75,019 research outputs found
Quantity and number
Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity
Mathematical models of avascular cancer
This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions
Computing Invariants of Simplicial Manifolds
This is a survey of known algorithms in algebraic topology with a focus on
finite simplicial complexes and, in particular, simplicial manifolds. Wherever
possible an elementary approach is chosen. This way the text may also serve as
a condensed but very basic introduction to the algebraic topology of simplicial
manifolds.
This text will appear as a chapter in the forthcoming book "Triangulated
Manifolds with Few Vertices" by Frank H. Lutz.Comment: 13 pages, 3 figure
Parameterized complexity of machine scheduling: 15 open problems
Machine scheduling problems are a long-time key domain of algorithms and
complexity research. A novel approach to machine scheduling problems are
fixed-parameter algorithms. To stimulate this thriving research direction, we
propose 15 open questions in this area whose resolution we expect to lead to
the discovery of new approaches and techniques both in scheduling and
parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc
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