Follow-the-leader Formation Marching Through a Scalable O(log2n) Parallel Architecture.

An important topic in the field of Multi Robot Systems focuses on motion coordination and synchronization for formation keeping. Although several works have addressed such problem, little attention has been devoted to study the computational complexity within the framework of large-scale systems. This paper presents our current work on how to achieve high computational performance for systems composed by a large number of robots that must fulfill with a marching and formation task. A scalable Multi-Processor Parallel Architecture is introduced with the purpose of achieving scalability, i.e., computation time of O(log2n) for a n-robots system. Our architecture has been tested onto a multi-processor system and validated against several simulations testing

The formal generation of models for scientific simulations

It is now commonplace for complex physical systems such as the climate system to be studied indirectly via computer simulations. Often, the equations that govern the underlying physical system are known but detailed or highresolution computer models of these equations (“governing models”) are not practical because of limited computational resources; so the models are simplified or “parameterised”. However, if the output of a simplified model is to lead to conclusions about a physical system, we must prove that these outputs reflect reality and are not merely artifacts of the simplifications. At present, simplifications are usually based on informal, ad-hoc methods making it difficult or impossible to provide such a proof rigorously. Here we introduce a set of formal methods for generating computer models. We present a newly developed computer program, “iGen”, which syntactically analyses the computer code of a high-resolution, governing model and, without executing it, automatically produces a much faster, simplified model with provable bounds on error compared to the governing model. These bounds allow scientists to rigorously distinguish real world phenomena from artifact in subsequent numerical experiments using the simplified model. Using simple physical systems as examples, we illustrate that iGen produces simplified models that execute typically orders of magnitude faster than their governing models. Finally, iGen is used to generate a model of entrainment in marine stratocumulus. The resulting simplified model is appropriate for use as part of a parameterisation of marine stratocumulus in a Global Climate Model

Contributions to computational phylogenetics and algorithmic self-assembly

This dissertation addresses some of the algorithmic and combinatorial problems at the interface between biology and computation. In particular, it focuses on problems in both computational phylogenetics, an area of study in which computation is used to better understand evolutionary relationships, and algorithmic self-assembly, an area of study in which biological processes are used to perform computation. The first set of results investigate inferring phylogenetic trees from multi-state character data. We give a novel characterization of when a set of three-state characters has a perfect phylogeny and make progress on a long-standing conjecture regarding the compatibility of multi-state characters. The next set of results investigate inferring phylogenetic supertrees from collections of smaller input trees when the input trees do not fully agree on the relative positions of the taxa. Two approaches to dealing with such conflicting input trees are considered. The first is to contract a set of edges in the input trees so that the resulting trees have an agreement supertree. The second is to remove a set of taxa from the input trees so that the resulting trees have an agreement supertree. We give fixed-parameter tractable algorithms for both approaches. We then turn to the algorithmic self-assembly of fractal structures from DNA tiles and investigate approximating the Sierpinski triangle and the Sierpinski carpet with strict self-assembly. We prove tight bounds on approximating the Sierpinski triangle and exhibit a class of fractals that are generalizations of the Sierpinski carpet that can approximately self-assemble. We conclude by discussing some ideas for further research

Geostry - a Peer-to-Peer System for Location-based Information

An interesting development is summarized by the notion of ”Ubiquitous Computing”: In this area, miniature systems are integrated into everyday objects making these objects ”smart” and able to communicate. Thereby, everyday objects can gather information about their state and their environment. By embedding this information into a model of the real world, which nowadays can be modeled very realistically using sophisticated 3D modeling techniques, it is possible to generate powerful digital world models. Not only can existing objects of the real world and their state be mapped into these world models, but additional information can be linked to these objects as well. The result is a symbiosis of the real world and digital information spaces. In this thesis, we present a system that allows for an easy access to this information. In contrast to existing solutions our approach is not based on a server-client architecture. Geostry bases on a peer-to-peer system and thus incorporates all the advantages, such as self-organization, fairness (in terms of costs), scalability and many more. Setting up the network is realized through a decentralized bootstrapping protocol based on an existing Internet service to provide robustness and availability. To selectively find geographic-related information Geostry supports spatial queries. They - among other things - enable the user to search for information e.g. in a certain district only. Sometimes, a certain piece of information raises particular interest. To cope with the run on the single computer that provides this specific information, Geostry offers dynamic replication mechanisms. Thereby, the information is replicated for as long as the rush lasts. Thus, Geostry offers all aspects from setting up a network, providing access to geo-related information and replication methods to provide accessibility in times of high loads