On Globally Deterministic CD-Systems of Stateless R-Automata with Window Size One

It is known that cooperating distributed systems (CD-systems) of stateless deterministic restarting automata with window size 1 accept a class of semi-linear languages that properly includes all rational trace languages. Although the component automata of such a CD-system are all deterministic, in general the CD-system itself is not, as in each of its computations, the initial component and the successor components are still chosen nondeterministically. Here we study CD-systems of stateless deterministic restarting automata with window size 1 that are themselves completely deterministic. In fact, we consider two such types of CD-systems, the strictly deterministic systems and the globally deterministic systems.

Hyperbolic Geometry

Exercises, exam questions and solutions for a fourth year hyperbolic geometry course. Diagrams for the questions are all together in the support.zip file, as .eps files

Branching random motions, nonlinear hyperbolic systems and traveling waves

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) have a so-called McKean representation via such processes. Commonly this system possesses traveling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed.This Paper realizes the McKean programme for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.

Breeding distribution and population decline of globally threatened Grey-necked Picathartes Picathartes oreas in Mbam Minkom Mountain Forest, southern Cameroon

The Grey-necked Picathartes Picathartes oreas, considered 'Vulnerable', is an enigmatic ground-dwelling bird endemic to the central African equatorial rainforest and belongs to a family of only two species. Its distribution extends to the two Endemic Bird Areas within Cameroon (Guinea Congo forest biome and Cameroon mountain arc) and its population is thought to be in decline throughout its range due to increasing habitat fragmentation and disturbance. During March-April 2003 and June and October 2007 we surveyed Grey-necked Picathartes in the north-western region of the Mbam Minkom Mountain Forest. In January-March 2006 we surveyed the entire mountain range and found go breeding and 24 potential breeding sites, mostly located on the western slopes. From the complete survey, we estimated the population at 44 breeding individuals. Populations were highest in the north-west region but had apparently declined from 40 breeding individuals in 2003 to 20 in 2007. This region accounted for 41% of the entire population on the mountain range during the 2006 survey. The Mbam Minkom/Kala Important Bird Area was designated based on the presence of Grey-necked Picathartes but is under high pressure of imminent destruction from agricultural encroachment and illegal timber exploitation. These results have important implications for decision making in delimiting forest boundaries and core areas for protection in the development of management plans. We suggest possible remedial actions, appropriate repeatable methods for future monitoring and opportunities for community involvement in the management and conservation of the site.

MetUM-GOML: a near-globally coupled atmosphere–ocean-mixed-layer model

Well-resolved air–sea interactions are simulated in a new ocean mixed-layer, coupled configuration of the Met Office Unified Model (MetUM-GOML), comprising the MetUM coupled to the Multi-Column K Profile Parameterization ocean (MC-KPP). This is the first globally coupled system which provides a vertically resolved, high near-surface resolution ocean at comparable computational cost to running in atmosphere-only mode. As well as being computationally inexpensive, this modelling framework is adaptable– the independent MC-KPP columns can be applied selectively in space and time – and controllable – by using temperature and salinity corrections the model can be constrained to any ocean state. The framework provides a powerful research tool for process-based studies of the impact of air–sea interactions in the global climate system. MetUM simulations have been performed which separate the impact of introducing inter- annual variability in sea surface temperatures (SSTs) from the impact of having atmosphere–ocean feedbacks. The representation of key aspects of tropical and extratropical variability are used to assess the performance of these simulations. Coupling the MetUM to MC-KPP is shown, for example, to reduce tropical precipitation biases, improve the propagation of, and spectral power associated with, the Madden–Julian Oscillation and produce closer-to-observed patterns of springtime blocking activity over the Euro-Atlantic region.