Search results for "algorithm."
showing 10 items of 4617 documents
On the problem of visualizing point distributions in high dimensional spaces
1995
Abstract Exploring dynamical systems with the aid of computer graphics requires that the relevant structures can be seen and be noticed. This poses special problems if the system is multidimensional, and it has to be decided which kind of projection serves the purpose. I propose using the mathematical frame of categories and functors to describe the process of visualization. This allows detecting and analyzing possible sources of misinterpretation in a formal way. The distribution of distances of embedded electroencephalographic data from a fixed reference point is used as an example for discussing some aspects of the visualization process. The multidimensional p-norms are an example of a p…
Text Compression Using Antidictionaries
1999
International audience; We give a new text compression scheme based on Forbidden Words ("antidictionary"). We prove that our algorithms attain the entropy for balanced binary sources. They run in linear time. Moreover, one of the main advantages of this approach is that it produces very fast decompressors. A second advantage is a synchronization property that is helpful to search compressed data and allows parallel compression. Our algorithms can also be presented as "compilers" that create compressors dedicated to any previously fixed source. The techniques used in this paper are from Information Theory and Finite Automata.
Asymmetric Comparison and Querying of Biological Networks
2011
Comparing and querying the protein-protein interaction (PPI) networks of different organisms is important to infer knowledge about conservation across species. Known methods that perform these tasks operate symmetrically, i.e., they do not assign a distinct role to the input PPI networks. However, in most cases, the input networks are indeed distinguishable on the basis of how the corresponding organism is biologically well characterized. In this paper a new idea is developed, that is, to exploit differences in the characterization of organisms at hand in order to devise methods for comparing their PPI networks. We use the PPI network (called Master) of the best characterized organism as a …
Shrinking language models by robust approximation
2002
We study the problem of reducing the size of a language model while preserving recognition performance (accuracy and speed). A successful approach has been to represent language models by weighted finite-state automata (WFAs). Analogues of classical automata determinization and minimization algorithms then provide a general method to produce smaller but equivalent WFAs. We extend this approach by introducing the notion of approximate determinization. We provide an algorithm that, when applied to language models for the North American Business task, achieves 25-35% size reduction compared to previous techniques, with negligible effects on recognition time and accuracy.
Communication complexity in a 3-computer model
1996
It is proved that the probabilistic communication complexity of the identity function in a 3-computer model isO(√n).
Building Construction Sets by Tiling Grammar Simplification
2016
This paper poses the problem of fabricating physical construction sets from example geometry: A construction set provides a small number of different types of building blocks from which the example model as well as many similar variants can be reassembled. This process is formalized by tiling grammars. Our core contribution is an approach for simplifying tiling grammars such that we obtain physically manufacturable building blocks of controllable granularity while retaining variability, i.e., the ability to construct many different, related shapes. Simplification is performed by sequences of two types of elementary operations: non-local joint edge collapses in the tile graphs reduce the gra…
Kolmogorov superposition theorem for image compression
2012
International audience; The authors present a novel approach for image compression based on an unconventional representation of images. The proposed approach is different from most of the existing techniques in the literature because the compression is not directly performed on the image pixels, but is rather applied to an equivalent monovariate representation of the wavelet-transformed image. More precisely, the authors have considered an adaptation of Kolmogorov superposition theorem proposed by Igelnik and known as the Kolmogorov spline network (KSN), in which the image is approximated by sums and compositions of specific monovariate functions. Using this representation, the authors trad…
Algorithmics for the Life Sciences
2013
The life sciences, in particular molecular biology and medicine, have wit- nessed fundamental progress since the discovery of the “the Double Helix”. A rele- vant part of such an incredible advancement in knowledge has been possible thanks to synergies with the mathematical sciences, on the one hand, and computer science, on the other. Here we review some of the most relevant aspects of this cooperation focusing on contributions given by the design, analysis and engineering of fast al- gorithms for the life sciences.
Parallel Collision Queries on the GPU
2013
We present parallel algorithms to accelerate collision tests of rigid body objects for a high number of independent transformations as they occur in sampling-based motion planning and path validation problems. We compare various GPU approaches with a different level of parallelism against each other and against a parallel CPU implementation. Our algorithms require no sophisticated load balancing schemes. They make no assumption on the distribution of the input transformations and require no pre-processing. Yet, we can perform up to 1 million collision tests per second with our best GPU implementation in our benchmarks. This is about 2.5X faster than our reference multi-core CPU implementati…
A simple algorithm for drawing large graphs on small screens
1995
Viewing a large graph in limited display space has traditionally been accomplished using either reduced scale rendering of the graph or by attaching scrollbars to a view window which shows only a small portion of the entire graph. Recent work, however, has concentrated on integrating a locally detailed view with a globally scaled view. We present an algorithm for constructing a view which smoothly integrates local detail and global context in a single view window and describe user interaction with such a display.