Tagged particle process in continuum with singular interactions

By using Dirichlet form techniques we construct the dynamics of a tagged particle in an infinite particle environment of interacting particles for a large class of interaction potentials. In particular, we can treat interaction potentials having a singularity at the origin, non-trivial negative part and infinite range, as e.g., the Lennard-Jones potential.Comment: 27 pages, proof for conservativity added, tightened presentatio

On q-Gaussians and Exchangeability

The q-Gaussians are discussed from the point of view of variance mixtures of normals and exchangeability. For each q< 3, there is a q-Gaussian distribution that maximizes the Tsallis entropy under suitable constraints. This paper shows that q-Gaussian random variables can be represented as variance mixtures of normals. These variance mixtures of normals are the attractors in central limit theorems for sequences of exchangeable random variables; thereby, providing a possible model that has been extensively studied in probability theory. The formulation provided has the additional advantage of yielding process versions which are naturally q-Brownian motions. Explicit mixing distributions for q-Gaussians should facilitate applications to areas such as option pricing. The model might provide insight into the study of superstatistics.Comment: 14 page

Maximizing the Conditional Expected Reward for Reaching the Goal

The paper addresses the problem of computing maximal conditional expected accumulated rewards until reaching a target state (briefly called maximal conditional expectations) in finite-state Markov decision processes where the condition is given as a reachability constraint. Conditional expectations of this type can, e.g., stand for the maximal expected termination time of probabilistic programs with non-determinism, under the condition that the program eventually terminates, or for the worst-case expected penalty to be paid, assuming that at least three deadlines are missed. The main results of the paper are (i) a polynomial-time algorithm to check the finiteness of maximal conditional expectations, (ii) PSPACE-completeness for the threshold problem in acyclic Markov decision processes where the task is to check whether the maximal conditional expectation exceeds a given threshold, (iii) a pseudo-polynomial-time algorithm for the threshold problem in the general (cyclic) case, and (iv) an exponential-time algorithm for computing the maximal conditional expectation and an optimal scheduler.Comment: 103 pages, extended version with appendices of a paper accepted at TACAS 201

Quantum Process Tomography: Resource Analysis of Different Strategies

Characterization of quantum dynamics is a fundamental problem in quantum physics and quantum information science. Several methods are known which achieve this goal, namely Standard Quantum Process Tomography (SQPT), Ancilla-Assisted Process Tomography (AAPT), and the recently proposed scheme of Direct Characterization of Quantum Dynamics (DCQD). Here, we review these schemes and analyze them with respect to some of the physical resources they require. Although a reliable figure-of-merit for process characterization is not yet available, our analysis can provide a benchmark which is necessary for choosing the scheme that is the most appropriate in a given situation, with given resources. As a result, we conclude that for quantum systems where two-body interactions are not naturally available, SQPT is the most efficient scheme. However, for quantum systems with controllable two-body interactions, the DCQD scheme is more efficient than other known QPT schemes in terms of the total number of required elementary quantum operations.Comment: 15 pages, 5 figures, published versio

Condensation in randomly perturbed zero-range processes

The zero-range process is a stochastic interacting particle system that exhibits a condensation transition under certain conditions on the dynamics. It has recently been found that a small perturbation of a generic class of jump rates leads to a drastic change of the phase diagram and prevents condensation in an extended parameter range. We complement this study with rigorous results on a finite critical density and quenched free energy in the thermodynamic limit, as well as quantitative heuristic results for small and large noise which are supported by detailed simulation data. While our new results support the initial findings, they also shed new light on the actual (limited) relevance in large finite systems, which we discuss via fundamental diagrams obtained from exact numerics for finite systems.Comment: 18 pages, 6 figure

On Hilberg's Law and Its Links with Guiraud's Law

Hilberg (1990) supposed that finite-order excess entropy of a random human text is proportional to the square root of the text length. Assuming that Hilberg's hypothesis is true, we derive Guiraud's law, which states that the number of word types in a text is greater than proportional to the square root of the text length. Our derivation is based on some mathematical conjecture in coding theory and on several experiments suggesting that words can be defined approximately as the nonterminals of the shortest context-free grammar for the text. Such operational definition of words can be applied even to texts deprived of spaces, which do not allow for Mandelbrot's ``intermittent silence'' explanation of Zipf's and Guiraud's laws. In contrast to Mandelbrot's, our model assumes some probabilistic long-memory effects in human narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic

Instability of condensation in the zero-range process with random interaction

The zero-range process is a stochastic interacting particle system that is known to exhibit a condensation transition. We present a detailed analysis of this transition in the presence of quenched disorder in the particle interactions. Using rigorous probabilistic arguments we show that disorder changes the critical exponent in the interaction strength below which a condensation transition may occur. The local critical densities may exhibit large fluctuations and their distribution shows an interesting crossover from exponential to algebraic behaviour.Comment: 4 pages, 4 figures; included new simulation data (Fig. 4), small changes in introduction and conclusio

Urine levels of HMGB1 in Systemic Lupus Erythematosus patients with and without renal manifestations

INTRODUCTION: Lupus nephritis (LN) is a severe and frequent manifestation of systemic lupus erythematosus (SLE). Its pathogenesis has not been fully elucidated but immune complexes are considered to contribute to the inflammatory pathology in LN. High Mobility Group Box 1 (HMGB1) is a nuclear non-histone protein which is secreted from different types of cells during activation and/or cell death and may act as a pro-inflammatory mediator, alone or as part of DNA-containing immune complexes in SLE. Urinary excretion of HMGB1 might reflect renal inflammatory injury. To assess whether urinary HMGB1 reflects renal inflammation we determined serum levels of HMGB1 simultaneously with its urinary levels in SLE patients with and without LN in comparison to healthy controls (HC). We also analyzed urinary HMGB1 levels in relation with clinical and serological disease activity. METHODS: The study population consisted of 69 SLE patients and 17 HC. Twenty-one patients had biopsy proven active LN, 15 patients had a history of LN without current activity, and 33 patients had non-renal SLE. Serum and urine levels of HMGB1 were both measured by western blotting. Clinical and serological parameters were assessed according to routine procedures. In 17 patients with active LN a parallel analysis was performed on the expression of HMGB1 in renal biopsies. RESULTS: Serum and urinary levels of HMGB1 were significantly increased in patients with active LN compared to patients without active LN and HC. Similarly, renal tissue of active LN patients showed strong expression of HMGB1 at cytoplasmic and extracellular sites suggesting active release of HMGB1. Serum and urinary levels in patients without active LN were also significantly higher compared to HC. Urinary HMGB1 levels correlated with SLEDAI, and showed a negative correlation with complement C3 and C4. CONCLUSION: Levels of HMGB1 in urine of SLE patients, in particular in those with active LN, are increased and correlate with SLEDAI scores. Renal tissue of LN patients shows increased release of nuclear HMGB1 compared to control renal tissue. HMGB1, although at lower levels, is, however, also present in the urine of patients without active LN. These data suggest that urinary HMGB1 might reflect both local renal inflammation as well as systemic inflammation

Is serum HMGB1 a biomarker in ANCA-associated vasculitis?

Background: Antineutrophil cytoplasmic antibody (ANCA)-associated vasculitides (AAV) are systemic inflammatory disorders that include granulomatosis with polyangiitis (GPA), microscopic polyangiitis (MPA), Churg-Strauss syndrome and renal limited vasculitis (RLV). Extracellular high-mobility group box 1 (HMGB1) acts as an alarmin and has been shown to be a biomarker of disease activity as well as an autoantigen in systemic lupus erythematosus (SLE) and, possibly, in AAV. This study aims to assess antibodies against HMGB1 and HMGB1 levels as biomarkers for AAV disease activity and predictors of relapsing disease.Methods: AAV patients with active disease and healthy controls (HC) were evaluated for anti-HMGB1 antibodies while serum HMGB1 levels were measured longitudinally in AAV patients at presentation, during remission, prior to and at relapses.Results: HMGB1 levels were similar between AAV patients at presentation (n = 52) and HC (n = 35) (2.64 +/- 1.80 ng/ml vs. 2.39 +/- 1.09 ng/ml; P = 0.422) and no difference regarding HMGB1 levels could be found among AAV disease subsets (GPA: 2.66 +/- 1.83 ng/ml vs. MPA: 3.11 +/- 1.91 ng/ml vs. RLV: 1.92 +/- 1.48 ng/ml; P = 0.369). AAV patients with renal involvement had lower HMGB1 levels than patients without renal involvement at presentation (2.35 +/- 1.48 ng/ml vs. 3.52 +/- 2.41 ng/ml; P = 0.042). A negative correlation was observed between HMGB1 levels and 24-hour proteinuria (rho = -0.361, P = 0.028). Forty-nine AAV patients were evaluated for HMGB1 levels during follow-up and no differences were observed between relapsing and nonrelapsing patients (P = 0.350). No significant increase in HMGB1 levels was observed prior to a relapse compared with the remission period and changes in HMGB1 levels were not associated with an increased risk for relapse in AAV. Positivity for anti-HMGB1 antibodies was low in patients with active AAV (three out of 24 patients).Conclusions: Serum HMGB1 levels at presentation are not increased and are lower in patients with renal involvement. Relapses are not preceded or accompanied by significant rises in HMGB1 levels and changes in HMGB1 levels are not related to ensuing relapses. Anti-HMGB1 antibodies are present in only a few patients in AAV. in contrast to SLE, HMGB1 is not a useful biomarker in AAV.Univ Groningen, Univ Med Ctr Groningen, Dept Rheumatol & Clin Immunol, NL-9713 GZ Groningen, NetherlandsUniversidade Federal de São Paulo, Escola Paulista Med Unifesp EPM, Div Rheumatol, BR-04023900 São Paulo, BrazilUniv Groningen, Univ Med Ctr Groningen, Dept Lab Med, NL-9713 GZ Groningen, NetherlandsUniv Groningen, Univ Med Ctr Groningen, Div Nephrol, Dept Internal Med, NL-9713 GZ Groningen, NetherlandsMartini Hosp, Dept Rheumatol & Internal Med, NL-9728 NT Groningen, NetherlandsUniversidade Federal de São Paulo, Escola Paulista Med Unifesp EPM, Div Rheumatol, BR-04023900 São Paulo, BrazilWeb of Scienc