The Birth-Death-Mutation process: a new paradigm for fat tailed distributions

Fat tailed statistics and power-laws are ubiquitous in many complex systems. Usually the appearance of of a few anomalously successful individuals (bio-species, investors, websites) is interpreted as reflecting some inherent "quality" (fitness, talent, giftedness) as in Darwin's theory of natural selection. Here we adopt the opposite, "neutral", outlook, suggesting that the main factor explaining success is merely luck. The statistics emerging from the neutral birth-death-mutation (BDM) process is shown to fit marvelously many empirical distributions. While previous neutral theories have focused on the power-law tail, our theory economically and accurately explains the entire distribution. We thus suggest the BDM distribution as a standard neutral model: effects of fitness and selection are to be identified by substantial deviations from it

Nonlocal competition and logistic growth: patterns, defects and fronts

Logistic growth of diffusing reactants on spatial domains with long range competition is studied. The bifurcations cascade involved in the transition from the homogenous state to a spatially modulated stable solution is presented, and a distinction is made between a modulated phase, dominated by single or few wavenumbers, and the spiky phase, where localized colonies are separated by depleted region. The characteristic defects in the periodic structure are presented for each phase, together with the invasion dynamics in case of local initiation. It is shown that the basic length scale that controls the bifurcation is the width of the Fisher front, and that the total population grows as this width decreases. A mix of analytic results and extensive numerical simulations yields a comprehensive examination of the possible phases for logistic growth in the presence of nonlocal competition

Spin Model for Inverse Melting and Inverse Glass Transition

A spin model that displays inverse melting and inverse glass transition is presented and analyzed. Strong degeneracy of the interacting states of an individual spin leads to entropic preference of the "ferromagnetic" phase, while lower energy associated with the non-interacting states yields a "paramagnetic" phase as temperature decreases. An infinite range model is solved analytically for constant paramagnetic exchange interaction, while for its random exchange, analogous results based on the replica symmetric solution are presented. The qualitative features of this model are shown to resemble a large class of inverse melting phenomena. First and second order transition regimes are identified

Rupture Depth-Varying Seismicity Patterns for Major and Great (M_W ≥ 7.0) Megathrust Earthquakes

Large earthquakes on subduction zone plate boundary megathrusts result from intervals of strain accumulation and release. The mechanism diversity and spatial distribution of moderate-size aftershocks is influenced by the mainshock rupture depth extent. Mainshocks that rupture across the shallow megathrust to near the trench have greater intraplate aftershock faulting diversity than events with rupture confined to deeper portions of the megathrust. Diversity of intraplate aftershock faulting also increases as the size of the mainshock approaches the largest size event to have ruptured that region of the megathrust. Based on these tendencies, we identify “breakthrough” ruptures as those involving shallow rupture of the megathrust with volumetrically extensive elastic strain drop around the plate boundary that allows activation of diverse intraplate faulting influenced by long-term ambient deformation stresses. In contrast, homogeneity of the aftershock faulting mechanisms indicates only partial release of elastic strain energy and remaining potential for another large rupture

Systematic deficiency of aftershocks in areas of high coseismic slip for large subduction zone earthquakes

Fault slip during plate boundary earthquakes releases a portion of the shear stress accumulated due to frictional resistance to relative plate motions. Investigation of 101 large [moment magnitude (M_w) ≥ 7] subduction zone plate boundary mainshocks with consistently determined coseismic slip distributions establishes that 15 to 55% of all master event–relocated aftershocks with M_w ≥ 5.2 are located within the slip regions of the mainshock ruptures and few are located in peak slip regions, allowing for uncertainty in the slip models. For the preferred models, cumulative deficiency of aftershocks within the central three-quarters of the scaled slip regions ranges from 15 to 45%, increasing with the total number of observed aftershocks. The spatial gradients of the mainshock coseismic slip concentrate residual shear stress near the slip zone margins and increase stress outside the slip zone, driving both interplate and intraplate aftershock occurrence near the periphery of the mainshock slip. The shear stress reduction in large-slip regions during the mainshock is generally sufficient to preclude further significant rupture during the aftershock sequence, consistent with large-slip areas relocking and not rupturing again for a substantial time

Eigenfunction statistics for a point scatterer on a three-dimensional torus

In this paper we study eigenfunction statistics for a point scatterer (the Laplacian perturbed by a delta-potential) on a three-dimensional flat torus. The eigenfunctions of this operator are the eigenfunctions of the Laplacian which vanish at the scatterer, together with a set of new eigenfunctions (perturbed eigenfunctions). We first show that for a point scatterer on the standard torus all of the perturbed eigenfunctions are uniformly distributed in configuration space. Then we investigate the same problem for a point scatterer on a flat torus with some irrationality conditions, and show uniform distribution in configuration space for almost all of the perturbed eigenfunctions.Comment: Revised according to referee's comments. Accepted for publication in Annales Henri Poincar

The giant eyes of giant squid are indeed unexpectedly large, but not if used for spotting sperm whales

© The Author(s), 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in BMC Evolutionary Biology 13 (2013): 187, doi:10.1186/1471-2148-13-187.We recently reported (Curr Biol 22:683–688, 2012) that the eyes of giant and colossal squid can grow to three times the diameter of the eyes of any other animal, including large fishes and whales. As an explanation to this extreme absolute eye size, we developed a theory for visual performance in aquatic habitats, leading to the conclusion that the huge eyes of giant and colossal squid are uniquely suited for detection of sperm whales, which are important squid-predators in the depths where these squid live. A paper in this journal by Schmitz et al. (BMC Evol Biol 13:45, 2013) refutes our conclusions on the basis of two claims: (1) using allometric data they argue that the eyes of giant and colossal squid are not unexpectedly large for the size of the squid, and (2) a revision of the values used for modelling indicates that large eyes are not better for detection of approaching sperm whales than they are for any other task. We agree with Schmitz et al. that their revised values for intensity and abundance of planktonic bioluminescence may be more realistic, or at least more appropriately conservative, but argue that their conclusions are incorrect because they have not considered some of the main arguments put forward in our paper. We also present new modelling to demonstrate that our conclusions remain robust, even with the revised input values suggested by Schmitz et al

Early Biometric Lag in the Prediction of Small for Gestational Age Neonates and Preeclampsia

OBJECTIVE: An early fetal growth lag may be a marker of future complications. We sought to determine the utility of early biometric variables in predicting adverse pregnancy outcomes. METHODS: In this retrospective cohort study, the crown-rump length at 11 to 14 weeks and the head circumference, biparietal diameter, abdominal circumference, femur length, humerus length, transverse cerebellar diameter, and estimated fetal weight at 18 to 24 weeks were converted to an estimated gestational age using published regression formulas. Sonographic fetal growth (difference between each biometric gestational age and the crown-rump length gestational age) minus expected fetal growth (number of days elapsed between the two scans) yielded the biometric growth lag. These lags were tested as predictors of small for gestational age (SGA) neonates (≤10th percentile) and preeclampsia. RESULTS: A total of 245 patients were included. Thirty-two (13.1%) delivered an SGA neonate, and 43 (17.6%) had the composite outcome. The head circumference, biparietal diameter, abdominal circumference, and estimated fetal weight lags were identified as significant predictors of SGA neonates after adjusted analyses (P \u3c .05). The addition of either the estimated fetal weight or abdominal circumference lag to maternal characteristics alone significantly improved the performance of the predictive model, achieving areas under the curve of 0.72 and 0.74, respectively. No significant association was found between the biometric lag variables and the development of preeclampsia. CONCLUSIONS: Routinely available biometric data can be used to improve the prediction of adverse outcomes such as SGA. These biometric lags should be considered in efforts to develop screening algorithms for adverse outcomes