Blow-up behavior of collocation solutions to Hammerstein-type volterra integral equations

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the exact solution. Based on the local convergence of the collocation methods for VIEs, we present the convergence analysis for the numerical blow-up time. Numerical experiments illustrate the analysis

Experimental certification of millions of genuinely entangled atoms in a solid

Quantum theory predicts that entanglement can also persist in macroscopic physical systems, albeit difficulties to demonstrate it experimentally remain. Recently, significant progress has been achieved and genuine entanglement between up to 2900 atoms was reported. Here we demonstrate 16 million genuinely entangled atoms in a solid-state quantum memory prepared by the heralded absorption of a single photon. We develop an entanglement witness for quantifying the number of genuinely entangled particles based on the collective effect of directed emission combined with the nonclassical nature of the emitted light. The method is applicable to a wide range of physical systems and is effective even in situations with significant losses. Our results clarify the role of multipartite entanglement in ensemble-based quantum memories as a necessary prerequisite to achieve a high single-photon process fidelity crucial for future quantum networks. On a more fundamental level, our results reveal the robustness of certain classes of multipartite entangled states, contrary to, e.g., Schr\"odinger-cat states, and that the depth of entanglement can be experimentally certified at unprecedented scales.Comment: 11 pages incl. Methods and Suppl. Info., 4 figures, 1 table. v2: close to published version. See also parallel submission by Zarkeshian et al (1703.04709

Macroscopic quantum entanglement between an optomechanical cavity and a continuous field in presence of non-Markovian noise

Probing quantum entanglement with macroscopic objects allows us to test quantum mechanics in new regimes. One way to realize such behavior is to couple a macroscopic mechanical oscillator to a continuous light field via radiation pressure. In view of this, the system that is discussed comprises an optomechanical cavity driven by a coherent optical field in the unresolved sideband regime where we assume Gaussian states and dynamics. We develop a framework to quantify the amount of entanglement in the system numerically. Different from previous work, we treat non-Markovian noise and take into account both the continuous optical field and the cavity mode. We apply our framework to the case of the Advanced Laser Interferometer Gravitational-Wave Observatory and discuss the parameter regimes where entanglement exists, even in the presence of quantum and classical noises

Care Home Research : Future Challenges and Opportunities

Funding: This research was funded by Tennovus Scotland Research Project No. G16-08 and NHS-Grampian Research and Development Endowment Research Grants Project No: 16/11/043 and Scottish Government as part of the Strategic Research Programme at the Rowett Institute (award 1st April 2016–31st March 2021). Acknowledgments: Achieving the Age-GB study aims is a team effort and the authors gratefully acknowledge the efforts from Grant holders, colleagues & students: Phyo Myint, Karen Scott, Jenny Martin, Roy Soiza, Emma Law, Sandra Mann, Eunice Morgan, Claire Fyfe, Nicola Smith, Mitrysha Kishor.Peer reviewedPublisher PD

Mentoring New Faculty: An Appreciative Approach

During this period of dramatic social and institutional change in higher education, positive induction and ongoing support for early-career and faculty members new to the campus community is essential. Disparities remain in the recruitment, development, retention, and promotion of diverse faculty, in large part because of the lack of mentoring. The purpose of this article is to enhance approaches for supporting early-career and otherwise new faculty members. Based upon the principles and processes of Appreciative Inquiry, the Appreciative Mentoring Model is presented. Each of the Appreciative Inquiry “D-phases” is described in detail together with research-based best practices that can be employed in mentoring. Prompts, questions, and specific examples designed to support the growing need for a more collaborative, fluid, dynamic, and transformative approach to mentoring are provided.

Information recovery from low coverage whole-genome bisulfite sequencing.

The cost of whole-genome bisulfite sequencing (WGBS) remains a bottleneck for many studies and it is therefore imperative to extract as much information as possible from a given dataset. This is particularly important because even at the recommend 30X coverage for reference methylomes, up to 50% of high-resolution features such as differentially methylated positions (DMPs) cannot be called with current methods as determined by saturation analysis. To address this limitation, we have developed a tool that dynamically segments WGBS methylomes into blocks of comethylation (COMETs) from which lost information can be recovered in the form of differentially methylated COMETs (DMCs). Using this tool, we demonstrate recovery of ∼30% of the lost DMP information content as DMCs even at very low (5X) coverage. This constitutes twice the amount that can be recovered using an existing method based on differentially methylated regions (DMRs). In addition, we explored the relationship between COMETs and haplotypes in lymphoblastoid cell lines of African and European origin. Using best fit analysis, we show COMETs to be correlated in a population-specific manner, suggesting that this type of dynamic segmentation may be useful for integrated (epi)genome-wide association studies in the future

A Bose-Einstein Approach to the Random Partitioning of an Integer

Consider N equally-spaced points on a circle of circumference N. Choose at random n points out of $N$ on this circle and append clockwise an arc of integral length k to each such point. The resulting random set is made of a random number of connected components. Questions such as the evaluation of the probability of random covering and parking configurations, number and length of the gaps are addressed. They are the discrete versions of similar problems raised in the continuum. For each value of k, asymptotic results are presented when n,N both go to infinity according to two different regimes. This model may equivalently be viewed as a random partitioning problem of N items into n recipients. A grand-canonical balls in boxes approach is also supplied, giving some insight into the multiplicities of the box filling amounts or spacings. The latter model is a k-nearest neighbor random graph with N vertices and kn edges. We shall also briefly consider the covering problem in the context of a random graph model with N vertices and n (out-degree 1) edges whose endpoints are no more bound to be neighbors