# Timoteo CarlettiUniversity of Namur | FUNDP · Department of Mathematics

Timoteo Carletti

Full Professor

## About

210

Publications

29,084

Reads

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1,889

Citations

Introduction

Timoteo Carletti currently works at the Department of Mathematics, University of Namur. Timoteo does research in Applied Mathematics, Dynamical Systems, Complex Networks and their application.

Additional affiliations

September 2011 - present

January 2008 - present

**Università degli Studi di Firenze**

September 2007 - August 2011

## Publications

Publications (210)

The study of reaction-diffusion systems on networks is of paramount relevance for the understanding of nonlinear processes in systems where the topology is intrinsically discrete, such as the brain. Until now reaction-diffusion systems have been studied only when species are defined on the nodes of a network. However, in a number of real systems in...

Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing patterns have been thoroughly investigated on continuous support and on networks, only a few attempts have been mad...

We present a general framework that enables one to model high-order interactions among entangled dynamical systems, via hypergraphs. Several relevant processes can be ideally traced back to the proposed scheme. We shall here solely elaborate on the conditions that seed the spontaneous emergence of patterns, spatially heterogeneous solutions resulti...

To connect structure, dynamics and function in systems with multibody interactions, network scientists model random walks on hypergraphs and identify communities that confine the walks for a long time. The two flow-based community-detection methods Markov stability and the map equation identify such communities based on different principles and sea...

Non-reciprocal interactions play a crucial role in many social and biological complex systems. While directionality has been thoroughly accounted for in networks with pairwise interactions, its effects in systems with higher-order interactions have not yet been explored as deserved. Here, we introduce the concept of M-directed hypergraphs, a genera...

A novel strategy to automated classification is introduced which exploits a fully trained dynamical system to steer items belonging to different categories toward distinct asymptotic attractors. These latter are incorporated into the model by taking advantage of the spectral decomposition of the operator that rules the linear evolution across the p...

We study the problem of existence of harmonic solutions for some generalisations
of the periodically perturbed Liénard equation, where the damping function depends
both on the position and the velocity. In the associated phase-space this corresponds
to a term of the form f (x, y) instead of the standard dependence on x alone. We
introduce suitable...

We reply to the recent note "Comment on Synchronization dynamics in non-normal networks: the trade-off for optimality" showing that the authors base their claims mainly on general theoretical arguments that do not necessarily invalidate the adequacy of our previous study. In particular, they do not specifically tackle the correctness of our analysi...

Lagrangian Descriptors (LDs) are scalar quantities able to reveal separatrices, manifolds of hyperbolic saddles, and chaotic seas of dynamical systems. They rely on computing arc-length of trajectories over a calibrated time-window. Herein we introduce and exploit an intrinsic geometrical parametrisation of LDs, free of the time variable, for 1 deg...

Complex interactions are at the root of the population dynamics of many natural systems, particularly for being responsible for the allocation of species and individuals across apposite ecological niches. On the other side, the randomness that unavoidably characterises complex systems has increasingly challenged the niche paradigm providing alterna...

Deep neural networks can be trained in reciprocal space by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues while freezing the eigenvectors yields a substantial compression of the parameter space. This latter scales by definition with the number of computing neurons. The classifica...

We study a process of pattern formation for a model of species anchored to the nodes of a network, where local reactions take place, and that experience non-reciprocal long-range interactions. We show that the system exhibits a stable homogeneous equilibrium whenever only local interactions are considered; we prove that such equilibrium can turn un...

We hereby develop the theory of Turing instability for reaction–diffusion systems defined on complex networks assuming finite propagation. Extending to networked systems the framework introduced by Cattaneo in the 40s, we remove the unphysical assumption of infinite propagation velocity holding for reaction–diffusion systems, thus allowing to propo...

Cooperative co-evolution is recognized as an effective approach for solving large-scale optimization problems. It breaks down the problem dimensionality by splitting a large-scale problem into ones focusing on a smaller number of variables. This approach is successful when the studied problem is decomposable. However, many practical optimization pr...

Object transport by a single robot or by a swarm of robots can be considered a very challenging scenario for odometry since wheel slippage caused by pushing forces exerted on static objects and/or by relatively frequent collisions with other robots (for the cooperative transport case) tend to undermine the precision of the position and orientation...

Deep neural networks can be trained in reciprocal space, by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues, while freezing the eigenvectors, yields a substantial compression of the parameter space. This latter scales by definition with the number of computing neurons. The classif...

To connect structure, dynamics and function in systems with multibody interactions, network scientists model random walks on hypergraphs and identify communities that confine the walks for a long time. The two flow-based community-detection methods Markov stability and the map equation identify such communities based on different principles and sea...

Purpose
Ultrasound-guided fine-needle aspiration is the most sensitive investigation procedure in the evaluation of patients with thyroid nodules; however, despite the level of achieved precision, it is still impossible to preoperatively discriminate between follicular adenomas and carcinomas. Thus, no current detection tool of thyroid nodule has b...

We hereby develop the theory of Turing instability for relativistic reaction-diffusion systems defined on complex networks. Extending the framework introduced by Cattaneo in the 40's, we remove the unphysical assumption of infinite propagation velocity holding for reaction-diffusion systems, reducing thus the gap between theory and experiments. We...

We present a general framework that enables one to model high-order interaction among entangled dynamical systems, via hypergraphs. Several relevant processes can be ideally traced back to the proposed scheme. We shall here solely elaborate on the conditions that seed the spontaneous emergence of patterns, spatially heterogeneous solutions resultin...

Synthetic populations are tools widely spread in the agent-based community for representing a baseline population of interest whose dynamics and evolution will be simulated and studied. The dynamic evolution of the synthetic population has been typically performed using a discrete and fixed time step. A continuous approach based on the Gillespie al...

Deep neural networks are usually trained in the space of the nodes, by adjusting the weights of existing links via suitable optimization protocols. We here propose a radically new approach which anchors the learning process to reciprocal space. Specifically, the training acts on the spectral domain and seeks to modify the eigenvalues and eigenvecto...

Synchronization is an important behavior that characterizes many natural and human made systems that are composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention a few. Such systems synchronize because of the complex set of coupling they exhibit, with the latter...

Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention a few. Such systems synchronize because of the complex set of coupling they exhibit, the latter being modeled...

We propose a one parameter family of random walk processes on hypergraphs, where a parameter biases the dynamics of the walker towards hyperedges of low or high cardinality. We show that for each value of the parameter the resulting process defines its own hypergraph projection on a weighted network. We then explore the differences between them by...

Geometry, calculus and in particular integrals, are too often seen by young students as technical tools with no link to the reality. This fact generates into the students a loss of interest with a consequent removal of motivation in the study of such topics and more widely in pursuing scientific curricula [1-5]. With this note we put to the fore a...

Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider a general class of dynamical systems anchored on hypergraphs. Hyperedges of arbitrary size ideally encircle in...

Random walks are the simplest way to explore or search a graph and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world. For instance, they have been used to identify the modules of a given network, its most central nodes and paths, or to determine the typical times to re...

A general framework for the generation of long wavelength patterns in multi-cellular (discrete) systems is proposed, which extends beyond conventional reaction-diffusion (continuum) paradigms. The standard partial differential equations of reaction-diffusion framework can be considered as a mean-field like ansatz which corresponds, in the biologica...

Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the modules of a given network, its most central nodes and paths, or to determine the typical times to reach a ta...

This collection of essays offers an analysis of issues that biological systems raise from a network perspective. It brings together scholars from biology, neuroscience, process philosophy, computer science and mathematics to explore this theme. As a whole, the contributors highlight the depth of the nexial dimension of biological systems, from the...

Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider a general class of dynamical systems anchored on hypergraphs. Hyperedges of arbitrary size ideally encircle in...

When the novel coronavirus disease SARS-CoV2 (COVID-19) was officially declared a pandemic by the WHO in March 2020, the scientific community had already braced up in the effort of making sense of the fast-growing wealth of data gathered by national authorities all over the world. However, despite the diversity of novel theoretical approaches and t...

Deep neural networks are usually trained in the space of the nodes, by adjusting the weights of existing links via suitable optimization protocols. We here propose a radically new approach which anchors the learning process to reciprocal space. Specifically, the training acts on the spectral domain and seeks to modify the eigenvectors and eigenvalu...

When the novel coronavirus disease SARS-CoV2 (COVID-19) was officially declared a pandemic by the WHO in March 2020, the scientific community had already braced up in the effort of making sense of the fast-growing wealth of data gathered by national authorities all over the world. However, despite the diversity of novel theoretical approaches and t...

When the novel coronavirus disease SARS-CoV2 (COVID-19) was officially declared a pandemic by the WHO in March 2020, the scientific community had already braced up in the effort of making sense of the fast-growing wealth of data gathered by national authorities all over the world. However, despite the diversity of novel theoretical approaches and t...

Complex real-world phenomena are often modeled as dynamical systems on networks. In many cases of interest, the spectrum of the underlying graph Laplacian sets the system stability and ultimately shapes the matter or information flow. This motivates devising suitable strategies, with rigorous mathematical foundation, to generate Laplacian that poss...

A class of systems is considered, where immobile species associated to distinct patches, the nodes of a network, interact both locally and at a long-range, as specified by an (interaction) adjacency matrix. Non local interactions are treated in a mean-field setting which enables the system to reach a homogeneous consensus state, either constant or...

In the past 20 years network science has proven its strength in modeling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Nevertheless, in many relevant cases, interactions are not pairwise but involve larger sets of nodes at a time. These systems are thus better described in the framework of hypergraph...

Reduction of a two-component FitzHugh-Nagumo model to a single-component model with long-range connection is considered on general networks. The reduced model describes a single chemical species reacting on the nodes and diffusing across the links with weighted long-range connections, which can be interpreted as a class of networked dynamical syste...

We study the problem of existence of periodic solutions for some generalisations of the relativistic Liénard equation
\begin{equation*}
\frac{d}{dt}\frac{\dot{x}}{\sqrt{1-\dot{x}^{2}}}+\hat{f}(x,\dot{x})\dot{x}+g(x)=0 ,
\end{equation*}
and the prescribed curvature Liénard equation
\begin{equation*}
\frac{d}{dt}\frac{\dot{x}}{\sqrt{1+\dot{x}^{2}}}+...

In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but involve larger sets of nodes, at a time. These systems are thus better described in the framework of hypergraphs,...

Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs, where classical methods would become computationally intractable. Through an approximation procedure, the sta...

Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the co-existence of different timescales in the system. Here, we introduce random walks on general stochastic temporal netwo...

Synthetic populations are tools widely spread in the agent-based community for representing a baseline population of interest whose dynamics and evolution will be simulated and studied. The dynamic evolution of the synthetic population has been typically performed using a discrete and fixed time step. A continuous approach based on the Gillespie al...

Reduction of a two-component FitzHugh-Nagumo model to a single-component model with long-range connection is considered on general networks. The reduced model describes a single chemical species reacting on the nodes and diffusing across the links of a multigraph with weighted long-range connections that naturally emerge from the adiabatic eliminat...

A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network, two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear lattice, noise gets amplified via a self-consistent process, which we trace back to the degenerate spectrum of...

Several mechanisms have been proposed to explain the spontaneous generation of self-organised patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the system under scrutiny displays a homogeneous equilibrium, which is destabilised via a symmetry breaking instabi...

Self-organization, the ability of a system of microscopically interacting entities to shape macroscopically ordered structures, is ubiquitous in Nature. Spatio-temporal patterns are abundantly observed in a large plethora of applications, encompassing different fields and scales. Examples of emerging patterns are the spots and stripes on the coat o...

A procedure is developed and tested to recover the distribution of connectivity of an a priori unknown network, by sampling the dynamics of an ensemble made of reactive walkers. The relative weight between reaction and relocation is gauged by a scalar control parameter, which can be adjusted at will. Different equilibria are attained by the system,...