Weak equivalence and non-classifiability of measure preserving actions

Abért and Weiss have shown that the Bernoulli shift s_Γ of a countably infinite group Γ is weakly contained in any free measure preserving action ɑ of Γ. Proving a conjecture of Ioana, we establish a strong version of this result by showing that s_Γ×ɑ is weakly equivalent to ɑ. Using random Bernoulli shifts introduced by Abért, Glasner, and Virag, we generalize this to non-free actions, replacing s_Γ with a random Bernoulli shift associated to an invariant random subgroup, and replacing the product action with a relatively independent joining. The result for free actions is used along with the theory of Borel reducibility and Hjorth’s theory of turbulence to show that, on the weak equivalence class of a free measure preserving action, the equivalence relations of isomorphism, weak isomorphism, and unitary equivalence are not classifiable by countable structures. This in particular shows that there are no free weakly rigid actions, that is, actions whose weak equivalence class and isomorphism class coincide, answering negatively a question of Abért and Elek. We also answer a question of Kechris regarding two ergodic theoretic properties of residually finite groups. A countably infinite residually finite group Γ is said to have property EMD∗ if the action p_Γ of Γ on its profinite completion weakly contains all ergodic measure preserving actions of Γ, and Γ is said to have property MD if ι×p_Γ weakly contains all measure preserving actions of Γ, where ι denotes the identity action on a standard non-atomic probability space. Kechris has shown that EMD∗ implies MD and asked if the two properties are actually equivalent. We provide a positive answer to this question by studying the relationship between convexity and weak containment in the space of measure preserving actions

Evidence for a meteoritic origin of the September 15, 2007, Carancas crater

On September 15th, 2007, around 11:45 local time in Peru, near the Bolivian border, the atmospheric entry of a meteoroid produced bright lights in the sky and intense detonations. Soon after, a crater was discovered south of Lake Titicaca. These events have been detected by the Bolivian seismic network and two infrasound arrays operating for the Comprehensive Nuclear-Test-Ban Treaty Organization, situated at about 80 and 1620 km from the crater. The localization and origin time computed with the seismic records are consistent with the reported impact. The entry elevation and azimuthal angles of the trajectory are estimated from the observed signal time sequences and backazimuths. From the crater diameter and the airwave amplitudes, the kinetic energy, mass and explosive energy are calculated. Using the estimated velocity of the meteoroid and similarity criteria between orbital elements, an association with possible parent asteroids is attempted. The favorable setting of this event provides a unique opportunity to evaluate physical and kinematic parameters of the object that generated the first actual terrestrial meteorite impact seismically recorded

Ultraproducts of measure preserving actions and graph combinatorics

Ultraproducts of measure preserving actions of countable groups are used to study the graph combinatorics associated with such actions, including chromatic, independence and matching numbers. Applications are also given to the theory of random colorings of Cayley graphs and sofic actions and equivalence relations

A general dimension of genetic sharing across diverse cognitive traits inferred from molecular data

It has been known since 1904 that, in humans, diverse cognitive traits are positively inter correlated. This forms the basis for the general factor of intelligence (g). Here, we directly test whether there is a partial genetic basis for individual differences in g using data from seven different cognitive tests (N = 11,263 to N = 331,679) and genome-wide autosomal single nucleotide polymorphisms. A genetic g factor accounts for an average of 58.4% (SE = 4.8%) of the genetic variance in the cognitive traits, with the proportion varying widely across traits (range: 9% to 95%). We distill genetic loci that are broadly relevant for many cognitive traits (g) from loci associated specifically with individual cognitive traits. These results contribute to elucidating the etiology of a long-known yet poorly-understood phenomenon, revealing a fundamental dimension of genetic sharing across diverse cognitive traits

Optimization of cw sodium laser guide star efficiency

Context: Sodium laser guide stars (LGS) are about to enter a new range of laser powers. Previous theoretical and numerical methods are inadequate for accurate computations of the return flux and hence for the design of the next-generation LGS systems. Aims: We numerically optimize the cw (continuous wave) laser format, in particular the light polarization and spectrum. Methods: Using Bloch equations, we simulate the mesospheric sodium atoms, including Doppler broadening, saturation, collisional relaxation, Larmor precession, and recoil, taking into account all 24 sodium hyperfine states and on the order of 100 velocity groups. Results: LGS return flux is limited by "three evils": Larmor precession due to the geomagnetic field, atomic recoil due to radiation pressure, and transition saturation. We study their impacts and show that the return flux can be boosted by repumping (simultaneous excitation of the sodium D2a and D2b lines with 10-20% of the laser power in the latter). Conclusions: We strongly recommend the use of circularly polarized lasers and repumping. As a rule of thumb, the bandwidth of laser radiation in MHz (at each line) should approximately equal the launched laser power in Watts divided by six, assuming a diffraction-limited spot size.Comment: 15 pages, 12 figures, to be published in Astronomy & Astrophysics, AA/2009/1310

The Influence of Social Stereotypes and Conventional Attitudes on the Involvement of Women in Destructive Groups: the Paradox of Freedom

В статье рассматриваются факторы и риски социо-культурной среды и патриархатных установок, которые могут оказывать влияние на манипулирование женщинами с целью вовлечения их в деструктивные группы. Анализируются ложные и имитационные критерии женской идентичности в реалиях современного общества.The article is about the factors of the socio-cultural environment and the risks of patriarchal attitudes, which can affect the manipulation of women in order to engage them in destructive groups. Much attention is given to the false and imitation criteria of female identity in the realities of modern society

NRLMSIS 2.1: An Empirical Model of Nitric Oxide Incorporated Into MSIS

We have developed an empirical model of nitric oxide (NO) number density at altitudes from similar to 73 km to the exobase, as a function of altitude, latitude, day of year, solar zenith angle, solar activity, and geomagnetic activity. The model is part of the NRLMSIS (R) 2.1 empirical model of atmospheric temperature and species densities; this upgrade to NRLMSIS 2.0 consists solely of the addition of NO. MSIS 2.1 assimilates observations from six space-based instruments: UARS/HALOE, SNOE, Envisat/MIPAS, ACE/FTS, Odin/SMR, and AIM/SOFIE. We additionally evaluated the new model against independent extant NO data sets. In this paper, we describe the formulation and fitting of the model, examine biases between the data sets and model and among the data sets, compare with another empirical NO model (NOEM), and discuss scientific aspects of our analysis