Relativistic Coulomb Green's function in dd-dimensions

Using the operator method, the Green's functions of the Dirac and Klein-Gordon equations in the Coulomb potential $-Z\alpha/r$ are derived for the arbitrary space dimensionality $d$. Nonrelativistic and quasiclassical asymptotics of these Green's functions are considered in detail.Comment: 9 page

Temporal Aspects of Smart Contracts for Financial Derivatives

Implementing smart contracts to automate the performance of high-value over-the-counter (OTC) financial derivatives is a formidable challenge. Due to the regulatory framework and the scale of financial risk if a contract were to go wrong, the performance of these contracts must be enforceable in law and there is an absolute requirement that the smart contract will be faithful to the intentions of the parties as expressed in the original legal documentation. Formal methods provide an attractive route for validation and assurance, and here we present early results from an investigation of the semantics of industry-standard legal documentation for OTC derivatives. We explain the need for a formal representation that combines temporal, deontic and operational aspects, and focus on the requirements for the temporal aspects as derived from the legal text. The relevance of this work extends beyond OTC derivatives and is applicable to understanding the temporal semantics of a wide range of legal documentation

Nonlinear dynamic intertwining of rods with self-contact

Twisted marine cables on the sea floor can form highly contorted three-dimensional loops that resemble tangles. Such tangles or hockles are topologically equivalent to the plectomenes that form in supercoiled DNA molecules. The dynamic evolution of these intertwined loops is studied herein using a computational rod model that explicitly accounts for dynamic self-contact. Numerical solutions are presented for an illustrative example of a long rod subjected to increasing twist at one end. The solutions reveal the dynamic evolution of the rod from an initially straight state, through a buckled state in the approximate form of a helix, through the dynamic collapse of this helix into a near-planar loop with one site of self-contact, and the subsequent intertwining of this loop with multiple sites of self-contact. This evolution is controlled by the dynamic conversion of torsional strain energy to bending strain energy or, alternatively by the dynamic conversion of twist (Tw) to writhe (Wr). KEY WORDS Rod Dynamics, Self-contact, Intertwining, DNA Supercoiling, Cable HocklingComment: 35 pages, 9 figures, submitted to Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science

Similarity-Based Models of Word Cooccurrence Probabilities

In many applications of natural language processing (NLP) it is necessary to determine the likelihood of a given word combination. For example, a speech recognizer may need to determine which of the two word combinations ``eat a peach'' and ``eat a beach'' is more likely. Statistical NLP methods determine the likelihood of a word combination from its frequency in a training corpus. However, the nature of language is such that many word combinations are infrequent and do not occur in any given corpus. In this work we propose a method for estimating the probability of such previously unseen word combinations using available information on ``most similar'' words. We describe probabilistic word association models based on distributional word similarity, and apply them to two tasks, language modeling and pseudo-word disambiguation. In the language modeling task, a similarity-based model is used to improve probability estimates for unseen bigrams in a back-off language model. The similarity-based method yields a 20% perplexity improvement in the prediction of unseen bigrams and statistically significant reductions in speech-recognition error. We also compare four similarity-based estimation methods against back-off and maximum-likelihood estimation methods on a pseudo-word sense disambiguation task in which we controlled for both unigram and bigram frequency to avoid giving too much weight to easy-to-disambiguate high-frequency configurations. The similarity-based methods perform up to 40% better on this particular task.Comment: 26 pages, 5 figure

Talon cusp affecting primary dentition in two siblings: a case report

The term talon cusp refers to a rare developmental dental anomaly characterized by a cusp-like structure projecting from the cingulum area or cement-enamel junction. This condition can occur in the maxillary and mandibular arches of the primary and permanent dentitions. The purpose of this paper is to report on the presence of talon cusps in the primary dentition of two southern Chinese siblings. The 4 years and 2 months old girl had a talon cusp on her maxillary right primary central incisor, while her 2 years and 9 months old brother had bilateral talon cusps on the maxillary primary central incisors. The presence of this rare dental anomaly in two siblings has scarcely been reported in the literature and this may provide further evidence of a hereditary etiology.Article Link: http://www.rjme.ro/RJME/resources/files/540113211213.pd

Are the Kepler Near-Resonance Planet Pairs due to Tidal Dissipation?

The multiple-planet systems discovered by the Kepler mission show an excess of planet pairs with period ratios just wide of exact commensurability for first-order resonances like 2:1 and 3:2. In principle, these planet pairs could have both resonance angles associated with the resonance librating if the orbital eccentricities are sufficiently small, because the width of first-order resonances diverges in the limit of vanishingly small eccentricity. We consider a widely-held scenario in which pairs of planets were captured into first-order resonances by migration due to planet-disk interactions, and subsequently became detached from the resonances, due to tidal dissipation in the planets. In the context of this scenario, we find a constraint on the ratio of the planet's tidal dissipation function and Love number that implies that some of the Kepler planets are likely solid. However, tides are not strong enough to move many of the planet pairs to the observed separations, suggesting that additional dissipative processes are at play.Comment: 20 pages, including 7 figures; accepted for publication in Ap