Related papers: Maximum Likelihood, permutohedra and Associativity…
We consider the moduli space $\mathcal{R}_n$ of pairs of monic, degree $n$ polynomials whose resultant equals $1$. We relate the topology of these algebraic varieties to their geometry and arithmetic. In particular, we compute their…
We study the problem of maximum likelihood estimation of densities that are log-concave and lie in the graphical model corresponding to a given undirected graph $G$. We show that the maximum likelihood estimate (MLE) is the product of the…
In a recent paper, Hauenstein, Sturmfels, and the second author discovered a conjectural bijection between critical points of the likelihood function on the complex variety of matrices of rank r and critical points on the complex variety of…
The harmonic polytope and the bipermutahedron are two related polytopes which arose in Ardila, Denham, and Huh's work on the Lagrangian geometry of matroids. We study the bipermutahedron. We show that its faces are in bijection with the…
We give an a priori construction of the two-dimensional reduction of three-dimensional quantum Chern-Simons theory. This reduction is a two-dimensional topological quantum field theory and so determines to a Frobenius ring, which here is…
Maximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded rank. These represent mixtures of distributions of two independent discrete random variables. We…
Coherence in a monoidal category asserts that all morphisms built from structural isomorphisms with a fixed source and target coincide. These structural isomorphisms include, in particular, the associators. Linearly distributive categories…
We give a short proof of the log-concavity of the coefficients of the reduced characteristic polynomial of a matroid. The proof uses an extension of the theory of Lorentzian polynomials to convex cones, and reproves the Hodge-Riemann…
A fundamental question in the field of molecular computation is what computational tasks a biochemical system can carry out. In this work, we focus on the problem of finding the maximum likelihood estimate (MLE) for log-affine models. We…
This work adresses the question of density of piecewise constant (resp. rigid) functions in the space of vector valued functions with bounded variation (resp. deformation) with respect to the strict convergence. Such an approximation…
In this paper, Monge-Kantorovich problem is considered in the infinite dimension on an abstract Wiener space $(W, H,\mu)$, where $H$ is Cameron-Martin space and $\mu$ is the Gaussian measure. We study the regularity of optimal transport…
We establish a "second vanishing theorem" for local cohomology modules over regular rings of unramified mixed characteristic, which relates the connectedness of the spectrum of a ring with the vanishing of local cohomology. Applying this,…
We introduce and study different compactifications of the moduli space of $n$ distinct weighted labeled points in a flag of affine spaces. We construct these spaces via the weighted and generalized Fulton-MacPherson compactifications of…
We study the preferential attachment model $G_n^h$. A graph $G_n^h$ is generated from a finite initial graph by adding new vertices one at a time. Each new vertex connects to $h\ge 1$ already existing vertices, and these are chosen with…
We explore some properties of wide subcategories of the category mod$\,(\Lambda)$ of finitely generated left $\Lambda$-modules, for some artin algebra $\Lambda.$ In particular we look at wide finitely generated subcategories and give a…
Positive modalities in systems in the vicinity of S4 and S5 are investigated in terms of categorial proof theory. Coherence and maximality results are demonstrated, and connections with mixed distributive laws and Frobenius algebras are…
Let $R$ be a commutative ring. A quasi-Gorenstein $R$-module is an $R$-module such that the grade of the module and the projective dimension of the module are equal and the canonical module of the module is isomorphic to the module itself.…
In this paper we present a condition on a local Cohen-Macaulay F-injective ring of positive characteristic $p > 2$ which implies that its top local cohomology module with support in the maximal ideal has finitely many Frobenius compatible…
Algebra and representation theory in modular tensor categories can be combined with tools from topological field theory to obtain a deeper understanding of rational conformal field theories in two dimensions: It allows us to establish the…
As in the case of the associahedron and cyclohedron, the permutohedron can also be defined as an appropriate compactification of a configuration space of points on an interval or on a circle. The construction of the compactification endows…