A bstract We study tropical Grassmanians Tr (k, n) in relation to cluster algebras, and assess
their applicability to n-particle amplitudes for n= 7, 8. In\(\mathcal {N}\)= 4 super Yang-Mills …

Combinatorial geometry takes the lead Page 1 Combinatorial geometry takes the lead Andrei
Okounkov Abstract While the author is a professional mathematician, he is by no means an …

The emergence of single-cell RNA sequencing (RNA-seq) has radically changed the
observation of cellular diversity. Although annotations of RNA-seq data require preserved …

Tropical geometry is a relatively new field of mathematics that studies the tropicalization
map: a map that assigns a certain type of polyhedral complex, called a tropical variety, to an …

Recent advancements in visualizing deep neural networks provide insights into their
structures and mesh extraction from Continuous Piecewise Affine (CPWA) functions …

Scattering amplitudes are key observables that describe the probability of possible
outcomes in the interaction of fundamental particles. These interactions are investigated in …

We apply operad theory to enumerative combinatorics in order to count the number of
shuffles between series-parallel posets and chains. We work with three types of shuffles, at …

The main purpose of this work is to build a refinement of Grigoriev's framework that records
the valuations of the coefficients in a power series solution so that convergence information …

We explore the operad of finite posets and its algebras. We use order polytopes to
investigate the combinatorial properties of zeta values. By generalizing a family of zeta value …

The dynamics of species concentrations of chemical reaction networks are given by
autonomous first-order ordinary differential equations. Singular perturbation methods allow …