Hans Sagan

Bio: Hans Sagan is an academic researcher. The author has contributed to research in topics: Peano curve & Space-filling curve. The author has an hindex of 1, co-authored 1 publications receiving 1247 citations.

Space-filling curves

Abstract: The subject of space-filling curves has generated a great deal of interest in the 100 years since the first such curve was discovered by Peano. Cantor, Hilbert, Moore, Knopp, Lebesgue and Polya are among the prominent mathematicians who have contributed to the field. However, there have been no comprehensive treatment of the subject since Siepinsky's in 1912. Cantor showed in 1878 that the number of points on an interval is the same as the number of points in a square, while in 1890 Peano showed that there is indeed a continuous curve that maps all points of a line onto all points of a square, although the curve exists only as a limit of very convoluted curves. This book discusses generalizations of Peano's solution and the properties that such curves must possess. It also discusses fractals in this context.

Multidimensional access methods

Abstract: Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that overlap a given search region). More than ten years of spatial database research have resulted in a great variety of multidimensional access methods to support such operations. We give an overview of that work. After a brief survey of spatial data management in general, we first present the class of point access methods, which are used to search sets of points in two or more dimensions. The second part of the paper is devoted to spatial access methods to handle extended objects, such as rectangles or polyhedra. We conclude with a discussion of theoretical and experimental results concerning the relative performance of various approaches.

Joint mobility and routing for lifetime elongation in wireless sensor networks

Abstract: Although many energy efficient/conserving routing protocols have been proposed for wireless sensor networks, the concentration of data traffic towards a small number of base stations remains a major threat to the network lifetime. The main reason is that the sensor nodes located near a base station have to relay data for a large part of the network and thus deplete their batteries very quickly. The solution we propose in this paper suggests that the base station be mobile; in this way, the nodes located close to it change over time. Data collection protocols can then be optimized by taking both base station mobility and multi-hop routing into account. We first study the former, and conclude that the best mobility strategy consists in following the periphery of the network (we assume that the sensors are deployed within a circle). We then consider jointly mobility and routing algorithms in this case, and show that a better routing strategy uses a combination of round routes and short paths. We provide a detailed analytical model for each of our statements, and corroborate it with simulation results. We show that the obtained improvement in terms of network lifetime is in the order of 500%.

Searching in high-dimensional spaces: Index structures for improving the performance of multimedia databases

Abstract: During the last decade, multimedia databases have become increasingly important in many application areas such as medicine, CAD, geography, and molecular biology. An important research issue in the field of multimedia databases is the content-based retrieval of similar multimedia objects such as images, text, and videos. However, in contrast to searching data in a relational database, a content-based retrieval requires the search of similar objects as a basic functionality of the database system. Most of the approaches addressing similarity search use a so-called feature transformation that transforms important properties of the multimedia objects into high-dimensional points (feature vectors). Thus, the similarity search is transformed into a search of points in the feature space that are close to a given query point in the high-dimensional feature space. Query processing in high-dimensional spaces has therefore been a very active research area over the last few years. A number of new index structures and algorithms have been proposed. It has been shown that the new index structures considerably improve the performance in querying large multimedia databases. Based on recent tutorials [Berchtold and Keim 1998], in this survey we provide an overview of the current state of the art in querying multimedia databases, describing the index structures and algorithms for an efficient query processing in high-dimensional spaces. We identify the problems of processing queries in high-dimensional space, and we provide an overview of the proposed approaches to overcome these problems.

Fractal design concepts for stretchable electronics

Abstract: Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.