Scaling transformation and probability distributions for financial time series

The price of financial assets are, since Bachelier, considered to be described by a (discrete or continuous) time sequence of random variables, i.e a stochastic process. Sharp scaling exponents or unifractal behavior of such processes has been reported in several works. In this letter we investigate the question of scaling transformation of price processes by establishing a new connexion between non-linear group theoretical methods and multifractal methods developed in mathematical physics. Using two sets of financial chronological time series, we show that the scaling transformation is a non-linear group action on the moments of the price increments. Its linear part has a spectral decomposition that puts in evidence a multifractal behavior of the price increments.Comment: 10 pages, 4 figures, latex and ps file

Punctuated vortex coalescence and discrete scale invariance in two-dimensional turbulence

We present experimental evidence and theoretical arguments showing that the time-evolution of freely decaying 2-d turbulence is governed by a {\it discrete} time scale invariance rather than a continuous time scale invariance. Physically, this reflects that the time-evolution of the merging of vortices is not smooth but punctuated, leading to a prefered scale factor and as a consequence to log-periodic oscillations. From a thorough analysis of freely decaying 2-d turbulence experiments, we show that the number of vortices, their radius and separation display log-periodic oscillations as a function of time with an average log-frequency of ~ 4-5 corresponding to a prefered scaling ratio of ~ 1.2-1.3Comment: 22 pages and 38 figures. Submitted to Physica

Evidence of Intermittent Cascades from Discrete Hierarchical Dissipation in Turbulence

We present the results of a search of log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number (2500) of three-dimensional fully developed turbulence. A simple dynamical representation of the Richardson-Kolmogorov cartoon of a cascade shows that standard averaging techniques erase by their very construction the possible existence of log-periodic corrections to scaling associated with a discrete hierarchy. To remedy this drawback, we introduce a novel ``canonical'' averaging that we test extensively on synthetic examples constructed to mimick the interplay between a weak log-periodic component and rather strong multiplicative and phase noises. Our extensive tests confirm the remarkable observation of statistically significant log-periodic corrections to scaling, with a prefered scaling ratio for length scales compatible with the value gamma = 2. A strong confirmation of this result is provided by the identification of up to 5 harmonics of the fundamental log-periodic undulations, associated with up to 5 levels of the underlying hierarchical dynamical structure. A natural interpretation of our results is that the Richardson-Kolmogorov mental picture of a cascade becomes a realistic description if one allows for intermittent births and deaths of discrete cascades at varying scales.Comment: Latex document of 40 pages, including 18 eps figure

Epidemiological profile, treatment outcomes and factors associated with unfavorable treatment outcomes among patients co-infected with Tuberculosis and Human Immunodeficiency Virus in the Centrale Health Region in Togo, 2008 – 2017

Introduction: Co-infection with Tuberculosis and Human Immunodeficiency Virus (TB/HIV) is highly lethal and Africa hosts 74% of cases. In Togo, the prevalence of TB/HIV co-infection was 22% in 2016 with a 42% mortality among the TB/HIV co-infected cases. There is limited data on TB/HIV co-infection in Centrale health region to inform control and commitment efforts towards end TB by 2030. We aimed to describe epidemiological characteristics, treatment outcomes and identify factors associated with unfavorable outcomes among TB/HIV co-infected cases. Methods: We conducted a descriptive analysis of secondary data on TB cases recorded in the four Centers of Diagnosis and Treatment (CDTs) of the Togolese Centrale health region from 2008 to 2017. Socio-demographical, clinical and treatment data were collected on a designed questionnaire by reviewing all TB management tools of the four CDTs. We subsequently entered data in Epi-Info-7 and calculated means, ratio and proportions for descriptive analysis. In multivariate analysis, logistic regression was performed to obtain Adjusted Odd Ratio (AOR), 95% Confidence Interval (CI) and p-value to identify factors associated with unfavorable outcomes. Results: Over the period, 1,448 patients were screened for HIV among 1,825 TB patients recorded. Overall, TB/HIV prevalence was 30.87% (447/1448) range 43.8% in 2008 to 27.6% in 2017 (p=0.01). The mean age of TB/HIV patients varied from 28.80±7.70 years in 2008 to 33.48±8.11 years in 2017. Female to Male sex ratio varied from 9.7 in 2008 to 2.5 in 2017. Pulmonary TB form cases accounted for 94.41% (422/447) of which 74.41% (314/422) were smear positive (SPT+) and 25.59% (108/422) were smear negative, while extra-pulmonary form cases represented 5.59% (25/447). The proportion of TB/HIV patients on Antiretroviral Treatment (ART) varied from 5.25% (2/32) in 2008 to 94.29% (33/35) in 2017. Lost to follow up patients represented 1.57% (7/447) while treatment success rate varied from 62.29% in 2008 to 82.00% in 2017. Case fatality rate decreased from 34.48% in 2008 to 23.53% in 2017. Smear-positive TB (AOR=2.11, 95% CI (1.21-3.60)), TB treatment initiation in the second quarters of the year (AOR=1.71, 95% CI (1.03-2.85)) and having been taken care of between 2015 and 2017 (AOR=1.90, 95% CI (1.14 – 3.12)) were independently associated with unfavorable outcome. When stratified by type of outcome, the absence of ART (AOR=2.62, 95% CI (1.46 – 4.69) were associated with deaths. Conclusion: TB/HIV co-infection affected young people particularly women with high mortality. The TB form, period of treatment initiation and lack of HIV care influenced treatment outcomes. Systematic HIV screening and ART earlier initiation, practice of DOTS whether based on family or based on caregivers for each patient and caregivers training on TB/HIV co-infection management are necessary to improve patients' survival

Comprehensive structural classification of ligand binding motifs in proteins

Comprehensive knowledge of protein-ligand interactions should provide a useful basis for annotating protein functions, studying protein evolution, engineering enzymatic activity, and designing drugs. To investigate the diversity and universality of ligand binding sites in protein structures, we conducted the all-against-all atomic-level structural comparison of over 180,000 ligand binding sites found in all the known structures in the Protein Data Bank by using a recently developed database search and alignment algorithm. By applying a hybrid top-down-bottom-up clustering analysis to the comparison results, we determined approximately 3000 well-defined structural motifs of ligand binding sites. Apart from a handful of exceptions, most structural motifs were found to be confined within single families or superfamilies, and to be associated with particular ligands. Furthermore, we analyzed the components of the similarity network and enumerated more than 4000 pairs of ligand binding sites that were shared across different protein folds.Comment: 13 pages, 8 figure

Evolution thermique de la structure magnétique dans Tb3Fe5O12

L'étude de l'évolution thermique de la structure magnétique du ferrite grenat de terbium (Tb3Fe5O12) a été réalisée par diffraction neutronique entre 4.2K et 614K. Elle a permis de mettre en évidence en dessous de 130K, l'apparition de la structure non colinéaire "en double parapluie" qui existe à 4.2K. Son évolution thermique vers une structure colinéaire de Néel au dessus de 130K est continue. L'application des modèles théoriques de l'analyse de représentation du groupe d'espace rhomboédrique (R-3c) avec k = [000] a montré qu'à toute température entre 4.2K et la température d'ordre TN (560K) la structure magnétique de TbIG appartient à la seule représentation irréductible à une dimension Γ2g(A2g) pour laquelle les caractères des éléments générateurs 3, -1, c sont respectivement +1, +1, -1 : le groupe de Shubnikov correspondant est (R-3c')

Evidence for a modulated ordering in the intermetallic compounds TbGe0,2Si0,8 and ErSi of CrB-type

Neutron diffraction experiments have been performed on powder samples of TbGe0.2Si0.8 and ErSi. They order respectively at TN = 55 K and 11.5 K with a pure sine wave modulation propagating along the [100] direction of the orthorhombic unit cell. The wave vector k = [kx, 0, 1/2] is incommensurate with the lattice and is temperature dependent down to TIC (TIC = 43.5 K and 7.25 K respectively for TbGe0.2Si0.8, and ErSi) at which a magnetic transition to a commensurate phase described, by the wave vector k = [1/2, 0, 1/2] takes place. At any temperatures, the erbium magnetic moments are aligned along the a-axis, whereas for TbGe 0.2Si0.8, the terbium magnetic moments are in the (a, c) plane and make an angle of 20° with the c-axis.Les composés TbGe0,2Si0,8 et ErSi s'ordonnent antiferromagnétiquement au-dessous des températures de Néel respectives TN = 55 K et 11,5 K. Entre TN et TIC (TIC = 43,5 K et 7,25 K pour TbGe 0,2Si0,8 et ErSi), les composés étudiés s'ordonnent selon une double sinusoïde définie par le vecteur de propagation k = [kx, 0, 1/2]. La composante irrationnelle kx varie avec la température et à TIC a lieu une transition magnétique vers une structure commensurable décrite par le vecteur de propagation k = [1/2, 0, 1/2]. A toute température inférieure à TN, les moments des ions terbium sont dans le plan (a, c) près de l'axe c, alors que les moments des ions d'erbium sont dirigés selon l'axe a

Multifractal Scaling of Probability Density Function : a Tool for Turbulent Data Analysis

The probabilistic reformulation of the multifractal model [1] is obtained directly from the structure functions written as integrals over cumulative distribution functions (c.d.f.) by the steepest descent method. The saddle point being a function of scale, we perform a change of variable to obtain expressions that are asymptotically valid in the inertial range. Starting directly from the inertial range behavior of the c.d.f., our algorithm yields values for the scaling exponents and codimension that are identical to those obtained from structure functions. Furthermore, a simple interpretation of multifractality in terms of global c.d.f. scaling is shown to collapse the inertial range c.d.f. into a single curve, directly related to the codimension. Our method determines a new length scale, larger than the integral scale, that gives a quantitative measure of the degree of multifractality of the data. Finally, some possible future applications are mentioned

NEUTRON DIFFRACTION STUDY OF SOME RARE EARTH IRON GARNETS RIG (R = Er, Dy, Yb, Tm)

Dans les ferrites grenats de Terres Rares les moments magnétiques des ions Fe3+ et Terres Rares sont généralement orientés selon [111]. Cependant l'étude de ErIG, DyIG et YbIG à basse température met en évidence une déviation des moments magnétiques de Terres Rares par rapport à la direction [111]. Nous avons déterminé les structures magnétiques ainsi que les angles de déviation de ces grenats à l'aide des valeurs du tenseur d'anisotropie g. Comme le diagramme de TmIG à 1,5 °K ne contient aucune raie de surstructure magnétique, nous déduisons que l'angle de déviation est inférieur à 15°.In rare-earth-iron garnets, the Iron and rare-earth moments are generally oriented along [111]. Deviation from [111] at low temperature have been observed for ErIG, DyIG and YbIG. Following the values of the magnetic g-tensors we have elaborated models for the magnetic structures of these garnets. The study of TmIG showed no evidence of magnetic superstructure lines at 1.5 °K. This result leads to the conclusion that a canting angle of rare earth moments in TmIG, if any, could be smaller than 15° [111]