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We present a simplified version of the DFS-based Left-Right planarity testing and embedding algorithm implemented in Pigale which has been considered as the fastest implemented one [J.M. Boyer, P.F. Cortese, M. Patrignani, and G. Di…
We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusion in real Hilbert space. The algorithm allows to use the inexact computations of the Lipschitzian and cocoercive…
The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…
We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the $\Sigma_\beta$ hierarchy. We focus on linear orderings. We show that at the $\Sigma_1$ level all linear…
A coarse group is a group endowed with a coarse structure so that the group multiplication and inversion are coarse mappings. Let $(X, \mathcal{E})$ be a coarse space and let $\mathfrak{M}$ be a variety of groups different from the variety…
We analyze the finite sample mean squared error (MSE) performance of regression trees and forests in the high dimensional regime with binary features, under a sparsity constraint. We prove that if only $r$ of the $d$ features are relevant…
Bio-inspired composites are a great promise for mimicking the extraordinary and highly efficient properties of natural materials. Recent developments in voxel-by-voxel 3D printing have enabled extreme levels of control over the material…
Determining the interaction partners among protein/domain families poses hard computational problems, in particular in the presence of paralogous proteins. Available approaches aim to identify interaction partners among protein/domain…
Despite the success of neural models in solving reasoning tasks, their compositional generalization capabilities remain unclear. In this work, we propose a new setting of the structured explanation generation task to facilitate…
This study presents a theoretical model for a self-replicating mechanical system inspired by biological processes within living cells and supported by computer simulations. The model decomposes self-replication into core components, each of…
We devise a generalization of tree approximation that generates conforming meshes, i.e., meshes with a particular structure like edge-to-edge triangulations. A key feature of this generalization is that the choices of the cells to be…
The decision tree recursively partitions the input space into regions and derives axis-aligned decision boundaries from data. Despite its simplicity and interpretability, decision trees lack parameterized representation, which makes it…
In this work we answer an open question asked by Johnson--Scoville. We show that each merge tree is represented by a discrete Morse function on a path. Furthermore, we present explicit constructions for two different but related kinds of…
An important problem in geometric computing is defining and computing similarity between two geometric shapes, e.g. point sets, curves and surfaces, etc. Important geometric and topological information of many shapes can be captured by…
We present Team asdfo123's submission to the LLMSR@XLLM25 shared task, which evaluates large language models on producing fine-grained, controllable, and interpretable reasoning processes. Systems must extract all problem conditions,…
In this paper we explore a connection between descriptive set theory and inner model theory. From descriptive set theory, we will take a countable, definable set of reals, A. We will then show that A is equal to the reals of M, where M is a…
Proposed here is a dynamic Monte-Carlo algorithm that is efficient in simulating dense systems of long flexible chain molecules. It expands on the configurational-bias Monte-Carlo method through the simultaneous generation of a large set of…
While most neural generative models generate outputs in a single pass, the human creative process is usually one of iterative building and refinement. Recent work has proposed models of editing processes, but these mostly focus on editing…
We investigate iterating the construction of $C^{*}$, the $L$-like inner model constructed using first order logic augmented with the "cofinality $\omega$" quantifier. We first show that $\left(C^{*}\right)^{C^{*}}=C^{*}\ne L$ is…
Language models (LMs) can perform complex reasoning either end-to-end, with hidden latent state, or compositionally, with transparent intermediate state. Composition offers benefits for interpretability and safety, but may need workflow…