The problem of targeted network immunization can be defined as the one of finding a subset of nodes in a network to immunize or vaccinate in order to minimize a tradeoff between the cost of vaccination and the final (stationary) expected infection under a given epidemic model. Although computing the expected infection is a hard computational problem, simple and efficient mean-field approximations have been put forward in the literature in recent years. The optimization problem can be recast into a constrained one in which the constraints enforce local mean-field equations describing the average stationary state of the epidemic process. For a wide class of epidemic models, including the susceptible-infected-removed and the susceptible-infected-susceptible models, we define a message-passing approach to network immunization that allows us to study the statistical properties of epidemic outbreaks in the presence of immunized nodes as well as to find (nearly) optimal immunization sets for a given choice of parameters and costs. The algorithm scales linearly with the size of the graph, and it can be made efficient even on large networks. We compare its performance with topologically based heuristics, greedy methods, and simulated annealing on both random graphs and real-world networks.

Networks in the real world do not exist as isolated entities, but they are often part of more complicated structures composed of many interconnected network layers. Recent studies have shown that such mutual dependence makes real networked systems potentially exposed to atypical structural and dynamical behaviors, and thus there is an urgent necessity to better understand the mechanisms at the basis of these anomalies. Previous research has mainly focused on the emergence of atypical properties in relation to the moments of the intra- and interlayer degree distributions. In this paper, we show that an additional ingredient plays a fundamental role for the possible scenario that an interconnected network can face: the correlation between intra- and interlayer degrees. For sufficiently high amounts of correlation, an interconnected network can be tuned, by varying the moments of the intra- and interlayer degree distributions, in distinct topological and dynamical regimes. When instead the correlation between intra- and interlayer degrees is lower than a critical value, the system enters in a supercritical regime where dynamical and topological phases are no longer distinguishable.

A shortcut to adiabaticity is a driving protocol that reproduces in a short time the same final state that would result from an adiabatic, infinitely slow process. A powerful technique to engineer such shortcuts relies on the use of auxiliary counterdiabatic fields. Determining the explicit form of the required fields has generally proven to be complicated. We present explicit counterdiabatic driving protocols for scale-invariant dynamical processes, which describe, for instance, expansion and transport. To this end, we use the formalism of generating functions and unify previous approaches independently developed in classical and quantum studies. The resulting framework is applied to the design of shortcuts to adiabaticity for a large class of classical and quantum, single-particle, nonlinear, and many-body systems.

The rapid worldwide spread of severe viral infections, often involving novel mutations of viruses, poses major challenges to our health-care systems. This means that tools that can efficiently and specifically diagnose viruses are much needed. To be relevant for broad applications in local health-care centers, such tools should be relatively cheap and easy to use. In this paper, we discuss the biophysical potential for the macroscopic detection of viruses based on the induction of a mechanical stress in a bundle of prestretched DNA molecules upon binding of viruses to the DNA. We show that the affinity of the DNA to the charged virus surface induces a local melting of the double helix into two single-stranded DNA. This process effects a mechanical stress along the DNA chains leading to an overall contraction of the DNA. Our results suggest that when such DNA bundles are incorporated in a supporting matrix such as a responsive hydrogel, the presence of viruses may indeed lead to a significant, macroscopic mechanical deformation of the matrix. We discuss the biophysical basis for this effect and characterize the physical properties of the associated DNA melting transition. In particular, we reveal several scaling relations between the relevant physical parameters of the system. We promote this DNA-based assay as a possible tool for efficient and specific virus screening.

Discovering and characterizing the large-scale topological features in empirical networks are crucial steps in understanding how complex systems function. However, most existing methods used to obtain the modular structure of networks suffer from serious problems, such as being oblivious to the statistical evidence supporting the discovered patterns, which results in the inability to separate actual structure from noise. In addition to this, one also observes a resolution limit on the size of communities, where smaller but well-defined clusters are not detectable when the network becomes large. This phenomenon occurs for the very popular approach of modularity optimization, which lacks built-in statistical validation, but also for more principled methods based on statistical inference and model selection, which do incorporate statistical validation in a formally correct way. Here, we construct a nested generative model that, through a complete description of the entire network hierarchy at multiple scales, is capable of avoiding this limitation and enables the detection of modular structure at levels far beyond those possible with current approaches. Even with this increased resolution, the method is based on the principle of parsimony, and is capable of separating signal from noise, and thus will not lead to the identification of spurious modules even on sparse networks. Furthermore, it fully generalizes other approaches in that it is not restricted to purely assortative mixing patterns, directed or undirected graphs, and ad hoc hierarchical structures such as binary trees. Despite its general character, the approach is tractable and can be combined with advanced techniques of community detection to yield an efficient algorithm that scales well for very large networks.

We show that the self-assembly of a diverse collection of building blocks can be understood within a common physical framework. These building blocks, which form periodic honeycomb networks and nonperiodic variants thereof, range in size from atoms to micron-scale polymers and interact through mechanisms as different as hydrogen bonds and covalent forces. A combination of statistical mechanics and quantum mechanics shows that one can capture the physics that governs the assembly of these networks by resolving only the geometry and strength of building-block interactions. The resulting framework reproduces a broad range of phenomena seen experimentally, including periodic and nonperiodic networks in thermal equilibrium, and nonperiodic supercooled and glassy networks away from equilibrium. Our results show how simple “design criteria” control the assembly of a wide variety of networks and suggest that kinetic trapping can be a useful way of making functional assemblies.

In this work, we treat the Poisson-Nernst-Planck (PNP) equations as the basis for a consistent framework of the electrokinetic effects. The static limit of the PNP equations is shown to be the charge-conserving Poisson-Boltzmann (CCPB) equation, with guaranteed charge neutrality within the computational domain. We propose a surface potential trap model that attributes an energy cost to the interfacial charge dissociation. In conjunction with the CCPB, the surface potential trap can cause a surface-specific adsorbed charge layer $\sigma$. By defining a chemical potential $\mu$ that arises from the charge neutrality constraint, a reformulated CCPB can be reduced to the form of the Poisson-Boltzmann equation, whose prediction of the Debye screening layer profile is in excellent agreement with that of the Poisson-Boltzmann equation when the channel width is much larger than the Debye length. However, important differences emerge when the channel width is small, so the Debye screening layers from the opposite sides of the channel overlap with each other. In particular, the theory automatically yields a variation of $\sigma$ that is generally known as the “charge regulation” behavior, attendant with predictions of force variation as a function of nanoscale separation between two charged surfaces that are in good agreement with the experiments, with no adjustable or additional parameters. We give a generalized definition of the $\zeta$ potential that reflects the strength of the electrokinetic effect; its variations with the concentration of surface-specific and surface-nonspecific salt ions are shown to be in good agreement with the experiments. To delineate the behavior of the electro-osmotic (EO) effect, the coupled PNP and Navier-Stokes equations are solved numerically under an applied electric field tangential to the fluid-solid interface. The EO effect is shown to exhibit an intrinsic time dependence that is noninertial in its origin. Under a step-function applied electric field, a pulse of fluid flow is followed by relaxation to a new ion distribution, owing to the diffusive counter current. We have numerically evaluated the Onsager coefficients associated with the EO effect, $L_{\text{21}}$, and its reverse streaming potential effect, $L_{12}$, and show that $L_{\text{12}}=L_{\text{21}}$ in accordance with the Onsager relation. We conclude by noting some of the challenges ahead.

We demonstrate that femtosecond filaments can set up an extended and robust thermal waveguide structure in air with a lifetime of several milliseconds, making possible the very-long-range guiding and distant projection of high-energy laser pulses and high-average power beams. As a proof of principle, we demonstrate guiding of 110-mJ, 7-ns, 532-nm pulses with 90% throughput over $\sim 15$ Rayleigh lengths in a 70-cm-long air waveguide generated by the long time-scale thermal relaxation of an array of femtosecond filaments. The guided pulse was limited only by our available laser energy. In general, these waveguides should be robust against the effects of thermal blooming of extremely high-average-power laser beams.

We report both subdiffraction-limited quantum metrology and quantum-enhanced spatial resolution for the first time in a biological context. Nanoparticles are tracked with quantum-correlated light as they diffuse through an extended region of a living cell in a quantum-enhanced photonic-force microscope. This allows spatial structure within the cell to be mapped at length scales down to 10 nm. Control experiments in water show a 14% resolution enhancement compared to experiments with coherent light. Our results confirm the long-standing prediction that quantum-correlated light can enhance spatial resolution at the nanoscale and in biology. Combined with state-of-the-art quantum light sources, this technique provides a path towards an order of magnitude improvement in resolution over similar classical imaging techniques.

Chirality occupies a central role in fields ranging from biological self-assembly to the design of optical metamaterials. The definition of chirality, as given by Lord Kelvin, associates chirality with the lack of mirror symmetry: the inability to superpose an object on its mirror image. While this definition has guided the classification of chiral objects for over a century, the quantification of handed phenomena based on this definition has proven elusive, if not impossible, as manifest in the paradox of chiral connectedness. In this work, we put forward a quantification scheme in which the handedness of an object depends on the direction in which it is viewed. While consistent with familiar chiral notions, such as the right-hand rule, this framework allows objects to be simultaneously right and left handed. We demonstrate this orientation dependence in three different systems—a biomimetic elastic bilayer, a chiral propeller, and optical metamaterial—and find quantitative agreement with chirality pseudotensors whose form we explicitly compute. The use of this approach resolves the existing paradoxes and naturally enables the design of handed metamaterials from symmetry principles.

We report here a novel fiber-based test bed using tailored spectral shaping of an optical-frequency comb to excite the formation of two Akhmediev breathers that collide during propagation. We have found specific initial conditions by controlling the phase and velocity differences between breathers that lead, with certainty, to their efficient collision and the appearance of a giant-amplitude wave. Temporal and spectral characteristics of the collision dynamics are in agreement with the corresponding analytical solution. We anticipate that experimental evidence of breather-collision dynamics is of fundamental importance in the understanding of extreme ocean waves and in other disciplines driven by the continuous nonlinear Schrödinger equation.

A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates generalizing “traditional” network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper, we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of several important network descriptors and dynamical processes—including degree centrality, clustering coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion—for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems.

Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavior is therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionarily advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding, and punishment, a fourth strategy that combines the latter two competes for space. We find rich dynamical behavior that gives rise to intricate phase diagrams where continuous and discontinuous phase transitions occur in succession. Indirect territorial competition, spontaneous emergence of cyclic dominance, as well as divergent fluctuations of oscillations that terminate in an absorbing phase are observed. Yet, despite the high complexity of solutions, the combined strategy can survive only in very narrow and unrealistic parameter regions. Elementary strategies, either in pure or mixed phases, are much more common and likely to prevail. Our results highlight the importance of patterns and structure in human cooperation, which should be considered in future experiments.

Ratchets are devices that are able to rectify an otherwise oscillatory behavior by exploiting an asymmetry of the system. In rocking ratchets, the asymmetry is induced through a proper choice of external forces and modulations of nonlinear symmetric potentials. The ratchet currents thus obtained in systems as different as semiconductors, Josephson junctions, optical lattices, or ferrofluids show a set of universal features. A satisfactory explanation for them has challenged theorists for decades, and so far, we still lack a general theory of this phenomenon. Here, we provide such a theory by exploring—through functional analysis—the constraints that the simple assumption of time-shift invariance of the ratchet current imposes on its dependence on the external drivings. Because the derivation is based on so general a principle, the resulting expression is valid irrespective of the details and the nature of the physical systems to which it is applied, and of whether they are classical, quantum, or stochastic. The theory also explains deviations observed from universality under special conditions and allows us to make predictions of phenomena not yet observed in any experiment or simulation.

Stromatolites can grow under the influence of microbial processes, but it is often unclear whether and how the macroscopic morphology of these rocks records biological processes. Conical stromatolites, which formed in the absence of sedimentation, provide a comparatively simple record of the interplay between microbial growth and lithification. Here, we show that the dynamics shaping conical stromatolites result from diffusive gradients within the overlying microbial mat. These gradients cause minerals to precipitate faster in regions of high curvature, resulting in measurable properties of the shapes of stromatolite laminas. This model allows us to estimate the thickness of ancient stromatolite-forming mats to be approximately $1\mathrm{mm}$, consistent with modern systems. Proceeding from the assumption that the ubiquitous process of diffusion is recorded in the translating form of a stromatolite, we derive the shape of a diffusion-driven stromatolite. The conical morphology—a distinctive feature of stromatolites growing in the absence of sedimentation—arises from these dynamics. This form is quantitatively consistent with the shape of conical stromatolites that grew for more than $2.9\times {10}^9$ yrs of Earth history.

We present a powerful and versatile technique that enables exquisite spatial and temporal control over local solution chemistry in microfluidic devices. Using a microscope and a UV lamp, we use projection lithography to photopolymerize thin ($10–25\mu \mathrm{m}$) hydrogel membrane “microwindows” (HMMs) into standard microfluidic devices. These microwindows are permeable to solute and solvent diffusion and to electric fields, yet act as rigid walls from the standpoint of fluid flow. Reservoirs of solution may thus be rapidly imposed, switched, and maintained on one side of a HMM using standard microfluidic techniques, provoking changes in solution conditions on the other side without active mixing, stirring, or diluting. We highlight three paradigmatic experimental capabilities enabled by HMMs: (1) rapid dialysis and swapping of solute and/or solvent, (2) stable and convection-free localized concentration gradients, and (3) local electric permeability. The functional versatility of hydrogel microwindow membranes, coupled with the ease and speed of their fabrication and integration into simple microchannels or multilayer devices, will open a variety of novel applications and studies in a broad range of fields.

We obtain generalizations of the Kelvin-Planck, Clausius, and Carnot statements of the second law of thermodynamics for situations involving information processing. To this end, we consider an information reservoir (representing, e.g., a memory device) alongside the heat and work reservoirs that appear in traditional thermodynamic analyses. We derive our results within an inclusive framework in which all participating elements—the system or device of interest, together with the heat, work, and information reservoirs—are modeled explicitly by a time-independent, classical Hamiltonian. We place particular emphasis on the limits and assumptions under which cyclic motion of the device of interest emerges from its interactions with work, heat, and information reservoirs.

We propose a stochastic model for the number of different words in a given database which incorporates the dependence on the database size and historical changes. The main feature of our model is the existence of two different classes of words: (i) a finite number of core words, which have higher frequency and do not affect the probability of a new word to be used, and (ii) the remaining virtually infinite number of noncore words, which have lower frequency and, once used, reduce the probability of a new word to be used in the future. Our model relies on a careful analysis of the Google Ngram database of books published in the last centuries, and its main consequence is the generalization of Zipf’s and Heaps’ law to two-scaling regimes. We confirm that these generalizations yield the best simple description of the data among generic descriptive models and that the two free parameters depend only on the language but not on the database. From the point of view of our model, the main change on historical time scales is the composition of the specific words included in the finite list of core words, which we observe to decay exponentially in time with a rate of approximately 30 words per year for English.

The voltage-gated potassium channel from Aeropyrum pernix operates by coupling the voltage-driven motion of a charged group of amino acids to the opening and closing of the pore. In this experiment, we drive this charged group with an ac field and observe the effect on the gating. The measurements for different frequencies and amplitudes of the forcing reveal an essential nonlinearity in the mechanical behavior of the molecule. Within a continuum-mechanics description, we extract the effective dissipation parameter $\gamma$ for this conformational motion and find $\gamma \approx 0.2\mathrm{g}/\mathrm{s}$, similar to recent nanorheology measurements on the conformational motion of an enzyme.

Ordered lipid assemblies are responsible for important physiological functions including skin barrier and axon conductivity. However, techniques commonly used to probe molecular order such as X-ray scattering and nuclear magnetic resonance are not suited for in-situ tissue studies. Here, we identify and characterize a novel contrast mechanism in nonlinear optical microscopy which is sensitive to molecular ordering in multilamellar lipid vesicles (MLVs) and in samples obtained from human skin biopsy: polarized third-harmonic generation (P-THG). We develop a multiscale theoretical framework to calculate the anisotropic, nonlinear optical response of lipid arrays as a function of molecular order. This analysis reveals that conserved carbon-carbon bond and aliphatic tail directionality are the atomic- and molecular-scale sources of the observed P-THG response, respectively. Agreement between calculations and experiments on lipid droplets and MLVs validates the use of P-THG as a probe of lipid ordering. Finally, we show that P-THG can be used to map molecular ordering in the multilamellar, intercorneocyte lipid matrix of the stratum corneum of human skin. These results provide the foundation for the use of P-THG in probing molecular order and highlight a novel biomedical application of multiphoton microscopy in an optically accessible tissue relevant to monitoring lipid-related disorder.