Fast simulation of new coins from old

Let S\subset (0,1). Given a known function f:S\to (0,1), we consider the problem of using independent tosses of a coin with probability of heads p (where p\in S is unknown) to simulate a coin with probability of heads f(p). We prove that if S is a closed interval and f is real analytic on S, then f has a fast simulation on S (the number of p-coin tosses needed has exponential tails). Conversely, if a function f has a fast simulation on an open set, then it is real analytic on that set.Comment: Published at http://dx.doi.org/10.1214/105051604000000549 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Random soups, carpets and fractal dimensions

We study some properties of a class of random connected planar fractal sets induced by a Poissonian scale-invariant and translation-invariant point process. Using the second-moment method, we show that their Hausdorff dimensions are deterministic and equal to their expectation dimension. We also estimate their low-intensity limiting behavior. This applies in particular to the "conformal loop ensembles" defined via Poissonian clouds of Brownian loops for which the expectation dimension has been computed by Schramm, Sheffield and Wilson.Comment: To appear in J. London Math. So

Channel Uncertainty in Ultra Wideband Communication Systems

Wide band systems operating over multipath channels may spread their power over bandwidth if they use duty cycle. Channel uncertainty limits the achievable data rates of power constrained wide band systems; Duty cycle transmission reduces the channel uncertainty because the receiver has to estimate the channel only when transmission takes place. The optimal choice of the fraction of time used for transmission depends on the spectral efficiency of the signal modulation. The general principle is demonstrated by comparing the channel conditions that allow different modulations to achieve the capacity in the limit. Direct sequence spread spectrum and pulse position modulation systems with duty cycle achieve the channel capacity, if the increase of the number of channel paths with the bandwidth is not too rapid. The higher spectral efficiency of the spread spectrum modulation lets it achieve the channel capacity in the limit, in environments where pulse position modulation with non-vanishing symbol time cannot be used because of the large number of channel paths

Eléments d'éclairage sociologiques sur la fibromyalgie : du problème public à l’expérience vécue

Il s’agit d’abord d’explorer les conditions de l’émergence et de la diffusion de la fibromyalgie ainsi que les controverses qui ont animé le monde médical à son propos. Il s’agit ensuite de rendre compte de l’expérience des patients, de leur relation avec les professionnels de santé ainsi que des principales difficultés qu’ils sont susceptibles de rencontrer, avant et après le diagnostic

Sets which are not tube null and intersection properties of random measures

We show that in $\mathbb{R}^d$ there are purely unrectifiable sets of Hausdorff (and even box counting) dimension $d-1$ which are not tube null, settling a question of Carbery, Soria and Vargas, and improving a number of results by the same authors and by Carbery. Our method extends also to "convex tube null sets", establishing a contrast with a theorem of Alberti, Cs\"{o}rnyei and Preiss on Lipschitz-null sets. The sets we construct are random, and the proofs depend on intersection properties of certain random fractal measures with curves.Comment: 24 pages. Referees comments incorporated. JLMS to appea

New coins from old, smoothly

Given a (known) function $f:[0,1] \to (0,1)$, we consider the problem of simulating a coin with probability of heads $f(p)$ by tossing a coin with unknown heads probability $p$, as well as a fair coin, $N$ times each, where $N$ may be random. The work of Keane and O'Brien (1994) implies that such a simulation scheme with the probability $\P_p(N<\infty)$ equal to 1 exists iff $f$ is continuous. Nacu and Peres (2005) proved that $f$ is real analytic in an open set $S \subset (0,1)$ iff such a simulation scheme exists with the probability $\P_p(N>n)$ decaying exponentially in $n$ for every $p \in S$. We prove that for $\alpha>0$ non-integer, $f$ is in the space $C^\alpha [0,1]$ if and only if a simulation scheme as above exists with $\P_p(N>n) \le C (\Delta_n(p))^\alpha$, where \Delta_n(x)\eqbd \max \{\sqrt{x(1-x)/n},1/n \}. The key to the proof is a new result in approximation theory: Let \B_n be the cone of univariate polynomials with nonnegative Bernstein coefficients of degree $n$. We show that a function $f:[0,1] \to (0,1)$ is in $C^\alpha [0,1]$ if and only if $f$ has a series representation $\sum_{n=1}^\infty F_n$ with F_n \in \B_n and $\sum_{k>n} F_k(x) \le C(\Delta_n(x))^\alpha$ for all $x \in [0,1]$ and $n \ge 1$. We also provide a counterexample to a theorem stated without proof by Lorentz (1963), who claimed that if some \phi_n \in \B_n satisfy $|f(x)-\phi_n(x)| \le C (\Delta_n(x))^\alpha$ for all $x \in [0,1]$ and $n \ge 1$, then $f \in C^\alpha [0,1]$.Comment: 29 pages; final version; to appear in Constructive Approximatio

Accidentul vascular cerebral recurent la pacienții tineri

Department of Neurology no. 1, Nicolae Testemitanu SUMPh, Diomid Gherman Institute of Neurology and NeurosurgeryBackground. According to the studies, approximately 10% of ischemic strokes occur in people aged less than 50 years. The risk of recurrent stroke in young stroke survivors varies from 9.4% in the next 5 years, up to 19.4% in the next 20 years. Objective of the study. To analyze the symptomatology presented by young patients (<50 years) with recurrent stroke, and to compare them, with clinical signs presented by people of the same age category, with the first-ever stroke. Material and Methods. A retrospective analysis of 1687 medical records of patients with ischemic stroke was performed from January 2018 to December 2019. 56 patients (≤ 50 years old) were included in the study. Risk factors, clinical signs, neuroimaging were analyzed - all of these were stratified by the presence of recurrent stroke criteria. SPSS Statistics, Version 25.0 was used. Results. The cohort study consisted of 2 groups: the first group- patients with the first-ever stroke (46); the second one– patients with recurrent stroke (10). The frequency of clinical signs between these two groups was compared: speech disorders (30.0% vs. 37.0%); sensitivity disorders (20.0% vs. 13.0%); cranial nerve damage (20.0% vs. 15.2%); paresis/ plegia (90.0% vs. 65.2%); bulbar syndrome (20.0% vs. 28.3%). Changes on cerebral CT: leukoaraiosis (30.0% vs. 28.3%); old infarcts on imaging (80.0% vs. 6.5%, t = 5.29, ˂0.001); Doppler Ultrasound of intra and extracranial arteries: stenotic atherosclerosis (42.9% vs. 40.5%); vertebral artery hypoplasia (42.9% vs. 32.4%). Conclusion. Recurrent ischemic stroke in young patients has more variable symptoms, with a more unfavorable prognosis if compared with the first ever stroke in the same category of patients. So, it requires the establishment of recurrence risk factors and an efficient secondary prophylaxis.Introducere. Conform studiilor efectuate, aproximativ 10% dintre accidentele vasculare cerebrale ischemice apar la persoanele cu vârsta sub 50 de ani. Riscul de AVC recurent la pacienții tineri variază de la 9,4% în primii 5 ani, până la 19,4% în primii 20 de ani. Scopul lucrării. Analiza simptomatologiei prezentate de pacienții tineri (< 50 ani) cu AVC recurent, prin compararea clinicii date, cu clinica prezentată de persoanele de aceeași categorie de vârstă cu AVC primar. Material și Metode. A fost efectuată analiza retrospectivă a 1 687de fișe medicale ale pacienților cu AVC ischemic, din ianuarie 2018- până în decembrie 2019. 56 de pacienți (≤ 50 ani) au fost incluși în studiu. Au fost analizați factorii de risc, semnele clinice, neuroimagistica – toate fiind stratificate după criteriul prezenței AVC-ului repetat. A fost utilizată Statistica SPSS, Versiunea 25.0. Rezultate. Studiul a constat din 2 grupuri: primul – AVC primar depistat (46 de pacienți) și grupul II – AVC repetat (10 pacienți). A fost comparată frecvența semnelor clinice din cadrul AVC-ului repetat și primar: tulburări de vorbire (30.0% vs 37.0 %); tulburări de sensibilitate (20.0% vs 13.0 %); afectarea nervilor cranieni (20.0% vs 15.2 %); prezența parezei/plegiei (90.0% vs 65.2 %); sindrom bulbar (20.0% vs 28,3 %). TC cerebrală leucoaraioza (30.0% vs. 28,3 %); focare vechi (80.0% vs 6,5%, t=5.29, ˂0.001). Dopplerografia vaselor intra- și extracraniene: ateroscleroza stenozantă (42,9% vs 40,5%); hipoplazia arterei vertebrale (42,9% vs 32,4%). Concluzii. Accidentul vascular ischemic recurent la pacienții tineri prezintă o clinică mai vastă, cu prognostic mai nefavorabil comparativ cu cea din AVC-ul primar, ceea ce necesită stabilirea factorilor de risc de recurență și a unei ulterioare profilaxii secundare