Mod-phi convergence I: Normality zones and precise deviations

In this paper, we use the framework of mod-$\phi$ convergence to prove precise large or moderate deviations for quite general sequences of real valued random variables $(X_{n})_{n \in \mathbb{N}}$, which can be lattice or non-lattice distributed. We establish precise estimates of the fluctuations $P[X_{n} \in t_{n}B]$, instead of the usual estimates for the rate of exponential decay $\log( P[X_{n}\in t_{n}B])$. Our approach provides us with a systematic way to characterise the normality zone, that is the zone in which the Gaussian approximation for the tails is still valid. Besides, the residue function measures the extent to which this approximation fails to hold at the edge of the normality zone. The first sections of the article are devoted to a proof of these abstract results and comparisons with existing results. We then propose new examples covered by this theory and coming from various areas of mathematics: classical probability theory, number theory (statistics of additive arithmetic functions), combinatorics (statistics of random permutations), random matrix theory (characteristic polynomials of random matrices in compact Lie groups), graph theory (number of subgraphs in a random Erd\H{o}s-R\'enyi graph), and non-commutative probability theory (asymptotics of random character values of symmetric groups). In particular, we complete our theory of precise deviations by a concrete method of cumulants and dependency graphs, which applies to many examples of sums of "weakly dependent" random variables. The large number as well as the variety of examples hint at a universality class for second order fluctuations.Comment: 103 pages. New (final) version: multiple small improvements ; a new section on mod-Gaussian convergence coming from the factorization of the generating function ; the multi-dimensional results have been moved to a forthcoming paper ; and the introduction has been reworke

Statistical Curse of the Second Half Rank

In competitions involving many participants running many races the final rank is determined by the score of each participant, obtained by adding its ranks in each individual race. The "Statistical Curse of the Second Half Rank" is the observation that if the score of a participant is even modestly worse than the middle score, then its final rank will be much worse (that is, much further away from the middle rank) than might have been expected. We give an explanation of this effect for the case of a large number of races using the Central Limit Theorem. We present exact quantitative results in this limit and demonstrate that the score probability distribution will be gaussian with scores packing near the center. We also derive the final rank probability distribution for the case of two races and we present some exact formulae verified by numerical simulations for the case of three races. The variant in which the worst result of each boat is dropped from its final score is also analyzed and solved for the case of two races.Comment: 16 pages, 10 figure

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

Dual random fragmentation and coagulation and an application to the genealogy of Yule processes

The purpose of this work is to describe a duality between a fragmentation associated to certain Dirichlet distributions and a natural random coagulation. The dual fragmentation and coalescent chains arising in this setting appear in the description of the genealogy of Yule processes.Comment: 14 page

Glioma infiltration of the corpus callosum: early signs detected by DTI

The most frequent primary brain tumors, anaplastic astrocytomas (AA) and glioblastomas (GBM): tend to invasion of the surrounding brain. Histopathological studies found malignant cells in macroscopically unsuspicious brain parenchyma remote from the primary tumor, even affecting the contralateral hemisphere. In early stages, diffuse interneural infiltration with changes of the apparent diffusion coefficient (ADC) and fractional anisotropy (FA) is suspected. The purpose of this study was to investigate the value of DTI as a possible instrument of depicting evidence of tumor invasion into the corpus callosum (CC). Preoperatively, 31 patients with high-grade brain tumors (8 AA and 23 GBM) were examined by MRI at 3 T, applying a high-resolution diffusion tensor imaging (DTI) sequence. ADC- and FA-values were analyzed in the tumor-associated area of the CC as identified by fiber tracking, and were compared to matched healthy controls. In (MR-)morphologically normal appearing CC the ADC values were elevated in the tumor patients (n = 22; 0.978 × 10(−3) mm²/s) compared to matched controls (0.917 × 10(−3) mm²/s, p < 0.05), and the corresponding relative FA was reduced (rFA: 88 %, p < 0.01). The effect was pronounced in case of affection of the CC visible on MRI (n = 9; 0.978 × 10(−3) mm²/s, p < 0.05; rFA: 72 %, p < 0.01). Changes in diffusivity and anisotropy in the CC can be interpreted as an indicator of tumor spread into the contralateral hemisphere not visible on conventional MRI

Reactivity against Complementary Proteinase-3 Is Not Increased in Patients with PR3-ANCA-Associated Vasculitis

The etiology of anti-neutrophil cytoplasmic antibodies (ANCA) associated vasculitides (AAV) is unknown, but the association between infections and autoimmunity has been studied extensively. In 2004, a novel theory was proposed that could link infection and autoimmunity. This ‘theory of autoantigen complementarity’ was based on the serendipitous finding of antibodies against complementary-PR3 (cPR3) in patients with PR3-ANCA-associated vasculitis. cPR3 demonstrated homology to several bacterial proteins, and it was hypothesized that PR3-ANCA develop in response to anti-cPR3 antibodies, as a consequence of the anti-idiotypic network. These data have not been confirmed in other patient cohorts. We investigated the presence of anti-cPR3 antibodies in a Dutch cohort of PR3-ANCA-associated vasculitis patients. Anti-cPR3 reactivity was determined in serum using ELISA. Two separate batches of cPR3 were used to determine reactivity in two separate cohorts of PR3-ANCA-associated vasculitis patients. We found that anti-cPR3-reactivity was not increased in our PR3-ANCA-associated vasculitis patients, in comparison to control groups. Further research will be necessary to prove the concept of autoantigen complementarity in autoimmune diseases

New distance measures for classifying X-ray astronomy data into stellar classes

The classification of the X-ray sources into classes (such as extragalactic sources, background stars, ...) is an essential task in astronomy. Typically, one of the classes corresponds to extragalactic radiation, whose photon emission behaviour is well characterized by a homogeneous Poisson process. We propose to use normalized versions of the Wasserstein and Zolotarev distances to quantify the deviation of the distribution of photon interarrival times from the exponential class. Our main motivation is the analysis of a massive dataset from X-ray astronomy obtained by the Chandra Orion Ultradeep Project (COUP). This project yielded a large catalog of 1616 X-ray cosmic sources in the Orion Nebula region, with their series of photon arrival times and associated energies. We consider the plug-in estimators of these metrics, determine their asymptotic distributions, and illustrate their finite-sample performance with a Monte Carlo study. We estimate these metrics for each COUP source from three different classes. We conclude that our proposal provides a striking amount of information on the nature of the photon emitting sources. Further, these variables have the ability to identify X-ray sources wrongly catalogued before. As an appealing conclusion, we show that some sources, previously classified as extragalactic emissions, have a much higher probability of being young stars in Orion Nebula.Comment: 29 page

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

Baseline predictors of response and discontinuation of tumor necrosis factor-alpha blocking therapy in ankylosing spondylitis: a prospective longitudinal observational cohort study

Contains fulltext : 96669.pdf (publisher's version ) (Open Access)INTRODUCTION: Identifying ankylosing spondylitis (AS) patients who are likely to benefit from tumor necrosis factor-alpha (TNF-alpha) blocking therapy is important, especially in view of the costs and potential side effects of these agents. Recently, the AS Disease Activity Score (ASDAS) has been developed to assess both subjective and objective aspects of AS disease activity. However, data about the predictive value of the ASDAS with respect to clinical response to TNF-alpha blocking therapy are lacking. The aim of the present study was to identify baseline predictors of response and discontinuation of TNF-alpha blocking therapy in AS patients in daily clinical practice. METHODS: AS outpatients who started TNF-alpha blocking therapy were included in the Groningen Leeuwarden Ankylosing Spondylitis (GLAS) study, an ongoing prospective longitudinal observational cohort study with follow-up visits according to a fixed protocol. For the present analysis, patients were excluded if they had previously received anti-TNF-alpha treatment. Predictor analyses of response and treatment discontinuation were performed using logistic and Cox regression models, respectively. RESULTS: Between November 2004 and April 2010, 220 patients started treatment with infliximab (n = 32), etanercept (n = 137), or adalimumab (n = 51). At three and six months, 68% and 63% of patients were Assessments in Ankylosing Spondylitis (ASAS)20 responders, 49% and 46% ASAS40 responders, and 49% and 50% Bath Ankylosing Spondylitis Disease Activity Index (BASDAI)50 responders, respectively. Baseline predictors of response were younger age, male gender, higher ASDAS score, higher erythrocyte sedimentation rate (ESR) level, higher C-reactive protein (CRP) level, presence of peripheral arthritis, higher patient's global assessment of disease activity, and lower modified Schober test. In August 2010, 64% of patients were still using their TNF-alpha blocking agent with a median follow-up of 33.1 months (range 2.4 to 68.2). Baseline predictors of discontinuation of TNF-alpha blocking therapy were female gender, absence of peripheral arthritis, higher BASDAI, lower ESR level, and lower CRP level. CONCLUSIONS: Besides younger age and male gender, objective variables such as higher inflammatory markers or ASDAS score were identified as independent baseline predictors of response and/or continuation of TNF-alpha blocking therapy. In contrast, higher baseline BASDAI score was independently associated with treatment discontinuation. Based on these results, it seems clinically relevant to include more objective variables in the evaluation of anti-TNF-alpha treatment

MRI and clinical syndrome in dura materrelated Creutzfeldt-Jakob disease

Objective : Iatrogenic Creutzfeldt-Jakob disease (iCJD) is mainly associated with dura mater (DM) grafts and administration of human growth hormones (hGH). Data on disease course in DM-CJD are limited. We describe the clinical and diagnostic findings in this patient group with special emphasis on MRI signal alterations. Methods : Ten DM-CJD patients were studied for their clinical symptoms and diagnostic findings. The MRIs were evaluated for signal increase of the cortical and subcortical structures. Results : DM-CJD patients had a median incubation time of 18 years and median disease duration of 7 months. The majority of patients were MM homozygous at codon 129 of the prion protein gene (PRNP) and presented with gait ataxia and psychiatric symptoms. No correlation between the graft site and the initial disease course was found. The MRI showed cortical and basal ganglia signal increase each in eight out of ten patients and thalamic hyperintensity in five out of ten cases. Of interest, patients with thalamic signal increase were homozygous for methionine. Conclusion : The MRI findings in DM-CJD largely resemble those seen in sporadic CJD, as the cortex and basal ganglia are mainly affecte