Pedestrian Solution of the Two-Dimensional Ising Model

The partition function of the two-dimensional Ising model with zero magnetic field on a square lattice with m x n sites wrapped on a torus is computed within the transfer matrix formalism in an explicit step-by-step approach inspired by Kaufman's work. However, working with two commuting representations of the complex rotation group SO(2n,C) helps us avoid a number of unnecessary complications. We find all eigenvalues of the transfer matrix and therefore the partition function in a straightforward way.Comment: 10 pages, 2 figures; eqs. (101) and (102) corrected, files for fig. 2 fixed, minor beautification

A polynomial oracle-time algorithm for convex integer minimization

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex $N$-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex $N$-fold integer minimization problems for which our approach provides polynomial time solution algorithms.Comment: 19 pages, 1 figur

Genome-wide functional perturbation of human microsatellite repeats using engineered zinc finger transcription factors.

Repeat elements can be dysregulated at a genome-wide scale in human diseases. For example, in Ewing sarcoma, hundreds of inert GGAA repeats can be converted into active enhancers when bound by EWS-FLI1. Here we show that fusions between EWS and GGAA-repeat-targeted engineered zinc finger arrays (ZFAs) can function at least as efficiently as EWS-FLI1 for converting hundreds of GGAA repeats into active enhancers in a Ewing sarcoma precursor cell model. Furthermore, a fusion of a KRAB domain to a ZFA can silence GGAA microsatellite enhancers genome wide in Ewing sarcoma cells, thereby reducing expression of EWS-FLI1-activated genes. Remarkably, this KRAB-ZFA fusion showed selective toxicity against Ewing sarcoma cells compared with non-Ewing cancer cells, consistent with its Ewing sarcoma-specific impact on the transcriptome. These findings demonstrate the value of ZFAs for functional annotation of repeats and illustrate how aberrant microsatellite activities might be regulated for potential therapeutic applications

The Influence of Foreign vs North American Emissions on Surface Ozone in the US

As part of the Hemispheric Transport of Air Pollution (HTAP; www.htap.org) project, we analyze results from 16 global and hemispheric chemical transport models and compare these to Clean Air Status and Trends Network (CASTNet) observations in the United States (US) for 2001. Using the policy-relevant maximum daily 8-h ozone (MDA8 O3) statistic, the multi-model ensemble represents the observations well (mean r2=0.57, ensemble bias=+4.1 ppbv for all regions and all seasons) despite a wide range in the individual model results. Correlations are strongest in the NorthEastern US during spring and fall (r2=0.68); and weakest in the Midwestern US in summer (r2=0.46). However, large positive mean biases exist during summer for all Eastern US regions, ranging from 10¿20 ppbv, and a smaller negative bias is present in the Western US during spring (3 ppbv). In most all other regions and seasons, the biases of the model ensemble simulations are 5 ppbv. Sensitivity simulations in which anthropogenic O3-precursor emissions (NOx+NMVOC+CO+aerosols) were decreased by 20% in each of four source regions: East Asia (EA), South Asia (SA), Europe (EU) and North America (NA) show that the greatest response of MDA8 O3 to the summed foreign emissions reductions occurs during spring in the West (0.9 ppbv reduction due to 20% reductions from EA+SA+EU). East Asia is the largest contributor to MDA8 O3 at all ranges of the O3 distribution for most regions (typically 0.45 ppbv). The exception is in the NorthEastern US where European emissions reductions had the greatest impact on MDA8 O3, particularly in the middle of the MDA8 O3 distribution (response of 0.35 ppbv between 35¿55 ppbv). In all regions and seasons, however, O3-precursor emissions reductions of 20% in the NA source region decrease MDA8 O3 the most by a factor of 2 to nearly 10 relative to foreign emissions reductions. The O3 response to anthropogenic NA emissions is greatest in the Eastern US during summer at the high end of the O3 distribution (5-6 ppbv for 20% reductions). While the impact of foreign emissions on surface O3 in the US is not negligible and is of increasing concern given the growth in emissions upwind of the US - domestic emissions reductions remain a farmore effective means of decreasing MDA8 O3 values, particularly those above 75 ppb(the current US standard).JRC.H.2-Air and Climat

Modelling spectral and timing properties of accreting black holes: the hybrid hot flow paradigm

The general picture that emerged by the end of 1990s from a large set of optical and X-ray, spectral and timing data was that the X-rays are produced in the innermost hot part of the accretion flow, while the optical/infrared (OIR) emission is mainly produced by the irradiated outer thin accretion disc. Recent multiwavelength observations of Galactic black hole transients show that the situation is not so simple. Fast variability in the OIR band, OIR excesses above the thermal emission and a complicated interplay between the X-ray and the OIR light curves imply that the OIR emitting region is much more compact. One of the popular hypotheses is that the jet contributes to the OIR emission and even is responsible for the bulk of the X-rays. However, this scenario is largely ad hoc and is in contradiction with many previously established facts. Alternatively, the hot accretion flow, known to be consistent with the X-ray spectral and timing data, is also a viable candidate to produce the OIR radiation. The hot-flow scenario naturally explains the power-law like OIR spectra, fast OIR variability and its complex relation to the X-rays if the hot flow contains non-thermal electrons (even in energetically negligible quantities), which are required by the presence of the MeV tail in Cyg X-1. The presence of non-thermal electrons also lowers the equilibrium electron temperature in the hot flow model to <100 keV, making it more consistent with observations. Here we argue that any viable model should simultaneously explain a large set of spectral and timing data and show that the hybrid (thermal/non-thermal) hot flow model satisfies most of the constraints.Comment: 26 pages, 13 figures. To be published in the Space Science Reviews and as hard cover in the Space Sciences Series of ISSI - The Physics of Accretion on to Black Holes (Springer Publisher

Electron Dynamics in Nd1.85_{1.85}Ce.15_{.15}CuO4+δ_{4+\delta}: Evidence for the Pseudogap State and Unconventional c-axis Response

Infrared reflectance measurements were made with light polarized along the a- and c-axis of both superconducting and antiferromagnetic phases of electron doped Nd$_{1.85}$Ce$_{.15}$CuO$_{4+\delta}$. The results are compared to characteristic features of the electromagnetic response in hole doped cuprates. Within the CuO$_2$ planes the frequency dependent scattering rate, 1/$\tau(\omega)$, is depressed below $\sim$ 650 cm$^{-1}$; this behavior is a hallmark of the pseudogap state. While in several hole doped compounds the energy scales associated with the pseudogap and superconducting states are quite close, we are able to show that in Nd$_{1.85}$Ce$_{.15}$CuO$_{4+\delta}$ the two scales differ by more than one order of magnitude. Another feature of the in-plane charge response is a peak in the real part of the conductivity, $\sigma_1(\omega)$, at 50-110 cm$^{-1}$ which is in sharp contrast with the Drude-like response where $\sigma_1(\omega)$ is centered at $\omega=0$. This latter effect is similar to what is found in disordered hole doped cuprates and is discussed in the context of carrier localization. Examination of the c-axis conductivity gives evidence for an anomalously broad frequency range from which the interlayer superfluid is accumulated. Compelling evidence for the pseudogap state as well as other characteristics of the charge dynamics in Nd$_{1.85}$Ce$_{.15}$CuO$_{4+\delta}$ signal global similarities of the cuprate phase diagram with respect to electron and hole doping.Comment: Submitted to PR