Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments

We consider a population living in a patchy environment that varies stochastically in space and time. The population is composed of two morphs (that is, individuals of the same species with different genotypes). In terms of survival and reproductive success, the associated phenotypes differ only in their habitat selection strategies. We compute invasion rates corresponding to the rates at which the abundance of an initially rare morph increases in the presence of the other morph established at equilibrium. If both morphs have positive invasion rates when rare, then there is an equilibrium distribution such that the two morphs coexist; that is, there is a protected polymorphism for habitat selection. Alternatively, if one morph has a negative invasion rate when rare, then it is asymptotically displaced by the other morph under all initial conditions where both morphs are present. We refine the characterization of an evolutionary stable strategy for habitat selection from [Schreiber, 2012] in a mathematically rigorous manner. We provide a necessary and sufficient condition for the existence of an ESS that uses all patches and determine when using a single patch is an ESS. We also provide an explicit formula for the ESS when there are two habitat types. We show that adding environmental stochasticity results in an ESS that, when compared to the ESS for the corresponding model without stochasticity, spends less time in patches with larger carrying capacities and possibly makes use of sink patches, thereby practicing a spatial form of bet hedging.Comment: Revised in light of referees' comments, Published on-line Journal of Mathematical Biology 2014 http://link.springer.com/article/10.1007/s00285-014-0824-

Coordinate sum and difference sets of dd-dimensional modular hyperbolas

Many problems in additive number theory, such as Fermat's last theorem and the twin prime conjecture, can be understood by examining sums or differences of a set with itself. A finite set $A \subset \mathbb{Z}$ is considered sum-dominant if $|A+A|>|A-A|$. If we consider all subsets of ${0, 1, ..., n-1}$, as $n\to\infty$ it is natural to expect that almost all subsets should be difference-dominant, as addition is commutative but subtraction is not; however, Martin and O'Bryant in 2007 proved that a positive percentage are sum-dominant as $n\to\infty$. This motivates the study of "coordinate sum dominance". Given $V \subset (\Z/n\Z)^2$, we call $S:={x+y: (x,y) \in V}$ a coordinate sumset and $D:=\{x-y: (x,y) \in V\}$ a coordinate difference set, and we say $V$ is coordinate sum dominant if $|S|>|D|$. An arithmetically interesting choice of $V$ is $\bar{H}_2(a;n)$, which is the reduction modulo $n$ of the modular hyperbola $H_2(a;n) := {(x,y): xy \equiv a \bmod n, 1 \le x,y < n}$. In 2009, Eichhorn, Khan, Stein, and Yankov determined the sizes of $S$ and $D$ for $V=\bar{H}_2(1;n)$ and investigated conditions for coordinate sum dominance. We extend their results to reduced $d$-dimensional modular hyperbolas $\bar{H}_d(a;n)$ with $a$ coprime to $n$.Comment: Version 1.0, 14 pages, 2 figure

Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity

It has become widely accepted that the most dangerous cardiac arrhythmias are due to re- entrant waves, i.e., electrical wave(s) that re-circulate repeatedly throughout the tissue at a higher frequency than the waves produced by the heart's natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic currents in the cell, has made it extremely difficult to pinpoint the detailed mechanisms of these life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac action potential (AP), which can be fitted to a wide variety of experimentally and numerically obtained mesoscopic characteristics of cardiac tissue such as AP shape and restitution of AP duration and conduction velocity, is used to explain many different mechanisms of spiral wave breakup which in principle can occur in cardiac tissue. Some, but not all, of these mechanisms have been observed before using other models; therefore, the purpose of this paper is to demonstrate them using just one framework model and to explain the different parameter regimes or physiological properties necessary for each mechanism (such as high or low excitability, corresponding to normal or ischemic tissue, spiral tip trajectory types, and tissue structures such as rotational anisotropy and periodic boundary conditions). Each mechanism is compared with data from other ionic models or experiments to illustrate that they are not model-specific phenomena. The fact that many different breakup mechanisms exist has important implications for antiarrhythmic drug design and for comparisons of fibrillation experiments using different species, electromechanical uncoupling drugs, and initiation protocols.Comment: 128 pages, 42 figures (29 color, 13 b&w

Information Management to Mitigate Loss of Control Airline Accidents

Loss of control inflight continues to be the leading contributor to airline accidents worldwide and unreliable airspeed has been a contributing factor in many of these accidents. Airlines and the FAA developed training programs for pilot recognition of these airspeed events and many checklists have been designed to help pilots troubleshoot. In addition, new aircraft designs incorporate features to detect and respond in such situations. NASA has been using unreliable airspeed events while conducting research recommended by the Commercial Aviation Safety Team. Even after significant industry focus on unreliable airspeed, research and other evidence shows that highly skilled and trained pilots can still be confused by the condition and there is a lack of understanding of what the associated checklist(s) attempts to uncover. Common mode failures of analog sensors designed for measuring airspeed continue to confound both humans and automation when determining which indicators are correct. This paper describes failures that have occurred in the past and where/how pilots may still struggle in determining reliable airspeed when confronted with conflicting information. Two latest generation aircraft architectures will be discussed and contrasted. This information will be used to describe why more sensors used in classic control theory will not solve the problem. Technology concepts are suggested for utilizing existing synoptic pages and a new synoptic page called System Interactive Synoptic (SIS). SIS details the flow of flight critical data through the avionics system and how it is used by the automation. This new synoptic page as well as existing synoptics can be designed to be used in concert with a simplified electronic checklist (sECL) to significantly reduce the time to configure the flight deck avionics in the event of a system or sensor failure

Progressive dehydration in decomposing bone: a potential tool for forensic anthropology

The aim of this pilot study was to determine whether collagen and/or water content of bone vary during soft tissue putrefaction by thermogravimetric analysis with a view to eventually developing a possible forensic application to determine post-mortem interval. Porcine bone decomposed in a shallow burial showed an approximate difference in average mass loss of 15  ± 8% when heated between 22 and 100 °C, compared to 14 ± 3% for porcine bone decomposed in a surface deposition, equating to water loss. Mass loss showed peaks at 0, 250–500 and 1200–1500 cumulative cooling degree days’ (CCDD) deposition for the experimental porcine bone. Should these measurements prove consistent in future studies on a wider variety of porcine and eventually human skeletal elements, they may have potential to be corroborated with other data when determining post-mortem interval, especially with disarticulated bones. A downward trend in mass loss was apparent within shallow burial and surface deposition scenarios (inclusive of freeze-dried controls) for the thermolysis of collagen (and other proteins) between 220 and 650 °C during thermogravimetric analysis. This was inconsistent within the time frame examined (0–1450 cumulative cooling degree days), and so demonstrates less potential as an indicator of post-mortem interval during soft tissue putrefaction

Neutral B-meson mixing from three-flavor lattice QCD: Determination of the SU(3)-breaking ratio \xi

We study SU(3)-breaking effects in the neutral B_d-\bar B_d and B_s-\bar B_s systems with unquenched N_f=2+1 lattice QCD. We calculate the relevant matrix elements on the MILC collaboration's gauge configurations with asqtad-improved staggered sea quarks. For the valence light-quarks (u, d, and s) we use the asqtad action, while for b quarks we use the Fermilab action. We obtain \xi=f_{B_s}\sqrt{B_{B_s}}/f_{B_d}\sqrt{B_{B_d}}=1.268+-0.063. We also present results for the ratio of bag parameters B_{B_s}/B_{B_d} and the ratio of CKM matrix elements |V_{td}|/|V_{ts}|. Although we focus on the calculation of \xi, the strategy and techniques described here will be employed in future extended studies of the B mixing parameters \Delta M_{d,s} and \Delta\Gamma_{d,s} in the Standard Model and beyond.Comment: 36 pages, 7 figure

Autistic Masking

This study investigated the relationships between autistic masking and depression, anxiety, gender identity, sexual orientation, social trauma, self-esteem, authenticity, and autistic community involvement. Participants were autistic adults (n=342) recruited through autistic social media groups. The majority of participants (63%) reported being members of sexual minorities. The study found higher self-reported autistic masking behaviors were associated with higher reports of past social trauma (p \u3c .001, b = .26), greater anxiety (p \u3c .001, b = .37) and depression symptoms (p \u3c .001, b = .312), lower self-esteem (p \u3c .001, b = -.25), lower authentic living (p = .005, b = -.16), greater accepting of external influence (p \u3c .001, b= .33), higher self-alienation (p \u3c .001, b = .26), and lower participation within the autistic community (p \u3c .001, b = -.19). Autistic masking was not found to be associated with gender identity or sexual orientation. Participants who reported involvement in previous ABA therapy reported higher past social trauma than participants involved in some other forms of therapy such as cognitive behavior therapy

A Parameter Study of the Dust and Gas Temperature in a Field of Young Stars

We model the thermal effect of young stars on their surrounding environment in order to understand clustered star formation. We take radiative heating of dust, dust-gas collisional heating, cosmic-ray heating, and molecular cooling into account. Using Dusty, a spherical continuum radiative transfer code, we model the dust temperature distribution around young stellar objects with various luminosities and surrounding gas and dust density distributions. We have created a grid of dust temperature models, based on our modeling with Dusty, which we can use to calculate the dust temperature in a field of stars with various parameters. We then determine the gas temperature assuming energy balance. Our models can be used to make large-scale simulations of clustered star formation more realistic.Comment: 29 pages, 19 figures. Submitted to Ap

Shape-based peak identification for ChIP-Seq

We present a new algorithm for the identification of bound regions from ChIP-seq experiments. Our method for identifying statistically significant peaks from read coverage is inspired by the notion of persistence in topological data analysis and provides a non-parametric approach that is robust to noise in experiments. Specifically, our method reduces the peak calling problem to the study of tree-based statistics derived from the data. We demonstrate the accuracy of our method on existing datasets, and we show that it can discover previously missed regions and can more clearly discriminate between multiple binding events. The software T-PIC (Tree shape Peak Identification for ChIP-Seq) is available at http://math.berkeley.edu/~vhower/tpic.htmlComment: 12 pages, 6 figure

The King–Devick test for sideline concussion screening in collegiate football

AbstractPurposeSports-related concussion has received increasing attention as a result of neurologic sequelae seen among athletes, highlighting the need for a validated, rapid screening tool. The King–Devick (K–D) test requires vision, eye movements, language function and attention in order to perform and has been proposed as a promising tool for assessment of concussion. We investigated the K–D test as a sideline screening tool in a collegiate cohort to determine the effect of concussion.MethodsAthletes (n=127, mean age 19.6±1.2 years) from the Wheaton College football and men's and women's basketball teams underwent baseline K–D testing at pre-season physicals for the 2012–2013 season. K–D testing was administered immediately on the sidelines for football players with suspected head injury during regular games and changes compared to baseline were determined. Post-season testing was also performed to compare non-concussed athletes’ test performance.ResultsConcussed athletes (n=11) displayed sideline K–D scores that were significantly higher (worse) than baseline (36.5±5.6s vs. 31.3±4.5s, p<0.005, Wilcoxon signed-rank test). Post-season testing demonstrated improvement of scores and was consistent with known learning effects (35.1±5.2s vs. 34.4±5.0s, p<0.05, Wilcoxon signed-rank test). Test-retest reliability was analyzed between baseline and post-season administrations of the K–D test resulting in high levels of test-retest reliability (intraclass correlation coefficient (ICC)=0.95 [95% Confidence Interval 0.85–1.05]).ConclusionsThe data show worsening of K–D test scores following concussion further supporting utility of the K–D test as an objective, reliable and effective sideline visual screening tool to help identify athletes with concussion