Largest Empty Circle Centered on a Query Line

The Largest Empty Circle problem seeks the largest circle centered within the convex hull of a set $P$ of $n$ points in $\mathbb{R}^2$ and devoid of points from $P$. In this paper, we introduce a query version of this well-studied problem. In our query version, we are required to preprocess $P$ so that when given a query line $Q$, we can quickly compute the largest empty circle centered at some point on $Q$ and within the convex hull of $P$. We present solutions for two special cases and the general case; all our queries run in $O(\log n)$ time. We restrict the query line to be horizontal in the first special case, which we preprocess in $O(n \alpha(n) \log n)$ time and space, where $\alpha(n)$ is the slow growing inverse of the Ackermann's function. When the query line is restricted to pass through a fixed point, the second special case, our preprocessing takes $O(n \alpha(n)^{O(\alpha(n))} \log n)$ time and space. We use insights from the two special cases to solve the general version of the problem with preprocessing time and space in $O(n^3 \log n)$ and $O(n^3)$ respectively.Comment: 18 pages, 13 figure

A two-coil mutual inductance technique to study matching effect in disordered NbN thin films

Although matching effects in superconducting anti-dot arrays have been studied extensively through magneto-resistance oscillations, these investigations have been restricted to a very narrow temperature window close to the superconducting transition. Here we report a "two coil" mutual inductance technique, which allows the study of this phenomenon deep in the superconducting state, through a direct measurement of the magnetic field variation of the shielding response. We demonstrate how this technique can be used to resolve outstanding issues on the origin of matching effects in superconducting thin films with periodic array of holes grown on anodized alumina membranes

Spin Filtering and Entanglement Swapping through Coherent Evolution of a Single Quantum Dot

We exploit the non-dissipative dynamics of a pair of electrons in a large square quantum dot to perform singlet-triplet spin measurement through a single charge detection and show how this may be used for entanglement swapping and teleportation. The method is also used to generate the AKLT ground state, a further resource for quantum computation. We justify, and derive analytic results for, an effective charge-spin Hamiltonian which is valid over a wide range of parameters and agrees well with exact numerical results of a realistic effective-mass model. Our analysis also indicates that the method is robust to choice of dot-size and initialization errors, as well as decoherence introduced by the hyperfine interaction.Comment: 5 pages, 3 figure

Biophysical evidence for intrinsic disorder in the C-terminal tails of the epidermal growth factor receptor (EGFR) and HER3 receptor tyrosine kinases

The epidermal growth factor receptor (EGFR)/ErbB family of receptor tyrosine kinases includes oncogenes important in the progression of breast and other cancers, and they are targets for many drug development strategies. Each member of the ErbB family possesses a unique, structurally uncharacterized C-terminal tail that plays an important role in autophosphorylation and signal propagation. To determine whether these C-terminal tails are intrinsically disordered regions, we conducted a battery of biophysical experiments on the EGFR and HER3 tails. Using hydrogen/deuterium exchange mass spectrometry, we measured the conformational dynamics of intracellular half constructs and compared the tails with the ordered kinase domains. The C-terminal tails demonstrate more rapid deuterium exchange behavior when compared with the kinase domains. Next, we expressed and purified EGFR and HER3 tail-only constructs. Results from circular dichroism spectroscopy, size exclusion chromatography with multiangle light scattering, dynamic light scattering, analytical ultracentrifugation, and small angle X-ray scattering each provide evidence that the EGFR and HER3 C-terminal tails are intrinsically disordered with extended, non-globular structure in solution. The intrinsic disorder and extended conformation of these tails may be important for their function by increasing the capture radius and reducing the thermodynamic barriers for binding of downstream signaling proteins

Origin of Matching Effect in Anti-dot Array of Superconducting NbN Thin Films

We investigate the origin of matching effect observed in disordered superconducting NbN thin films with periodic array of holes. In addition to the periodic variation in the electrical resistance just above the superconducting transition temperature, Tc0, we find pronounced periodic variations with magnetic field in all dynamical quantities which can be influenced by flux-line motion under an external drive such as the magnetic shielding response and the critical current which survive in some samples down to temperatures as low as 0.09Tc0. In contrast, the superconducting energy gap, D which is a true thermodynamic quantity does not show any periodic variation with magnetic fields for the same films. Our results show that commensurate pinning of the flux line lattice driven by vortex-vortex interaction is the dominant mechanism for the observed matching effects in these superconducting anti-dot films rather than Little-Parks like quantum interference effect.Comment: 18 pages, 6 figure

Inhibition of the EGF receptor by binding of MIG6 to an activating kinase domain interface.

Members of the epidermal growth factor receptor family (EGFR/ERBB1, ERBB2/HER2, ERBB3/HER3 and ERBB4/HER4) are key targets for inhibition in cancer therapy. Critical for activation is the formation of an asymmetric dimer by the intracellular kinase domains, in which the carboxy-terminal lobe (C lobe) of one kinase domain induces an active conformation in the other. The cytoplasmic protein MIG6 (mitogen-induced gene 6; also known as ERRFI1) interacts with and inhibits the kinase domains of EGFR and ERBB2 (refs 3-5). Crystal structures of complexes between the EGFR kinase domain and a fragment of MIG6 show that a approximately 25-residue epitope (segment 1) from MIG6 binds to the distal surface of the C lobe of the kinase domain. Biochemical and cell-based analyses confirm that this interaction contributes to EGFR inhibition by blocking the formation of the activating dimer interface. A longer MIG6 peptide that is extended C terminal to segment 1 has increased potency as an inhibitor of the activated EGFR kinase domain, while retaining a critical dependence on segment 1. We show that signalling by EGFR molecules that contain constitutively active kinase domains still requires formation of the asymmetric dimer, underscoring the importance of dimer interface blockage in MIG6-mediated inhibition

Data Structures for Halfplane Proximity Queries and Incremental Voronoi Diagrams

We consider preprocessing a set $S$ of $n$ points in convex position in the plane into a data structure supporting queries of the following form: given a point $q$ and a directed line $\ell$ in the plane, report the point of $S$ that is farthest from (or, alternatively, nearest to) the point $q$ among all points to the left of line $\ell$. We present two data structures for this problem. The first data structure uses $O(n^{1+\varepsilon})$ space and preprocessing time, and answers queries in $O(2^{1/\varepsilon} \log n)$ time, for any $0 < \varepsilon < 1$. The second data structure uses $O(n \log^3 n)$ space and polynomial preprocessing time, and answers queries in $O(\log n)$ time. These are the first solutions to the problem with $O(\log n)$ query time and $o(n^2)$ space. The second data structure uses a new representation of nearest- and farthest-point Voronoi diagrams of points in convex position. This representation supports the insertion of new points in clockwise order using only $O(\log n)$ amortized pointer changes, in addition to $O(\log n)$-time point-location queries, even though every such update may make $\Theta(n)$ combinatorial changes to the Voronoi diagram. This data structure is the first demonstration that deterministically and incrementally constructed Voronoi diagrams can be maintained in $o(n)$ amortized pointer changes per operation while keeping $O(\log n)$-time point-location queries.Comment: 17 pages, 6 figures. Various small improvements. To appear in Algorithmic

Evaluation: Perspectives of Students and Graduates

Women\u27s studies, now in its second phase, is making its presence felt within institutions, developing a new curriculum, and building a new body of intellectual knowledge. Women\u27s studies\u27 original purpose continues: to change the sexist and other biased values, practices, and structures within and outside traditional educational spheres. How much change has occurred? Impact within colleges, high schools, and women\u27s centers is easier to judge than effect in other arenas . Outside educational institutions, impact may be observed through two channels: first, the ties which programs explicitly make with community groups; second, students who graduate and choose not to continue their formal education. Although we assume that students are changed by their women\u27s studies experience, we often do not know what happens to them after leaving. Do they become involved in social change? Or do they feel their education has not influenced what they are now doing? The answers to these questions measure the strengths and deficiencies of women\u27s studies and provide one solid basis on which to build the curriculum during its second phase