Sub-Planckian black holes and the Generalized Uncertainty Principle

The Black Hole Uncertainty Principle correspondence suggests that there could exist black holes with mass beneath the Planck scale but radius of order the Compton scale rather than Schwarzschild scale. We present a modified, self-dual Schwarzschild-like metric that reproduces desirable aspects of a variety of disparate models in the sub-Planckian limit, while remaining Schwarzschild in the large mass limit. The self-dual nature of this solution under $M \leftrightarrow M^{-1}$ naturally implies a Generalized Uncertainty Principle with the linear form $\Delta x \sim \frac{1}{\Delta p} + \Delta p$. We also demonstrate a natural dimensional reduction feature, in that the gravitational radius and thermodynamics of sub-Planckian objects resemble that of $(1+1)$-D gravity. The temperature of sub-Planckian black holes scales as $M$ rather than $M^{-1}$ but the evaporation of those smaller than $10^{-36}$g is suppressed by the cosmic background radiation. This suggests that relics of this mass could provide the dark matter.Comment: 12 pages, 9 figures, version published in J. High En. Phy

From resource to document: Scaffolding content and organising student learning in teachers’ documentation work on the teaching of series

We examine teachers’ use of resources as they prepare to teach the topic of numerical series of real numbers in order to identify how their personal relationship with mathematical content—and its teaching—interacts with their use of a commonly used textbook. We describe this interplay between textbook and personal relationship, a term coined in the Anthropological Theory of the Didactic (ATD, Chevallard, 2003), in the terms of documentation work (resources, aims, rules of action, operational invariants), a key construct from the documentational approach (DA, Gueudet & Trouche, 2009). We do so in the case of five post-secondary teachers who use the same textbook as a main resource to teach the topic. Documentational analysis of interviews with the teachers led to the identification of their aims and rules of action (the what and how of their resource use as they organise their teaching of the topic) as well as the operational invariants (the why for this organisation of their teaching). We describe the teachers’ documentation work in two sets of aims/rules of action: scaffolding mathematical content (series as a stepping stone to learning about Taylor polynomials and Maclaurin series) and organising student learning about series through drill exercises, visualisation, examples, and applications. Our bridging (networking) of theoretical constructs originating in one theoretical framework (personal relationship, ATD) with the constructs of a different, yet compatible, framework (documentation work, DA) aims to enrich the latter (teachers’ documentation work) with the individual agency (teachers’ personal relationship with the topic) provided by the former

Form factor π0→γ∗+γ∗\pi^0\to \gamma^* +\gamma^* at different photon virtualities

The $\pi^0 \gamma\gamma$ vertex for virtual photons of squared masses $q_1^2$ and $q_2^2$ plays a vital r\^ole in several physical processes; for example for $q_1^2<0$, $q_2^2<0$, in the two-photon physics reaction $e^+ e^-\to e^+ e^- \pi^0$, and for $q_1^2>0$, $q_2^2>0$, in the annihilation process $e^+ e^-\to \pi^0 l^+ l^-$. It is also of interest because of its link to the axial anomaly. We suggest a new approach to this problem. We have obtained a closed analytic expression for the vertex in the limit in which at least one of $|q_1^2|$ and $|q_2^2|$ is large for arbitrary fixed values of the ratio $q_1^2/q_2^2$. We compare our results with those obtained previously by Brodsky and Lepage. It should be straightforward to test our predictions experimentally.Comment: harvmac tex, 30 pages, 11 figures; references are correcte

Socioeconomic status and prostate cancer incidence and mortality rates among the diverse population of California

The racial/ethnic disparities in prostate cancer rates are well documented, with the highest incidence and mortality rates observed among African-Americans followed by non-Hispanic Whites, Hispanics, and Asian/Pacific Islanders. Whether socioeconomic status (SES) can account for these differences in risk has been investigated in previous studies, but with conflicting results. Furthermore, previous studies have focused primarily on the differences between African-Americans and non-Hispanic Whites, and little is known for Hispanics and Asian/Pacific Islanders. To further investigate the relationship between SES and prostate cancer among African-Americans, non-Hispanic Whites, Hispanics, and Asian/Pacific Islanders, we conducted a large population-based cross-sectional study of 98,484 incident prostate cancer cases and 8,997 prostate cancer deaths from California. Data were abstracted from the California Cancer Registry, a population-based surveillance, epidemiology, and end results (SEER) registry. Each prostate cancer case and death was assigned a multidimensional neighborhood-SES index using the 2000 US Census data. SES quintile-specific prostate cancer incidence and mortality rates and rate ratios were estimated using SEER*Stat for each race/ethnicity categorized into 10-year age groups. For prostate cancer incidence, we observed higher levels of SES to be significantly associated with increased risk of disease [SES Q1 vs. Q5: relative risk (RR) = 1.28; 95% confidence interval (CI): 1.25–1.30]. Among younger men (45–64 years), African-Americans had the highest incidence rates followed by non-Hispanic Whites, Hispanics, and Asian/Pacific Islanders for all SES levels. Yet, among older men (75–84 years) Hispanics, following African-Americans, displayed the second highest incidence rates of prostate cancer. For prostate cancer deaths, higher levels of SES were associated with lower mortality rates of prostate cancer deaths (SES Q1 vs. Q5: RR = 0.88; 95% CI: 0.92–0.94). African-Americans had a twofold to fivefold increased risk of prostate cancer deaths in comparison to non-Hispanic Whites across all levels of SES. Our findings suggest that SES alone cannot account for the greater burden of prostate cancer among African-American men. In addition, incidence and mortality rates of prostate cancer display different age and racial/ethnic patterns across gradients of SES

Axion-like-particle search with high-intensity lasers

We study ALP-photon-conversion within strong inhomogeneous electromagnetic fields as provided by contemporary high-intensity laser systems. We observe that probe photons traversing the focal spot of a superposition of Gaussian beams of a single high-intensity laser at fundamental and frequency-doubled mode can experience a frequency shift due to their intermittent propagation as axion-like-particles. This process is strongly peaked for resonant masses on the order of the involved laser frequencies. Purely laser-based experiments in optical setups are sensitive to ALPs in the $\mathrm{eV}$ mass range and can thus complement ALP searches at dipole magnets.Comment: 25 pages, 2 figure

Dynamic Chromatin Localization of Sirt6 Shapes Stress- and Aging-Related Transcriptional Networks

The sirtuin Sirt6 is a NAD-dependent histone deacetylase that is implicated in gene regulation and lifespan control. Sirt6 can interact with the stress-responsive transcription factor NF-κB and regulate some NF-κB target genes, but the full scope of Sirt6 target genes as well as dynamics of Sirt6 occupancy on chromatin are not known. Here we map Sirt6 occupancy on mouse promoters genome-wide and show that Sirt6 occupancy is highly dynamic in response to TNF-α. More than half of Sirt6 target genes are only revealed upon stress-signaling. The majority of genes bound by NF-κB subunit RelA recruit Sirt6, and dynamic Sirt6 relocalization is largely driven in a RelA-dependent manner. Integrative analysis with global gene expression patterns in wild-type, Sirt6−/−, and double Sirt6−/− RelA−/− cells reveals the epistatic relationships between Sirt6 and RelA in shaping diverse temporal patterns of gene expression. Genes under the direct joint control of Sirt6 and RelA include several with prominent roles in cell senescence and organismal aging. These data suggest dynamic chromatin relocalization of Sirt6 as a key output of NF-κB signaling in stress response and aging

The course of mental health after miscarriage and induced abortion: a longitudinal, five-year follow-up study

BACKGROUND: Miscarriage and induced abortion are life events that can potentially cause mental distress. The objective of this study was to determine whether there are differences in the patterns of normalization of mental health scores after these two pregnancy termination events. METHODS: Forty women who experienced miscarriages and 80 women who underwent abortions at the main hospital of Buskerud County in Norway were interviewed. All subjects completed the following questionnaires 10 days (T1), six months (T2), two years (T3) and five years (T4) after the pregnancy termination: Impact of Event Scale (IES), Quality of Life, Hospital Anxiety and Depression Scale (HADS), and another addressing their feelings about the pregnancy termination. Differential changes in mean scores were determined by analysis of covariance (ANCOVA) and inter-group differences were assessed by ordinary least squares methods. RESULTS: Women who had experienced a miscarriage had more mental distress at 10 days and six months after the pregnancy termination than women who had undergone an abortion. However, women who had had a miscarriage exhibited significantly quicker improvement on IES scores for avoidance, grief, loss, guilt and anger throughout the observation period. Women who experienced induced abortion had significantly greater IES scores for avoidance and for the feelings of guilt, shame and relief than the miscarriage group at two and five years after the pregnancy termination (IES avoidance means: 3.2 vs 9.3 at T3, respectively, p < 0.001; 1.5 vs 8.3 at T4, respectively, p < 0.001). Compared with the general population, women who had undergone induced abortion had significantly higher HADS anxiety scores at all four interviews (p < 0.01 to p < 0.001), while women who had had a miscarriage had significantly higher anxiety scores only at T1 (p < 0.01). CONCLUSION: The course of psychological responses to miscarriage and abortion differed during the five-year period after the event. Women who had undergone an abortion exhibited higher scores during the follow-up period for some outcomes. The difference in the courses of responses may partly result from the different characteristics of the two pregnancy termination events

Herbivory and eutrophication mediate grassland plant nutrient responses across a global climatic gradient

Plant stoichiometry, the relative concentration of elements, is a key regulator of ecosystem functioning and is also being altered by human activities. In this paper we sought to understand the global drivers of plant stoichiometry and compare the relative contribution of climatic vs. anthropogenic effects. We addressed this goal by measuring plant elemental (C, N, P and K) responses to eutrophication and vertebrate herbivore exclusion at eighteen sites on six continents. Across sites, climate and atmospheric N deposition emerged as strong predictors of plot‐level tissue nutrients, mediated by biomass and plant chemistry. Within sites, fertilization increased total plant nutrient pools, but results were contingent on soil fertility and the proportion of grass biomass relative to other functional types. Total plant nutrient pools diverged strongly in response to herbivore exclusion when fertilized; responses were largest in ungrazed plots at low rainfall, whereas herbivore grazing dampened the plant community nutrient responses to fertilization. Our study highlights (1) the importance of climate in determining plant nutrient concentrations mediated through effects on plant biomass, (2) that eutrophication affects grassland nutrient pools via both soil and atmospheric pathways and (3) that interactions among soils, herbivores and eutrophication drive plant nutrient responses at small scales, especially at water‐limited sites

Cell autonomous expression of inflammatory genes in biologically aged fibroblasts associated with elevated NF-kappaB activity

<p>Abstract</p> <p>Background</p> <p>Chronic inflammation is a well-known corollary of the aging process and is believed to significantly contribute to morbidity and mortality of many age-associated chronic diseases. However, the mechanisms that cause age-associated inflammatory changes are not well understood. Particularly, the contribution of cell stress responses to age-associated inflammation in 'non-inflammatory' cells remains poorly defined. The present cross-sectional study focused on differences in molecular signatures indicative of inflammatory states associated with biological aging of human fibroblasts from donors aged 22 to 92 years.</p> <p>Results</p> <p>Gene expression profiling revealed elevated steady-state transcript levels consistent with a chronic inflammatory state in fibroblast cell-strains obtained from older donors. We also observed enhanced NF-κB DNA binding activity in a subset of strains, and the NF-κB profile correlated with mRNA expression levels characteristic of inflammatory processes, which include transcripts coding for cytokines, chemokines, components of the complement cascade and MHC molecules. This intrinsic low-grade inflammatory state, as it relates to aging, occurs in cultured cells irrespective of the presence of other cell types or the <it>in vivo </it>context.</p> <p>Conclusion</p> <p>Our results are consistent with the view that constitutive activation of inflammatory pathways is a phenomenon prevalent in aged fibroblasts. It is possibly part of a cellular survival process in response to compromised mitochondrial function. Importantly, the inflammatory gene expression signature described here is cell autonomous, i.e. occurs in the absence of prototypical immune or pro-inflammatory cells, growth factors, or other inflammatory mediators.</p