Crisis Meets Opportunity: Empowering Faculty when Returning to the Higher Education Classroom​

Access the online Pressbooks version of this article here. This article presents information surrounding how the COVID-19 crisis can lead to opportunities for empowering growth in faculty course development and delivery. The authors show how higher education instructors have implemented remote teaching experiences they used during the pandemic to create engaging learning opportunities for students as they are returning to the higher education classroom. The article explores innovative ideas for communication and instruction, equity issues, and inclusive practices. The authors address the overall changing higher education climate and share their personal experiences transitioning from teaching in a face-to-face setting to going fully remote and back again

Pricing European Options with a Log Student's t-Distribution: a Gosset Formula

The distribution of the returns for a stock are not well described by a normal probability density function (pdf). Student's t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of European call or put options using a log Student's t-distribution, which we call a Gosset approach in honour of W.S. Gosset, the author behind the nom de plume Student. The approach that we present can be used to price European options using other distributions and yields the Black-Scholes formula for returns described by a normal pdf.Comment: 12 journal pages, 9 figures and 3 tables (Submitted to Physica A

The Hartree limit of Born's ensemble for the ground state of a bosonic atom or ion

The non-relativistic bosonic ground state is studied for quantum N-body systems with Coulomb interactions, modeling atoms or ions made of N "bosonic point electrons" bound to an atomic point nucleus of Z "electron" charges, treated in Born--Oppenheimer approximation. It is shown that the (negative) ground state energy E(Z,N) yields the monotonically growing function (E(l N,N) over N cubed). By adapting an argument of Hogreve, it is shown that its limit as N to infinity for l > l* is governed by Hartree theory, with the rescaled bosonic ground state wave function factoring into an infinite product of identical one-body wave functions determined by the Hartree equation. The proof resembles the construction of the thermodynamic mean-field limit of the classical ensembles with thermodynamically unstable interactions, except that here the ensemble is Born's, with the absolute square of the ground state wave function as ensemble probability density function, with the Fisher information functional in the variational principle for Born's ensemble playing the role of the negative of the Gibbs entropy functional in the free-energy variational principle for the classical petit-canonical configurational ensemble.Comment: Corrected version. Accepted for publication in Journal of Mathematical Physic

Statistical mechanics approach to some problems in conformal geometry

A weak law of large numbers is established for a sequence of systems of N classical point particles with logarithmic pair potential in \bbR^n, or \bbS^n, n\in \bbN, which are distributed according to the configurational microcanonical measure $\delta(E-H)$, or rather some regularization thereof, where H is the configurational Hamiltonian and E the configurational energy. When $N\to\infty$ with non-extensive energy scaling E=N^2 \vareps, the particle positions become i.i.d. according to a self-consistent Boltzmann distribution, respectively a superposition of such distributions. The self-consistency condition in n dimensions is some nonlinear elliptic PDE of order n (pseudo-PDE if n is odd) with an exponential nonlinearity. When n=2, this PDE is known in statistical mechanics as Poisson-Boltzmann equation, with applications to point vortices, 2D Coulomb and magnetized plasmas and gravitational systems. It is then also known in conformal differential geometry, where it is the central equation in Nirenberg's problem of prescribed Gaussian curvature. For constant Gauss curvature it becomes Liouville's equation, which also appears in two-dimensional so-called quantum Liouville gravity. The PDE for n=4 is Paneitz' equation, and while it is not known in statistical mechanics, it originated from a study of the conformal invariance of Maxwell's electromagnetism and has made its appearance in some recent model of four-dimensional quantum gravity. In differential geometry, the Paneitz equation and its higher order n generalizations have applications in the conformal geometry of n-manifolds, but no physical applications yet for general n. Interestingly, though, all the Paneitz equations have an interpretation in terms of statistical mechanics.Comment: 17 pages. To appear in Physica

The Vlasov continuum limit for the classical microcanonical ensemble

For classical Hamiltonian N-body systems with mildly regular pair interaction potential it is shown that when N tends to infinity in a fixed bounded domain, with energy E scaling quadratically in N proportional to e, then Boltzmann's ergodic ensemble entropy S(N,E) has the asymptotic expansion S(N,E) = - N log N + s(e) N + o(N); here, the N log N term is combinatorial in origin and independent of the rescaled Hamiltonian while s(e) is the system-specific Boltzmann entropy per particle, i.e. -s(e) is the minimum of Boltzmann's H-function for a perfect gas of "energy" e subjected to a combination of externally and self-generated fields. It is also shown that any limit point of the n-point marginal ensemble measures is a linear convex superposition of n-fold products of the H-function-minimizing one-point functions. The proofs are direct, in the sense that (a) the map E to S(E) is studied rather than its inverse S to E(S); (b) no regularization of the microcanonical measure Dirac(E-H) is invoked, and (c) no detour via the canonical ensemble. The proofs hold irrespective of whether microcanonical and canonical ensembles are equivalent or not.Comment: Final version; a few typos corrected; minor changes in the presentatio

The multifaceted presentation of chronic recurrent multifocal osteomyelitis: a series of 486 cases from the Eurofever international registry

Objectives: Chronic non-bacterial osteomyelitis (CNO) or chronic recurrent multifocal osteomyelitis (CRMO) is an autoinflammatory disorder characterized by sterile bone osteolytic lesions. The aim of this study was to evaluate the demographic data and clinical, instrumental and therapeutic features at baseline in a large series of CNO/CRMO patients enrolled in the Eurofever registry. Methods: A web-based registry collected retrospective data on patients affected by CRMO/CNO. Both paediatric and adult centres were involved. Results: Complete baseline information on 486 patients was available (176 male, 310 female). The mean age of onset was 9.9 years. Adult onset (>18 years of age) was observed in 31 (6.3%) patients. The mean time from disease onset to final diagnosis was 1 year (range 0-15). MRI was performed at baseline in 426 patients (88%), revealing a mean number of 4.1 lesions. More frequent manifestations not directly related to bone involvement were myalgia (12%), mucocutaneous manifestations (5% acne, 5% palmoplantar pustulosis, 4% psoriasis, 3% papulopustular lesions, 2% urticarial rash) and gastrointestinal symptoms (8%). A total of 361 patients have been treated with NSAIDs, 112 with glucocorticoids, 61 with bisphosphonates, 58 with MTX, 47 with SSZ, 26 with anti-TNF and 4 with anakinra, with a variable response. Conclusion: This is the largest reported case series of CNO patients, showing that the range of associated clinical manifestations is rather heterogeneous. The study confirms that the disease usually presents with an early teenage onset, but it may also occur in adults, even in the absence of mucocutaneous manifestations

Attosecond pulse shaping using a seeded free-electron laser

Attosecond pulses are central to the investigation of valence- and core-electron dynamics on their natural timescales1–3. The reproducible generation and characterization of attosecond waveforms has been demonstrated so far only through the process of high-order harmonic generation4–7. Several methods for shaping attosecond waveforms have been proposed, including the use of metallic filters8,9, multilayer mirrors10 and manipulation of the driving field11. However, none of these approaches allows the flexible manipulation of the temporal characteristics of the attosecond waveforms, and they suffer from the low conversion efficiency of the high-order harmonic generation process. Free-electron lasers, by contrast, deliver femtosecond, extreme-ultraviolet and X-ray pulses with energies ranging from tens of microjoules to a few millijoules12,13. Recent experiments have shown that they can generate subfemtosecond spikes, but with temporal characteristics that change shot-to-shot14–16. Here we report reproducible generation of high-energy (microjoule level) attosecond waveforms using a seeded free-electron laser17. We demonstrate amplitude and phase manipulation of the harmonic components of an attosecond pulse train in combination with an approach for its temporal reconstruction. The results presented here open the way to performing attosecond time-resolved experiments with free-electron lasers