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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 Global Topological Dirac Synchronization on higher-order networks such as cell and simplicial complexes. This is a state where oscillators associated to simplices and cells of arbitrary dimension, coupled by the Topological Dirac operator, operate at unison. By combining algebraic topology with non-linear dynamics and machine learning, we derive the topological conditions under which this state exists and the dynamical conditions under which it is stable. We provide evidence of 1-dimensional simplicial complexes (networks) and 2-dimensional simplicial and cell complexes where Global Topological Dirac Synchronization can be observed. Our results point out that Global Topological Dirac Synchronization is a possible dynamical state of simplicial and cell complexes that occur only in some specific network topologies and geometries, the latter ones being determined by the weights of the higher-order networks

The spin structure functions of the proton and the deuteron were measured during the EG4 experiment at Jefferson Lab in 2006. Data were collected for longitudinally polarized electron scattering off longitudinally polarized NH$_3$ and ND$_3$ targets, for $Q^2$ values as small as 0.012 and 0.02 GeV$^2$, respectively, using the CEBAF Large Acceptance Spectrometer (CLAS). This is the archival paper of the EG4 experiment that summaries the previously reported results of the polarized structure functions $g_1$, $A_1F_1$, and their moments $\overline \Gamma_1$, $\overline \gamma_0$, and $\overline I_{TT}$, for both the proton and the deuteron. In addition, we report on new results on the neutron $g_1$ extracted by combining proton and deuteron data and correcting for Fermi smearing, and on the neutron moments $\overline \Gamma_1$, $\overline \gamma_0$, and $\overline I_{TT}$ formed directly from those of the proton and the deuteron. Our data are in good agreement with the Gerasimov-Drell-Hearn sum rule for the proton, deuteron, and neutron. Furthermore, the isovector combination was formed for $g_1$ and the Bjorken integral $\overline \Gamma_1^{p-n}$, and compared to available theoretical predictions. All of our results provide for the first time extensive tests of spin observable predictions from chiral effective field theory ($\chi$EFT) in a $Q^2$ range commensurate with the pion mass. They motivate further improvement in $\chi$EFT calculations from other approaches such as the lattice gauge method., Comment: 33 pages. 26 figures. Data table provided in supplementary material (30 pages)

Gravity is derived from an entropic action coupling matter fields with geometry. The fundamental idea is to relate the metric of Lorentzian spacetime to a density matrix and to describe the matter fields topologically, according to a Dirac-K\"ahler description, as the direct sum of a zero-form, a one-form and a two-form. While the geometry of spacetime is defined by its metric, the matter fields can be used to define an alternative metric, the metric induced by the matter fields, which geometrically describes the interplay between spacetime and matter. The proposed entropic action is the quantum relative entropy between the metric of spacetime and the metric induced by the matter fields. The modified Einstein equations obtained from this action reduce to the Einstein equations with zero cosmological constant in the regime of low coupling. By introducing the G-field, which acts as a set of Lagrangian multipliers, the proposed entropic action reduces to a dressed Einstein-Hilbert action with an emergent small and positive cosmological constant only dependent on the G-field. The obtained equations of modified gravity remains second order in the metric and in the G-field. A canonical quantization of this field theory could bring new insights into quantum gravity while further research might clarify the role that the G-field could have for dark matter., Comment: (14 pages, 1 figure)

Frequency-agile lasers that can simultaneously feature low noise characteristics as well as fast mode hop-free frequency tuning are keystone components for applications ranging from frequency modulated continuous wave (FMCW) LiDAR, to coherent optical communication and gas sensing. The hybrid integration of III-V gain media with low-loss photonic integrated circuits (PICs) has recently enabled integrated lasers with faster tuning and lower phase noise than the best legacy systems, including fiber lasers. In addition, lithium niobate on insulator (LNOI) PICs have enabled to exploit the Pockels effect to demonstrate self-injection locked hybrid lasers with tuning rates reaching peta-hertz per second. However, Pockels-tunable laser archetypes relying on high-Q optical microresonators have thus far only achieved limited output powers, are difficult to operate and stabilize due to the dynamics of self-injection locking, and require many analog control parameters. Here, we overcome this challenge by leveraging an extended distributed Bragg reflector (E-DBR) architecture to demonstrate a simple and turn-key operable frequency-agile Pockels laser that can be controlled with single analog operation and modulation inputs. Our laser supports a continuous mode hop-free tuning range of over 10 GHz with good linearity and flat actuation bandwidth up to 10 MHz, while achieving over 15 mW in-fiber output power at 1545 nm and kHz-level intrinsic linewidth, a combination unmet by legacy bulk lasers. This hybrid laser design combines an inexpensive reflective semiconductor optical amplifier (RSOA) with an electro-optic DBR PIC manufactured at wafer-scale on a LNOI platform. We showcase the performance and flexibility of this laser in proof-of-concept coherent optical ranging (FMCW LiDAR) demonstration, achieving a 4 cm distance resolution and in a hydrogen cyanide spectroscopy experiment., Comment: 10 pages, 5 figures

While the search of high Tc superconductivity was driven mostly by trial and error methodology searching for novel materials, here we provide a quasi-first-principle quantum theory for engineering superconductivity in artificial high-Tc superlattices (AHTS) with period d, ranging from 5.28 down to 3 nanometers, made of superconducting quantum wells of variable thickness L. An important feature of our quantum design is the key role of the interface internal electric field giving Rashba spin-orbit coupling (SOC) in the nanoscale quantum superconducting building blocks. By tuning the geometrical conformational parameter L/d around its magic ratio 2/3 we predict the superconducting dome of Tc versus doping characteristic of unconventional superconductors. Quantum size effects, controlled by L/d, change the energy width and splitting of two quantum subbands formed by the electronic space charge confined in superconducting nano-layers. The theoretical superconducting dome Tc versus charge density controlled by the Fano-Feshbach resonance between two superconducting gaps has been able to predict experimental results on cuprate AHTS by tuning the geometry of superlattices of quantum wells made of superconducting layers (S) of thickness L of modulation doped stoichiometric Mott insulator La2CuO4 with no chemical dopants, with interface space charge confined within normal metal (N) overdoped cuprate layers, Comment: 12 pages, 12 figures. arXiv admin note: text overlap with arXiv:2211.11547

Recently, the quest for high-Tc superconductivity has evolved from the trial-and-error methodology to the growth of nanostructured artificial high-Tc superlattices (AHTS) with tailor-made superconducting functional properties by quantum design. Superlattices are composed of nanoscale superconducting units of modulation doped Mott insulator La2CuO4 with thickness L intercalated by metallic overdoped La1.55Sr0.45CuO4 and period d. Quantum design based on the multi-gap Bogoliubov theory including spin-orbit coupling (SOC). has been employed for prediction of the amplification of the critical temperature as a function of the conformational parameter L/d. At the top of the superconducting dome, at the magic ratio L/d=2/3, the heterostructures are tuned at the Fano-Feshbach resonance and the normal phase exhibits the Planckian T-linear resistivity. Here, we report experimental evidence that the Kondo proximity effect competes with the Fano-Feshbach resonance suppressing Tc on both sides of the superconducting dome. The Kondo proximity effect is expected in electrical resistance of AHTS nanoscale heterostructures following a Kondo universal scaling obtained by numerical renormalization group theory. We show the vanishing Kondo temperature TK and Kondo scattering amplitude R0K at L/d=2/3, while TK and R0K increase on the underdoped (L/d>2/3) and overdoped (L/d<2/3) side of the superconducting dome., Comment: 11 pages, 3 figures

In this work, we propose a comprehensive theoretical framework combining percolation theory with nonlinear dynamics in order to study hypergraphs with a time-varying giant component. We consider in particular hypergraphs with higher-order triadic interactions that can upregulate or downregulate the hyperedges. Triadic interactions are a general type of signed regulatory interaction that occurs when a third node regulates the interaction between two other nodes. For example, in brain networks, the glia can facilitate or inhibit synaptic interactions between neurons. However, the regulatory interactions may not only occur between regulator nodes and pairwise interactions but also between regulator nodes and higher-order interactions (hyperedges), leading to higher-order triadic interactions. For instance, in biochemical reaction networks, the enzymes regulate the reactions involving multiple reactants. Here we propose and investigate higher-order triadic percolation on hypergraphs showing that the giant component can have a non-trivial dynamics. Specifically, we demonstrate that, under suitable conditions, the order parameter of this percolation problem, i.e., the fraction of nodes in the giant component, undergoes a route to chaos in the universality class of the logistic map. In hierarchical higher-order triadic percolation, we extend this paradigm in order to treat hierarchically nested triadic interactions demonstrating the non-trivial effect of their increased combinatorial complexity on the critical phenomena and the dynamical properties of the process. Finally, we consider other generalizations of the model studying the effect of considering interdependencies and node regulation instead of hyperedge regulation., Comment: 23 pages, 17 figures

Extended-range percolation is a robust percolation process that has relevance for quantum communication problems. In extended-range percolation nodes can be trusted or untrusted. Untrusted facilitator nodes are untrusted nodes that can still allow communication between trusted nodes if they lie on a path of distance at most R between two trusted nodes. In extended-range percolation the extended-range giant component (ERGC) includes trusted nodes connected by paths of trusted and untrusted facilitator nodes. Here, based on a message passing algorithm, we develop a general theory of extended-range percolation, valid for arbitrary values of R as long as the networks are locally tree-like. This general framework allows us to investigate the properties of extended-range percolation on interdependent multiplex networks. While the extended-range nature makes multiplex networks more robust, interdependency makes them more fragile. From the interplay between these two effects a rich phase diagram merges including discontinuous phase transitions and reentrant phases. The theoretical predictions are in excellent agreement with extensive Monte-Carlo simulations. The proposed exactly solvable model constitutes a fundamental reference for the study of models defined through properties of extended-range paths., Comment: 21 pages, 9 figures

Measuring Deeply Virtual Compton Scattering on the neutron is one of the necessary steps to understand the structure of the nucleon in terms of Generalized Parton Distributions (GPDs). Neutron targets play a complementary role to transversely polarized proton targets in the determination of the GPD $E$. This poorly known and poorly constrained GPD is essential to obtain the contribution of the quarks' angular momentum to the spin of the nucleon. DVCS on the neutron was measured for the first time selecting the exclusive final state by detecting the neutron, using the Jefferson Lab longitudinally polarized electron beam, with energies up to 10.6 GeV, and the CLAS12 detector. The extracted beam-spin asymmetries, combined with DVCS observables measured on the proton, allow a clean quark-flavor separation of the imaginary parts of the GPDs $H$ and $E$., Comment: 7 pages, 6 figures

The WHT Enhanced Area Velocity Explorer (WEAVE) is a new, massively multiplexing spectrograph. This new instrument will be exploited to obtain high S/N spectra of $\sim$25000 galaxies at intermediate redshifts for the WEAVE Stellar Population Survey (WEAVE-StePS). We test machine learning methods for retrieving the key physical parameters of galaxies from WEAVE-StePS-like spectra using both photometric and spectroscopic information at various S/Ns and redshifts. We simulated $\sim$105000 galaxy spectra assuming SFH with an exponentially declining star formation rate, covering a wide range of ages, stellar metallicities, sSFRs, and dust extinctions. We then evaluated the ability of the random forest and KNN algorithms to correctly predict such parameters assuming no measurement errors. We checked how much the predictive ability deteriorates for different S/Ns and redshifts, finding that both algorithms still accurately estimate the ages and metallicities with low bias. The dispersion varies from 0.08-0.16 dex for ages and 0.11-0.25 dex for metallicity, depending on the redshift and S/N. For dust attenuation, we find a similarly low bias and dispersion. For the sSFR, we find a very good constraining power for star-forming galaxies, log sSFR$\gtrsim$ -11, where the bias is $\sim$ 0.01 dex and the dispersion is $\sim$ 0.10 dex. For more quiescent galaxies, with log sSFR$\lesssim$ -11, we find a higher bias, 0.61-0.86 dex, and a higher dispersion, $\sim$ 0.4 dex, for different S/Ns and redshifts. Generally, we find that the RF outperforms the KNN. Finally, the retrieved sSFR was used to successfully classify galaxies as part of the blue cloud, green valley, or red sequence. We demonstrate that machine learning algorithms can accurately estimate the physical parameters of simulated galaxies even at relatively low S/N=10 per angstrom spectra with available ancillary photometric information., Comment: 19 pages, 10 + 2 figures, 4 tables, accepted in A&A

Galaxy clusters are located in the densest areas of the universe and are intricately connected to larger structures through the filamentary network of the Cosmic Web. In this scenario, matter flows from areas of lower density to higher density. As a result, the properties of galaxy clusters are deeply influenced by the filaments that are attached to them, which are quantified by a parameter known as connectivity. We explore the dependence of gas-traced filaments connected to galaxy clusters on the mass and dynamical state of the cluster. Moreover, we evaluate the effectiveness of the cosmic web extraction procedure from the gas density maps of simulated cluster regions. Using the DisPerSE cosmic web finder, we identify filamentary structures from 3D gas particle distribution in 324 simulated regions of $30 \, h^{-1}$ Mpc side from The Three Hundred hydrodynamical simulation at redshifts z=0, 1, and 2. We estimate the connectivity at various apertures for $\sim3000$ groups and clusters spanning a mass range from $10^{13} \, h^{-1} \, M_{\odot}$ to $10^{15} \, h^{-1} \, M_{\odot}$. Relationships between connectivity and cluster properties like radius, mass, dynamical state and hydrostatic mass bias are explored. We show that the connectivity is strongly correlated with the mass of galaxy clusters, with more massive clusters being on average more connected. This finding aligns with previous studies in literature, both from observational and simulated data sets. Additionally, we observe a dependence of the connectivity on the aperture at which it is estimated. We find that connectivity decreases with cosmic time, while no dependencies on the dynamical state and hydrostatic mass bias of the cluster are found. Lastly, we observe a significant agreement between the connectivity measured from gas-traced and mock-galaxies-traced filaments in the simulation., Comment: 12 pages, 11 figures Accepted for publication in A&A on 28/10/2024. Reproduced with permission from Astronomy & Astrophysics, copyright ESO

Complex systems often present higher-order interactions which require us to go beyond their description in terms of pairwise networks. Triadic interactions are a fundamental type of higher-order interaction that occurs when one node regulates the interaction between two other nodes. Triadic interactions are a fundamental type of higher-order networks, found in a large variety of biological systems, from neuron-glia interactions to gene-regulation and ecosystems. However, triadic interactions have been so far mostly neglected. In this article, we propose a theoretical principle to model and mine triadic interactions from node metadata, and we apply this framework to gene expression data finding new candidates for triadic interactions relevant for Acute Myeloid Leukemia. Our work reveals important aspects of higher-order triadic interactions often ignored, which can transform our understanding of complex systems and be applied to a large variety of systems ranging from biology to the climate.

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 complexes can sustain topological signals, i.e., dynamical variables not only defined on nodes of the network but also on their edges, triangles, and so on. Topological signals can undergo collective phenomena such as synchronization, however, only some higher-order network topologies can sustain global synchronization of topological signals. Here we consider global topological synchronization of topological signals on weighted simplicial complexes. We demonstrate that topological signals can globally synchronize on weighted simplicial complexes, even if they are odd-dimensional, e.g., edge signals, overcoming thus a limitation of the unweighted case. These results thus demonstrate that weighted simplicial complexes are more advantageous for observing these collective phenomena than their unweighted counterpart. In particular, we present two weighted simplicial complexes the Weighted Triangulated Torus and the Weighted Waffle. We completely characterize their higher-order spectral properties and we demonstrate that, under suitable conditions on their weights, they can sustain global synchronization of edge signals. Our results are interpreted geometrically by showing, among the other results, that in some cases edge weights can be associated with the lengths of the sides of curved simplices., Comment: 18 pages, 10 figures

We propose a theory for coupling matter fields with discrete geometry on higher-order networks, i.e. cell complexes. The key idea of the approach is to associate to a higher-order network the quantum entropy of its metric. Specifically we propose an action having two contributions. The first contribution is proportional to the logarithm of the volume associated to the higher-order network by the metric. In the vacuum this contribution determines the entropy of the geometry. The second contribution is the quantum relative entropy between the metric of the higher-order network and the metric induced by the matter and gauge fields. The induced metric is defined in terms of the topological spinors and the discrete Dirac operators. The topological spinors, defined on nodes, edges and higher-dimensional cells, encode for the matter fields. The discrete Dirac operators act on topological spinors, and depend on the metric of the higher-order network as well as on the gauge fields via a discrete version of the minimal substitution. We derive the coupled dynamical equations for the metric, the matter and the gauge fields, providing an information theory principle to obtain the field theory equations in discrete curved space., Comment: (33 pages, 1 figure)

Higher-order networks encode the many-body interactions existing in complex systems, such as the brain, protein complexes, and social interactions. Simplicial complexes are higher-order networks that allow a comprehensive investigation of the interplay between topology and dynamics. However, simplicial complexes have the limitation that they only capture undirected higher-order interactions while in real-world scenarios, often there is a need to introduce the direction of simplices, extending the popular notion of direction of edges. On graphs and networks the Magnetic Laplacian, a special case of Connection Laplacian, is becoming a popular operator to treat edge directionality. Here we tackle the challenge of treating directional simplicial complexes by formulating Higher-order Connection Laplacians taking into account the configurations induced by the simplices' directions. Specifically, we define all the Connection Laplacians of directed simplicial complexes of dimension two and we discuss the induced higher-order diffusion dynamics by considering instructive synthetic examples of simplicial complexes. The proposed higher-order diffusion processes can be adopted in real scenarios when we want to consider higher-order diffusion displaying non-trivial frustration effects due to conflicting directionalities of the incident simplices., Comment: 34 pages, 13 figures

In superconductivity, a surge of interests in enhancing $T_{\rm c}$ is ever mounting, where a recent focus is toward multi-band superconductivity. In $T_{\rm c}$ enhancements specific to two-band cases, especially around the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover considered here, we have to be careful about how quantum fluctuations affect the many-body states, i.e., particle-hole fluctuations suppressing the pairing for attractive interactions. Here we explore how to circumvent the suppression by examining multichannel pairing interactions in two-band systems. With the Gor'kov-Melik-Barkhudarov (GMB) formalism for particle-hole fluctuations in a continuous space, we look into the case of a deep dispersive band accompanied by an incipient heavy-mass (i.e., quasi-flat) band. We find that, while the GMB corrections usually suppress $T_{\rm c}$ significantly, this in fact competes with the enhanced pairing arising from the heavy band, with the trade-off leading to a peaked structure in $T_{\rm c}$ against the band-mass ratio when the heavy band is incipient. The system then plunges into a strong-coupling regime with the GMB screening vastly suppressed. This occurs prominently when the chemical potential approaches the bound state lurking just below the heavy band, which can be viewed as a Fano-Feshbach resonance, with its width governed by the pair-exchange interaction. The diagrammatic structure comprising particle-particle and particle-hole channels is heavily entangled, so that the emergent Fano-Feshbach resonance dominates all the channels, suggesting a universal feature in multiband superconductivity., Comment: 12 pages, 9 figures, Accepted version for Physical Review B

These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is flourishing proving an ideal mathematical and computational framework to capture the complexity of large interacting systems. Here we provide a comprehensive and timely review of the rising field of complex quantum networks. On one side, this subject is key to harness the potential of complex networks in order to provide design principles to boost and enhance quantum algorithms and quantum technologies. On the other side this subject can provide a new generation of quantum algorithms to infer significant complex network properties. The field features fundamental research questions as diverse as designing networks to shape Hamiltonians and their corresponding phase diagram, taming the complexity of many-body quantum systems with network theory, revealing how quantum physics and quantum algorithms can predict novel network properties and phase transitions, and studying the interplay between architecture, topology and performance in quantum communication networks. Our review covers all of these multifaceted aspects in a self-contained presentation aimed both at network-curious quantum physicists and at quantum-curious network theorists. We provide a framework that unifies the field of quantum complex networks along four main research lines: network-generalized, quantum-applied, quantum-generalized and quantum-enhanced. Finally we draw attention to the connections between these research lines, which can lead to new opportunities and new discoveries at the interface between quantum physics and network science., Comment: 94 pages + 25 pages of references, 26 figures. Updated to accepted version

Triadic interactions are higher-order interactions that occur when a set of nodes affects the interaction between two other nodes. Examples of triadic interactions are present in the brain when glia modulate the synaptic signals among neuron pairs or when interneuron axon-axonic synapses enable presynaptic inhibition and facilitation, and in ecosystems when one or more species can affect the interaction among two other species. On random graphs, triadic percolation has been recently shown to turn percolation into a fully-fledged dynamical process in which the size of the giant component undergoes a route to chaos. However, in many real cases, triadic interactions are local and occur on spatially embedded networks. Here we show that triadic interactions in spatial networks induce a very complex spatio-temporal modulation of the giant component which gives rise to triadic percolation patterns with significantly different topology. We classify the observed patterns (stripes, octopus, and small clusters) with topological data analysis and we assess their information content (entropy and complexity). Moreover, we illustrate the multistability of the dynamics of the triadic percolation patterns and we provide a comprehensive phase diagram of the model. These results open new perspectives in percolation as they demonstrate that in presence of spatial triadic interactions, the giant component can acquire a time-varying topology. Hence, this work provides a theoretical framework that can be applied to model realistic scenarios in which the giant component is time-dependent as in neuroscience., Comment: 59 pages, 11 figures

The interaction of a high-current $O$(100~\textmu A), medium energy $O$(10\,GeV) electron beam with a thick target $O$(1m) produces an overwhelming shower of standard matter particles in addition to hypothetical Light Dark Matter particles. While most of the radiation (gamma, electron/positron, and neutron) is contained in the thick target, deep penetrating particles (muons, neutrinos, and light dark matter particles) propagate over a long distance, producing high-intense secondary beams. Using sophisticated Monte Carlo simulations based on FLUKA and GEANT4, we explored the characteristics of secondary muons and neutrinos and (hypothetical) dark scalar particles produced by the interaction of Jefferson Lab 11 GeV intense electron beam with the experimental Hall-A beam dump. Considering the possible beam energy upgrade, this study was repeated for a 20 GeV CEBAF beam.

Increasing the efficiency and reducing the footprint of on-chip photodetectors enables dense optical interconnects for emerging computational and sensing applications. Avalanche photodetectors (APD) are currently the dominating on-chip photodetectors. However, the physics of avalanche multiplication leads to low energy efficiencies and prevents device operation at a high gain, due to a high excess noise, resulting in the need for electrical amplifiers. These properties significantly increase power consumption and footprint of current optical receivers. In contrast, heterojunction phototransistors (HPT) exhibit high efficiency and very small excess noise at high gain. However, HPT's gain-bandwidth product (GBP) is currently inferior to that of APDs at low optical powers. Here, we demonstrate that the type-II energy band alignment in an antimony-based HPT results in a significantly smaller junction capacitance and higher GBP at low optical powers. We used a CMOS-compatible heterogeneous integration method to create compact optical receivers on silicon with an energy efficiency that is about one order of magnitude higher than that of the best reported integrated APDs on silicon at a similar GBP of 270 GHz. Bitrate measurements show data rate spatial density above 800 Tbps per mm2, and an energy-per-bit consumption of only 6 fJ/bit at 3 Gbps. These unique features suggest new opportunities for creating highly efficient and compact on-chip optical receivers based on devices with type-II band alignment.

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. In particular, dynamical patterns require at least three topological signals, here taken to be two node signals and one link signal. In order to couple these signals, we formulate the 3-way topological Dirac operator that generalizes previous definitions of the 2-way and 4-way topological Dirac operators. We characterize the spectral properties of the 3-way Dirac operator and we investigate the dynamical properties of the resulting Turing and Dirac induced patterns. Here we emphasize the distinct dynamical properties of the Dirac induced patterns which involve topological signals only coupled by the 3-way topological Dirac operator in absence of the Hodge-Laplacian coupling. While the observed Turing patterns generalize the Turing patterns typically investigated on networks, the Dirac induced patterns have no equivalence within the framework of node based Turing patterns. These results open new scenarios in the study of Turing patterns with possible application to neuroscience and more generally to the study of emergent patterns in complex systems.

The parameterization of the nucleon structure through Generalized Parton Distributions (GPDs) shed a new light on the nucleon internal dynamics. For its direct interpretation, Deeply Virtual Compton Scattering (DVCS) is the golden channel for GPDs investigation. The DVCS process interferes with the Bethe-Heitler (BH) mechanism to constitute the leading order amplitude of the $eN \to eN\gamma$ process. The study of the $ep\gamma$ reaction with polarized positron and electron beams gives a complete set of unique observables to unravel the different contributions to the $ep \gamma$ cross section. This separates the different reaction amplitudes, providing a direct access to their real and imaginary parts which procures crucial constraints on the model dependences and associated systematic uncertainties on GPDs extraction. The real part of the BH-DVCS interference amplitude is particularly sensitive to the $D$-term which parameterizes the Gravitational Form Factors of the nucleon. The separation of the imaginary parts of the interference and DVCS amplitudes provides insights on possible higher-twist effects. We propose to measure the unpolarized and polarized Beam Charge Asymmetries (BCAs) of the $\vec{e}^{\pm}p \to e^{\pm}p \gamma$ process on an unpolarized hydrogen target with {\tt CLAS12}, using polarized positron and electron beams at 10.6 GeV. The azimuthal and $t$-dependences of the unpolarized and polarized BCAs will be measured over a large $(x_B,Q^2)$ phase space using a 100 day run with a luminosity of 0.66$\times 10^{35}$cm$^{-2}\cdot$s$^{-1}$., Comment: Proposal to the Jefferson Lab Program Advisory Committee (PAC51)

We propose a theoretical framework that explains how the mass of simple and higher-order networks emerges from their topology and geometry. We use the discrete topological Dirac operator to define an action for a massless self-interacting topological Dirac field inspired by the Nambu-Jona Lasinio model. The mass of the network is strictly speaking the mass of this topological Dirac field defined on the network; it results from the chiral symmetry breaking of the model and satisfies a self-consistent gap equation. Interestingly, it is shown that the mass of a network depends on its spectral properties, topology, and geometry. Due to the breaking of the matter-antimatter symmetry observed for the harmonic modes of the discrete topological Dirac operator, two possible definitions of the network mass can be given. For both possible definitions, the mass of the network comes from a gap equation with the difference among the two definitions encoded in the value of the bare mass. Indeed, the bare mass can be determined either by the Betti number $\beta_0$ or by the Betti number $\beta_1$ of the network. We provide numerical results on the mass of different networks, including random graphs, scale-free, and real weighted collaboration networks. We also discuss the generalization of these results to higher-order networks, defining the mass of simplicial complexes. The observed dependence of the mass of the considered topological Dirac field with the topology and geometry of the network could lead to interesting physics in the scenario in which the considered Dirac field is coupled with a dynamical evolution of the underlying network structure., Comment: (25 pages, 4 figures)

Higher-order networks are gaining significant scientific attention due to their ability to encode the many-body interactions present in complex systems. However, higher-order networks have the limitation that they only capture many-body interactions of the same type. To address this limitation, we present a mathematical framework that determines the topology of higher-order multiplex networks and illustrates the interplay between their topology and dynamics. Specifically, we examine the diffusion of topological signals associated not only to the nodes but also to the links and to the higher-dimensional simplices of multiplex simplicial complexes. We leverage on the ubiquitous presence of the overlap of the simplices to couple the dynamics among multiplex layers, introducing a definition of multiplex Hodge Laplacians and Dirac operators. We show that the spectral properties of these operators determine higher-order diffusion on higher-order multiplex networks and encode their multiplex Betti numbers. Our numerical investigation of the spectral properties of synthetic and real (connectome, microbiome) multiplex simplicial complexes indicates that the coupling between the layers can either speed up or slow down the higher-order diffusion of topological signals. This mathematical framework is very general and can be applied to study generic higher-order systems with interactions of multiple types. In particular, these results might find applications in brain networks which are understood to be both multilayer and higher-order., Comment: (35 pages, 8 figures)

We provide and critically analyze a framework to learn critical behavior in classical partition functions through the application of non-parametric methods to data sets of thermal configurations. We illustrate our approach in phase transitions in 2D and 3D Ising models. First, we extend previous studies on the intrinsic dimension of 2D partition function data sets, by exploring the effect of volume in 3D Ising data. We find that as opposed to 2D systems for which this quantity has been successfully used in unsupervised characterizations of critical phenomena, in the 3D case its estimation is far more challenging. To circumvent this limitation, we then use the principal component analysis (PCA) entropy, a "Shannon entropy" of the normalized spectrum of the covariance matrix. We find a striking qualitative similarity to the thermodynamic entropy, which the PCA entropy approaches asymptotically. The latter allows us to extract -- through a conventional finite-size scaling analysis with modest lattice sizes -- the critical temperature with less than $1\%$ error for both 2D and 3D models while being computationally efficient. The PCA entropy can readily be applied to characterize correlations and critical phenomena in a huge variety of many-body problems and suggests a (direct) link between easy-to-compute quantities and entropies., Comment: 20 pages, 10 figures, Submission to SciPost. Comments are welcome

Network science provides very powerful tools for extracting information from interacting data. Although recently the unsupervised detection of phases of matter using machine learning has raised significant interest, the full prediction power of network science has not yet been systematically explored in this context. Here we fill this gap by providing an in-depth statistical, combinatorial, geometrical and topological characterization of 2D Ising snapshot networks (IsingNets) extracted from Monte Carlo simulations of the $2$D Ising model at different temperatures, going across the phase transition. Our analysis reveals the complex organization properties of IsingNets in both the ferromagnetic and paramagnetic phases and demonstrates the significant deviations of the IsingNets with respect to randomized null models. In particular percolation properties of the IsingNets reflect the existence of the symmetry between configurations with opposite magnetization below the critical temperature and the very compact nature of the two emerging giant clusters revealed by our persistent homology analysis of the IsingNets. Moreover, the IsingNets display a very broad degree distribution and significant degree-degree correlations and weight-degree correlations demonstrating that they encode relevant information present in the configuration space of the $2$D Ising model. The geometrical organization of the critical IsingNets is reflected in their spectral properties deviating from the one of the null model. This work reveals the important insights that network science can bring to the characterization of phases of matter. The set of tools described hereby can be applied as well to numerical and experimental data., Comment: 17 pages, 18 figures

The upcoming generation of optical spectrographs on four meter-class telescopes, with their huge multiplexing capabilities, excellent spectral resolution, and unprecedented wavelength coverage, will provide high-quality spectra for thousands of galaxies. These data will allow us to examine of the stellar population properties at intermediate redshift, an epoch that remains unexplored by large and deep surveys. We assess our capability to retrieve the mean stellar metallicity in galaxies at different redshifts and S/N, while simultaneously exploiting the UV and optical rest-frame wavelength coverage. The work is based on a comprehensive library of spectral templates of stellar populations, covering a wide range of age and metallicity values and built assuming various SFHs. We simulated realistic observations of a large sample of galaxies carried out with WEAVE at the WHT at different redshifts and S/N values. We measured all the reliable indices on the simulated spectra and on the comparison library. We then adopted a Bayesian approach to obtain the probability distribution of stellar metallicity. The analysis of the spectral indices has shown how some mid-UV indices can provide reliable constraints on stellar metallicity, along with optical indicators. The analysis of the mock observations has shown that even at S/N=10, the metallicity can be derived within 0.3 dex, in particular, for stellar populations older than 2 Gyr. Our results are in good agreement with other theoretical and observational works in the literature and show how the UV indicators can be advantageous in constraining metallicities. This is very promising for the upcoming surveys carried out with new, highly multiplexed, large-field spectrographs, such as StePS at the WEAVE and 4MOST, which will provide spectra of thousands of galaxies covering large spectral ranges at relatively high S/N., Comment: 16 pages, 14 figures. Submitted 31/03/2023, Accepted 20/07/2023

Hypergraphs are higher-order networks that capture the interactions between two or more nodes. Hypergraphs can always be represented by factor graphs, i.e. bipartite networks between nodes and factor nodes (representing groups of nodes). Despite this universal representation, here we reveal that $k$-core percolation on hypergraphs can be significantly distinct from $k$-core percolation on factor graphs. We formulate the theory of hypergraph $k$-core percolation based on the assumption that a hyperedge can only be intact if all its nodes are intact. This scenario applies for instance to supply chains where the production of a product requires all raw materials and all processing steps; in biology it applies to protein-interaction networks where protein complexes can only function if all the proteins are present, and it applies as well to chemical reaction networks where a chemical reaction can take place only when all the reactants are present. Formulating a message-passing theory for hypergraph $k$-core percolation, and combining it with the theory of critical phenomena on networks we demonstrate sharp differences with previously studied factor graph $k$-core percolation processes where it is allowed for hyperedges to have one or more damaged nodes and still be intact. To solve the dichotomy between $k$-core percolation on hypergraphs and on factor graphs, we define a set of pruning processes that act either exclusively on nodes or exclusively on hyperedges and depend of their second-neighborhood connectivity. We show that the resulting second-neighbor $k$-core percolation problems are significantly distinct from each other. Moreover we reveal that although these processes remain distinct from factor graphs $k$-core processes, when the pruning process acts exclusively on hyperedges the phase diagram is reduced to the one of factor graph $k$-cores., Comment: (18 pages, 8 figures)

The temperature dependence of the two superconducting gaps in pressurised H_3S at 155 GPa with a critical temperature of 203 K has been determined by data analysis of the experimental curve of the upper critical magnetic field as a function of temperature in the framework of the two bands s-wave Eliashberg theory, with two different phonon mediated intra-band Cooper pairing channels in a regime of moderate strong couplings with the key role of the pair exchange interaction between the two gaps giving the two non-diagonal terms of the coupling tensor which are missing in the single band s wave Eliashberg theory. The results provide the prediction of the different temperature dependence of the small and large gaps as a function of temperature which provide evidence of multi-gap superconductivity in H_3S., Comment: 11 pages, 3 figures

The new experimental measurements of beam spin asymmetry were performed for the deeply virtual exclusive $\pi^0$ production in a wide kinematic region with the photon virtualities $Q^2$ up to 8 GeV$^2$ and the Bjorken scaling variable $x_B$ in the valence regime. The data were collected by the CEBAF Large Acceptance Spectrometer (CLAS12) at Jefferson Lab with longitudinally polarized 10.6 GeV electrons scattered on an unpolarized liquid-hydrogen target. Sizable asymmetry values indicate a substantial contribution from transverse virtual photon amplitudes to the polarized structure functions.The interpretation of these measurements in terms of the Generalized Parton Distributions (GPDs) demonstrates their sensitivity to the chiral-odd GPD $\bar E_T$, which contains information on quark transverse spin densities in unpolarized and polarized nucleons and provides access to the proton's transverse anomalous magnetic moment. Additionally, the data were compared to a theoretical model based on a Regge formalism that was extended to the high photon virtualities., Comment: arXiv admin note: substantial text overlap with arXiv:2210.14557

This document presents the initial scientific case for upgrading the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab (JLab) to 22 GeV. It is the result of a community effort, incorporating insights from a series of workshops conducted between March 2022 and April 2023. With a track record of over 25 years in delivering the world's most intense and precise multi-GeV electron beams, CEBAF's potential for a higher energy upgrade presents a unique opportunity for an innovative nuclear physics program, which seamlessly integrates a rich historical background with a promising future. The proposed physics program encompass a diverse range of investigations centered around the nonperturbative dynamics inherent in hadron structure and the exploration of strongly interacting systems. It builds upon the exceptional capabilities of CEBAF in high-luminosity operations, the availability of existing or planned Hall equipment, and recent advancements in accelerator technology. The proposed program cover various scientific topics, including Hadron Spectroscopy, Partonic Structure and Spin, Hadronization and Transverse Momentum, Spatial Structure, Mechanical Properties, Form Factors and Emergent Hadron Mass, Hadron-Quark Transition, and Nuclear Dynamics at Extreme Conditions, as well as QCD Confinement and Fundamental Symmetries. Each topic highlights the key measurements achievable at a 22 GeV CEBAF accelerator. Furthermore, this document outlines the significant physics outcomes and unique aspects of these programs that distinguish them from other existing or planned facilities. In summary, this document provides an exciting rationale for the energy upgrade of CEBAF to 22 GeV, outlining the transformative scientific potential that lies within reach, and the remarkable opportunities it offers for advancing our understanding of hadron physics and related fundamental phenomena., Comment: Updates to the list of authors; Preprint number changed from theory to experiment; Updates to sections 4 and 6, including additional figures