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Homomorphism Calculus for User-Defined Aggregations
Ziteng Wang, Ruijie Fang, Linus Zheng, Dixin Tang, Isil Dillig
https://arxiv.org/abs/2508.15109 https://

Homomorphism Calculus for User-Defined Aggregations
Data processing frameworks like Apache Spark and Flink provide built-in support for user-defined aggregation functions (UDAFs), enabling the integration of domain-specific logic. However, for these frameworks to support \emph{efficient} UDAF execution, the function needs to satisfy a \emph{homomorphism property}, which ensures that partial results from independent computations can be merged correctly. Motivated by this problem, this paper introduces a novel \emph{homomorphism calculus} that can…

Regular homomorphisms and mixed motives
Ivan Hernandez, Pablo Pelaez
https://arxiv.org/abs/2509.15920 https://arxiv.org/pdf/2509.15920

Regular homomorphisms and mixed motives
Let $X$ be a smooth projective variety of dimension $d$ over an algebraically closed field $k$. The main goal of this paper is to study, in the context of Voevodsky's triangulated category of motives $DM_k$, the group $CH^n_{\mathrm{alg}}(X)$ of codimension $n$ algebraic cycles of $X$, algebraically equivalent to zero, modulo rational equivalence, $1\leq n \leq d$. Namely, for any regular homomorphism $ψ$ (in the sense of Samuel) defined on $CH^n_{\mathrm{alg}}(X)$, we construct $M^n_ψ(X)\in …

The sectional number of a group homomorphism
Cesar A. Ipanaque Zapata, Joe Palacios
https://arxiv.org/abs/2509.15407 https://arxiv.org/pdf/2509.15407

The sectional number of a group homomorphism
We explore the notion of sectional number of a group homomorphism, leading to a generalization of the covering number of a group, and present several characterizations when the sectional number is finite, providing estimates for computing this invariant.

Volumes of end-periodic mapping tori
Marissa Loving
https://arxiv.org/abs/2508.14244 https://arxiv.org/pdf/2508.14244…

Volumes of end-periodic mapping tori
In this expository paper, we provide an intuition and illustration-driven overview of two recent results that tie the dynamics of certain homeomorphisms of infinite-type surfaces, called end-periodic homeomorphisms, to the geometry of their associated (compactified) mapping tori. These results are analogues of a theorem of Brock in the finite-type setting for mapping tori of pseudo-Anosov homeomorphisms.

Constraint satisfaction problems, compactness and non-measurable sets
Claude Tardif
https://arxiv.org/abs/2508.14838 https://arxiv.org/pdf/2508.14838

Constraint satisfaction problems, compactness and non-measurable sets
A finite relational structure A is called compact if for any infinite relational structure B of the same type, the existence of a homomorphism from B to A is equivalent to the existence of homomorphisms from all finite substructures of B to A. We show that if A has width one, then the compactness of A can be proved in the axiom system of Zermelo and Fraenkel, but otherwise, the compactness of A implies the existence of non-measurable sets in 3-space.

Homeowner sees negative energy bill after leasing solar panels - a glimpse into the future of sustainable energy. #climatechange #climatesolutions #climate

Homeowner reveals massive negative energy bill after leasing solar panels: '[The] panels are producing way more than ... estimated'
One homeowner proved that you can get a negative energy bill with solar panels.

Privacy-Preserving Drone Navigation Through Homomorphic Encryption for Collision Avoidance
Allan Luedeman, Nicholas Baum, Andrew Quijano, Kemal Akkaya
https://arxiv.org/abs/2507.14713

Privacy-Preserving Drone Navigation Through Homomorphic Encryption for Collision Avoidance
As drones increasingly deliver packages in neighborhoods, concerns about collisions arise. One solution is to share flight paths within a specific zip code, but this compromises business privacy by revealing delivery routes. For example, it could disclose which stores send packages to certain addresses. To avoid exposing path information, we propose using homomorphic encryption-based comparison to compute path intersections. This allows drones to identify potential collisions without revealing …

Interessante Betrachtung: was wäre Eigentum - bei manchen Männern, die die Welt verbrennen, höher im Wert als Benzin oder unsere Verfassung - wert, wenn es nicht durch menschgemachte Klimakatastrophen bedroht wäre.
From: @…

Post by AJ Sadauskas, @aj@gts.sadauskas.id.au
New research shows the economic impact of increased flooding from global warming from fossil fuel pollution. Properties in Australia's flood-prone areas are worth $42 billion less than they would be if they weren't in a flood-prone area. https://www.sbs.com.au/news/article/homeowners-flood-4...

Reifenberg Theorem for Locally Finitely Almost Splitting Sets
Jiaqi Zang
https://arxiv.org/abs/2508.14805 https://arxiv.org/pdf/2508.14805

Reifenberg Theorem for Locally Finitely Almost Splitting Sets
The well-known Reifenberg theorem states that if a subset of $\mathbb{R}^n$ can be well approximated by $k$-planes at every point and every scale, then it is biHölder homeomorphic to a $k$-disk. This article concerns a subset $S$ of $\mathbb{R}^n$ which can be approximated by at most $N$ parallel $k$ planes at each point and scale. As a subset of $\mathbb{R}^n$ such an $S$ may be quite degenerate; $S$ may clearly not be homeomorphic to a disk, and indeed we will see may not be homeomorphic to …

HEIR: A Universal Compiler for Homomorphic Encryption
Asra Ali, Jaeho Choi, Bryant Gipson, Shruthi Gorantala, Jeremy Kun, Wouter Legiest, Lawrence Lim, Alexander Viand, Meron Zerihun Demissie, Hongren Zheng
https://arxiv.org/abs/2508.11095

HEIR: A Universal Compiler for Homomorphic Encryption
This work presents Homomorphic Encryption Intermediate Representation (HEIR), a unified approach to building homomorphic encryption (HE) compilers. HEIR aims to support all mainstream techniques in homomorphic encryption, integrate with all major software libraries and hardware accelerators, and advance the field by providing a platform for research and benchmarking. Built on the MLIR compiler framework, HEIR introduces HE-specific abstraction layers at which existing optimizations and new rese…