The Digrams of Webster\u27s Unabridged Dictionary

For many years word buffs at these laboratories have made a game out of finding words which contain strange digrams (pairs of letters side-by-side). The problem, as originally posed by M.D. McIlroy, was to complete a table with 26 rows and 26 columns, labeled by the letters A, B, ... , Z. The space where row L crossed column L\u27 was to be filled by a word containing the digram LL\u27

The algebra of rewriting for presentations of inverse monoids

We describe a formalism, using groupoids, for the study of rewriting for presentations of inverse monoids, that is based on the Squier complex construction for monoid presentations. We introduce the class of pseudoregular groupoids, an example of which now arises as the fundamental groupoid of our version of the Squier complex. A further key ingredient is the factorisation of the presentation map from a free inverse monoid as the composition of an idempotent pure map and an idempotent separating map. The relation module of a presentation is then defined as the abelianised kernel of this idempotent separating map. We then use the properties of idempotent separating maps to derive a free presentation of the relation module. The construction of its kernel - the module of identities - uses further facts about pseudoregular groupoids.Comment: 22 page

Accuracy thresholds of topological color codes on the hexagonal and square-octagonal lattices

Accuracy thresholds of quantum error correcting codes, which exploit topological properties of systems, defined on two different arrangements of qubits are predicted. We study the topological color codes on the hexagonal lattice and on the square-octagonal lattice by the use of mapping into the spin glass systems. The analysis for the corresponding spin glass systems consists of the duality, and the gauge symmetry, which has succeeded in deriving locations of special points, which are deeply related with the accuracy thresholds of topological error correcting codes. We predict that the accuracy thresholds for the topological color codes would be $1-p_c = 0.1096-8$ for the hexagonal lattice and $1-p_c = 0.1092-3$ for the square-octagonal lattice, where $1-p$ denotes the error probability on each qubit. Hence both of them are expected to be slightly lower than the probability $1-p_c = 0.110028$ for the quantum Gilbert-Varshamov bound with a zero encoding rate.Comment: 6 pages, 4 figures, the previous title was "Threshold of topological color code". This is the published version in Phys. Rev.

Differential Expression Of Gap Junction mRNAs And Proteins In The Developing Murine Kidney And In Experimentally Induced Nephric Mesenchymes

The expression of three gap junction (GJ) proteins, alpha-1 (Cx43), beta-1 (Cx32), and beta-2 (Cx26), and their transcripts were examined during the ontogeny of the mouse and rat kidney. These proteins were expressed in two non-overlapping patterns. The alpha-1 GJ protein was first observed in mesenchymal cells in the 12-day mouse kidney. By day 14 and thereafter, the ai protein was detected in the transient S-shaped bodies, but not in the podocytes of the maturing glomeruli. After birth the antigen was retained in a small subset of secretory tubules.The beta-1 and beta-2 GJ proteins were similar in their developmental patterns. They were first detected in a small subset of secretory tubules in the subcortical zone of day 17 embryos. These tubules were identified by immunohistochemical markers to be proximal. At birth, practically all proximal tubules expressed the two antigens.This analysis of GJ proteins was consistent with the results of S1 nuclease protection assays showing that, while the alpha-1 mRNA appeared early during kidney development and declined around birth, the two beta mRNAs appeared later and became intensified during the last days of intrauterine development.In experimentally induced metanephric mesenchymes, a transient expression of the alpha-1 GJ protein was seen during the segregation of the tubular anlagen. beta-1 and beta-2 GJ proteins were not detected in such induced mesenchymes cultivated up to 7 days.These observations provide evidence for the cell-specific utilization of different GJ genes during different stages of kidney organogenesis. The alpha-1 gene is activated during the early segregation of the secretory tubule and might contribute to its compartmentalization, while the beta-1 and beta-2 gene products are not detected until advanced stages of development. The latter gene products might be correlated with the physiological activity of the proximal tubules in vivo, as they are not expressed in experimentally induced tubules detectable with markers for proximal tubules

A Bioclimatic Laboratory in Southern Ohio

Author Institution: Department of Botany and Plant Pathology, The Ohio State University, Columbus 1

Grid-enabled SIMAP utility: Motivation, integration technology and performance results

A biological system comprises large numbers of functionally diverse and frequently multifunctional sets of elements that interact selectively and nonlinearly to produce coherent behaviours. Such a system can be anything from an intracellular biological process (such as a biochemical reaction cycle, gene regulatory network or signal transduction pathway) to a cell, tissue, entire organism, or even an ecological web. Biochemical systems are responsible for processing environmental signals, inducing the appropriate cellular responses and sequence of internal events. However, such systems are not fully or even poorly understood. Systems biology is a scientific field that is concerned with the systematic study of biological and biochemical systems in terms of complex interactions rather than their individual molecular components. At the core of systems biology is computational modelling (also called mathematical modelling), which is the process of constructing and simulating an abstract model of a biological system for subsequent analysis. This methodology can be used to test hypotheses via insilico experiments, providing predictions that can be tested by in-vitro and in-vivo studies. For example, the ERbB1-4 receptor tyrosine kinases (RTKs) and the signalling pathways they activate, govern most core cellular processes such as cell division, motility and survival (Citri and Yarden, 2006) and are strongly linked to cancer when they malfunction due to mutations etc. An ODE (ordinary differential equation)-based mass action ErbB model has been constructed and analysed by Chen et al. (2009) in order to depict what roles of each protein plays and ascertain to how sets of proteins coordinate with each other to perform distinct physiological functions. The model comprises 499 species (molecules), 201 parameters and 828 reactions. These in silico experiments can often be computationally very expensive, e.g. when multiple biochemical factors are being considered or a variety of complex networks are being simulated simultaneously. Due to the size and complexity of the models and the requirement to perform comprehensive experiments it is often necessary to use high-performance computing (HPC) to keep the experimental time within tractable bounds. Based on this as part of an EC funded cancer research project, we have developed the SIMAP Utility that allows the SImulation modeling of the MAP kinase pathway (http://www.simap-project.org). In this paper we present experiences with Grid-enabling SIMAP using Condor

Level density of a Fermi gas and integer partitions: a Gumbel-like finite-size correction

We investigate the many-body level density of gas of non-interacting fermions. We determine its behavior as a function of the temperature and the number of particles. As the temperature increases, and beyond the usual Sommerfeld expansion that describes the degenerate gas behavior, corrections due to a finite number of particles lead to Gumbel-like contributions. We discuss connections with the partition problem in number theory, extreme value statistics as well as differences with respect to the Bose gas.Comment: 5 pages, 1 figure, one figure added, accepted for publication in Phys. Rev.