Riccardo Muolo

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• Doctor of Philosophy
• PostDoc Position at Institute of Science Tokyo

Nature is a blossoming of regular structures, signature of self-organization of the underlying microscopic interacting agents. Turing theory of pattern formation is one of the most studied mechanisms to address such phenomena and has been applied to a widespread gallery of disciplines. Turing himself used a spatial discretization of the hosting sup...

Understanding and controlling the mechanisms behind synchronization phenomena is of paramount importance in nonlinear science. In particular, chimera states, patterns in which order and disorder coexist simultaneously , continue to puzzle scholars, due to their elusive nature. Recently, it has been shown that higher-order interactions greatly promo...

We analyze the simplest model of identical coupled phase oscillators subject to two-body and three-body interactions with permutation symmetry and phase lags. This model is derived from an ensemble of weakly coupled nonlinear oscillators by phase reduction, where the first and second harmonic interactions with phase lags naturally appear. Our study...

Synchronization is a fundamental dynamical state of interacting oscillators, observed, e.g., in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a network display the same dynamics has received great attention in network theory. Here we propose and investi...

Phase reduction is a powerful technique in the study of nonlinear oscillatory systems. Under certain assumptions, it allows us to describe each multidimensional oscillator by a single phase variable, giving rise to simple phase models such as the Kuramoto model. Classically, the method has been applied in the case where the interactions are only pa...

We hereby develop the theory of Turing instability for reaction-diffusion systems defined on-directed hypergraphs, the latter being a generalization of hypergraphs where nodes forming hyperedges can be shared into two disjoint sets, the head nodes and the tail nodes. This framework encodes thus for a privileged direction for the reaction to occur:...

Synchronization is a fundamental dynamical state of interacting oscillators, observed in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a network display the same dynamics as received great attention in network theory. Here we propose and investigate Glo...

In this opinion article, we gathered some reflections and practical tips on what Early Stage Researchers do against inequalities in academia. This is the longer version of an opinion paper that was recently published on the website of the International Society for Optics and Photonics (spie.org), containing more details and suggestions.

From the outside, scientific research might seem like a realm where everyone is assessed solely based on their merits, free from discrimination resulting from inequalities. From the inside, however, we notice that this is not the case. Discrimination and inequality exist in academia because it is part of larger society where these harms are intrins...

We hereby develop the theory of Turing instability for reaction-diffusion systems defined on m-directed hypergraphs, the latter being generalization of hypergraphs where nodes forming hyperedges can be shared into two disjoint sets, the head nodes and the tail nodes. This framework encodes thus for a privileged direction for the reaction to occur:...

Higher-order networks are able to capture the many-body interactions present in complex systems and to unveil fundamental phenomena revealing the rich interplay between topology, geometry, and dynamics. Simplicial complexes are higher-order networks that encode higher-order topology and dynamics of complex systems. Specifically, simplicial complexe...

Nature is a blossoming of regular structures, signature of self-organization of the underlying microscopic interacting agents. Turing theory of pattern formation is one of the most studied mechanisms to address such phenomena and has been applied to a widespread gallery of disciplines. Turing himself used a spatial discretiza-tion of the hosting su...

Higher-order networks are able to capture the many-body interactions present in complex systems and to unveil new fundamental phenomena revealing the rich interplay between topology, geometry, and dynamics. Simplicial complexes are higher-order networks that encode higher-order topology and dynamics of complex systems. Specifically, simplicial comp...

Chimera states are dynamical states where regions of synchronous trajectories coexist with incoherent ones. A significant amount of research has been devoted to studying chimera states in systems of identical oscillators, nonlocally coupled through pairwise interactions. Nevertheless, there is increasing evidence, also supported by available data,...

Topological signals are dynamical variables not only defined on nodes but also on links of a network that are gaining significant attention in non-linear dynamics and topology and have important applications in brain dynamics. Here we show that topological signals on nodes and links of a network can generate dynamical patterns when coupled together...

Quantum measurement is one of the most fascinating and discussed phenomena in quantum physics, due to the impact on the system of the measurement action and the resulting interpretation issues. Scholars proposed weak measurements to amplify measured signals by exploiting a quantity called a weak value, but also to overcome philosophical difficultie...

Chimera states are dynamical states where regions of synchronous trajectories coexist with incoherent ones. A significant amount of research has been devoted to study chimera states in systems of identical oscillators, non-locally coupled through pairwise interactions. Nevertheless, there is an increasing evidence, also supported by available data,...

Topological signals are dynamical variables not only defined on nodes but also on links of a network that are gaining significant attention in non-linear dynamics and topology and have important applications in brain dynamics. Here we show that topological signals on nodes and links of a network can generate dynamical patterns when coupled together...

Self-organization in natural and engineered systems causes the emergence of ordered spatio-temporal motifs. In the presence of diffusive species, Turing theory has been widely used to understand the formation of such patterns on continuous domains obtained from a diffusion-driven instability mechanism. The theory was later extended to networked sys...

We analyze the simplest model of identical coupled phase oscillators subject to two-body and three-body interactions with permutation symmetry. This model is derived from an ensemble of weakly coupled nonlinear oscillators by phase reduction. Our study indicates that higher-order interactions induce anomalous transitions to synchrony. Unlike the co...

The classical Routh-Hurwitz criterion is one of the most popular methods to study the stability of polynomials with real coefficients, given its simplicity and ductility. However, when moving to polynomials with complex coefficients, a generalization exists but it is rather cumbersome and not as easy to apply. In this paper, we make such generaliza...

The classical Routh-Hurwitz criterion is one of the most popular methods to study the stability of polynomials with real coefficients, given its simplicity and ductility. However, when moving to polynomials with complex coefficients, a generalization exists but it is rather cumbersome and not as easy to apply. In this paper, we make such generaliza...

Quantum measurement is one of the most fascinating and discussed phenomena in quantum physics, due to the impact on the system of the measurement action and the resulting interpretation issues. Scholars proposed weak measurements to amplify measured signals by exploiting a quantity called a weak value, but also to overcome philosophical difficultie...

The emergence of order in nature manifests in different phenomena, with synchronization being one of the most representative examples. Understanding the role played by the interactions between the constituting parts of a complex system in synchronization has become a pivotal research question bridging network science and dynamical systems. Particul...

Self-organization in natural and engineered systems causes the emergence of ordered spatio-temporal motifs. In presence of diffusive species, Turing theory has been widely used to understand the formation of such patterns obtained from a diffusion-driven instability mechanism. The theory was later extended to networked systems, where the reaction p...

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...

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 i...

We study a process of pattern formation for a generic model of species anchored to the nodes of a network where local reactions take place, and that experience non-reciprocal non-local long-range interactions, encoded by the network directed links. By assuming the system to exhibit a stable homogeneous equilibrium whenever only local interactions a...

The world population is almost equally split between men and women 1 and the same statistics stands for Europe. Yet, when a girl enters a European Physics class, the teacher or the lecturer is most likely a man, probably white and in his middle age or older. out by women. Examples abound: Chien-Shiung Wu, who experimentally demonstrated that parity...

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 gener...

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...

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...

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...

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...

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...

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...

Living cells can express different metabolic pathways that support growth. The criteria that determine which pathways are selected in which environment remain unclear. One recurrent selection is overflow metabolism: the simultaneous usage of an ATP-efficient and -inefficient pathway, shown for example in Escherichia coli, Saccharomyces cerevisiae a...

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...

In each environment, living cells can express different metabolic pathways that support growth. The criteria that determine which pathways are selected remain unclear. One recurrent selection is overflow metabolism: the seemingly wasteful, simultaneous usage of an efficient and an inefficient pathway, shown for example in E. coli, S. cerevisiae and...

Several mechanisms have been proposed to explain the spontaneous generation of self-organized 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 destabilized via a symmetry breaking instabi...