A new characterization of the center of a polytope

The main contribution of this work is the introduction of a new function which has the analytic center of a polytope as its maximizer. At the function's optimal point, it assumes a value equal to m, the total number of constraints used to define the polytope. For this reason we call it the m-function of the polytope. We also prove that given a p-dimensional face of a nondegenerate polytope the m-function for that polytope assumes the value m-(n-p) at the analytic center of the face. In particular the m-function assumes the value m at the analytic center of the polytope.16318520

A Sparse Stress Model

Force-directed layout methods constitute the most common approach to draw general graphs. Among them, stress minimization produces layouts of comparatively high quality but also imposes comparatively high computational demands. We propose a speed-up method based on the aggregation of terms in the objective function. It is akin to aggregate repulsion from far-away nodes during spring embedding but transfers the idea from the layout space into a preprocessing phase. An initial experimental study informs a method to select representatives, and subsequent more extensive experiments indicate that our method yields better approximations of minimum-stress layouts in less time than related methods.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Determination of an optimal dosing regimen for aspirin chemoprevention of 1,2-dimethylhydrazine-induced colon tumours in rats

In order to establish an optimal timing and duration of aspirin treatment in the chemoprevention of 1,2-dimethylhydrazine (DMH)-induced colon cancer in rats, colon tumours were induced using an established protocol and aspirin was given in the diet at 500 p.p.m. during various stages of colon carcinogenesis. Results indicate that only aspirin treatment throughout the entire carcinogenic period significantly reduced tumour incidence and volume whereas intermittent aspirin dosing increased tumour number and/or volume, suggesting that aspirin must be used for an extended period in order to gain any chemopreventive benefit. © 1999 Cancer Research Campaig

Intermediate phases during solid to liquid transitions in long-chain n-alkanes

© the Owner Societies 2017. The solid to liquid phase transition of n-alkanes with more than ten carbon atoms is an interesting phenomenon relevant to many fields, from cosmetics to automotive. Here we report Raman spectroscopy of tetradecane, pentadecane and hexadecane as a function of temperature. In order to gain information on the structural changes that the hydrocarbons undergo during melting, and to determine the temperature and the speed at which the phase change occurs, their temperature-dependent Raman spectra are acquired. The spectra are analysed not only with respect to frequency shifts, band widths, and intensity ratio of certain bands, but also using a principal component analysis. The spectroscopic data suggest that the solid to liquid phase transition in hexadecane, differently from tetradecane and pentadecane, is almost instantaneous. Tetradecane shows a slightly faster transition than pentadecane. In addition, a rotator phase as an intermediate state between the liquid and crystalline solid phases is identified in pentadecane. Different characteristic features in the solid spectra of the hydrocarbons relate tetradecane and hexadecane to a tryclinic crystalline structure, and pentadecane to an orthorhombic structure

Survivin expression in in situ and invasive breast cancer relates to COX-2 expression and DCIS recurrence

In lung cancer cyclooxygenase-2 (COX-2) expression has been reported to stabilise survivin, an inhibitor of apoptosis (IAP) which prevents cell death by blocking activated caspases. COX-2 expression limits the ubiquitination of survivin, protecting it from degradation. To determine if COX-2 expression in breast cancer showed an association with survivin expression, we assessed the levels of each protein in ductal carcinoma in situ (DCIS) and invasive breast cancer (IBC); relating expression patterns to recurrence of DCIS after surgery. Patterns of COX-2 and survivin expression were determined by intensity-graded immunohistochemistry of the primary tumours. Patients with DCIS (n=161) which had either recurred (n=47) or shown no evidence of recurrence (n=114) 5 years following primary surgery were studied. These were compared to 58 cases of IBC. Survivin was expressed in the cytoplasm of 59% of DCIS and 17% of IBC. High levels of both cytoplasmic survivin and COX-2 expression significantly correlated to DCIS recurrence. COX-2 expression was present in 72% of DCIS, and levels of expression positively correlated with cytoplasmic survivin expression in DCIS and invasive disease. The majority of DCIS that recurred expressed both proteins (69%) vs 39% nonrecurrent. Recurrence was not seen in DCIS lacking both proteins at 5 years (P=0.001). Expression of the IAP survivin is increased in DCIS and correlates closely with COX-2 expression. Increased expression of IAP, (leading to reduced apoptosis) may explain the effect of COX-2 in increasing recurrence of DCIS after surgical treatment

The dynamical evolution of molecular clouds near the Galactic Centre - II. Spatial structure and kinematics of simulated clouds

The evolution of molecular clouds in galactic centres is thought to differ from that in galactic discs due to a significant influence of the external gravitational potential. We present a set of numerical simulations of molecular clouds orbiting on the 100-pc stream of the Central Molecular Zone (the central $\sim500$ pc of the Galaxy) and characterise their morphological and kinematic evolution in response to the background potential and eccentric orbital motion. We find that the clouds are shaped by strong shear and torques, by tidal and geometric deformation, and by their passage through the orbital pericentre. Within our simulations, these mechanisms control cloud sizes, aspect ratios, position angles, filamentary structure, column densities, velocity dispersions, line-of-sight velocity gradients, spin angular momenta, and kinematic complexity. By comparing these predictions to observations of clouds on the Galactic Centre 'dust ridge', we find that our simulations naturally reproduce a broad range of key observed morphological and kinematic features, which can be explained in terms of well-understood physical mechanisms. We argue that the accretion of gas clouds onto the central regions of galaxies, where the rotation curve turns over and the tidal field is fully compressive, is accompanied by transformative dynamical changes to the clouds, leading to collapse and star formation. This can generate an evolutionary progression of cloud collapse with a common starting point, which either marks the time of accretion onto the tidally-compressive region or of the most recent pericentre passage. Together, these processes may naturally produce the synchronised starbursts observed in numerous (extra)galactic nuclei

Opening a new window to other worlds with spectropolarimetry

A high level of diversity has already been observed among the planets of our own Solar System. As such, one expects extrasolar planets to present a wide range of distinctive features, therefore the characterisation of Earth- and super Earth-like planets is becoming of key importance in scientific research. The SEARCH (Spectropolarimetric Exoplanet AtmospheRe CHaracerisation) mission proposal of this paper represents one possible approach to realising these objectives. The mission goals of SEARCH include the detailed characterisation of a wide variety of exoplanets, ranging from terrestrial planets to gas giants. More specifically, SEARCH will determine atmospheric properties such as cloud coverage, surface pressure and atmospheric composition, and may also be capable of identifying basic surface features. To resolve a planet with a semi major axis of down to 1.4AU and 30pc distant SEARCH will have a mirror system consisting of two segments, with elliptical rim, cut out of a parabolic mirror. This will yield an effective diameter of 9 meters along one axis. A phase mask coronagraph along with an integral spectrograph will be used to overcome the contrast ratio of star to planet light. Such a mission would provide invaluable data on the diversity present in extrasolar planetary systems and much more could be learned from the similarities and differences compared to our own Solar System. This would allow our theories of planetary formation, atmospheric accretion and evolution to be tested, and our understanding of regions such as the outer limit of the Habitable Zone to be further improved.Comment: 23 pages, accepted for publication in Experimental Astronom