Light-Cone Quantization of Electrodynamics

Light-cone quantization of (3+1)-dimensional electrodynamics is discussed, using discretization as an infrared regulator and paying careful attention to the interplay between gauge choice and boundary conditions. In the zero longitudinal momentum sector of the theory a general gauge fixing is performed and the corresponding relations that determine the constrained modes of the gauge field are obtained. The constraints are solved perturbatively and the structure of the theory is studied to lowest nontrivial order. (Talk presented at ``Theory of Hadrons and Light-Front QCD,'' Polana Zgorzelisko, Poland, August 1994.)Comment: 6 pages, LaTeX, OSU-NT-94-0

Physical Coupling Schemes and QCD Exclusive Processes

I discuss application of the BLM method to obtain commensurate scale relations connecting QCD exclusive amplitudes to other observables, in particular the heavy quark potential.Comment: 7 pages, Latex, uses l-school.sty. Talk given at "New Nonperturbative Methods and Quantization on the Light Cone," Les Houches, France, 24 Feb.-7 March 1997. To appear in the proceeding

C∗C^*-algebras associated to C∗C^*-correspondences and applications to mirror quantum spheres

The structure of the $C^*$-algebras corresponding to even-dimensional mirror quantum spheres is investigated. It is shown that they are isomorphic to both Cuntz-Pimsner algebras of certain $C^*$-correspondences and $C^*$-algebras of certain labelled graphs. In order to achieve this, categories of labelled graphs and $C^*$-correspondences are studied. A functor from labelled graphs to $C^*$-correspondences is constructed, such that the corresponding associated $C^*$-algebras are isomorphic. Furthermore, it is shown that $C^*$-correspondences for the mirror quantum spheres arise via a general construction of restricted direct sum.Comment: 27 page

Declarative Specification

Deriving formal specifications from informal requirements is extremely difficult since one has to overcome the conceptual gap between an application domain and the domain of formal specification methods. To reduce this gap we introduce application-specific specification languages, i.e., graphical and textual notations that can be unambiguously mapped to formal specifications in a logic language. We describe a number of realised approaches based on this idea, and evaluate them with respect to their domain specificity vs. generalit

Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs

In previous work, the authors showed that the C*-algebra C*(\Lambda) of a row-finite higher-rank graph \Lambda with no sources is simple if and only if \Lambda is both cofinal and aperiodic. In this paper, we generalise this result to row-finite higher-rank graphs which are locally convex (but may contain sources). Our main tool is Farthing's "removing sources" construction which embeds a row-finite locally convex higher-rank graph in a row-finite higher-rank graph with no sources in such a way that the associated C*-algebras are Morita equivalent.Comment: 18 pages, 1 figure, figure drawn using Tikz/PGF. Version 2: the hypothesis "with no sources" has been removed from Theorem 3.4; it appeared there in error since the main point of the theorem is that it applies in the absence of this hypothesis (cf Theorem 3.1 of arXiv:math/0602120

De Novo Assembly of Nucleotide Sequences in a Compressed Feature Space

Sequencing technologies allow for an in-depth analysis of biological species but the size of the generated datasets introduce a number of analytical challenges. Recently, we demonstrated the application of numerical sequence representations and data transformations for the alignment of short reads to a reference genome. Here, we expand out approach for de novo assembly of short reads. Our results demonstrate that highly compressed data can encapsulate the signal suffi- ciently to accurately assemble reads to big contigs or complete genomes

On the origins of Mendelian disease genes in man: the impact of gene duplication

Over 3,000 human diseases are known to be linked to heritable genetic variation, mapping to over 1,700 unique genes. Dating of the evolutionary age of these disease-associated genes has suggested that they have a tendency to be ancient, specifically coming into existence with early metazoa. The approach taken by past studies, however, assumes that the age of a disease is the same as the age of its common ancestor, ignoring the fundamental contribution of duplication events in the evolution of new genes and function. Here, we date both the common ancestor and the duplication history of known human disease-associated genes. We find that the majority of disease genes (80%) are genes that have been duplicated in their evolutionary history. Periods for which there are more disease-associated genes, for example, at the origins of bony vertebrates, are explained by the emergence of more genes at that time, and the majority of these are duplicates inferred to have arisen by whole-genome duplication. These relationships are similar for different disease types and the disease-associated gene's cellular function. This indicates that the emergence of duplication-associated diseases has been ongoing and approximately constant (relative to the retention of duplicate genes) throughout the evolution of life. This continued until approximately 390 Ma from which time relatively fewer novel genes came into existence on the human lineage, let alone disease genes. For single-copy genes associated with disease, we find that the numbers of disease genes decreases with recency. For the majority of duplicates, the disease-associated mutation is associated with just one of the duplicate copies. A universal explanation for heritable disease is, thus, that it is merely a by-product of the evolutionary process; the evolution of new genes (de novo or by duplication) results in the potential for new diseases to emerge

Groupoid algebras as Cuntz-Pimsner algebras

We show that if $G$ is a second countable locally compact Hausdorff \'etale groupoid carrying a suitable cocycle $c:G\to\mathbb{Z}$, then the reduced $C^*$-algebra of $G$ can be realised naturally as the Cuntz-Pimsner algebra of a correspondence over the reduced $C^*$-algebra of the kernel $G_0$ of $c$. If the full and reduced $C^*$-algebras of $G_0$ coincide, we deduce that the full and reduced $C^*$-algebras of $G$ coincide. We obtain a six-term exact sequence describing the $K$-theory of $C^*_r(G)$ in terms of that of $C^*_r(G_0)$.Comment: 5 pages. V2: James Fletcher discovered an error Lemma 9. No other results are affected. In this version, statements (2) and (3), and the proof, of Lemma 9 have been corrected. Remark 10 has been added to give details of the error. An erratum will appear in Math Scand, referring to this version of the arXiv posting for detail