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Is mathematics consistent?

by Hitoshi Kitada , 2003
"... Abstract: A question is proposed whether or not set theory is consistent. We consider a formal set theory S, where we can develop a number theory. As no generality is lost, in the following we consider a number theory that can be regarded as a subsystem of S, and will call it S (0). Definition 1. 1) ..."
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Abstract: A question is proposed whether or not set theory is consistent. We consider a formal set theory S, where we can develop a number theory. As no generality is lost, in the following we consider a number theory that can be regarded as a subsystem of S, and will call it S (0). Definition 1. 1

Typesetting Concrete Mathematics

by Donald E. Knuth - TUGBOAT , 1989
"... ... tried my best to make the book mathematically interesting, but I also knew that it would be typographically interesting-because it would be the first major use of a new typeface by Hermann Zapf, commissioned by the American Mathematical Society. This typeface, called AMS Euler, had been carefull ..."
Abstract - Cited by 661 (1 self) - Add to MetaCart
closes together smoothly when the curve returns to its starting point. A handwritten rather than mechanical style is appropriate for mathematics because people generally create math with pen, pencil, or chalk. The Euler letters are upright, not italic, so that there is a general consistency

Understanding Normal and Impaired Word Reading: Computational Principles in Quasi-Regular Domains

by David C. Plaut , James L. McClelland, Mark S. Seidenberg, Karalyn Patterson - PSYCHOLOGICAL REVIEW , 1996
"... We develop a connectionist approach to processing in quasi-regular domains, as exemplified by English word reading. A consideration of the shortcomings of a previous implementation (Seidenberg & McClelland, 1989, Psych. Rev.) in reading nonwords leads to the development of orthographic and phono ..."
Abstract - Cited by 613 (94 self) - Add to MetaCart
to read pronounceable nonwords as well as skilled readers. A mathematical analysis of the effects of word frequency and spelling-sound consistency in a related but simpler system serves to clarify the close relationship of these factors in influencing naming latencies. These insights are verified

HyTech: A Model Checker for Hybrid Systems

by Thomas A. Henzinger, Pei-Hsin Ho, Howard Wong-toi - Software Tools for Technology Transfer , 1997
"... A hybrid system is a dynamical system whose behavior exhibits both discrete and continuous change. A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete change with differential equations for capturing conti ..."
Abstract - Cited by 473 (6 self) - Add to MetaCart
A hybrid system is a dynamical system whose behavior exhibits both discrete and continuous change. A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete change with differential equations for capturing

Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex

by Elie L. Bienenstock, Leon N Cooper, Paul W. Munro - J. Neurosci , 1982
"... The development of stimulus selectivity in the primary sensory cortex of higher vertebrates is considered in a general mathematical framework. A synaptic evolution scheme of a new kind is proposed in which incoming patterns rather than converging afferents compete. The change in the efficacy of a gi ..."
Abstract - Cited by 432 (20 self) - Add to MetaCart
The development of stimulus selectivity in the primary sensory cortex of higher vertebrates is considered in a general mathematical framework. A synaptic evolution scheme of a new kind is proposed in which incoming patterns rather than converging afferents compete. The change in the efficacy of a

Q2003 The Institute of Statistical Mathematics CONSISTENT AND ASYMPTOTICALLY NORMAL ESTIMATORS FOR CYCLICALLY TIME-DEPENDENT LINEAR MODELS

by Abdelouahab Bibi, Christian Francq , 2000
"... Abstract. We consider ageneral class of time series linear models where parameters switch according to a known fixed calendar. These parameters are estimated by means of quasi-generalized l ast squares estimators. Conditions for strong consistency and asymptotic normality are given. Applications to ..."
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Abstract. We consider ageneral class of time series linear models where parameters switch according to a known fixed calendar. These parameters are estimated by means of quasi-generalized l ast squares estimators. Conditions for strong consistency and asymptotic normality are given. Applications

Proof of a Fundamental Result in Self-Similar Traffic Modeling

by Murad S. Taqqu , Walter Willinger, Robert Sherman - COMPUTER COMMUNICATION REVIEW , 1997
"... We state and prove the following key mathematical result in self-similar traffic modeling: the superposition of many ON/OFF sources (also known as packet trains) with strictly alternating ON- and OFF-periods and whose ON-periods or OFF-periods exhibit the Noah Effect (i.e., have high variability or ..."
Abstract - Cited by 290 (8 self) - Add to MetaCart
-similarity). This provides a simple physical explanation for the presence of self-similar traffic patterns in modern high-speed network traffic that is consistent with traffic measurements at the source level. We illustrate how this mathematical result can be combined with modern high-performance computing capabilities

Experimental Quantum Cryptography

by Charles Bennett, François Bessette, Gilles Brassard, Louis Salvail, John Smolin - Journal of Cryptology , 1992
"... We describe results from an apparatus and protocol designed to implement quantum key distribution, by which two users, who share no secret information initially: 1) exchange a random quantum transmission, consisting of very faint flashes of polarized light; 2) by subsequent public discussion of the ..."
Abstract - Cited by 266 (20 self) - Add to MetaCart
We describe results from an apparatus and protocol designed to implement quantum key distribution, by which two users, who share no secret information initially: 1) exchange a random quantum transmission, consisting of very faint flashes of polarized light; 2) by subsequent public discussion

Ill-posed problems in early vision

by Mario Bertero, Tomaso A. Pogcio, Vincent Torre - Proceedings of the IEEE , 1988
"... The first processing stage in computational vision, also called early vision, consists of decoding two-dimensional images in terms of properties of 3-0 surfaces. Early vision includes problems such as the recovery of motion and optical flow, shape from shading, surface interpolation, and edge detect ..."
Abstract - Cited by 227 (14 self) - Add to MetaCart
The first processing stage in computational vision, also called early vision, consists of decoding two-dimensional images in terms of properties of 3-0 surfaces. Early vision includes problems such as the recovery of motion and optical flow, shape from shading, surface interpolation, and edge

Mathematical Textbook Of Deformable Neuroanatomies

by Michael I. Miller, Gary E. Christensen, Yali Amit, Ulf Grenander , 1993
"... Mathematical techniques are presented for the transformation of digital anatomical textbooks from the ideal to the individual, allowing for the representation of the variabilities manifest in normal human anatomies. The ideal textbook is constructed on a fixed coordinate system to contain all of the ..."
Abstract - Cited by 140 (21 self) - Add to MetaCart
with individuals is accommodated by defining probabilistic transformations on the textbook coordinate system, the transformations forming mathematical translation groups of high dimension. The ideal is applied to the individual patient by finding the transformation which is consistent with physical properties
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