Computing multi-scale organizations built through assembly

The ability to generate and control assembling structures built over many orders of magnitude is an unsolved challenge of engineering and science. Many of the presumed transformational benefits of nanotechnology and robotics are based directly on this capability. There are still significant theoretical difficulties associated with building such systems, though technology is rapidly ensuring that the tools needed are becoming available in chemical, electronic, and robotic domains. In this thesis a simulated, general-purpose computational prototype is developed which is capable of unlimited assembly and controlled by external input, as well as an additional prototype which, in structures, can emulate any other computing device. These devices are entirely finite-state and distributed in operation. Because of these properties and the unique ability to form unlimited size structures of unlimited computational power, the prototypes represent a novel and useful blueprint on which to base scalable assembly in other domains. A new assembling model of Computational Organization and Regulation over Assembly Levels (CORAL) is also introduced, providing the necessary framework for this investigation. The strict constraints of the CORAL model allow only an assembling unit of a single type, distributed control, and ensure that units cannot be reprogrammed - all reprogramming is done via assembly. Multiple units are instead structured into aggregate computational devices using a procedural or developmental approach. Well-defined comparison of computational power between levels of organization is ensured by the structure of the model. By eliminating ambiguity, the CORAL model provides a pragmatic answer to open questions regarding a framework for hierarchical organization. Finally, a comparison between the designed prototypes and units evolved using evolutionary algorithms is presented as a platform for further research into novel scalable assembly. Evolved units are capable of recursive pairing ability under the control of a signal, a primitive form of unlimited assembly, and do so via symmetry-breaking operations at each step. Heuristic evidence for a required minimal threshold of complexity is provided by the results, and challenges and limitations of the approach are identified for future evolutionary studies

Huge networks, tiny faulty nodes

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 87-91).Can one build, and efficiently use, networks of arbitrary size and topology using a "standard" node whose resources, in terms of memory and reliability, do not need to scale up with the complexity and size of the network? This thesis addresses two important aspects of this question. The first is whether one can achieve efficient connectivity despite the presence of a constant probability of faults per node/link. Efficient connectivity means (informally) having every pair of regions connected by a constant fraction of the independent, entirely non-faulty paths that would be present if the entire network were fault free - even at distances where each path has only a vanishingly small probability of being fault-free. The answer is yes, as long as some very mild topological conditions on the high level structure of the network are met - informally, if the network is not too "thin" and if it does not contain too many large "holes". The results go against some established "empyrical wisdom" in the networking community. The second issue addressed by this thesis is whether one can route efficiently on a network of arbitrary size and topology using only a constant number c of bits/node (even if c is less than the logarithm of the network's size!). Routing efficiently means (informally) that message delivery should only stretch the delivery path by a constant factor. The answer again is yes, as long as the volume of the network grows only polynomially with its radius (otherwise, we run into established lower bounds). This effectively captures every network one may build in a universe (like our own) with finite dimensionality using links of a fixed, maximum length and nodes with a fixed, minimum volume. The results extend the current results for compact routing, allowing one to route efficiently on a much larger class of networks than had previously been known, with many fewer bits.by Enoch Peserico.Ph.D

Measuring and improving the readability of network visualizations

Network data structures have been used extensively for modeling entities and their ties across such diverse disciplines as Computer Science, Sociology, Bioinformatics, Urban Planning, and Archeology. Analyzing networks involves understanding the complex relationships between entities as well as any attributes, statistics, or groupings associated with them. The widely used node-link visualization excels at showing the topology, attributes, and groupings simultaneously. However, many existing node-link visualizations are difficult to extract meaning from because of (1) the inherent complexity of the relationships, (2) the number of items designers try to render in limited screen space, and (3) for every network there are many potential unintelligible or even misleading visualizations. Automated layout algorithms have helped, but frequently generate ineffective visualizations even when used by expert analysts. Past work, including my own described herein, have shown there can be vast improvements in network visualizations, but no one can yet produce readable and meaningful visualizations for all networks. Since there is no single way to visualize all networks effectively, in this dissertation I investigate three complimentary strategies. First, I introduce a technique called motif simplification that leverages the repeating patterns or motifs in a network to reduce visual complexity. I replace common, high-payoff motifs with easily understandable glyphs that require less screen space, can reveal otherwise hidden relationships, and improve user performance on many network analysis tasks. Next, I present new Group-in-a-Box layouts that subdivide large, dense networks using attribute- or topology-based groupings. These layouts take group membership into account to more clearly show the ties within groups as well as the aggregate relationships between groups. Finally, I develop a set of readability metrics to measure visualization effectiveness and localize areas needing improvement. I detail optimization recommendations for specific user tasks, in addition to leveraging the readability metrics in a user-assisted layout optimization technique. This dissertation contributes an understanding of why some node-link visualizations are difficult to read, what measures of readability could help guide designers and users, and several promising strategies for improving readability which demonstrate that progress is possible. This work also opens several avenues of research, both technical and in user education

Fractal analyses of some natural systems

Fractal dimensions are estimated by the box-counting method for real world data sets and for mathematical models of three natural systems. 1 he natural systems are nearshore sea wave profiles, the topography of Shei-pa National Park in Taiwan, and the normalised difference vegetation index (NDV1) image of a fresh fern. I he mathematical models which represent the natural systems utilise multi-frequency sinusoids for the sea waves, a synthetic digital elevation model constructed by the mid-point displacement method for the topography and the Iterated Function System (IFS) codes for the fern leaf. The results show that similar fractal dimensions are obtained for discrete sub-sections of the real and synthetic one-dimensional wave data, whilst different fractal dimensions are obtained for discrete sections of the real and synthetic topographical and fern data. The similarities and differences are interpreted in the context of system evolution which was introduced by Mandelbrot (1977). Finally, the results for the fern images show that use of fractal dimensions can successfully separate void and filled elements of the two-dimensional series

Explorative Graph Visualization

Netzwerkstrukturen (Graphen) sind heutzutage weit verbreitet. Ihre Untersuchung dient dazu, ein besseres Verständnis ihrer Struktur und der durch sie modellierten realen Aspekte zu gewinnen. Die Exploration solcher Netzwerke wird zumeist mit Visualisierungstechniken unterstützt. Ziel dieser Arbeit ist es, einen Überblick über die Probleme dieser Visualisierungen zu geben und konkrete Lösungsansätze aufzuzeigen. Dabei werden neue Visualisierungstechniken eingeführt, um den Nutzen der geführten Diskussion für die explorative Graphvisualisierung am konkreten Beispiel zu belegen.Network structures (graphs) have become a natural part of everyday life and their analysis helps to gain an understanding of their inherent structure and the real-world aspects thereby expressed. The exploration of graphs is largely supported and driven by visual means. The aim of this thesis is to give a comprehensive view on the problems associated with these visual means and to detail concrete solution approaches for them. Concrete visualization techniques are introduced to underline the value of this comprehensive discussion for supporting explorative graph visualization

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

Proceedings of the 1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020)

International audienceOriginating in arithmetics and logic, the theory of ordered sets is now a field of combinatorics that is intimately linked to graph theory, universal algebra and multiple-valued logic, and that has a wide range of classical applications such as formal calculus, classification, decision aid and social choice.This international conference “Algebras, graphs and ordered set” (ALGOS) brings together specialists in the theory of graphs, relational structures and ordered sets, topics that are omnipresent in artificial intelligence and in knowledge discovery, and with concrete applications in biomedical sciences, security, social networks and e-learning systems. One of the goals of this event is to provide a common ground for mathematicians and computer scientists to meet, to present their latest results, and to discuss original applications in related scientific fields. On this basis, we hope for fruitful exchanges that can motivate multidisciplinary projects.The first edition of ALgebras, Graphs and Ordered Sets (ALGOS 2020) has a particular motivation, namely, an opportunity to honour Maurice Pouzet on his 75th birthday! For this reason, we have particularly welcomed submissions in areas related to Maurice’s many scientific interests:• Lattices and ordered sets• Combinatorics and graph theory• Set theory and theory of relations• Universal algebra and multiple valued logic• Applications: formal calculus, knowledge discovery, biomedical sciences, decision aid and social choice, security, social networks, web semantics..