Percolation transition and distribution of connected components in generalized random network ensembles

In this work, we study the percolation transition and large deviation properties of generalized canonical network ensembles. This new type of random networks might have a very rich complex structure, including high heterogeneous degree sequences, non-trivial community structure or specific spatial dependence of the link probability for networks embedded in a metric space. We find the cluster distribution of the networks in these ensembles by mapping the problem to a fully connected Potts model with heterogeneous couplings. We show that the nature of the Potts model phase transition, linked to the birth of a giant component, has a crossover from second to first order when the number of critical colors $q_c = 2$ in all the networks under study. These results shed light on the properties of dynamical processes defined on these network ensembles.Comment: 27 pages, 15 figure

Supercondutor-Insulator Transition on Annealed Complex Networks

Cuprates show multiphase complexity that has hindered physicists search for the mechanism of high T_c for many years. A fingerprint of electronic scale invariance has been reported recently by Fratini et al. by detecting the structural scale invariance of dopants using scanning micro x-ray diffraction. In order to shed light on critical phenomena on these materials, here we propose a stylized model capturing the essential characteristics of the superconducting-isulator transition of a highly dynamical, heterogenous granular material: the Disordered Quantum Tranverse Ising Model (DQTIM) on Annealed Complex Network. We show that when the networks encode for high heterogeneity of the expected degrees described by a power law distribution, the critical temperature for the onset of the supercoducting phase diverges to infinity as the power-law exponent \gamma of the expected degree distribution is less than 3, i.e. \gamma<3. Moreover we investigate the case in which the critical state of the electronic background is triggered by an external parameter g that determines an exponential cutoff in the power law expected degree distribution characterized by an exponent \gamma. We find that for g=g_c the critical temperature for the superconduting-insulator transition has a maximum is \gamma>3 and diverges if \gamma<3.Comment: 4 pages, 2 figure

An experimental study on micro-milling of a medical grade Co-Cr-Mo alloy produced by selective laser melting

Cobalt-chromium-molybdenum (Co-Cr-Mo) alloys are very promising materials, in particular, in the biomedical field where their unique properties of biocompatibility and wear resistance can be exploited for surgery applications, prostheses, and many other medical devices. While Additive Manufacturing is a key technology in this field, micro-milling can be used for the creation of micro-scale details on the printed parts, not obtainable with Additive Manufacturing techniques. In particular, there is a lack of scientific research in the field of the fundamental material removal mechanisms involving micro-milling of Co-Cr-Mo alloys. Therefore, this paper presents a micro-milling characterization of Co-Cr-Mo samples produced by Additive Manufacturing with the Selective Laser Melting (SLM) technique. In particular, microchannels with different depths were made in order to evaluate the material behavior, including the chip formation mechanism, in micro-milling. In addition, the resulting surface roughness (Ra and Sa) and hardness were analyzed. Finally, the cutting forces were acquired and analyzed in order to ascertain the minimum uncut chip thickness for the material. The results of the characterization studies can be used as a basis for the identification of a machining window for micro-milling of biomedical grade cobalt-chromium-molybdenum (Co-Cr-Mo) alloys

Dirac synchronization is rhythmic and explosive

G.B. acknowledges funding from the Alan Turing Institute and from Royal Society IEC \NSFC\191147. J.J.T. acknowledges financial support from the Consejería de Transformación Económica, Industria, Conocimiento y Universidades, Junta de Andalucía and European Regional Development Funds, Ref. P20_00173. This work is also part of the Project of I+D+i Ref. PID2020-113681GB-I00, financed by MICIN/AEI/10.13039/ 501100011033 and FEDER “A way to make Europe". This research utilized Queen Mary’s Apocrita HPC facility, supported by QMUL Research-IT. https://doi.org/10.5281/zenodo. 438045.Topological signals defined on nodes, links and higher dimensional simplices define the dynamical state of a network or of a simplicial complex. As such, topological signals are attracting increasing attention in network theory, dynamical systems, signal processing and machine learning. Topological signals defined on the nodes are typically studied in network dynamics, while topological signals defined on links are much less explored. Here we investigate Dirac synchronization, describing locally coupled topological signals defined on the nodes and on the links of a network, and treated using the topological Dirac operator. The dynamics of signals defined on the nodes is affected by a phase lag depending on the dynamical state of nearby links and vice versa. We show that Dirac synchronization on a fully connected network is explosive with a hysteresis loop characterized by a discontinuous forward transition and a continuous backward transition. The analytical investigation of the phase diagram provides a theoretical understanding of this topological explosive synchronization. The model also displays an exotic coherent synchronized phase, also called rhythmic phase, characterized by non-stationary order parameters which can shed light on topological mechanisms for the emergence of brain rhythms.Alan Turing Institute and from Royal Society IEC \NSFC\191147. J.J.TConsejería de Transformación Económica, Industria, Conocimiento y Universidades, Junta de Andalucía and European Regional Development Funds, Ref. P20_00173Project of I+D+i Ref. PID2020-113681GB-I00, financed by MICIN/AEI/10.13039/ 501100011033 and FEDER “A way to make Europe"QMUL Research-I

Dirac synchronization is rhythmic and explosive

G.B. acknowledges funding from the Alan Turing Institute and from Royal Society IEC \NSFC\191147. J.J.T. acknowledges financial support from the Consejería de Transformación Económica, Industria, Conocimiento y Universidades, Junta de Andalucía and European Regional Development Funds, Ref. P20_00173. This work is also part of the Project of I+D+i Ref. PID2020-113681GB-I00, financed by MICIN/AEI/10.13039/ 501100011033 and FEDER “A way to make Europe". This research utilized Queen Mary’s Apocrita HPC facility, supported by QMUL Research-IT. https://doi.org/10.5281/zenodo. 438045.Topological signals defined on nodes, links and higher dimensional simplices define the dynamical state of a network or of a simplicial complex. As such, topological signals are attracting increasing attention in network theory, dynamical systems, signal processing and machine learning. Topological signals defined on the nodes are typically studied in network dynamics, while topological signals defined on links are much less explored. Here we investigate Dirac synchronization, describing locally coupled topological signals defined on the nodes and on the links of a network, and treated using the topological Dirac operator. The dynamics of signals defined on the nodes is affected by a phase lag depending on the dynamical state of nearby links and vice versa. We show that Dirac synchronization on a fully connected network is explosive with a hysteresis loop characterized by a discontinuous forward transition and a continuous backward transition. The analytical investigation of the phase diagram provides a theoretical understanding of this topological explosive synchronization. The model also displays an exotic coherent synchronized phase, also called rhythmic phase, characterized by non-stationary order parameters which can shed light on topological mechanisms for the emergence of brain rhythms.Alan Turing Institute and from Royal Society IEC \NSFC\191147. J.J.TConsejería de Transformación Económica, Industria, Conocimiento y Universidades, Junta de Andalucía and European Regional Development Funds, Ref. P20_00173Project of I+D+i Ref. PID2020-113681GB-I00, financed by MICIN/AEI/10.13039/ 501100011033 and FEDER “A way to make Europe"QMUL Research-I

Dynamical and bursty interactions in social networks

We present a modeling framework for dynamical and bursty contact networks made of agents in social interaction. We consider agents' behavior at short time scales, in which the contact network is formed by disconnected cliques of different sizes. At each time a random agent can make a transition from being isolated to being part of a group, or vice-versa. Different distributions of contact times and inter-contact times between individuals are obtained by considering transition probabilities with memory effects, i.e. the transition probabilities for each agent depend both on its state (isolated or interacting) and on the time elapsed since the last change of state. The model lends itself to analytical and numerical investigations. The modeling framework can be easily extended, and paves the way for systematic investigations of dynamical processes occurring on rapidly evolving dynamical networks, such as the propagation of an information, or spreading of diseases

Geometry, Topology and Simplicial Synchronization

Simplicial synchronization reveals the role that topology and geometry have in determining the dynamical properties of simplicial complexes. Simplicial network geometry and topology are naturally encoded in the spectral properties of the graph Laplacian and of the higher-order Laplacians of simplicial complexes. Here we show how the geometry of simplicial complexes induces spectral dimensions of the simplicial complex Laplacians that are responsible for changing the phase diagram of the Kuramoto model. In particular, simplicial complexes displaying a non-trivial simplicial network geometry cannot sustain a synchronized state in the infinite network limit if their spectral dimension is smaller or equal to four. This theoretical result is here verified on the Network Geometry with Flavor simplicial complex generative model displaying emergent hyperbolic geometry. On its turn simplicial topology is shown to determine the dynamical properties of the higher- order Kuramoto model. The higher-order Kuramoto model describes synchronization of topological signals, i.e. phases not only associated to the nodes of a simplicial complexes but associated also to higher-order simplices, including links, triangles and so on

Growing Cayley trees described by Fermi distribution

We introduce a model for growing Cayley trees with thermal noise. The evolution of these hierarchical networks reduces to the Eden model and the Invasion Percolation model in the limit $T\to 0$, $T\to \infty$ respectively. We show that the distribution of the bond strengths (energies) is described by the Fermi statistics. We discuss the relation of the present results with the scale-free networks described by Bose statistics

Statistical Mechanics of the Chinese Restaurant Process: lack of self-averaging, anomalous finite-size effects and condensation

The Pitman-Yor, or Chinese Restaurant Process, is a stochastic process that generates distributions following a power-law with exponents lower than two, as found in a numerous physical, biological, technological and social systems. We discuss its rich behavior with the tools and viewpoint of statistical mechanics. We show that this process invariably gives rise to a condensation, i.e. a distribution dominated by a finite number of classes. We also evaluate thoroughly the finite-size effects, finding that the lack of stationary state and self-averaging of the process creates realization-dependent cutoffs and behavior of the distributions with no equivalent in other statistical mechanical models.Comment: (5pages, 1 figure