term sales/feedback/revenue). So if generative AI genuinely lets you write more emails in a shorter period of time, or close more tickets, or something else along these lines, how can I say it isn't increasing your ability to meet your boss' expectations?
The problem is simple: your boss' expectations are not a fixed target. Never have been. In virtue of being someone who oversees and pays wages to others under capitalism, your boss' game has always been: pay you less than the worth of your labor, so that they can accumulate profit and this more capital to remain in charge instead of being forced into working for a wage themselves. Sure, there are layers of manservant caught in between who aren't fully in this mode, but they are irrelevant to this analysis. It matters not how much you please your manager if your CEO thinks your work is not worth the wages you are being paid. And using AI actively lowers the value of your work relative to your wages.
Why do I say that? It's actually true in several ways. The most obvious: using generative AI lowers the quality of your work, because the work it produces is shot through with errors, and when your job is reduced to proofreading slop, you are bound to tire a bit, relax your diligence, and let some mistakes through. More than you would have if you are actually doing and taking pride in the work. Examples are innumerable and frequent, from journalists to lawyers to programmers, and we laugh at them "haha how stupid to not check whether the books the AI reviewed for you actually existed!" but on a deeper level if we're honest we know we'd eventually make the same mistake ourselves (bonus game: spot the swipe-typing typos I missed in this post; I'm sure there will be some).
But using generative AI also lowers the value of your work in another much more frightening way: in this era of hype, it demonstrates to your boss that you could be replaced by AI. The more you use it, and no matter how much you can see that your human skills are really necessary to correct its mistakes, the more it appears to your boss that they should hire the AI instead of you. Or perhaps retain 10% of the people in roles like yours to manage the AI doing the other 90% of the work. Paradoxically, the *more* you get done in terms of raw output using generative AI, the more it looks to your boss as if there's an opportunity to get enough work done with even fewer expensive humans. Of course, the decision to fire you and lean more heavily into AI isn't really a good one for long-term profits and success, but the modern boss did not get where they are by considering long-term profits. By using AI, you are merely demonstrating your redundancy, and the more you get done with it, the more redundant you seem.
In fact, there's even a third dimension to this: by using generative AI, you're also providing its purveyors with invaluable training data that allows them to make it better at replacing you. It's generally quite shitty right now, but the more use it gets by competent & clever people, the better it can become at the tasks those specific people use it for. Using the currently-popular algorithm family, there are limits to this; I'm not saying it will eventually transcend the mediocrity it's entwined with. But it can absolutely go from underwhelmingly mediocre to almost-reasonably mediocre with the right training data, and data from prompting sessions is both rarer and more useful than the base datasets it's built on.
For all of these reasons, using generative AI in your job is a mistake that will likely lead to your future unemployment. To reiterate, you should already not be using it because it is evil and causes specific and inexcusable harms, but in case like so many you just don't care about those harms, I've just explained to you why for entirely selfish reasons you should not use it.
If you're in a position where your boss is forcing you to use it, my condolences. I suggest leaning into its failures instead of trying to get the most out of it, and as much as possible, showing your boss very clearly how it wastes your time and makes things slower. Also, point out the dangers of legal liability for its mistakes, and make sure your boss is aware of the degree to which any of your AI-eager coworkers are producing low-quality work that harms organizational goals.
Also, if you've read this far and aren't yet of an anarchist mindset, I encourage you to think about the implications of firing 75% of (at least the white-collar) workforce in order to make more profit while fueling the climate crisis and in most cases also propping up dictatorial figureheads in government. When *either* the AI bubble bursts *or* if the techbros get to live out the beginnings of their worker-replacement fantasies, there are going to be an unimaginable number of economically desperate people living in increasingly expensive times. I'm the kind of optimist who thinks that the resulting social crucible, though perhaps through terrible violence, will lead to deep social changes that effectively unseat from power the ultra-rich that continue to drag us all down this destructive path, and I think its worth some thinking now about what you might want the succeeding stable social configuration to look like so you can advocate towards that during points of malleability.
As others have said more eloquently, generative AI *should* be a technology that makes human lives on average easier, and it would be were it developed & controlled by humanists. The only reason that it's not, is that it's developed and controlled by terrible greedy people who use their unfairly hoarded wealth to immiserate the rest of us in order to maintain their dominance. In the long run, for our very survival, we need to depose them, and I look forward to what the term "generative AI" will mean after that finally happens.

"The big problem is 'bottlenecks' that make it harder to produce housing, expand energy production, or build new roads and bridges."
vs.
"The big problem is that big corporations have way too much power over our economy and our government."
By 12pts all voters and by 42pts Dem voters prefer the second statement. They're right!

Poll: Democratic voters prefer "populism" over "abundance"
Democrats are asking themselves some hard questions as they ponder how they lost the 2024 election.

lmao @ this aliexpress vendor complaining about supply chains
we've all been there mate

AbRank: A Benchmark Dataset and Metric-Learning Framework for Antibody-Antigen Affinity Ranking
Chunan Liu, Aurelien Pelissier, Yanjun Shao, Lilian Denzler, Andrew C. R. Martin, Brooks Paige, Mariia Rodriguez Martinez
https://arxiv.org/abs/2506.17857

AbRank: A Benchmark Dataset and Metric-Learning Framework for Antibody-Antigen Affinity Ranking
Accurate prediction of antibody-antigen (Ab-Ag) binding affinity is essential for therapeutic design and vaccine development, yet the performance of current models is limited by noisy experimental labels, heterogeneous assay conditions, and poor generalization across the vast antibody and antigen sequence space. We introduce AbRank, a large-scale benchmark and evaluation framework that reframes affinity prediction as a pairwise ranking problem. AbRank aggregates over 380,000 binding assays from…

Asymptotic Plateau problem for $2$-convex hypersurface in $\mathbb{H}^4$
Defa Chen, Zhenan Sui, Letao Sun
https://arxiv.org/abs/2506.00565 https://

Asymptotic Plateau problem for $2$-convex hypersurface in $\mathbb{H}^4$
We prove the existence of smooth complete $2$-convex hypersurface which satisfies prescribed curvature equation $(κ_1 + κ_2)(κ_1 + κ_3)(κ_2 + κ_3) = (2 σ)^3$ and has prescribed asymptotic boundary at infinity of hyperbolic space of dimension 4, where $σ\in (0, 1)$ is a constant. We also prove the existence for $σ_k (κ_2 + \cdots + κ_n, \cdots, κ_1 + \cdots + κ_{n - 1}) = C_n^k (n - 1)^k σ^k$ with $k < n$ in $\mathbb{H}^{n + 1}$.

The maximum-average subtensor problem: equilibrium and out-of-equilibrium properties
Vittorio Erba, Nathan Malo Kupferschmid, Rodrigo P\'erez Ortiz, Lenka Zdeborov\'a
https://arxiv.org/abs/2506.15400

The maximum-average subtensor problem: equilibrium and out-of-equilibrium properties
In this paper we introduce and study the Maximum-Average Subtensor ($p$-MAS) problem, in which one wants to find a subtensor of size $k$ of a given random tensor of size $N$, both of order $p$, with maximum sum of entries. We are motivated by recent work on the matrix case of the problem in which several equilibrium and non-equilibrium properties have been characterized analytically in the asymptotic regime $1 \ll k \ll N$, and a puzzling phenomenon was observed involving the coexistence of a c…

This https://arxiv.org/abs/1907.13457 has been replaced.
link: https://scholar.google.com/scholar?q=a

Universal Entanglement and an Information-Complete Quantum Theory
The most challenging problem of modern physics is how to reconcile quantum theory and general relativity, namely, to find a consistent quantum theory in which gravity is quantized. This Progress Report focuses on such a tentative theory called the information-complete quantum theory (ICQT), in which (1) spacetime (gravity) as a physical quantum system plays a central role for formulating the theory, and (2) there are no any classical systems and concepts. Here universal spacetime-matter entangl…

This https://arxiv.org/abs/2412.16740 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hilbert's tenth problem for systems of diagonal quadratic forms, and Büchi's problem
In this paper we complete Büchi's proof that there is no decision algorithm for the solubility in integers of arbitrary systems of diagonal quadratic form equations, by proving the assertion that whenever $x_1^2, \cdots, x_5^2$ are five squares such that the second differences satisfy \[x_{k+2}^2 - 2 x_{k+1}^2 + x_k^2 = 2\] for $k = 1,2,3$, then they must be consecutive. This answers a question of J.~Richard~Büchi.

Irgendetwas stimmt mit nvmi nicht :(

There’s exactly 1 narrow way that it’s true. Before widespread #WFH, attackers often had an insurmountable barrier: no way into the business network from the Internet. At the last gig (2008) where I had to visit a “workplace” regularly, inbound remote access was officially non-existent & outbound Internet access all went through restrictive web proxies.

Kevin Beaumont (@GossiTheDog@cyberplace.social)
Attached: 1 image This Daily Mail piece about security leaders thinking work-from-home means they will be crippled is horseshit, I'm not linking it. They've taken a survey about how security people think their businesses couldn't survive ransomware, and linked it to working from home. WFH isn't the problem: business IT and resilience being built on quicksand is the problem.

I like @…’s analysis here in many respects, both its broad conclusion (when the hype dies down, the useful parts remain and we take them for granted as normal tools), and this gem here:
Machine learning is well-suited for ❝any problem where we don’t actually know the rules and where the cost of a wrong answer is significantly lower than the benefit of a right answer.❞
1/2 https://infosec.exchange/@david_chisnall/112716199046923540

Non-individuality and experience
Raoni Arroyo
https://arxiv.org/abs/2505.15627 https://arxiv.org/pdf/2505.15627

Non-individuality and experience
This chapter acknowledges a gap between the ``non-individuals'' interpretation of quantum mechanics and our world of experience, and begins to bridge it. Section 1 states the problem with Abner Shimony's ``Phenomenological principle''; section 2 briefly presents the interpretation with connection to standard quantum mechanics; section 3 presents the measurement problem in connection with the Phenomenological principle, the standard way out of it, and why the ``non-individuals'' interpretation o…

A Minkowski problem for $\alpha$-concave functions via optimal transport
Xiao Li, Nguyen Nguyen, Deping Ye
https://arxiv.org/abs/2506.14735 https://…

A Minkowski problem for $α$-concave functions via optimal transport
The notions of the Euclidean surface area measure and the spherical surface area measure of $α$-concave functions in $\mathbb{R}^n$, with $-\frac{1}{n}<α<0$, are introduced via a first variation of the total mass functional with respect to the $α$-sum operation. Subsequently, these notions are extended to those for $α$-concave measures. We then study the Minkowski problem associated with the Euclidean surface area measures of $α$-concave measures via optimal transport.

Free boundary regularity and well-posedness of physical solutions to the supercooled Stefan problem
Sebastian Munoz
https://arxiv.org/abs/2506.18741 https:…

Free boundary regularity and well-posedness of physical solutions to the supercooled Stefan problem
We study the regularity and well-posedness of physical solutions to the supercooled Stefan problem. Assuming only that the initial temperature is integrable, we prove that the free boundary, known to have jump discontinuities as a function of the time variable, is $C^1$ as a function of the space variable, and is $C^{\infty}$ outside of a closed, countable set, which we describe explicitly. We also prove that, as conjectured in arXiv:1902.05174, the set of positive times when a jump occurs cann…

Large grid subsets without many cospherical points
Zichao Dong, Zijian Xu
https://arxiv.org/abs/2506.18113 https://arxiv.org/pdf/2506…

Large grid subsets without many cospherical points
Motivated by intuitions from projective algebraic geometry, we provide a novel construction of subsets of the $d$-dimensional grid $[n]^d$ of size $n - o(n)$ with no $d + 2$ points on a sphere or a hyperplane. For $d = 2$, this improves the previously best known lower bound of $n/4$ toward the Erdős--Purdy problem due to Thiele in 1995. For $d \ge 3$, this improves the recent $Ω\bigl( n^{\frac{3}{d+1}-o(1)} \bigr)$ bound due to Suk and White, confirming their conjectured $Ω\bigl( n^{\frac{d}…

A remarkable dynamical symmetry of the Landau problem
Tekin Dereli, Philippe Nounahon, Todor Popov
https://arxiv.org/abs/2506.11642 https://

A remarkable dynamical symmetry of the Landau problem
We show that the dynamical group of an electron in a constant magnetic field is the group of symplectomorphisms $Sp(4,\mathbb{R})$. It is generated by the spinorial realization of the conformal algebra $\mathfrak{so}(2,3)$ considered in Dirac's seminal paper "A Remarkable Representation of the 3 + 2 de Sitter Group". The symplectic group $Sp(4,\mathbb{R})$ is the double covering of the conformal group $SO(2,3)$ of 2+1 dimensional Minkowski spacetime which is in turn the dynamical group of a hyd…

Detection and Reconstruction of a Random Hypergraph from Noisy Graph Projection
Shuyang Gong, Zhangsong Li, Qiheng Xu
https://arxiv.org/abs/2506.17527 http…

Detection and Reconstruction of a Random Hypergraph from Noisy Graph Projection
For a $d$-uniform random hypergraph on $n$ vertices in which hyperedges are included i.i.d.\ so that the average degree in the hypergraph is $n^{δ+o(1)}$, the projection of such a hypergraph is a graph on the same $n$ vertices where an edge connects two vertices if and only if they belong to a same hyperedge. In this work, we study the inference problem where the observation is a \emph{noisy} version of the graph projection where each edge in the projection is kept with probability $p=n^{-1+α…

Semirandom Planted Clique via 1-norm Isometry Property
Venkatesan Guruswami, Hsin-Po Wang
https://arxiv.org/abs/2506.17916 https://ar…

Semirandom Planted Clique via 1-norm Isometry Property
We give a polynomial-time algorithm that finds a planted clique of size $k \ge \sqrt{n \log n}$ in the semirandom model, improving the state-of-the-art $\sqrt{n} (\log n)^2$ bound. This $\textit{semirandom planted clique problem}$ concerns finding the planted subset $S$ of $k$ vertices of a graph $G$ on $V$, where the induced subgraph $G[S]$ is complete, the cut edges in $G[S; V \setminus S]$ are random, and the remaining edges in $G[V \setminus S]$ are adversarial. An elegant greedy algorith…

Physics-Informed Neural Networks for the Korteweg-de Vries Equation for Internal Solitary Wave Problem: Forward Simulation and Inverse Parameter Estimation
Ming Kang, Hang Li, Qiwen Tan, Zhan Wang, Ruipeng Li, Junfang Zhao, Hui Xiang, Dixia Fan
https://arxiv.org/abs/2506.14236

Physics-Informed Neural Networks for the Korteweg-de Vries Equation for Internal Solitary Wave Problem: Forward Simulation and Inverse Parameter Estimation
Physics-informed neural networks (PINNs) have emerged as a transformative framework for addressing operator learning and inverse problems involving the Korteweg-de Vries (KdV) equation for internal solitary waves. By integrating physical constraints with data-driven optimization, PINNs overcome the critical challenges of parameter unmeasurability in the KdV equation for internal solitary waves in two-layer fluid systems. This work addresses two problems: (1) Operator learning constructs a mappi…

Isoperimetric Problem and Weierstrass Necessary Condition for Fractional Calculus of Variations
Shakir Sh. Yusubov, Shikhi Sh. Yusubov, Elimhan N. Mahmudov
https://arxiv.org/abs/2506.12926

Isoperimetric Problem and Weierstrass Necessary Condition for Fractional Calculus of Variations
Summary]{In this paper, we study problems of minimization of a functional depending on the fractional Caputo derivative of order $0<α\leq 1$ and the fractional Riemann- Liouville integral of order $β> 0$ at fixed endpoints. A fractional analogue of the Du Bois-Reymond lemma is proved, and the Euler-Lagrange conditions are proved for the simplest problem of fractional variational calculus with fixed ends and for the fractional isoperimetric problem. An approach is proposed to obtain the necess…

Partial Domination in Some Geometric Intersection Graphs and Some Complexity Results
Madhura Dutta, Anil Maheshwari, Subhas C. Nandy, Bodhayan Roy
https://arxiv.org/abs/2505.15949

Partial Domination in Some Geometric Intersection Graphs and Some Complexity Results
{\em Partial domination problem} is a generalization of the {\em minimum dominating set problem} on graphs. Here, instead of dominating all the nodes, one asks to dominate at least a fraction of the nodes of the given graph by choosing a minimum number of nodes. For any real number $α\in(0,1]$, $α$-partial domination problem can be proved to be NP-complete for general graphs. In this paper, we define the {\em maximum dominating $k$-set} of a graph, which is polynomially transformable to the p…

Witnessing PPT entanglement via rank analysis of (sub)matrices
Aabhas Gulati
https://arxiv.org/abs/2506.11346 https://arxiv.org/pdf/2…

Witnessing PPT entanglement via rank analysis of (sub)matrices
We develop a new method for entanglement detection in bipartite quantum states, using the violation of the rank-1 generated property of matrices. The positive-semidefinite matrices form a convex cone that has extremal elements of only rank-1. But convex conic subsets resulting from presence of linear constraints allow extremal elements of rank > 1. The problem of deciding when a matrix is rank-1 generated, i.e a sum of rank-1 PSD matrices, has been studied extensively in optimization theory. Th…

Two Higgs Doublet Solutions to the Strong CP Problem
Quentin Bonnefoy, Lawrence J. Hall, Claudio Andrea Manzari, Bea Noether
https://arxiv.org/abs/2506.13853

Two Higgs Doublet Solutions to the Strong CP Problem
We solve the strong CP problem in a broad class of two Higgs doublet theories that will be probed at the Large Hadron Collider and at future colliders.These theories feature CP and Abelian flavor symmetries, both broken softly in the scalar potential, that yield realistic quark masses and mixings. The flavor symmetry charges are chosen so that $\barθ=0$ at tree level for all values of the Yukawa and quartic couplings of the theory. We prove that in all such theories the 1-loop contribution to …

Maximum Reachability Orientation of Mixed Graphs
Florian H\"orsch
https://arxiv.org/abs/2506.16171 https://arxiv.org/pdf/2506.16…

Maximum Reachability Orientation of Mixed Graphs
We aim to find orientations of mixed graphs optimizing the total reachability, a problem that has applications in causality and biology. For given a digraph $D$, we use $P(D)$ for the set of ordered pairs of distinct vertices in $V(D)$ and we define $κ_D:P(D)\rightarrow \{0,1\}$ by $κ_D(u,v)=1$ if $v$ is reachable from $u$ in $D$, and $κ_D(u,v)=0$, otherwise. We use $R(D)=\sum_{(u,v)\in P(D)}κ_D(u,v)$. Now, given a mixed graph $G$, we aim to find an orientation $\vec{G}$ of $G$ that maxim…

Low regularity well-posedness of nonlocal dispersive perturbations of Burgers' equation
Luc Molinet, Didier Pilod, St\'ephane Vento
https://arxiv.org/abs/2506.17801

Low regularity well-posedness of nonlocal dispersive perturbations of Burgers' equation
We consider the Cauchy problem associated to a class of dispersive perturbations of Burgers' equations, which contains the low dispersion Benjamin-Ono equation, (also known as low dispersion fractional KdV equation), $$ \partial_tu-D_x^α\partial_xu=\partial_x(u^2) \, ,$$ and prove that it is locally well-posed in $H^s(\mathbb K)$, $\mathbb K=\mathbb R$ or $\mathbb T$, for $s>s_α$, where \begin{equation*} s_α=\begin{cases} 1-\frac{3α}4 & \text{for} \quad \frac23 \le α\le 1; \frac 32(1-�…

Finite-Time Information-Theoretic Bounds in Queueing Control
Yujie Liu, Vincent Y. F. Tan, Yunbei Xu
https://arxiv.org/abs/2506.18278 https://

Finite-Time Information-Theoretic Bounds in Queueing Control
We establish the first finite-time information-theoretic lower bounds-and derive new policies that achieve them-for the total queue length in scheduling problems over stochastic processing networks with both adversarial and stochastic arrivals. Prior analyses of MaxWeight guarantee only stability and asymptotic optimality in heavy traffic; we prove that, at finite horizons, MaxWeight can incur strictly larger backlog by problem-dependent factors which we identify. Our main innovations are 1) a …

Generative model for optimal density estimation on unknown manifold
Arthur St\'ephanovitch
https://arxiv.org/abs/2506.19587 https://

Generative model for optimal density estimation on unknown manifold
We propose a generative model that achieves minimax-optimal convergence rates for estimating probability distributions supported on unknown low-dimensional manifolds. Building on Fefferman's solution to the geometric Whitney problem, our estimator is itself supported on a submanifold that matches the regularity of the data's support. This geometric adaptation enables the estimator to be simultaneously minimax-optimal for all \( γ\)-Hölder Integral Probability Metrics (IPMs) with \( γ\geq 1 \…

Simultaneous recovery of corroded boundaries and admittance using the Kohn-Vogelius method
Moustapha Essahraoui, Elmehdi Cherrat, Lekbir Afraites, Julius Fergy Tiongson Rabago
https://arxiv.org/abs/2506.17938

Simultaneous recovery of corroded boundaries and admittance using the Kohn-Vogelius method
We address the problem of identifying an unknown portion $Γ$ of the boundary of a $d$-dimensional ($d \in \{1, 2\}$) domain $Ω$ and its associated Robin admittance coefficient, using two sets of boundary Cauchy data $(f, g)$--representing boundary temperature and heat flux--measured on the accessible portion $Σ$ of the boundary. Identifiability results \cite{Bacchelli2009,PaganiPierotti2009} indicate that a single measurement on $Σ$ is insufficient to uniquely determine both $Γ$ and $α$, …

Triangle-free subsets of the Hypercube
Padmini Mukkamala
https://arxiv.org/abs/2506.18782 https://arxiv.org/pdf/2506.18782

Triangle-free subsets of the Hypercube
We study the problem of determining the largest subset of vertices of the $n$ dimensional hypercube without three vertices at a Hamming distance of exactly $r$ from each other. In particular, we provide a lower bound of $\frac{c2^n}{e^r2^{\frac r2} (\frac nr)^{\frac{3r}{4}}}$ and an upper bound of $O(\frac{r2^n}{n+1})$ when $2r \le n$. In particular, when $r$ is a constant, the lower bound is $\frac{c2^n}{n^{3r/4}}$, while the upper bound is $\frac{c'2^n}{n}$.

The Densest SWAMP problem: subhypergraphs with arbitrary monotonic partial edge rewards
Vedangi Bengali, Nikolaj Tatti, Iiro Kumpulainen, Florian Adriaens, Nate Veldt
https://arxiv.org/abs/2506.12998

The Densest SWAMP problem: subhypergraphs with arbitrary monotonic partial edge rewards
We consider a generalization of the densest subhypergraph problem where nonnegative rewards are given for including partial hyperedges in a dense subhypergraph. Prior work addressed this problem only in cases where reward functions are convex, in which case the problem is poly-time solvable. We consider a broader setting where rewards are monotonic but otherwise arbitrary. We first prove hardness results for a wide class of non-convex rewards, then design a 1/k-approximation by projecting to th…

An extension of Dembo-Hammer's reduction algorithm for the 0-1 knapsack problem
Yang Yang
https://arxiv.org/abs/2506.06138 https://

An extension of Dembo-Hammer's reduction algorithm for the 0-1 knapsack problem
Dembo-Hammer's Reduction Algorithm (DHR) is one of the classical algorithms for the 0-1 Knapsack Problem (0-1 KP) and its variants, which reduces an instance of the 0-1 KP to a sub-instance of smaller size with reduction time complexity $O(n)$. We present an extension of DHR (abbreviated as EDHR), which reduces an instance of 0-1 KP to at most $n^i$ sub-instances for any positive integer $i$. In practice, $i$ can be set as needed. In particular, if we choose $i=1$ then EDHR is exactly DHR. Fina…

Analysis and conditional optimization of projection estimates for the distribution of random variable using Legendre polynomials
Tatyana A. Averina, Konstantin A. Rybakov
https://arxiv.org/abs/2506.14822

Analysis and conditional optimization of projection estimates for the distribution of random variable using Legendre polynomials
Algorithms for jointly obtaining projection estimates of the density and distribution function of a random variable using the Legendre polynomials are proposed. For these algorithms, a problem of the conditional optimization is solved. Such an optimization allows one increasing the approximation accuracy with a minimum computational costs. The proposed algorithms are tested on examples with different degree of smoothness of the density.

Accuracy and componentwise accuracy in multilinear PageRank
Mehdi Najafi Kalyani, Federico Poloni
https://arxiv.org/abs/2506.18356 https://

Accuracy and componentwise accuracy in multilinear PageRank
We study the stability with respect to perturbations and the accuracy of numerical algorithms for computing solutions to the multilinear PageRank problem $\mathbf{x} = (1-α)\mathbf{v} + α\mathcal{P} \mathbf{x}^2$. Our results reveal that the solution can be more stable with respect to perturbations and numerical errors with respect to the classical bounds for nonlinear systems of equations (based on the norm of the Jacobian). In detail, one can obtain bounds for the minimal solution which ign…

Large solutions to semilinear equations for subordinate Laplacians in $C^{1,1}$ bounded open sets
Indranil Chowdhury, Zoran Vondra\v{c}ek, Vanja Wagner
https://arxiv.org/abs/2506.13462

Large solutions to semilinear equations for subordinate Laplacians in $C^{1,1}$ bounded open sets
We study the existence of a large solution to a semilinear problem in a bounded open $C^{1,1}$ set for a class of nonlocal operators obtained by an appropriate subordination of the Laplacian. These operators are classical generalisations of the fractional Laplacian. The existence result is shown under a nonlocal version of the Keller-Osserman condition, stated in terms of the subordinator and the source term $f$.

Optimal Convergence Rates of Deep Neural Network Classifiers
Zihan Zhang, Lei Shi, Ding-Xuan Zhou
https://arxiv.org/abs/2506.14899 https://

Optimal Convergence Rates of Deep Neural Network Classifiers
In this paper, we study the binary classification problem on $[0,1]^d$ under the Tsybakov noise condition (with exponent $s \in [0,\infty]$) and the compositional assumption. This assumption requires the conditional class probability function of the data distribution to be the composition of $q+1$ vector-valued multivariate functions, where each component function is either a maximum value function or a Hölder-$β$ smooth function that depends only on $d_*$ of its input variables. Notably, $d_…

Quantum SAT Problems with Finite Sets of Projectors are Complete for a Plethora of Classes
Ricardo Rivera Cardoso, Alex Meiburg, Daniel Nagaj
https://arxiv.org/abs/2506.07244

Quantum SAT Problems with Finite Sets of Projectors are Complete for a Plethora of Classes
Previously, all known variants of the Quantum Satisfiability (QSAT) problem, i.e. deciding whether a $k$-local ($k$-body) Hamiltonian is frustration-free, could be classified as being either in $\mathsf{P}$; or complete for $\mathsf{NP}$, $\mathsf{MA}$, or $\mathsf{QMA_1}$. Here, we demonstrate new qubit variants of this problem that are complete for $\mathsf{BQP_1}$, $\mathsf{coRP}$, $\mathsf{QCMA}$, $\mathsf{PI(coRP,NP)}$, $\mathsf{PI(BQP_1,NP)}$, $\mathsf{PI(BQP_1,MA)}$, $\mathsf{SoPU(coRP,N…

Contextual Pattern Mining and Counting
Ling Li, Daniel Gibney, Sharma V. Thankachan, Solon P. Pissis, Grigorios Loukides
https://arxiv.org/abs/2506.17613 h…

Contextual Pattern Mining and Counting
Given a string $P$ of length $m$, a longer string $T$ of length $n>m$, and two integers $l\geq 0$ and $r\geq 0$, the context of $P$ in $T$ is the set of all string pairs $(L,R)$, with $|L|=l$ and $|R|=r$, such that the string $LPR$ occurs in $T$. We introduce two problems related to the notion of context: (1) the Contextual Pattern Mining (CPM) problem, which given $T$, $(m,l,r)$, and an integer $τ>0$, asks for outputting the context of each substring $P$ of length $m$ of $…

Large solutions for subordinate spectral Laplacian
Ivan Bio\v{c}i\'c, Vanja Wagner
https://arxiv.org/abs/2506.16780 https://arxiv…

Large solutions for subordinate spectral Laplacian
We find a large solution to a semilinear Dirichlet problem in a bounded $C^{1,1}$ domain for a non-local operator $ϕ(-Δ\vert_{D})$, an extension of the infinitesimal generator of a subordinate killed Brownian motion. The setting covers and extends the case of the spectral fractional Laplacian. The upper bound for the explosion rate of the large solution is obtained, and is given in terms of the renewal function, distance to the boundary, and the Keller-Osserman-type transformation of the semi…

Spectral Tur\'{a}n problem of non-bipartite graphs: Forbidden books
Ruifang Liu, Lu Miao
https://arxiv.org/abs/2506.04884 https://

Spectral Turán problem of non-bipartite graphs: Forbidden books
A book graph $B_{r+1}$ is a set of $r+1$ triangles with a common edge, where $r\geq0$ is an integer. Zhai and Lin [J. Graph Theory 102 (2023) 502-520] proved that for $n\geq\frac{13}{2}r$, if $G$ is a $B_{r+1}$-free graph of order $n$, then $ρ(G)\leqρ(T_{n,2})$, with equality if and only if $G\cong T_{n,2}$. Note that the extremal graph $T_{n,2}$ is bipartite. Motivated by the above elegant result, we investigate the spectral Turán problem of non-bipartite $B_{r+1}$-free graphs of order $n$.…

This https://arxiv.org/abs/2411.13348 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCC_…

Parameterized Complexity of the Star Decomposition Problem
A star of length $ \ell $ is defined as the complete bipartite graph $ K_{1,\ell } $. In this paper we deal with the problem of edge decomposition of graphs into stars of varying lengths. Given a graph $ G $ and a list of integers $S=(s_1,\ldots, s_t) $, an $S$-star decomposition of $ G $ is an edge decomposition of $ G $ into graphs $G_1 ,G_2 ,\ldots,G_t $ such that $G_i$ is isomorphic to an star of length $s_i$, for each $i \in\{1,2,\ldots,t\}$. Given a graph $G$ and a list of integers $S$,…

Berezin-Li-Yau inequality for mixed local-nonlocal Dirichlet-Laplacian
Aidyn Kassymov, Berikbol T. Torebek
https://arxiv.org/abs/2506.17780 https://…

Berezin-Li-Yau inequality for mixed local-nonlocal Dirichlet-Laplacian
In this paper, we consider an eigenvalue problem for mixed local-nonlocal Laplacian $$\mathcal{L}^{a,b}_{\Om}:=-aΔ+b(-Δ)^s,\,a>0,\,b\in\mathbb{R},\,s\in (0,1),$$ with Dirichlet boundary conditions. First, the case $a>0$ and $b>0$ is considered and the Berezin-Li-Yau inequality (lower bounds of the sum of eigenvalues) is established. This inequality is characterised as the maximum of the classical and fractional versions of the Berezin-Li-Yau inequality, and, in particular, yields both the cla…

On Domination Exponents for Pairs of Graphs
Grigoriy Blekherman, Annie Raymond, Alexander Razborov, Fan Wei
https://arxiv.org/abs/2506.12151 https://

On Domination Exponents for Pairs of Graphs
Understanding graph density profiles is notoriously challenging. Even for pairs of graphs, complete characterizations are known only in very limited cases, such as edges versus cliques. This paper explores a relaxation of the graph density profile problem by examining the homomorphism density domination exponent $C(H_1, H_2)$. This is the smallest real number $c \geq 0$ such that $t(H_1, T) \geq t(H_2, T)^c$ for all target graphs $T$ (if such a $c$ exists) where $t(H,T)$ is the homomorphism den…

Cazenave-Dickstein-Weissler-type extension of Fujita's problem on Heisenberg groups
Mokhtar Kirane, Ahmad Z. Fino, Berikbol T. Torebek, Zineb Sabbagh
https://arxiv.org/abs/2506.10611

Cazenave-Dickstein-Weissler-type extension of Fujita's problem on Heisenberg groups
This paper examines the critical exponents for the existence of global solutions to the equation \begin{equation*} \begin{array}{ll} \displaystyle u_t-Δ_{\mathbb{H}}u=\int_0^t(t-s)^{-γ}|u(s)|^{p-1}u(s)\,ds,&\qquad 0\leqγ<1,\,\,\, {η\in \mathbb{H}^n,\,\,\,t>0,} \end{array}\end{equation*} on the Heisenberg groups $\mathbb{H}^n.$ There exists a critical exponent $$p_c= \max\Big\{\frac{1}γ,p_γ\Big\}\in(0,+\infty],\quad\hbox{with}\quad p_γ=1+\frac{2(2-γ)}{Q-2+2γ},\,\,Q=2n+2$$ such…

Algebraic aspects of the polynomial Littlewood-Offord problem
Zhihan Jin, Matthew Kwan, Lisa Sauermann, Yiting Wang
https://arxiv.org/abs/2505.23335 https:…

Algebraic aspects of the polynomial Littlewood-Offord problem
Consider a degree-$d$ polynomial $f(ξ_1,\dots,ξ_n)$ of independent Rademacher random variables $ξ_1,\dots,ξ_n$. To what extent can $f(ξ_1,\dots,ξ_n)$ concentrate on a single point? This is the so-called polynomial Littlewood-Offord problem. A nearly optimal bound was proved by Meka, Nguyen and Vu: the point probabilities are always at most about $1/\sqrt n$, unless $f$ is "close to the zero polynomial" (having only $o(n^d)$ nonzero coefficients). In this paper we prove several results s…

Generalized Poisson kernel and solution of the Dirichlet problem for the radial Schr\"odinger equation
V\'ictor A Vicente-Ben\'itez
https://arxiv.org/abs/2506.10273

Generalized Poisson kernel and solution of the Dirichlet problem for the radial Schrödinger equation
We present an explicit construction of the solution to the Dirichlet boundary value problem for the radial Schrödinger equation in the unit ball, with a complex-valued potential $V$ satisfying the condition $\int_0^1r|V(r)|dr<\infty$. The solution is based on the construction of an explicit orthogonal set of solutions for the radial equation. In the case of a Dirichlet problem with boundary data in $W^{\frac{1}{2},2}(\mathbb{S}^{d-1})$, the solution is expressed as a series expansion…

Modica type estimates and curvature results for overdetermined $p$-Laplace problems
Yuanyuan Lian, Jing Wu
https://arxiv.org/abs/2506.14579 https://…

Modica type estimates and curvature results for overdetermined $p$-Laplace problems
In this paper we prove Modica type estimates for the following overdetermined $p$-Laplace problem \begin{equation*} \begin{cases} \mathrm{div} \left(|\nabla u|^{p-2}\nabla u\right)+f(u) =0& \mbox{in $Ω$, } u>0 &\mbox{in $Ω$, } u=0 &\mbox{on $\partialΩ$, } \partial_ν u=-κ&\mbox{on $\partialΩ$, } \end{cases} \end{equation*} where $1

Melting and freezing rates of the radial interior Stefan problem in two dimension
Jeongheon Park
https://arxiv.org/abs/2506.13175 https://

Melting and freezing rates of the radial interior Stefan problem in two dimension
We consider the interior Stefan problem under radial symmetry in two dimension. A water ball surrounded by ice undergoes melting or freezing. We construct a discrete family of global-in-time solutions, both melting and freezing scenarios. The evolution of the free boundary, represented by the radius of the water ball, $λ(t)$ exhibits exponential convergence to a limiting radius value $λ_\infty > 0$, characterized by the asymptotic expression \[ λ(t) = λ_\infty + (1 - λ_\infty)\, e^{-\frac{…