Kinetic collision detection for balls rolling on a plane

This abstract presents a first step towards kinetic col- lision detection in 3 dimensions. In particular, we design a compact and responsive kinetic data struc- ture (KDS) for detecting collisions between n balls of arbitrary sizes rolling on a plane. The KDS has size O(n log n) and can handle events in O(log n) time. The structure processes O(n2) events in the worst case, assuming that the objects follow low-degree al- gebraic trajectories. The full paper [1] presents ad- ditional results for convex fat 3-dimensional objects that are free-flying in R3

Five-year follow-up of underexpanded and overexpanded bioresorbable scaffolds: Self-correction and impact on shear stress

Underexpansion and overexpansion have been incriminated as causative factors of adverse cardiac events. However, dynamic biological interaction between vessel wall and scaffold may attenuate the adverse haemodynamic impact of overexpansion or underexpansion

Correlations Between Charge Ordering and Local Magnetic Fields in Overdoped YBa2_2Cu3_3O6+x_{6+x}

Zero-field muon spin relaxation (ZF-$\mu$SR) measurements were undertaken on under- and overdoped samples of superconducting YBa$_2$Cu$_3$O$_{6+x}$ to determine the origin of the weak static magnetism recently reported in this system. The temperature dependence of the muon spin relaxation rate in overdoped crystals displays an unusual behavior in the superconducting state. A comparison to the results of NQR and lattice structure experiments on highly doped samples provides compelling evidence for strong coupling of charge, spin and structural inhomogeneities.Comment: 4 pages, 4 figures, new data, new figures and modified tex

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele

On Unfolding Trees and Polygons on Various Lattices

We consider the problem of unfolding lattice trees and polygons in hexagonal or triangular lattice in two dimensions. We show that a hexagonal/triangular lattice chain (resp. tree) can be straightened in O(n) (resp. O(n 2)) moves and time, and a hexagonal/triangular lattice polygon can be convexified in O(n 2) moves and time. We hope that the techniques we used shed some light on solving the more general conjecture that a unit tree in two dimensions can always be straightened.

Pants decomposition of the punctured plane

A pants decomposition of an orientable surface ?? is a collection of simple cycles that partition ?? into pants, i.e., surfaces of genus zero with three boundary cycles. Given a set P of n points in the plane E2, we consider the problem of computing a pants decomposition of ?? = E2 \ P of minimum total length. We give a polynomial-time approximation scheme using Mitchell’s guillotine rectilinear subdivisions. We give an O(n4)-time algorithm to compute the shortest pants decomposition of ?? when the cycles are restricted to be axis-aligned boxes, and an O(n2)-time algorithm when all the points lie on a line; both exact algorithms use dynamic programming with Yao’s speedup

On unfolding trees and polygons on various lattices

We consider the problem of unfolding lattice trees and polygons in hexagonal or triangular lattice in two dimensions. We show that a hexagonal/triangular lattice chain (resp. tree) can be straightened in O(n) (resp. O(n2)) moves and time, and a hexagonal/triangular lattice polygon can be convexified in O(n2) moves and time. We hope that the techniques we used shed some light on solving the more general conjecture that a unit tree in two dimensions can always be straightened

Few optimal foldings of HP protein chains on various letters

We consider whether or not protein chains in the HP model have unique or few optimal foldings. We solve the conjecture proposed by Aichholzer et al. that the open chain L2k-1 = (HP)k(PH)k-1 for k ?? 3 has exactly two optimal foldings on the square lattice. We show that some closed and open chains have unique optimal foldings on the hexagonal and triangular lattices, respectively

On unfolding lattice polygons/trees and diameter-4 trees

We consider the problems of straightening polygonal trees and convexifying polygons by continuous motions such that rigid edges can rotate around vertex joints and no edge crossings are allowed. A tree can be straightened if all its edges can be aligned along a common straight line such that each edge points "away" from a designated leaf node. A polygon can be convexified if it can be reconfigured to a convex polygon. A lattice tree (resp. polygon) is a tree (resp. polygon) containing only edges from a square or cubic lattice. We first show that a 2D lattice chain or a 3D lattice tree can be straightened efficiently in O(n) moves and time, where n is the number of tree edges. We then show that a 2D lattice tree can be straightened efficiently in O(n2) moves and time. Furthermore, we prove that a 2D lattice polygon or a 3D lattice polygon with simple shadow can be convexified efficiently in O(n2) moves and time. Finally, we show that two special classes of diameter-4 trees in two dimensions can always be straightened