Magnetic Fourier Integral Operators

In some previous papers we have defined and studied a 'magnetic' pseudodifferential calculus as a gauge covariant generalization of the Weyl calculus when a magnetic field is present. In this paper we extend the standard Fourier Integral Operators Theory to the case with a magnetic field, proving composition theorems, continuity theorems in 'magnetic' Sobolev spaces and Egorov type theorems. The main application is the representation of the evolution group generated by a 1-st order 'magnetic' pseudodifferential operator (in particular the relativistic Schr\"{o}dinger operator with magnetic field) as such a 'magnetic' Fourier Integral Operator. As a consequence of this representation we obtain some estimations for the distribution kernel of this evolution group and a result on the propagation of singularities

PDFS: Practical Data Feed Service for Smart Contracts

Smart contracts are a new paradigm that emerged with the rise of the blockchain technology. They allow untrusting parties to arrange agreements. These agreements are encoded as a programming language code and deployed on a blockchain platform, where all participants execute them and maintain their state. Smart contracts are promising since they are automated and decentralized, thus limiting the involvement of third trusted parties, and can contain monetary transfers. Due to these features, many people believe that smart contracts will revolutionize the way we think of distributed applications, information sharing, financial services, and infrastructures. To release the potential of smart contracts, it is necessary to connect the contracts with the outside world, such that they can understand and use information from other infrastructures. For instance, smart contracts would greatly benefit when they have access to web content. However, there are many challenges associated with realizing such a system, and despite the existence of many proposals, no solution is secure, provides easily-parsable data, introduces small overheads, and is easy to deploy. In this paper we propose PDFS, a practical system for data feeds that combines the advantages of the previous schemes and introduces new functionalities. PDFS extends content providers by including new features for data transparency and consistency validations. This combination provides multiple benefits like content which is easy to parse and efficient authenticity verification without breaking natural trust chains. PDFS keeps content providers auditable, mitigates their malicious activities (like data modification or censorship), and allows them to create a new business model. We show how PDFS is integrated with existing web services, report on a PDFS implementation and present results from conducted case studies and experiments.Comment: Blockchain; Smart Contracts; Data Authentication; Ethereu

New selection rules for resonant Raman scattering on quantum wires

The bosonisation technique is used to calculate the resonant Raman spectrum of a quantum wire with two electronic sub-bands occupied. Close to resonance, the cross section at frequencies in the region of the inter sub-band transitions shows distinct peaks in parallel polarisation of the incident and scattered light that are signature of collective higher order spin density excitations. This is in striking contrast to the conventional selection rule for non-resonant Raman scattering according to which spin modes can appear only in perpendicular polarisation. We predict a new selection rule for the excitations observed near resonance, namely that, apart from charge density excitations, only spin modes with positive group velocities can appear as peaks in the spectra in parallel configuration close to resonance. The results are consistent with all of the presently available experimental data.Comment: 7 pages, 2 figure

Ab initio theory of helix-coil phase transition

In this paper we suggest a theoretical method based on the statistical mechanics for treating the alpha-helix-random coil transition in alanine polypeptides. We consider this process as a first-order phase transition and develop a theory which is free of model parameters and is based solely on fundamental physical principles. It describes essential thermodynamical properties of the system such as heat capacity, the phase transition temperature and others from the analysis of the polypeptide potential energy surface calculated as a function of two dihedral angles, responsible for the polypeptide twisting. The suggested theory is general and with some modification can be applied for the description of phase transitions in other complex molecular systems (e.g. proteins, DNA, nanotubes, atomic clusters, fullerenes).Comment: 24 pages, 3 figure

Delineation of the Native Basin in Continuum Models of Proteins

We propose two approaches for determining the native basins in off-lattice models of proteins. The first of them is based on exploring the saddle points on selected trajectories emerging from the native state. In the second approach, the basin size can be determined by monitoring random distortions in the shape of the protein around the native state. Both techniques yield the similar results. As a byproduct, a simple method to determine the folding temperature is obtained.Comment: REVTeX, 6 pages, 5 EPS figure

A review of implant provision for hypodontia patients within a Scottish referral centre

Background: Implant treatment to replace congenitally missing teeth often involves multidisciplinary input in a secondary care environment. High quality patient care requires an in-depth knowledge of treatment requirements. Aim: This service review aimed to determine treatment needs, efficiency of service and outcomes achieved in hypodontia patients. It also aimed to determine any specific difficulties encountered in service provision, and suggest methods to overcome these. Methods: Hypodontia patients in the Unit of Periodontics of the Scottish referral centre under consideration, who had implant placement and fixed restoration, or review completed over a 31 month period, were included. A standardised data collection form was developed and completed with reference to the patient's clinical record. Information was collected with regard to: the indication for implant treatment and its extent; the need for, complexity and duration of orthodontic treatment; the need for bone grafting and the techniques employed and indicators of implant success. Conclusion: Implant survival and success rates were high for those patients reviewed. Incidence of biological complications compared very favourably with the literature

Iron and Nickel Line Diagnostics for the Galactic Center Diffuse Emission

We have observed the diffuse X-ray emission from the Galactic center (GC) using the X-ray Imaging Spectrometer (XIS) on Suzaku. The high-energy resolution and the low-background orbit provide excellent spectra of the GC diffuse X-rays (GCDX). The XIS found many emission lines in the GCDX near the energy of K-shell transitions of iron and nickel. The most pronounced features are FeI K alpha at 6.4 keV and K-shell absorption edge at 7.1 keV, which are from neutral and/or low ionization states of iron, and the K-shell lines at 6.7 keV and 6.9 keV from He-like (FeXXV K alpha) and hydrogenic (FeXXVI Ly alpha) ions of iron. In addition, K alpha lines from neutral or low ionization nickel (NiI K alpha) and He-like nickel (NiXXVII K alpha), and FeI K beta, FeXXV K beta, FeXXVI Ly beta, FeXXV K gamma and FeXXVI Ly gamma are detected for the first time. The line center energies and widths of FeXXV K alpha and FeXXVI Ly alpha favor a collisional excitation (CE) plasma for the origin of the GCDX. The electron temperature determined from the line flux ratio of FeXXV K alpha / FeXXV K beta is similar to the ionization temperature determined from that of FeXXV K alpha /FeXXVI Ly alpha. Thus it would appear that the GCDX plasma is close to ionization equilibrium. The 6.7 keV flux and temperature distribution to the galactic longitude is smooth and monotonic,in contrast to the integrated point source flux distribution. These facts support the hypothesis that the GCDX is truly diffuse emission rather than the integration of the outputs of a large number of unresolved point sources. In addition, our results demonstrate that the chemical composition of Fe in the interstellar gas near the GC is constrained to be about 3.5 times solar.Comment: 11 pages, 19 figures. Accepted for publication in PASJ Suzaku Special Issue (vol. 59 sp. 1

Geometric Path Integrals. A Language for Multiscale Biology and Systems Robustness

In this paper we suggest that, under suitable conditions, supervised learning can provide the basis to formulate at the microscopic level quantitative questions on the phenotype structure of multicellular organisms. The problem of explaining the robustness of the phenotype structure is rephrased as a real geometrical problem on a fixed domain. We further suggest a generalization of path integrals that reduces the problem of deciding whether a given molecular network can generate specific phenotypes to a numerical property of a robustness function with complex output, for which we give heuristic justification. Finally, we use our formalism to interpret a pointedly quantitative developmental biology problem on the allowed number of pairs of legs in centipedes