Elements composing complex systems usually interact in several different ways, and as such, the interaction architecture is well modeled by a network with multiple layers—a multiplex network—where the system’s complex dynamics is often the result of several intertwined processes taking place at different levels. However, only in a few cases can such multilayered architecture be empirically observed, as one usually only has experimental access to such structure from an aggregated projection. A fundamental challenge is thus to determine whether the hidden underlying architecture of complex systems is better modeled as a single interaction layer or if it results from the aggregation and interplay of multiple layers. Assuming a prior of intralayer Markovian diffusion, here we show that by using local information provided by a random walker navigating the aggregated network, it is possible to determine, in a robust manner, whether these dynamics can be more accurately represented by a single layer or if they are better explained by a (hidden) multiplex structure. In the latter case, we also provide Bayesian methods to estimate the most probable number of hidden layers and the model parameters, thereby fully reconstructing its architecture. The whole methodology enables us to decipher the underlying multiplex architecture of complex systems by exploiting the non-Markovian signatures on the statistics of a single random walk on the aggregated network. In fact, the mathematical formalism presented here extends above and beyond detection of physical layers in networked complex systems, as it provides a principled solution for the optimal decomposition and projection of complex, non-Markovian dynamics into a Markov switching combination of diffusive modes. We validate the proposed methodology with numerical simulations of both (i) random walks navigating hidden multiplex networks (thereby reconstructing the true hidden architecture) and (ii) Markovian and non-Markovian continuous stochastic processes (thereby reconstructing an effective multiplex decomposition where each layer accounts for a different diffusive mode). We also state and prove two existence theorems guaranteeing that an exact reconstruction of the dynamics in terms of these hidden jump-Markov models is always possible for arbitrary finite-order Markovian and fully non-Markovian processes. Finally, we showcase the applicability of the method to experimental recordings from (i) the mobility dynamics of human players in an online multiplayer game and (ii) the dynamics of RNA polymerases at the single-molecule level.

In vitro and in vivo spiking activity clearly differ. Whereas networks in vitro develop strong bursts separated by periods of very little spiking activity, in vivo cortical networks show continuous activity. This is puzzling considering that both networks presumably share similar single-neuron dynamics and plasticity rules. We propose that the defining difference between in vitro and in vivo dynamics is the strength of external input. In vitro, networks are virtually isolated, whereas in vivo every brain area receives continuous input. We analyze a model of spiking neurons in which the input strength, mediated by spike rate homeostasis, determines the characteristics of the dynamical state. In more detail, our analytical and numerical results on various network topologies show consistently that under increasing input, homeostatic plasticity generates distinct dynamic states, from bursting, to close-to-critical, reverberating, and irregular states. This implies that the dynamic state of a neural network is not fixed but can readily adapt to the input strengths. Indeed, our results match experimental spike recordings in vitro and in vivo: The in vitro bursting behavior is consistent with a state generated by very low network input ($<0.1\%$), whereas in vivo activity suggests that on the order of 1% recorded spikes are input driven, resulting in reverberating dynamics. Importantly, this predicts that one can abolish the ubiquitous bursts of in vitro preparations, and instead impose dynamics comparable to in vivo activity by exposing the system to weak long-term stimulation, thereby opening new paths to establish an in vivo-like assay in vitro for basic as well as neurological studies.

We present a fundamentally new approach to laboratory acoustic and seismic wave experimentation that enables full immersion of a physical wave propagation experiment within a virtual numerical environment. Using a recent theory of immersive boundary conditions that relies on measurements made on an inner closed surface of sensors, the output of numerous closely spaced sources around the physical domain is continuously varied in time and space. This allows waves to seamlessly propagate back and forth between both domains, without being affected by reflections at the boundaries between both domains, which enables us to virtually expand the size of the physical laboratory and operate at much lower frequencies than previously possible (sonic frequencies as low as 1 kHz). While immersive boundary conditions have been rigorously tested numerically, here we present the first proof of concept for their physical implementation with experimental results from a one-dimensional sound wave tube. These experiments demonstrate the performance and capabilities of immersive boundary conditions in canceling boundary reflections and accounting for long-range interactions with a virtual domain outside the physical experiment. Moreover, we introduce a unique high-performance acquisition, computation, and control system that will enable the real-time implementation of immersive boundary conditions in three dimensions. The system is capable of extrapolating wave fields recorded on 800 simultaneous inputs to 800 simultaneous outputs, through arbitrarily complex virtual background media with an extremely low total system latency of $200\mu \mathrm{s}$. The laboratory allows studying a variety of long-standing problems and poorly understood aspects of wave physics and imaging. Moreover, such real-time immersive experimentation opens up exciting possibilities for the future of laboratory acoustic and seismic experiments and for fields such as active acoustic cloaking and holography.

The generation of abnormal excitations in pathological regions of the heart is a main trigger for lethal cardiac arrhythmias. Such abnormal excitations, also called ectopic activity, often arise from areas with local tissue heterogeneity or damage accompanied by localized depolarization. Finding the conditions that lead to ectopy is important to understand the basic biophysical principles underlying arrhythmia initiation and might further refine clinical procedures. In this study, we are the first to address the question of how geometry of the abnormal region affects the onset of ectopy using a combination of experimental, in silico, and theoretical approaches. We paradoxically find that, for any studied geometry of the depolarized region in optogenetically modified monolayers of cardiac cells, primary ectopic excitation originates at areas of maximal curvature of the boundary, where the stimulating electrotonic currents are minimal. It contradicts the standard critical nucleation theory applied to nonlinear waves in reaction-diffusion systems, where a higher stimulus is expected to produce excitation more easily. Our in silico studies reveal that the nonconventional ectopic activity is caused by an oscillatory instability at the boundary of the damaged region, the occurrence of which depends on the curvature of that boundary. The onset of this instability is confirmed using the Schrödinger equation methodology proposed by Rinzel and Keener [SIAM J. Appl. Math. 43, 907 (1983)]. Overall, we show distinctively novel insight into how the geometry of a heterogeneous cardiac region determines ectopic activity, which can be used in the future to predict the conditions that can trigger cardiac arrhythmias.

The interaction between water protons and suitable quadrupolar nuclei (QN) can lead to quadrupole relaxation enhancement (QRE) of proton spins, provided the resonance condition between both spin transitions is fulfilled. This effect could be utilized as a frequency selective mechanism in novel, responsive $T_1$ shortening contrast agents (CAs) for magnetic resonance imaging (MRI). In particular, the proposed contrast mechanism depends on the applied external flux density—a property that can be exploited by special field-cycling MRI scanners. For the design of efficient CA molecules, exhibiting narrow and pronounced peaks in the proton $T_1$ relaxation dispersion, the nuclear quadrupole resonance (NQR) properties, as well as the spin dynamics of the system $\mathrm{QN}\text{−}{}^1\mathrm{H}$, have to be well understood and characterized for the compounds in question. In particular, the energy-level structure of the QN is a central determinant for the static flux densities at which the contrast enhancement appears. The energy levels depend both on the QN and the electronic environment, i.e., the chemical bonding structure in the CA molecule. In this work, the NQR properties of a family of promising organometallic compounds containing ${}^{209}\mathrm{Bi}$ as QN have been characterized. Important factors like temperature, chemical structure, and chemical environment have been considered by NQR spectroscopy and ab initio quantum chemistry calculations. The investigated Bi-aryl compounds turned out to fulfill several crucial requirements: NQR transition frequency range applicable to clinical 1.5- and 3 T MRI systems, low temperature dependency, low toxicity, and tunability in frequency by chemical modification.

Streaking of photoelectrons with optical lasers has been widely used for temporal characterization of attosecond extreme ultraviolet pulses. Recently, this technique has been adapted to characterize femtosecond x-ray pulses in free-electron lasers with the streaking imprinted by far-infrared and terahertz (THz) pulses. Here, we report successful implementation of THz streaking for time stamping of an ultrashort relativistic electron beam, whose energy is several orders of magnitude higher than photoelectrons. Such an ability is especially important for MeV ultrafast electron diffraction (UED) applications, where electron beams with a few femtosecond pulse width may be obtained with longitudinal compression, while the arrival time may fluctuate at a much larger timescale. Using this laser-driven THz streaking technique, the arrival time of an ultrashort electron beam with a 6-fs (rms) pulse width has been determined with 1.5-fs (rms) accuracy. Furthermore, we have proposed and demonstrated a noninvasive method for correction of the timing jitter with femtosecond accuracy through measurement of the compressed beam energy, which may allow one to advance UED towards a sub-10-fs frontier, far beyond the approximate 100-fs (rms) jitter.

Biopolymer translocation is a key step in viral infection processes. The transfer of information-encoding genomes allows viruses to reprogram the cell fate of their hosts. Constituting 96% of all known bacterial viruses [A. Fokine and M. G. Rossmann, Molecular architecture of tailed double-stranded DNA phages, Bacteriophage 4, e28281 (2014)], the tailed bacteriophages deliver their DNA into host cells via an “ejection” process, leaving their protein shells outside of the bacteria; a similar scenario occurs for mammalian viruses like herpes, where the DNA genome is ejected into the nucleus of host cells, while the viral capsid remains bound outside to a nuclear-pore complex. In light of previous experimental measurements of in vivo bacteriophage $\lambda$ ejection, we analyze here the physical processes that give rise to the observed dynamics. We propose that, after an initial phase driven by self-repulsion of DNA in the capsid, the ejection is driven by anomalous diffusion of phage DNA in the crowded bacterial cytoplasm. We expect that this two-step mechanism is general for phages that operate by pressure-driven ejection, and we discuss predictions of our theory to be tested in future experiments.

Collective migration dominates many phenomena, from cell movement in living systems to abiotic self-propelling particles. Focusing on the early stages of tumor evolution, we enunciate the principles involved in cell dynamics and highlight their implications in understanding similar behavior in seemingly unrelated soft glassy materials and possibly chemokine-induced migration of $\mathrm{CD}{8}^{+}\mathrm{T}$ cells. We performed simulations of tumor invasion using a minimal three-dimensional model, accounting for cell elasticity and adhesive cell-cell interactions, as well as cell birth and death, to establish that cell-growth-rate-dependent tumor expansion results in the emergence of distinct topological niches. Cells at the periphery move with higher velocity perpendicular to the tumor boundary, while the motion of interior cells is slower and isotropic. The mean-square displacement $\mathrm{\Delta }(t)$ of cells exhibits glassy behavior at times comparable to the cell cycle time, while exhibiting superdiffusive behavior, $\mathrm{\Delta }(t)\approx t^{\alpha }$ ($\alpha >1$), at longer times. We derive the value of $\alpha \approx 1.33$ using a field theoretic approach based on stochastic quantization. In the process, we establish the universality of superdiffusion in a class of seemingly unrelated nonequilibrium systems. Superdiffusion at long times arises only if there is an imbalance between cell birth and death rates. Our findings for the collective migration, which also suggest that tumor evolution occurs in a polarized manner, are in quantitative agreement with in vitro experiments. Although set in the context of tumor invasion, the findings should also hold in describing the collective motion in growing cells and in active systems, where creation and annihilation of particles play a role.

Many complex systems are modular. Such systems can be represented as “component systems,” i.e., sets of elementary components, such as LEGO bricks in LEGO sets. The bricks found in a LEGO set reflect a target architecture, which can be built following a set-specific list of instructions. In other component systems, instead, the underlying functional design and constraints are not obvious a priori, and their detection is often a challenge of both scientific and practical importance, requiring a clear understanding of component statistics. Importantly, some quantitative invariants appear to be common to many component systems, most notably a common broad distribution of component abundances, which often resembles the well-known Zipf’s law. Such “laws” affect in a general and nontrivial way the component statistics, potentially hindering the identification of system-specific functional constraints or generative processes. Here, we specifically focus on the statistics of shared components, i.e., the distribution of the number of components shared by different system realizations, such as the common bricks found in different LEGO sets. To account for the effects of component heterogeneity, we consider a simple null model, which builds system realizations by random draws from a universe of possible components. Under general assumptions on abundance heterogeneity, we provide analytical estimates of component occurrence, which quantify exhaustively the statistics of shared components. Surprisingly, this simple null model can positively explain important features of empirical component-occurrence distributions obtained from large-scale data on bacterial genomes, LEGO sets, and book chapters. Specific architectural features and functional constraints can be detected from occurrence patterns as deviations from these null predictions, as we show for the illustrative case of the “core” genome in bacteria.

Mainstream machine-learning techniques such as deep learning and probabilistic programming rely heavily on sampling from generally intractable probability distributions. There is increasing interest in the potential advantages of using quantum computing technologies as sampling engines to speed up these tasks or to make them more effective. However, some pressing challenges in state-of-the-art quantum annealers have to be overcome before we can assess their actual performance. The sparse connectivity, resulting from the local interaction between quantum bits in physical hardware implementations, is considered the most severe limitation to the quality of constructing powerful generative unsupervised machine-learning models. Here, we use embedding techniques to add redundancy to data sets, allowing us to increase the modeling capacity of quantum annealers. We illustrate our findings by training hardware-embedded graphical models on a binarized data set of handwritten digits and two synthetic data sets in experiments with up to 940 quantum bits. Our model can be trained in quantum hardware without full knowledge of the effective parameters specifying the corresponding quantum Gibbs-like distribution; therefore, this approach avoids the need to infer the effective temperature at each iteration, speeding up learning; it also mitigates the effect of noise in the control parameters, making it robust to deviations from the reference Gibbs distribution. Our approach demonstrates the feasibility of using quantum annealers for implementing generative models, and it provides a suitable framework for benchmarking these quantum technologies on machine-learning-related tasks.

Economic experiments have shown that punishment can increase public goods game contributions over time. However, the effectiveness of punishment is challenged by second-order free-riding and antisocial punishment. The latter implies that noncooperators punish cooperators, while the former implies unwillingness to shoulder the cost of punishment. Here, we extend the theory of cooperation in the spatial public goods game by considering four competing strategies, which are traditional cooperators and defectors, as well as cooperators who punish defectors and defectors who punish cooperators. We show that if the synergistic effects are high enough to sustain cooperation based on network reciprocity alone, antisocial punishment does not deter public cooperation. Conversely, if synergistic effects are low and punishment is actively needed to sustain cooperation, antisocial punishment does is viable, but only if the cost-to-fine ratio is low. If the costs are relatively high, cooperation again dominates as a result of spatial pattern formation. Counterintuitively, defectors who do not punish cooperators, and are thus effectively second-order free-riding on antisocial punishment, form an active layer around punishing cooperators, which protects them against defectors that punish cooperators. A stable three-strategy phase that is sustained by the spontaneous emergence of cyclic dominance is also possible via the same route. The microscopic mechanism behind the reported evolutionary outcomes can be explained by the comparison of invasion rates that determine the stability of subsystem solutions. Our results reveal an unlikely evolutionary escape from adverse effects of antisocial punishment, and they provide a rationale for why second-order free-riding is not always an impediment to the evolutionary stability of punishment.

Single nanoparticle tracking using optical microscopy is a powerful technique with many applications in biology, chemistry, and material sciences. Despite significant advances, localizing objects with nanometric position precision in a scattering environment remains challenging. Applied methods to achieve contrast are dominantly fluorescence based, with fundamental limits in the emitted photon fluxes arising from the excited-state lifetime as well as photobleaching. Here, we show a new four-wave-mixing interferometry technique, whereby the position of a single nonfluorescing gold nanoparticle of 25-nm radius is determined with 16 nm precision in plane and 3 nm axially from rapid single-point measurements at 1-ms acquisition time by exploiting optical vortices. The precision in plane is consistent with the photon shot-noise, while axially it is limited by the nano-positioning sample stage, with an estimated photon shot-noise limit of 0.5 nm. The detection is background-free even inside biological cells. The technique is also uniquely sensitive to particle asymmetries of only 0.5% ellipticity, corresponding to a single atomic layer of gold, as well as particle orientation. This method opens new ways of unraveling single-particle trafficking within complex 3D architectures.

The spontaneous transformations associated with symmetry-breaking phase transitions generate domain structures and defects that may be topological in nature. The formation of these defects can be described according to the Kibble-Zurek mechanism, which provides a generic relation that applies from cosmological to interatomic length scales. Its verification is challenging, however, in particular at the cosmological scale where experiments are impractical. While it has been demonstrated for selected condensed-matter systems, major questions remain regarding, e.g., its degree of universality. Here, we develop a global Kibble-Zurek picture from the condensed-matter level. We show theoretically that a transition between two fluctuation regimes (Ginzburg and mean field) can lead to an intermediate region with reversed scaling, and we verify experimentally this behavior for the structural transition in the series of multiferroic hexagonal manganites. Trends across the series allow us to identify additional intrinsic features of the defect formation beyond the original Kibble-Zurek paradigm.

Applied network science often involves preprocessing network data before applying a network-analysis method, and there is typically a theoretical disconnect between these steps. For example, it is common to aggregate time-varying network data into windows prior to analysis, and the trade-offs of this preprocessing are not well understood. Focusing on the problem of detecting small communities in multilayer networks, we study the effects of layer aggregation by developing random-matrix theory for modularity matrices associated with layer-aggregated networks with $N$ nodes and $L$ layers, which are drawn from an ensemble of Erdős–Rényi networks with communities planted in subsets of layers. We study phase transitions in which eigenvectors localize onto communities (allowing their detection) and which occur for a given community provided its size surpasses a detectability limit $K^{*}$. When layers are aggregated via a summation, we obtain $K^{*}\propto \mathcal{O}(\sqrt{NL}/T)$, where $T$ is the number of layers across which the community persists. Interestingly, if $T$ is allowed to vary with $L$, then summation-based layer aggregation enhances small-community detection even if the community persists across a vanishing fraction of layers, provided that $T/L$ decays more slowly than $\mathcal{O}(L^{-1/2})$. Moreover, we find that thresholding the summation can, in some cases, cause $K^{*}$ to decay exponentially, decreasing by orders of magnitude in a phenomenon we call super-resolution community detection. In other words, layer aggregation with thresholding is a nonlinear data filter enabling detection of communities that are otherwise too small to detect. Importantly, different thresholds generally enhance the detectability of communities having different properties, illustrating that community detection can be obscured if one analyzes network data using a single threshold.

For nearly a century, the concept of needle radiation has captured the attention of the electromagnetics communities in both physics and engineering, with various types of contributions reoccurring every decade. With the near-term needs for highly directive, electrically small radiators and scatterers for a variety of communications and sensor applications, superdirectivity has again become a topic of interest. While it is well known that superdirective solutions exist and suffer ill-posedness issues in principle, a detailed needle solution has not been reported previously. We demonstrate explicitly, for the first time, how needle radiation can be obtained theoretically from currents driven on an arbitrary spherical surface, and we explain why such a result can only be attained in practice with electrically large spheres. On the other hand, we also demonstrate, more practically, how broadside radiating Huygens source multipoles can be combined into an end-fire array configuration to achieve needle-like radiation performance without suffering the traditional problems that have previously plagued superdirectivity.

Brillouin and Raman scattering spectroscopy are established techniques for the nondestructive contactless and label-free readout of mechanical, chemical, and structural properties of condensed matter. Brillouin-Raman investigations currently require separate measurements and a site-matched approach to obtain complementary information from a sample. Here, we demonstrate a new concept of fully scanning multimodal microspectroscopy for simultaneous detection of Brillouin and Raman light scattering in an exceptionally wide spectral range, from fractions of GHz to hundreds of THz. It yields an unprecedented 150-dB contrast, which is especially important for the analysis of opaque or turbid media such as biomedical samples, and spatial resolution on a subcellular scale. We report the first applications of this new multimodal method to a range of systems, from a single cell to the fast reaction kinetics of a curing process, and the mechanochemical mapping of highly scattering biological samples.

The geographical pattern of human dialects is a result of history. Here, we formulate a simple spatial model of language change which shows that the final result of this historical evolution may, to some extent, be predictable. The model shows that the boundaries of language dialect regions are controlled by a length minimizing effect analogous to surface tension, mediated by variations in population density which can induce curvature, and by the shape of coastline or similar borders. The predictability of dialect regions arises because these effects will drive many complex, randomized early states toward one of a smaller number of stable final configurations. The model is able to reproduce observations and predictions of dialectologists. These include dialect continua, isogloss bundling, fanning, the wavelike spread of dialect features from cities, and the impact of human movement on the number of dialects that an area can support. The model also provides an analytical form for Séguy’s curve giving the relationship between geographical and linguistic distance, and a generalization of the curve to account for the presence of a population center. A simple modification allows us to analytically characterize the variation of language use by age in an area undergoing linguistic change.

A system of Majorana zero modes with random infinite-range interactions—the Sachdev-Ye-Kitaev (SYK) model—is thought to exhibit an intriguing relation to the horizons of extremal black holes in two-dimensional anti–de Sitter space. This connection provides a rare example of holographic duality between a solvable quantum-mechanical model and dilaton gravity. Here, we propose a physical realization of the SYK model in a solid-state system. The proposed setup employs the Fu-Kane superconductor realized at the interface between a three-dimensional topological insulator and an ordinary superconductor. The requisite $N$ Majorana zero modes are bound to a nanoscale hole fabricated in the superconductor that is threaded by $N$ quanta of magnetic flux. We show that when the system is tuned to the surface neutrality point (i.e., chemical potential coincident with the Dirac point of the topological insulator surface state) and the hole has sufficiently irregular shape, the Majorana zero modes are described by the SYK Hamiltonian. We perform extensive numerical simulations to demonstrate that the system indeed exhibits physical properties expected of the SYK model, including thermodynamic quantities and two-point as well as four-point correlators, and discuss ways in which these can be observed experimentally.

Laser guide stars employed at astronomical observatories provide artificial wavefront reference sources to help correct (in part) the impact of atmospheric turbulence on astrophysical observations. Following the recent commissioning of the 4 Laser Guide Star Facility (4LGSF) on Unit Telescope 4 (UT4) of the Very Large Telescope (VLT), we characterize the spectral signature of the uplink beams from the 22-W lasers to assess the impact of laser scattering from the 4LGSF on science observations. We use the Multi-Unit Spectroscopic Explorer (MUSE) optical integral field spectrograph mounted on the Nasmyth B focus of UT4 to acquire spectra at a resolution of $R\cong 3000$ of the uplink laser beams over the wavelength range of 4750 Å–9350 Å. We report the first detection of laser-induced Raman scattering by ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, ${\mathrm{CO}}_2$, ${\mathrm{H}}_2\mathrm{O}$, and (tentatively) ${\mathrm{CH}}_4$ molecules in the atmosphere above the astronomical observatory of Cerro Paranal. In particular, our observations reveal the characteristic spectral signature of laser photons—but 480 Å to 2210 Å redder than the original laser wavelength of 5889.959 Å—landing on the 8.2-m primary mirror of UT4 after being Raman-scattered on their way up to the sodium layer. Laser-induced Raman scattering, a phenomenon not usually discussed in the astronomical context, is not unique to the observatory of Cerro Paranal, but it is common to any astronomical telescope employing a laser guide star (LGS) system. It is thus essential for any optical spectrograph coupled to a LGS system to thoroughly handle the possibility of a Raman spectral contamination via a proper baffling of the instrument and suitable calibrations procedures. These considerations are particularly applicable for the HARMONI optical spectrograph on the upcoming Extremely Large Telescope (ELT). At sites hosting multiple telescopes, laser-collision-prediction tools should also account for the presence of Raman emission from the uplink laser beam(s) to avoid the unintentional contamination of observations acquired with telescopes in the vicinity of a LGS system.

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the susceptible-infected-susceptible (SIS) and susceptible-infected-recovered dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasistationary state method, we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. At variance with what is observed in single-layer networks, we show that disease localization takes place on the layers and not on the nodes of a given layer. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: If the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we report on an interesting phenomenon, the barrier effect; i.e., for a three-layer configuration, when the layer with the lowest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems, opening new possibilities for the study of spreading processes.