Deformation Quantization: Quantum Mechanics Lives and Works in Phase-Space

Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It is also of importance in signal processing. Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal, has only emerged in the last quarter-century: It furnishes a third, alternative, formulation of Quantum Mechanics, independent of the conventional Hilbert Space, or Path Integral formulations. In this logically complete and self-standing formulation, one need not choose sides--coordinate or momentum space. It works in full phase-space, accommodating the uncertainty principle. This is an introductory overview of the formulation with simple illustrations.Comment: LaTeX, 22 pages, 2 figure

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

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

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

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

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

Contour identical implants to bridge mandibular continuity defects - individually generated by LaserCUSING® - A feasibility study in animal cadavers

Background Ablative tumor surgery often results in continuity defects of the mandible. When an immediate reconstruction using autologous bone grafts is not possible the bridging of the defects with a variety of bridging plates might be achieved. However, those bridging plates have the risk of plate fractures or exposure. Customized titanium implants manufactured using CAD/CAM and the LaserCUSING® technique might be an alternative. Methods In the present study, computed tomographies (CT) of porcine cadaver mandibles were generated and transferred into DICOM data. Following, different continuity defects were surgically created in the mandibles. Based on the DICOM data customized titanium implants were manufactured using CAD/CAM procedures and the LaserCUSING® technique. The implants were fixed to the remaining stumps with screws. Subsequently, the accuracy of the reconstructed mandibles was tested using plaster casts. Results The workflow from the CT to the application of the customized implants was proved to be practicable. Furthermore, a stable fixation of the customized implant to the remaining stumps could be achieved. The control of the accuracy showed no frictions or obstacles. Conclusion The customized titanium implant seems to be a promising approach to bridge continuity defects of the mandible whenever an immediate reconstruction with autologous bone is not possible