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The Diophantine Frobenius Problem

Jorge L. Ramírez Alfonsín

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568209
eISBN:
9780191718229
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568209.001.0001
Subject:
Mathematics, Algebra, Combinatorics / Graph Theory / Discrete Mathematics

During the early part of the last century, F. G. Frobenius raised, in his lectures, the following problem (called the Diophantine Frobenius Problem FP): given relatively prime positive integers a1, . ... More


Random Geometric Graphs

Mathew Penrose

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.001.0001
Subject:
Mathematics, Probability / Statistics

This book sets out a body of rigorous mathematical theory for finite graphs with nodes placed randomly in Euclidean d-space according to a common probability density, and edges added to connect ... More


Statistics and Informatics in Molecular Cancer Research

Carsten Wiuf and Claus L. Andersen (eds)

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199532872
eISBN:
9780191714467
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199532872.001.0001
Subject:
Mathematics, Probability / Statistics, Biostatistics

This book discusses novel advances in informatics and statistics in molecular cancer research. Through eight chapters it discusses specific topics in cancer research, talks about how the topics give ... More


Plotinus on Number

Svetla Slaveva-Griffin

Published in print:
2009
Published Online:
May 2009
ISBN:
9780195377194
eISBN:
9780199869572
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195377194.001.1
Subject:
Classical Studies, Ancient Greek, Roman, and Early Christian Philosophy

This book examines Plotinus’ concept of number, one of the most difficult and obscure topics in Neoplatonism. The book argues that Plotinus is the first philosopher who explains the Platonic “true ... More


Physicists Multiply, Social Scientists Add—Even When It Does Not Add Up

Rein Taagepera

in Making Social Sciences More Scientific: The Need for Predictive Models

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199534661
eISBN:
9780191715921
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534661.003.0005
Subject:
Political Science, Comparative Politics, Political Economy

Most physics equations include few variables and at most one freely adjustable constant, which multiply or divide. In contrast, regression equations favored in social sciences often have many ... More


Conclusion: In Defense of Plato

Svetla Slaveva-Griffin

in Plotinus on Number

Published in print:
2009
Published Online:
May 2009
ISBN:
9780195377194
eISBN:
9780199869572
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195377194.003.0008
Subject:
Classical Studies, Ancient Greek, Roman, and Early Christian Philosophy

The concept of number is the troublemaker in the history of Platonism. It separated the followers of Plato and Aristotle into two camps for generations. For Plotinus, however, the concept becomes the ... More


Mental Number Lines

Marcus Giaquinto

in Visual Thinking in Mathematics

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199285945
eISBN:
9780191713811
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285945.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics

The main concern of this chapter is the association of numbers with a visually represented line. The association is usually acquired in junior school, and is then extended to provide an integrated ... More


Mental Number Line s

Marcus Giaquinto

in The Innate Mind: Volume 2: Culture and Cognition

Published in print:
2007
Published Online:
May 2007
ISBN:
9780195310139
eISBN:
9780199871209
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195310139.003.0008
Subject:
Philosophy, Philosophy of Mind

Along with our numeral systems, we have an innate sense of cardinal size at par with our sense of duration and distance, refined by cultural practices. The SNARC effect suggests that our number sense ... More


 What Doctors Must Know about Medical Practice

Bernard Gert, Charles M. Culver, and K. Danner Clouser

in Bioethics: A systematic approach

Published in print:
2006
Published Online:
September 2006
ISBN:
9780195159066
eISBN:
9780199786466
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195159063.003.0008
Subject:
Philosophy, Moral Philosophy

This chapter shows the importance of recognizing the probabilistic nature of medical diagnosis and treatment. It discusses the possibly serious effects of physicians not understanding Bayes theorem, ... More


Time for Aristotle: Physics IV. 10-14

Ursula Coope

Published in print:
2005
Published Online:
February 2006
ISBN:
9780199247905
eISBN:
9780191603082
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0199247900.001.0001
Subject:
Philosophy, Ancient Philosophy

This book is about Aristotle’s account of time in Physics IV.10-14. Aristotle claims that time is not a kind of change, but that it is something dependent on change. He defines it as a kind of ... More


Postprocessing

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter explains how to write a postprocessing code, and more specifically how to study the nonlinear simulations using computer graphics and analysis. It first considers how to compute and ... More


Predicting Party Sizes: The Logic of Simple Electoral Systems

Rein Taagepera

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199287741
eISBN:
9780191713408
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199287741.001.0001
Subject:
Political Science, Democratization

For a given electoral system, what average number and size distribution of parties can we expect? This book makes specific predictions that agree with world averages. The basic factors are assembly ... More


The Mean Duration of Cabinets

Rein Taagepera

in Predicting Party Sizes: The Logic of Simple Electoral Systems

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199287741
eISBN:
9780191713408
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199287741.003.0010
Subject:
Political Science, Democratization

Again the quantity to watch is the ‘seat product’. The inverse square law of cabinet durations says that the mean cabinet duration in a country is approximately forty-two years divided by the square ... More


How to Simplify Complex Electoral Systems

Rein Taagepera

in Predicting Party Sizes: The Logic of Simple Electoral Systems

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199287741
eISBN:
9780191713408
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199287741.003.0011
Subject:
Political Science, Democratization

Resistance to simplifying a complex electoral system is at its least when the existing number and size of parties are not altered. The existing effective number of parties is most likely to be ... More


The Law of Minority Attrition

Rein Taagepera

in Predicting Party Sizes: The Logic of Simple Electoral Systems

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199287741
eISBN:
9780191713408
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199287741.003.0013
Subject:
Political Science, Democratization

The more important levels have fewer positions, and the share of minorities goes down. The law of minority attrition is a quantitatively predictive logical model that expresses it more precisely. A ... More


The Institutional Impact on Votes and Deviation from PR

Rein Taagepera

in Predicting Party Sizes: The Logic of Simple Electoral Systems

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199287741
eISBN:
9780191713408
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199287741.003.0014
Subject:
Political Science, Democratization

Using nothing but the product of assembly size and district magnitude, a quantitatively predictive logical model allows us to estimate the average effective number of parties based on votes. Average ... More


How Electoral Systems Matter

Rein Taagepera

in Predicting Party Sizes: The Logic of Simple Electoral Systems

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199287741
eISBN:
9780191713408
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199287741.003.0001
Subject:
Political Science, Democratization

An electoral system helps determine the number and size distribution of parties in a country, as well as cabinet duration. Electoral systems are expressed in electoral laws. Their impact depends on ... More


Openness to Small Parties: The Micro‐Mega Rule and the Seat Product

Rein Taagepera

in Predicting Party Sizes: The Logic of Simple Electoral Systems

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199287741
eISBN:
9780191713408
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199287741.003.0006
Subject:
Political Science, Democratization

The micro-mega rule says that for representation of small parties, it helps to have large assembly sizes, large district magnitudes, and large quotas or large gaps between divisors in seat allocation ... More


The Number of Seat‐Winning Parties and the Largest Seat Share

Rein Taagepera

in Predicting Party Sizes: The Logic of Simple Electoral Systems

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199287741
eISBN:
9780191713408
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199287741.003.0008
Subject:
Political Science, Democratization

The quantity to watch is the ‘seat product’ — the product of the assembly size and district magnitude. The number of parties represented in the assembly is approximately the fourth root of the seat ... More


Seat Shares of All Parties and the Effective Number of Parties

Rein Taagepera

in Predicting Party Sizes: The Logic of Simple Electoral Systems

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199287741
eISBN:
9780191713408
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199287741.003.0009
Subject:
Political Science, Democratization

As with Chapter 8, the ‘seat product’ is the important quantity to watch. The effective number of parties represented in the assembly is approximately the sixth root of the seat product. The average ... More


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