Predicted 25-hydroxyvitamin D Score and Risk of Multiple Sclerosis in U.S. Women

Multiple sclerosis (MS) is a progressive, autoimmune neurodegenerative disorder affecting nearly 350,000 people in the United States and resulting in significant disability. As an immunomodulator, vitamin D may play a role in the development of MS. Previous studies have observed an inverse association of 25-hydroxyvitamin D (25(OH)D) levels and MS risk in younger populations; however, whether this relationship persists in older adults remains unclear. We prospectively investigated the association between predicted 25(OH)D level and incident MS in the Nurses’ Health Study (NHS) (n=121,701) and NHS II (n=116,430). 25(OH)D levels were predicted using validated regression models that include important determinants of vitamin D status, including race, UV-B flux (based on state of residence), physical activity, body mass index, dietary vitamin D intake, alcohol consumption and post-menopausal hormone use. Data on these factors were self-reported on NHS and NHS II questionnaires starting in 1986 and 1991, respectively, and updated every 2-4 years. MS diagnoses were ascertained by self-report and confirmed by medical records. Cox proportional hazards models adjusted for age, ethnicity, latitude of residence at age 15, and BMI at age 18 were used to estimate hazard ratios (HR)s and 95% confidence intervals (CI)s in each cohort. During up to 18 years of follow-up, we documented 179 definite/probable cases of MS with first symptoms after baseline. Multivariable HRs comparing highest and lowest quintiles of predicted 25(OH)D were 1.09 (95% CI: 0.40-2.96) in the NHS and 0.52 (95% CI: 0.28-0.95) in the NHS II. Higher predicted plasma 25(OH)D may be modestly associated with lower risk of MS, primarily in younger women

Approximate Inference via Fibrations of Statistical Games

We characterize a number of well known systems of approximate inference as loss models: lax sections of 2-fibrations of statistical games, constructed by attaching internally-defined loss functions to Bayesian lenses. Our examples include the relative entropy, which constitutes a strict section, and whose chain rule is formalized by the horizontal composition of the 2-fibration. In order to capture this compositional structure, we first introduce the notion of `copy-composition', alongside corresponding bicategories through which the composition of copy-discard categories factorizes. These bicategories are a variant of the $\mathbf{Copara}$ construction, and so we additionally introduce coparameterized Bayesian lenses, proving that coparameterized Bayesian updates compose optically, as in the non-coparameterized case.Comment: Accepted as a proceedings paper at ACT 202

Vitamin D, Calcium, and Dairy Consumption and Risk of Early Menopause

Early menopause, defined as the cessation of ovarian function before the age of 45, affects roughly 10% of women in Western populations. Current research suggests that women who experience early menopause are at increased risk for cardiovascular disease and other adverse health outcomes. Early menopause may also have substantial financial and psychological consequences for family planning, particularly as women increasingly delay childbearing into the later reproductive years. Emerging research suggests that modifiable lifestyle factors such as diet may play an important role in ovarian aging. According to our review of the current biologic and epidemiologic literature in Chapter 1, vitamin D, calcium, and dairy consumption may be related to the physiologic processes involved in ovarian aging. However, no prior epidemiologic studies have evaluated these exposures with regard to risk of early menopause. Thus, the aim of this dissertation was to evaluate these associations in the prospective Nurses’ Health Study II (NHS2) (n=112,429). In Chapter 2, we evaluated how intakes of vitamin D and calcium are associated with risk of early menopause. Results of this study suggest that high versus low intakes of vitamin D and calcium from food sources, particularly dairy foods, are associated with 17% and 13% lower risk of early menopause, respectively. In Chapter 3, we evaluated how total and free plasma 25-hydroxyvitamin D (25(OH)D) and vitamin D binding protein levels (VDBP) are associated with risk of early menopause. According to our findings, total and free 25(OH)D levels are not associated with risk of early menopause, and VDBP may be positively associated with risk. In Chapter 4, we evaluated how intakes of total, low-fat, high-fat, and individual dairy foods are associated with risk of early menopause. Findings indicate that high versus low intake of low-fat dairy foods is associated with 23% lower risk of early menopause. In particular, intakes of skim milk and yogurt intake were associated with lower risk of early menopause. In conclusion, vitamin D and calcium are not importantly related to early menopause risk. Intake of low-fat dairy foods is associated with lower risk of early menopause, but findings should be replicated in future studies

Mathematical Foundations for a Compositional Account of the Bayesian Brain

This dissertation reports some first steps towards a compositional account of active inference and the Bayesian brain. Specifically, we use the tools of contemporary applied category theory to supply functorial semantics for approximate inference. To do so, we define on the `syntactic' side the new notion of Bayesian lens and show that Bayesian updating composes according to the compositional lens pattern. Using Bayesian lenses, and inspired by compositional game theory, we define fibrations of statistical games and classify various problems of statistical inference as corresponding sections: the chain rule of the relative entropy is formalized as a strict section, while maximum likelihood estimation and the free energy give lax sections. In the process, we introduce a new notion of `copy-composition'. On the `semantic' side, we present a new formalization of general open dynamical systems (particularly: deterministic, stochastic, and random; and discrete- and continuous-time) as certain coalgebras of polynomial functors, which we show collect into monoidal opindexed categories (or, alternatively, into algebras for multicategories of generalized polynomial functors). We use these opindexed categories to define monoidal bicategories of cilia: dynamical systems which control lenses, and which supply the target for our functorial semantics. Accordingly, we construct functors which explain the bidirectional compositional structure of predictive coding neural circuits under the free energy principle, thereby giving a formal mathematical underpinning to the bidirectionality observed in the cortex. Along the way, we explain how to compose rate-coded neural circuits using an algebra for a multicategory of linear circuit diagrams, showing subsequently that this is subsumed by lenses and polynomial functors.Comment: DPhil thesis; as submitted. Main change from v1: improved treatment of statistical games. A number of errors also fixed, and some presentation improved. Comments most welcom

Open Dynamical Systems as Coalgebras for Polynomial Functors, with Application to Predictive Processing

We present categories of open dynamical systems with general time evolution as categories of coalgebras opindexed by polynomial interfaces, and show how this extends the coalgebraic framework to capture common scientific applications such as ordinary differential equations, open Markov processes, and random dynamical systems. We then extend Spivak's operad Org to this setting, and construct associated monoidal categories whose morphisms represent hierarchical open systems; when their interfaces are simple, these categories supply canonical comonoid structures. We exemplify these constructions using the 'Laplace doctrine', which provides dynamical semantics for active inference, and indicate some connections to Bayesian inversion and coalgebraic logic.Comment: In Proceedings ACT 2022, arXiv:2307.1551

Perfectly Matched Layers in a Divergence Preserving ADI Scheme for Electromagnetics

For numerical simulations of highly relativistic and transversely accelerated charged particles including radiation fast algorithms are needed. While the radiation in particle accelerators has wavelengths in the order of 100 um the computational domain has dimensions roughly 5 orders of magnitude larger resulting in very large mesh sizes. The particles are confined to a small area of this domain only. To resolve the smallest scales close to the particles subgrids are envisioned. For reasons of stability the alternating direction implicit (ADI) scheme by D. N. Smithe et al. (J. Comput. Phys. 228 (2009) pp.7289-7299) for Maxwell equations has been adopted. At the boundary of the domain absorbing boundary conditions have to be employed to prevent reflection of the radiation. In this paper we show how the divergence preserving ADI scheme has to be formulated in perfectly matched layers (PML) and compare the performance in several scenarios.Comment: 8 pages, 6 figure