Tootfinder

Improved Search-to-Decision Reduction for Random Local Functions
Kel Zin Tan, Prashant Nalini Vasudevan
https://arxiv.org/abs/2510.02944 https://arxiv.org/…

Improved Search-to-Decision Reduction for Random Local Functions
A random local function defined by a $d$-ary predicate $P$ is one where each output bit is computed by applying $P$ to $d$ randomly chosen bits of its input. These represent natural distributions of instances for constraint satisfaction problems. They were put forward by Goldreich as candidates for low-complexity one-way functions, and have subsequently been widely studied also as potential pseudo-random generators. We present a new search-to-decision reduction for random local functions defi…

Non-symmetric solutions to an overdetermined problem for the Helmholtz equation in the plane
Miles H. Wheeler
https://arxiv.org/abs/2509.00455 https://arxi…

Non-symmetric solutions to an overdetermined problem for the Helmholtz equation in the plane
In this note we construct smooth bounded domains $Ω\subset \mathbb R^2$, other than disks, for which the overdetermined problem $$ \left\{ \begin{alignedat}{2} Δu + λu &= 0 &\qquad& \text{ in } Ω, \newline u &= b &\qquad& \text{ on } \partial Ω, \newline \frac{\partial u}{\partial n} &= c &\qquad& \text{ on } \partial Ω \end{alignedat} \right. $$ has a solution for some constants $λ,b,c \ne 0$. These appear to be the first counterexamples to a conjecture of Willms and Gladw…

Family Matters: Language Transfer and Merging for Adapting Small LLMs to Faroese
Jenny Kunz, Iben Nyholm Debess, Annika Simonsen
https://arxiv.org/abs/2510.00810 https://…

Family Matters: Language Transfer and Merging for Adapting Small LLMs to Faroese
We investigate how to adapt small, efficient LLMs to Faroese, a low-resource North Germanic language. Starting from English models, we continue pre-training on related Scandinavian languages, either individually or combined via merging, before fine-tuning on Faroese. We compare full fine-tuning with parameter-efficient tuning using LoRA, evaluating their impact on both linguistic accuracy and text comprehension. Due to the lack of existing Faroese evaluation data, we construct two new minimal-p…

Replaced article(s) found for nlin.AO. https://arxiv.org/list/nlin.AO/new
[1/1]:
- Kuramoto meets Koopman: Constants of motion, symmetries, and network motifs
Vincent Thibeault, Benjamin Claveau, Antoine Allard, Patrick Desrosiers

Arm events in critical planar loop soups
Yijie Bi, Yifan Gao, Pierre Nolin, Wei Qian
https://arxiv.org/abs/2509.25024 https://arxiv.org/pdf/2509.25024

Arm events in critical planar loop soups
We establish up-to-constants estimates for arm events in the Brownian loop soup on the 2D metric graph associated with the square lattice. More specifically, we consider two natural geometric events: first, ``bulk'' four-arm events, corresponding to two large connected components of loops getting close to each other; and then, two-arm events in the half-plane, used to estimate the probability that a cluster of loops approaches the boundary. Our proof relies on an estimate by Lupu-Werner [Probab…

Replaced article(s) found for nlin.SI. https://arxiv.org/list/nlin.SI/new
[1/1]:
- Kuramoto meets Koopman: Constants of motion, symmetries, and network motifs
Vincent Thibeault, Benjamin Claveau, Antoine Allard, Patrick Desrosiers

Uncertainty Quantification of Bacterial Microcompartment Permeability
Andre Archer, Brett J. Palmero, Charlotte Abrahamson, Carolyn E. Mills, Nolan W. Kennedy, Danielle Tullman-Ercek, Niall M. Mangan
https://arxiv.org/abs/2509.23445

Uncertainty Quantification of Bacterial Microcompartment Permeability
$\textit{Salmonella}$ expresses bacterial microcompartments (MCPs) upon 1,2-propanediol exposure. MCPs are nanoscale protein-bound shells that encase enzymes for the cofactor-dependent 1,2-propanediol metabolism. They are hypothesized to limit exposure to the toxic intermediate, propionaldehyde, decrease cofactor involvement in competing reactions, and enhance flux. We construct a mass-action mathematical model of purified MCPs and calibrate parameters to measured metabolite concentrations. We …

Three Generalizations of Erd\H{o}s Szekeres: $k$-Modal Subsequences
Charles Gong
https://arxiv.org/abs/2508.20360 https://arxiv.org/pdf/2508.20360

Three Generalizations of Erdős Szekeres: $k$-Modal Subsequences
Erdős and Szekeres showed that given a permutation $p$ of $[n]$, and the sequence defined by \newline $(p(1), p(2), \ldots, p(n))$, there exists either a decreasing or increasing subsequence, not necessarily contiguous, of length at least $\sqrt{n}$. Fan Chung considered subsequences that can have at most one change of direction, i.e. an increasing and then decreasing subsequence, or a decreasing and then increasing subsequence. She called these unimodal subsequences, and showed there exists a…

Equality condition for a matrix inequality by partial transpose
Nalan Wang, Lin Chen
https://arxiv.org/abs/2508.18644 https://arxiv.org/pdf/2508.18644

Equality condition for a matrix inequality by partial transpose
The partial transpose map is a linear map widely used quantum information theory. We study the equality condition for a matrix inequality generated by partial transpose, namely $\rank(\sum^K_{j=1} A_j^T \otimes B_j)\le K \cdot \rank(\sum^K_{j=1} A_j \otimes B_j)$, where $A_j$'s and $B_j$'s are respectively the matrices of the same size, and $K$ is the Schmidt rank. We explicitly construct the condition when $A_i$'s are column or row vectors, or $2\times 2$ matrices. For the case where the Schmi…

Crosslisted article(s) found for nlin.AO. https://arxiv.org/list/nlin.AO/new
[1/1]:
- A Social Force Model for Companion Groups Considering Relative-Weight Attraction
Lihui Dong, Yingshuang He, Yunfeng Deng, Qiuyu Zheng, Tianming Wang