Encryption methods using formal power series rings

Recently there has been a great deal of work on noncommutative algebraic cryptography. This involves the use of noncommutative algebraic objects as the platforms for encryption systems. Most of this work, such as the Anshel-Anshel-Goldfeld scheme, the Ko-Lee scheme and the Baumslag-Fine-Xu Modular group scheme use nonabelian groups as the basic algebraic object. Some of these encryption methods have been successful and some have been broken. It has been suggested that at this point further pure group theoretic research, with an eye towards cryptographic applications, is necessary.In the present study we attempt to extend the class of noncommutative algebraic objects to be used in cryptography. In particular we explore several different methods to use a formal power series ring R && x1; :::; xn && in noncommuting variables x1; :::; xn as a base to develop cryptosystems. Although R can be any ring we have in mind formal power series rings over the rationals Q. We use in particular a result of Magnus that a finitely generated free group F has a faithful representation in a quotient of the formal power series ring in noncommuting variables.

Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings

Three exceptional modular invariants of SU(4) exist at levels 4, 6 and 8. They can be obtained from appropriate conformal embeddings and the corresponding graphs have self-fusion. From these embeddings, or from their associated modular invariants, we determine the algebras of quantum symmetries, obtain their generators,and, as a by-product, recover the known graphs E4, E6 and E8 describing exceptional quantum subgroups of type SU(4). We also obtain characteristic numbers (quantum cardinalities, dimensions) for each of them and for their associated quantum groupoïds.

Neuroscience, quantum indeterminism and the Cartesian soul.

Quantum indeterminism is frequently invoked as a solution to the problem of how a disembodied soul might interact with the brain (as Descartes proposed), and is sometimes invoked in theories of libertarian free will even when they do not involve dualistic assumptions. Taking as example the Eccles-Beck model of interaction between self (or soul) and brain at the level of synaptic exocytosis, I here evaluate the plausibility of these approaches. I conclude that Heisenbergian uncertainty is too small to affect synaptic function, and that amplification by chaos or by other means does not provide a solution to this problem. Furthermore, even if Heisenbergian effects did modify brain functioning, the changes would be swamped by those due to thermal noise. Cells and neural circuits have powerful noise-resistance mechanisms, that are adequate protection against thermal noise and must therefore be more than sufficient to buffer against Heisenbergian effects. Other forms of quantum indeterminism must be considered, because these can be much greater than Heisenbergian uncertainty, but these have not so far been shown to play a role in the brain.

Fixed rings and strictures in Eosinophilic Esophagitis develop due to continuing inflammation over time

Background and Aims: Two distinct e ndoscopic phenotypes of E osinophilic Esophagitis (EoE) h ave been identified: t he inflammatory (IP) a nd the stenosing (SP) p henotype. I t is not known whether these EoE-associated phenotypes are reflective of different phases during disease course. We aimed to assess the phenotype a t initial EoE p resentation and d iagnosis and to evaluate if SP increases over time. Methods: R etrospective a nalysis of t he Swiss EoE Database (SEED) extended b y a review of p atients charts, endoscopy and pathology records. Results: F orty-four E oE p atients were a nalyzed (33 males, mean age at index visit 41 ± 14 years, all Caucasians). Median follow-up t ime was 3.1 years (IQR 1-4, r ange 1 -18 years). Median diagnostic delay w as 5 y ears (IQR 2-16, range 0-34 years). A t first diagnosis, 3 2% ( 14/44) o f EoE patients h ad already presented w ith a stenosis. T he mean d iameter o f the stenoses w as 1 0 ± 2 mm, and the mean length was 2 .8 ± 2 .9 cm. Peak e osinophil count d id n ot c hange over t ime (48 ± 39 eos/HPF at index visit vs. 59 ± 41 eos/HPF at end of follow-up, n=44). The risk of the presence of a stenosis at index visit was 0% f or a d isease duration of 0 -4 y ears, 37% f or a d isease duration between 5-10 years and 67% f or a d isease duration >10 years (p = 0.0035, trend test). Conclusions: T he frequency of e sophageal stenoses i s proportional to the disease duration, whereas the inflammatory activity does n ot s ignificantly c hange over t ime. O ur f indings underscore the necessity to reduce diagnostic delay in EoE and to control the underlying inflammatory processes to prevent esophageal remodeling.

The metaphysics of quantum gravity : a causal approach

The dissertation investigates some relevant metaphysical issues arising in the context of spacetime theories. In particular, the inquiry focuses on general relativity and canonical quantum gravity. A formal definition of spacetime theory is proposed and, against this framework, an analysis of the notions of general covariance, symmetry and background independence is performed. It is argued that many conceptual issues in general relativity and canonical quantum gravity derive from putting excessive emphasis on general covariance as an ontological prin-ciple. An original metaphysical position grounded in scientific essential- ism and causal realism (weak essentialism) is developed and defended. It is argued that, in the context of general relativity, weak essentialism supports spacetime substantivalism. It is also shown that weak essentialism escapes arguments from metaphysical underdetermination by positing a particular kind of causation, dubbed geometric. The proposed interpretive framework is then applied to Bohmian mechanics, pointing out that weak essentialism nicely fits into this theory. In the end, a possible Bohmian implementation of loop quantum gravity is considered, and such a Bohmian approach is interpreted in a geometric causal fashion. Under this interpretation, Bohmian loop quantum gravity straightforwardly commits us to an ontology of elementary extensions of space whose evolution is described by a non-local law. The causal mechanism underlying this evolution clarifies many conceptual issues related to the emergence of classical spacetime from the quantum regime. Although there is as yet no fully worked out physical theory of quantum gravity, it is argued that the proposed approach sets up a standard that proposals for a serious ontology in this field should meet.

The nature of the Cr-C bond: direct estimation of aromaticity in Fischer carbenes

Report for the scientific sojourn at the the Philipps-Universität Marburg, Germany, from september to december 2007. For the first, we employed the Energy-Decomposition Analysis (EDA) to investigate aromaticity on Fischer carbenes as it is related through all the reaction mechanisms studied in my PhD thesis. This powerful tool, compared with other well-known aromaticity indices in the literature like NICS, is useful not only for quantitative results but also to measure the degree of conjugation or hyperconjugation in molecules. Our results showed for the annelated benzenoid systems studied here, that electron density is more concentrated on the outer rings than in the central one. The strain-induced bond localization plays a major role as a driven force to keep the more substituted ring as the less aromatic. The discussion presented in this work was contrasted at different levels of theory to calibrate the method and ensure the consistency of our results. We think these conclusions can also be extended to arene chemistry for explaining aromaticity and regioselectivity reactions found in those systems.In the second work, we have employed the Turbomole program package and density-functionals of the best performance in the state of art, to explore reaction mechanisms in the noble gas chemistry. Particularly, we were interested in compounds of the form H--Ng--Ng--F (where Ng (Noble Gas) = Ar, Kr and Xe) and we investigated the relative stability of these species. Our quantum chemical calculations predict that the dixenon compound HXeXeF has an activation barrier for decomposition of 11 kcal/mol which should be large enough to identify the molecule in a low-temperature matrix. The other noble gases present lower activation barriers and therefore are more labile and difficult to be observable systems experimentally.

Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation

This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker–Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial–boundary value problem. This simplification requires the performance of the polar (modulus–argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.

RadA protein from Archaeoglobus fulgidus forms rings, nucleoprotein filaments and catalyses homologous recombination.

Proteins that catalyse homologous recombination have been identified in all living organisms and are essential for the repair of damaged DNA as well as for the generation of genetic diversity. In bacteria homologous recombination is performed by the RecA protein, whereas in the eukarya a related protein called Rad51 is required to catalyse recombination and repair. More recently, archaeal homologues of RecA/Rad51 (RadA) have been identified and isolated. In this work we have cloned and purified the RadA protein from the hyperthermophilic, sulphate-reducing archaeon Archaeoglobus fulgidus and characterised its in vitro activities. We show that (i) RadA protein forms ring structures in solution and binds single- but not double-stranded DNA to form nucleoprotein filaments, (ii) RadA is a single-stranded DNA-dependent ATPase at elevated temperatures, and (iii) RadA catalyses efficient D-loop formation and strand exchange at temperatures of 60-70 degrees C. Finally, we have used electron microscopy to visualise RadA-mediated joint molecules, the intermediates of homologous recombination. Intriguingly, RadA shares properties of both the bacterial RecA and eukaryotic Rad51 recombinases.

Use of quantum dots in aqueous solution to detect blood fingermarks on non-porous surfaces.

A new and original reagent based on the use of highly fluorescent cadmium telluride (CdTe) quantum dots (QDs) in aqueous solution is proposed to detect weak fingermarks in blood on non-porous surfaces. To assess the efficiency of this approach, comparisons were performed with one of the most efficient blood reagents on non-porous surfaces, Acid Yellow 7 (AY7). To this end, four non-porous surfaces were studied, i.e. glass, transparent polypropylene, black polyethylene, and aluminium foil. To evaluate the sensitivity of both reagents, sets of depleted fingermarks were prepared, using the same finger, initially soaked with blood, which was then successively applied on the same surface without recharging it with blood or latent secretions. The successive marks were then cut in halves and the halves treated separately with each reagent. The results showed that QDs were equally efficient to AY7 on glass, polyethylene and polypropylene surfaces, and were superior to AY7 on aluminium. The use of QDs in new, sensitive and highly efficient latent and blood mark detection techniques appears highly promising. Health and safety issues related to the use of cadmium are also discussed. It is suggested that applying QDs in aqueous solution (and not as a dry dusting powder) considerably lowers the toxicity risks.

Fuzzy set Theory and Quantum Chemistry

Es discuteixen breument algunes consideracions sobre l'aplicació de la Teoria delsConjunts difusos a la Química quàntica. Es demostra aqui que molts conceptes químics associats a la teoria són adequats per ésser connectats amb l'estructura dels Conjunts difusos. També s'explica com algunes descripcions teoriques dels observables quàntics espotencien tractant-les amb les eines associades als esmentats Conjunts difusos. La funciódensitat es pren com a exemple de l'ús de distribucions de possibilitat al mateix temps queles distribucions de probabilitat quàntiques

Quantum similarity topological indices definition, analysis and comparison with classical molecular topological indices

Es mostra que, gracies a una extensió en la definició dels Índexs Moleculars Topològics, s'arriba a la formulació d'índexs relacionats amb la teoria de la Semblança Molecular Quàntica. Es posa de manifest la connexió entre les dues metodologies: es revela que un marc de treball teòric sòlidament fonamentat sobre la teoria de la Mecànica Quàntica es pot connectar amb una de les tècniques més antigues relacionades amb els estudis de QSPR. Es mostren els resultats per a dos casos d'exemple d'aplicació d'ambdues metodologies