Splitting an Ordering into a Partition to Minimize Diameter

k consisting of k clusters, with k > 2. Bottom-up agglomerative approaches are also commonly used to construct partitions, and we discuss these in terms of worst-case performance for metric data sets. Our main contribution derives from a new restricted partition formulation that requires each cluster to be an interval of a given ordering of the objects being clustered. Dynamic programming can optimally split such an ordering into a partition P^k for a large class of objectives that includes min-diameter. We explore a variety of ordering heuristics and show that our algorithm, when combined with an appropriate ordering heuristic, outperforms traditional algorithms on both random and non-random data sets.     

Complex reorganization and predominant non-homologous repair following chromosomal breakage in karyotypically balanced germline rearrangements and transgenic integration

We defined the genetic landscape of balanced chromosomal rearrangements at nucleotide resolution by sequencing 141 breakpoints from cytogenetically interpreted translocations and inversions. We confirm that the recently described phenomenon of 'chromothripsis' (massive chromosomal shattering and reorganization) is not unique to cancer cells but also occurs in the germline, where it can resolve to a relatively balanced state with frequent inversions. We detected a high incidence of complex rearrangements (19.2%) and substantially less reliance on microhomology (31%) than previously observed in benign copy-number variants (CNVs). We compared these results to experimentally generated DNA breakage-repair by sequencing seven transgenic animals, revealing extensive rearrangement of the transgene and host genome with similar complexity to human germline alterations. Inversion was the most common rearrangement, suggesting that a combined mechanism involving template switching and non-homologous repair mediates the formation of balanced complex rearrangements that are viable, stably replicated and transmitted unaltered to subsequent generations.     

Anthropogenic ocean acidification over the twenty-first century and its impact on calcifying organisms

Today's surface ocean is saturated with respect to calcium carbonate, but increasing atmospheric carbon dioxide concentrations are reducing ocean pH and carbonate ion concentrations, and thus the level of calcium carbonate saturation. Experimental evidence suggests that if these trends continue, key marine organisms--such as corals and some plankton--will have difficulty maintaining their external calcium carbonate skeletons. Here we use 13 models of the ocean-carbon cycle to assess calcium carbonate saturation under the IS92a 'business-as-usual' scenario for future emissions of anthropogenic carbon dioxide. In our projections, Southern Ocean surface waters will begin to become undersaturated with respect to aragonite, a metastable form of calcium carbonate, by the year 2050. By 2100, this undersaturation could extend throughout the entire Southern Ocean and into the subarctic Pacific Ocean. When live pteropods were exposed to our predicted level of undersaturation during a two-day shipboard experiment, their aragonite shells showed notable dissolution. Our findings indicate that conditions detrimental to high-latitude ecosystems could develop within decades, not centuries as suggested previously.     

Algae acquire vitamin B12 through a symbiotic relationship with bacteria

Vitamin B12 (cobalamin) was identified nearly 80 years ago as the anti-pernicious anaemia factor in liver, and its importance in human health and disease has resulted in much work on its uptake, cellular transport and utilization. Plants do not contain cobalamin because they have no cobalamin-dependent enzymes. Deficiencies are therefore common in strict vegetarians, and in the elderly, who are susceptible to an autoimmune disorder that prevents its efficient uptake. In contrast, many algae are rich in vitamin B12, with some species, such as Porphyra yezoensis (Nori), containing as much cobalamin as liver. Despite this, the role of the cofactor in algal metabolism remains unknown, as does the source of the vitamin for these organisms. A survey of 326 algal species revealed that 171 species require exogenous vitamin B12 for growth, implying that more than half of the algal kingdom are cobalamin auxotrophs. Here we show that the role of vitamin B12 in algal metabolism is primarily as a cofactor for vitamin B12-dependent methionine synthase, and that cobalamin auxotrophy has arisen numerous times throughout evolution, probably owing to the loss of the vitamin B12-independent form of the enzyme. The source of cobalamin seems to be bacteria, indicating an important and unsuspected symbiosis.     

Chimaeric sounds reveal dichotomies in auditory perception

By Fourier's theorem, signals can be decomposed into a sum of sinusoids of different frequencies. This is especially relevant for hearing, because the inner ear performs a form of mechanical Fourier transform by mapping frequencies along the length of the cochlear partition. An alternative signal decomposition, originated by Hilbert, is to factor a signal into the product of a slowly varying envelope and a rapidly varying fine time structure. Neurons in the auditory brainstem sensitive to these features have been found in mammalian physiological studies. To investigate the relative perceptual importance of envelope and fine structure, we synthesized stimuli that we call 'auditory chimaeras', which have the envelope of one sound and the fine structure of another. Here we show that the envelope is most important for speech reception, and the fine structure is most important for pitch perception and sound localization. When the two features are in conflict, the sound of speech is heard at a location determined by the fine structure, but the words are identified according to the envelope. This finding reveals a possible acoustic basis for the hypothesized 'what' and 'where' pathways in the auditory cortex.     

Osteoclast-poor human osteopetrosis due to mutations in the gene encoding RANKL

Autosomal recessive osteopetrosis is usually associated with normal or elevated numbers of nonfunctional osteoclasts. Here we report mutations in the gene encoding RANKL (receptor activator of nuclear factor-KB ligand) in six individuals with autosomal recessive osteopetrosis whose bone biopsy specimens lacked osteoclasts. These individuals did not show any obvious defects in immunological parameters and could not be cured by hematopoietic stem cell transplantation; however, exogenous RANKL induced formation of functional osteoclasts from their monocytes, suggesting that they could, theoretically, benefit from exogenous RANKL administration.     

Association scan of 14,500 nonsynonymous SNPs in four diseases identifies autoimmunity variants

We have genotyped 14,436 nonsynonymous SNPs (nsSNPs) and 897 major histocompatibility complex (MHC) tag SNPs from 1,000 independent cases of ankylosing spondylitis (AS), autoimmune thyroid disease (AITD), multiple sclerosis (MS) and breast cancer (BC). Comparing these data against a common control dataset derived from 1,500 randomly selected healthy British individuals, we report initial association and independent replication in a North American sample of two new loci related to ankylosing spondylitis, ARTS1 and IL23R, and confirmation of the previously reported association of AITD with TSHR and FCRL3. These findings, enabled in part by increased statistical power resulting from the expansion of the control reference group to include individuals from the other disease groups, highlight notable new possibilities for autoimmune regulation and suggest that IL23R may be a common susceptibility factor for the major 'seronegative' diseases.     

Mutations in TTBK2, encoding a kinase implicated in tau phosphorylation, segregate with spinocerebellar ataxia type 11

The microtubule-associated protein tau (encoded by MAPT) and several tau kinases have been implicated in neurodegeneration, but only MAPT has a proven role in disease. We identified mutations in the gene encoding tau tubulin kinase 2 (TTBK2) as the cause of spinocerebellar ataxia type 11. Affected brain tissue showed substantial cerebellar degeneration and tau deposition. These data suggest that TTBK2 is important in the tau cascade and in spinocerebellar degeneration.     

Nucleation and growth mechanism of ferroelectric domain-wall motion

The motion of domain walls is critical to many applications involving ferroelectric materials, such as fast high-density non-volatile random access memory. In memories of this sort, storing a data bit means increasing the size of one polar region at the expense of another, and hence the movement of a domain wall separating these regions. Experimental measurements of domain growth rates in the well-established ferroelectrics PbTiO3 and BaTiO3 have been performed, but the development of new materials has been hampered by a lack of microscopic understanding of how domain walls move. Despite some success in interpreting domain-wall motion in terms of classical nucleation and growth models, these models were formulated without insight from first-principles-based calculations, and they portray a picture of a large, triangular nucleus that leads to unrealistically large depolarization and nucleation energies. Here we use atomistic molecular dynamics and coarse-grained Monte Carlo simulations to analyse these processes, and demonstrate that the prevailing models are incorrect. Our multi-scale simulations reproduce experimental domain growth rates in PbTiO3 and reveal small, square critical nuclei with a diffuse interface. A simple analytic model is also proposed, relating bulk polarization and gradient energies to wall nucleation and growth, and thus rationalizing all experimental rate measurements in PbTiO3 and BaTiO3.