Generic singular spectrum for ergodic Schrödinger operators

We consider Schrödinger operators with ergodic potential V_ω(n) = f(T^n(ω)), n Є Z, ω Є Ω, where T : Ω → Ω is a nonperiodic homeomorphism. We show that for generic f Є C(Ω), the spectrum has no absolutely continuous component. The proof is based on approximation by discontinuous potentials which can be treated via Kotani theory

Assessment of Mercury Content in Louisiana\u27s Freshwater Fish and its Association to Se Concentrations

Ample evidence has demonstrated the neurotoxic properties of organic Hg to humans. However, recent studies have proposed the protective effects of Se against organic Hg detected in marine fish. Louisiana’s freshwater bodies are exploited by recreational anglers that enjoy fishing as recreational activity and food source. Thus, testing of Hg in Louisiana was resumed in 2017 to update the state advisories. However, before drawing conclusions based solely on organic Hg, it might be useful to see how much Se is present in freshwater fish. The main objective of this study was to determine the Se:Hg molar ratio in Louisiana’s freshwater fish; the ratios should be greater than 1.0 to expect Se’s protective effects. Five waterbodies were surveyed (University lake, Calcasieu lake, Toledo Bend, Atchafalaya River, and Henderson lake). The last three are listed in the state advisory. The fish’s fillet from species such as: Black drum, Catfish, Largemouth bass, Bluegill, Gizzard shad; were tested for total Hg via Direct Mercury Analyzer. Testing for Se used the same fish samples for determination via ICP-MS. The results revealed Hg concentrations on Louisiana’s fish were all under the 1 ppm EPA limit and LDEQ limit of 0.88 ppm (from 0.0063 to 0.67 ppm). However, Se concentrations were variable for different species and locations (from 0.024 to 0.886 ppm). Therefore, the calculated Se:Hg molar ratios were variable. Some ratios may suggest a relationship by species; like in Black drum and Catfish. Notwithstanding, large species (Bass) accumulate large amounts of Hg that exceed Se concentrations. That explained the low ratios for Se in Henderson lake’s bass but, is not true for Atchafalaya’s bass. Thus, fish from locations highly polluted with Hg apparently have Se:Hg molar ratios less than 1. There is no clear dominant variable (species or location) on the ratio determination. In conclusion, the predicted variability of Se in freshwater fish by other scholars were observed in this study. Apparently, location and species are variables with unpredictable dominant roles. For proper evaluation of state advisory, both might be considered independently for any particular freshwater body

Explaining Aviation Safety Incidents Using Deep Temporal Multiple Instance Learning

Although aviation accidents are rare, safety incidents occur more frequently and require a careful analysis to detect and mitigate risks in a timely manner. Analyzing safety incidents using operational data and producing event-based explanations is invaluable to airline companies as well as to governing organizations such as the Federal Aviation Administration (FAA) in the United States. However, this task is challenging because of the complexity involved in mining multi-dimensional heterogeneous time series data, the lack of time-step-wise annotation of events in a flight, and the lack of scalable tools to perform analysis over a large number of events. In this work, we propose a precursor mining algorithm that identifies events in the multidimensional time series that are correlated with the safety incident. Precursors are valuable to systems health and safety monitoring and in explaining and forecasting safety incidents. Current methods suffer from poor scalability to high dimensional time series data and are inefficient in capturing temporal behavior. We propose an approach by combining multiple-instance learning (MIL) and deep recurrent neural networks (DRNN) to take advantage of MIL's ability to learn using weakly supervised data and DRNN's ability to model temporal behavior. We describe the algorithm, the data, the intuition behind taking a MIL approach, and a comparative analysis of the proposed algorithm with baseline models. We also discuss the application to a real-world aviation safety problem using data from a commercial airline company and discuss the model's abilities and shortcomings, with some final remarks about possible deployment directions

The Spectrum of Schr\"odinger Operators with Randomly Perturbed Ergodic Potentials

We consider Schr\"odinger operators in $\ell^2(\mathbb{Z})$ whose potentials are given by the sum of an ergodic term and a random term of Anderson type. Under the assumption that the ergodic term is generated by a homeomorphism of a connected compact metric space and a continuous sampling function, we show that the almost sure spectrum arises in an explicitly described way from the unperturbed spectrum and the topological support of the single-site distribution. In particular, assuming that the latter is compact and contains at least two points, this explicit description of the almost sure spectrum shows that it will always be given by a finite union of non-degenerate compact intervals. The result can be viewed as a far reaching generalization of the well known formula for the spectrum of the classical Anderson model.Comment: 11 page

Schrödinger operators with potentials generated by hyperbolic transformations: I—positivity of the Lyapunov exponent

We consider discrete one-dimensional Schrödinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation. Specifically, we show that if the sampling function is a non-constant Hölder continuous function defined on a subshift of finite type with a fully supported ergodic measure admitting a local product structure and a fixed point, then the Lyapunov exponent is positive away from a discrete set of energies. Moreover, for sampling functions in a residual subset of the space of Hölder continuous functions, the Lyapunov exponent is positive everywhere. If we consider locally constant or globally fiber bunched sampling functions, then the Lyapuonv exponent is positive away from a finite set. Moreover, for sampling functions in an open and dense subset of the space in question, the Lyapunov exponent is uniformly positive. Our results can be applied to any subshift of finite type with ergodic measures that are equilibrium states of Hölder continuous potentials. In particular, we apply our results to Schrödinger operators defined over expanding maps on the unit circle, hyperbolic automorphisms of a finite-dimensional torus, and Markov chains