The Geometry of Triadic Distances

Consider N entities to be classified (e.g., geographical areas), a matrix of dissimilarities between pairs of entities, a graph H with vertices associated with these entities such that the edges join the vertices corresponding to contiguous entities. The split of a cluster is the smallest dissimilarity between an entity of this cluster and an entity outside of it. The single-linkage algorithm (ignoring contiguity between entities) provides partitions into M clusters for which the smallest split of the clusters, called split of the partition, is maximum. We study here the partitioning of the set of entities into M connected clusters for all M between N - 1 and 2 (i.e., clusters such that the subgraphs of H induced by their corresponding sets of entities are connected) with maximum split subject to that condition. We first provide an exact algorithm with a (N²) complexity for the particular case in which H is a tree. This algorithm suggests in turn a first heuristic algorithm for the general problem. Several variants of this heuristic are Also explored. We then present an exact algorithm for the general case based on iterative determination of cocycles of subtrees and on the solution of auxiliary set covering problems. As solution of the latter problems is time-consuming for large instances, we provide another heuristic in which the auxiliary set covering problems are solved approximately. Computational results obtained with the exact and heuristic algorithms are presented on test problems from the literature.     

A splicing mutation affecting expression of ataxia-telangiectasia and Rad3-related protein (ATR) results in Seckel syndrome

Seckel syndrome (OMIM 210600) is an autosomal recessive disorder characterized by intrauterine growth retardation, dwarfism, microcephaly and mental retardation. Clinically, Seckel syndrome shares features in common with disorders involving impaired DNA-damage responses, such as Nijmegen breakage syndrome (OMIM 251260) and LIG4 syndrome (OMIM 606593). We previously mapped a locus associated with Seckel syndrome to chromosome 3q22.1-q24 in two consanguineous Pakistani families. Further marker analysis in the families, including a recently born unaffected child with a recombination in the critical region, narrowed the region to an interval of 5 Mbp between markers D3S1316 and D3S1557 (145.29 Mbp and 150.37 Mbp). The gene encoding ataxia-telangiectasia and Rad3-related protein (ATR) maps to this region. A fibroblast cell line derived from an affected individual displays a defective DNA damage response caused by impaired ATR function. We identified a synonymous mutation in affected individuals that alters ATR splicing. The mutation confers a phenotype including marked microcephaly (head circumference 12 s.d. below the mean) and dwarfism (5 s.d. below the mean). Our analysis shows that UV-induced ATR activation can occur in non-replicating cells following processing by nucleotide excision repair.     

Heterozygous mutations of the kinesin KIF21A in congenital fibrosis of the extraocular muscles type 1 (CFEOM1)

Congenital fibrosis of the extraocular muscles type 1 (CFEOM1; OMIM #135700) is an autosomal dominant strabismus disorder associated with defects of the oculomotor nerve. We show that individuals with CFEOM1 harbor heterozygous missense mutations in a kinesin motor protein encoded by KIF21A. We identified six different mutations in 44 of 45 probands. The primary mutational hotspots are in the stalk domain, highlighting an important new role for KIF21A and its stalk in the formation of the oculomotor axis.     

An early lunar core dynamo driven by thermochemical mantle convection

Although the Moon currently has no internally generated magnetic field, palaeomagnetic data, combined with radiometric ages of Apollo samples, provide evidence for such a magnetic field from approximately 3.9 to 3.6 billion years (Gyr) ago, possibly owing to an ancient lunar dynamo. But the presence of a lunar dynamo during this time period is difficult to explain, because thermal evolution models for the Moon yield insufficient core heat flux to power a dynamo after approximately 4.2 Gyr ago. Here we show that a transient increase in core heat flux after an overturn of an initially stratified lunar mantle might explain the existence and timing of an early lunar dynamo. Using a three-dimensional spherical convection model, we show that a dense layer, enriched in radioactive elements (a 'thermal blanket'), at the base of the lunar mantle can initially prevent core cooling, thereby inhibiting core convection and magnetic field generation. Subsequent radioactive heating progressively increases the buoyancy of the thermal blanket, ultimately causing it to rise back into the mantle. The removal of the thermal blanket, proposed to explain the eruption of thorium- and titanium-rich lunar mare basalts, plausibly results in a core heat flux sufficient to power a short-lived lunar dynamo.     

Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer

Determining classically whether a coin is fair (head on one side, tail on the other) or fake (heads or tails on both sides) requires an examination of each side. However, the analogous quantum procedure (the Deutsch-Jozsa algorithm) requires just one examination step. The Deutsch-Jozsa algorithm has been realized experimentally using bulk nuclear magnetic resonance techniques, employing nuclear spins as quantum bits (qubits). In contrast, the ion trap processor utilises motional and electronic quantum states of individual atoms as qubits, and in principle is easier to scale to many qubits. Experimental advances in the latter area include the realization of a two-qubit quantum gate, the entanglement of four ions, quantum state engineering and entanglement-enhanced phase estimation. Here we exploit techniques developed for nuclear magnetic resonance to implement the Deutsch-Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion. Our ion-based implementation of a full quantum algorithm serves to demonstrate experimental procedures with the quality and precision required for complex computations, confirming the potential of trapped ions for quantum computation.     

Controlling the double helix

Chromatin is the complex of DNA and proteins in which the genetic material is packaged inside the cells of organisms with nuclei. Chromatin structure is dynamic and exerts profound control over gene expression and other fundamental cellular processes. Changes in its structure can be inherited by the next generation, independent of the DNA sequence itself.     

Cell fusion is the principal source of bone-marrow-derived hepatocytes

Evidence suggests that haematopoietic stem cells might have unexpected developmental plasticity, highlighting therapeutic potential. For example, bone-marrow-derived hepatocytes can repopulate the liver of mice with fumarylacetoacetate hydrolase deficiency and correct their liver disease. To determine the underlying mechanism in this murine model, we performed serial transplantation of bone-marrow-derived hepatocytes. Here we show by Southern blot analysis that the repopulating hepatocytes in the liver were heterozygous for alleles unique to the donor marrow, in contrast to the original homozygous donor cells. Furthermore, cytogenetic analysis of hepatocytes transplanted from female donor mice into male recipients demonstrated 80,XXXY (diploid to diploid fusion) and 120,XXXXYY (diploid to tetraploid fusion) karyotypes, indicative of fusion between donor and host cells. We conclude that hepatocytes derived form bone marrow arise from cell fusion and not by differentiation of haematopoietic stem cells.