Stability of Tsallis antropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they can apparently be derived from three different generalized entropies: the Renyi entropy, the Tsallis entropy, and the normalized Tsallis entropy. Accordingly, mere fittings of observed data by the q-exponential distributions do not lead to identification of the correct physical entropy. Here, stabilities of these entropies, i.e., their behaviors under arbitrary small deformation of a distribution, are examined. It is shown that, among the three, the Tsallis entropy is stable and can provide an entropic basis for the q-exponential distributions, whereas the others are unstable and cannot represent any experimentally observable quantities.Comment: 20 pages, no figures, the disappeared "primes" on the distributions are added. Also, Eq. (65) is correcte

A nonextensive approach to the dynamics of financial observables

We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy $S_{q}=k\frac{1-\sum\limits_{i=1}^{W} p_{i} ^{q}}{1-q} (q\in \Re)$ ($S_{1} \equiv S_{BG}=-k\sum\limits_{i=1}^{W}p_{i} \ln p_{i}$). More precisely, we present stochastic dynamical mechanisms which mimic probability density functions empirically observed. These mechanisms provide possible interpretations for the emergence of the entropic indices $q$ in the time evolution of the corresponding observables. In addition to this, through multi-fractal analysis of return time series, we verify that the dual relation $q_{stat}+q_{sens}=2$ is numerically satisfied, $q_{stat}$ and $q_{sens}$ being associated to the probability density function and to the sensitivity to initial conditions respectively. This type of simple relation, whose understanding remains ellusive, has been empirically verified in various other systems.Comment: Invited paper to appear in special issue of Eur. Phys. J. B dedicated to econophysics, edited by T. Di Matteo and T. Aste. 7 page

Continuity and Stability of Partial Entropic Sums

Extensions of Fannes' inequality with partial sums of the Tsallis entropy are obtained for both the classical and quantum cases. The definition of kth partial sum under the prescribed order of terms is given. Basic properties of introduced entropic measures and some applications are discussed. The derived estimates provide a complete characterization of the continuity and stability properties in the refined scale. The results are also reformulated in terms of Uhlmann's partial fidelities.Comment: 9 pages, no figures. Some explanatory and technical improvements are made. The bibliography is extended. Detected errors and typos are correcte

Generalized entropy optimized by an arbitrary distribution

We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a great variety of distributions observed in nature, which can hardly be described by the conventional methods. As a simple example, we explicitly derive the entropy associated with the stretched exponential distribution. To include the distributions with the divergent moments (e.g., the Levy stable distributions), it is necessary to modify the definition of the expectation value.Comment: 10 pages, no figure

Validity of the second law in nonextensive quantum thermodynamics

The second law of thermodynamics in nonextensive statistical mechanics is discussed in the quantum regime. Making use of the convexity property of the generalized relative entropy associated with the Tsallis entropy indexed by q, Clausius' inequality is shown to hold in the range of q between zero and two. This restriction on the range of the entropic index, q, is purely quantum mechanical and there exists no upper bound of q for validity of the second law in classical theory.Comment: 12 pages, no figure

On observability of Renyi's entropy

Despite recent claims we argue that Renyi's entropy is an observable quantity. It is shown that, contrary to popular belief, the reported domain of instability for Renyi entropies has zero measure (Bhattacharyya measure). In addition, we show the instabilities can be easily emended by introducing a coarse graining into an actual measurement. We also clear up doubts regarding the observability of Renyi's entropy in (multi--)fractal systems and in systems with absolutely continuous PDF's.Comment: 18 pages, 1 EPS figure, REVTeX, minor changes, accepted to Phys. Rev.

Relations for certain symmetric norms and anti-norms before and after partial trace

Changes of some unitarily invariant norms and anti-norms under the operation of partial trace are examined. The norms considered form a two-parametric family, including both the Ky Fan and Schatten norms as particular cases. The obtained results concern operators acting on the tensor product of two finite-dimensional Hilbert spaces. For any such operator, we obtain upper bounds on norms of its partial trace in terms of the corresponding dimensionality and norms of this operator. Similar inequalities, but in the opposite direction, are obtained for certain anti-norms of positive matrices. Through the Stinespring representation, the results are put in the context of trace-preserving completely positive maps. We also derive inequalities between the unified entropies of a composite quantum system and one of its subsystems, where traced-out dimensionality is involved as well.Comment: 11 pages, no figures. A typo error in Eq. (5.15) is corrected. Minor improvements. J. Stat. Phys. (in press

OP0137 GENOME-WIDE WHOLE-BLOOD TRANSCRIPTOME PROFILING IN A LARGE EUROPEAN COHORT OF SYSTEMIC SCLEROSIS PATIENTS

Background:The analysis of annotated transcripts from genome-wide expression studies data is of paramount importance to understand the molecular phenomena underlying the occurrence of complex diseases, such as systemic sclerosis (SSc).Objectives:To perform whole-blood transcriptome and pathway analysis on whole-blood (WB) RNA collected in two cohorts of European SSc patients. Via a discovery and validation strategy we aimed at characterizing the molecular pathways that differentiate SSc from controls and that are reproducible in geographically diverse populations.Methods:WB samples from 252 controls and 162 SSc patients were collected in RNA stabilizers. Patients were divided into a discovery (n=79; Southern Europe) and validation cohort (n=83; Central-Western Europe). RNA sequencing was performed by an Illumina assay. Functional annotations of Reactome pathways were performed with the FAIME algorithm. In parallel, a immunophenotyping analysis on 28 circulating cell populations was assessed. We then tested: the presence of differentially expressed genes or pathways and the correlation between absolute cell counts and RNA transcripts/FAIME scores in regression models. Results significant in both populations were considered as replicated.Results:A total of 15224 genes and 1277 related functional pathways were available for analysis. Among these, 99 genes and 225 pathways were significant in both sets. The heatmap in figure shows the relative expression of replicated pathways and the distribution of cases and controls (red and green bars). Among the significant pathways we found a deregulation in: type-I IFN, TLR-cascade and signalling, function of the tumor suppressor p53 protein, platelet degranulation and activation. Correlation analysis showed that the count of several cell subtypes is jointly associated with RNA transcripts or FAIME scores with strong differences in relation to the geographical origin of samples; neutrophils emerged as the major determinant of gene expression in SSc-whole-blood samples.Conclusion:We discovered a set of differentially expressed genes and pathways that could be validated in two independent sets of SSc patients highlighting a number of deregulated molecular processes that have relevance for the pathogenesis of autoimmunity and SSc.Acknowledgments:This work was supported by EU/EFPIA/Innovative Medicines Initiative Joint Undertaking PRECISESADS grant No. 115565.Disclosure of Interests:Lorenzo Beretta Grant/research support from: Pfizer, Guillermo Barturen: None declared, Barbara Vigone: None declared, Chiara Bellocchi: None declared, Nicolas Hunzelmann: None declared, Ellen Delanghe: None declared, László Kovács: None declared, Ricard Cervera: None declared, Maria Gerosa: None declared, Rafaela Ortega Castro: None declared, Isabel Almeida: None declared, Divi Cornec: None declared, Carlo Chizzolini Consultant of: Boehringer Ingelheim, Roche, Jacques-Olivier Pers: None declared, Zuzanna Makowska Employee of: Bayer AG, Anne buttgereit Employee of: Bayer AG, Ralf Lesche Employee of: Bayer, Martin Kerick: None declared, Marta Alarcon-Riquelme: None declared, Javier Martin Ibanez: None declare

Essential oil from leaves of Lantana camara: a potential source of medicine against leishmaniasis

Leishmaniasis is an infection of viscera or tegument caused by protozoa Leishmania sp. The extensive period required for the treatment, which involves the use of toxic medicines, leads patients to drop treatment increasing the development of resistant forms of Leishmania sp. Lantana camara L., Verbenaceae, is a tropical plant native from America. Folk uses have been described for treatment of tumors, tetanus, rheumatism and malaria. This study evaluates the leishmanicidal activity of the essential oil of leaves from L. camara on promastigote forms of Leishmania chagasi and L. amazonensis and its toxic effects on Artemia salina (brine shrimp test), macrophage cultures and BALB/c mice. The chemical composition was evaluated using the gas chromatography coupled with mass spectrometer (GC-MS). Thirty substances, mostly mono and sesquiterpenes were identified. The most representative constituents were: germacrene D (24.90%), farnesene derivatives (22%) and (E)-cariophylene (14.31%). Bioassays revealed a significant leishmanicidal activity of essential oil against L. amazonensis (IC50 0.25 µg/ mL) and a potential toxic effect on Brine shrimp (LC50 10 µg/mL) and macrophage assays (CC50 4 µg/mL), while there was no toxic manifestation on mice. The data show the relevant potential of L. camara as a source of medicine for leishmaniasis treatment

A Transplantable Phosphorylation Probe for Direct Assessment of G Protein-Coupled Receptor Activation

The newly developed multireceptor somatostatin analogs pasireotide (SOM230), octreotide and somatoprim (DG3173) have primarily been characterized according to their binding profiles. However, their ability to activate individual somatostatin receptor subtypes (sst) has not been directly assessed so far. Here, we transplanted the carboxyl-terminal phosphorylation motif of the sst2 receptor to other somatostatin receptors and assessed receptor activation using a set of three phosphosite-specific antibodies. Our comparative analysis revealed unexpected efficacy profiles for pasireotide, octreotide and somatoprim. Pasireotide was able to activate sst3 and sst5 receptors but was only a partial agonist at the sst2 receptor. Octreotide exhibited potent agonistic properties at the sst2 receptor but produced very little sst5 receptor activation. Like octreotide, somatoprim was a full agonist at the sst2 receptor. Unlike octreotide, somatoprim was also a potent agonist at the sst5 receptor. Together, we propose the application of a phosphorylation probe for direct assessment of G protein-coupled receptor activation and demonstrate its utility in the pharmacological characterization of novel somatostatin analogs