18 papers · ranked by Valyu relevance
Sanjay Mishra
This paper develops a complete foundational treatment of simplicial complexes from Euclidean spaces through geometric realizations, emphasizing concrete computations, examples, and practical verification methods. Beginning with finite point sets in finite and infinite-dimensional Euclidean spaces, geometric…
Zhaoyang Wang, Xianghui Fu, Bo Deng, Yang Chen + 1 more
In algebraic topology, a k-dimensional simplex is defined as a convex polytope consisting of k + 1 vertices. If spatial dimensionality is not considered, it corresponds to the complete graph with k + 1 vertices in graph theory. The alternating sum of the number of simplices across dimensions yields a topological…
Daniel Gibor
In this paper, we present a randomized polynomial-time simplex algorithm with higher probability and tighter bounds for linear programming by applying improved quasi-convex properties, a logarithmic rounding on a given polytope and its logarithmic perturbation. We base our work on the first randomized polynomial-time…
Nikita Smirnov, Semen Kurkin, Alexander E. Hramov
Introduction Real-world networks possess complex, higher-order structures that are not captured by traditional pairwise analysis methods. Q-analysis provides a powerful mathematical framework based on simplicial complexes to uncover and quantify these multi-node interactions. However, its adoption has been limited by a…
Freij-Hollanti, Ragnar, Lundström, Teemu
In this paper, we study the simplex faces of the order polytope O(P) and the chain polytope C(P) of a finite poset P. We show that, if P can be recursively constructed from X-free posets using disjoint unions and ordinal sums, then C(P) has at least as many k-dimensional simplex faces as O(P) does, for each dimension…
Colin Lynch, Kaitlin Baudier, Douglas Montgomery, Meghan Barrett
Animal nutritionists seek to understand how animals regulate the intake and balance of multiple nutrients, yet the design and analysis of such experiments are often limited by how nutrient spaces are represented. The geometric framework for nutrition (GFN) provides a powerful means to visualize nutrient interactions…
Hanlin Zhu, Assia Chericoni, Taha Ismail, Elizabeth A. Mickiewicz + 17 more
Humans handle numbers nimbly, suggesting a richer neural manifold structure than the prevalent mental number line model. In populations of medial temporal lobe (MTL) neurons in humans performing two simple tasks (dot counting and arithmetic), we find robust neural coding of numerosity that results in high dimensional…
Anna Pietrenko-Dabrowska, Slawomir Koziel
Formal optimization is nowadays ubiquitous in microwave design. It is frequently conducted using electromagnetic (EM) simulations, which guarantee dependability. Yet, it is computationally expensive. Local tuning may involve hundreds of system analyses, whereas global EM-driven optimization typically generates…
Kirill Kukharenko, Laura Sanità
The simplex algorithm is one of the most popular algorithms to solve linear programs (LPs). Starting at an extreme point solution of an LP, it performs a sequence of basis exchanges (called pivots) that allows one to move to a better extreme point along an improving edge-direction of the underlying polyhedron. A key…
Wei Liu, Roberto dos Reis, Chad A. Mirkin, Vinayak P. Dravid + 2 more
Grain identification in polycrystalline nanoparticles, for example, determining which crystal phases are present at each spatial location, is fundamental to materials characterisation. This is particularly challenging when grains overlap extensively, as commonly occurs in four-dimensional scanning transmission electron…
Luqian Wang, Jun Yin, Xiujuan Ma, Hongyu Chen + 1 more
Cascading failures in complex networks occur when local node or edge failures propagate to trigger large-scale collapse. Traditional pairwise network models cannot adequately capture group coordination and multi-agent higher-order interactions. Higher-order networks incorporating simplicial structures more accurately…
Yong Hyun Kwon, Ljubica Mihaljević, Keehun Kim, David E. Kim + 14 more
Glycosyltransferases (GTs) catalyze the formation of new glycosidic bonds and thus are vital for synthesizing nature’s vast repertoire of glycans and glycoconjugates and for engineering glycan-related medicines and materials. However, obtaining detailed structural and functional insights for the >750,000 known GTs is…
Haoyu Cheng, Han Qu, Sean McKenzie, Katherine R. Lawrence + 4 more
Telomere-to-telomere (T2T) assembly is the ultimate goal for de novo genome assembly. Existing algorithms capable of near T2T assembly all require Oxford Nanopore Technologies (ONT) ultra-long reads which are costly and experimentally challenging to obtain and are thus often unavailable for samples without established…
Esteban A. Hernandez-Vargas
Evolutionary therapies regulate heterogeneous populations by altering selective pressures through treatment sequences in cancer and infections. This letter develops an invariant-set framework for treatment-induced containment based on positive triangular invariant sets. For periodically switched systems, sufficient…
Dimitar Kostadinov, Beverley A. Clark, Michael Häusser
Learning on both fast and slow timescales is required to enable us to adapt to a dynamic environment. Whether the mechanisms mediating fast and slow learning are implemented by the same, or different, circuit elements remains an important open question. Learning involving the cerebellum is known to be driven primarily…
Ramin Ardalani, Anno C. Kurth, Aitor Morales-Gregorio
Cortical population activity often evolves along low-dimensional manifolds, shaped by external activity, task-demands and the underlying neuronal network structure. The structure of population activity has been studied across many brain areas and species. However, the influence of retinotopic organization in the…
Michael Kerber, Elena Xinyi Wang
The Persistent Homology Transform (PHT) summarizes a shape in R m by collecting persistence diagrams obtained from linear height filtrations in all directions on S m−1 . It enjoys strong theoretical guarantees, including continuity, stability, and injectivity on broad classes of shapes. A natural way to compare two…
Songlin Wei, Zhenhao Ni, Jie Liu, Zhenyu Zhao + 8 more
Humanoid foundation models are advancing faster than we can evaluate them. While real-world testing is expensive and difficult to reproduce, existing simulation benchmarks focus primarily on table-top or wheeled robots. A scalable and reproducible benchmark for whole-body humanoid loco-manipulation remains an open…