Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Dark sectors 2016 Workshop: community report

This report, based on the Dark Sectors workshop at SLAC in April 2016, summarizes the scientific importance of searches for dark sector dark matter and forces at masses beneath the weak-scale, the status of this broad international field, the important milestones motivating future exploration, and promising experimental opportunities to reach these milestones over the next 5-10 years

The home environment and childhood obesity in low-income households: indirect effects via sleep duration and screen time

Background Childhood obesity disproportionally affects children from low-income households. With the aim of informing interventions, this study examined pathways through which the physical and social home environment may promote childhood overweight/obesity in low-income households. Methods Data on health behaviors and the home environment were collected at home visits in low-income, urban households with either only normal weight (n = 48) or predominantly overweight/obese (n = 55) children aged 6–13 years. Research staff conducted comprehensive, in-person audits of the foods, media, and sports equipment in each household. Anthropometric measurements were collected, and children’s physical activity was assessed through accelerometry. Caregivers and children jointly reported on child sleep duration, screen time, and dietary intake of foods previously implicated in childhood obesity risk. Path analysis was used to test direct and indirect associations between the home environment and child weight status via the health behaviors assessed. Results Sleep duration was the only health behavior associated with child weight status (OR = 0.45, 95% CI: 0.27, 0.77), with normal weight children sleeping 33.3 minutes/day longer on average than overweight/obese children. The best-fitting path model explained 26% of variance in child weight status, and included paths linking chaos in the home environment, lower caregiver screen time monitoring, inconsistent implementation of bedtime routines, and the presence of a television in children’s bedrooms to childhood overweight/obesity through effects on screen time and sleep duration. Conclusions This study adds to the existing literature by identifying aspects of the home environment that influence childhood weight status via indirect effects on screen time and sleep duration in children from low-income households. Pediatric weight management interventions for low-income households may be improved by targeting aspects of the physical and social home environment associated with sleep

Polymorphisms in the Estrogen Receptor 1 and Vitamin C and Matrix Metalloproteinase Gene Families Are Associated with Susceptibility to Lymphoma

BACKGROUND: Non-Hodgkin lymphoma (NHL) is the fifth most common cancer in the U.S. and few causes have been identified. Genetic association studies may help identify environmental risk factors and enhance our understanding of disease mechanisms. METHODOLOGY/PRINCIPAL FINDINGS: 768 coding and haplotype tagging SNPs in 146 genes were examined using Illumina GoldenGate technology in a large population-based case-control study of NHL in the San Francisco Bay Area (1,292 cases 1,375 controls are included here). Statistical analyses were restricted to HIV- participants of white non-Hispanic origin. Genes involved in steroidogenesis, immune function, cell signaling, sunlight exposure, xenobiotic metabolism/oxidative stress, energy balance, and uptake and metabolism of cholesterol, folate and vitamin C were investigated. Sixteen SNPs in eight pathways and nine haplotypes were associated with NHL after correction for multiple testing at the adjusted q<0.10 level. Eight SNPs were tested in an independent case-control study of lymphoma in Germany (494 NHL cases and 494 matched controls). Novel associations with common variants in estrogen receptor 1 (ESR1) and in the vitamin C receptor and matrix metalloproteinase gene families were observed. Four ESR1 SNPs were associated with follicular lymphoma (FL) in the U.S. study, with rs3020314 remaining associated with reduced risk of FL after multiple testing adjustments [odds ratio (OR) = 0.42, 95% confidence interval (CI) = 0.23-0.77) and replication in the German study (OR = 0.24, 95% CI = 0.06-0.94). Several SNPs and haplotypes in the matrix metalloproteinase-3 (MMP3) and MMP9 genes and in the vitamin C receptor genes, solute carrier family 23 member 1 (SLC23A1) and SLC23A2, showed associations with NHL risk. CONCLUSIONS/SIGNIFICANCE: Our findings suggest a role for estrogen, vitamin C and matrix metalloproteinases in the pathogenesis of NHL that will require further validation

Expression of SPIG1 Reveals Development of a Retinal Ganglion Cell Subtype Projecting to the Medial Terminal Nucleus in the Mouse

Visual information is transmitted to the brain by roughly a dozen distinct types of retinal ganglion cells (RGCs) defined by a characteristic morphology, physiology, and central projections. However, our understanding about how these parallel pathways develop is still in its infancy, because few molecular markers corresponding to individual RGC types are available. Previously, we reported a secretory protein, SPIG1 (clone name; D/Bsp120I #1), preferentially expressed in the dorsal region in the developing chick retina. Here, we generated knock-in mice to visualize SPIG1-expressing cells with green fluorescent protein. We found that the mouse retina is subdivided into two distinct domains for SPIG1 expression and SPIG1 effectively marks a unique subtype of the retinal ganglion cells during the neonatal period. SPIG1-positive RGCs in the dorsotemporal domain project to the dorsal lateral geniculate nucleus (dLGN), superior colliculus, and accessory optic system (AOS). In contrast, in the remaining region, here named the pan-ventronasal domain, SPIG1-positive cells form a regular mosaic and project exclusively to the medial terminal nucleus (MTN) of the AOS that mediates the optokinetic nystagmus as early as P1. Their dendrites costratify with ON cholinergic amacrine strata in the inner plexiform layer as early as P3. These findings suggest that these SPIG1-positive cells are the ON direction selective ganglion cells (DSGCs). Moreover, the MTN-projecting cells in the pan-ventronasal domain are apparently composed of two distinct but interdependent regular mosaics depending on the presence or absence of SPIG1, indicating that they comprise two functionally distinct subtypes of the ON DSGCs. The formation of the regular mosaic appears to be commenced at the end of the prenatal stage and completed through the peak period of the cell death at P6. SPIG1 will thus serve as a useful molecular marker for future studies on the development and function of ON DSGCs

A Multi-cell, Multi-scale Model of Vertebrate Segmentation and Somite Formation

Somitogenesis, the formation of the body's primary segmental structure common to all vertebrate development, requires coordination between biological mechanisms at several scales. Explaining how these mechanisms interact across scales and how events are coordinated in space and time is necessary for a complete understanding of somitogenesis and its evolutionary flexibility. So far, mechanisms of somitogenesis have been studied independently. To test the consistency, integrability and combined explanatory power of current prevailing hypotheses, we built an integrated clock-and-wavefront model including submodels of the intracellular segmentation clock, intercellular segmentation-clock coupling via Delta/Notch signaling, an FGF8 determination front, delayed differentiation, clock-wavefront readout, and differential-cell-cell-adhesion-driven cell sorting. We identify inconsistencies between existing submodels and gaps in the current understanding of somitogenesis mechanisms, and propose novel submodels and extensions of existing submodels where necessary. For reasonable initial conditions, 2D simulations of our model robustly generate spatially and temporally regular somites, realistic dynamic morphologies and spontaneous emergence of anterior-traveling stripes of Lfng. We show that these traveling stripes are pseudo-waves rather than true propagating waves. Our model is flexible enough to generate interspecies-like variation in somite size in response to changes in the PSM growth rate and segmentation-clock period, and in the number and width of Lfng stripes in response to changes in the PSM growth rate, segmentation-clock period and PSM length

A large genome-wide association study of age-related macular degeneration highlights contributions of rare and common variants.

This is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/ng.3448Advanced age-related macular degeneration (AMD) is the leading cause of blindness in the elderly, with limited therapeutic options. Here we report on a study of >12 million variants, including 163,714 directly genotyped, mostly rare, protein-altering variants. Analyzing 16,144 patients and 17,832 controls, we identify 52 independently associated common and rare variants (P < 5 × 10(-8)) distributed across 34 loci. Although wet and dry AMD subtypes exhibit predominantly shared genetics, we identify the first genetic association signal specific to wet AMD, near MMP9 (difference P value = 4.1 × 10(-10)). Very rare coding variants (frequency <0.1%) in CFH, CFI and TIMP3 suggest causal roles for these genes, as does a splice variant in SLC16A8. Our results support the hypothesis that rare coding variants can pinpoint causal genes within known genetic loci and illustrate that applying the approach systematically to detect new loci requires extremely large sample sizes.We thank all participants of all the studies included for enabling this research by their participation in these studies. Computer resources for this project have been provided by the high-performance computing centers of the University of Michigan and the University of Regensburg. Group-specific acknowledgments can be found in the Supplementary Note. The Center for Inherited Diseases Research (CIDR) Program contract number is HHSN268201200008I. This and the main consortium work were predominantly funded by 1X01HG006934-01 to G.R.A. and R01 EY022310 to J.L.H

Large-scale analyses of common and rare variants identify 12 new loci associated with atrial fibrillation

Atrial fibrillation affects more than 33 million people worldwide and increases the risk of stroke, heart failure, and death. Fourteen genetic loci have been associated with atrial fibrillation in European and Asian ancestry groups. To further define the genetic basis of atrial fibrillation, we performed large-scale, trans-ancestry meta-analyses of common and rare variant association studies. The genome-wide association studies (GWAS) included 17,931 individuals with atrial fibrillation and 115,142 referents; the exome-wide association studies (ExWAS) and rare variant association studies (RVAS) involved 22,346 cases and 132,086 referents. We identified 12 new genetic loci that exceeded genome-wide significance, implicating genes involved in cardiac electrical and structural remodeling. Our results nearly double the number of known genetic loci for atrial fibrillation, provide insights into the molecular basis of atrial fibrillation, and may facilitate the identification of new potential targets for drug discovery