TT-adic exponential sums of polynomials in one variable

The $T$-adic exponential sum of a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function of the T-adic exponential sum. This bound gives lower bounds for the Newton polygon of the $L$-function of exponential sums of $p$-power order

The Ising model and Special Geometries

We show that the globally nilpotent G-operators corresponding to the factors of the linear differential operators annihilating the multifold integrals $\chi^{(n)}$ of the magnetic susceptibility of the Ising model ($n \le 6$) are homomorphic to their adjoint. This property of being self-adjoint up to operator homomorphisms, is equivalent to the fact that their symmetric square, or their exterior square, have rational solutions. The differential Galois groups are in the special orthogonal, or symplectic, groups. This self-adjoint (up to operator equivalence) property means that the factor operators we already know to be Derived from Geometry, are special globally nilpotent operators: they correspond to "Special Geometries". Beyond the small order factor operators (occurring in the linear differential operators associated with $\chi^{(5)}$ and $\chi^{(6)}$), and, in particular, those associated with modular forms, we focus on the quite large order-twelve and order-23 operators. We show that the order-twelve operator has an exterior square which annihilates a rational solution. Then, its differential Galois group is in the symplectic group $Sp(12, \mathbb{C})$. The order-23 operator is shown to factorize in an order-two operator and an order-21 operator. The symmetric square of this order-21 operator has a rational solution. Its differential Galois group is, thus, in the orthogonal group $SO(21, \mathbb{C})$.Comment: 33 page

Mixed Braid Group Actions From Deformations of Surface Singularities

We consider a set of toric Calabi-Yau varieties which arise as deformations of the small resolutions of type A surface singularities. By careful analysis of the heuristics of B-brane transport in the associated GLSMs, we predict the existence of a mixed braid group action on the derived category of each variety, and then prove that this action does indeed exist. This generalizes the braid group action found by Seidel and Thomas for the undeformed resolutions. We also show that the actions for different deformations are related, in a way that is predicted by the physical heuristics.Comment: 37 pages, including many figures and example

Biorefinery and Hydrogen Fuel Cell Research

In this project we focused on several aspects of technology development that advances the formation of an integrated biorefinery. These focus areas include: [1] establishment of pyrolysis processing systems and characterization of the product oils for fuel applications, including engine testing of a preferred product and its pro forma economic analysis; [2] extraction of sugars through a novel hotwater extaction process, and the development of levoglucosan (a pyrolysis BioOil intermediate); [3] identification and testing of the use of biochar, the coproduct from pyrolysis, for soil applications; [4] developments in methods of atomic layer epitaxy (for efficient development of coatings as in fuel cells); [5] advancement in fermentation of lignocellulosics, [6] development of algal biomass as a potential substrate for the biorefinery, and [7] development of catalysts from coproducts. These advancements are intended to provide a diverse set of product choices within the biorefinery, thus improving the cost effectiveness of the system. Technical effectiveness was demonstrated in the pyrolysis biooil based diesel fuel supplement, sugar extraction from lignocelluose, use of biochar, production of algal biomass in wastewaters, and the development of catalysts. Economic feasibility of algal biomass production systems seems attractive, relative to the other options. However, further optimization in all paths, and testing/demonstration at larger scales are required to fully understand the economic viabilities. The various coproducts provide a clear picture that multiple streams of value can be generated within an integrated biorefinery, and these include fuels and products

Biorefinery and Carbon Cycling Research Project

In this project we focused on several aspects of technology development that advances the formation of an integrated biorefinery. These focus areas include: [ 1] pretreatment of biomass to enhance quality of products from thermochemical conversion; [2] characterization of and development of coproduct uses; [3] advancement in fermentation of lignocellulosics and particularly C5 and C6 sugars simultaneously, and [ 4] development of algal biomass as a potential substrate for the biorefinery. These advancements are intended to provide a diverse set of product choices within the biorefinery, thus improving the cost effectiveness of the system. Technical effectiveness was demonstrated in the thermochemical product quality in the form of lower tar production, simultaneous of use of multiple sugars in fermentation, use ofbiochar in environmental (ammonia adsorption) and agricultural applications, and production of algal biomass in wastewaters. Economic feasibility of algal biomass production systems seems attractive, relative to the other options. However, further optimization in all paths, and testing/demonstration at larger scales are required to fully understand the economic viabilities. The coproducts provide a clear picture that multiple streams of value can be generated within an integrated biorefinery, and these include fuels and products

Are health systems interventions gender blind? examining health system reconstruction in conflict affected states

Background Global health policy prioritizes improving the health of women and girls, as evident in the Sustainable Development Goals (SDGs), multiple women’s health initiatives, and the billions of dollars spent by international donors and national governments to improve health service delivery in low-income countries. Countries recovering from fragility and conflict often engage in wide-ranging institutional reforms, including within the health system, to address inequities. Research and policy do not sufficiently explore how health system interventions contribute to the broader goal of gender equity. Methods This paper utilizes a framework synthesis approach to examine if and how rebuilding health systems affected gender equity in the post-conflict contexts of Mozambique, Timor Leste, Sierra Leone, and Northern Uganda. To undertake this analysis, we utilized the WHO health systems building blocks to establish benchmarks of gender equity. We then identified and evaluated a broad range of available evidence on these building blocks within these four contexts. We reviewed the evidence to assess if and how health interventions during the post-conflict reconstruction period met these gender equity benchmarks. Findings Our analysis shows that the four countries did not meet gender equitable benchmarks in their health systems. Across all four contexts, health interventions did not adequately reflect on how gender norms are replicated by the health system, and conversely, how the health system can transform these gender norms and promote gender equity. Gender inequity undermined the ability of health systems to effectively improve health outcomes for women and girls. From our findings, we suggest the key attributes of gender equitable health systems to guide further research and policy. Conclusion The use of gender equitable benchmarks provides important insights into how health system interventions in the post-conflict period neglected the role of the health system in addressing or perpetuating gender inequities. Given the frequent contact made by individuals with health services, and the important role of the health system within societies, this gender blind nature of health system engagement missed an important opportunity to contribute to more equitable and peaceful societies

An index theorem for 𝑝-adic differential operators

A system of first order linear differential operators satisfying conditions arising naturally in geometry (rational function coefficients, regular singularities, non-Liouville exponents) is considered. It is shown that the index of the system on certain spaces of holomorphic functions can be calculated by restricting to a subspace of rational functions. This is applied to obtain an explicit formula for the index of a single kth order linear differential operator.</p