Bounds for point recolouring in geometric graphs

We examine a recolouring scheme ostensibly used to assist in classifying geographic data. Given a drawing of a graph with bi-chromatic points, where the points are the vertices of the graph, a point can be recoloured if it is surrounded by neighbours of the opposite colour. The notion of surrounded is defined as a contiguous subset of neighbours that span an angle greater than 180 degrees. The recolouring of surrounded points continues in sequence, in no particular order, until no point remains surrounded. We show that for some classes of graphs the process terminates in a polynomial number of steps. On the other hand, there are classes of graphs with infinite recolouring sequences.     

Removal of the PsaF Polypeptide Biases Electron Transfer in Favor of the PsaB Branch of Cofactors in Triton X‐100 Photosystem I Complexes from Synechococcus sp. PCC 7002†

Continuous wave (CW) and transient electron paramagnetic resonance studies have implied that when PsaF is removed genetically, the double reduction of A_1A is facile, the lifetime of A_1A^? is shorter and the ratio of fast to slow kinetic phases increases in PS I complexes isolated with Triton X‐100 (Van der Est, A., A. I. Valieva, Y. E. Kandrashkin, G. Shen, D. A. Bryant and J. H. Golbeck [2004] Biochemistry 43 , 1264–1275). Changes in the lifetimes of A_1A^? and A_1B^? are characteristic of mutants involving the quinone binding sites, but changes in the relative amplitudes of A_1A^? and A_1B^? are characteristic of mutants involving the primary electron acceptors, A_0A and A_0B. Here, we measured the fast and slow phases of electron transfer from A_1B^? and A_1A^? to F_X in psaF and psaE psaF null mutants using time‐resolved CW and pump‐probe optical absorption spectroscopy. The lifetime of the fast kinetic phase was found to be unaltered, but the lifetime of the slow kinetic phase was shorter in the psaF null mutant and even more so in the psaE psaF null mutant. Concomitantly, the amplitude of the fast kinetic phase increased by a factor of 1.8 and 2.0 in the psaF and psaE psaF null mutants, respectively, at the expense of the slow kinetic phase. The change in ratio of the fast to slow kinetic phases is explained as either a redirection of electron transfer through A_1B at the expense of A_1A, or a shortening of the lifetime of A_1A^? to become identical to that of A_1B^?. The constant lifetime and the characteristics of the near‐UV spectrum of the fast kinetic phase favor the former explanation. A unified hypothesis is presented of a displacement of the A‐jk(1) α‐helix and switchback loop, which would weaken the H‐bond from Leu₇₂₂ to A_1A, accounting for the acceleration of the slow kinetic phase, as well as weaken the H‐bond from Tyr₆₉₆ to A_0A, accounting for the bias of electron transfer in favor of the PsaB branch of cofactors.     

Computing simple circuits from a set of line segments

We address the problem of connecting line segments to form the boundary of a simple polygon—a simple circuit. However, not every set of segments can be so connected. We present anO(n logn)-time algorithm to determine whether a set of segments, constrained so that each segment has at least one endpoint on the boundary of the convex hull of the segments, admits a simple circuit. Furthermore, this technique can also be used to compute a simple circuit of minimum perimeter, or a simple circuit that bounds the minimum area, with no increase in computational complexity.     

ESI‐MS/MS of expanded porphyrins: a look into their structure and aromaticity

Electrospray mass spectrometry/mass spectrometry was used to investigate the gas‐phase properties of protonated expanded porphyrins, in order to correlate those with their structure and conformation. We have selected five expanded meso‐pentafluorophenyl porphyrins, respectively, a pair of oxidized/reduced fused pentaphyrins (22 and 24 π electrons), a pair of oxidized/reduced regular hexaphyrins (26 and 28 π electrons) and a regular doubly N‐fused hexaphyrin (28 π electrons). The gas‐phase behavior of the protonated species of oxidized and reduced expanded porphyrins is different. The oxidized species (aromatic Hückel systems) fragment more extensively, mainly by the loss of two HF molecules. The reduced species (Möbius aromatic or Möbius‐like aromatic systems) fragment less than their oxidized counterparts because of their increased flexibility. The protonated regular doubly fused hexaphyrin (non‐aromatic Hückel system) shows the least fragmentation even at higher collision energies. In general, cyclization through losses of HF molecules decreases from the aromatic Hückel systems to Möbius aromatic or Möbius‐like aromatic systems to non‐aromatic Hückel systems and is related to an increase in conformational distortion. Copyright © 2016 John Wiley & Sons, Ltd.     

Melting of heterogeneous vortex matter: The vortex ‘nanoliquid’

Disorder and porosity are parameters that strongly influence the physical behavior of materials, including their mechanical, electrical, magnetic and optical properties. Vortices in superconductors can provide important insight into the effects of disorder because their size is comparable to characteristic sizes of nanofabricated structures. Here we present experimental evidence for a novel form of vortex matter that consists of inter-connected nanodroplets of vortex liquid caged in the pores of a solid vortex structure, like a liquid permeated into a nanoporous solid skeleton. Our nanoporous skeleton is formed by vortices pinned by correlated disorder created by high-energy heavy ion irradiation. By sweeping the applied magnetic field, the number of vortices in the nanodroplets is varied continuously from a few to several hundred. Upon cooling, the caged nanodroplets freeze into ordered nanocrystals through either a first-order or a continuous transition, whereas at high temperatures a uniform liquid phase is formed upon delocalization-induced melting of the solid skeleton. This new vortex nanoliquid displays unique properties and symmetries that are distinct from both solid and liquid phases.     

Multiple changes of order of the vortex melting transition in Bi2Sr2CaCu2O8 with dilute columnar defects

A low concentration of columnar defects is reported to transform a first-order vortex lattice melting line in Bi2Sr2CaCu2O8 crystals into alternating segments of first- and second-order transitions separated by two critical points. As the density of columnar defects is increased, the critical points shift apart and the range of the intermediate second-order transition expands. The measurement of equilibrium magnetization and the mapping of the melting line down to 27 K was made possible by employment of the shaking technique.