Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials

We investigate the construction of diffusions consisting of infinitely numerous Brownian particles moving in $\mathbb{R}^d$ and interacting via logarithmic functions (two-dimensional Coulomb potentials). These potentials are very strong and act over a long range in nature. The associated equilibrium states are no longer Gibbs measures. We present general results for the construction of such diffusions and, as applications thereof, construct two typical interacting Brownian motions with logarithmic interaction potentials, namely the Dyson model in infinite dimensions and Ginibre interacting Brownian motions. The former is a particle system in $\mathbb{R}$, while the latter is in $\mathbb{R}^2$. Both models are translation and rotation invariant in space, and as such, are prototypes of dimensions $d=1,2$, respectively. The equilibrium states of the former diffusion model are determinantal or Pfaffian random point fields with sine kernels. They appear in the thermodynamical limits of the spectrum of the ensembles of Gaussian random matrices such as GOE, GUE and GSE. The equilibrium states of the latter diffusion model are the thermodynamical limits of the spectrum of the ensemble of complex non-Hermitian Gaussian random matrices known as the Ginibre ensemble.Comment: Published in at http://dx.doi.org/10.1214/11-AOP736 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Management of Kawasaki disease

Kawasaki disease (KD) is an acute self-limiting inflammatory disorder, associated with vasculitis, affecting predominantly medium-sized arteries, particularly the coronary arteries. In developed countries KD is the commonest cause of acquired heart disease in childhood. The aetiology of KD remains unknown, and it is currently believed that one or more as yet unidentified infectious agents induce an intense inflammatory host response in genetically susceptible individuals. Genetic studies have identified several susceptibility genes for KD and its sequelae in different ethnic populations, including FCGR2A, CD40, ITPKC, FAM167A-BLK and CASP3, as well as genes influencing response to intravenous immunoglobulin (IVIG) and aneurysm formation such as FCGR3B, and transforming growth factor (TGF) β pathway genes. IVIG and aspirin are effective therapeutically, but recent clinical trials and meta-analyses have demonstrated that the addition of corticosteroids to IVIG is beneficial for the prevention of coronary artery aneurysms (CAA) in severe cases with highest risk of IVIG resistance. Outside of Japan, however, clinical scores to predict IVIG resistance perform suboptimally. Furthermore, the evidence base does not provide clear guidance on which corticosteroid regimen is most effective. Other therapies, including anti-TNFα, could also have a role for IVIG-resistant KD. Irrespective of these caveats, it is clear that therapy that reduces inflammation in acute KD, improves outcome. This paper summarises recent advances in the understanding of KD pathogenesis and therapeutics, and provides an approach for managing KD patients in the UK in the light of these advances

Has HERA reached a new QCD regime?

These notes are a summary of our efforts to answer the question in the title. Our answer is in the affirmative as: (i) HERA data indicate a large value of the gluon structure function; (ii) no contradictions with the asymptotic predictions of high density QCD have been observed; and (iii) the numerical estimates of our model give a natural description of the size of deviation from the routine DGLAP explanation. We discuss the alternative approaches and possible new experiments.Comment: 29 pages, 37 figures in eps file

On the nature of long-range contributions to pair interactions between charged colloids in two dimensions

We perform a detailed analysis of solutions of the inverse problem applied to experimentally measured two-dimensional radial distribution functions for highly charged latex dispersions. The experiments are carried out at high colloidal densities and under low-salt conditions. At the highest studied densities, the extracted effective pair potentials contain long-range attractive part. At the same time, we find that for the best distribution functions available the range of stability of the solutions is limited by the nearest neighbour distance between the colloidal particles. Moreover, the measured pair distribution functions can be explained by purely repulsive pair potentials contained in the stable part of the solution.Comment: 6 pages, 5 figure

Stable isotopic composition of fossil mammal teeth and environmental change in southwestern South Africa during the Pliocene and Pleistocene

The past 5 million years mark a global change from the warmer, more stable climate of the Pliocene to the initiation of glacial-interglacial cycles during the Pleistocene. Marine core sediment records located off the coast of southwestern Africa indicate aridification and intensified upwelling in the Benguela Current over the Pliocene and Pleistocene. However, few terrestrial records document environmental change in southwestern Africa over this time interval. Here we synthesize new and published carbon and oxygen isotope data of the teeth from large mammals (>6 kg) at Langebaanweg (~5 million years ago, Ma), Elandsfontein (1.0 – 0.6 Ma), and Hoedjiespunt (0.35 – 0.20 Ma), to evaluate environmental change in southwestern Africa between the Pliocene and Pleistocene. The majority of browsing and grazing herbivores from these sites yield enamel 13 C values within the range expected for animals with a pure C3 diet, however some taxa have enamel 13C values that suggest the presence of small amounts C4 grasses at times during the Pleistocene. Considering that significant amounts of C4 grasses require a warm growing season, these results indicate that the winter rainfall zone, characteristic of the region today, could have been in place for the past 5 million years. The average 18O value of the herbivore teeth increases ~4.4‰ between Langebaanweg and Elandsfontein for all taxa except suids. This increase may solely be a function of a change in hydrology between the fluvial system at Langebaanweg and the spring-fed environments at Elandsfontein, or a combination of factors that include depositional context, regional circulation and global climate. However, an increase in regional aridity or global cooling between the early Pliocene and mid-Pleistocene cannot explain the entire increase in enamel 18O values. Spring-fed environments like those at Elandsfontein may have 75 provided critical resources for mammalian fauna in the mid-Pleistocene within an increasingly arid southwestern Africa ecosystem

Weak gauge principle and electric charge quantization

Starting from a weak gauge principle we give a new and critical revision of the argument leading to charge quantization on arbitrary spacetimes. The main differences of our approach with respect to previous works appear on spacetimes with non trivial torsion elements on its second integral cohomology group. We show that in these spacetimes there can be topologically non-trivial configurations of charged fields which do not imply charge quantization. However, the existence of a non-exact electromagnetic field always implies the quantization of charges. Another consequence of the theory for spacetimes with torsion is the fact that it gives rise to two natural quantization units that could be identified with the electric quantization unit (realized inside the quarks) and with the electron charge. In this framework the color charge can have a topological origin, with the number of colors being related to the order of the torsion subgroup. Finally, we discuss the possibility that the quantization of charge may be due to a weak non-exact component of the electromagnetic field extended over cosmological scales.Comment: Latex2e, 24 pages, no figure

Pseudogap effects induced by resonant pair scattering

We demonstrate how resonant pair scattering of correlated electrons above T_c can give rise to pseudogap behavior. This resonance in the scattering T-matrix appears for superconducting interactions of intermediate strength, within the framework of a simple fermionic model. It is associated with a splitting of the single peak in the spectral function into a pair of peaks separated by an energy gap. Our physical picture is contrasted with that derived from other T-matrix schemes, with superconducting fluctuation effects, and with preformed pair (boson-fermion) models. Implications for photoemission and tunneling experiments in the cuprates are discussed.Comment: REVTeX3.0; 4 pages, 4 EPS figures (included

Postnatal DNA demethylation and its role in tissue maturation.

Development in mammals is accompanied by specific de novo and demethylation events that are thought to stabilize differentiated cell phenotypes. We demonstrate that a large percentage of the tissue-specific methylation pattern is generated postnatally. Demethylation in the liver is observed in thousands of enhancer-like sequences associated with genes that undergo activation during the first few weeks of life. Using. conditional gene ablation strategy we show that the removal of these methyl groups is stable and necessary for assuring proper hepatocyte gene expression and function through its effect on chromatin accessibility. These postnatal changes in methylation come about through exposure to hormone signaling. These results define the molecular rules of 5-methyl-cytosine regulation as an epigenetic mechanism underlying cellular responses to. changing environment

Algorithms for Cut Problems on Trees

We study the {\sc multicut on trees} and the {\sc generalized multiway Cut on trees} problems. For the {\sc multicut on trees} problem, we present a parameterized algorithm that runs in time $O^{*}(\rho^k)$, where $\rho = \sqrt{\sqrt{2} + 1} \approx 1.555$ is the positive root of the polynomial $x^4-2x^2-1$. This improves the current-best algorithm of Chen et al. that runs in time $O^{*}(1.619^k)$. For the {\sc generalized multiway cut on trees} problem, we show that this problem is solvable in polynomial time if the number of terminal sets is fixed; this answers an open question posed in a recent paper by Liu and Zhang. By reducing the {\sc generalized multiway cut on trees} problem to the {\sc multicut on trees} problem, our results give a parameterized algorithm that solves the {\sc generalized multiway cut on trees} problem in time $O^{*}(\rho^k)$, where $\rho = \sqrt{\sqrt{2} + 1} \approx 1.555$ time

Protostellar Disks: Formation, Fragmentation, and the Brown Dwarf Desert

We argue that gravitational instability of typical protostellar disks is not a viable mechanism for the fragmentation into multiple systems -- binary stars, brown dwarf companions, or gas giant planets -- except at periods above roughly 20,000 years. Our conclusion is based on a comparison between prior numerical work on disk self-gravity by Gammie (2001) with our own analytical models for the dynamical and thermal state of protostellar disks. For this purpose we first develop a simple theory for the initial conditions of low-mass star formation, accounting for the effect of turbulence on the characteristic mass, accretion rate, and angular momentum of collaping cores. Second, we examine the criterion for fragmentation to occur during star formation, concentrating on the self-gravitational instabilities of protostellar accretion disks in their main accretion phase. Self-gravitational instabilities are strongly dependent on the thermal state of the disk, and we find that the combination of viscous heating and stellar irradiation quenches fragmentation due to Toomre's local instability. Global instability of the disk may be required to process mass supply, but is unlikely to produce fragments. Our findings help to explain the dearth of substellar companions to stellar type stars: the brown dwarf desert.Comment: 22 pages, 2 figures, accepted by ApJ. Improved discussions of the criterion for local fragmentation and of the effects of stellar radiation; expanded comparisons to numerical simulations and to observation