1,108 research outputs found

    Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving

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    We derive efficient algorithms for coarse approximation of algebraic hypersurfaces, useful for estimating the distance between an input polynomial zero set and a given query point. Our methods work best on sparse polynomials of high degree (in any number of variables) but are nevertheless completely general. The underlying ideas, which we take the time to describe in an elementary way, come from tropical geometry. We thus reduce a hard algebraic problem to high-precision linear optimization, proving new upper and lower complexity estimates along the way.Comment: 15 pages, 9 figures. Submitted to a conference proceeding

    Fish heating tolerance scales similarly across individual physiology and populations

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    Extrapolating patterns from individuals to populations informs climate vulnerability models, yet biological responses to warming are uncertain at both levels. Here we contrast data on the heating tolerances of fishes from laboratory experiments with abundance patterns of wild populations. We find that heating tolerances in terms of individual physiologies in the lab and abundance in the wild decline with increasing temperature at the same rate. However, at a given acclimation temperature or optimum temperature, tropical individuals and populations have broader heating tolerances than temperate ones. These congruent relationships implicate a tight coupling between physiological and demographic processes underpinning macroecological patterns, and identify vulnerability in both temperate and tropical species

    Froth-like minimizers of a non local free energy functional with competing interactions

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    We investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one. The competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down, with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction. In this sense, the optimal or quasi-optimal profiles are "froth-like": if seen on the scale of the antiferromagnetic potential they look neutral, but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other. In this paper we prove the validity of this picture, we compute the oscillation scale of the quasi-optimal profiles and we quantify their distance in norm from a reference periodic profile. The proof consists of two main steps: we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale; in this way we reduce the original functional to an effective "sharp interface" one. Next, we study the latter by reflection positivity methods, which require as a key ingredient the exact locality of the short range term. Our proof has the conceptual interest of combining coarse graining with reflection positivity methods, an idea that is presumably useful in much more general contexts than the one studied here.Comment: 38 pages, 2 figure

    Complementarity of information sent via different bases

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    We discuss quantitatively the complementarity of information transmitted by a quantum system prepared in a basis state in one out of several different mutually unbiased bases (MUBs). We obtain upper bounds on the information available to a receiver who has no knowledge of which MUB was chosen by the sender. These upper bounds imply a complementarity of information encoded via different MUBs and ultimately ensure the security in quantum key distribution protocols.Comment: 9 pages, references adde

    Stressful life events, intimate partner violence, and perceived stress in the postpartum period: longitudinal findings in rural Pakistan

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    Purpose: While the association between intimate partner violence (IPV) and stress is well documented, the directionality of this relationship is unclear. We use an adjusted longitudinal study design to better understand if stressful life events in the home precipitate or exacerbate intimate partner violence (IPV) and if experiences of IPV, in turn, increase levels of perceived stress. Methods: Longitudinal data were collected among married women in rural Pakistan at 12 and 24 months postpartum (N = 815). Adjusted Poisson and linear regression models were used to examine stressful life events, past year IPV and severity (number and frequency of violent acts), and perceived stress (Cohen Perceived Stress Scale). Results: At 12 months postpartum, the prevalence of past year physical, psychological, and sexual IPV was 8.5%, 25.7%, and 25.1%, respectively, with 42.6% experiencing any IPV. After adjustment, stressful life events were associated with a subsequent increased likelihood of all IPV types and increased severity of all but physical IPV. Any past year IPV (versus none) and greater IPV severity were associated with 3.43 (95% CI 2.33–4.52) and 2.57 (95% CI 1.87–3.27) point subsequent increases in perceived stress. Physical, psychological, and sexual IPV and their respective severities were all independently associated with increased perceived stress. Conclusions: Among postpartum women in Pakistan, stressful life events increase the likelihood of IPV and, in turn, experiences of IPV increase stress levels. Support to families undergoing stressful circumstances may be critical to reducing women’s IPV exposure and resulting elevated stress
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