Asymptotics of 10j symbols

The Riemannian 10j symbols are spin networks that assign an amplitude to each 4-simplex in the Barrett-Crane model of Riemannian quantum gravity. This amplitude is a function of the areas of the 10 faces of the 4-simplex, and Barrett and Williams have shown that one contribution to its asymptotics comes from the Regge action for all non-degenerate 4-simplices with the specified face areas. However, we show numerically that the dominant contribution comes from degenerate 4-simplices. As a consequence, one can compute the asymptotics of the Riemannian 10j symbols by evaluating a `degenerate spin network', where the rotation group SO(4) is replaced by the Euclidean group of isometries of R^3. We conjecture formulas for the asymptotics of a large class of Riemannian and Lorentzian spin networks in terms of these degenerate spin networks, and check these formulas in some special cases. Among other things, this conjecture implies that the Lorentzian 10j symbols are asymptotic to 1/16 times the Riemannian ones.Comment: 25 pages LaTeX with 8 encapsulated Postscript figures. v2 has various clarifications and better page breaks. v3 is the final version, to appear in Classical and Quantum Gravity, and has a few minor corrections and additional reference

(Non)Parallel Evolution

Parallel evolution across replicate populations has provided evolutionary biologists with iconic examples of adaptation. When multiple populations colonize seemingly similar habitats, they may evolve similar genes, traits, or functions. Yet, replicated evolution in nature or in the laboratory often yields inconsistent outcomes: Some replicate populations evolve along highly similar trajectories, whereas other replicate populations evolve to different extents or in distinct directions. To understand these heterogeneous outcomes, biologists are increasingly treating parallel evolution not as a binary phenomenon but rather as a quantitative continuum ranging from parallel to nonparallel. By measuring replicate populations’ positions along this (non)parallel continuum, we can test hypotheses about evolutionary and ecological factors that influence the extent of repeatable evolution. We review evidence regarding the manifestation of (non)parallel evolution in the laboratory, in natural populations, and in applied contexts such as cancer. We enumerate the many genetic, ecological, and evolutionary processes that contribute to variation in the extent of parallel evolution

Numerical evidence of regularized correlations in spin foam gravity

We report on the numerical analysis of the area correlations in spin foam gravity on a single 4-simplex considered by Rovelli in PRL 97 (2006) 151301. We compare the asymptotics and confirm the inverse squared distance leading behaviour at large scales. This supports the recent advances on testing the semiclassical limit of the theory. Furthermore, we show that the microscopic discreteness of the theory dynamically suppresses and regularizes the correlations at the Planck scale.Comment: 5 pages, 3 figure

DEVELOPMENTAL ORIGINS OF METABOLIC DISEASES

Almost 2 billion adults in the world are overweight, and more than half of them are classified as obese, while nearly one-third of children globally experience poor growth and development. Given the vast amount of knowledge that has been gleaned from decades of research on growth and development, a number of questions remain as to why the world is now in the midst of a global epidemic of obesity accompanied by the “double burden of malnutrition,” where overweight coexists with underweight and micronutrient deficiencies. This challenge to the human condition can be attributed to nutritional and environmental exposures during pregnancy that may program a fetus to have a higher risk of chronic diseases in adulthood. To explore this concept, frequently called the developmental origins of health and disease (DOHaD), this review considers a host of factors and physiological mechanisms that drive a fetus or child toward a higher risk of obesity, fatty liver disease, hypertension, and/or type 2 diabetes (T2D). To that end, this review explores the epidemiology of DOHaD with discussions focused on adaptations to human energetics, placental development, dysmetabolism, and key environmental exposures that act to promote chronic diseases in adulthood. These areas are complementary and additive in understanding how providing the best conditions for optimal growth can create the best possible conditions for lifelong health. Moreover, understanding both physiological as well as epigenetic and molecular mechanisms for DOHaD is vital to most fully address the global issues of obesity and other chronic diseases

Texas charter school legislation and the evolution of open-enrollment charter schools.

This article chronicles the evolution of legislation for Texas open-enrollment charter schools to their implementation by demonstrating how these schools have (or have not) used their freedom from state-mandated requirements to develop innovative learning environments as well as to bring innovative curricula into the classroom. The investigative focus was on an analysis of Texas open-enrollment charter school legislation, from 1995 (74th legislative session) to the 77th legislative session in 2001, and the characteristics of the state's 159 open-enrollment charter schools that were in operation during the 2001-2002 academic year. The authors found that charter school legislation has changed in response to concerns of all involved, and focuses on the need for balance between choice, innovation, and public accountability. Although charter schools are free from most state regulations, legislators were clearly interested in ensuring that this freedom does not impede charter schools' ability to provide a quality education to all students who attend them. The currently operating open-enrollment charter schools in Texas are more racially and economically segregated than other public schools in the state, and charter schools that targeted students most at risk for dropping out of school (and returning students who had previously dropped out) differ from other schools in their stated teaching methods. Teacher turnover remains significantly greater than that for other public schools in the state. However, it does not appear to be specifically associated with schools that target disadvantaged students or minority students. The schools' mission statements suggest that innovative school environments are a factor in school design. Texas is poised to continue along the public education choice model. Charter school legislation provides a framework upon which charter schools may build to meet the educational needs of the students who choose to attend them, including the freedom to be creative in meeting students' unique needs. Questions remain about how and why charter schools exist and the contributions they make to the overall public school system, including whether charters are making a difference in what and how much children are learning

Desove de calamares ommastréfidos en el mar del Norte: oceanografía, cambio climático y ampliación del rango de distribución de especies

The lesser flying squid (Todaropsis eblanae) and the shortfin squid (Illex coindetii) are two abundant ommastrephids of the northeast Atlantic. Spawning ground existence was inferred from the captures of mature, mated females in summer 2016–2019 and their occurrences were compared with respective oceanographic data from international surveys to gain insight into environmental predictors of their presence throughout the North Sea. Spawning T. eblanae were found in relatively cooler and more saline waters (6–8°C, 34.2–35.1 psu) in the northern North Sea linked to the Fair Isle Current and East Shetland Atlantic Inflow, whilst spawning I. coindetii occurred across the entire North Sea (mostly at 9–10.5°C, 34.1–34.8 psu). We hypothesize that a combination of water salinity and water temperature are key factors in the spatiotemporal distribution of spawning ommastrephid squids as they define water density that is crucial for pelagic egg mass to attain neutral buoyancy.La pota costera (Todaropsis eblanae) y la pota voladora (Illex coindetii) son dos ommastréfidos abundantes del Atlántico nororiental. La existencia de una zona de desove se ha inferido a partir de capturas de hembras maduras y copuladas durante los veranos de 2016-2019. Su presencia se ha comparado con datos oceanográficos de estudios internacionales para conocer los predictores ambientales de su presencia en el Mar del Norte. El desove de T. eblanae se halló en aguas relativamente frías y salinas (6–8°C, 34,2–35,1 psu) del norte del Mar del Norte, vinculadas a la corriente de Fair Isle y el aporte de aguas atlánticas provenientes de Este de las Shetland. El desove de I. coindetii aconteció en todo el Mar del Norte (principalmente entre los 9–10.5°C, 34,1–34.8 psu). Se sugiere que una combinación de salinidad y temperatura del agua son factores clave en la distribución espacio-temporal de los calamares ommastréfidos desovantes, ya que la densidad del agua es crucial para que las masas de huevos pelágicos alcancen una flotabilidad neutra

Positivity of Spin Foam Amplitudes

The amplitude for a spin foam in the Barrett-Crane model of Riemannian quantum gravity is given as a product over its vertices, edges and faces, with one factor of the Riemannian 10j symbols appearing for each vertex, and simpler factors for the edges and faces. We prove that these amplitudes are always nonnegative for closed spin foams. As a corollary, all open spin foams going between a fixed pair of spin networks have real amplitudes of the same sign. This means one can use the Metropolis algorithm to compute expectation values of observables in the Riemannian Barrett-Crane model, as in statistical mechanics, even though this theory is based on a real-time (e^{iS}) rather than imaginary-time (e^{-S}) path integral. Our proof uses the fact that when the Riemannian 10j symbols are nonzero, their sign is positive or negative depending on whether the sum of the ten spins is an integer or half-integer. For the product of 10j symbols appearing in the amplitude for a closed spin foam, these signs cancel. We conclude with some numerical evidence suggesting that the Lorentzian 10j symbols are always nonnegative, which would imply similar results for the Lorentzian Barrett-Crane model.Comment: 15 pages LaTeX. v3: Final version, with updated conclusions and other minor changes. To appear in Classical and Quantum Gravity. v4: corrects # of samples in Lorentzian tabl

Theta-burst transcranial magnetic stimulation to the prefrontal or parietal cortex does not impair metacognitive visual awareness

Neuroimaging studies commonly associate dorsolateral prefrontal cortex (DLPFC) and pos- terior parietal cortex with conscious perception. However, such studies only investigate cor- relation, rather than causation. In addition, many studies conflate objective performance with subjective awareness. In an influential recent paper, Rounis and colleagues addressed these issues by showing that continuous theta burst transcranial magnetic stimulation (cTBS) applied to the DLPFC impaired metacognitive (subjective) awareness for a percep- tual task, while objective performance was kept constant. We attempted to replicate this finding, with minor modifications, including an active cTBS control site. Using a between- subjects design for both DLPFC and posterior parietal cortices, we found no evidence of a cTBS-induced metacognitive impairment. In a second experiment, we devised a highly rig- orous within-subjects cTBS design for DLPFC, but again failed to find any evidence of meta- cognitive impairment. One crucial difference between our results and the Rounis study is our strict exclusion of data deemed unsuitable for a signal detection theory analysis. Indeed, when we included this unstable data, a significant, though invalid, metacognitive impairment was found. These results cast doubt on previous findings relating metacognitive awareness to DLPFC, and inform the current debate concerning whether or not prefrontal regions are preferentially implicated in conscious perception