A New Interdisciplinary Mathematics and Science Course

As Norfolk State University has been considering how to adequately prepare students to teach the challenging new mathematics and science called for the Virginia Standards of Learning [1], we have reached the conclusion that the student programs need to provide interdisciplinary experiences linking mathematics and science. We reached the conclusion for two reasons. First, even with the larger number of courses called for in the new licensure regulations, there are not enough course hours available to teach all of the different mathematics and science topics that future teachers need to have studied. Second, elementary and middle school students do not study science and mathematics organized in the same way as these topics are organized in universities. Rather, students are interested in, and study, broader topics such as the working of the human body or the structure of a broad ecological system. In order for teachers to teach these subjects in this way, making use of the appropriate mathematics behind these structures, they must have themselves studied these topics in this manner. The new course, Interdisciplinary Mathematics and Science, that has been developed at Norfolk State University, provides students with an interdisciplinary background, then requires each student to study a broad interdisciplinary topic as a member of a team, and then to prepare oral and written presentations on this topic. The course, and the experience of students with this course, will be described in this paper

Kaon Condensation in a Nambu--Jona-Lasinio (NJL) Model at High Density

We demonstrate a fully self-consistent microscopic realization of a kaon-condensed colour-flavour locked state (CFLK0) within the context of a mean-field NJL model at high density. The properties of this state are shown to be consistent with the QCD low-energy effective theory once the proper gauge neutrality conditions are satisfied, and a simple matching procedure is used to compute the pion decay constant, which agrees with the perturbative QCD result. The NJL model is used to compare the energies of the CFLK0 state to the parity even CFL state, and to determine locations of the metal/insulator transition to a phase with gapless fermionic excitations in the presence of a non-zero hypercharge chemical potential and a non-zero strange quark mass. The transition points are compared with results derived previously via effective theories and with partially self-consistent NJL calculations. We find that the qualitative physics does not change, but that the transitions are slightly lower.Comment: 21 pages, ReVTeX4. Clarified discussion and minor change

A modal model for diffraction gratings

A description of an algorithm for a rather general modal grating calculation is presented. Arbitrary profiles, depth, and permittivity are allowed. Gratings built up from sub-gratings are allowed, as are coatings on the sidewalls of lines, and arbitrary complex structure. Conical angles and good conductors are supported

Where the wild things are: Seasonal variation in caribou distribution in relation to climate change

In this study, we develop a method to analyse the relationships between seasonal caribou distribution and climate, to estimate how climatic conditions affect interactions between humans and caribou, and ultimately to predict patterns of distribution relative to climate change. Satellite locations for the Porcupine (Rangifer tarandus granti) and Bathurst (R. t. groenlandicus) caribou herds were analysed for eight ecologically-defined seasons. For each season, two levels of a key environmental factor influencing caribou distribution were identified, as well as the best climate data available to indicate the factor's annual state. Satellite locations were grouped according to the relevant combination of season and environmental factor. Caribou distributions were compared for opposing environmental factors; this comparison was undertaken relative to hunting access for the Porcupine Herd and relative to exposure to mining activity for the Bathurst Herd. Expected climate trends suggest an overall increase in access to Porcupine caribou for Aklavik (NWT) hunters during the winter and rut seasons, for Venetie (Alaska) hunters during midsummer and fall migration and for Arctic Village (Alaska) during midsummer. Arctic Village may experience reduced availability with early snowfalls in the fall, but we expect there to be little directional shift in the spring migration patterns. For the Bathurst Herd, we expect that fewer caribou would be exposed to the mines during the winter, while more caribou would be exposed to the combined Ekati and Diavik mining zone in the early summer and to the Lupin-Jericho mining zone during the fall migration. If changes in climate cause an increased presence of caribou in the mining sites, monitoring and mitigation measures may need to be intensified

Capital allocation for credit portfolios with kernel estimators

Determining contributions by sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often economic capital is measured as Value-at-Risk (VaR) of the portfolio loss distribution. For many of the credit portfolio risk models used in practice, the VaR contributions then have to be estimated from Monte Carlo samples. In the context of a partly continuous loss distribution (i.e. continuous except for a positive point mass on zero), we investigate how to combine kernel estimation methods with importance sampling to achieve more efficient (i.e. less volatile) estimation of VaR contributions.Comment: 22 pages, 12 tables, 1 figure, some amendment

Distorted Copulas: Constructions and Tail Dependence

Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails

Exploring Zeptosecond Quantum Equilibration Dynamics: From Deep-Inelastic to Fusion-Fission Outcomes in 58^{58}Ni+60^{60}Ni Reactions

Energy dissipative processes play a key role in how quantum many-body systems dynamically evolve towards equilibrium. In closed quantum systems, such processes are attributed to the transfer of energy from collective motion to single-particle degrees of freedom; however, the quantum many-body dynamics of this evolutionary process are poorly understood. To explore energy dissipative phenomena and equilibration dynamics in one such system, an experimental investigation of deep-inelastic and fusion-fission outcomes in the $^{58}$Ni+$^{60}$Ni reaction has been carried out. Experimental outcomes have been compared to theoretical predictions using Time Dependent Hartree Fock and Time Dependent Random Phase Approximation approaches, which respectively incorporate one-body energy dissipation and fluctuations. Excellent quantitative agreement has been found between experiment and calculations, indicating that microscopic models incorporating one-body dissipation and fluctuations provide a potential tool for exploring dissipation in low-energy heavy ion collisions.Comment: 11 pages, 9 figures, 1 table, including Supplemental Material - Version accepted for publication in Physical Review Letter

Intermediate Tail Dependence: A Review and Some New Results

The concept of intermediate tail dependence is useful if one wants to quantify the degree of positive dependence in the tails when there is no strong evidence of presence of the usual tail dependence. We first review existing studies on intermediate tail dependence, and then we report new results to supplement the review. Intermediate tail dependence for elliptical, extreme value and Archimedean copulas are reviewed and further studied, respectively. For Archimedean copulas, we not only consider the frailty model but also the recently studied scale mixture model; for the latter, conditions leading to upper intermediate tail dependence are presented, and it provides a useful way to simulate copulas with desirable intermediate tail dependence structures.Comment: 25 pages, 1 figur