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and Theoretical Results
, 1995
"... Three-dimensional numerical predictions and experimental data have been obtained for natural convection from a 3 X 3 array of discrete heat sources flush-mounted on one vertical wall of a rectangular cavity and cooled by the opposing wall. Predictions performed in a companion paper (Heindel et al, 1 ..."
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Three-dimensional numerical predictions and experimental data have been obtained for natural convection from a 3 X 3 array of discrete heat sources flush-mounted on one vertical wall of a rectangular cavity and cooled by the opposing wall. Predictions performed in a companion paper (Heindel et al, 1995a) revealed that three-dimen-sional edge effects are significant and that, with increasing Rayleigh number, flow and heat transfer become more uniform across each heater face. The three-dimensional predictions are in excellent agreement with the data of this study, whereas a two-dimensional model of the experimental geometry underpredlcts average heat transfer by as much as 20 percent. Experimental row-averaged Nusselt numbers are well correlated with a Rayleigh number exponent of 0.25 for RaLi S 1.2 X 70s.
New results in linear filtering and prediction theory
- TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 607 (0 self)
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in this field. The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed side-by-side. Properties of the variance equation are of great interest
Impulses and Physiological States in Theoretical Models of Nerve Membrane
- Biophysical Journal
, 1961
"... ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing excitabi ..."
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Cited by 505 (0 self)
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ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing
The ensemble Kalman Filter: Theoretical formulation and practical implementation.
- Ocean Dynamics,
, 2003
"... Abstract The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group and numerous publications have discussed applications and theoretical aspects of it. This paper rev ..."
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Cited by 496 (5 self)
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reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal
Dropout from higher education: A theoretical synthesis of recent research
- Review of Educational Research
, 1975
"... Despite the very extensive literature on dropout from higher education, much remains unknown about the nature of the dropout process. In large measure, the failure of past research to delineate more clearly the multiple characteristics of dropout can be traced to two major shortcomings; namely, inad ..."
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Cited by 798 (2 self)
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, inadequate atten-tion given to questions of definition and to the development of theoretical models that seek to explain, not simply to describe, the processes that bring individuals to leave institutions of higher education. With regard to the former, inadequate attention given to definition has often led
Theoretical results on sparse representations of multiple-measurement vectors
- IEEE Trans. Signal Process
, 2006
"... Abstract — Multiple measurement vector (MMV) is a relatively new problem in sparse representations. Efficient methods have been proposed. Considering many theoretical results that are available in a simple case – single measure vector (SMV) – the theoretical analysis regarding MMV is lacking. In th ..."
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Cited by 147 (2 self)
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Abstract — Multiple measurement vector (MMV) is a relatively new problem in sparse representations. Efficient methods have been proposed. Considering many theoretical results that are available in a simple case – single measure vector (SMV) – the theoretical analysis regarding MMV is lacking
Computational Lambda-Calculus and Monads
, 1988
"... The λ-calculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with λ-terms. However, if one goes further and uses fij-conversion to prove equivalence of programs, then a gross simplification is introduced, that may jeopardise the ap ..."
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Cited by 501 (6 self)
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the applicability of theoretical results to real situations. In this paper we introduce a new calculus based on a categorical semantics for computations. This calculus provides a correct basis for proving equivalence of programs, independent from any specific computational model.
Notions of Computation and Monads
, 1991
"... The i.-calculus is considered a useful mathematical tool in the study of programming languages, since programs can be identified with I-terms. However, if one goes further and uses bn-conversion to prove equivalence of programs, then a gross simplification is introduced (programs are identified with ..."
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Cited by 867 (15 self)
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with total functions from calues to values) that may jeopardise the applicability of theoretical results, In this paper we introduce calculi. based on a categorical semantics for computations, that provide a correct basis for proving equivalence of programs for a wide range of notions of computation.
A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection
- INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1995
"... We review accuracy estimation methods and compare the two most common methods: cross-validation and bootstrap. Recent experimental results on artificial data and theoretical results in restricted settings have shown that for selecting a good classifier from a set of classifiers (model selection), te ..."
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Cited by 1283 (11 self)
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We review accuracy estimation methods and compare the two most common methods: cross-validation and bootstrap. Recent experimental results on artificial data and theoretical results in restricted settings have shown that for selecting a good classifier from a set of classifiers (model selection
Optimizing Search Engines using Clickthrough Data
, 2002
"... This paper presents an approach to automatically optimizing the retrieval quality of search engines using clickthrough data. Intuitively, a good information retrieval system should present relevant documents high in the ranking, with less relevant documents following below. While previous approaches ..."
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Cited by 1314 (23 self)
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theoretical perspective, this method is shown to be well-founded in a risk minimization framework. Furthermore, it is shown to be feasible even for large sets of queries and features. The theoretical results are verified in a controlled experiment. It shows that the method can effectively adapt the retrieval
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