A5002343159- Limits and Structures in Graph Theory
- Advanced Graph Theory Research
- Astro and Planetary Science
- Graph theory and applications
- Graph Labeling and Dimension Problems
- Planetary Science and Exploration
- graph theory and CDMA systems
- Stellar, planetary, and galactic studies
- Advanced Topology and Set Theory
- Computability, Logic, AI Algorithms
- Isotope Analysis in Ecology
- Point processes and geometric inequalities
- Structural Analysis of Composite Materials
- History and Theory of Mathematics
- Caching and Content Delivery
- Space Exploration and Technology
- Atmospheric Ozone and Climate
- Digital Image Processing Techniques
- Astronomical Observations and Instrumentation
- Recommender Systems and Techniques
- Cellular Automata and Applications
- Geographic Information Systems Studies
- Traffic control and management
- Historical Astronomy and Related Studies
- Topological and Geometric Data Analysis
University College London
2008-2022
Royal Astronomical Society
2011-2022
Digital Research Alliance of Canada
2020
Royal Society Te Apārangi
2015-2019
UCL Australia
2006-2012
Royal Hallamshire Hospital
2007
University of Oxford
2002-2004
Langley Research Center
1984
ABSTRACT We present results from a multi-chord Pluto stellar occultation observed on 2015 June 29 New Zealand and Australia. This occurred only two weeks before the NASA Horizons flyby of system serves as useful comparison between ground-based space results. find that Pluto's atmosphere is still expanding, with significant pressure increase 5 ± 2% since 2013 factor almost three 1988. trend rules out, today, an atmospheric collapse associated recession Sun. A central flash, rare occurrence,...
We say that α ∈ [0, 1) is a jump for an integer r ≥ 2 if there exists c (α) > 0 such all ϵ and t 1, any -graph with n (α, ϵ, ) vertices density at least + contains subgraph on of . The Erdős–Stone–Simonovits theorem [4, 5] implies = 2, every jump. Erdős [3] showed 3, !/ Moreover he made his famous ‘jumping constant conjecture’, Frankl Rödl [7] disproved this conjecture by giving sequence values non-jumps 3. use Razborov's flag algebra method [9] to show jumps exist 3 in the interval [2/9,...
Disk-integrated photometric data of asteroids do not contain accurate information on shape details or size scale. Additional such as disk-resolved images stellar occultation measurements further constrain asteroid shapes and allow estimates. We aim to use all available about forty obtained by the Near-InfraRed Camera (Nirc2) mounted W.M. Keck II telescope together with disk-integrated photometry determine their volumes. can then volume, in combination known mass, derive bulk density....
Context. Pluto's tenuous nitrogen (N2) atmosphere undergoes strong seasonal effects due to high obliquity and orbital eccentricity, has been recently (July 2015) observed by the New Horizons spacecraft. Goals are (i) construct a well calibrated record of evolution surface pressure on Pluto (ii) constrain structure lower using central flash in 2015. Method: eleven stellar occultations between 2002 2016 used retrieve atmospheric profiles (density, pressure, temperature) $\sim$5 km $\sim$380...
How large can the Lagrangian of an r -graph with m edges be? Frankl and Füredi [1] conjectured that size formed by taking first sets in colex ordering N ( ) has largest all -graphs . We prove ‘interesting’ case this conjecture, namely 3-graph t 3 is [ ] (3) also conjecture true for 3-graphs several other sizes. For general we a weaker result: sufficiently large, supported on + 1 vertices Lagrangian, ]( ).
Cryptography plays a crucial role in many aspects of today's world, from internet banking and ecommerce to email web-based business processes. Understanding the principles on which it is based an important topic that requires knowledge both computational complexity range topics pure mathematics. This book provides knowledge, combining informal style with rigorous proofs key results give accessible introduction. It comes plenty examples exercises (many hints solutions), highly successful...
Occultations of stars by asteroids have been observed since 1961, increasing from a very small number to now over 500 annually. We created and regularly maintain growing data-set more than 5,000 asteroidal occultations. The includes: the raw observations; astrometry at 1 mas level based on centre mass or figure (not illumination); where possible asteroid's diameter 5 km better, fits shape models; separation diameters satellites; double star discoveries with typical separations being in tens...
A set ⊆ {1,2,…,n} is said to be k-separated if, when considered on the circle, any two elements of are separated by a gap size at least k. conjecture due Holroyd and Johnson that an analogue Erdős–Ko–Rado theorem holds for sets proved. In particular, result vertex-critical subgraph Kneser graph identified Schrijver, collection sets. version weighted also given.
If $\mathcal{F}$ is a family of graphs then the Turán density determined by minimum chromatic number members $\mathcal{F}$.The situation for densities 3-graphs far more complex and still very unclear. Our aim in this paper to present new exact individual finite families $3$-graphs, many cases we are also able give corresponding stability results. As well as providing examples $3$-graphs with equal $2/9,4/9,5/9$ $3/4$ irrational 3-graphs, disproving conjecture Chung Graham. (Pikhurko has...
Context. In 2009, the Sun and Earth passed through equatorial plane of Jupiter therefore orbital planes its main satellites. It was equinox on Jupiter. This occurrence made mutual occultations eclipses between satellites possible. Experience has shown that observations such events provide accurate astrometric data able to bring new information dynamics Galilean Observations are under form photometric measurements, but need be organization a worldwide observation campaign maximizing number...
We prove a vertex domination conjecture of Erdös, Faudree, Gould, Gyárfás, Rousseau, and Schelp that for every $n$-vertex complete graph with edges colored using three colors there exists set at most vertices which have least 2n/3 neighbors in one the colors. Our proof makes extensive use ideas presented [D. Král' et al., A new bound 2/3 conjecture, Combin. Probab. Comput. 22 (2013), pp. 384--393].
We consider a new type of extremal hypergraph problem: given an r-graph F and integer k≥2 determine the maximum number edges in F-free, k-colourable on n vertices. Our motivation for studying such problems is that it allows us to give upper bound old Turán problem. show 3-graph which any four points span at most two has density less than 0.32975<13−1280, improving previous bounds 13 due de Caen [D. Caen, Extension theorem Moon Moser complete subgraphs, Ars Combin. 16 (1983) 5–10],...
Fix integers $t \ge r 2$ and an $r$-uniform hypergraph $F$. We prove that the maximum number of edges in a $t$-partite on $n$ vertices contains no copy $F$ is $c_{t, F}{n \choose r} +o(n^r)$, where F}$ can be determined by finite computation. explicitly define sequence $F_1, F_2, \ldots$ hypergraphs, $t$-chromatic containing $F_i$ $\alpha_{t,r,i}{n $\alpha_{t,r,i}$ computation for each $i\ge 1$. In several cases, irrational. The main tool used proofs Lagrangian hypergraph.
Action anticipation, intent prediction, and proactive behavior are all desirable characteristics for autonomous driving policies in interactive scenarios. Paramount, however, is ensuring safety on the road --- a key challenge doing so accounting uncertainty human driver actions without unduly impacting planner performance. This paper introduces minimally-interventional controller operating within an vehicle control stack with role of collision-free interaction externally controlled (e.g.,...
We determine the minimal density of triangles in a tripartite graph with prescribed edge densities. This extends previous result Bondy, Shen, Thomass\'e and Thomassen characterizing those densities guaranteeing existence triangle graph. To be precise we show that suitably weighted copy formed by deleting certain 9-cycle from $K_{3,3,3}$ has among all graphs