Contamination Estimation via Convex Relaxations

Identifying anomalies and contamination in datasets is important in a wide variety of settings. In this paper, we describe a new technique for estimating contamination in large, discrete valued datasets. Our approach considers the normal condition of the data to be specified by a model consisting of a set of distributions. Our key contribution is in our approach to contamination estimation. Specifically, we develop a technique that identifies the minimum number of data points that must be discarded (i.e., the level of contamination) from an empirical data set in order to match the model to within a specified goodness-of-fit, controlled by a p-value. Appealing to results from large deviations theory, we show a lower bound on the level of contamination is obtained by solving a series of convex programs. Theoretical results guarantee the bound converges at a rate of $O(\sqrt{\log(p)/p})$, where p is the size of the empirical data set.Comment: To appear, ISIT 201

Can Quantum Lattice Fluctuations Destroy the Peierls Broken Symmetry Ground State?

The study of bond alternation in one-dimensional electronic systems has had a long history. Theoretical work in the 1930s predicted the absence of bond alternation in the limit of infinitely long conjugated polymers; a result later contradicted by experimental investigations. When this issue was re-examined in the 1950s it was shown in the adiabatic limit that bond alternation occurs for any value of electron-phonon coupling. The question of whether this conclusion remains valid for quantized nuclear degrees of freedom was first addressed in the 1980s. Since then a series of numerical calculations on models with gapped, dispersionless phonons have suggested that bond alternation is destroyed by quantum fluctuations below a critical value of electron-phonon coupling. In this work we study a more realistic model with gapless, dispersive phonons. By solving this model with the DMRG method we show that bond alternation remains robust for any value of electron-phonon coupling

Effective theories of scattering with an attractive inverse-square potential and the three-body problem

A distorted-wave version of the renormalisation group is applied to scattering by an inverse-square potential and to three-body systems. In attractive three-body systems, the short-distance wave function satisfies a Schroedinger equation with an attractive inverse-square potential, as shown by Efimov. The resulting oscillatory behaviour controls the renormalisation of the three-body interactions, with the renormalisation-group flow tending to a limit cycle as the cut-off is lowered. The approach used here leads to single-valued potentials with discontinuities as the bound states are cut off. The perturbations around the cycle start with a marginal term whose effect is simply to change the phase of the short-distance oscillations, or the self-adjoint extension of the singular Hamiltonian. The full power counting in terms of the energy and two-body scattering length is constructed for short-range three-body forces.Comment: 19 pages (RevTeX), 2 figure

The low-lying excitations of polydiacetylene

The Pariser-Parr-Pople Hamiltonian is used to calculate and identify the nature of the low-lying vertical transition energies of polydiacetylene. The model is solved using the density matrix renormalisation group method for a fixed acetylenic geometry for chains of up to 102 atoms. The non-linear optical properties of polydiacetylene are considered, which are determined by the third-order susceptibility. The experimental 1Bu data of Giesa and Schultz are used as the geometric model for the calculation. For short chains, the calculated E(1Bu) agrees with the experimental value, within solvation effects (ca. 0.3 eV). The charge gap is used to characterise bound and unbound states. The nBu is above the charge gap and hence a continuum state; the 1Bu, 2Ag and mAg are not and hence are bound excitons. For large chain lengths, the nBu tends towards the charge gap as expected, strongly suggesting that the nBu is the conduction band edge. The conduction band edge for PDA is agreed in the literature to be ca. 3.0 eV. Accounting for the strong polarisation effects of the medium and polaron formation gives our calculated E(nBu) ca. 3.6 eV, with an exciton binding energy of ca. 1.0 eV. The 2Ag state is found to be above the 1Bu, which does not agree with relaxed transition experimental data. However, this could be resolved by including explicit lattice relaxation in the Pariser- Parr-Pople-Peierls model. Particle-hole separation data further suggest that the 1Bu, 2Ag and mAg are bound excitons, and that the nBu is an unbound exciton.Comment: LaTeX, 23 pages, 4 postscript tables and 8 postscript figure

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

Simultaneous and extensive removal of the East Asian lithospheric root

Much evidence points to a dramatic thinning of East Asian lithosphere during the Mesozoic, but with little precision on when, or over what time scale. Using geochemical constraints, we examine an extensive compilation of dated volcanic samples from Russia, Mongolia and North China to determine when the lithosphere thinned and how long that process took. Geochemical results suggest that magmatism before 107 Ma derived from metasomatised subcontinental lithospheric mantle (SCLM), whereas after 107 Ma, melt predominantly derived from an asthenospheric source. The switch to an asthenospheric magma source at ~107 Ma occurred in both Mongolia and North China (>1600 km apart), whereas in eastern Russia the switch occurred a little later (~85 Ma). Such a dramatic change to an asthenospheric contribution appears to have taken, from beginning to end, just ~30 Myrs, suggesting this is the duration for lithospheric mantle weakening and removal. Subsequent volcanism, through the Cenozoic in Mongolia and North China does not appear to include any contribution from the removed SCLM, despite melts predominantly deriving from the asthenosphere

Evidence for southward subduction of the Mongol-Okhotsk oceanic plate: Implications from Mesozoic adakitic lavas from Mongolia

A combination of new 40Ar/39Ar dating results, major- and trace-element data, plus Sr-Nd-Pb-Hf isotope data, are used to investigate the petrogenesis of Triassic high-Si adakite (HSA), Cretaceous low-Si adakite-like (LSA) lavas, and Cretaceous high-K and shoshonitic trachyandesite lavas, from eastern and south-central Mongolia. All samples are light rare-earth element and large-ion lithophile element enriched but depleted in some high-field strength elements (notably Nb, Ta and Ti). Two alternative models are proposed to explain the petrogenesis of the HSA samples. (1) A southward-subducting Mongol-Okhotsk slab underwent partial melting in the Triassic during the closure of the Mongol-Okhotsk Ocean, with the resultant melts assimilating mantle and crustal material. Alternatively (2), a basaltic underplate of thickened (>50 km; >1.5 GPa), eclogitic lower crust foundered into the underlying mantle, and underwent partial melting with minor contamination from mantle material and some shallow-level crustal contamination. The LSA samples are interpreted as melts derived from a lithospheric mantle wedge that was previously metasomatised by slab melts. Similarly, the trachyandesite lavas are interpreted as melts deriving from a subduction-enriched subcontinental lithospheric mantle. The spatial distribution of these samples implies that metasomatism likely occurred due to a southward-subducting Mongol-Okhotsk slab associated with the closure of the Mongol-Okhotsk Ocean. When this interpretation is combined with previous evidence for a northward-subducting Mongol-Okhotsk slab it advocates that the Mongol-Okhotsk Ocean closed with double-sided subduction

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

Effective field theory of 3He

3He and the triton are studied as three-body bound states in the effective field theory without pions. We study 3He using the set of integral equations developed by Kok et al. which includes the full off-shell T-matrix for the Coulomb interaction between the protons. To leading order, the theory contains: two-body contact interactions whose renormalized strengths are set by the NN scattering lengths, the Coulomb potential, and a three-body contact interaction. We solve the three coupled integral equations with a sharp momentum cutoff, Lambda, and find that a three-body interaction is required in 3He at leading order, as in the triton. It also exhibits the same limit-cycle behavior as a function of Lambda, showing that the Efimov effect remains in the presence of the Coulomb interaction. We also obtain the difference between the strengths of the three-body forces in 3He and the triton.Comment: 18 pages, 6 figures; further discussion and references adde

Renormalisation-group analysis of repulsive three-body systems

A coordinate space approach, based on that used by Efimov, is applied to three-body systems with contact interactions between pairs of particles. In systems with nonzero orbital angular momentum or with asymmetric spatial wave functions, the hyperradial equation contains a repulsive 1/r^2 potential. The resulting wave functions are used in a renormalisation group analysis. This confirms Griesshammer's power counting for short-range three-body forces in these systems. The only exceptions are ones like the 4S channel for three nucleons, where any derivatives needed in the interaction are found to be already counted by the scaling with the cut-off.Comment: 5 pages, RevTe