The human papillomavirus 16 E2 protein is stabilised in S phase

The human papillomavirus 16 E2 protein regulates transcription from, and replication of, the viral genome and is also required for segregation of the viral genome via interaction with mitotic bodies. To regulate DNA replication E2 interacts with sequences around the origin of replication and recruits the viral helicase E1 via a protein-protein interaction, which then initiates viral genome replication. The replication role of E2 must originally function in a host cell S phase. In this report, we demonstrate that E2 is stabilised in the S phase of the cell cycle and that this stabilisation is accompanied by an increase in phosphorylation of the protein. This increased phosphorylation and stability are likely required for optimum viral DNA replication and therefore identification of the enzymes involved in regulating these properties of E2 will provide targets for therapeutic intervention in the viral life cycle. Preliminary studies have identified E2 as a Cdk2 substrate demonstrating this enzyme as a candidate kinase for mediating the in vivo phosphorylation of HPV16 E2

Symmetrized models of last passage percolation and non-intersecting lattice paths

It has been shown that the last passage time in certain symmetrized models of directed percolation can be written in terms of averages over random matrices from the classical groups $U(l)$, $Sp(2l)$ and $O(l)$. We present a theory of such results based on non-intersecting lattice paths, and integration techniques familiar from the theory of random matrices. Detailed derivations of probabilities relating to two further symmetrizations are also given.Comment: 21 pages, 5 figure

Q-systems, Heaps, Paths and Cluster Positivity

We consider the cluster algebra associated to the $Q$-system for $A_r$ as a tool for relating $Q$-system solutions to all possible sets of initial data. We show that the conserved quantities of the $Q$-system are partition functions for hard particles on particular target graphs with weights, which are determined by the choice of initial data. This allows us to interpret the simplest solutions of the Q-system as generating functions for Viennot's heaps on these target graphs, and equivalently as generating functions of weighted paths on suitable dual target graphs. The generating functions take the form of finite continued fractions. In this setting, the cluster mutations correspond to local rearrangements of the fractions which leave their final value unchanged. Finally, the general solutions of the $Q$-system are interpreted as partition functions for strongly non-intersecting families of lattice paths on target lattices. This expresses all cluster variables as manifestly positive Laurent polynomials of any initial data, thus proving the cluster positivity conjecture for the $A_r$ $Q$-system. We also give an alternative formulation in terms of domino tilings of deformed Aztec diamonds with defects.Comment: 106 pages, 38 figure

GaAs Nanowire pn-Junctions Produced by Low-Cost and High-Throughput Aerotaxy

Semiconductor nanowires could significantly boost the functionality and performance of future electronics, light-emitting diodes, and solar cells. However, realizing this potential requires growth methods that enable high-throughput and low-cost production of nanowires with controlled doping. Aerotaxy is an aerosol-based method with extremely high growth rate that does not require a growth substrate, allowing mass-production of high-quality nanowires at a low cost. So far, pn-junctions, a crucial element of solar cells and light-emitting diodes, have not been realized by Aerotaxy growth. Here we report a further development of the Aerotaxy method and demonstrate the growth of GaAs nanowire pn-junctions. Our Aerotaxy system uses an aerosol generator for producing the catalytic seed particles, together with a growth reactor with multiple consecutive chambers for growth of material with different dopants. We show that the produced nanowire pn-junctions have excellent diode characteristics with a rectification ratio of >105, an ideality factor around 2, and very promising photoresponse. Using electron beam induced current and hyperspectral cathodoluminescence, we determined the location of the pn-junction and show that the grown nanowires have high doping levels, as well as electrical properties and diffusion lengths comparable to nanowires grown using metal organic vapor phase epitaxy. Our findings demonstrate that high-quality GaAs nanowire pn-junctions can be produced using a low-cost technique suitable for mass-production, paving the way for industrial-scale production of nanowire-based solar cells

On Eigenvalues of the sum of two random projections

We study the behavior of eigenvalues of matrix P_N + Q_N where P_N and Q_N are two N -by-N random orthogonal projections. We relate the joint eigenvalue distribution of this matrix to the Jacobi matrix ensemble and establish the universal behavior of eigenvalues for large N. The limiting local behavior of eigenvalues is governed by the sine kernel in the bulk and by either the Bessel or the Airy kernel at the edge depending on parameters. We also study an exceptional case when the local behavior of eigenvalues of P_N + Q_N is not universal in the usual sense.Comment: 14 page

Instabilities and Bifurcations of Nonlinear Impurity Modes

We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schr{\"o}dinger equation with a single on-site nonlinear impurity emphasizing the effects of interplay between discreteness, nonlinearity and disorder. We show how the interaction of a nonlinear localized mode (a discrete soliton or discrete breather) with a repulsive impurity generates a family of stationary states near the impurity site, as well as examine both theoretical and numerical criteria for the transition between different localized states via a cascade of bifurcations.Comment: 8 pages, 8 figures, Phys. Rev. E in pres

Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state. Our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems. They also provide a rare exactly solvable case for the distribution of the minimum of a set of N {\em strongly correlated} random variables for all values of N (and not just for large N).Comment: 13 pages, 2 figures included; typos corrected; to appear in J. Stat. Phy

Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensemble

The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.Comment: This is an extended version of my talk at the QMath 9 conference at Giens, France on September 13-17, 200

Statistical distribution of quantum entanglement for a random bipartite state

We compute analytically the statistics of the Renyi and von Neumann entropies (standard measures of entanglement), for a random pure state in a large bipartite quantum system. The full probability distribution is computed by first mapping the problem to a random matrix model and then using a Coulomb gas method. We identify three different regimes in the entropy distribution, which correspond to two phase transitions in the associated Coulomb gas. The two critical points correspond to sudden changes in the shape of the Coulomb charge density: the appearance of an integrable singularity at the origin for the first critical point, and the detachement of the rightmost charge (largest eigenvalue) from the sea of the other charges at the second critical point. Analytical results are verified by Monte Carlo numerical simulations. A short account of some of these results appeared recently in Phys. Rev. Lett. {\bf 104}, 110501 (2010).Comment: 7 figure

Using Simulation to Assess the Opportunities of Dynamic Waste Collection

In this paper, we illustrate the use of discrete event simulation to evaluate how dynamic planning methodologies can be best applied for the collection of waste from underground containers. We present a case study that took place at the waste collection company Twente Milieu, located in The Netherlands. Even though the underground containers are already equipped with motion sensors, the planning of container emptying’s is still based on static cyclic schedules. It is expected that the use of a dynamic planning methodology, that employs sensor information, will result in a more efficient collection process with respect to customer satisfaction, profits, and CO2 emissions. In this research we use simulation to (i) evaluate the current planning methodology, (ii) evaluate various dynamic planning possibilities, (iii) quantify the benefits of switching to a dynamic collection process, and (iv) quantify the benefits of investing in fill‐level sensors. After simulating all scenarios, we conclude that major improvements can be achieved, both with respect to logistical costs as well as customer satisfaction