Spectral Difference Equations Satisfied by KP Soliton Wavefunctions

The Baker-Akhiezer (wave) functions corresponding to soliton solutions of the KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring of translational operators in the spectral parameter. In the rational limit, these translational operators converge to the differential operators in the spectral parameter previously discussed as part of the theory of "bispectrality". Consequently, these translational operators can be seen as demonstrating a form of bispectrality for the non-rational solitons as well.Comment: to appear in "Inverse Problems

Quartz-based flat-crystal resonant inelastic x-ray scattering spectrometer with sub-10 meV energy resolution

Continued improvement of the energy resolution of resonant inelastic x-ray scattering (RIXS) spectrometers is crucial for fulfilling the potential of this technique in the study of electron dynamics in materials of fundamental and technological importance. In particular, RIXS is the only alternative tool to inelastic neutron scattering capable of providing fully momentum resolved information on dynamic spin structures of magnetic materials, but is limited to systems whose magnetic excitation energy scales are comparable to the energy resolution. The state-of-the-art spherical diced crystal analyzer optics provides energy resolution as good as 25 meV but has already reached its theoretical limit. Here, we demonstrate a novel sub-10meV RIXS spectrometer based on flat-crystal optics at the Ir-L$_3$ absorption edge (11.215$\sim$ keV) that achieves an analyzer energy resolution of 3.9$\sim$meV, very close to the theoretical value of 3.7$\sim$meV. In addition, the new spectrometer allows efficient polarization analysis without loss of energy resolution. The performance of the instrument is demonstrated using longitudinal acoustical and optical phonons in diamond, and magnon in Sr$_3$Ir$_2$O$_7$. The novel sub-10$\sim$meV RIXS spectrometer thus provides a window into magnetic materials with small energy scales

Recurrence relations for exceptional Hermite polynomials.

The bispectral anti-isomorphism is applied to differential operators involving elements of the stabilizer ring to produce explicit formulas for all difference operators having any of the Hermite exceptional orthogonal polynomials as eigenfunctions with eigenvalues that are polynomials in x

Male Infertility and Future Cardiometabolic Health: Does the Association Vary by Sociodemographic Factors?

Objective: To determine whether the association between male infertility and incident cardiometabolic disease is modified by socioeconomics, race, or geographic region. / Materials and Method: Retrospective review of data from insurance claims from Optum's de-identified Clinformatics Data Mart Database. Subjects were men, 18-50 years old, with an associated diagnosis of infertility in the United States between 2003 and 2016. Analytical sample were men captured by the Optum's de-identified Clinformatics Data Mart Database with an associated diagnosis of infertility. Men were classified as either infertile, or not, based on diagnosis or procedural codes. Cardiometabolic health outcomes were then assessed using current procedural terminology codes for diabetes, hypertension, hyperlipidemia, and heart disease. Confounding factors were controlled for such as race, education, socioecomonic status, and region. The main outcomes were development of diabetes, hypertension, hyperlipidemia, and heart disease. / Results: A total of 76,343 males were diagnosed with male factor infertility, 60,072 males who underwent fertility testing, and 183,742 males that underwent vasectomy (control population). For all men, infertile men had a higher risk of incident hypertension, diabetes, hyperlipidemia, and heart disease when compared to those undergoing vasectomy. Identical associations were found across all education, income, racial, and geographic strata. / Conclusion: Our study suggests that men with infertility have a higher risk of cardiometabolic disease in the years following a fertility evaluation regardless of race, region, or socioeconomic status

General methods for constructing bispectral operators

We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.Comment: 11 pages, LaTeX2e, uses amsfonts.sty and latexsym.sty, no figure

The role of novelty and fat and sugar concentration in food selection by captive tufted capuchins (Sapajus apella)

Capuchins, like other primates, use feedback from sensory cues and digestion to make decisions about which foods to consume and which to avoid. However, little is known about how capuchins make consumption decisions when simultaneously presented with novel and familiar foods, or how food familiarity and macronutrient concentration together influence food choice, topics with potential implications for developmental and health research. In this study, we evaluated the role of familiarity, as well as fat and sugar concentration, in the food selections of captive tufted capuchins (Sapajus apella). In the first experiment, over ten sessions, subjects were assigned to either a group that chose between one familiar and one novel food item both high in fat or sugar (high condition), or to a group that chose between one familiar and one novel food item both low in fat or sugar (low condition). In the second experiment, subjects were divided into three groups, familiarized with a food over five feeding sessions, and then offered the familiarized food and a novel food that varied in fat or sugar for 10 sessions. When offered foods high in fat, capuchins showed no clear signs of neophobia, forming an initial preference for the novel food, rejecting foods less frequently, and selecting foods faster than when offered foods low in fat. These trends were generally not observed in response to foods with sugar. When presented with options that varied in macronutrient concentration, subjects showed an initial interest in the novel food irrespective of whether it was high in fat or sugar, yet formed a final preference for the higher-concentration item. Findings suggest that the concentration of fat or sugar in novel foods may be an important mediator of exploratory behavior, and that capuchins rely on immediate feedback from taste and other sensory cues to make consumption decisions

Askey-Wilson Type Functions, With Bound States

The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a beautiful symmetry property. It essentially means that the geometric and the spectral parameters are interchangeable in these functions. We call the resulting functions the Askey-Wilson functions. Then, we show that by adding bound states (with arbitrary weights) at specific points outside of the continuous spectrum of some instances of the Askey-Wilson difference operator, we can generate functions that satisfy a doubly infinite three-term recursion relation and are also eigenfunctions of $q$-difference operators of arbitrary orders. Our result provides a discrete analogue of the solutions of the purely differential version of the bispectral problem that were discovered in the pioneering work [8] of Duistermaat and Gr\"unbaum.Comment: 42 pages, Section 3 moved to the end, minor correction

From nonassociativity to solutions of the KP hierarchy

A recently observed relation between 'weakly nonassociative' algebras A (for which the associator (A,A^2,A) vanishes) and the KP hierarchy (with dependent variable in the middle nucleus A' of A) is recalled. For any such algebra there is a nonassociative hierarchy of ODEs, the solutions of which determine solutions of the KP hierarchy. In a special case, and with A' a matrix algebra, this becomes a matrix Riccati hierarchy which is easily solved. The matrix solution then leads to solutions of the scalar KP hierarchy. We discuss some classes of solutions obtained in this way.Comment: 7 pages, 4 figures, International Colloquium 'Integrable Systems and Quantum Symmetries', Prague, 15-17 June 200

Toward optimal implementation of cancer prevention and control programs in public health: A study protocol on mis-implementation

Abstract Background Much of the cancer burden in the USA is preventable, through application of existing knowledge. State-level funders and public health practitioners are in ideal positions to affect programs and policies related to cancer control. Mis-implementation refers to ending effective programs and policies prematurely or continuing ineffective ones. Greater attention to mis-implementation should lead to use of effective interventions and more efficient expenditure of resources, which in the long term, will lead to more positive cancer outcomes. Methods This is a three-phase study that takes a comprehensive approach, leading to the elucidation of tactics for addressing mis-implementation. Phase 1: We assess the extent to which mis-implementation is occurring among state cancer control programs in public health. This initial phase will involve a survey of 800 practitioners representing all states. The programs represented will span the full continuum of cancer control, from primary prevention to survivorship. Phase 2: Using data from phase 1 to identify organizations in which mis-implementation is particularly high or low, the team will conduct eight comparative case studies to get a richer understanding of mis-implementation and to understand contextual differences. These case studies will highlight lessons learned about mis-implementation and identify hypothesized drivers. Phase 3: Agent-based modeling will be used to identify dynamic interactions between individual capacity, organizational capacity, use of evidence, funding, and external factors driving mis-implementation. The team will then translate and disseminate findings from phases 1 to 3 to practitioners and practice-related stakeholders to support the reduction of mis-implementation. Discussion This study is innovative and significant because it will (1) be the first to refine and further develop reliable and valid measures of mis-implementation of public health programs; (2) bring together a strong, transdisciplinary team with significant expertise in practice-based research; (3) use agent-based modeling to address cancer control implementation; and (4) use a participatory, evidence-based, stakeholder-driven approach that will identify key leverage points for addressing mis-implementation among state public health programs. This research is expected to provide replicable computational simulation models that can identify leverage points and public health system dynamics to reduce mis-implementation in cancer control and may be of interest to other health areas