The saga of the Ising susceptibility

We review developments made since 1959 in the search for a closed form for the susceptibility of the Ising model. The expressions for the form factors in terms of the nome $q$ and the modulus $k$ are compared and contrasted. The $\lambda$ generalized correlations $C(M,N;\lambda)$ are defined and explicitly computed in terms of theta functions for $M=N=0,1$.Comment: 19 pages, 1 figur

Deuterium on Venus: Observations from Earth

In view of the importance of the deuterium-to-hydrogen ratio in understanding the evolutionary scenario of planetary atmospheres and its relationship to understanding the evolution of our own Earth, we undertook a series of observations designed to resolve previous observational conflicts. We observed the dark side of Venus in the 2.3 micron spectral region in search of both H2O and HDO, which would provide us with the D/H ratio in Venus' atmosphere. We identified a large number of molecular lines in the region, belonging to both molecules, and, using synthetic spectral techniques, obtained mixing ratios of 34 plus or minus 10 ppm and 1.3 plus or minus 0.2 ppm for H2O and HDO, respectively. These mixing ratios yield a D/H ratio for Venus of D/H equals 1.9 plus or minus 0.6 times 10 (exp 12) and 120 plus or minus 40 times the telluric ratio. Although the detailed interpretation is difficult, our observations confirm that the Pioneer Venus Orbiter results and establish that indeed Venus had a period in its early history in which it was very wet, perhaps not unlike the early wet period that seems to have been present on Mars, and that, in contrast to Earth, lost much of its water over geologic time

A Fast and Efficient Incremental Approach toward Dynamic Community Detection

Community detection is a discovery tool used by network scientists to analyze the structure of real-world networks. It seeks to identify natural divisions that may exist in the input networks that partition the vertices into coherent modules (or communities). While this problem space is rich with efficient algorithms and software, most of this literature caters to the static use-case where the underlying network does not change. However, many emerging real-world use-cases give rise to a need to incorporate dynamic graphs as inputs. In this paper, we present a fast and efficient incremental approach toward dynamic community detection. The key contribution is a generic technique called $\Delta-screening$, which examines the most recent batch of changes made to an input graph and selects a subset of vertices to reevaluate for potential community (re)assignment. This technique can be incorporated into any of the community detection methods that use modularity as its objective function for clustering. For demonstration purposes, we incorporated the technique into two well-known community detection tools. Our experiments demonstrate that our new incremental approach is able to generate performance speedups without compromising on the output quality (despite its heuristic nature). For instance, on a real-world network with 63M temporal edges (over 12 time steps), our approach was able to complete in 1056 seconds, yielding a 3x speedup over a baseline implementation. In addition to demonstrating the performance benefits, we also show how to use our approach to delineate appropriate intervals of temporal resolutions at which to analyze an input network

Random Matrix Theory and Classical Statistical Mechanics. I. Vertex Models

A connection between integrability properties and general statistical properties of the spectra of symmetric transfer matrices of the asymmetric eight-vertex model is studied using random matrix theory (eigenvalue spacing distribution and spectral rigidity). For Yang-Baxter integrable cases, including free-fermion solutions, we have found a Poissonian behavior, whereas level repulsion close to the Wigner distribution is found for non-integrable models. For the asymmetric eight-vertex model, however, the level repulsion can also disappearand the Poisson distribution be recovered on (non Yang--Baxter integrable) algebraic varieties, the so-called disorder varieties. We also present an infinite set of algebraic varieties which are stable under the action of an infinite discrete symmetry group of the parameter space. These varieties are possible loci for free parafermions. Using our numerical criterion we have tested the generic calculability of the model on these algebraic varieties.Comment: 25 pages, 7 PostScript Figure

Closer to the Source: Notch and the Nature of Thymus-Settling Cells

Questions regarding T cell development have recently received much attention, but the earliest intrathymic differentiation steps in adult mice have remained controversial. Three new papers together show that for at least some thymus-settling precursors, the loss of B lineage potential occurs in the thymus, and Notch acts on multipotent progenitors early after thymic entry

Multiple Molecular H2 Outflows in AFGL 618

We report high spatial (0.5 arcsec) and high spectral (9 km/s) resolution spectro-imaging of the 2.12 micron H2 1-0 S(1) line in the proto-planetary nebula AFGL 618 using BEAR at the CFHT. The observations reveal the presence of multiple, high-velocity, molecular outflows that align with the remarkable optical jets seen in HST images. The structure and kinematics of the outflows show how jets interact with circumstellar gas and shape the environment in which planetary nebulae form.Comment: 14 pages, 5 figures. To appear in The Astrophysical Journal Letter

Near-infrared oxygen airglow from the Venus nightside

Groundbased imaging and spectroscopic observations of Venus reveal intense near-infrared oxygen airglow emission from the upper atmosphere and provide new constraints on the oxygen photochemistry and dynamics near the mesopause (approximately 100 km). Atomic oxygen is produced by the Photolysis of CO2 on the dayside of Venus. These atoms are transported by the general circulation, and eventually recombine to form molecular oxygen. Because this recombination reaction is exothermic, many of these molecules are created in an excited state known as O2(delta-1). The airglow is produced as these molecules emit a photon and return to their ground state. New imaging and spectroscopic observations acquired during the summer and fall of 1991 show unexpected spatial and temporal variations in the O2(delta-1) airglow. The implications of these observations for the composition and general circulation of the upper venusian atmosphere are not yet understood but they provide important new constraints on comprehensive dynamical and chemical models of the upper mesosphere and lower thermosphere of Venus

Random Projections For Large-Scale Regression

Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool in machine learning and statistics. We discuss the applications of random projections in linear regression problems, developed to decrease computational costs, and give an overview of the theoretical guarantees of the generalization error. It can be shown that the combination of random projections with least squares regression leads to similar recovery as ridge regression and principal component regression. We also discuss possible improvements when averaging over multiple random projections, an approach that lends itself easily to parallel implementation.Comment: 13 pages, 3 Figure