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Proportional Lumpability

2019
We deal with the lumpability approach to cope with the state space explosion problem inherent to the computation of the performance indices of large stochastic models using a state aggregation technique. The lumpability method applies to Markov chains exhibiting some structural regularity and allows one to efficiently compute the exact values of the ...
Andrea Marin, Carla Piazza, Sabina Rossi
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Proportion: Learning Proportional Reasoning Together

2012
Proportional reasoning is a broadly applicable skill that is fundamental to mathematical understanding. While the cognitive development of proportional reasoning is well understood, traditional learning methods are often ineffective. They provide neither real-time feedback nor sophisticated tools to scaffold learning.
Jochen Rick   +3 more
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The Proportional Effect

Mathematical Geosciences, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Manchuk, J. G.   +2 more
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Distribution and proportion

Journal of Philosophical Logic, 1995
The author's aim is to defend the Aristotelian concept of distribution against Geach's criticism (see section IV) by applying it to extended syllogistic systems. Section I deals with ``fractional'' syllogistics containing statements of the form ``more than 1/2 of the \(S\) are \(P\)'' or ``at least 7/8 of \(S\) are not \(P\)''.
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How proportional is proportional representation?

The Mathematical Intelligencer, 1986
In a very popular way the author discusses the problem of division of seats in some assembly between parties provided the number of votes received by these parties at the elections is known. The author shows why the proportional distribution is not adequate and discusses different quota methods, e.g. D'Hondt's rule, Droop quota etc.
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On proportional plus proportional-integral suboptimal control

IEEE Transactions on Automatic Control, 1975
Two suboptimal control policies employing integral state feedback suitable for nonlinear systems and nonquadratic performance functionals have been proposed. Necessary conditions are obtained using the variational approach to select optimally the time-invariant parameters for a general control structure of which the two suboptimal policies proposed are
Bharathan, P. K.   +2 more
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Proportional Budgeting and Decentralization

Econometrica, 1995
Summary: Governments, universities, and other not-for-profit organizations frequently employ two -- potentially incongruent -- budgeting procedures: proportional budgeting and decentralization. The former entails allocating budget increments or decrements uniformly across divisions or sectors of the organization.
Blackorby, Charles, Russell, R Robert
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Proportional Ventilatory Support: A Comparison of Proportional Assist Ventilation, Proportional Pressure Support and Proportional Pressure Ventilation

Respiratory Care, 2018
Background: Proportional ventilatory support (PVS) refers to modes of ventilation that provide support that is proportional to the patient's inspiratory effort. Research has shown that PVS improves patient ventilator synchrony. Several ventilators are now available that provide a type of PVS.
Sanders, Alex   +3 more
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Case Fatality Proportion

Bulletin of Mathematical Biology, 2007
A precise definition of case fatality proportion for compartmental disease transmission models with disease induced mortality rate is given. This is applied in classical epidemic modeling frameworks to models with multiple infectious stages, with multi-groups, with spatial patches, and with age of infection.
Ma, Junling, van den Driessche, P.
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CONSISTENCY FOR PROPORTIONAL SOLUTIONS

International Game Theory Review, 2002
One of the properties characterizing cooperative game solutions is consistency connecting solution vectors of a cooperative game with finite set of players and its reduced game defined by removing one or more players and by assigning them the payoffs according to some specific principle (e.g., a proposed payoff vector). Consistency of a solution means
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