Tootfinder

Dynamic Space Filling
P. L. Krapivsky
https://arxiv.org/abs/2506.01128 https://arxiv.org/pdf/2506.01128

Dynamic Space Filling
Dynamic space filling (DSF) is a stochastic process defined on any connected graph. Each vertex can host an arbitrary number of particles forming a pile, with every arriving particle landing on the top of the pile. Particles in a pile, except for the particle at the bottom, can hop to neighboring vertices. Eligible particles hop independently and stochastically, with the overall hopping rate set to unity for every eligible particle at every vertex. When the number of vertices in a graph is equa…

In Ursula K. Le Guin's "A Man of the People" (part of "Four Ways to Forgiveness") there's a scene where the Hainish protagonist begins studying history. It's excellent in many respects, but what stood out the most to me was the softly incomprehensible idea of a people with multiple millions of years of recorded history. As one's mind starts to try to trace out the implications of that, it dawns on you that you can't actually comprehend the concept. Like, you read the sentence & understood all the words, and at first you were able to assemble them into what seemed like a conceptual understanding, but as you started to try to fill out that understating, it began to slip away, until you realized you didn't in fact have the mental capacity to build a full understanding and would have you paper things over with a shallow placeholder instead.
I absolutely love that feeling, as one of the ways in which reading science fiction can stretch the brain, and I connected it to a similar moment in Tsutomu Nihei's BLAME, where the android protagonists need to ride an elevator through the civilization/galaxy-spanning megastructure, and turn themselves off for *millions of years* to wait out the ride.
I'm not sure why exactly these scenes feel more beautifully incomprehensible than your run-of-the-mill "then they traveled at lightspeed for a millennia, leaving all their family behind" scene, other than perhaps the authors approach them without trying to use much metaphor to make them more comprehensible (or they use metaphor to emphasize their incomprehensibility).
Do you have a favorite mind=expanded scene of this nature?
#AmReading

Comparing Optimization Algorithms Through the Lens of Search Behavior Analysis
Gjorgjina Cenikj, Ga\v{s}per Petelin, Tome Eftimov
https://arxiv.org/abs/2507.01668

Comparing Optimization Algorithms Through the Lens of Search Behavior Analysis
The field of numerical optimization has recently seen a surge in the development of "novel" metaheuristic algorithms, inspired by metaphors derived from natural or human-made processes, which have been widely criticized for obscuring meaningful innovations and failing to distinguish themselves from existing approaches. Aiming to address these concerns, we investigate the applicability of statistical tests for comparing algorithms based on their search behavior. We utilize the cross-match statis…

On Loops in critical high-dimensional percolation
Amelia Carpenter, Wendelin Werner
https://arxiv.org/abs/2507.02676 https://arxiv.or…

On Loops in critical high-dimensional percolation
We discuss the following type of results about critical Bernoulli percolation in high dimensions: The collection of clusters that do contain large (self-avoiding) loops in a large box is tight. The collection of these large loops has scaling limits that one will be able to relate to Brownian loop-soups (each of these atypical loop-containing clusters does in some sense only contain one large self-avoiding loop in the sense that any two such loops will be very close). This feature contrasts with…

#Deutschland hat ein #Männerproblem.
(Bild: picture alliance / dpa / Katharina Kausche)
#MadeForGermany

Dual-Stage Value-Guided Inference with Margin-Based Reward Adjustment for Fast and Faithful VLM Captioning
Ankan Deria, Adinath Madhavrao Dukre, Feilong Tang, Sara Atito, Sudipta Roy, Muhammad Awais, Muhammad Haris Khan, Imran Razzak
https://arxiv.org/abs/2506.15649

Dual-Stage Value-Guided Inference with Margin-Based Reward Adjustment for Fast and Faithful VLM Captioning
Despite significant advances in inference-time search for vision-language models (VLMs), existing approaches remain both computationally expensive and prone to unpenalized, low-confidence generations which often lead to persistent hallucinations. We introduce \textbf{Value-guided Inference with Margin-based Reward (ViMaR)}, a two-stage inference framework that improves both efficiency and output fidelity by combining a temporal-difference value model with a margin-aware reward adjustment. In th…

On the rank of a random symmetric matrix in the large deviation regime
Yi Han
https://arxiv.org/abs/2506.01155 https://arxiv.org/pdf/…

On the rank of a random symmetric matrix in the large deviation regime
Let $A$ be an $n\times n$ random symmetric matrix with independent identically distributed subgaussian entries of unit variance. We prove the following large deviation inequality for the rank of $A$: for all $1\leq k\leq c\sqrt{n}$, $$\mathbb{P}(\operatorname{Rank}(A)\geq n-k)\geq 1-\exp(-c'kn),$$ for some fixed constants $c,c'>0$. A similar large deviation inequality is proven for the rank of the adjacency matrix of dense Erdos-Renyi graphs. This corank estimate enhances the recent breakthroug…

Non-local random deposition models for earthquakes and energy propagation
Philippe Carmona, Fran\c{c}ois P\'etr\'elis, Nicolas P\'etr\'elis
https://arxiv.org/abs/2506.23853

Non-local random deposition models for earthquakes and energy propagation
We investigate a new class of non-local random deposition models, initially introduced by physicists to study the field of mechanical constraints (stress) applied along a line or on a given area located in a seismic zone. The non-local features are twofold. First, the falling objects have random and heavy-tailed dimensions. Second, the locations where the objects are falling are at least for some of the models that we consider, depending on the shape of the surface before deposition. We conside…

Lower deviation probabilities for supercritical multi-type Galton--Watson processes
Tan Jiangrui
https://arxiv.org/abs/2506.23647 https://

Lower deviation probabilities for supercritical multi-type Galton--Watson processes
This paper provides a detailed analysis of the lower deviation probability properties for a $d$-type ($d>1$) Galton--Watson (GW) process $\{\textbf{Z}_n=(Z_n^{(i)})_{1\le i\le d};n\ge0\}$ in both Schröder and Böttcher cases. We establish explicit decay rates for the following probabilities: $$\mathbb{P}(\textbf{Z}_n=\textbf{k}_n),~ \mathbb{P}(|\textbf{Z}_n|\le k_n), ~\mathbb{P}(Z^{(i)}_n=k_n)~~\text{and}~~\mathbb{P}(Z^{(i)}_n\le k_n), 1\le i \le d,$$ respectively, where $\textbf{k}_…

A stochastic model for the diffusion of competing opinions with trend-following, opposition, and indifference
Manuel Gonz\'alez-Navarrete
https://arxiv.org/abs/2506.18313

A stochastic model for the diffusion of competing opinions with trend-following, opposition, and indifference
We study a stochastic model for the diffusion of competing opinions in a population composed of three types of agents: trend-followers, opposers, and indifferent individuals. The decision dynamics are driven by reinforcement mechanisms, modulated by a latent trend process, allowing us to capture realistic features such as amplification, resistance, and randomness in opinion formation. We derive explicit formulas for the finite-time moments of the opinion count vector and establish a set of stro…