Tootfinder

Toward Valid Measurement Of (Un)fairness For Generative AI: A Proposal For Systematization Through The Lens Of Fair Equality of Chances
Kimberly Le Truong, Annette Zimmermann, Hoda Heidari
https://arxiv.org/abs/2507.04641

Toward Valid Measurement Of (Un)fairness For Generative AI: A Proposal For Systematization Through The Lens Of Fair Equality of Chances
Disparities in the societal harms and impacts of Generative AI (GenAI) systems highlight the critical need for effective unfairness measurement approaches. While numerous benchmarks exist, designing valid measurements requires proper systematization of the unfairness construct. Yet this process is often neglected, resulting in metrics that may mischaracterize unfairness by overlooking contextual nuances, thereby compromising the validity of the resulting measurements. Building on established (u…

Effective Equation of State Oscillations at Matter-Radiation Equality and Primordial Gravitational Waves
S. D. Odintsov, V. K. Oikonomou
https://arxiv.org/abs/2507.04571

Effective Equation of State Oscillations at Matter-Radiation Equality and Primordial Gravitational Waves
The theory controlling the Universe's evolution in the classical regime has to be motivated by particle physics reasoning and should also generate inflation and dark energy eras in a unified way. One such framework is $F(R)$ gravity. In this work we examine a class of exponential deformations of $R^2$ gravity motivated by fundamental physics of scalaron evolution in a de Sitter background. As we show this class of models describe both inflation and the dark energy era in a viable way compatible…

A Note on Categorical Entropy of Bielliptic Surfaces and Enriques Surfaces
Tomoki Yoshida
https://arxiv.org/abs/2507.03890 https://ar…

A Note on Categorical Entropy of Bielliptic Surfaces and Enriques Surfaces
In this note, we show that there exists an autoequivalence of positive categorical entropy on the derived category of certain bielliptic surfaces. This gives the first example of a surface admitting positive categorical entropy in the absence of both positive topological entropy and any spherical objects. Moreover, we prove a Gromov-Yomdin type equality for the categorical entropy of autoequivalences on bielliptic surfaces and give a counterexample of this equality on Enriques surfaces.

Cyclic Equalizability of Words and Its Application to Card-Based Cryptography
Kazumasa Shinagawa, Koji Nuida
https://arxiv.org/abs/2507.04916 https://

Cyclic Equalizability of Words and Its Application to Card-Based Cryptography
Card-based cryptography is a research area to implement cryptographic procedures using a deck of physical cards. In recent years, it has been found to be related to finite group theory and algebraic combinatorics, and is becoming more and more closely connected to the field of mathematics. In this paper, we discuss the relationship between card-based cryptography and combinatorics on words for the first time. In particular, we focus on cyclic equality of words. We say that a set of words are cy…

ASPEN: An Additional Sampling Penalty Method for Finite-Sum Optimization Problems with Nonlinear Equality Constraints
Nata\v{s}a Kreji\'c, Nata\v{s}a Krklec Jerinki\'c, Tijana Ostoji\'c, Nemanja Vu\v{c}i\'cevi\'c
https://arxiv.org/abs/2508.02299

ASPEN: An Additional Sampling Penalty Method for Finite-Sum Optimization Problems with Nonlinear Equality Constraints
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework of quadratic penalty methods. Thus, depending on the problem at hand, the resulting method may exhibit a sample size strategy ranging from a mini-batch on one end, to increasing sample size that achieves the full sample eventually, on the other end of the spec…

Welcome all Americans who wish to join a moral movement in defense of: 
Freedom, Equality, Justice and
The Constitution
https://www.thesaveamericamovement.org/

The Save America Movement
We welcome all Americans who wish to join a moral movement in defense of freedom, equality, justice and the Constitution.

Oregon, Oregon Health Plan (OHP)
Pennsylvania, Medical Assistance
Rhode Island, RI Medical Assistance Program
South Carolina, Healthy Connections
South Dakota, Medicaid
Tennessee, TennCare
Texas, STAR PLUS
Utah, Medicaid
Vermont, Green Mountain Care
Virginia, Cardinal Care
Washington, Apple Health
West Virginia, Medicaid
Wisconsin, Forward Health, BadgerCare
Wyoming, Equality Care

This https://arxiv.org/abs/2407.08829 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Certain Extremal Banach-Mazur Distances and Ader's Characterization of Distance Ellipsoids
A classical consequence of the John Ellipsoid Theorem is the upper bound $\sqrt{n}$ on the Banach-Mazur distance between the Euclidean ball and any symmetric convex body in $\mathbb{R}^n$. Equality is attained for the parallelotope and the cross-polytope. While it is known that they are unique with this property for $n=2$ but not for $n \geq 4$, no proof of the characterization of the three-dimensional equality case seems to have ever been published. We fill this gap by showing that the paralle…

According to @…'s newsletter this morning, the Citizen's Advice Bureau is now requiring #Trans employees (? and clients?) to use toilets according to their gender assigned at birth, which, if true, is not a good look at all. Journalist is Steph Paton, who I sli…

Scots charity in trans rights row after announcing change to bathroom access
A Scottish charity may be discriminating against transgender staff after announcing a change to bathroom access following the recent UK Supreme Court ruling on the Equality Act, say legal experts.

"It’s a set of impudent and improbable goals: the rule of law and equality before it, liberty, freedom of speech and conscience, decency. We have always fallen short of them and always will, but we wrote them down and decided to dedicate ourselves to pursuing them. That’s worth something."
The Fourth Of July, Rethought
https://www.popehat.com/p/the-fourth-of-july-rethought

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 $n$.…

HEC: Equivalence Verification Checking for Code Transformation via Equality Saturation
Jiaqi Yin, Zhan Song, Nicolas Bohm Agostini, Antonino Tumeo, Cunxi Yu
https://arxiv.org/abs/2506.02290

HEC: Equivalence Verification Checking for Code Transformation via Equality Saturation
In modern computing systems, compilation employs numerous optimization techniques to enhance code performance. Source-to-source code transformations, which include control flow and datapath transformations, have been widely used in High-Level Synthesis (HLS) and compiler optimization. While researchers actively investigate methods to improve performance with source-to-source code transformations, they often overlook the significance of verifying their correctness. Current tools cannot provide…

A universal relation among Euclidean integrals for black holes in higher-derivative gravity theories
Yong Xiao, Qiang Wang, Aonan Zhang
https://arxiv.org/abs/2508.05326 https://…

A universal relation among Euclidean integrals for black holes in higher-derivative gravity theories
In this paper, we establish a universal equality governing Euclidean integrals of gravitational actions in higher-derivative theories. This relation is shown to hold universally for asymptotically flat black holes in pure gravity, and is generalized to asymptotically anti-de Sitter (AdS) spacetimes through appropriate regularization. We further examine its validity in systems with matter-gravity coupling, identifying that violations occur only when matter fields exhibit pathological behaviors: …

Tomorrow's my first day at the new job and looks like all my bosses identify as women, which I guess would be good when you have femdom fantasies but it's absolutely great when you have equality ones.

Last week's Supreme Court rulings show just how fragile marriage equality may be - LGBTQ Nation
https://www.lgbtqnation.com/2025/06/last-weeks-supreme-court-rulings-show-just-how-fragile-marriage-equality-may-be/

Donald Trump is charging us into a “controlled disintegration” of everything that made America the envy of the world—that includes any appeal to equality under the law, rules-based order, and evidence-based science and economics.
Original post: https://bsky.app/profile/did:plc:yobyq

Reading in a Swedish paper about the harassment of trans migrants by *other migrants* from the same countries.
"It's important they understand that behaviour that was accepted or normalised in their old countries is not allowed in Sweden."
No one is forcing migrants to shop at IKEA or eat smorgasbord. But those who come from patriarchal religious countries have to accept that Sweden has a long tradition of human rights and sexual equality.
Too much to ask in r…

Towards Relational Contextual Equality Saturation
Tyler Hou, Shadaj Laddad, Joseph M. Hellerstein
https://arxiv.org/abs/2507.11897 https://

Towards Relational Contextual Equality Saturation
Equality saturation is a powerful technique for program optimization. Contextual equality saturation extends this to support rewrite rules that are conditioned on where a term appears in an expression. Existing work has brought contextual reasoning to egg; in this paper, we share our ongoing work to extend this to relational equality saturation in egglog. We summarize the existing approaches to contextual equality saturation, outline its main applications, and identify key challenges in combini…

Tumblr is shit, and the Fediverse is equality shit because it doesn’t have much genderfluid material unlike Tumblr!
I'm not leaving the Fediverse, just looking for gender-fluid material, and Tumblr has me served for years.
I’ll crosspost to Mastodon.
https://www.tumblr.com/midtsveen

Another donation made to The Good Law Project. Honestly, they have already made some great progress on defending my safety in relation to the Equality Act and EHRC, its money well spent.
Can you join me?
https://goodlawproject.org/donate/

Support us | Good Law Project
We can only keep fighting thanks to individual donations. Our people-powered model keeps us fiercely independent, so we can hold power to account.  

"During his time at IBM, he wrote some of the first artificial intelligence software—his "geometry theorem machine" was the first advanced AI program, and the third AI program ever. It is a logical AI system that can prove theorems in planar geometry about parallel lines, congruence, and equality and inequality of segments and angles. Like Logic Theorist, it uses heuristics."

This https://arxiv.org/abs/2406.10189 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Topological rigidity of small RCD(K,N) spaces with maximal rank
For a polycyclic group $Λ$, $\text{rank} ( Λ)$ is defined as the number of $\mathbb{Z}$ factors in a polycyclic decomposition of $Λ$. For a finitely generated group $G$, $\text{rank} (G)$ is defined as the infimum of $ \text{rank} (Λ)$ among finite index polycyclic subgroups $Λ\leq G$. For a compact $\text{RCD} (K,N)$ space $(X,\mathsf{d}, \mathfrak{m})$ with $\text{diam} (X) \leq \varepsilon (K,N)$, the rank of $π_1(X)$ is at most $N$. We show that in case of equality, $X$ is homeomorphi…

This https://arxiv.org/abs/2412.08118 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A remark on a generalized Suita conjecture for finite points case
In this article, we use a class of harmonic functions (maybe multi-valued) to study the equality part in a weighted version of Suita conjecture for higher derivatives and finite points case, and we obtain some sufficient and necessary conditions for the equality part to hold when the harmonic part $u$ of the weight is trivial.

Global Optimality in Multi-Flyby Asteroid Trajectory Optimization: Theory and Application Techniques
Zhong Zhang, Xiang Guo, Di Wu, Hexi Baoyin, Junfeng Li, Francesco Topputo
https://arxiv.org/abs/2508.02904

Global Optimality in Multi-Flyby Asteroid Trajectory Optimization: Theory and Application Techniques
Designing optimal trajectories for multi-flyby asteroid missions is scientifically critical but technically challenging due to nonlinear dynamics, intermediate constraints, and numerous local optima. This paper establishes a method that approaches global optimality for multi-flyby trajectory optimization under a given sequence. The original optimal control problem with interior-point equality constraints is transformed into a multi-stage decision formulation. This reformulation enables direct a…

$L$-packets and the generic Arthur packet conjectures for even unitary similitude groups
Yeansu Kim, Muthu Krishnamurthy, Freydoon Shahidi
https://arxiv.org/abs/2506.00892

$L$-packets and the generic Arthur packet conjectures for even unitary similitude groups
We establish the generic local Langlands correspondence by showing the equality of the Langlands-Shahidi $L$-functions and Artin $L$-functions in the case of even unitary similitude groups. As an application, we prove both weak and strong versions of the generic Arthur packet conjectures in the cases of even unitary similitude groups and even unitary groups. We further describe (not necessarily generic) $L$-packets for even unitary similitude groups and establish their expected properties, incl…

We hold these truths to be self-evident: that all people are created equal, endowed with inherent dignity and unalienable rights—among these are life, liberty, equality, and the pursuit of justice.
 
That to secure these rights, governments derive their power from the consent of the governed. When a leader becomes destructive of these ends, it is the right and duty of the people to refuse allegiance and to stand united in the defense of their freedoms.

Fairly Wired: Towards Leximin-Optimal Division of Electricity
Eden Hartman, Dinesh Kumar Baghel, Erel Segal-Halevi
https://arxiv.org/abs/2506.02193 https:/…

Fairly Wired: Towards Leximin-Optimal Division of Electricity
In many parts of the world - particularly in developing countries - the demand for electricity exceeds the available supply. In such cases, it is impossible to provide electricity to all households simultaneously. This raises a fundamental question: how should electricity be allocated fairly? In this paper, we explore this question through the lens of egalitarianism - a principle that emphasizes equality by prioritizing the welfare of the worst-off households. One natural rule that aligns with …

Bochner-type theorems for distributional category
Ekansh Jauhari, John Oprea
https://arxiv.org/abs/2505.21763 https://arxiv.org/pdf/2…

Bochner-type theorems for distributional category
We show that in the presence of a geometric condition such as non-negative Ricci curvature, the distributional category of a manifold may be used to bound invariants, such as the first Betti number and macroscopic dimension, from above. Moreover, à la Bochner, when the bound is an equality, special constraints are imposed on the manifold. We show that the distributional category of a space also bounds the rank of the Gottlieb group, with equality imposing constraints on the fundamental group. …

This https://arxiv.org/abs/2505.18811 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An Anarchist Approach to the Undergraduate Mathematics Curriculum
Contemporary anarchism centers around three tenets: (1) a constant challenge of and resistance to all forms of domination, (2) so-called "prefigurative politics", in which all decisions are made in a manner that is consistent with a set of non-hierarchical values such as equality, decentralization and voluntary cooperation, (3) a focus on diversity and open-endedness (Gordon, 2008). Within this philosophy the notion of end goals becomes moot; progress, then, is measured by process, in which the…

A geometric model for the non-$\tau$-rigid modules of type $\widetilde{D}_n$
Blake Jackson
https://arxiv.org/abs/2507.02218 https://a…

A geometric model for the non-$τ$-rigid modules of type $\widetilde{D}_n$
We give a geometric model for the non-$τ$-rigid modules over acyclic path algebras of type $\widetilde{D}_n$. Similar models have been provided for module categories over path algebras of types $A_n, D_n,$ and $\widetilde{A}_n$ as well as the $τ$-rigid modules of type $\widetilde{D}_n$. A major draw of these geometric models is the "intersection-dimension formulas" they often come with. These formulas give an equality between the intersection number of the curves representing the modules in t…

Equality is Far Weaker than Constant-Cost Communication
Mika G\"o\"os, Nathaniel Harms, Artur Riazanov
https://arxiv.org/abs/2507.11162 https://

Equality is Far Weaker than Constant-Cost Communication
We exhibit an $n$-bit communication problem with a constant-cost randomized protocol but which requires $n^{Ω(1)}$ deterministic (or even non-deterministic) queries to an Equality oracle. Therefore, even constant-cost randomized protocols cannot be efficiently "derandomized" using Equality oracles. This improves on several recent results and answers a question from the survey of Hatami and Hatami (SIGACT News 2024). It also gives a significantly simpler and quantitatively superior proof of the…

As Israel announces 22 new West Bank colonies:
RT:
Apartheid South Africa was destroyed.
That didn't mean that white South Africans were massacred or expelled.
Likewise, Apartheid Israel will end. Not with 2 States (an Apartheid State and a Bantustan), but with one, plurinational State, based on equality and reparations, from the river to the sea.
It's a big ask, a hard to realise dream, but no less realistic than the fantastical non-solutions that dominate m…

Integer inequalities between knot invariants, skein tree depth and delta-crossing numbers
Michal Jablonowski
https://arxiv.org/abs/2506.00937 https://

Integer inequalities between knot invariants, skein tree depth and delta-crossing numbers
This survey collects known (and one new) inequalities between integer-valued classical knot invariants. It features: a visual graph of the relations; proof of the new inequality relating skein tree depth and delta-crossing numbers; and examples where the inequality becomes equality.

Bo Burnham once said:
“Why do you rich fucking white people Insist on seeing every socio-political conflict through the myopic lens of your own self-actualization? This isn't about you. So either get with it, or get out of the fucking way”

This https://arxiv.org/abs/2209.03243 has been replaced.
link: https://scholar.google.com/scholar?q=a

Adapted Wasserstein distance between the laws of SDEs
We consider the bicausal optimal transport problem between the laws of scalar time-homogeneous stochastic differential equations, and we establish the optimality of the synchronous coupling between these laws. The proof of this result is based on time-discretisation and reveals a novel connection between the synchronous coupling and the celebrated discrete-time Knothe--Rosenblatt rearrangement. We also prove a result on equality of topologies restricted to a certain subset of laws of continuous…

Solution Methods and Perturbation Analysis for the Equality-Constrained Total Least Squares Problem over Reduced Biquaternions
Neha Bhadala
https://arxiv.org/abs/2506.18319

Solution Methods and Perturbation Analysis for the Equality-Constrained Total Least Squares Problem over Reduced Biquaternions
This paper proposes a theoretical framework to address the reduced biquaternion equality-constrained total least squares (RBTLSE) problem. The objective is to find an approximate solution to the system $AX \approx B$, subject to linear constraints $CX = D$, while explicitly accounting for errors in both the coefficient matrix $A$ and the observation matrix $B$. We establish conditions under which real and complex solutions exist and develop corresponding solution methods using real and complex …

IAE Optimized PID Tuning with Phase Margin and Crossover Frequency Constraints
Senol Gulgonul
https://arxiv.org/abs/2506.00923 https://

IAE Optimized PID Tuning with Phase Margin and Crossover Frequency Constraints
This paper presents PMwc-Tune, a novel PID tuning method that uniquely combines frequency-domain robustness constraints with time-domain performance optimization through constrained nonlinear programming. The key contribution is a unified formulation that simultaneously enforces phase margin and crossover frequency requirements (via nonlinear equality constraints) while minimizing the Integral Absolute Error (IAE) of the closed-loop response. The algorithm employs Sequential Quadratic Programmi…

This https://arxiv.org/abs/2407.17708 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The index of lattice Dirac operators and $K$-theory
We mathematically show an equality between the index of a Dirac operator on a flat continuum torus and the $η$ invariant of a lattice Dirac operator known as the Wilson Dirac operator with a negative mass when the lattice spacing is sufficiently small. Unlike the standard approach, our formulation using $K$-theory does not require modified chiral symmetry on the lattice. We prove that a one-parameter family of continuum massive Dirac operators and the corresponding Wilson Dirac operators belon…

PRIDE -- Parameter-Efficient Reduction of Identity Discrimination for Equality in LLMs
Maluna Menke, Thilo Hagendorff
https://arxiv.org/abs/2507.13743 http…

PRIDE -- Parameter-Efficient Reduction of Identity Discrimination for Equality in LLMs
Large Language Models (LLMs) frequently reproduce the gender- and sexual-identity prejudices embedded in their training corpora, leading to outputs that marginalize LGBTQIA+ users. Hence, reducing such biases is of great importance. To achieve this, we evaluate two parameter-efficient fine-tuning (PEFT) techniques - Low-Rank Adaptation (LoRA) and soft-prompt tuning - as lightweight alternatives to full-model fine-tuning for mitigating such biases. Using the WinoQueer benchmark, we quantify bias…

An equality for balanced digraphs
Darij Grinberg, Benjamin Liber
https://arxiv.org/abs/2507.22388 https://arxiv.org/pdf/2507.22388

An equality for balanced digraphs
Consider a directed multigraph $D$ that is balanced (i.e., at each vertex, the indegree equals the outdegree). Let $A$ be its set of arcs. Fix an integer $k$. Let $s$ be a vertex of $D$. We show that the number of $k$-element subsets $B$ of $A$ that contain no cycles but contain a path from each vertex to $s$ (we call them "$s$-convergences") is independent on $s$. This generalizes known facts about spanning arborescences, acyclic orientations and maximal acyclic subdigraphs (or, equivalently, …

The current holder of high office has shown himself to be unfit to lead a free and just society.
* He disrespects women, mocking survivors of violence and stripping away their rights.
* He fuels racism and white supremacy, scapegoating communities of color and denying their equality.
* He assaults free speech, attacking the press, punishing dissent, and spreading disinformation.

Multi-sample rank tests for location against Lehmann-type alternatives
Nikolay I. Nikolov, Eugenia Stoimenova
https://arxiv.org/abs/2506.01914 https://

Multi-sample rank tests for location against Lehmann-type alternatives
This paper deals with testing the equality of $k$ ($k\ge 2$) distribution functions against possible stochastic ordering among them. Two classes of rank tests are proposed for this testing problem. The statistics of the tests under study are based on precedence and exceedance statistics and are natural extension of corresponding statistics for the two-sample testing problem. Furthermore, as an extension of the Lehmann alternative for the two-sample location problem, we propose a new subclass of…

Term Ordering Diagrams
M\'arton Hajdu, Robin Coutelier, Laura Kov\'acs, Andrei Voronkov
https://arxiv.org/abs/2505.22181 https://

Term Ordering Diagrams
The superposition calculus for reasoning in first-order logic with equality relies on simplification orderings on terms. Modern saturation provers use the Knuth-Bendix order (KBO) and the lexicographic path order (LPO) for discovering redundant clauses and inferences. Implementing term orderings is however challenging. While KBO comparisons can be performed in linear time and LPO checks in quadratic time, using the best known algorithms for these orders is not enough. Indeed, our experiments sh…

from my link log —
Thoughts on hashing in Rust.
https://purplesyringa.moe/blog/thoughts-on-rust-hashing/
saved 2024-12-13

Thoughts on Rust hashing
In languages like Python, Java, or C++, values are hashed by calling a “hash me” method on them, implemented by the type author. This fixed-hash size is then immediately used by the hash table or what have you. This design suffers from some obvious problems, like: How do you hash an integer? If you use a no-op hasher (booo), DoS attacks on hash tables are inevitable. If you hash it thoroughly, consumers that only cache hashes to optimize equality checks lose out of performance.

Adjoint-Based Aerodynamic Shape Optimization with a Manifold Constraint Learned by Diffusion Models
Long Chen, Emre Oezkaya, Jan Rottmayer, Nicolas R. Gauger, Zebang Shen, Yinyu Ye
https://arxiv.org/abs/2507.23443

Adjoint-Based Aerodynamic Shape Optimization with a Manifold Constraint Learned by Diffusion Models
We introduce an adjoint-based aerodynamic shape optimization framework that integrates a diffusion model trained on existing designs to learn a smooth manifold of aerodynamically viable shapes. This manifold is enforced as an equality constraint to the shape optimization problem. Central to our method is the computation of adjoint gradients of the design objectives (e.g., drag and lift) with respect to the manifold space. These gradients are derived by first computing shape derivatives with res…

The strong log-concavity for first eigenfunction of the Ornstein-Uhlenbeck operator in the class of convex bodies
Lei Qin
https://arxiv.org/abs/2507.00819 …

The strong log-concavity for first eigenfunction of the Ornstein-Uhlenbeck operator in the class of convex bodies
In this paper, we prove that the first (positive) Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator \[ L(u)=Δu-(\nabla u,x), \] is strongly log-concave if the domain is bounded and convex, which improves the conclusion in [6]. We also provide a characterization of the equality case of the Brunn-Minkowski inequality for the principal frequency of $L(u)$ in the class of convex bodies.

Therefore, we, the people of conscience and conviction, do solemnly declare our independence from this tyrant and all he represents.
We withdraw our consent.
 
We refuse to be complicit in cruelty.
We reject the abuse of power for personal gain.
We stand for dignity, truth, equality, and justice for all people.

Non-archimedean topological mirror symmetry for $SL_n$ and $PGL_n$ Higgs bundles
Elsa Maneval
https://arxiv.org/abs/2507.02588 https://

Non-archimedean topological mirror symmetry for $SL_n$ and $PGL_n$ Higgs bundles
The Hausel-Thaddeus conjectures concern topological mirror symmetry between moduli spaces of $SL_n$ and $PGL_n$ Higgs bundles on a curve. A non-archimedean approach was introduced by Groechenig, Wyss and Ziegler, proving the conjecture for coprime rank and degree. This article is concerned with its generalisation to the non-coprime case. We treat both the classical ($D=K$) and meromorphic ($D>K$) settings. We prove an equality of $p$-adic volumes twisted by gerbes between moduli spaces of $SL_n…

Rudolf Rocker argued that true social liberation requires the abolition of all forms of political, economic, and social oppression, he maintained that even complete economic equality is meaningless without freedom, and that any system enforcing authority or coercion undermines genuine emancipation.
When I think about it, I strongly agree with this view, because real freedom can only exist where no one is subject to outside control, where each person has the space to shape their own lif…

Activities of Women in Physics Group in Spain 2022 to 2023
Pascuala Garcia-Martinez, Carmen Ocal, Ana Xesus Lopez, Mariam Tortola, Milagros F. Morcillo-Arencibia, Alberto Martin-Molina, Sonia Estrade
https://arxiv.org/abs/2506.18816

Activities of Women in Physics Group in Spain 2022 to 2023
In this paper, we present the main actions of the Women in Physics Group of the Spanish Royal Physics Society over the period of 2022 to 2023, in which we celebrated the 20th anniversary of the group. We also outline relevant equality initiatives implemented during this period by the Spanish Government as well as analyse their impact on the status of women in Physics in our country. In 2023, our scientific society approved the Gender Equality Plan, thus becoming a pioneer scientific society in …

Homological Invariants of Left and Right Serial Path Algebras
Ruoyu Guo
https://arxiv.org/abs/2506.02307 https://arxiv.org/pdf/2506.0…

Homological Invariants of Left and Right Serial Path Algebras
We investigate the relationship between the delooping level (dell) and the finitistic dimension of left and right serial path algebras. These 2-syzygy finite algebras have finite delooping level, and it can be calculated with an easy and finite algorithm. When the algebra is right serial, its right finitistic dimension is equal to its left delooping level. When the algebra is left serial, the above equality only holds under certain conditions. We provide examples to demonstrate this and include…

Hamburg police have understood what “defensive #democracy” means:
“Does flying the 🏳️‍🌈 flag violate the neutrality requirement? No! Our neutrality means political impartiality – but not neutrality in value. The flag represents values like diversity, tolerance & equality of rights, which are deeply embedded in our constitution.
Positioning ourselves against hate & discrimi…

Andreas Froese (@Andreas_Froese@mastodon.social)
Attached: 1 image Im Bundestag geht die Polizei auf Anordnung der Präsidentin und der Verwaltung gegen die #Regenbogenfahne vor. Die Hamburger Polizei hat dagegen dieses stabile Statement offiziell veröffentlicht. Klare Worte zur #Neutralität mit einer klaren #Haltung! #LGBTQIA+ #Regenbogenflagge #Queer

On a spherically lifted spin model at finite temperature
Xun Tang, Yuehaw Khoo, Lexing Ying
https://arxiv.org/abs/2506.02220 https://…

On a spherically lifted spin model at finite temperature
We investigate an \(n\)-vector model over \(k\) sites with generic pairwise interactions and spherical constraints. The model is a lifting of the Ising model whereby the support of the spin is lifted to a hypersphere. We show that the \(n\)-vector model converges to a limiting distribution at a rate of \(n^{-1/2 + o(1)}\). We show that the limiting distribution for \(n \to \infty\) is determined by the solution of an equality-constrained maximization task over positive definite matrices. We pro…

Marriage Equality Pioneer Stan Baker Dies At Age 79 - Joe.My.God.
https://www.joemygod.com/2025/06/marriage-equality-pioneer-stan-baker-dies-at-age-79/

Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality
Karoly J. Boroczky, Ferenc Fodor, Pavlos Kalantzopoulos
https://arxiv.org/abs/2507.13462

Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality
We use the characterization of the case of equality in Barthe's Geometric Reverse Brascamp-Lieb inequality in order to characterize equality in Liakopoulos's volume estimate in terms of sections by certain lower-dimensional linear subspaces.

I once embraced the Zionist dream. Now I’m protesting the genocide in Gaza on the streets of Toronto
https://www.thestar.com/opinion/contributors/i-once-e…

A study on preservation of parallel pairs and triangle equality attainment pairs
Jayanta Manna, Kalidas Mandal, Kallol Paul, Debmalya Sain
https://arxiv.org/abs/2507.07774

A study on preservation of parallel pairs and triangle equality attainment pairs
This paper investigates the structure and preservation of parallel pairs and triangle equality attainment (TEA) pairs in normed linear spaces. We begin by providing functional characterizations of these pairs in normed linear spaces and provide a characterization of finite-dimensional Banach spaces with numerical index one. We then study parallel pairs and TEA pairs in the $p$-direct sum of normed linear spaces. Next, we show that in finite-dimensional Banach spaces, a bijective bounded linear …

«What “win the center” pragmatists would have us believe is that the shock of the Missouri ladies over the shabby treatment of one of their “good ‘uns” means that they share our common value of universal human equality, even though there is scant evidence that this value is shared. This seems to be standard rhetorical practice when one is a pragmatic “win the center” type.»
Applies to all places where parties try to beat the fascists by moving towards the right
https://www.the-reframe.com/winning-the-middle/

This https://arxiv.org/abs/2505.06750 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

LPrL: An Asynchronous Linear Time Hyper Logic
We present a novel asynchronous hyper linear time temporal logic named LPrL (Linear Time Predicate Logic) and establish its basic theory. LPrL is a natural first order extension of LTL (Linear time temporal logic), in which the predicates specify the properties of and the relationships between traces (infinite sequences of actions) using Boolean combinations of LTL formulas. To augment the expressive power of the logic, we introduce a simple language of terms and add the equality predicate t = …

On the asymptotic behavior of a higher-order extrapolation primal-dual interior-point method for nonlinear programming
Pim Heeman, Anders Forsgren
https://arxiv.org/abs/2507.01866

On the asymptotic behavior of a higher-order extrapolation primal-dual interior-point method for nonlinear programming
A trajectory-following primal--dual interior-point method solves nonlinear optimization problems with inequality and equality constraints by approximately finding points satisfying perturbed Karush--Kuhn--Tucker optimality conditions for a decreasing order of perturbation controlled by the barrier parameter. Under some conditions, there is a unique local correspondence between small residuals of the optimality conditions and points yielding that residual, and the solution on the barrier traject…

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints
Ashfaq Iftakher, Rahul Golder, M. M. Faruque Hasan
https://arxiv.org/abs/2507.08124 https://arxiv.org/pdf/2507.08124 https://arxiv.org/html/2507.08124
arXiv:2507.08124v1 Announce Type: new
Abstract: Traditional physics-informed neural networks (PINNs) do not guarantee strict constraint satisfaction. This is problematic in engineering systems where minor violations of governing laws can significantly degrade the reliability and consistency of model predictions. In this work, we develop KKT-Hardnet, a PINN architecture that enforces both linear and nonlinear equality and inequality constraints up to machine precision. It leverages a projection onto the feasible region through solving Karush-Kuhn-Tucker (KKT) conditions of a distance minimization problem. Furthermore, we reformulate the nonlinear KKT conditions using log-exponential transformation to construct a general sparse system with only linear and exponential terms, thereby making the projection differentiable. We apply KKT-Hardnet on both test problems and a real-world chemical process simulation. Compared to multilayer perceptrons and PINNs, KKT-Hardnet achieves higher accuracy and strict constraint satisfaction. This approach allows the integration of domain knowledge into machine learning towards reliable hybrid modeling of complex systems.
toXiv_bot_toot

On lower bounds for the F-pure threshold of equigenerated ideals
Benjamin Baily
https://arxiv.org/abs/2506.18891 https://arxiv.org/pd…

On lower bounds for the F-pure threshold of equigenerated ideals
Let $k$ be a field of characteristic $p > 0$ and $R = k[x_0,\dots, x_n]$. We consider ideals $I\subseteq R$ generated by homogeneous polynomials of degree $d$. Takagi and Watanabe proved that $\mathrm{fpt}(I)\geq \mathrm{height}(I)/d$; we classify ideals $I$ for which equality is attained. Additionally, we describe a new relationship between $\mathrm{fpt}(I)$ and $\mathrm{fpt}(I|_H)$, where $H$ is a general hyperplane through the origin. As an application, for degree-$d$ homogeneous polyno…

Die pakistanische Frauen- und Kinderrechtsaktivistin Malala Yousafzai wird 28 Jahre.
Sie gründete jüngst eine Investitionsplattform, die sich auf Frauensport konzentriert.
https://edition.cnn.com/2025/06/24/spo

Malala turns her fight for equality to women in sports
Malala Yousafzai is known by millions around the world as an activist and human rights campaigner, a voice of power and inspiration who survived an assassination attempt by the Taliban at age 15. Perhaps less well known is her life as a sports fanatic.

Kalai's flag conjecture for locally anti-blocking polytopes
Arnon Chor
https://arxiv.org/abs/2507.22284 https://arxiv.org/pdf/2507.22284

Kalai's flag conjecture for locally anti-blocking polytopes
We prove Kalai's full flag conjecture for the class of locally anti-blocking polytopes, and show that there is equality if and only if the polytope is a (generalized) Hanner polytope.

Fokker-Planck Score Learning: Efficient Free-Energy Estimation under Periodic Boundary Conditions
Daniel Nagel, Tristan Bereau
https://arxiv.org/abs/2506.15653

Fokker-Planck Score Learning: Efficient Free-Energy Estimation under Periodic Boundary Conditions
Accurate free-energy estimation is essential in molecular simulation, yet the periodic boundary conditions (PBC) commonly used in computer simulations have rarely been explicitly exploited. Equilibrium methods such as umbrella sampling, metadynamics, and adaptive biasing force require extensive sampling, while non-equilibrium pulling with Jarzynski's equality suffers from poor convergence due to exponential averaging. Here, we introduce a physics-informed, score-based diffusion framework: by ma…

Maximum number of zeroes of polynomials on weighted projective spaces over a finite field
Jade Nardi, Rodrigo San-Jos\'e
https://arxiv.org/abs/2507.22597 https://

Maximum number of zeroes of polynomials on weighted projective spaces over a finite field
We compute the maximum number of rational points at which a homogeneous polynomial can vanish on a weighted projective space over a finite field, provided that the first weight is equal to one. This solves a conjecture by Aubry, Castryck, Ghorpade, Lachaud, O'Sullivan and Ram, which stated that a Serre-like bound holds with equality for weighted projective spaces when the first weight is one, and when considering polynomials whose degree is divisible by the least common multiple of the weights.…

Replaced article(s) found for econ.EM. https://arxiv.org/list/econ.EM/new
[1/1]:
- biastest: Testing parameter equality across different models in Stata
Hasraddin Guliyev

Can a multi-tracer approach improve the constraints on the turnover scale?
Yan Lai, Cullan Howlett, Tamara Davis
https://arxiv.org/abs/2507.11823 https://

Can a multi-tracer approach improve the constraints on the turnover scale?
The turnover scale of the power spectrum is related to the size of the particle horizon at the matter-radiation equality, which can be used as a standard ruler to constrain cosmological parameters. In this work, we apply a model-independent method to mock datasets to forecast constraints on the turnover scale below a redshift of 0.5, investigating for the first time with a multi-tracer approach. We find that combining the galaxy density with peculiar velocity does not improve the turnover scale…

Sharp lower bounds for the first eigenvalue of Steklov-type eigenvalue problems on a compact surface
Gunhee Cho, Keomkyo Seo
https://arxiv.org/abs/2506.21376

Sharp lower bounds for the first eigenvalue of Steklov-type eigenvalue problems on a compact surface
Let $Ω$ be a compact surface with smooth boundary and the geodesic curvature $k_g \ge {c > 0}$ along $\partial Ω$ for some constant $c \in \mathbb{R}$. We prove that, if the Gaussian curvature satisfies $K \ge -α$ for a constant $α\ge 0$, then the first eigenvalue $σ_1$ of the Steklov-type eigenvalue problem satisfies \[ σ_1 + \fracα{σ_1} \ge c. \] Moreover, equality holds if and only if $Ω$ is a Euclidean disk of radius $\frac{1}{c}$ and $α= 0$. Furthermore, we obtain a sharp lower b…

This https://arxiv.org/abs/2503.13678 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

EGGs are adhesive!
The use of rewriting-based visual formalisms is on the rise. In the formal methods community, this is due also to the introduction of adhesive categories, where most properties of classical approaches to graph transformation, such as those on parallelism and confluence, can be rephrased and proved in a general and uniform way.E-graphs (EGGs) are a formalism for program optimisation via an efficient implementation of equality saturation. In short, EGGs can be defined as (acyclic) term graphs wit…

Homeownership as Life Cycle Goldmine: Evidence from Macrohistory
Yang Bai, Shize Li, Jialu Shen
https://arxiv.org/abs/2507.17624 https://arxiv.org/pdf/2507…

Homeownership as Life Cycle Goldmine: Evidence from Macrohistory
Should a household buy a home? Using data from 16 developed countries spanning 1870 to 2020, this study provides a resounding affirmative answer. Contrary to popular expert advice, homeownership enhances life cycle wealth by up to 9% and welfare by up to 23%, compared to all-equity investment strategy. Homeownership reduces wealth portfolio risk and improves wealth equality, though it comes at the cost of lower working-life wealth and curtailed financial asset holdings. Gains are heterogeneous:…

MDR-DeePC: Model-Inspired Distributionally Robust Data-Enabled Predictive Control
Shihao Li, Jiachen Li, Christopher Martin, Soovadeep Bakshi, Dongmei Chen
https://arxiv.org/abs/2506.19744

MDR-DeePC: Model-Inspired Distributionally Robust Data-Enabled Predictive Control
This paper presents a Model-Inspired Distributionally Robust Data-enabled Predictive Control (MDR-DeePC) framework for systems with partially known and uncertain dynamics. The proposed method integrates model-based equality constraints for known dynamics with a Hankel matrix-based representation of unknown dynamics. A distributionally robust optimization problem is formulated to account for parametric uncertainty and stochastic disturbances. Simulation results on a triple-mass-spring-damper sys…

An Anarchist Approach to the Undergraduate Mathematics Curriculum
Asia Matthews, Vincent Bouchard
https://arxiv.org/abs/2505.18811 https://

An Anarchist Approach to the Undergraduate Mathematics Curriculum
Contemporary anarchism centers around three tenets: (1) a constant challenge of and resistance to all forms of domination, (2) so-called "prefigurative politics", in which all decisions are made in a manner that is consistent with a set of non-hierarchical values such as equality, decentralization and voluntary cooperation, (3) a focus on diversity and open-endedness (Gordon, 2008). Within this philosophy the notion of end goals becomes moot; progress, then, is measured by process, in which the…

Polynomial-Time Algorithms for Black-Box Distributive Expanded Groups
Mikhail Anokhin
https://arxiv.org/abs/2505.20497 https://arxiv.…

Polynomial-Time Algorithms for Black-Box Distributive Expanded Groups
Let $Ω$ be a finite set of finitary operation symbols. An $Ω$-expanded group is a group (written additively and called the additive group of the $Ω$-expanded group) with an $Ω$-algebra structure. We use the black-box model of computation in $Ω$-expanded groups. In this model, elements of a finite $Ω$-expanded group $H$ are represented (not necessarily uniquely) by bit strings of the same length, say, $n$. Given representations of elements of $H$, equality testing and the fundamental opera…

Symmetrization of measures and the one-dimensional Poisson equation with Dirichlet boundary conditions
Christos Papadimitriou
https://arxiv.org/abs/2506.13311

Symmetrization of measures and the one-dimensional Poisson equation with Dirichlet boundary conditions
Let \(μ\) be a finite Borel measure on \((-π,π)\). Consider the one-dimensional Poisson equation \(-u''=μ\), where equality holds in the sense of distributions, with Dirichlet boundary conditions \(u(\pmπ)=0\). In this paper, we define measures that are transformations of \(μ\), we compare the convex integral means of the original solutions \(u_μ\) and the transformed ones, and we prove the uniqueness of a solution that maximizes the convex integral means.

I love communism because of its vision of a society based on equality, solidarity, and the abolition of class and state oppression. The idea of real communism, as envisioned by thinkers like Peter Kropotkin and Karl Marx, inspires me deeply. It’s a world where people freely associate, manage their own workplaces, and share resources according to need. This ideal has never truly been realized in history, which makes it all the more important to keep striving for it.
At the same time, I …

A derivative-free regularization algorithm for equality constrained nonlinear least squares problems
Xi Chen, Jinyan Fan
https://arxiv.org/abs/2507.05623 h…

A derivative-free regularization algorithm for equality constrained nonlinear least squares problems
In this paper, we study the equality constrained nonlinear least squares problem, where the Jacobian matrices of the objective function and constraints are unavailable or expensive to compute. We approximate the Jacobian matrices via orthogonal spherical smoothing and propose a derivative-free regularization algorithm for solving the problem. At each iteration, a regularized augmented Lagrangian subproblem is solved to obtain a Newton-like step. If a sufficient decrease in the merit function of…

Methodological considerations for semialgebraic hypothesis testing with incomplete U-statistics
David Barnhill, Marina Garrote-L\'opez, Elizabeth Gross, Max Hill, Bryson Kagy, John A. Rhodes, Joy Z. Zhang
https://arxiv.org/abs/2507.13531

Methodological considerations for semialgebraic hypothesis testing with incomplete U-statistics
Recently, Sturma, Drton, and Leung proposed a general-purpose stochastic method for hypothesis testing in models defined by polynomial equality and inequality constraints. Notably, the method remains theoretically valid even near irregular points, such as singularities and boundaries, where traditional testing approaches often break down. In this paper, we evaluate its practical performance on a collection of biologically motivated models from phylogenetics. While the method performs remarkably…

The second Hilbert coefficient of modules with almost maximal depth
Van Duc Trung
https://arxiv.org/abs/2506.17591 https://arxiv.org/…

The second Hilbert coefficient of modules with almost maximal depth
Let $\mathbb{M} = \{ M_n \}$ be a good $\mathfrak{q}$-filtration of a finitely generated $R$-module $M$ of dimension $d$, where $(R,\mathfrak{m})$ is a local ring and $\mathfrak{q}$ is an $\mathfrak{m}$-primary ideal of $R$. In case $depth(M) \geq d-1$, we give an upper bound for the second Hilbert coefficient $e_2(\mathbb{M})$ generalizing results by Huckaba-Marley and Rossi-Valla proved assuming that $M$ is Cohen-Macaulay. We also give a condition for the equality, which relates to the depth …

On Minkowski's monotonicity problem
Ramon van Handel, Shouda Wang
https://arxiv.org/abs/2507.20082 https://arxiv.org/pdf/2507.20082

On Minkowski's monotonicity problem
We address an old open question in convex geometry that dates back to the work of Minkowski: what are the equality cases of the monotonicity of mixed volumes? The problem is equivalent to that of providing a geometric characterization of the support of mixed area measures. A conjectural characterization was put forward by Schneider (1985), but has been verified to date only for special classes of convex bodies. In this paper we resolve one direction of Schneider's conjecture for arbitrary conve…

As Canada Day approaches, this story of a Mom finding her Canadian identity through helping Syrian refugees settle here after 2015 is poignant.
"In 2025, being a Canadian woman to me means looking out for our neighbours, leaning into differences in culture, religious practices and learning how to help others in need. Because we are not different at all. We are all just looking for safety and peace. It's our Canadian values of equality, respect and freedom in action.
It is the singular privilege of my life to walk alongside these families from Cape Breton and those who are newcomers to Canada. It's changed how I live, and I intend to do this work as long as I am able. I learn from them grace, service, faith and hope. They taught me how to be a Canadian.”
#Canada #CanPoli #CdnPoli #Refugees #Immigration #Syria #AlanKurdi
https://www.cbc.ca/news/canada/nova-scotia/first-person-cape-breton-welcomes-syrian-refugees-1.7559341

Eigenvalue bounds for distance-edge colorings
Aida Abiad, Luuk Reijnders
https://arxiv.org/abs/2506.20976 https://arxiv.org/pdf/2506.…

Eigenvalue bounds for distance-edge colorings
For a fixed positive integer $t$, we consider the graph colouring problem in which edges at distance at most $t$ are given distinct colours. We obtain sharp lower bounds for the distance-$t$ chromatic index, the least number of colours necessary for such a colouring. Our bounds are of algebraic nature; they depend on the eigenvalues of the line graph and on a polynomial which can be found using integer linear programming methods. We show several graph classes that attain equality for our bounds…

The U.S. Is Abandoning the Global Fight for LGBTQ Equality
https://foreignpolicy.com/2025/07/24/us-funding-cuts-state-department-rubio-trump-lgbtq-rights/

Green schoolyard investments influence local-level economic and equity outcomes through spatial-statistical modeling and geospatial analysis in urban contexts
Mahshid Gorjian
https://arxiv.org/abs/2507.14232

Green schoolyard investments influence local-level economic and equity outcomes through spatial-statistical modeling and geospatial analysis in urban contexts
Investing in urban green schoolyards is becoming more popular around the world because they could enhance health, education, and community outcomes. There is still considerable debate regarding the impact of urban green schoolyards on economic growth, equity, and community stability, particularly when analyzed using spatial-statistical and geospatial methods. The current study focuses mostly on health or individual case results and avoids looking at broader economic and equality concerns. It al…

Serrin-type problem in divergence form on Riemannian manifolds
M\'arcio Batista, M\'arcio Santos, Ant\^onio da Silva, Joyce Sindeaux
https://arxiv.org/abs/2507.17838 htt…

Serrin-type problem in divergence form on Riemannian manifolds
In this paper, we investigate an overdetermined boundary value problem of divergence type on bounded domains in Riemannian manifolds with non-negative Ricci curvature. Using integral identities and the $P$-function method, we derive geometric inequalities and rigidity results. Under natural conditions on the nonlinearity, we prove that equality implies the domain is isometric to a Euclidean ball, thereby extending classical symmetry results to the Riemannian setting.

On the volume of K-semistable Fano manifolds
Chi Li, Minghao Miao
https://arxiv.org/abs/2506.17420 https://arxiv.org/pdf/2506.17420…

On the volume of K-semistable Fano manifolds
We prove that the volume of an $n$-dimensional K-semistable Fano manifold that is not $\mathbb{P}^n$ is at most $2n^n$. Moreover, the equality holds only if $X\cong \mathbb{P}^1\times \mathbb{P}^{n-1}$ or $X$ is a smooth quadric hypersurface $Q\subset \mathbb{P}^{n+1}$. Our proof is based on a new connection between K-semistability and minimal rational curves. More generally, we show that the volume of a K-semistable Fano manifold with a minimal rational curve of degree $d$ is bounded above by …

From Graphical Lasso to Atomic Norms: High-Dimensional Pattern Recovery
Piotr Graczyk, Bartosz Ko{\l}odziejek, Hideto Nakashima, Maciej Wilczy\'nski
https://arxiv.org/abs/2506.13353

From Graphical Lasso to Atomic Norms: High-Dimensional Pattern Recovery
Estimating high-dimensional precision matrices is a fundamental problem in modern statistics, with the graphical lasso and its $\ell_1$-penalty being a standard approach for recovering sparsity patterns. However, many statistical models, e.g. colored graphical models, exhibit richer structures like symmetry or equality constraints, which the $\ell_1$-norm cannot adequately capture. This paper addresses the gap by extending the high-dimensional analysis of pattern recovery to a general class of …

On $t$-intersecting Families of Spanning Trees
Pitchayut Saengrungkongka
https://arxiv.org/abs/2507.18629 https://arxiv.org/pdf/2507.18629

On $t$-intersecting Families of Spanning Trees
We prove that there exists a constant $c>0$ such that for all integers $2\leq t\leq cn$, if $\calA$ is a collection of spanning trees in $K_n$ such that any two intersect at at least $t$ edges, then $|\calA|\leq 2^tn^{n-t-2}$. This bound is tight; the equality is achieved when $\calA$ is a collection of spanning trees containing a fixed $t$ disjoint edges. This is an improvement of a result by Frankl, Hurlbert, Ihringer, Kupavskii, Lindzey, Meagher, and Pantagi, who proved such a resu…

LISA -- A Modern Proof System
Simon Guilloud, Sankalp Gambhir, Viktor Kun\v{c}ak
https://arxiv.org/abs/2507.11167 https://arxiv.org/p…

LISA -- A Modern Proof System
We present LISA, a proof system and proof assistant for constructing proofs in schematic first-order logic and axiomatic set theory. The logical kernel of the system is a proof checker for first-order logic with equality and schematic predicate and function symbols. It implements polynomial-time proof checking and uses the axioms of ortholattices (which implies the irrelevance of the order of conjuncts and disjuncts and additional propositional laws). The kernel supports the notion of theorems …

An anticanonical perspective on G/P Schubert varieties
Changzheng Li, Konstanze Rietsch, Mingzhi Yang
https://arxiv.org/abs/2506.18388 https://

An anticanonical perspective on G/P Schubert varieties
We describe a natural basis of the Cartier class group of an arbitrary Schubert variety $X_{w,P}$ in a flag variety $G/P$ of general Lie type. We then characterise when the Schubert variety is factorial/Fano, along with an explicit formula for the anticanonical line bundle in these cases. We also prove that, for Schubert varieties in simply-laced types (only), being factorial is equivalent to being $Q$-factorial, and is equivalent to the equality of the Betti numbers $b_2(X_{w,P})=b_{2\ell(w)-2…

Definitions of the volume of a big cohomology class
Tiernan Cartwright
https://arxiv.org/abs/2506.09486 https://arxiv.org/pdf/2506.09…

Definitions of the volume of a big cohomology class
We elaborate on how two definitions of the volume of a big cohomology class are consistent. The first definition involves taking the absolutely continuous part of a closed positive current, and the second involves the non-pluripolar product. We also describe how a similar equality holds for the numerical restricted volume introduced by Collins and Tosatti.

Practically significant differences between conditional distribution functions
Holger Dette, Kathrin M\"ollenhoff, Dominik Wied
https://arxiv.org/abs/2506.06545

Practically significant differences between conditional distribution functions
In the framework of semiparametric distribution regression, we consider the problem of comparing the conditional distribution functions corresponding to two samples. In contrast to testing for exact equality, we are interested in the (null) hypothesis that the $L^2$ distance between the conditional distribution functions does not exceed a certain threshold in absolute value. The consideration of these hypotheses is motivated by the observation that in applications, it is rare, and perhaps impos…

Reilly inequality for Varifolds
Jean-Fran\c{c}ois Grosjean, Antoine Lemenant, R\'emy Mougenot
https://arxiv.org/abs/2507.08354 https://

Reilly inequality for Varifolds
The famous Reilly inequality gives an upper bound for the first eigenvalue of the Laplacian defined on compact submanifolds of the Euclidean space in terms of the $L^2$-norm of the mean curvature vector. In this paper, we generalize this inequality in a Varifold context. In particular we generalize it for the class of $H(2)$ varifolds and for polygons and we analyse the equality case.

On ideals of product of commutative rings and their applications
Mehdi Badie, Ali Rezaie Aliabad, Foad Obeidavi
https://arxiv.org/abs/2506.08537 https://…

On ideals of product of commutative rings and their applications
In this paper, leveraging the recent achievements of researchers, we have revisited the family of ideals of product of commutative rings. We demonstrate that if $ \{ R_α\}_{α\in A} $ is an infinite family of rings, then $ \left| Max \left( \prod_{α\in A} R_α\right) \right| \geqslant 2^{2^{|A|}} $. Notably, if these rings are local then the equality holds. We establish that $ Max(R_α) $ is homeomorphic to a closed subset of $ Max \left( \prod_{α\in A} R_α\right) $, for…

Spectral extremal problems for non-bipartite graphs without odd cycles
Lantao Zou, Lihua Feng, Yongtao Li
https://arxiv.org/abs/2507.11817 https://

Spectral extremal problems for non-bipartite graphs without odd cycles
A well-known result of Mantel asserts that every $n$-vertex triangle-free graph $G$ has at most $\lfloor n^2/4 \rfloor$ edges. Moreover, Erdős proved that if $G$ is further non-bipartite, then $e(G)\le \lfloor {(n-1)^2}/{4}\rfloor +1$. Recently, Lin, Ning and Wu [Combin. Probab. Comput. 30 (2021)] established a spectral version by showing that if $G$ is a triangle-free non-bipartite graph on $n$ vertices, then $λ(G)\le λ(S_1(T_{n-1,2}))$, with equality if and only if $G=S_1(T_{n-1,2})$, wher…

Invariants and equidecomposability in rings of polygons with sides of given directions
Gergely Kiss, Mikl\'os Laczkovich
https://arxiv.org/abs/2507.08608

Invariants and equidecomposability in rings of polygons with sides of given directions
We investigate equidecomposability in the ring of polygons with sides restricted to given directions and using only translations. Extending classical results of Dehn and Hadwiger, we prove that equidecomposability in these rings is equivalent to the equality of some invariants. We also consider the algebraic structure of direction sets. We show that under mild conditions, equidecomposability with respect to a set $S$ of slopes of the given directions is equivalent to equidecomposability with re…

Nestorv's Accelerated Proximal Gradient Method with Backtracking for Multiobjective Optimization
Chengzhi Huang
https://arxiv.org/abs/2507.06737 https:…

Nestorv's Accelerated Proximal Gradient Method with Backtracking for Multiobjective Optimization
In this paper, we propose a novel extrapolation coefficient scheme within the Nesterov framework and develop an accelerated proximal gradient algorithm. We establish that the algorithm achieves a sublinear convergence rate. The proposed scheme only requires the Lipschitz constant estimate sequence to satisfy mild initial conditions, under which a key equality property can be derived to support the convergence analysis. Numerical experiments are provided to demonstrate the effectiveness and prac…

Fenchel-Willmore inequality for submanifolds in manifolds with non-negative $k$-Ricci curvature
Meng Ji, Kwok-Kun Kwong
https://arxiv.org/abs/2507.07655 ht…

Fenchel-Willmore inequality for submanifolds in manifolds with non-negative $k$-Ricci curvature
We establish a sharp Fenchel-Willmore inequality for closed submanifolds of arbitrary dimension and codimension immersed in a complete Riemannian manifold with non-negative intermediate Ricci curvature and Euclidean volume growth. In the hypersurface case, this reduces to non-negative Ricci curvature. We also characterize the equality case. This generalizes the recent work of Agostiniani, Fogagnolo, and Mazzieri \cite{Agostiniani-Fogagnolo-Mazzieri}, as well as classical results by Chen, Fenche…

A Generalized $\ell_1$-Merit Function SQP Method Using Function Approximations with Tunable Accuracy
Dane S. Grundvig, Matthias Heinkenschloss
https://arxiv.org/abs/2507.06199

A Generalized $\ell_1$-Merit Function SQP Method Using Function Approximations with Tunable Accuracy
This paper develops a generalization of the line-search sequential quadratic programming (SQP) algorithm with $\ell_1$-merit function that uses objective and constraint function approximations with tunable accuracy to solve smooth equality-constrained optimization problems. The evaluation of objective and constraint functions and their gradients is potentially computationally expensive, but it is assumed that one can construct effective, computationally inexpensive models of these functions. Th…

Curvature inequalities for anti-invariant submersion from quaternionic space forms
Kirti Gupta, Punam Gupta, R. K. Gangele
https://arxiv.org/abs/2507.06259

Curvature inequalities for anti-invariant submersion from quaternionic space forms
This paper focuses on deriving several curvature inequalities involving the Ricci and scalar curvatures of the horizontal and vertical distributions in anti-invariant Riemannian submersions from quaternionic space forms onto Riemannian manifolds. In addition, a Ricci curvature inequality for anti-invariant Riemannian submersions is established. The equality cases for all derived inequalities are also examined.