Phase coherence in tight-binding models with nonrandom long-range hopping

The density of states, even for a perfectly ordered tight-binding model, can exhibit a tail-like feature at the top of the band, provided the hopping integral falls off in space slowly enough. We apply the coherent potential approximation to study the eigenstates of a tight-binding Hamiltonian with uncorrelated diagonal disorder and long-range hopping, falling off as a power mu of the intersite distance. For a certain interval of hopping-range exponent mu, we show that the phase-coherence length is infinite for the outermost state of the tail, irrespectively of the strength of disorder. Such an anomalous feature can be explained by the smallness of the phase-space volume for the disorder scattering from this state. As an application of the theory, we mention that ballistic regime can be realized for Frenkel excitons in two-dimensional molecular aggregates, affecting to a large extent the optical response and energy transport

Event-driven Temporal Models for Explanations - ETeMoX: Explaining Reinforcement Learning

Modern software systems are increasingly expected to show higher degrees of autonomy and self-management to cope with uncertain and diverse situations. As a consequence, autonomous systems can exhibit unexpected and surprising behaviours. This is exacerbated due to the ubiquity and complexity of Artificial Intelligence (AI)-based systems. This is the case of Reinforcement Learning (RL), where autonomous agents learn through trial-and-error how to find good solutions to a problem. Thus, the underlying decision-making criteria may become opaque to users that interact with the system and who may require explanations about the system’s reasoning. Available work for eXplainable Reinforcement Learning (XRL) offers different trade-offs: e.g. for runtime explanations, the approaches are model-specific or can only analyse results after-the-fact. Different from these approaches, this paper aims to provide an online model-agnostic approach for XRL towards trustworthy and understandable AI. We present ETeMoX, an architecture based on temporal models to keep track of the decision-making processes of RL systems. In cases where the resources are limited (e.g. storage capacity or time to response), the architecture also integrates complex event processing, an event-driven approach, for detecting matches to event patterns that need to be stored, instead of keeping the entire history. The approach is applied to a mobile communications case study that uses RL for its decision-making. In order to test the generalisability of our approach, three variants of the underlying RL algorithms are used: Q-Learning, SARSA and DQN. The encouraging results show that using the proposed configurable architecture, RL developers are able to obtain explanations about the evolution of a metric, relationships between metrics, and were able to track situations of interest happening over time windows

Effective interactions of colloids on nematic films

The elastic and capillary interactions between a pair of colloidal particles trapped on top of a nematic film are studied theoretically for large separations $d$. The elastic interaction is repulsive and of quadrupolar type, varying as $d^{-5}$. For macroscopically thick films, the capillary interaction is likewise repulsive and proportional to $d^{-5}$ as a consequence of mechanical isolation of the system comprised of the colloids and the interface. A finite film thickness introduces a nonvanishing force on the system (exerted by the substrate supporting the film) leading to logarithmically varying capillary attractions. However, their strength turns out to be too small to be of importance for the recently observed pattern formation of colloidal droplets on nematic films.Comment: 13 pages, accepted by EPJ

Historical Biogeography and Diversification of Truffles in the Tuberaceae and Their Newly Identified Southern Hemisphere Sister Lineage

Truffles have evolved from epigeous (aboveground) ancestors in nearly every major lineage of fleshy fungi. Because accelerated rates of morphological evolution accompany the transition to the truffle form, closely related epigeous ancestors remain unknown for most truffle lineages. This is the case for the quintessential truffle genus Tuber, which includes species with socio-economic importance and esteemed culinary attributes. Ecologically, Tuber spp. form obligate mycorrhizal symbioses with diverse species of plant hosts including pines, oaks, poplars, orchids, and commercially important trees such as hazelnut and pecan. Unfortunately, limited geographic sampling and inconclusive phylogenetic relationships have obscured our understanding of their origin, biogeography, and diversification. To address this problem, we present a global sampling of Tuberaceae based on DNA sequence data from four loci for phylogenetic inference and molecular dating. Our well-resolved Tuberaceae phylogeny shows high levels of regional and continental endemism. We also identify a previously unknown epigeous member of the Tuberaceae - the South American cup-fungus Nothojafnea thaxteri (E.K. Cash) Gamundi. Phylogenetic resolution was further improved through the inclusion of a previously unrecognized Southern hemisphere sister group of the Tuberaceae. This morphologically diverse assemblage of species includes truffle (e.g. Gymnohydnotrya spp.) and non-truffle forms that are endemic to Australia and South America. Southern hemisphere taxa appear to have diverged more recently than the Northern hemisphere lineages. Our analysis of the Tuberaceae suggests that Tuber evolved from an epigeous ancestor. Molecular dating estimates Tuberaceae divergence in the late Jurassic (~156 million years ago), with subsequent radiations in the Cretaceous and Paleogene. Intra-continental diversification, limited long-distance dispersal, and ecological adaptations help to explain patterns of truffle evolution and biodiversity