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Proper Reparametrization of Rational Ruled Surface
 Journal of Computer Science and Technology
, 2008
"... Abstract. In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. ..."
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Cited by 3 (1 self)
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Abstract. In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface.
Epidemic Spreading in ScaleFree Networks
, 2000
"... The Internet, as well as many other networks, has a very complex connectivity recently modeled by the class of scalefree networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze real data from c ..."
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Cited by 575 (15 self)
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framework rationalize data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks. PACS numbers: 05.70.Ln, 05.50.+q Typeset using REVT E X 1 Many social, biological, and communication systems can be properly described by complex
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
, 2001
"... Variable selection is fundamental to highdimensional statistical modeling, including nonparametric regression. Many approaches in use are stepwise selection procedures, which can be computationally expensive and ignore stochastic errors in the variable selection process. In this article, penalized ..."
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Cited by 948 (62 self)
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penalized likelihood functions. The proposed ideas are widely applicable. They are readily applied to a variety of parametric models such as generalized linear models and robust regression models. They can also be applied easily to nonparametric modeling by using wavelets and splines. Rates of convergence
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
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Cited by 474 (3 self)
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Field Theories are defined, and it is proved that tree level theories are determined by their correlation functions. Application to counting rational curves on del Pezzo surfaces and projective spaces are given. Let V be a projective algebraic manifold. Methods of quantum field theory recently led to a
Proper Reparametrization of Rational Ruled Surface
, 2008
"... Abstract In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. The algorithm consists of three steps. We first reparametriz ..."
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Abstract In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. The algorithm consists of three steps. We first
Finding rational solutions of rational systems of autonomous ODEs
"... In this paper we provide an algorithm to find explicitly rational solutions of a rational system of autonomous ordinary differential equations (ODEs) from its invariant algebraic curves. The method is based on the rational parametrization of the rational invariant algebraic curves and intensively us ..."
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using of linear fractional transformations between two proper rational parametrizations of the same algebraic curve. 1.
Implicitization of rational Parametric Equations
 Journal of Symbolic Computation
, 1992
"... Based on the Gröbner basis method, we present algorithms for a complete solution to the following problems in the implicitization of a set of rational parametric equations. (1) Find a basis of the implicit prime ideal determined by a set of rational parametric equations. (2) Decide whether the param ..."
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Cited by 21 (6 self)
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Based on the Gröbner basis method, we present algorithms for a complete solution to the following problems in the implicitization of a set of rational parametric equations. (1) Find a basis of the implicit prime ideal determined by a set of rational parametric equations. (2) Decide whether
Rational Parametrizations of Neural Networks
"... A connection is drawn between rational functions, the realization theory of dynamical systems, and feedforward neural networks. This allows us to parametrize single hidden layer scalar neural networks with (almost) arbitrary analytic activation functions in terms of strictly proper rational function ..."
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A connection is drawn between rational functions, the realization theory of dynamical systems, and feedforward neural networks. This allows us to parametrize single hidden layer scalar neural networks with (almost) arbitrary analytic activation functions in terms of strictly proper rational
Risk as analysis and risk as feelings: Some thoughts about affect, reason, risk, and rationality
 Risk Analysis
, 2004
"... Modern theories in cognitive psychology and neuroscience indicate that there are two fundamental ways in which human beings comprehend risk. The “analytic system ” uses algorithms and normative rules, such as the probability calculus, formal logic, and risk assessment. It is relatively slow, effortf ..."
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Cited by 234 (12 self)
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it is guided by emotion and affect. Rational decision making requires proper integration of both modes of
Computations with Differential Rational Parametric Equations
, 1999
"... This paper studies several computational problems about differential rational parametric equations. We present a method of implicitization for general differential rational parametric equations. We also present a method to decide whether the parameters of a set of parametric equations are independ ..."
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This paper studies several computational problems about differential rational parametric equations. We present a method of implicitization for general differential rational parametric equations. We also present a method to decide whether the parameters of a set of parametric equations
Results 1  10
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3,053