Related papers: The Generic Degree of Autonomy
Decentralized learning offers privacy and communication efficiency when data are naturally distributed among agents communicating over an underlying graph. Motivated by overparameterized learning settings, in which models are trained to…
For a positive integer $r$, a distance-$r$ independent set in an undirected graph $G$ is a set $I\subseteq V(G)$ of vertices pairwise at distance greater than $r$, while a distance-$r$ dominating set is a set $D\subseteq V(G)$ such that…
We discuss controllability of systems that are initially given by boundary coupled p.d.e. of second order. Those systems may be described by modules over a certain subring R of the ring of Mikusinski operators with compact support. We show…
Chern-Simons topological quantum computer is a device that can be effectively described by the Chern-Simons topological quantum field theory and used for quantum computations. Quantum qudit gates of this quantum computer are represented by…
In this paper, we present a rigorous modular statistical approach for arguing safety or its insufficiency of an autonomous vehicle through a concrete illustrative example. The methodology relies on making appropriate quantitative studies of…
The purpose of this paper is to present a universal approach to the study of controllability/observability problems for infinite dimensional systems governed by some stochastic/deterministic partial differential equations. The crucial…
The numerical controllability transition makes the success of control can be achieved by increasing the number of driver nodes to a certain point. Motivated by the fact that the degree correlation has vast role in the dynamics on networks,…
The $k$-independence number of a graph $G$ is the maximum size of a set of vertices at pairwise distance greater than $k$. In this paper, for each positive integer $k$, we prove sharp upper bounds for the $k$-independence number in an…
Our technologies complexify our environments. Thus, new technologies need to deal with more and more complexity. Several efforts have been made to deal with this complexity using the concept of self-organization. However, in order to…
This paper builds on an existing notion of group responsibility and proposes two ways to define the degree of group responsibility: structural and functional degrees of responsibility. These notions measure the potential responsibilities of…
Let G be a graph. The independence-domination number is the maximum over all independent sets I in G of the minimal number of vertices needed to dominate I. In this paper we investigate the computational complexity of independence…
The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most…
The degree-restricted random process is a natural algorithmic model for generating graphs with degree sequence D_n=(d_1, \ldots, d_n): starting with an empty n-vertex graph, it sequentially adds new random edges so that the degree of each…
Let $G$ be a simple, connected and finite graph with order $n$. Denote the independence number, edge independence number and total independence number by $\alpha(G), \alpha'(G)$ and $\alpha"(G)$ respectively. This paper establishes a…
We discuss the use of machine learning techniques in effectively nonparametric modelling of generalised parton distributions (GPDs) in view of their future extraction from experimental data. Current parameterisations of GPDs suffer from…
Let $\mathbf{p}$ be a configuration of $n$ points in $\mathbb{R}^d$ for some $n$ and some $d \ge 2$. Each pair of points has a Euclidean length in the configuration. Given some graph $G$ on $n$ vertices, we measure the point-pair lengths…
The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set $\cal A$ of operationally relevant observables. The algebraic structure of $\cal A$ selects a preferred tensor product…
A general methodology is proposed to engineer a system of interacting components (particles) which is able to self-regulate their concentrations in order to produce any prescribed output in response to a particular input. The methodology is…
The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…
The maximum efficiency of autonomous engines with finite chemical potential difference is investigated. We show that without a particular type of singularity autonomous engines cannot attain the Carnot efficiency. In addition, we…