Highly Connected Multicoloured Subgraphs of Multicoloured Graphs

Suppose the edges of the complete graph on n vertices, E(Kn), are coloured using r colours; how large a k-connected subgraph are we guaranteed to find, which uses only at most s of the colours? This question is due to Bollobás, and the case s=1 was considered in Liu et al. [Highly connected monochromatic subgraphs of multicoloured graphs, J. Graph Theory, to appear]. Here we shall consider the case s is greater than or equal to 2, proving in particular that when s=2 and r+1 is a power of 2 then the answer lies between 4n/(r+1)-17kr(r+2k+1) and 4n/(r+1)+4 and that phase transitions occur at s=r/2 and when s is of order r^{1/2}. We shall also mention some of the more glaring open problems relating to this question

A Group Theoretical Identification of Integrable Equations in the Li\'enard Type Equation x¨+f(x)x˙+g(x)=0\ddot{x}+f(x)\dot{x}+g(x) = 0 : Part II: Equations having Maximal Lie Point Symmetries

In this second of the set of two papers on Lie symmetry analysis of a class of Li\'enard type equation of the form $\ddot {x} + f(x)\dot {x} + g(x)= 0$, where over dot denotes differentiation with respect to time and $f(x)$ and $g(x)$ are smooth functions of their variables, we isolate the equations which possess maximal Lie point symmetries. It is well known that any second order nonlinear ordinary differential equation which admits eight parameter Lie point symmetries is linearizable to free particle equation through point transformation. As a consequence all the identified equations turn out to be linearizable. We also show that one can get maximal Lie point symmetries for the above Li\'enard equation only when $f_{xx} =0$ (subscript denotes differentiation). In addition, we discuss the linearising transformations and solutions for all the nonlinear equations identified in this paper.Comment: Accepted for publication in Journal of Mathematical Physic

Three New Long Period X-ray Pulsars Discovered in the Small Magellanic Cloud

The Small Magellanic Cloud is increasingly an invaluable laboratory for studying accreting and isolated X-ray pulsars. We add to the class of compact SMC objects by reporting the discovery of three new long period X-ray pulsars detected with the {\it Chandra X-ray Observatory}. The pulsars, with periods of 152, 304 and 565 seconds, all show hard X-ray spectra over the range from 0.6 - 7.5 keV. The source positions of the three pulsars are consistent with known H-alpha emission sources, indicating they are likely to be Be type X-ray binary star systems.Comment: Accepted for publication in the Astrophysical Journa

A Finite Element Computation of the Gravitational Radiation emitted by a Point-like object orbiting a Non-rotating Black Hole

The description of extreme-mass-ratio binary systems in the inspiral phase is a challenging problem in gravitational wave physics with significant relevance for the space interferometer LISA. The main difficulty lies in the evaluation of the effects of the small body's gravitational field on itself. To that end, an accurate computation of the perturbations produced by the small body with respect the background geometry of the large object, a massive black hole, is required. In this paper we present a new computational approach based on Finite Element Methods to solve the master equations describing perturbations of non-rotating black holes due to an orbiting point-like object. The numerical computations are carried out in the time domain by using evolution algorithms for wave-type equations. We show the accuracy of the method by comparing our calculations with previous results in the literature. Finally, we discuss the relevance of this method for achieving accurate descriptions of extreme-mass-ratio binaries.Comment: RevTeX 4. 18 pages, 8 figure

Observable Signatures of EMRI Black Hole Binaries Embedded in Thin Accretion Disks

We examine the electromagnetic (EM) and gravitational wave (GW) signatures of stellar-mass compact objects (COs) spiraling into a supermassive black hole (extreme mass-ratio inspirals or EMRIs), embedded in a thin, radiation-pressure dominated, accretion disk. At large separations, the tidal effect of the secondary CO clears a gap. We show that the gap refills during the late GW-driven phase of the inspiral, leading to a sudden EM brightening of the source. The accretion disk leaves an imprint on the GW through its angular momentum exchange with the binary, the mass increase of the binary members due to accretion, and its gravity. We compute the disk-modified GWs both in an analytical Newtonian approximation and in a numerical effective-one-body approach. We find that disk-induced migration provides the dominant perturbation to the inspiral, with weaker effects from the mass accretion onto the CO and hydrodynamic drag. Depending on whether a gap is present, the perturbation of the GW phase is between 10 and 1000 radians per year, detectable with the future Laser Interferometer Space Antenna (LISA) at high significance. The Fourier transform of the disk-modified GW in the stationary phase approximation is sensitive to disk parameters with a frequency trend different from post-Newtonian vacuum corrections. Our results suggest that observations of EMRIs may place new sensitive constraints on the physics of accretion disks.Comment: 42 pages, 8 figures, 3 tables, submitted to Phys. Rev.

Mapping the spatial distribution and changes of oil palm land cover using an open source cloud-based mapping platform

Oil palm has become well known for its oil palm yields that can be used to produce food, biodiesel and biogas. The rapid expansion of oil palm plantations over large areas has changed the land use and land cover of surroundings. Changes in land covers can be mapped and later used for further analysis. However, obtaining and classifying large coverages require massive amounts of data and computing resources and the skills and time of analysts. The Remote Ecosystem Monitoring Assessment Pipeline (REMAP) provides a cloud computing platform that hosts an open-source stacked Landsat data that allows land cover classification to be implemented using a built-in random forest supervised machine learning algorithm. Classifications were performed with the aid of predictor layers to discriminate the following land covers in Peninsular Malaysia: oil palm, built-up, bare soil, water, forest, other vegetation and paddy. The classification performed on period 1 (1999–2003) and period 2 (2014–2017) data produced an overall accuracy of 80.34% and 79.53% respectively. The analysis of the changes in oil palm distributions from period 1 to period 2 indicated an increment of 23.59%. Further analysis revealed that oil palm expansion in Peninsular Malaysia only minimally affected forested area and is mostly resulted from the conversion of less productive crops to oil palm. Results prove the land cover mapping and change detection capabilities of REMAP as a cloud computing platform for large areas. Despite its limitations, REMAP has the potential to achieve fast-paced mapping over large areas and monitor land changes in oil palm distributions

Mapping the spatial distribution and changes of oil palm land cover using an open source cloud-based mapping platform

Oil palm has become well known for its oil palm yields that can be used to produce food, biodiesel and biogas. The rapid expansion of oil palm plantations over large areas has changed the land use and land cover of surroundings. Changes in land covers can be mapped and later used for further analysis. However, obtaining and classifying large coverages require massive amounts of data and computing resources and the skills and time of analysts. The Remote Ecosystem Monitoring Assessment Pipeline (REMAP) provides a cloud computing platform that hosts an open-source stacked Landsat data that allows land cover classification to be implemented using a built-in random forest supervised machine learning algorithm. Classifications were performed with the aid of predictor layers to discriminate the following land covers in Peninsular Malaysia: oil palm, built-up, bare soil, water, forest, other vegetation and paddy. The classification performed on period 1 (1999–2003) and period 2 (2014–2017) data produced an overall accuracy of 80.34% and 79.53% respectively. The analysis of the changes in oil palm distributions from period 1 to period 2 indicated an increment of 23.59%. Further analysis revealed that oil palm expansion in Peninsular Malaysia only minimally affected forested area and is mostly resulted from the conversion of less productive crops to oil palm. Results prove the land cover mapping and change detection capabilities of REMAP as a cloud computing platform for large areas. Despite its limitations, REMAP has the potential to achieve fast-paced mapping over large areas and monitor land changes in oil palm distributions

The Outbursts and Orbit of the Accreting Pulsar GS 1843-02 = 2S 1845-024

We present observations of a series of 10 outbursts of pulsed hard X-ray flux from the transient 10.6 mHz accreting pulsar GS 1843-02, using the Burst and Transient Source Experiment on the Compton Gamma Ray Observatory. These outbursts occurred regularly every 242 days, coincident with the ephemeris of the periodic transient GRO J1849-03 (Zhang et al. 1996), which has recently been identified with the SAS 3 source 2S 1845-024 (Soffitta et al. 1998). Our pulsed detection provides the first clear identification of GS 1843-02 with 2S 1845-024. We present a pulse timing analysis which shows that the 2S 1845-024 outbursts occur near the periastron passage of the neutron star's highly eccentric (e = 0.88+-0.01) 242.18+-0.01 day period binary orbit about a high mass (M > 7 solar masses) companion. The orbit and transient outburst pattern strongly suggest the pulsar is in a binary system with a Be star. Our observations show a long-term spin-up trend, with most of the spin-up occurring during the outbursts. From the measured spin-up rates and inferred luminosities we conclude that an accretion disk is present during the outbursts.Comment: Accepted for publication in Astrophysical Journa