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In this note, we study monotone dynamical systems with respect to polyhedral cones. Using the half-space representation and the vertex representation, we propose three equivalent conditions to certify monotonicity of a dynamical system with…

In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…

The event-triggered consensus problem of first-order multi-agent systems under directed topology is investigated. The event judgements are only implemented at periodic time instants. Under the designed consensus algorithm, the sampling…

A primary goal of online deliberation platforms is to identify ideas that are broadly agreeable to a community of users through their expressed preferences. Yet, consensus elicitation should ideally extend beyond the specific statements…

The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…

The behaviour is investigated of solutions to a diffusion equation on the real line with nonlocal and singular reaction term, i.e., given by a Dirac source or sink at the origin. It gives a simplified representation of for example a control…

Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…

In this chapter, we derive and analyse models for consensus dynamics on hypergraphs. As we discuss, unless there are nonlinear node interaction functions, it is always possible to rewrite the system in terms of a new network of effective…

Perron-Frobenius theory developed for irreducible non-negative kernels deals with so-called $R$-positive recurrent kernels. If kernel $M$ is $R$-positive recurrent, then the main result determines the limit of the scaled kernel iterations…

We propose a batchwise monotone algorithm for dictionary learning. Unlike the state-of-the-art dictionary learning algorithms which impose sparsity constraints on a sample-by-sample basis, we instead treat the samples as a batch, and impose…

This paper focuses on analyzing the finite-time convergence of a nonlinear consensus algorithm for multi-agent networks with unknown inherent nonlinear dynamics. Due to the existence of the unknown inherent nonlinear dynamics, the stability…

A non-linear Black-Scholes-type equation is studied within counterparty risk models. The classical hypothesis on the uniform Lipschitz-continuity of the non-linear reaction function allows for an equivalent transformation of the semi-linear…

This paper presents a finite-time heterogeneous cyclic pursuit scheme that ensures consensus among agents modelled as integrators. It is shown that for the proposed sliding mode control, even when the gains corresponding to each agent are…

We propose a general framework for geometric approximation of circular arcs by parametric polynomial curves. The approach is based on constrained uniform approximation of an error function by scalar polynomials. The system of nonlinear…

We consider continuous-time consensus systems whose interactions satisfy a form or reciprocity that is not instantaneous, but happens over time. We show that these systems have certain desirable properties: They always converge…

We consider the average-consensus problem in a multi-node network of finite size. Communication between nodes is modeled by a sequence of directed signals with arbitrary communication delays. Four distributed algorithms that achieve…

We generalize to noncommutative cylinder the solution generation technique, originally suggested for gauge theories on noncommutative plane. For this purpose we construct partial isometry operators and complete set of orthogonal projectors…

Self-consuming generative models have received significant attention over the last few years. In this paper, we study a self-consuming generative model with heterogeneous preferences that is a generalization of the model in Ferbach et al.…

Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…

A novel framework for consensus clustering is presented which has the ability to determine both the number of clusters and a final solution using multiple algorithms. A consensus similarity matrix is formed from an ensemble using multiple…