On the discrete spectrum of quantum layers

Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, $\mathcal C^2$ smooth surface embedded in $\mathbb{R}^3$. We assume that the surface is asymptotically flat in the sense that the second fundamental form vanishes at infinity, and that the surface is not totally geodesic. This geometric setting is known as a quantum layer. We consider the quantum particle to be governed by the Dirichlet Laplacian as Hamiltonian. Our work concerns the existence of bound states with energy beneath the essential spectrum, which implies the existence of discrete spectrum. We first prove that if the Gauss curvature is integrable, and the surface is weakly $\kappa$-parabolic, then the discrete spectrum is non-empty. This result implies that if the total Gauss curvature is non-positive, then the discrete spectrum is non-empty. We next prove that if the Gauss curvature is non-negative, then the discrete spectrum is non-empty. Finally, we prove that if the surface is parabolic, then the discrete spectrum is non-empty if the layer is sufficiently thin.Comment: Clarifications and corrections to previous version, conjecture from previous version is proven here (Theorem 1.5), additional references include

Comparative and integrative single cell analysis reveals new insights into the transcriptional immaturity of stem cell-derived β cells

Diabetes cell replacement therapy has the potential to be transformed by human pluripotent stem cell-derived β cells (SC-β cells). However, the precise identity of SC-β cells in relationship to primary fetal and adult β-cells remains unclear. Here, we used single-cell sequencing datasets to characterize the transcriptional identity of islets from in vitro differentiation, fetal islets, and adult islets. Our analysis revealed that SC-β cells share a core β-cell transcriptional identity with human adult and fetal β-cells, however SC-β cells possess a unique transcriptional profile characterized by the persistent expression and activation of progenitor and neural-biased gene networks. These networks are present in SC-β cells, irrespective of the derivation protocol used. Notably, fetal β-cells also exhibit this neural signature at the transcriptional level. Our findings offer insights into the transcriptional identity of SC-β cells and underscore the need for further investigation of the role of neural transcriptional networks in their development

The state of education provision for enterprise and entrepreneurship: A mapping study of England’s HEIs

The aim of this paper is to provide a comprehensive overview of the state of provision for enterprise and entrepreneurship education within England’s Higher Education Institutions (HEIs). The paper is based on the National Council for Graduate Entrepreneurship (NCGE) Mapping Study of enterprise education in England. Research commissioned by NCGE (ISBA 2004) has shown that there is a growing knowledge base about the nature of enterprise education but less so evidence concerning the provision for enhancing student enterprise and graduate entrepreneurship. Although studies have taken place in the US and Levie undertook a study of the UK published in 1999, there has been no recent study that has comprehensively mapped enterprise education activity in all higher education institutions across England. Institutional contacts in 94% of all the HEIs for this study entered data into an online institutional mapping template containing questions on modules/courses, non-accredited support and other institutional characteristics. The researchers maintained regular telephone contact and made personal visits to maximise data entry and to provide support where needed. This approach has led to the collection of a unique and robust data set that has been analysed using SPSS. The paper presents a national overview and highlights selected regional variations in enterprise education and non–accredited entrepreneurship support. This includes: current and planned course provision over time; student profiles and targets; primary learning outcomes; non-accredited provision and student engagement; primary funding sources; and the development of a range of institutional characteristics conducive to supporting student enterprise and graduate entrepreneurship. The findings from the mapping study illuminate the current HE landscape of support for enterprise and entrepreneurship thereby providing HEIs and educators with a valuable national resource. Additionally, this informs other key stakeholders – RDAs and central government – of the scope and scale of the contribution that HEIs offer to regional economic and social agendas. From such a unique evidence base more informed decisions can be taken when considering effective mechanisms for the future growth and development of HEI contributions. This paper offers the findings from a unique and current comprehensive dataset on the HE provision of enterprise and entrepreneurship education in England. With 94% of the HEIs in the study providing data online the study has created a national database that can be a platform for sharing knowledge and experience across the community. Furthermore conducting a repeat online study on an annual basis will provide valuable time series data. The study findings will help shape the future environment for student enterprise and graduate entrepreneurship across England

Dynamics of filaments and membranes in a viscous fluid

Motivated by the motion of biopolymers and membranes in solution, this article presents a formulation of the equations of motion for curves and surfaces in a viscous fluid. We focus on geometrical aspects and simple variational methods for calculating internal stresses and forces, and we derive the full nonlinear equations of motion. In the case of membranes, we pay particular attention to the formulation of the equations of hydrodynamics on a curved, deforming surface. The formalism is illustrated by two simple case studies: (1) the twirling instability of straight elastic rod rotating in a viscous fluid, and (2) the pearling and buckling instabilities of a tubular liposome or polymersome.Comment: 26 pages, 12 figures, to be published in Reviews of Modern Physic

The compensation of Gaussian curvature in developable cones is local

In this paper we use the angular deficit scheme [V. Borrelli, F. Cazals, and J.-M. Morvan, {\sl Computer Aided Geometric Design} {\bf 20}, 319 (2003)] to determine the distribution of Gaussian curvature in developable cones (d-cones) [E. Cerda, S. Chaieb, F. Melo, and L. Mahadevan, {\sl Nature} {\bf 401}, 46 (1999)] numerically. These d-cones are formed by pushing a thin elastic sheet into a circular container. Negative Gaussian curvatures are identified at the rim where the sheet touches the container. Around the rim there are two narrow bands with positive Gaussian curvatures. The integral of the (negative) Gaussian curvature near the rim is almost completely compensated by that of the two adjacent bands. This suggests that the Gauss-Bonnet theorem which constrains the integral of Gaussian curvature globally does not explain the spontaneous curvature cancellation phenomenon [T. Liang and T. A. Witten, {\sl Phys. Rev. E} {\bf 73}, 046604 (2006)]. The locality of the compensation seems to increase for decreasing d-cone thickness. The angular deficit scheme also provides a new way to confirm the curvature cancellation phenomenon.Comment: 12 pages; 5 figure

Towards a sensitive search for variation of the fine structure constant using radio-frequency E1 transitions in atomic dysprosium

It has been proposed that the radio-frequency electric-dipole (E1) transition between two nearly degenerate opposite-parity states in atomic dysprosium should be highly sensitive to possible temporal variation of the fine structure constant ($\alpha$) [V. A. Dzuba, V. V. Flambaum, and J. K. Webb, Phys. Rev. A {\bf 59}, 230 (1999)]. We analyze here an experimental realization of the proposed search in progress in our laboratory, which involves monitoring the E1 transition frequency over a period of time using direct frequency counting techniques. We estimate that a statistical sensitivity of |\adota| \sim 10^{-18}/yr may be achieved and discuss possible systematic effects that may limit such a measurement.Comment: 8 pages, 7 figure

Single-nucleus multi-omics of human stem cell-derived islets identifies deficiencies in lineage specification

Insulin-producing β cells created from human pluripotent stem cells have potential as a therapy for insulin-dependent diabetes, but human pluripotent stem cell-derived islets (SC-islets) still differ from their in vivo counterparts. To better understand the state of cell types within SC-islets and identify lineage specification deficiencies, we used single-nucleus multi-omic sequencing to analyse chromatin accessibility and transcriptional profiles of SC-islets and primary human islets. Here we provide an analysis that enabled the derivation of gene lists and activity for identifying each SC-islet cell type compared with primary islets. Within SC-islets, we found that the difference between β cells and awry enterochromaffin-like cells is a gradient of cell states rather than a stark difference in identity. Furthermore, transplantation of SC-islets in vivo improved cellular identities overtime, while long-term in vitro culture did not. Collectively, our results highlight the importance of chromatin and transcriptional landscapes during islet cell specification and maturation

Is 8:30 a.m. Still Too Early to Start School? A 10:00 a.m. School Start Time Improves Health and Performance of Students Aged 13-16.

While many studies have shown the benefits of later school starts, including better student attendance, higher test scores, and improved sleep duration, few have used starting times later than 9:00 a.m. Here we report on the implementation and impact of a 10 a.m. school start time for 13 to 16-year-old students. A 4-year observational study using a before-after-before (A-B-A) design was carried out in an English state-funded high school. School start times were changed from 8:50 a.m. in study year 0, to 10 a.m. in years 1-2, and then back to 8:50 a.m. in year 3. Measures of student health (absence due to illness) and academic performance (national examination results) were used for all students. Implementing a 10 a.m. start saw a decrease in student illness after 2 years of over 50% (p < 0.0005 and effect size: Cohen's d = 1.07), and reverting to an 8:50 a.m. start reversed this improvement, leading to an increase of 30% in student illness (p < 0.0005 and Cohen's d = 0.47). The 10:00 a.m. start was associated with a 12% increase in the value-added number of students making good academic progress (in standard national examinations) that was significant (<0.0005) and equivalent to 20% of the national benchmark. These results show that changing to a 10:00 a.m. high school start time can greatly reduce illness and improve academic performance. Implementing school start times later than 8:30 a.m., which may address the circadian delay in adolescents' sleep rhythms more effectively for evening chronotypes, appears to have few costs and substantial benefits

Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications

This review presents an overview of the thermal properties of mesoscopic structures. The discussion is based on the concept of electron energy distribution, and, in particular, on controlling and probing it. The temperature of an electron gas is determined by this distribution: refrigeration is equivalent to narrowing it, and thermometry is probing its convolution with a function characterizing the measuring device. Temperature exists, strictly speaking, only in quasiequilibrium in which the distribution follows the Fermi-Dirac form. Interesting nonequilibrium deviations can occur due to slow relaxation rates of the electrons, e.g., among themselves or with lattice phonons. Observation and applications of nonequilibrium phenomena are also discussed. The focus in this paper is at low temperatures, primarily below 4 K, where physical phenomena on mesoscopic scales and hybrid combinations of various types of materials, e.g., superconductors, normal metals, insulators, and doped semiconductors, open up a rich variety of device concepts. This review starts with an introduction to theoretical concepts and experimental results on thermal properties of mesoscopic structures. Then thermometry and refrigeration are examined with an emphasis on experiments. An immediate application of solid-state refrigeration and thermometry is in ultrasensitive radiation detection, which is discussed in depth. This review concludes with a summary of pertinent fabrication methods of presented devices.Comment: Close to the version published in RMP; 59 pages, 35 figure