Related papers: Generalised Evasive Subspaces
This paper investigates the construction of rank-metric codes with specified Ferrers diagram shapes. These codes play a role in the multilevel construction for subspace codes. A conjecture from 2009 provides an upper bound for the dimension…
Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…
The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…
We introduce and initiate the study of new parameters associated with any norm and any log-concave measure on $\mathbb R^n$, which provide sharp distributional inequalities. In the Gaussian context this investigation sheds light to the…
The desirable properties when constructing collections of subspaces often include the algebraic constraint that the projections onto the subspaces yield a resolution of the identity like the projections onto lines spanned by vectors of an…
Coding in the projective space has received recently a lot of attention due to its application in network coding. Reduced row echelon form of the linear subspaces and Ferrers diagram can play a key role for solving coding problems in the…
Associated to any finite metric space are a large number of objects and quantities which provide some degree of structural or geometric information about the space. In this paper we show that in the setting of subsets of weighted Hamming…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
Partial spread is important in finite geometry and can be used to construct linear codes. From the results in (Designs, Codes and Cryptography 90:1-15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a…
The notion of maximal-spacing in several dimensions was introduced and studied by Deheuvels (1983) for data uniformly distributed on the unit cube. Later on, Janson (1987) extended the results to data uniformly distributed on any bounded…
Bayesian latent space models offer a principled approach to network representation, but rely on correct specification of both geometry and link function. Real-world networks often violate these assumptions, exhibiting geometric mismatch and…
A subspace code is defined as a collection of subspaces of an ambient vector space, where each information-encoding codeword is a subspace. This paper studies a class of spatial sensing problems, notably direction of arrival (DoA)…
Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on…
It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…
Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we…
Necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Generalized conceptions of distances and dimensionality evaluation are…
This thesis deals with applications of experimental mathematics to a number of problems. The first problem is related to random graph statistics. We consider a certain class of Galton-Watson random trees and look at the total height…