Filters








222,642 Hits in 5.0 sec

Euclidean Functions of Computable Euclidean Domains

Rodney G. Downey, Asher M. Kach
2011 Notre Dame Journal of Formal Logic  
We study the complexity of (finitely-valued and transfinitely-valued) Euclidean functions for computable Euclidean domains.  ...  We examine both the complexity of the minimal Euclidean function and any Euclidean function.  ...  There, Schrieber showed that there is a computable Euclidean domain with no computable finitely-valued Euclidean function, that there is a computable Euclidean domain with a computable Euclidean function  ... 
doi:10.1215/00294527-1306172 fatcat:yzrln7vxbzht3og24osrdpeyzm

Unique factorization in ACL2

John R. Cowles, Ruben Gamboa
2006 Proceedings of the sixth international workshop on the ACL2 theorem prover and its applications - ACL2 '06  
Euclidean domains are an algebraic abstraction, of both the positive integers and the rational polynomials, in which the usual proofs of unique factorization, for both the integers and the polynomials,  ...  ACL2 is used to systematically study domains whose elements can be "uniquely" factored into products of "irreducible" elements.  ...  Instances of particular domains, with unique factorization, can then be established via functional instantiation of this general theory of Euclidean domains.  ... 
doi:10.1145/1217975.1217980 dblp:conf/acl2/CowlesG06 fatcat:yj7crd53ezao5asu52wo3efop4

Application of the Non-Local Log-Euclidean Mean to Radar Target Detection in NonHomogeneous Sea Clutter

Wei Chen, SIYU CHENa
2019 IEEE Access  
Then, the Log-Euclidean distance is introduced and the non-local method is employed for computing the Log-Euclidean mean.  ...  Firstly, the mathematical model of the received signal returned from a target is established.  ...  in the quality of the paper.  ... 
doi:10.1109/access.2019.2955968 fatcat:rwfs6gmedzfs3hdz2bmvbfp33q

A Multi-metric Index for Euclidean and Periodic Matching [chapter]

Michail Vlachos, Zografoula Vagena, Vittorio Castelli, Philip S. Yu
2005 Lecture Notes in Computer Science  
Also, in several cases, different distance functions can provide diverse but equally intuitive results (according to the specific focus of each measure).  ...  This new measure is phase-invariant and can provide flexible sequence characterizations, loosely resembling the Dynamic Time Warping, requiring only a fraction of the computational cost of the latter.  ...  Parseval's theorem states that the energy P of the signal computed in the frequency domain is equal to the energy computed in the Fourier domain: P(x) = x 2 = N −1 k=0 x 2 k = P(X) = X 2 = N −1 k=0 X k  ... 
doi:10.1007/11564126_36 fatcat:e3m2l7l26rh75mcszuuqhbwjqi

Geometric Deep Learning: Going beyond Euclidean data

Michael M. Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, Pierre Vandergheynst
2017 IEEE Signal Processing Magazine  
Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds.  ...  Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in  ...  The second class of problems deals with analyzing functions defined on a given non-Euclidean domain (these two classes are related, since understanding the properties of functions defined on a domain conveys  ... 
doi:10.1109/msp.2017.2693418 fatcat:ppyimvcbwfd55lsc5mkcmsy7ai

Centroidal Voronoi tessellation in universal covering space of manifold surfaces

Guodong Rong, Miao Jin, Liang Shuai, Xiaohu Guo
2011 Computer Aided Geometric Design  
In this paper, we first extend the concept of CVT from Euclidean space to spherical space and hyperbolic space, and then combine all of them into a unified framework -the CVT in universal covering space  ...  As an example of the application, we utilize the CVT in universal covering space to compute uniform partitions and high-quality remeshing results for genus-0, genus-1, and high-genus (genus>1) surfaces  ...  The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper. Guodong Rong, Liang Shuai, and Xiaohu  ... 
doi:10.1016/j.cagd.2011.06.005 fatcat:6rsqa5ozc5ewjm4oh7frs22ggm

Teaching Computational Abstract Algebra

ERICH KALTOFEN
1997 Journal of symbolic computation  
We report on the contents and pedagogy of a course in abstract algebra that was taught with the aid of educational software developed within the Mathematica system.  ...  We describe the topics covered and the didactical use of the corresponding Mathematica packages, as well as draw conclusions for future such courses from the students' comments and our own experience.  ...  Acknowlegdement I would like to express my gratitude to the two unnamed referees, whose suggestions have improved the final version of the paper.  ... 
doi:10.1006/jsco.1996.0104 fatcat:bfxwe7mws5gtzkc2eezs5bfzvy

Non-Galois cubic fields which are Euclidean but not norm-Euclidean

David A. Clark
1996 Mathematics of Computation  
Using a method recently introduced by us, we give two examples of cubic fields which are Euclidean but not norm-Euclidean.  ...  ideal domain.  ...  Weinberger [9] showed that, under the assumption of the Generalized Riemann Hypothesis for Dedekind zeta functions, if there are infinitely many units in R, then R is a Euclidean domain if and only if  ... 
doi:10.1090/s0025-5718-96-00764-8 fatcat:bt6lei4s7zfs7jz373yop7o4xq

Global Illumination of non-Euclidean spaces [article]

Tiago Novello, Vinicius da Silva, Luiz Velho
2020 arXiv   pre-print
This paper presents a path tracer algorithm to compute the global illumination of non-Euclidean manifolds. We use the 3D torus as an example.  ...  Global illumination in non-Euclidean manifolds. We remember the classical global illumination function of the Euclidean space E 3 introduced by Kajiya [2] .  ...  Because we are considering the light constant along geodesics, the function L only needs to be computed on the scene surface objects. There are many approaches to compute the illumination function.  ... 
arXiv:2003.11133v1 fatcat:ugjhq37lobafxgix3tspntlnvm

Nonuniform Coverage and Cartograms

Francois Lekien, Naomi Ehrich Leonard
2009 SIAM Journal of Control and Optimization  
We derive centralized non-uniform coverage control laws from uniform coverage algorithms using cartograms, transformations that map non-uniform metrics to a near Euclidean metric.  ...  In this paper, we investigate non-uniform coverage of a planar region by a network of autonomous, mobile agents.  ...  Galerkin approximations of the linear PDE problems defining the extended density function between the domain of interest and a larger embedding square were obtained using libsparse, a C++ wrapper to the  ... 
doi:10.1137/070681120 fatcat:5as56rdczjay7npy62izbw343a

Nonuniform coverage and cartograms

Francois Lekien, Naomi Ehrich Leonard
2010 49th IEEE Conference on Decision and Control (CDC)  
We derive centralized non-uniform coverage control laws from uniform coverage algorithms using cartograms, transformations that map non-uniform metrics to a near Euclidean metric.  ...  In this paper, we investigate non-uniform coverage of a planar region by a network of autonomous, mobile agents.  ...  Galerkin approximations of the linear PDE problems defining the extended density function between the domain of interest and a larger embedding square were obtained using libsparse, a C++ wrapper to the  ... 
doi:10.1109/cdc.2010.5717953 dblp:conf/cdc/LekienL10 fatcat:dord3psew5a2db46zqlj6gtfdq

Fast and Simple Calculus on Tensors in the Log-Euclidean Framework [chapter]

Vincent Arsigny, Pierre Fillard, Xavier Pennec, Nicholas Ayache
2005 Lecture Notes in Computer Science  
Indeed, Log-Euclidean computations are Euclidean computations in the domain of matrix logarithms.  ...  Computations on tensors have become common with the use of DT-MRI. But the classical Euclidean framework has many defects, and affine-invariant Riemannian metrics have been proposed to correct them.  ...  A patent is pending for the Log-Euclidean processing framework of tensors (Deposit Number 0503483, April 7th, 2005, property of INRIA, France).  ... 
doi:10.1007/11566465_15 fatcat:6hysztt6yrb3pjpzx5xvjf2vwu

Using a Mahalanobis-Like Distance to Train Radial Basis Neural Networks [chapter]

J. M. Valls, R. Aler, O. Fernández
2005 Lecture Notes in Computer Science  
However, the activation of each neuron depends on the euclidean distance between a pattern and the neuron center.  ...  However, this distance is computed directly from the variance-covariance matrix and does not consider the accuracy of the learning algorithm.  ...  The fitness function is computed by training a RBNN on a set of training data and determining the training error.  ... 
doi:10.1007/11494669_32 fatcat:fzozhlzaxbdu7indfng6piv7im

Euclidean space and their functional application for computation analysis

Jay Prakash Tiwari, Manish Pande
2019 International Journal of Advanced Technology and Engineering Exploration  
Conflicts of interest The authors have no conflicts of interest to declare.  ...  Focus on related research work in the same domain based on computational aspects. 3.  ...  been identified. 1) There is the need of data mining linkage with the Euclidean space for the better pattern point discovery in several domains. 2) There is the need of working on autocorrelation. 3)  ... 
doi:10.19101/ijatee.2019.650047 fatcat:stfezed5hnetfjopxoxyekv7ny

Lattice Network Coding Over Euclidean Domains

Frederique Oggier, Angeles Vazquez-Castro
2014 Zenodo  
Publication in the conference proceedings of EUSIPCO, Lisbon, Portugal, 2014  ...  Definition 1: A Euclidean domain is an integral domain R for which there exists a function d : R\{0} → Z ≥0 with the property that for any x, y ∈ R with y = 0, we can write x = qy + r with either r = 0  ...  Finally, the five of them are Euclidean domains, which explains the term quadratic imaginary Euclidean domains.  ... 
doi:10.5281/zenodo.43957 fatcat:vfvwrnwqejcv5jqjug4mq2zwsy
« Previous Showing results 1 — 15 out of 222,642 results