A combinatorial construction proves an identity for the product of the Pfaffian of a skew-symmetric matrix by the Pfaffian of one of its submatrices. Several applications of this identity are followed by a brief history of Pfaffians. 0. Definitions. Let X be a possibly infinite index set. We consider quantities f [xy] defined on ordered pairs of elements of X , satisfying the law of skew symmet...

An ideal system of n qubits has 2 dimensions. This exponential grants power, but also hinders characterizing the system’s state and dynamics. We study a new problem: the qubits in a physical system might not be independent. They can “overlap,” in the sense that an operation on one qubit slightly affects the others. We show that allowing for slight overlaps, n qubits can fit in just polynomially...

Many clustering algorithms are in favour of node-based methods, but a link between nodes has one single feature, so link-based is sometimes easier than methods. Being dependent on the characteristics links, detection algorithm for non-overlapping community put forward this paper. The method proposed also distinguishes differences with high degree accuracy and detects communities minimal number ...

Recombination activating gene-2 (RAG-2) and NWC are strongly evolutionarily conserved overlapping genes which are convergently transcribed. In non-lymphoid cells the NWC promoter is active whereas in lymphocytes it is inactive due to the DNA methylation. Analysing the mechanism responsible for lymphocyte-specific methylation and inactivation of NWC promoter we found that Ikaros, a lymphocyte-sp...

Large-scale public data mining will become more common as public release of microarray data sets becomes a corequisite for publication. Therefore, there is an urgent need to clarify whether data from different microarray platforms are comparable. To assess the compatibility of microarray data, results were compared from the two main types of high-throughput microarray expression technologies, n...

Presence of overlapping genes (OGs) is a common phenomenon in bacterial genomes. Most frequently, overlapping genes share coding regions with as few as one nucleotide to as many as thousands of nucleotides. Overlapping genes are often co-regulated, transcriptionally and translationally. Overlapping genes are also subject to the whims of evolution, as the gene overlap is known to be disrupted in...

The problem of overlapping markup has often been addressed using variant syntaxes, milestones, standoff markup and other means. This proposal combines the use of co-indexed milestones with a table structure in a database, plus CONCUR namespaces and "common location" (markup tokens that have no intervening PCDATA) information to illustrate one way to "parse" XML with more information than is ava...

BACKGROUND Our objective was to develop a consistent molecular definition of psoriasis. There have been several published microarray studies of psoriasis, and we compared disease-related genes identified across these different studies of psoriasis with our own in order to establish a consensus. METHODOLOGY/PRINCIPAL FINDINGS We present a psoriasis transcriptome from a group of 15 patients enr...

Prokaryotic unidirectional overlapping genes can be originated by disrupting and replacing of the start or stop codon of one protein-coding gene with another start or stop codon within the adjacent gene. However, the probability of disruption and replacement of a start or stop codon may differ significantly depending on the number and redundancy of the start and stop codons sets. Here, we perfo...