Parallel Algorithm and Dynamic Exponent for Diffusion-limited Aggregation

A parallel algorithm for ``diffusion-limited aggregation'' (DLA) is described and analyzed from the perspective of computational complexity. The dynamic exponent z of the algorithm is defined with respect to the probabilistic parallel random-access machine (PRAM) model of parallel computation according to $T \sim L^{z}$, where L is the cluster size, T is the running time, and the algorithm uses a number of processors polynomial in L\@. It is argued that z=D-D_2/2, where D is the fractal dimension and D_2 is the second generalized dimension. Simulations of DLA are carried out to measure D_2 and to test scaling assumptions employed in the complexity analysis of the parallel algorithm. It is plausible that the parallel algorithm attains the minimum possible value of the dynamic exponent in which case z characterizes the intrinsic history dependence of DLA.Comment: 24 pages Revtex and 2 figures. A major improvement to the algorithm and smaller dynamic exponent in this versio

Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model

A fast method is presented for simulating the dielectric-breakdown model using iterated conformal mappings. Numerical results for the dimension and for corrections to scaling are in good agreement with the recent RG prediction of an upper critical $\eta_c=4$, at which a transition occurs between branching fractal clusters and one-dimensional nonfractal clusters.Comment: 5 pages, 7 figures; corrections to scaling include

Characteristic distributions of finite-time Lyapunov exponents

We study the probability densities of finite-time or \local Lyapunov exponents (LLEs) in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are significant finite-size corrections which are coordinate dependent. Depending on the nature of the dynamical state, the distribution of local Lyapunov exponents has a characteristic shape. For intermittent dynamics, and at crises, dynamical correlations lead to distributions with stretched exponential tails, while for fully-developed chaos the probability density has a cusp. Exact results are presented for the logistic map, $x \to 4x(1-x)$. At intermittency the density is markedly asymmetric, while for `typical' chaos, it is known that the central limit theorem obtains and a Gaussian density results. Local analysis provides information on the variation of predictability on dynamical attractors. These densities, which are used to characterize the {\sl nonuniform} spatial organization on chaotic attractors are robust to noise and can therefore be measured from experimental data.Comment: To be appear in Phys. Rev

Fractal geometry of spin-glass models

Stability and diversity are two key properties that living entities share with spin glasses, where they are manifested through the breaking of the phase space into many valleys or local minima connected by saddle points. The topology of the phase space can be conveniently condensed into a tree structure, akin to the biological phylogenetic trees, whose tips are the local minima and internal nodes are the lowest-energy saddles connecting those minima. For the infinite-range Ising spin glass with p-spin interactions, we show that the average size-frequency distribution of saddles obeys a power law $\sim w^{-D}$, where w=w(s) is the number of minima that can be connected through saddle s, and D is the fractal dimension of the phase space

Curvature fluctuations and Lyapunov exponent at Melting

We calculate the maximal Lyapunov exponent in constant-energy molecular dynamics simulations at the melting transition for finite clusters of 6 to 13 particles (model rare-gas and metallic systems) as well as for bulk rare-gas solid. For clusters, the Lyapunov exponent generally varies linearly with the total energy, but the slope changes sharply at the melting transition. In the bulk system, melting corresponds to a jump in the Lyapunov exponent, and this corresponds to a singularity in the variance of the curvature of the potential energy surface. In these systems there are two mechanisms of chaos -- local instability and parametric instability. We calculate the contribution of the parametric instability towards the chaoticity of these systems using a recently proposed formalism. The contribution of parametric instability is a continuous function of energy in small clusters but not in the bulk where the melting corresponds to a decrease in this quantity. This implies that the melting in small clusters does not lead to enhanced local instability.Comment: Revtex with 7 PS figures. To appear in Phys Rev

Aszites, Pfortaderthrombose und hepatische Enzephalopathie bei Leberzirrhose: Aktuelle Therapieempfehlungen

Treatment of Ascites, Portal Vein Thrombosis and Hepatic Encephalopathy in Patients with Cirrhosis of the Liver Background: Ascites, portal vein thrombosis and hepatic encephalopathy are important complications of cirrhosis of the liver. Guidelines for the treatment of ascites have recently been published. Method: This manuscript summarizes up-to-date recommendations on the basis of the DGVS S3 guideline and of other guidelines as well as of the authors' experience. Results and Conclusions: TIPS (transjugular intrahepatic porto-systemic shunt) is the preferred treatment for refractory or recidivant ascites unless there are contraindications. The therapy of hepatorenal syndrome type 1 with albumin and the vasoconstrictor Terlipressin has been proven effective. Treatment of portal vein thrombosis comprises a strategy of anticoagulation, TIPS and liver transplantation. The most important therapeutic strategy for hepatic encephalopathy is the search for as well as the treatment of trigger events. Rifaximin is being increasingly used for the treatment and prophylaxis of hepatic encephalopathy

Portal vein thrombosis; risk factors, clinical presentation and treatment

<p>Abstract</p> <p>Background</p> <p>Portal vein thrombosis (PVT) is increasingly frequently being diagnosed, but systematic descriptions of the natural history and clinical handling of the condition are sparse. The aim of this retrospective study was to describe risk factors, clinical presentation, complications and treatment of portal vein thrombosis in a single-centre.</p> <p>Methods</p> <p>Sixty-seven patients were identified in the electronic records from 1992 to 2005. All data were obtained from the patient records.</p> <p>Results</p> <p>One or more risk factors (e.g. prothrombotic disorder or abdominal inflammation) were present in 87%. Symptoms were abdominalia, splenomegaly, fever, ascites, haematemesis, and weight loss. Abdominalia and fever occurred more frequently in patients with acute PVT. Frequent complications were splenomegaly, oesophageal- and gastric varices with or without bleeding, portal hypertensive gastropathy and ascites. Varices and bleeding were more frequent in patients with chronic PVT. Patients who received anticoagulant therapy more frequently achieved partial/complete recanalization. Patients with varices who were treated endoscopically in combination with β-blockade had regression of the varices. The overall mortality was 13% in one year, and was dependent on underlying causes.</p> <p>Conclusion</p> <p>Most patients had a combination of local and systemic risk factors for PVT. We observed that partial/complete recanalization was more frequent in patients treated with anticoagulation therapy, and that regression of varices was more pronounced in patients who where treated with active endoscopy combined with pharmacological treatment.</p

Scaling and Crossover in the Large-N Model for Growth Kinetics

The dependence of the scaling properties of the structure factor on space dimensionality, range of interaction, initial and final conditions, presence or absence of a conservation law is analysed in the framework of the large-N model for growth kinetics. The variety of asymptotic behaviours is quite rich, including standard scaling, multiscaling and a mixture of the two. The different scaling properties obtained as the parameters are varied are controlled by a structure of fixed points with their domains of attraction. Crossovers arising from the competition between distinct fixed points are explicitely obtained. Temperature fluctuations below the critical temperature are not found to be irrelevant when the order parameter is conserved. The model is solved by integration of the equation of motion for the structure factor and by a renormalization group approach.Comment: 48 pages with 6 figures available upon request, plain LaTe

Impact of chronic liver disease upon admission on COVID-19 in-hospital mortality: Findings from COVOCA study

Background Italy has been the first Western country to be heavily affected by the spread of SARS-COV-2 infection and among the pioneers of the clinical management of pandemic. To improve the outcome, identification of patients at the highest risk seems mandatory. Objectives Aim of this study is to identify comorbidities and clinical conditions upon admission associated with in-hospital mortality in several COVID Centers in Campania Region (Italy). Methods COVOCA is a multicentre retrospective observational cohort study, which involved 18 COVID Centers throughout Campania Region, Italy. Data were collected from patients who completed their hospitalization between March-June 2020. The endpoint was in-hospital mortality, assessed either from data at discharge or death certificate, whilst all exposure variables were collected at hospital admission. Results Among 618 COVID-19 hospitalized patients included in the study, 143 in-hospital mortality events were recorded, with a cumulative incidence of about 23%. At multivariable logistic analysis, male sex (OR 2.63, 95%CI 1.42–4.90; p = 0.001), Chronic Liver Disease (OR 5.88, 95%CI 2.39–14.46; p&lt;0.001) and malignancies (OR 2.62, 95%CI 1.21–5.68; p = 0.015) disclosed an independent association with a poor prognosis, Glasgow Coma Scale (GCS) and Respiratory Severity Scale allowed to identify at higher mortality risk. Sensitivity analysis further enhanced these findings. Conclusion Mortality of patients hospitalized for COVID-19 appears strongly affected by both clinical conditions on admission and comorbidities. Originally, we observed a very poor outcome in subjects with a chronic liver disease, alongside with an increase of hepatic damage

Clinical and molecular characterization of COVID-19 hospitalized patients

Clinical and molecular characterization by Whole Exome Sequencing (WES) is reported in 35 COVID-19 patients attending the University Hospital in Siena, Italy, from April 7 to May 7, 2020. Eighty percent of patients required respiratory assistance, half of them being on mechanical ventilation. Fiftyone percent had hepatic involvement and hyposmia was ascertained in 3 patients. Searching for common genes by collapsing methods against 150 WES of controls of the Italian population failed to give straightforward statistically significant results with the exception of two genes. This result is not unexpected since we are facing the most challenging common disorder triggered by environmental factors with a strong underlying heritability (50%). The lesson learned from Autism-Spectrum-Disorders prompted us to re-analyse the cohort treating each patient as an independent case, following a Mendelian-like model. We identified for each patient an average of 2.5 pathogenic mutations involved in virus infection susceptibility and pinpointing to one or more rare disorder(s). To our knowledge, this is the first report on WES and COVID-19. Our results suggest a combined model for COVID-19 susceptibility with a number of common susceptibility genes which represent the favorite background in which additional host private mutations may determine disease progression