Moment bounds for the Smoluchowski equation and their consequences

We prove uniform bounds on moments X_a = \sum_{m}{m^a f_m(x,t)} of the Smoluchowski coagulation equations with diffusion, valid in any dimension. If the collision propensities \alpha(n,m) of mass n and mass m particles grow more slowly than (n+m)(d(n) + d(m)), and the diffusion rate d(\cdot) is non-increasing and satisfies m^{-b_1} \leq d(m) \leq m^{-b_2} for some b_1 and b_2 satisfying 0 \leq b_2 < b_1 < \infty, then any weak solution satisfies X_a \in L^{\infty}(\mathbb{R}^d \times [0,T]) \cap L^1(\mathbb{R}^d \times [0,T]) for every a \in \mathbb{N} and T \in (0,\infty), (provided that certain moments of the initial data are finite). As a consequence, we infer that these conditions are sufficient to ensure uniqueness of a weak solution and its conservation of mass.Comment: 30 page

Correlation decay and recurrence estimates for some robust nonuniformly hyperbolic maps

We study decay of correlations, the asymptotic distribution of hitting times and fluctuations of the return times for a robust class of multidimensional non-uniformly hyperbolic transformations. Oliveira and Viana [15] proved that there is a unique equilibrium state for a large class of non- uniformly expanding transformations and Holder continuous potentials with small variation. For an open class of potentials with small variation, we prove quasi-compactness of the Ruelle-Perron-Frobenius operator in a space $V_\theta$ of functions with essential bounded variation that strictly contain Holder continuous observables. We deduce that the equilibrium states have exponential decay of correlations. Furthermore, we prove exponential asymptotic distribu- tion of hitting times and log-normal fluctuations of the return times around the average given by the metric entropy.Comment: 24 page

The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.Comment: To appear in Communications in Mathematical Physic

Robust exponential decay of correlations for singular-flows

We construct open sets of Ck (k bigger or equal to 2) vector fields with singularities that have robust exponential decay of correlations with respect to the unique physical measure. In particular we prove that the geometric Lorenz attractor has exponential decay of correlations with respect to the unique physical measure.Comment: Final version accepted for publication with added corrections (not in official published version) after O. Butterley pointed out to the authors that the last estimate in the argument in Subsection 4.2.3 of the previous version is not enough to guarantee the uniform non-integrability condition claimed. We have modified the argument and present it here in the same Subsection. 3 figures, 34 page

The disulphide isomerase DsbC cooperates with the oxidase DsbA in a DsbD-independent manner

In Escherichia coli , DsbA introduces disulphide bonds into secreted proteins. DsbA is recycled by DsbB, which generates disulphides from quinone reduction. DsbA is not known to have any proofreading activity and can form incorrect disulphides in proteins with multiple cysteines. These incorrect disulphides are thought to be corrected by a protein disulphide isomerase, DsbC, which is kept in the reduced and active configuration by DsbD. The DsbC/DsbD isomerization pathway is considered to be isolated from the DsbA/DsbB pathway. We show that the DsbC and DsbA pathways are more intimately connected than previously thought. dsbA - dsbC - mutants have a number of phenotypes not exhibited by either dsbA - , dsbC - or dsbA - dsbD - mutations: they exhibit an increased permeability of the outer membrane, are resistant to the lambdoid phage φ80, and are unable to assemble the maltoporin LamB. Using differential two-dimensional liquid chromatographic tandem mass spectrometry/mass spectrometry analysis, we estimated the abundance of about 130 secreted proteins in various dsb - strains. dsbA - dsbC - mutants exhibit unique changes at the protein level that are not exhibited by dsbA - dsbD - mutants. Our data indicate that DsbC can assist DsbA in a DsbD-independent manner to oxidatively fold envelope proteins. The view that DsbC's function is limited to the disulphide isomerization pathway should therefore be reinterpreted.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72894/1/MMI_6030_sm_Tables_S1-S4.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/72894/2/MMI_tables_s1-s4.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/72894/3/j.1365-2958.2007.06030.x.pd

The Clinical Variability of Maternally Inherited Diabetes and Deafness Is Associated with the Degree of Heteroplasmy in Blood Leukocytes

Context: Maternally inherited diabetes and deafness (MIDD) is a rare form of diabetes with a matrilineal transmission, sensorineural hearing loss, and macular pattern dystrophy due to an A to G transition at position 3243 of mitochondrial DNA (mtDNA) (m.3243A&gt;G). The phenotypic heterogeneity of MIDD may be the consequence of different levels of mutated mtDNA among mitochondria in a given tissue. Objective: The aim of the present study was thus to ascertain the correlation between the severity of the phenotype in patients with MIDD and the level of heteroplasmy in the blood leukocytes. Participants: The GEDIAM prospective multicenter register was initiated in 1995. Eighty-nine Europid patients from this register, with MIDD and the mtDNA 3243A&gt;G mutation, were included. Patients with MELAS (mitochondrial encephalomyopathy, lactic acidosis, and stroke-like episodes) or with mitochondrial diabetes related to other mutations or to deletions of mtDNA were excluded. Results: A significant negative correlation was found between levels of heteroplasmy and age of the patients at the time of sampling for molecular analysis, age at the diagnosis of diabetes, and body mass index. After adjustment for age at sampling for molecular study and gender, the correlation between heteroplasmy levels and age at the diagnosis of diabetes was no more significant. The two other correlations remained significant. A significant positive correlation between levels of heteroplasmy and HbA1c was also found and remained significant after adjustment for age at molecular sampling and gender. Conclusions: These results support the hypothesis that heteroplasmy levels are at least one of the determinants of the severity of the phenotype in MIDD. Heteroplasmy levels are at least one of the determinants of the severity of the phenotype of maternally inherited diabetes and deafness