Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes

We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates proportional to their sizes, conserving the total mass. The total number of clusters grows continuously but the full time-dependent distribution can be rescaled over at least 15 decades onto a universal curve which we derive analytically. This curve includes a scale free solution with a scaling exponent of -3/2 for the cluster sizes.Comment: 4 pages, 3 figure

Diffusion, Fragmentation and Coagulation Processes: Analytical and Numerical Results

We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the rate equation exactly leading to size distributions of Bessel type which fall off as $\exp(-x^{3/2})$ for large $x$-values. Moreover, we provide explicit formulas for the expansion coefficients in terms of Airy functions. Introducing the coagulation term, the full non-linear model is mapped exactly onto a Riccati equation that enables us to derive various asymptotic solutions for the distribution function. In particular, we find a standard exponential decay, $\exp(-x)$, for large $x$, and observe a crossover from the Bessel function for intermediate values of $x$. These findings are checked by numerical simulations and we find perfect agreement between the theoretical predictions and numerical results.Comment: (28 pages, 6 figures, v2+v3 minor corrections

Comprehensive genetic and epigenetic analysis of sporadic meningioma for macro-mutations on 22q and micro-mutations within the NF2 locus

BACKGROUND: Meningiomas are the most common intracranial neoplasias, representing a clinically and histopathologically heterogeneous group of tumors. The neurofibromatosis type 2 (NF2) tumor suppressor is the only gene known to be frequently involved in early development of meningiomas. The objective of this study was to identify genetic and/or epigenetic factors contributing to the development of these tumors. A large set of sporadic meningiomas were analyzed for presence of 22q macro-mutations using array-CGH in order to identify tumors carrying gene dosage aberrations not encompassing NF2. The NF2 locus was also comprehensively studied for point mutations within coding and conserved non-coding sequences. Furthermore, CpG methylation within the NF2 promoter region was thoroughly analyzed. RESULTS: Monosomy 22 was the predominant finding, detected in 47% of meningiomas. Thirteen percent of the tumors contained interstitial/terminal deletions and gains, present singly or in combinations. We defined at least two minimal overlapping regions outside the NF2 locus that are small enough (~550 kb and ~250 kb) to allow analysis of a limited number of candidate genes. Bialleinactivationo the NF2 gne was detected in 36% of meningiomas. Among the monosomy 22 cases, no additional NF2 mutations could be identified in 35% (17 out of 49) of tumors. Furthermore, the majority of tumors (9 out of 12) with interstitial/terminal deletions did not have any detectable NF2 mutations. Methylation within the NF2 promoter region was only identified at a single CpG site in one tumor sample. CONCLUSION: We confirmed previous findings of pronounced differences in mutation frequency between different histopathological subtypes. There is a higher frequency of biallelic NF2 inactivation in fibroblastic (52%) compared to meningothelial (18%) tumors. The presence of macro-mutations on 22q also shows marked differences between fibroblastic (86%) and meningothelial (39%) subtypes. Thus, inactivation of NF2, often combined with the presence of macro-mutation on 22q, is likely not as important for the development of the meningothelial subtype, as opposed to the fibroblastic form. Analysis of 40 CpG sites distributed within 750 bp of the promoter region suggests that NF2 promoter methylation does not play a major role in meningioma development

The cosmological free-free signal from galaxy groups and clusters

Using analytical models and cosmological N-body simulations, we study the free-free radio emission from ionized gas in clusters and groups of galaxies. The results obtained with the simulations are compared with analytical predictions based on the mass function and scaling relations. Earlier works based on analytical models have shown that the average free-free signal from small haloes (galaxies) during and after the reionization time could be detected with future experiments as a distortion of the CMB spectrum at low frequencies ($\nu <$ 5 GHz). We focus on the period after the reionization time (from redshift $z=0$ up to $z=7$) and on haloes that are more massive than in previous works (groups and clusters). We show how the average signal from haloes with $M > 10^{13} h^{-1} M_{\odot}$ is less than 10% the signal from the more abundant and colder smaller mass haloes. However, the individual signal from the massive haloes could be detected with future experiments opening the door for a new window to study the intracluster medium.Comment: 11 pages, 7 figure

XMM−NewtonXMM-Newton Ω\Omega project: III. Gas mass fraction shape in high redshift clusters

We study the gas mass fraction, $f\_{\rm gas},$ behavior in $XMM-Newton$ $\Omega$ project. The typical $f\_{\rm gas}$ shape of high redshift galaxy clusters follows the global shape inferred at low redshift quite well. This result is consistent with the gravitational instability picture leading to self similar structures for both the dark and baryonic matter. However, the mean $f\_{\rm gas} in distant clusters shows some differences to local ones, indicating a departure from strict scaling. This result is consistent with the observed evolution in the luminosity-temperature relation. We quantitatively investigate this departure from scaling laws. Within the local sample we used, a moderate but clear variation of the amplitude of the gas mass fraction with temperature is found, a trend that weakens in the outer regions. These variations do not explain departure from scaling laws of our distant clusters. An important implication of our results is that the gas fraction evolution, a test of the cosmological parameters, can lead to biased values when applied at radii smaller than the virial radius. From our$XMM$ clusters, the apparent gas fraction at the virial radius is consistent with a non-evolving universal value in a high matter density model and not with a concordance.Comment: Accepted, A&A, in pres

Viscous shocks in Hele-Shaw flow and Stokes phenomena of the Painleve I transcendent

In Hele-Shaw flows at vanishing surface tension, the boundary of a viscous fluid develops cusp-like singularities. In recent papers [1, 2] we have showed that singularities trigger viscous shocks propagating through the viscous fluid. Here we show that the weak solution of the Hele-Shaw problem describing viscous shocks is equivalent to a semiclassical approximation of a special real solution of the Painleve I equation. We argue that the Painleve I equation provides an integrable deformation of the Hele-Shaw problem which describes flow passing through singularities. In this interpretation shocks appear as Stokes level-lines of the Painleve linear problem.Comment: A more detailed derivation is include

Hypoglycemia in Type 1 Diabetic Pregnancy: Role of preconception insulin aspart treatment in a randomized study

Objective: A recent randomized trial compared prandial insulin aspart (IAsp) with human insulin in type 1 diabetic pregnancy. The aim of this exploratory analysis was to investigate the incidence of severe hypoglycemia during pregnancy and compare women enrolled preconception with women enrolled during early pregnancy. Research design and methods: IAsp administered immediately before each meal was compared with human insulin administered 30 min before each meal in 99 subjects (44 to IAsp and 55 to human insulin) randomly assigned preconception and in 223 subjects (113 for IAsp and 110 for human insulin) randomly assigned in early pregnancy (<10 weeks). NPH insulin was the basal insulin. Severe hypoglycemia (requiring third-party assistance) was recorded prospectively preconception (where possible), during pregnancy, and postpartum. Relative risk (RR) of severe hypoglycemia was evaluated with a gamma frailty model. Results: Of the patients, 23% experienced severe hypoglycemia during pregnancy with the peak incidence in early pregnancy. In the first half of pregnancy, the RR of severe hypoglycemia in women randomly assigned in early pregnancy/preconception was 1.70 (95% CI 0.91–3.18, P = 0.097); the RR in the second half of pregnancy was 1.35 (0.38–4.77, P = 0.640). In women randomly assigned preconception, severe hypoglycemia rates occurring before and during the first and second halves of pregnancy and postpartum for IAsp versus human insulin were 0.9 versus 2.4, 0.9 versus 2.4, 0.3 versus 1.2, and 0.2 versus 2.2 episodes per patient per year, respectively (NS). Conclusions: These data suggest that initiation of insulin analog treatment preconception rather than during early pregnancy may result in a lower risk of severe hypoglycemia in women with type 1 diabetes