Exactly solvable su(N) mixed spin ladders

It is shown that solvable mixed spin ladder models can be constructed from su(N) permutators. Heisenberg rung interactions appear as chemical potential terms in the Bethe Ansatz solution. Explicit examples given are a mixed spin-1/2 spin-1 ladder, a mixed spin-1/2 spin-3/2 ladder and a spin-1 ladder with biquadratic interactions.Comment: 7 pages, Latex, Presented at the Baxter Revolution in Mathematical Physics Conference, Feb 13-19, 200

Magnetisation distribution in the tetragonal phase of BaFe2As2

We have determined the spatial distribution of the magnetisation induced by a field of 9 T in the tetragonal phase of BaFe2As2 using polarised neutron diffraction. Magnetic structure factors derived from the polarisation dependence of the intensities of Bragg reflections were used to make a maximum entropy reconstruction of the distribution projected on the 110 plane. The reconstruction shows clearly that the magnetisation is confined to the region around the iron atoms and that there is no significant magnetisation associated with either the As or Ba atoms. The distribution of magnetisation around the Fe atom is significantly non-spherical with a shape which is extended in the directions in the projection. These results show that the electrons which give rise to the paramagnetic susceptibility are confined to the Fe atoms their distribution suggests that they occupy 3d t_2g type orbitals with about 60% in those of xy symmetry

Nematode distribution and damage to yam in central and eastern Uganda

Yams (Dioscorea spp.) are food crops of growing significance in sub Saharan Africa. Unfortunately, nematodes are major pests to their production. A study was undertaken in major yam growing areas of Uganda to investigate the association of plant parasitic nematodes with damage symptoms. Nematodes were assessed from tubers, roots and surrounding soil for seven cultivars belonging to Dioscorea alata, D. bulbisiana, D. burkilliana and D. cayenensis at harvest. Pratylenchus sudanensis was found in the greatest density and was followed byMeloidogyne spp. Higher densities of both nematodes were observed in the tubers rather than roots. Although symptoms of cracking and galling were relatively low, P. sudanensis incidence was strongly associated with cracking and Meloidogyne spp. with galling. Pratylenchus sudanensis and Meloidogyne spp. incidence their associated damage were, however, negatively correlated, suggesting inter-species competition. Principal components analysis of data suggested that differences in susceptibility to P. sudanensis occur between yam cultivars and species

Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to $J$, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.Comment: 26 latex pages. Final version published in J. Fourier Anal. App

Optimizing Illumina next-generation sequencing library preparation for extremely AT-biased genomes.

BAckground: Massively parallel sequencing technology is revolutionizing approaches to genomic and genetic research. Since its advent, the scale and efficiency of Next-Generation Sequencing (NGS) has rapidly improved. In spite of this success, sequencing genomes or genomic regions with extremely biased base composition is still a great challenge to the currently available NGS platforms. The genomes of some important pathogenic organisms like Plasmodium falciparum (high AT content) and Mycobacterium tuberculosis (high GC content) display extremes of base composition. The standard library preparation procedures that employ PCR amplification have been shown to cause uneven read coverage particularly across AT and GC rich regions, leading to problems in genome assembly and variation analyses. Alternative library-preparation approaches that omit PCR amplification require large quantities of starting material and hence are not suitable for small amounts of DNA/RNA such as those from clinical isolates. We have developed and optimized library-preparation procedures suitable for low quantity starting material and tolerant to extremely high AT content sequences. Results: We have used our optimized conditions in parallel with standard methods to prepare Illumina sequencing libraries from a non-clinical and a clinical isolate (containing ~53% host contamination). By analyzing and comparing the quality of sequence data generated, we show that our optimized conditions that involve a PCR additive (TMAC), produces amplified libraries with improved coverage of extremely AT-rich regions and reduced bias toward GC neutral templates. Conclusion: We have developed a robust and optimized Next-Generation Sequencing library amplification method suitable for extremely AT-rich genomes. The new amplification conditions significantly reduce bias and retain the complexity of either extremes of base composition. This development will greatly benefit sequencing clinical samples that often require amplification due to low mass of DNA starting material

Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras

We extend the results of spin ladder models associated with the Lie algebras $su(2^n)$ to the case of the orthogonal and symplectic algebras $o(2^n),\ sp(2^n)$ where n is the number of legs for the system. Two classes of models are found whose symmetry, either orthogonal or symplectic, has an explicit n dependence. Integrability of these models is shown for an arbitrary coupling of XX type rung interactions and applied magnetic field term.Comment: 7 pages, Late

Molecular basis of APC/C regulation by the spindle assembly checkpoint.

In the dividing eukaryotic cell, the spindle assembly checkpoint (SAC) ensures that each daughter cell inherits an identical set of chromosomes. The SAC coordinates the correct attachment of sister chromatid kinetochores to the mitotic spindle with activation of the anaphase-promoting complex (APC/C), the E3 ubiquitin ligase responsible for initiating chromosome separation. In response to unattached kinetochores, the SAC generates the mitotic checkpoint complex (MCC), which inhibits the APC/C and delays chromosome segregation. By cryo-electron microscopy, here we determine the near-atomic resolution structure of a human APC/C–MCC complex (APC/C(MCC)). Degron-like sequences of the MCC subunit BubR1 block degron recognition sites on Cdc20, the APC/C coactivator subunit responsible for substrate interactions. BubR1 also obstructs binding of the initiating E2 enzyme UbcH10 to repress APC/C ubiquitination activity. Conformational variability of the complex enables UbcH10 association, and structural analysis shows how the Cdc20 subunit intrinsic to the MCC (Cdc20(MCC)) is ubiquitinated, a process that results in APC/C reactivation when the SAC is silenced

Molecular mechanism of APC/C activation by mitotic phosphorylation.

In eukaryotes, the anaphase-promoting complex (APC/C, also known as the cyclosome) regulates the ubiquitin-dependent proteolysis of specific cell-cycle proteins to coordinate chromosome segregation in mitosis and entry into the G1 phase. The catalytic activity of the APC/C and its ability to specify the destruction of particular proteins at different phases of the cell cycle are controlled by its interaction with two structurally related coactivator subunits, Cdc20 and Cdh1. Coactivators recognize substrate degrons, and enhance the affinity of the APC/C for its cognate E2 (refs 4-6). During mitosis, cyclin-dependent kinase (Cdk) and polo-like kinase (Plk) control Cdc20- and Cdh1-mediated activation of the APC/C. Hyperphosphorylation of APC/C subunits, notably Apc1 and Apc3, is required for Cdc20 to activate the APC/C, whereas phosphorylation of Cdh1 prevents its association with the APC/C. Since both coactivators associate with the APC/C through their common C-box and Ile-Arg tail motifs, the mechanism underlying this differential regulation is unclear, as is the role of specific APC/C phosphorylation sites. Here, using cryo-electron microscopy and biochemical analysis, we define the molecular basis of how phosphorylation of human APC/C allows for its control by Cdc20. An auto-inhibitory segment of Apc1 acts as a molecular switch that in apo unphosphorylated APC/C interacts with the C-box binding site and obstructs engagement of Cdc20. Phosphorylation of the auto-inhibitory segment displaces it from the C-box-binding site. Efficient phosphorylation of the auto-inhibitory segment, and thus relief of auto-inhibition, requires the recruitment of Cdk-cyclin in complex with a Cdk regulatory subunit (Cks) to a hyperphosphorylated loop of Apc3. We also find that the small-molecule inhibitor, tosyl-l-arginine methyl ester, preferentially suppresses APC/C(Cdc20) rather than APC/C(Cdh1), and interacts with the binding sites of both the C-box and Ile-Arg tail motifs. Our results reveal the mechanism for the regulation of mitotic APC/C by phosphorylation and provide a rationale for the development of selective inhibitors of this state

Magnetization Plateaux in Bethe Ansatz Solvable Spin-S Ladders

We examine the properties of the Bethe Ansatz solvable two- and three-leg spin-$S$ ladders. These models include Heisenberg rung interactions of arbitrary strength and thus capture the physics of the spin-$S$ Heisenberg ladders for strong rung coupling. The discrete values derived for the magnetization plateaux are seen to fit with the general prediction based on the Lieb-Schultz- Mattis theorem. We examine the magnetic phase diagram of the spin-1 ladder in detail and find an extended magnetization plateau at the fractional value $= {1/2}$ in agreement with the experimental observation for the spin-1 ladder compound BIP-TENO.Comment: 11 pages, 1 figur

Phase diagram of the su(8) quantum spin tube

We calculate the phase diagram of an integrable anisotropic 3-leg quantum spin tube connected to the su(8) algebra. We find several quantum phase transitions for antiferromagnetic rung couplings. Their locations are calculated exactly from the Bethe Ansatz solution and we discuss the nature of each of the different phases.Comment: 10 pages, RevTeX, 1 postscript figur