Related papers: Singular Classical Solutions and Tree Multiparticl…
We study mathematical aspects concerning two site tree-level cosmological correlators with massive internal and external states in a de Sitter universe. We employ integration by parts identities, (relative) twisted cohomology and the method…
We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the…
The solution of the classical field equation generates the sum of all tree graphs. We show that the classical equation reduces to an easily solved ordinary differential equation for certain multiparticle threshold amplitudes and compute…
The goal of these lectures is to survey some of the recent progress on the description of large-scale structure of random trees. We use the framework of Markov-Branching sequences of trees and discuss several applications.
Classification of datasets into two or more distinct classes is an important machine learning task. Many methods are able to classify binary classification tasks with a very high accuracy on test data, but cannot provide any easily…
We elaborate the two-fold simplex-like structures of tree amplitudes in planar maximally supersymmetric Yang-Mills (N=4 SYM), through its connection to a mathematical structure known as the positive Grassmannian. Exploiting the reduced…
In this paper we present a novel mathematical optimization-based methodology to construct tree-shaped classification rules for multiclass instances. Our approach consists of building Classification Trees in which, except for the leaf nodes,…
We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…
A $p$-Laplacian elliptic problem in the presence of both strongly singular and $(p-1)$-superlinear nonlinearities is considered. We employ bifurcation theory, approximation techniques and sub-supersolution method to establish the existence…
We study in detail the general solution for a scalar field cosmology with an exponential potential, correcting some imprecisions, encountered previously in the literature. In addition, we generalize this solution for a piecewise exponential…
We shall discuss how the notions of multicategories and their linear representations are related with tensor categories. When one focuses on the ones arizing from planar diagrams, it particularly implies that there is a natural one-to-one…
We study the theory of equations in one variable over polyhedral semirings. The article revolves around a notion of solution to a polynomial equation over a polyhedral semiring. Our main results are a characterisation of local solutions in…
We make an attempt to describe the spectrum of masses of elementary particles, as it comes out empirically in six distinct scales. We argue for some rather well defined mass scales, like the electron mass: it seems to us that there is a…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree…
We have looked for evidence of large cross sections at large multiplicities in weakly coupled scalar field theory in three dimensions. We use spectral function sum rules to derive bounds on total cross sections where the sum can be expresed…
An overpartition is a partition such that the first occurrence (equivalently, the last occurrence) of a number may be overlined. In this article, we investigate three contents of overpartitions. We first consider the $r$-chain minimal and…
We present general exact solutions for two classes of exponential potentials in scalar field models for quintessence. The coupling is minimal and we consider only dust and scalar field. To some extent, it is possible to reproduce…
We study the possible values of the matching number among all trees with a given degree sequence as well as all bipartite graphs with a given bipartite degree sequence. For tree degree sequences, we obtain closed formulas for the possible…
We present a general method, based on a multiple-scale approach, for deriving the perturbative solutions of the scaling equations governing the expansion of superfluid ultracold quantum gases released from elongated harmonic traps. We…
We study several enumeration problems connected to linear trees, a broad class which includes stars, paths, generalized stars, and caterpillars. We provide generating functions for counting the number of linear trees on $n$ vertices,…