Results 141 to 150 of about 15,809 (305)
A Unifying Approach to Self‐Organizing Systems Interacting via Conservation Laws
Advanced Intelligent Discovery, EarlyView.The article develops a unified way to model and analyze self‐organizing systems whose interactions are constrained by conservation laws. It represents physical/biological/engineered networks as graphs and builds projection operators (from incidence/cycle structure) that enforce those constraints and decompose network variables into constrained versus ...
F. Barrows +7 more
wiley +1 more source
Reduced convex bodies in Euclidean space—A survey
, 2011 A convex body R in Euclidean space Ed is called reduced if the minimal width Δ(K) of each convex body K⊂R different from R is smaller than Δ(R). This definition yields a class of convex bodies which contains the class of complete sets, i.e., the family ...
Lassak, Marek +3 more
core +1 more source
Advanced Intelligent Discovery, EarlyView.This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley +1 more source
Stability of the Borell–Brascamp–Lieb Inequality for Multiple Power Concave Functions
AxiomsIn this paper, we prove the stability of the Brunn–Minkowski inequality for multiple convex bodies in terms of the concept of relative asymmetry. Using these stability results and the relationship of the compact support of functions, we establish the ...
Meng Qin +4 more
doaj +1 more source
Convex bodies and convexity on Grassmann cones
Archiv der Mathematik, 1962 Ewald, G., Shephard, G.C., Busemann, H.
openaire +1 more source
Explaining the Origin of Negative Poisson's Ratio in Amorphous Networks With Machine Learning
Advanced Intelligent Discovery, EarlyView.This review summarizes how machine learning (ML) breaks the “vicious cycle” in designing auxetic amorphous networks. By transitioning from traditional “black‐box” optimization to an interpretable “AI‐Physics” closed‐loop paradigm, ML is shown to not only discover highly optimized structures—such as all‐convex polygon networks—but also unveil hidden ...
Shengyu Lu, Xiangying Shen
wiley +1 more source
Convex bodies associated with a convex body [PDF]
Proceedings of the American Mathematical Society, 1951 openaire +2 more sources
Convex bodies and representation theory, Part 1
, 2014 Non UBCUnreviewedAuthor affiliation: University of ...
Khovanskii, Askold
core
Smart Bioinspired Material‐Based Actuators: Current Challenges and Prospects
Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.This work gathers, in a review style, an extensive and comprehensive literature overview on the development of autonomous actuators based on synthetic materials, bringing together valuable knowledge from several studies. Furthermore, the article identifies the fundamental principles of actuation mechanisms and defines key parameters to address the size
Alejandro Palacios +4 more
wiley +1 more source
A problem of Sallee on equidecomposable convex bodies
, 1985 We show that equidecomposable planar convex bodies need not be convex equidecomposable. This answers a question of Sallee. We also show that convex and scissors equidecomposability are equivalent notions for convex bodies in the plane, and include a ...
R. J. Gardner
core +1 more source