149,415 research outputs found
Ecological Modelling with the Calculus of Wrapped Compartments
The Calculus of Wrapped Compartments is a framework based on stochastic
multiset rewriting in a compartmentalised setting originally developed for the
modelling and analysis of biological interactions. In this paper, we propose to
use this calculus for the description of ecological systems and we provide the
modelling guidelines to encode within the calculus some of the main
interactions leading ecosystems evolution. As a case study, we model the
distribution of height of Croton wagneri, a shrub constituting the endemic
predominant species of the dry ecosystem in southern Ecuador. In particular, we
consider the plant at different altitude gradients (i.e. at different
temperature conditions), to study how it adapts under the effects of global
climate change.Comment: A preliminary version of this paper has been presented in CMC13 (LNCS
7762, pp 358-377, 2013
Problems in number theory from busy beaver competition
By introducing the busy beaver competition of Turing machines, in 1962, Rado
defined noncomputable functions on positive integers. The study of these
functions and variants leads to many mathematical challenges. This article
takes up the following one: How can a small Turing machine manage to produce
very big numbers? It provides the following answer: mostly by simulating
Collatz-like functions, that are generalizations of the famous 3x+1 function.
These functions, like the 3x+1 function, lead to new unsolved problems in
number theory.Comment: 35 page
Alternative Modes for Teaching Mathematical Problem Solving: An Overview
Various modes are proffered as alternatives for teaching mathematical problem solving. Each mode is described briefly, along with general purposes, advantages and disadvantages. Combinations of modes are suggested; general issues identified; recommendations offered; and feedback from teachers summarized
Stewardship of Test-Free Nuclear Arsenals
Maintaining nuclear arms in the current policy environment that frowns upon weapons testing coexists with a set of unresolved and disquieting issues regarding the disposition of test-free arsenals. Ivan Sanfrachuk, director of the World Security Institute's Moscow office explores the Russian perspective on international policies regarding the safety and reliability of the world's nuclear arsenals
The Busy Beaver Competition: a historical survey
Tibor Rado defined the Busy Beaver Competition in 1962. He used Turing
machines to give explicit definitions for some functions that are not
computable and grow faster than any computable function. He put forward the
problem of computing the values of these functions on numbers 1, 2, 3, ... More
and more powerful computers have made possible the computation of lower bounds
for these values. In 1988, Brady extended the definitions to functions on two
variables. We give a historical survey of these works. The successive record
holders in the Busy Beaver Competition are displayed, with their discoverers,
the date they were found, and, for some of them, an analysis of their behavior.Comment: 70 page
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