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We study the variety of complex $n$-dimensional Jordan algebras using techniques from Geometric Invariant Theory.
We present a selective review on probabilistic modeling of heterogeneity in random graphs. We focus on latent space models and more particularly on stochastic block models and their extensions that have undergone major developments in the…
Periodically forced turbulence is used as a test case to evaluate the predictions of two-equation and multiple-scale turbulence models in unsteady flows. The limitations of the two-equation model are shown to originate in the basic…
We give a short introduction to the methods of representing polynomial and trigonometric series that are often used in Celestial Mechanics. A few applications are also illustrated.
One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
This paper focuses on modeling the dynamic attributes of a dynamic network with a fixed number of vertices. These attributes are considered as time series which dependency structure is influenced by the underlying network. They are modeled…
We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…
We test the ability of a general low-dimensional model for turbulence to predict geometry-dependent dynamics of large-scale coherent structures, such as convection rolls. The model consists of stochastic ordinary differential equations,…
Number types for exact computation are usually based on directed acyclic graphs. A poor graph structure can impair the efficency of their evaluation. In such cases the performance of a number type can be drastically improved by…
The use of directed acyclic graphs (DAGs) to represent conditional independence relations among random variables has proved fruitful in a variety of ways. Recursive structural equation models are one kind of DAG model. However,…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
In this paper we consider plane quartics with to involutions. We compute the Dixmier invariants, the bitangents and the Matrix representation problem of these curves, showing that they have symbolic solutions for the last two questions.
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…
This paper is about the use of the Wallenius noncentral hypergeometric distribution for analysing contingency tables with two or more groups and two categories and with row margins and sample size, that is both margins, fixed. The…
We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem, we aim to distinguish effects of the two types of dynamics by choosing initial states as random product states from two factor spaces representing…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…