Spectral averaging techniques for Jacobi matrices

Spectral averaging techniques for one-dimensional discrete Schroedinger operators are revisited and extended. In particular, simultaneous averaging over several parameters is discussed. Special focus is put on proving lower bounds on the density of the averaged spectral measures. These Wegner type estimates are used to analyze stability properties for the spectral types of Jacobi matrices under local perturbations

Nootropics use in the workplace. Psychiatric and ethical aftermath towards the new frontier of bioengineering

OBJECTIVE: The authors have sought to expound upon and shed a light on the rise of nootropics, which have gradually taken on a more and more relevant role in workplaces and academic settings. MATERIALS AND METHODS: Multidisciplinary databases have been delved into by entering the following keys: "nootropics", "cognitive enhancement", "workplace", "productivity", "ethics", "bioengineering". In addition, a broad-ranging search has been undertaken on institutional websites in order to identify relevant analysis and recommendations issued by international institutions and agencies. Papers and reports have been independently pored over by each author. This search strategy has led to the identification of 988 sources but only 64 were considered appropriate for the purposes of the paper after being selected by at least 3 of the authors, independently. RESULTS: The notion of an artificially enhanced work performance - carried out by the 'superworker' - is particularly noteworthy and resonates with the conception of contemporary work on so many different levels: the rising need and demands for higher degrees of flexibility and productivity on the job, the implications of a '24/7' society, where more and more services are available at any time, the ever greater emphasis on entrepreneurial spirit, individual self-reliance and self-improvement, and last but not least, the impact of an ageing society on economic standards and performance. CONCLUSIONS: Moreover, it is worth mentioning that human enhancement technologies will predictably and increasingly go hand in hand with gene editing, bioengineering, cybernetics and nanotechnology. Applications are virtually boundless, and may ultimately affect all human traits (physical strength, endurance, vision, intelligence and even personality and mood)

Simultaneous Process Design and Control Optimization using Reinforcement Learning

With the ever-increasing numbers in population and quality in healthcare, it is inevitable for the demand of energy and natural resources to rise. Therefore, it is important to design highly efficient and sustainable chemical processes in the pursuit of sustainability. The performance of a chemical plant is highly affected by its design and control. A design cannot be evaluated without its controls and vice versa. To optimally address design and control simultaneously, one must formulate a bi-level mixed-integer nonlinear program with a dynamic optimization problem as the inner problem; this, is intractable. However, by computing an optimal policy using reinforcement learning, a controller with close-form expression can be found and embedded into the mathematical program. In this work, an approach using a policy gradient method along with mathematical programming to solve the problem simultaneously is proposed. The approach was tested in two case studies and the performance of the controller was evaluated. It was shown that the proposed approach outperforms current state-of-the-art control strategies. This opens a whole new range of possibilities to address the simultaneous design and control of engineering systems

Exponential dynamical localization for the almost Mathieu operator

We prove that the exponential moments of the position operator stay bounded for the supercritical almost Mathieu operator with Diophantine frequency

What is Localization?

We examine various issues relevant to localization in the Anderson model. We show there is more to localization than exponentially localized states by presenting an example with such states but where ⟨x(t)^2⟩/t^(2 − δ) is unbounded for any δ > 0. We show that the recently discovered instability of localization under rank one perturbations is only a weak instability

Regions without flux surfaces of given class for\\magnetic fields in toroidal geometry

A Converse KAM method for 3D vector fields, establishing regions through which pass no invariant 2-tori transverse to a given direction field, is tested on some helical perturbations of an axisymmetric magnetic field in toroidal geometry. It finds regions corresponding to magnetic islands and chaos for the fieldline flow. Minimization of these regions is proposed as a tool to help in the design of plasma confinement devices of tokamak and stellarator type

Measuring Population Transmission Potential for HIV: An Alternative Metric of Transmission Risk in Men who have Sex with Men (MSM) in the US

Background Various metrics for HIV burden and treatment success [e.g. HIV prevalence, community viral load (CVL), population viral load (PVL), percent of HIV-positive persons with undetectable viral load] have important public health limitations for understanding disparities. Methods and Findings Using data from an ongoing HIV incidence cohort of black and white men who have sex with men (MSM), we propose a new metric to measure the prevalence of those at risk of transmitting HIV and illustrate its value. …See full text for complete abstract