Differential equations for the cuspoid canonical integrals

Differential equations satisfied by the cuspoid canonical integrals I_n(a) are obtained for arbitrary values of n≥2, where n−1 is the codimension of the singularity and a=(ɑ_1,ɑ_2,...,ɑ_(n−1)). A set of linear coupled ordinary differential equations is derived for each step in the sequence I_n(0,0,...,0,0) →I_n(0,0,...,0,ɑ_(n−1)) →I_n(0,0,...,ɑ_(n−2),ɑ_(n−1)) →...→I_n(0,ɑ_2,...,ɑ_(n−2),ɑ_(n−1)) →I_n(ɑ_1,ɑ_2,...,ɑ_n−2,ɑ_(n−1)). The initial conditions for a given step are obtained from the solutions of the previous step. As examples of the formalism, the differential equations for n=2 (fold), n=3 (cusp), n=4 (swallowtail), and n=5 (butterfly) are given explicitly. In addition, iterative and algebraic methods are described for determining the parameters a that are required in the uniform asymptotic cuspoid approximation for oscillating integrals with many coalescing saddle points. The results in this paper unify and generalize previous researches on the properties of the cuspoid canonical integrals and their partial derivatives

FY 1998 Juvenile Justice and Delinquency Prevention Act Compliance Monitoring Report

This report was superseded by an amended FY 1998 compliance monitoring report prepared by Eric W. Weatherby, Juvenile Probabation Officer IV, Alaska Division of Juvenile Justice, July 2001.The Juvenile Justice and Delinquency Prevention Act (JJDPA) mandates removal of status offenders and nonoffenders from secure detention and correctional facilities, sight and sound separation of juveniles and adults, and removal of juveniles from adult jails and lockups. In Alaska, 3 instances of status offenders held in secure detention were recorded in FY 1998, compared with 485 violations in the baseline year of CY 1976. 2 separation violations were recorded in FY 1998, representing a 99.8% reduction from the CY 1976 baseline of 824 violations. 57 jail removal violations were projected (52 (actual), representing an 93% reduction from the CY 1980 baseline.Alaska Department of Health and Social Services, Division of Family and Youth ServicesA. General Information / B. Removal of Status Offenders and Nonoffenders from Secure Detention and Correctional Facilities / C. Full Compliance Request / D. Progress Made in Achieving Removal of Status Offenders and Nonoffenders from Secure Detention and Correctional Facilities / E. Separation of Juveniles and Adults / F. Removal of Juveniles from Adult Jails and Lockups / G. De Minimis Request: Substantive / APPENDICES / I. Method of Analysis / II. Fiscal Year 1998 Violations by Offense Type and Location / III. Common Offense Acronym

Construction of the SLO Botanical Gardens Foot Bridge - Interdisciplinary Project

In the Winter quarter of 2020, a project based senior project was sought out by a Cal Poly Construction Management student, and he was connected with the San Luis Obispo Botanical Gardens (SLO BG). SLO BG is a non-profit organization located on 150 acres in the El Chorro Regional Park. After meeting with the SLO BG staff and exploring their many needed projects, the student and the staff mutually concluded that he would build a bridge and accompanying stairs which resided on a well-traveled trail on the property. He successfully developed the project schedule, budget, recruited an architect for design assistance, and secured funding for the project. However, many delays were faced due to the COVID-19 pandemic and government bureaucracy. The scope of the project was subsequently changed to become a purely preconstruction and prefabrication project. Throughout the duration of work, the materials were acquired, prefabricated, plans were created and revised many times, the permitting process was started, and the site was prepared for the installation of the bridge. The project was brought to the point where the permitting process needed to be completed, and the bridge and stairs need only be installed on site

Evolving database systems : a persistent view

Submitted to POS7 This work was supported in St Andrews by EPSRC Grant GR/J67611 "Delivering the Benefits of Persistence"Orthogonal persistence ensures that information will exist for as long as it is useful, for which it must have the ability to evolve with the growing needs of the application systems that use it. This may involve evolution of the data, meta-data, programs and applications, as well as the users' perception of what the information models. The need for evolution has been well recognised in the traditional (data processing) database community and the cost of failing to evolve can be gauged by the resources being invested in interfacing with legacy systems. Zdonik has identified new classes of application, such as scientific, financial and hypermedia, that require new approaches to evolution. These applications are characterised by their need to store large amounts of data whose structure must evolve as it is discovered by the applications that use it. This requires that the data be mapped dynamically to an evolving schema. Here, we discuss the problems of evolution in these new classes of application within an orthogonally persistent environment and outline some approaches to these problems.Postprin

Effect of current corrugations on the stability of the tearing mode

The generation of zonal magnetic fields in laboratory fusion plasmas is predicted by theoretical and numerical models and was recently observed experimentally. It is shown that the modification of the current density gradient associated with such corrugations can significantly affect the stability of the tearing mode. A simple scaling law is derived that predicts the impact of small stationary current corrugations on the stability parameter $\Delta'$. The described destabilization mechanism can provide an explanation for the trigger of the Neoclassical Tearing Mode (NTM) in plasmas without significant MHD activity.Comment: Accepted to Physics of Plasma

Quantifying evolutionary constraints on B cell affinity maturation

The antibody repertoire of each individual is continuously updated by the evolutionary process of B cell receptor mutation and selection. It has recently become possible to gain detailed information concerning this process through high-throughput sequencing. Here, we develop modern statistical molecular evolution methods for the analysis of B cell sequence data, and then apply them to a very deep short-read data set of B cell receptors. We find that the substitution process is conserved across individuals but varies significantly across gene segments. We investigate selection on B cell receptors using a novel method that side-steps the difficulties encountered by previous work in differentiating between selection and motif-driven mutation; this is done through stochastic mapping and empirical Bayes estimators that compare the evolution of in-frame and out-of-frame rearrangements. We use this new method to derive a per-residue map of selection, which provides a more nuanced view of the constraints on framework and variable regions.Comment: Previously entitled "Substitution and site-specific selection driving B cell affinity maturation is consistent across individuals

Dynamical Phase Transitions In Driven Integrate-And-Fire Neurons

We explore the dynamics of an integrate-and-fire neuron with an oscillatory stimulus. The frustration due to the competition between the neuron's natural firing period and that of the oscillatory rhythm, leads to a rich structure of asymptotic phase locking patterns and ordering dynamics. The phase transitions between these states can be classified as either tangent or discontinuous bifurcations, each with its own characteristic scaling laws. The discontinuous bifurcations exhibit a new kind of phase transition that may be viewed as intermediate between continuous and first order, while tangent bifurcations behave like continuous transitions with a diverging coherence scale.Comment: 4 pages, 5 figure

Can restricting calories help you to live longer?

Excess calorie consumption is associated with metabolic disorders and increased incidence of morbidity. Restricting calorie content, either by daily calorie restriction or intermittent fasting periods, has multiple benefits including weight loss and improved body composition. Previous research has shown that restricting calories in this way can increase longevity and slow the ageing process in laboratory animals, although only sparse data exist in human populations. This review critically evaluates the benefits of these dietary interventions on age-related decline and longevity