Tootfinder

Minimal Velocity
- my first ode to minimalism in music -
#NowPlaying
https://muz4now.com/2023/minimal-velocity-nowplaying/

Minimal Velocity #NowPlaying
Stan Stewart - @muz4now

Asymptotics for moments of the minimal partition excludant in congruence classes
Shane Chern, Ernest X. W. Xia
https://arxiv.org/abs/2507.14431 https://

Asymptotics for moments of the minimal partition excludant in congruence classes
The minimal excludant statistic, which denotes the smallest positive integer that is not a part of an integer partition, has received great interest in recent years. In this paper, we move on to the smallest positive integer whose frequency is less than a given number. We establish an asymptotic formula for the moments of such generalized minimal excludants that fall in a specific congruence class. In particular, our estimation reveals that the moments associated with a fixed modulus are asympt…

A minimal model with stochastically broken reciprocity
Z. C. Tu
https://arxiv.org/abs/2507.14862 https://arxiv.org/pdf/2507.14862

A minimal model with stochastically broken reciprocity
We introduce a minimal model consisting of a two-body system with stochastically broken reciprocity (i.e., random violation of Newton's third law) and then investigate its statistical behaviors, including correlation functions, time evolution of probability distribution functions, energy gain, and entropy production. The effective temperature of this two-body system immersed in a thermal bath is derived. Furthermore, we heuristically present an extremely minimal model where the relative motion …

Minimal horizontal triods: Analysis and computation
Robert N\"urnberg, Paola Pozzi
https://arxiv.org/abs/2507.15740 https://arxi…

Minimal horizontal triods: Analysis and computation
In this article we investigate the question of finding a network configuration of minimal length connecting three given points in the Heisenberg group. After proving existence of (possibly degenerate) minimal horizontal triods, we investigate their characterization. We then formulate a horizontal curve shortening flow that deforms any given suitable initial triod into a critical point for the length functional. Numerical experiments based on a stable fully discrete finite element scheme provide…

Cosmology with a Non-minimally Coupled Dark Matter Fluid I. Background Evolution
Samuele Silveravalle, Andrea Lapi, Francesco Benetti, Stefano Liberati
https://arxiv.org/abs/2507.16614

Cosmology with a Non-minimally Coupled Dark Matter Fluid I. Background Evolution
We explore a cosmological model in which dark matter is non-minimally coupled to gravity at the fluid level. While typically subdominant compared to Standard Model forces, such couplings may dominate dark matter dynamics. We show that this interaction modifies the early-time Friedmann equations, driving a phase of accelerated expansion that can resolve the horizon and flatness problems without introducing additional fields. At even earlier times, the coupling to spatial curvature may give rise …

An Efficient Algorithm for Generating Minimal Unique-Cause MC/DC Test cases for Singular Boolean Expressions
Robin Lee, Youngho Nam
https://arxiv.org/abs/2507.14687

An Efficient Algorithm for Generating Minimal Unique-Cause MC/DC Test cases for Singular Boolean Expressions
Modified Condition/Decision Coverage (MC/DC) is a mandatory structural coverage criterion for ensuring the reliability and safety of critical systems. While its strictest form, Unique-Cause MC/DC, offers the highest assurance, research on its efficient test generation has been lacking. This gap is particularly significant, as an analysis of large-scale avionics systems shows that 99.7% of all conditional decisions are, in fact, Singular Boolean Expressions (SBEs) the ideal structure for applyin…

Singular minimal surfaces with constant curvature
Rafael L\'opez
https://arxiv.org/abs/2507.13668 https://arxiv.org/pdf/2507.1366…

Singular minimal surfaces with constant curvature
We prove that singular minimal surfaces with constant Gauss curvature are planes, spheres and cylindrical surfaces. We also classify all singular minimal surfaces with a constant principal curvature and singular minimal surfaces with constant mean curvature.

Basis partitions and their signature
Krishnaswami Alladi
https://arxiv.org/abs/2507.14734 https://arxiv.org/pdf/2507.14734

Basis partitions and their signature
Basis partitions are minimal partitions corresponding to successive rank vectors. We show combinatorially how basis partitions can be generated from primary partitions which are equivalent to the Rogers-Ramanujan partitions. This leads to the definition of a signature of a basis partition that we use to explain certain parity results. We then study a special class of basis partitions which we term as complete. Finally we discuss basis partitions and minimal basis partitions among partitions wit…

from my link log —
Modern minimal perfect hashing: a survey.
https://arxiv.org/abs/2506.06536
saved 2025-06-11 https://dotat.at/:…

Modern Minimal Perfect Hashing: A Survey
Given a set $S$ of $n$ keys, a perfect hash function for $S$ maps the keys in $S$ to the first $m \geq n$ integers without collisions. It may return an arbitrary result for any key not in $S$ and is called minimal if $m = n$. The most important parameters are its space consumption, construction time, and query time. Years of research now enable modern perfect hash functions to be extremely fast to query, very space-efficient, and scale to billions of keys. Different approaches give different tr…

A Note on Helicoidal Singular Minimal Surfaces
Rafael L\'opez
https://arxiv.org/abs/2507.13669 https://arxiv.org/pdf/2507.13669…

A Note on Helicoidal Singular Minimal Surfaces
Let $α\in\r$ and let $\vec{v}\in\r^3$ be a unit vector. A singular minimal surface $Σ$ in Euclidean space is a surface $Σ$ whose mean curvature $H$ satisfies $H=α\frac{\langle N,\vec{v}\rangle}{\langle p,\vec{v}\rangle}$, where $N$ is the unit normal vector of $Σ$. In this short note we study singular minimal surfaces which are invariant by a one-parameter group of helicoidal motions. We prove that if $Σ$ is a helicoidal singular minimal surface, then the axis of the helicoidal motion is …