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Mathematical Aspects of Neural Networks
 European Symposium of Artificial Neural Networks 2003
, 2003
"... In this tutorial paper about mathematical aspects of neural networks, we will focus on two directions: on the one hand, we will motivate standard mathematical questions and well studied theory of classical neural models used in machine learning. On the other hand, we collect some recent theoretic ..."
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Cited by 6 (4 self)
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In this tutorial paper about mathematical aspects of neural networks, we will focus on two directions: on the one hand, we will motivate standard mathematical questions and well studied theory of classical neural models used in machine learning. On the other hand, we collect some recent
Mathematical Aspects of Command Relations
"... In GB, the importance of phrasestructure rules has dwindled in favour of nearness conditions. Today, nearness conditions play a major role in defining the correct linguistic representations. They are expressed in terms of special binary relations on trees called command relations. Yet, while ..."
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Cited by 18 (7 self)
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In GB, the importance of phrasestructure rules has dwindled in favour of nearness conditions. Today, nearness conditions play a major role in defining the correct linguistic representations. They are expressed in terms of special binary relations on trees called command relations. Yet, while the formal theory of phrasestructure grammars is quite advanced, no formal investigation into the properties of command relations has been done. We will try to close this gap. In particular, we will study the intrinsic properties of command relations as relations on trees as well as the possibility to reduce nearness conditions expressed by command relations to phrasestructure rules.
Mathematical Aspects of Decoherence
, 2000
"... The aim of this lecture is to investigate the mathematical frame for environment induced superselection rules. Some exactly soluble models are dicussed in detail and norm estimates on decoherence effects are derived. ..."
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Cited by 4 (3 self)
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The aim of this lecture is to investigate the mathematical frame for environment induced superselection rules. Some exactly soluble models are dicussed in detail and norm estimates on decoherence effects are derived.
/ Mathematical Aspects of the Lifshitz Formula
, 2004
"... The applicability of the Lifshitz formula is discussed to the case of two thick parallel plates made of real metal. The usual description of the zeropoint vacuum oscillations on the background of the frequencydependent dielectric permittivity is shown to be in contradiction with thermodynamics. In ..."
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The applicability of the Lifshitz formula is discussed to the case of two thick parallel plates made of real metal. The usual description of the zeropoint vacuum oscillations on the background of the frequencydependent dielectric permittivity is shown to be in contradiction with thermodynamics. Instead, the Lifshitz formula for the Casimir free energy should be reformulated in terms of the reflection coefficients containing the surface impedance instead of the dielectric permittivity. This approach is presently confirmed experimentally by precision measurements of the van der Waals and Casimir forces in micromechanical systems and it is in agreement with thermodynamics. PoS(WC2004)
MATHEMATICAL ASPECTS OF SCIENTIFIC
, 1987
"... The goal is to survey the impact of scientific software on mathematics. Three types of impacts are identified and several topics from each are discussed in some depth. First is the impact on the structure of mathematics through its Tole as the scientific tool for problem solving. Scientific software ..."
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The goal is to survey the impact of scientific software on mathematics. Three types of impacts are identified and several topics from each are discussed in some depth. First is the impact on the structure of mathematics through its Tole as the scientific tool for problem solving. Scientific
MATHEMATICAL ASPECTS OF IMAGE PROCESSING
, 2014
"... In this thesis, image processing is explored from a mathematical point of view. After defining a digitized image, techniques for adjusting resolution are discussed. Image transformations defined on a neighborhood centered about a pixel and their relationships to convolution are considered. The Fouri ..."
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In this thesis, image processing is explored from a mathematical point of view. After defining a digitized image, techniques for adjusting resolution are discussed. Image transformations defined on a neighborhood centered about a pixel and their relationships to convolution are considered
Results 1  10
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546,473