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Peer reviewedPublisher PD

Moving Walkways, Escalators, and Elevators

We study a simple geometric model of transportation facility that consists of two points between which the travel speed is high. This elementary definition can model shuttle services, tunnels, bridges, teleportation devices, escalators or moving walkways. The travel time between a pair of points is defined as a time distance, in such a way that a customer uses the transportation facility only if it is helpful. We give algorithms for finding the optimal location of such a transportation facility, where optimality is defined with respect to the maximum travel time between two points in a given set.Comment: 16 pages. Presented at XII Encuentros de Geometria Computacional, Valladolid, Spai

Colorful Strips

Given a planar point set and an integer $k$, we wish to color the points with $k$ colors so that any axis-aligned strip containing enough points contains all colors. The goal is to bound the necessary size of such a strip, as a function of $k$. We show that if the strip size is at least $2k{-}1$, such a coloring can always be found. We prove that the size of the strip is also bounded in any fixed number of dimensions. In contrast to the planar case, we show that deciding whether a 3D point set can be 2-colored so that any strip containing at least three points contains both colors is NP-complete. We also consider the problem of coloring a given set of axis-aligned strips, so that any sufficiently covered point in the plane is covered by $k$ colors. We show that in $d$ dimensions the required coverage is at most $d(k{-}1)+1$. Lower bounds are given for the two problems. This complements recent impossibility results on decomposition of strip coverings with arbitrary orientations. Finally, we study a variant where strips are replaced by wedges

Asymmetric trehalose analogues to probe disaccharide processing pathways in mycobacteria

The uptake and metabolism of the disaccharide trehalose by Mycobacterium tuberculosis is essential for the virulence of this pathogen. Here we describe the chemoenzymatic synthesis of new azido-functionalised asymmetric trehalose probes that resist degradation by mycobacterial enzymes and are used to probe trehalose processing pathways in mycobacteria

N-Alkylation and Aminohydroxylation of 2-Azidobenzenesulfonamide gives a Pyrrolobenzothiadiazepine precursor whereas attempted N-Alkylation of 2-Azidobenzamide gives Benzotriazinones and Quinazolinones

N-Alkylation of 2-azidobenzenesulfonamide with 5-bromopent-1-ene gave an N-pentenyl sulfonamide which underwent intramolecular aminohydroxylation to give an N-(2-azidoaryl)sulfonyl prolinol, a precursor for the synthesis of a pyrrolobenzothiadiazepine. The attempted N-alkylation of 2-azidobenzamide gave a separable mixture (~1:1) of a benzotriazinone and a quinazolinone in 72% combined yield. Other primary alkyl halides (3 examples) gave similar mixtures of benzotriazinones and quinazolinones. Benzylic, allylic, secondary and tertiary alkyl halides (5 examples) gave only the benzotriazinones in moderate yields. The results of mechanistic studies show the likely involvement of nitrene intermediates in the quinazolinone pathway and a second pathway involving a DMSO or dimethylsulfide mediated conversion of 2-azidobenzamide into the benzotriazinones

Dimeric benzoboroxoles for targeted activity against Mycobacterium tuberculosis

Dimeric benzoboroxoles that are covalently linked by a short scaffold enhance selective anti-tubercular activity. These multimeric benzoboroxole compounds are capable of engaging the specific extracellular Mycobacterium tuberculosis glycans, do not lead to the evolution of resistance and bypass the need to cross the impermeable mycobacterial cell envelope barrier

Roles for Condensin in C. elegans Chromosome Dynamics.

Condensin complexes are essential for higher order organization of chromosome structure. Higher eukaryotes have two condensins (condensin I and II) dedicated to mitotic and meiotic chromosome dynamics. C. elegans was thought to be an anomaly, with only a single mitotic condensin (condensin II), and one specialized for dosage compensation (condensin IDC). Condensin IDC binds both hermaphrodite X chromosomes to reduce gene expression by half, equalizing X-linked gene product in males (XO) and hermaphrodites (XX), while condensin II is essential for efficient chromosome organization and segregation during mitosis and meiosis. It was proposed that the unusual holocentric chromosomes in C. elegans did not require condensin I and II to accomplish cell division, and therefore, condensin I was customized for X chromosome regulation. However, we showed that subunits from condensin IDC and condensin II interact to form a second mitotic/meiotic condensin, the bonafide C. elegans condensin I. Our findings raise C. elegans to a unique status, with three distinct condensins controlling holocentric chromosome dynamics. Condensin I and II have distinct localization patterns on mitotic and meiotic chromosomes, suggesting that their roles in chromosome organization may be distinct. During mitosis, condensin II colocalizes with the centromere while condensin I discontinuously coats chromosomes. Condensin I, but not II, colocalizes with aurora B kinase, AIR-2, and our data suggests that in mitosis, AIR-2 activity is required for the recruitment of condensin I, but not condensin II. In meiosis, condensin II localizes to the sister chromatid core, while condensin I localizes to the interface between homologous chromosomes. Condensin I and AIR-2 colocalize at this interface. Similar to mitosis, in AIR-2 depleted animals undergoing meiosis, condensin II is not affected but condensin I mislocalizes to the interface between sister chromatids, as well as homologous chromosomes. This work indicates that AIR-2 provides important spatial cues for condensin I localization on meiotic chromosomes. The contribution of condensin I to during mitosis and meiosis is not well-defined. A comparative analysis of chromosome organization and mitotic/ meiotic progression between wildtype and condensin I depleted animals will provide a better understanding of condensin I function in chromosome dynamics during cell division.Ph.D.Molecular, Cellular, and Developmental BiologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89697/1/karishms_1.pd

Entropy, Triangulation, and Point Location in Planar Subdivisions

A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More specifically, an algorithm is presented that preprocesses a connected planar subdivision G of size n and a query distribution D to produce a point location data structure for G. The expected number of point-line comparisons performed by this data structure, when the queries are distributed according to D, is H + O(H^{2/3}+1) where H=H(G,D) is a lower bound on the expected number of point-line comparisons performed by any linear decision tree for point location in G under the query distribution D. The preprocessing algorithm runs in O(n log n) time and produces a data structure of size O(n). These results are obtained by creating a Steiner triangulation of G that has near-minimum entropy.Comment: 19 pages, 4 figures, lots of formula

Measurement of the local aortic stiffness by a non-invasive bioelectrical impedance technique

Aortic stiffness measurement is well recognized as an independent predictor of cardiovascular mortality and morbidity. Recently, a simple method has been proposed for the evaluation of the local aortic stiffness (AoStiff) using a non-invasive bioelectrical impedance (BI) technique. This approach relies on a novel interpretation of the arterial stiffness where AoStiff is computed from the measurement of two new BI variables: (1) the local aortic flow resistance (AoRes) exerted by the drag forces onto the flow; (2) the local aortic wall distensibility (AoDist). Herein, we propose to detail and compare these three indices with the reference pulse wave velocity (PWV) measurement and the direct assessment of the aortic drag forces (DF) and distensibility (DS) obtained by the magnetic resonance imaging technique. Our results show a significant correlation between AoStiff and PWV (r = 0.79; P < 0.0001; 120 patients at rest; mean age 44 ± 16 years), and also between AoRes and DF (r = 0.95; P = 0.0011) and between AoDist and DS (r = 0.93; P = 0.0022) on eight patients at rest (mean age 52 ± 19 years). These first results suggest that local aortic stiffness can be explored reliably by the BI technique