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)

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

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

Upper bounds on wavepacket spreading for random Jacobi matrices

A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds on the diffusion exponents for random polymer models, coinciding with the lower bounds obtained in a prior work. The second application is an elementary argument (not using multiscale analysis or the Aizenman-Molchanov method) showing that under the condition of uniformly positive Lyapunov exponents, the moments of the position operator grow at most logarithmically in time.Comment: final version, to appear in CM

Predicting invasive breast cancer versus DCIS in different age groups.

BackgroundIncreasing focus on potentially unnecessary diagnosis and treatment of certain breast cancers prompted our investigation of whether clinical and mammographic features predictive of invasive breast cancer versus ductal carcinoma in situ (DCIS) differ by age.MethodsWe analyzed 1,475 malignant breast biopsies, 1,063 invasive and 412 DCIS, from 35,871 prospectively collected consecutive diagnostic mammograms interpreted at University of California, San Francisco between 1/6/1997 and 6/29/2007. We constructed three logistic regression models to predict the probability of invasive cancer versus DCIS for the following groups: women ≥ 65 (older group), women 50-64 (middle age group), and women < 50 (younger group). We identified significant predictors and measured the performance in all models using area under the receiver operating characteristic curve (AUC).ResultsThe models for older and the middle age groups performed significantly better than the model for younger group (AUC = 0.848 vs, 0.778; p = 0.049 and AUC = 0.851 vs, 0.778; p = 0.022, respectively). Palpability and principal mammographic finding were significant predictors in distinguishing invasive from DCIS in all age groups. Family history of breast cancer, mass shape and mass margins were significant positive predictors of invasive cancer in the older group whereas calcification distribution was a negative predictor of invasive cancer (i.e. predicted DCIS). In the middle age group--mass margins, and in the younger group--mass size were positive predictors of invasive cancer.ConclusionsClinical and mammographic finding features predict invasive breast cancer versus DCIS better in older women than younger women. Specific predictive variables differ based on age

Emergency contraception: unresolved clinical, ethical and legal quandaries still linger

Emergency contraception (EC) has been prescribed for decades, in order to lessen the risk of unplanned and unwanted pregnancy following unprotected intercourse, ordinary contraceptive failure, or rape. EC and the linked aspect of unintended pregnancy undoubtedly constitute highly relevant public health issues, in that they involve women's self-determination, reproductive freedom and family planning. Most European countries regulate EC access quite effectively, with solid information campaigns and supply mechanisms, based on various recommendations from international institutions herein examined. However, there is still disagreement on whether EC drugs should be available without a physician's prescription and on the reimbursement policies that should be implemented. In addition, the rights of health care professionals who object to EC on conscience grounds have been subject to considerable legal and ethical scrutiny, in light of their potential to damage patients who need EC drugs in a timely fashion. Ultimately, reproductive health, freedom and conscience-based refusal on the part of operators are elements that have proven extremely hard to reconcile; hence, it is essential to strike a reasonable balance for the sake of everyone's rights and well-being

ATRA mechanically reprograms pancreatic stellate cells to suppress matrix remodelling and inhibit cancer cell invasion

Pancreatic ductal adenocarcinoma (PDAC) is a highly aggressive malignancy with a dismal survival rate. Persistent activation of pancreatic stellate cells (PSCs) can perturb the biomechanical homoeostasis of the tumour microenvironment to favour cancer cell invasion. Here we report that ATRA, an active metabolite of vitamin A, restores mechanical quiescence in PSCs via a mechanism involving a retinoic acid receptor beta (RAR-β)-dependent downregulation of actomyosin (MLC-2) contractility. We show that ATRA reduces the ability of PSCs to generate high traction forces and adapt to extracellular mechanical cues (mechanosensing), as well as suppresses force-mediated extracellular matrix remodelling to inhibit local cancer cell invasion in 3D organotypic models. Our findings implicate a RAR-β/MLC-2 pathway in peritumoural stromal remodelling and mechanosensory-driven activation of PSCs, and further suggest that mechanical reprogramming of PSCs with retinoic acid derivatives might be a viable alternative to stromal ablation strategies for the treatment of PDAC