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On Measures of Non-Integrability of Pfaffian Systems

IFAC Proceedings Volumes 1996年第1期29卷 2132-2137页

作者： Andrzej Banaszuk John Hauser Willem M. Sluis Richard M. Murray Department of Mathematics University of California Davis CA 95616-8633 Department of Electrical and Computer Engineering University of Colorado Boulder CO 80309-0425 Control and Dynamical Systems 104-44 California Institute of Technology Pasadena CA 91125 Division of Engineering and Applied Science California Institute of Technology Pasadena CA 91125

Many problems in nonlinear control theory (like, for instance, feedback linearization problem) leed to examination of integrability of a Pfaffian system. In a generic case a Pfaffian system is not integrable. Therefore, how to approximate non-integrable Pfafian systems by integrable ones and how this approximation can applied in practice appears to be a natural and important problem. In the present paper we establish some measures of non-integrability of Pfaffian system of arbitrary dimension and discuss their relation to approximations of non-integrable Pfaffian systems by integrable ones. Our work is motivated by expected applications to approximate feedback linearization of multi-input nonlinear systems.

关键词： Nonlinear systems differential geometry differential forms Pfaffian systems feedback linearization

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Effect of Nutrient Diffusion and Flow on Coral Morphology

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Physical Review Letters 1996年第11期77卷 2328-2328页

作者： Jaap A. Kaandorp Christopher P. Lowe Daan Frenkel Peter M. A. Sloot Parallel Scientific Computing and Simulation Group Faculty of Mathematics Computer Science Physics & Astronomy University of Amsterdam Kruislaan 403 1098 SJ Amsterdam The Netherlands Computational Physics Faculty of Applied Physics Delft University of Technology Lorentzweg 1 2628 CJ Delft The Netherlands FOM Institute for Atomic and Molecular Physics Kruislaan 407 1098 SJ Amsterdam The Netherlands

We describe a method for modeling aggregation in a flowing fluid. In the model, aggregation proceeds by the accumulation of a “nutrient.” The nutrient is modeled using a lattice Boltzmann model of transport. The aggregate absorbs the nutrient, and the amount absorbed determines the local growth probability. This model contains some of the essential features of growth of stony corals. We find that the morphology of the aggregates changes drastically as we increase the Péclet number from a regime where nutrient transport is diffusion controlled to a regime where hydrodynamic transport dominates. This is in qualitative agreement with the morphogenesis of stony corals.

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An improvement of davies’ attack on DES

An improvement of davies’ attack on DES

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Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1994

作者： Biham, Eli Biryukovt, Alex Computer Science Department Technion - Israel Institute of Technology Haifa32000 Israel Applied Mathematics Department Technion- Israel Institute of Technology Haifa32000 Israel

ISBN: (纸本)3540601767

In this paper we improve Davies’ attack [2] on DES to become capable of breaking the full 16-round DES faster than the exhaustive search. Our attack requires 250 complexity of the data collection and 250 the complexity of analysis. An alternative approach finds 24 key bits of DES with 252 known plaintexts and the data analysis requires only several minutes on a SPARC. Therefore, this is the third successful attack on DES, faster than brute force, after differential cryptanalysis [1] and linear cryptanalysis [5]. We also suggest criteria which make the S-boxes immune to this attack. © Springer-Verlag Berlin Heidelberg 1995.

关键词： Cryptography

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An action system specification of the caltech asynchronous microprocessor 3rd

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3rd International Conference on mathematics of Program Construction, MPC '95

作者： Back, R.J.R. Martin, A.J. Sere, K. Åbo Akademi University Department of Computer Science TurkuFIN-20520 Finland California Institute of Technology Department of Computer Science PasadenaCA91125 United States University of Kuopio Department of Computer Science and Applied Mathematics KuopioFIN-70211 Finland

ISBN: (纸本)3540601171

The action system framework for modelling parallel programs is used to formally specify a microprocessor. First the microprocessor is specified as a sequential program. The sequential specification is then decomposed and refined into a concurrent program using correctness-preserving program transformations. Previously this microprocessor has been specified in a semi-formal manner at Caltech, where an asynchronous circuit for the microprocessor was derived from the specification. We propose a specification strategy that is based on the idea of spatial decomposition of the program variable space. Applying this strategy we give a completely formal derivation of a high level specification for the Caltech microprocessor. We also demonstrate the suitability of action systems and the stepwise refinement paradigm for formal VLSI circuit design. © Springer-Verlag Berlin Heidelberg 1998.

关键词： Specifications

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Information theory and noisy computation

Information theory and noisy computation

引用

IEEE International Symposium on Information Theory

作者： W.S. Evans L.J. Schulman Department of Computer Science University of British Columbia Canada Science College of Computing Technology Department of Applied Mathematics Georgia Institute of Technology USA

We report on two types of results. The first is a study of the rate of decay of information carried by a signal which is being propagated over a noisy channel. The second is a series of lower bounds on the depth, size, and component reliability of noisy logic circuits which are required to compute some function reliably. The arguments used for the circuit results are information-theoretic, and in particular, the signal decay result is essential to the depth lower bound. Our first result can be viewed as a quantified version of the data processing lemma, for the case of Boolean random variables.

关键词： Information theory Circuit noise Logic circuits Boolean functions Mutual information Reliability theory computer science Data processing Random variables Logic gates

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Splitters and near-optimal derandomization

Splitters and near-optimal derandomization

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Annual IEEE Symposium on Foundations of computer Science

作者： M. Naor L.J. Schulman A. Srinivasan Department of Applied Mathematics and Computer Science Weizmann Institute of Science Israel Department of Apllied Mathematics and Computer Science Weizmann Institute of Science Israel Georgia Inst. Technology College of Computing Georgia Institute of Technology Atlanta GA USA Department of Information Systems & Computer Science National University of Singapore Singapore

We present a fairly general method for finding deterministic constructions obeying what we call k-restrictions; this yields structures of size not much larger than the probabilistic bound. The structures constructed by our method include (n,k)-universal sets (a collection of binary vectors of length n such that for any subset of size k of the indices, all 2/sup k/ configurations appear) and families of perfect hash functions. The near-optimal constructions of these objects imply the very efficient derandomization of algorithms in learning, of fixed-subgraph finding algorithms, and of near optimal /spl Sigma/II/spl Sigma/ threshold formulae. In addition, they derandomize the reduction showing the hardness of approximation of set cover. They also yield deterministic constructions for a local-coloring protocol, and for exhaustive testing of circuits.

关键词： computer science Circuit testing mathematics Protocols Engineering profession Information systems Contracts Educational institutions Boosting Parallel algorithms

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Linearity testing in characteristic two

Linearity testing in characteristic two

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Annual IEEE Symposium on Foundations of computer Science

作者： M. Bellare D. Coppersmith J. Hastad M. Kiwi M. Sudan Department of Computer Science & Engineering University of California San Diego La Jolla CA USA Research Division IBM Thomas J. Watson Research Center Yorktown Heights NY USA Department of Computer Science Royal Institute of Technology Stockholm Sweden Department of Applied Mathematics Massachusetts Institute of Technology Cambridge MA USA

Let Dist(f,g)=Pr/sub u/ [f(u)/spl ne/g(u)] denote the relative distance between functions f,g mapping from a group G to a group H, and let Dist(f) denote the minimum, over all linear functions (homomorphisms) g, of Dist(f,g). Given a function f:G/spl rarr/H we let Err(f)=Pr/sub u/,v[f(u)+f(v)/spl ne/f(u+v)] denote the rejection probability of the BLR (Blum-Luby-Rubinfeld) linearity test. Linearity testing is the study of the relationship between Err(f) and Dist(f), and in particular the study of lower bounds on Err(f) in terms of Dist(f). The case we are interested in is when the underlying groups are G=GF(2)/sup n/ and H=GF(2). The corresponding test is used in the construction of efficient PCPs and thence in the derivation of hardness of approximation results, and, in this context, improved analyses translate into better non-approximability results. However, while several analyses of the relation of Err(f) to Dist(f) are known, none is tight. We present a description of the relationship between Err(f) and Dist(f) which is nearly complete in all its aspects, and entirely complete (i.e. tight) in some. In particular we present functions L,U:[0,1]/spl rarr/[0,1] such that for all x/spl isin/[0,1] we have L(x)

关键词： Linearity Testing computer science Upper bound Postal services Drives mathematics Scholarships Error correction codes

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Forward error correction in ATM networks: an analysis of cell loss distribution in a block

Forward error correction in ATM networks: an analysis of cel...

引用

IEEE Annual Joint Conference: INFOCOM, IEEE computer and Communications Societies

作者： K. Kawahara K. Kumazoe T. Takine Y. Oie Department of Computer Science and Electronics Kyushu Institute of Technology Iizuka Japan Department of Applied Mathematics and Physics Kyoto University Kyoto Japan

In almost all conventional transport protocols, ARQs (automatic repeat request) have been used to recover lost packets, in which receivers would request sources to retransmit lost packets. In these retransmission based error recovery schemes, the transmission delay can reach an unacceptable level for traffic with stringent delay constraints in high speed networks because their propagation delay is very large relative to packet transmission times. On the other hand, FEC (forward error correction) adds redundant packets to data ones, all of which are organized into a group called a block, and hence allows the receivers to correct some of the lost packets without retransmissions. This capability is desirable for high speed networks. The authors exactly analyze the distribution of the number of cells lost within a block in ATM networks with correlated cell arrivals, and examine the benefits due to FEC by means of the analysis.< >

关键词： Intelligent networks Forward error correction Propagation delay High-speed networks Transport protocols Automatic repeat request Optical losses Telecommunication traffic Traffic control computer science

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Incremental cryptography: The case of hashing and signing 14th

Incremental cryptography: The case of hashing and signing

引用

14th Annual International Cryptology Conference, CRYPTO 1994

作者： Bellare, Mihir Goldreich, Oded Goldwasser, Shafi Advanced Networking Laboratory IBM T.J. Watson Research Center P.O. Box 704 Yorktown HeightsNY10598 United States Department of Applied Mathematics and Computer Science Weizmann Institute of Science Rehovot Israel MIT Laboratory for Computer Science 545 Technology Square CambridgeMA02139 United States

ISBN: (纸本)9783540583332

We initiate the investigation of a new kind of efficiency for cryptographic transformations. The idea is that having once applied the transformation to some document M, the time to update the result upon modification of M should be "proportional" to the "amount of modification" done to M. Thereby one obtains much faster cryptographic primitives for environments where closely related documents are undergoing the same cryptographic transformations. We provide some basic definitions enabling treatment of the new notion. We then exemplify our approach by suggesting incremental schemes for hashing and signing which are efficient according to our new measure. © Springer-Verlag Berlin Heidelberg 1994.

关键词： Cryptography

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HANDPRINTED CHINESE CHARACTER RECOGNITION USING THE PROBABILITY DISTRIBUTION FEATURE

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International Journal of Pattern Recognition and Artificial Intelligence 1994年第5期8卷 1241-1258页

作者： TZE FEN LI SHIAW-SHIAN YU Department of Applied Mathematics Chung Hsing University Kuo-Kung Road Taichung (400) Taiwan ROC Advanced Technology Center Computer & Communication Research Laboratories Industrial Technology Research Institute Chutung Hsinchu Taiwan ROC

A simplified Bayes rule is used to classify 5401 categories of handwritten Chinese characters. The main feature for the Bayes rule deals with the probability distribution of black pixels of a thinned character. Our idea is that each Chinese character indicated by the black pixels represents a probability distribution in a two-dimensional plane. Therefore, an unknown pattern is classified into one of 5401 different distributions by the Bayes rule. Since the handwritten character has an irregular shape variation, the whole character is normalized and then thinned. Finally, a transformation is used to spread the black pixels uniformly over the whole square plane, but it still keeps the relative positions of the original black pixels. The main feature gives an 88.65% recognition rate. In order to raise the recognition rate, 4 more subsidiary features are elaborately selected such that they are not affected much by the irregularly shaped variation. The 4 features raise the recognition rate to 93.43%. A 99.30% recognition rate is achieved if the top 10 categories of HCC are selected by our recognition method and 99.61% if the top 20 are selected.

关键词： Bayes rule Chinese character recognition classification feature extraction pattern recognition relaxation matching

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