Epilepsy is widely regarded as a disorder driven by connectivity in the brain. We use a model of seizure dynamics on directed networks to investigate how structural properties affect seizure propensity. We find that properties such as trophic coherence, spectral radius, strong connectivity and non-normality are closely related to seizure propensity, and present a proof of a theoretical relationship between spectral radius and cycle structure. Our simulated results are robust to the kind of coupling used in the model and become stronger as network size is increased. They suggest that the overall directionality of information processing in the brain may be related to a propensity for epileptic seizures.

Trophic coherence and non-normality are both ways of describing the overall directionality of directed graphs or networks. Trophic coherence can be regarded as a measure of how neatly a graph can be divided into distinct layers, whereas non-normality is a measure of how unlike a matrix is with its transpose. We explore the relationship between trophic coherence and non-normality by first considering the connections that exist in literature and calculating the trophic coherence and non-normality for some toy networks. We then explore how persistence of an epidemic in an SIS model depends on coherence and how this relates to the non-normality. A similar effect on dynamics governed by a linear operator suggests that it may be useful to extend the concept of trophic coherence to matrices, which do not necessarily represent graphs.

Growing attention has been brought to the fact that many real directed networks exhibit hierarchy and directionality as measured through techniques like trophic analysis and non-normality. We propose a simple growing network model where the probability of connecting to a node is defined by a preferential attachment mechanism based on degree and the difference in fitness between nodes. In particular, we show how mechanisms such as degree-based preferential attachment and node fitness interactions can lead to the emergence of the spectrum of hierarchy and directionality observed in real networks. In this work, we study various features of this model relating to network hierarchy, as measured by trophic analysis. This includes (I) how preferential attachment can lead to network hierarchy, (II) how scale-free degree distributions and network hierarchy can coexist, (III) the correlation between node fitness and trophic level, (IV) how the fitness parameters can predict trophic incoherence and how the trophic level difference distribution compares to the fitness difference distribution, (V) the relationship between trophic level and degree imbalance and the unique role of nodes at the ends of the fitness hierarchy and (VI) how fitness interactions and degree-based preferential attachment can interplay to generate networks of varying coherence and degree distribution. We also provide an example of the intuition this work enables in the analysis of a real historical network. This work provides insight into simple mechanisms which can give rise to hierarchy in directed networks and quantifies the usefulness and limitations of using trophic analysis as an analysis tool for real networks.

Epilepsy is one of the most common neurological disorders in children. Diagnosing epilepsy in children can be very challenging, especially as it often coexists with neurodevelopmental conditions like autism and ADHD. Functional brain networks obtained from neuroimaging and electrophysiological data in wakefulness and sleep have been shown to contain signatures of neurological disorders, and can potentially support the diagnosis and management of co-occurring neurodevelopmental conditions. In this work, we use electroencephalography (EEG) recordings from children, in restful wakefulness and sleep, to extract functional connectivity networks in different frequency bands. We explore the relationship of these networks with epilepsy diagnosis and with measures of neurodevelopmental traits, obtained from questionnaires used as screening tools for autism and ADHD. We explore differences in network markers between children with and without epilepsy in wake and sleep, and quantify the correlation between such markers and measures of neurodevelopmental traits. Our findings highlight the importance of considering the interplay between epilepsy and neurodevelopmental traits when exploring network markers of epilepsy.

Compartmental models of epidemics are widely used to forecast the effects of communicable diseases such as COVID-19 and to guide policy. Although it has long been known that such processes take place on social networks, the assumption of random mixing is usually made, which ignores network structure. However, super-spreading events have been found to be power-law distributed, suggesting that the underlying networks may be scale free or at least highly heterogeneous. The random-mixing assumption would then produce an overestimation of the herd-immunity threshold for given $R_0$; and a (more significant) overestimation of $R_0$ itself. These two errors compound each other, and can lead to forecasts greatly overestimating the number of infections. Moreover, if networks are heterogeneous and change in time, multiple waves of infection can occur, which are not predicted by random mixing. A simple SIR model simulated on both Erd\H{o}s-R\'enyi and scale-free networks shows that details of the network structure can be more important than the intrinsic transmissibility of a disease. It is therefore crucial to incorporate network information into standard models of epidemics.

Optical antenna resonators enable control of light-matter interactions on the nano-scale via electron-photon hybrid states in strong coupling. Specifically, mid-infrared (MIR) nano-antennas coupled to saturable intersubband transitions in multi-quantum-well (MQW) semiconductor heterostructures allow for the coupling strength to be tuned through antenna resonance and field intensity. Here, tip-enhanced nano-scale variation of antenna-MQW coupling across the antenna is demonstrated, with a spatially-dependent coupling strength gaq$g_{\rm aq}$ varying from 73 (strong coupling) to 24 cm-1$\rm {cm}<^>{-1}$ (weak coupling). This behavior is modeled based on the spatially dependent local constructive and destructive interference between tip and antenna fields. Using a quantum-mechanical density-matrix model of the MQW system with its designed values of transition dipole moment, doping density, and population decay time, the picosecond IR pulse coupling to intersubband transitions and the associated tip induced strong-field saturation effects are described. These results present a new regime of nonlinear IR light-matter control based on the dynamic manipulation of quantum hybrid states on the nanoscale and in the infrared, with a perspective regarding extension to molecular vibrations. Optical antenna resonators provide for control of light-matter interaction on the nano-scale. Antenna resonance tuning to low-energy intersubband transitions of multi-quantum wells gives rise to strongly coupled electron-photon hybrid states in the mid-infrared at room temperature. Tip-enhanced near-field interference and laser fluence-dependent saturation allow for nanolocalized imaging, switching, and control between the weak and strong coupling. image

Knowing which nodes are influential in a complex network and whether the network can be influenced by a small subset of nodes is a key part of network analysis. However, many traditional measures of importance focus on node level information without considering the global network architecture. We use the method of trophic analysis to study directed networks and show that both 'influence' and 'influenceability' in directed networks depend on the hierarchical structure and the global directionality, as measured by the trophic levels and trophic coherence, respectively. We show that in directed networks trophic hierarchy can explain: the nodes that can reach the most others; where the eigenvector centrality localizes; which nodes shape the behaviour in opinion or oscillator dynamics; and which strategies will be successful in generalized rock-paper-scissors games. We show, moreover, that these phenomena are mediated by the global directionality. We also highlight other structural properties of real networks related to influenceability, such as the pseudospectra, which depend on trophic coherence. These results apply to any directed network and the principles highlighted-that node hierarchy is essential for understanding network influence, mediated by global directionality-are applicable to many real-world dynamics.

Heterodyne vis-pump IR-probe nano-imaging is developed to reveal, with simultaneous spatial, spectral, and temporal resolutions, solar-cell relevant polaron dynamics in perovskites and thermal transport across 2D heterointerfaces in phonon-polariton nano-thermometry.

In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean degree and degree-degree correlations. And it has important implications for other properties of real networks and the dynamical behavior of many complex systems. We find that strong connectivity depends crucially on the extent to which the network has an overall direction or hierarchical ordering-a property measured by trophic coherence. Using percolation theory, we find the critical point separating weakly and strongly connected regimes and confirm our results on many real-world networks, including ecological, neural, trade, and social networks. We show that the connectivity structure can be disrupted with minimal effort by a targeted attack on edges which run counter to the overall direction. This means that many dynamical processes on networks can depend significantly on a small fraction of edges.

Nanoscale infrared (IR) resonators with sub-diffraction limited mode volumes and open geometries have emerged as new platforms for implementing cavity quantum electrodynamics at room temperature. The use of IR nanoantennas and tip nanoprobes to study strong light-matter coupling of molecular vibrations with the vacuum field can be exploited for IR quantum control with nanometer spatial and femtosecond temporal resolution. In order to advance the development of molecule-based quantum nanophotonics in the mid-IR, we propose a generally applicable semi-empirical methodology based on quantum optics to describe light-matter interaction in systems driven by mid-IR femtosecond laser pulses. The theory is shown to reproduce recent experiments on the acceleration of the vibrational relaxation rate in infrared nanostructures. It also provides physical insights on the implementation of coherent phase rotations of the near-field using broadband nanotips. We then apply the quantum framework to develop general tip-design rules for the experimental manipulation of vibrational strong coupling and Fano interference effects in open infrared resonators. We finally propose the possibility of transferring the natural anharmonicity of molecular vibrational levels to the resonator near-field in the weak coupling regime to implement intensity-dependent phase shifts of the coupled system response with strong pulses and develop a vibrational chirping model to understand the effect. The semi-empirical quantum theory is equivalent to first-principles techniques based on Maxwell's equations, but its lower computational cost suggests its use as a rapid design tool for the development of strongly coupled infrared nanophotonic hardware for applications ranging from quantum control of materials to quantum information processing.

We perform ultrafast pump-probe nano-spectroscopic imaging of WSe 2 -SiO 2 interfaces. From transient phonon softening as a local probe of substrate temperature, we resolve heterogeneity in ps thermalization and quantify interfacial boundary conductance.

Many real-world networks are directed, sparse, and hierarchical, with a mixture of feedforward and feedback connections with respect to the hierarchy. Moreover, a small number of master nodes are often able to drive the whole system. We study the dynamics of pattern presentation and recovery on sparse, directed, Hopfield-like neural networks using trophic analysis to characterize their hierarchical structure. This is a recent method which quantifies the local position of each node in a hierarchy (trophic level) as well as the global directionality of the network (trophic coherence). We show that even in a recurrent network, the state of the system can be controlled by a small subset of neurons which can be identified by their low trophic levels. We also find that performance at the pattern recovery task can be significantly improved by tuning the trophic coherence and other topological properties of the network. This may explain the relatively sparse and coherent structures observed in the animal brain and provide insights for improving the architectures of artificial neural networks. Moreover, we expect that the principles we demonstrate here, through numerical analysis, will be relevant for a broad class of system whose underlying network structure is directed and sparse, such as biological, social, or financial networks.

Ultrafast infrared nano-imaging has demonstrated access to ultrafast carrier dynamics on the nanoscale in semiconductor, correlated-electron, or polaritonic materials. However, mostly limited to short-lived transient states, the contrast obtained has remained insufficient to probe important long-lived excitations, which arise from many-body interactions induced by strong perturbation among carriers, lattice phonons, or molecular vibrations. Here, we demonstrate ultrafast infrared nano-imaging based on excitation modulation and sideband detection to characterize electron and vibration dynamics with nano- to micro-second lifetimes. As an exemplary application to quantum materials, in phase-resolved ultrafast nano-imaging of the photoinduced insulator-to-metal transition in vanadium dioxide, a distinct transient nano-domain behavior is quantified. In another application to lead halide perovskites, transient vibrational nano-FTIR spatially resolves the excited-state polaron-cation coupling underlying the photovoltaic response. These examples show how heterodyne pump-probe nano-spectroscopy with low-repetition excitation extends ultrafast infrared nano-imaging to probe elementary processes in quantum and molecular materials in space and time.

In high fluence applications of lead halide perovskites for light-emitting diodes and lasers, multi-polaron interactions and associated Auger recombination limit the device performance. However, the relationship of the ultrafast and strongly lattice coupled carrier dynamics to nanoscale heterogeneities has remained elusive. Here, in ultrafast visible-pump infrared-probe nano-imaging of the photoinduced carrier dynamics in triple cation perovskite films, a ~20 % variation in sub-ns relaxation dynamics with spatial disorder on tens to hundreds of nanometer is resolved. We attribute the non-uniform relaxation dynamics to the heterogeneous evolution of polaron delocalization and increasing scattering time. The initial high-density excitation results in faster relaxation due to strong many-body interactions, followed by extended carrier lifetimes at lower densities. These results point towards the missing link between the optoelectronic heterogeneity and associated carrier dynamics to guide synthesis and device engineering for improved perovskites device performance.

In this work we explore a simple influence problem using a novel variation of the Bounded Confidence Model (BCM) of opinion dynamics that can be applied to varying types of social media platforms with transient user populations. Via simulation-based analyses, we set out to understand the extent to which the opinions of a transient population that divides their attention across multiple channels is either more or less susceptible to progressively more extreme opinions.

The COVID-19 pandemic has caused unprecedented disruption, particularly in retail. Where essential demand cannot be fulfilled online, or where more stringent measures have been relaxed, customers must visit shop premises in person. This naturally gives rise to some risk of susceptible individuals (customers or staff) becoming infected. It is essential to minimize this risk as far as possible while retaining economic viability of the shop. We therefore explore and compare the spread of COVID-19 in different shopping situations involving person-to-person interactions: (i) free-flowing, unstructured shopping; (ii) structured shopping (e.g. a queue). We examine which of (i) or (ii) may be preferable for minimizing the spread of COVID-19 in a given shop, subject to constraints such as the geometry of the shop; compliance of the population to local guidelines; and additional safety measures which may be available to the organizers of the shop. We derive a series of conclusions, such as unidirectional free movement being preferable to bidirectional shopping, and that the number of servers should be maximized as long as they can be well protected from infection.

Order, disorder, and domains affect many of the functional properties in self-assembled monolayers (SAMs). However, carrier transport, wettability, and chemical reactivity are often associated with collective effects, where conventional imaging techniques have limited sensitivity to the underlying intermolecular coupling. Here we demonstrate vibrational excitons as a molecular ruler of intermolecular wave function delocalization and nanodomain size in SAMs. In the model system of a 4-nitrothiophenol (4-NTP) SAM on gold, we resolve coupling-induced peak shifts of the nitro symmetric stretch mode with full spatio-spectral infrared scattering scanning near-field optical microscopy. From modeling of the underlying 2D Hamiltonian, we infer domain sizes and their distribution ranging from 3 to 12 nm across a field of view on the micrometer scale. This approach of vibrational exciton nanoimaging is generally applicable to study structural phases and domains in SAMs and other molecular interfaces.

Low permeability unconventional oil and gas resources may experience formation damage due to the emplacement of viscous petroleum in narrow pore throats during petroleum migration and production. The composition of such pore-clogging molecules remains under-characterized, as standard analytical techniques in organic geochemistry either lack the desired nano-scale spatial resolution with simultaneous chemical specificity, or require extraction and therefore averaging of the suite of compounds that make up bulk crude oil. A new correlative imaging technique with high spatial resolution is demonstrated for migrated residual petroleum in nanopores of Niobrara chalk samples. Imaging combines Infrared scattering-Scanning Near-field Optical Microscopy (IR s-SNOM) with nano-mechanical atomic force microscopy to map both chemical and mechanical properties at similar to 30 nm spatial resolution. These correlative images demonstrate that heterogeneity exists within emplaced petroleum in situ on the scale of hundreds of nanometers, visualized as clusters of petroleum having distinct adhesive forces. The chemical composition of these clusters remains ambiguous, but their geometry and mechanical properties may imply that they are phase-separated asphaltene preferentially associated with petroleum-attractive nano-domains on calcite pore walls. Despite outstanding challenges, correlative IR s-SNOM and nano-mechanical imaging offer a promising and novel analytical approach to understanding fluid behavior in nanoporous reservoir rocks.

We develop precision infrared nano-imaging and -spectroscopy to probe vibrational excitons and associated vibrational wavefunction delocalization as a molecular ruler to study order and domains in molecular materials and self-assembled monolayer on the molecular scale.