2,714 research outputs found
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
A Primer on the Tools and Concepts of Computable Economics
Computability theory came into being as a result of Hilbert's attempts to meet Brouwer's challenges, from an intuitionistc and constructive standpoint, to formalism as a foundation for mathematical practice. Viewed this way, constructive mathematics should be one vision of computability theory. However, there are fundamental differences between computability theory and constructive mathematics: the Church-Turing thesis is a disciplining criterion in the former and not in the latter; and classical logic - particularly, the law of the excluded middle - is not accepted in the latter but freely invoked in the former, especially in proving universal negative propositions. In Computable Economic an eclectic approach is adopted where the main criterion is numerical content for economic entities. In this sense both the computable and the constructive traditions are freely and indiscriminately invoked and utilised in the formalization of economic entities. Some of the mathematical methods and concepts of computable economics are surveyed in a pedagogical mode. The context is that of a digital economy embedded in an information society
An Introduction to Programming for Bioscientists: A Python-based Primer
Computing has revolutionized the biological sciences over the past several
decades, such that virtually all contemporary research in the biosciences
utilizes computer programs. The computational advances have come on many
fronts, spurred by fundamental developments in hardware, software, and
algorithms. These advances have influenced, and even engendered, a phenomenal
array of bioscience fields, including molecular evolution and bioinformatics;
genome-, proteome-, transcriptome- and metabolome-wide experimental studies;
structural genomics; and atomistic simulations of cellular-scale molecular
assemblies as large as ribosomes and intact viruses. In short, much of
post-genomic biology is increasingly becoming a form of computational biology.
The ability to design and write computer programs is among the most
indispensable skills that a modern researcher can cultivate. Python has become
a popular programming language in the biosciences, largely because (i) its
straightforward semantics and clean syntax make it a readily accessible first
language; (ii) it is expressive and well-suited to object-oriented programming,
as well as other modern paradigms; and (iii) the many available libraries and
third-party toolkits extend the functionality of the core language into
virtually every biological domain (sequence and structure analyses,
phylogenomics, workflow management systems, etc.). This primer offers a basic
introduction to coding, via Python, and it includes concrete examples and
exercises to illustrate the language's usage and capabilities; the main text
culminates with a final project in structural bioinformatics. A suite of
Supplemental Chapters is also provided. Starting with basic concepts, such as
that of a 'variable', the Chapters methodically advance the reader to the point
of writing a graphical user interface to compute the Hamming distance between
two DNA sequences.Comment: 65 pages total, including 45 pages text, 3 figures, 4 tables,
numerous exercises, and 19 pages of Supporting Information; currently in
press at PLOS Computational Biolog
VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts
The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)
First order algorithms in variational image processing
Variational methods in imaging are nowadays developing towards a quite
universal and flexible tool, allowing for highly successful approaches on tasks
like denoising, deblurring, inpainting, segmentation, super-resolution,
disparity, and optical flow estimation. The overall structure of such
approaches is of the form ; where the functional is a data fidelity term also
depending on some input data and measuring the deviation of from such
and is a regularization functional. Moreover is a (often linear)
forward operator modeling the dependence of data on an underlying image, and
is a positive regularization parameter. While is often
smooth and (strictly) convex, the current practice almost exclusively uses
nonsmooth regularization functionals. The majority of successful techniques is
using nonsmooth and convex functionals like the total variation and
generalizations thereof or -norms of coefficients arising from scalar
products with some frame system. The efficient solution of such variational
problems in imaging demands for appropriate algorithms. Taking into account the
specific structure as a sum of two very different terms to be minimized,
splitting algorithms are a quite canonical choice. Consequently this field has
revived the interest in techniques like operator splittings or augmented
Lagrangians. Here we shall provide an overview of methods currently developed
and recent results as well as some computational studies providing a comparison
of different methods and also illustrating their success in applications.Comment: 60 pages, 33 figure
Variations on the Theme of Conning in Mathematical Economics
The mathematization of economics is almost exclusively in terms of the mathematics of real analysis which, in turn, is founded on set theory (and the axiom of choice) and orthodox mathematical logic. In this paper I try to point out that this kind of mathematization is replete with economic infelicities. The attempt to extract these infelicities is in terms of three main examples: dynamics, policy and rational expectations and learning. The focus is on the role and reliance on standard xed point theorems in orthodox mathematical economics
From Legos and Logos to Lambda: A Hypothetical Learning Trajectory for Computational Thinking
This thesis utilizes design-based research to examine the integration of computational thinking and computer science into the Finnish elementary mathematics syllabus. Although its focus is on elementary mathematics, its scope includes the perspectives of students, teachers and curriculum planners at all levels of the Finnish school curriculum. The studied artifacts are the 2014 Finnish National Curriculum and respective learning solutions for computer science education. The design-based research (DBR) mandates educators, developers and researchers to be involved in the cyclic development of these learning solutions. Much of the work is based on an in-service training MOOC for Finnish mathematics teachers, which was developed in close operation with the instructors and researchers. During the study period, the MOOC has been through several iterative design cycles, while the enactment and analysis stages of the 2014 Finnish National Curriculum are still proceeding.The original contributions of this thesis lie in the proposed model for teaching computational thinking (CT), and the clarification of the most crucial concepts in computer science (CS) and their integration into a school mathematics syllabus. The CT model comprises the successive phases of abstraction, automation and analysis interleaved with the threads of algorithmic and logical thinking as well as creativity. Abstraction implies modeling and dividing the problem into smaller sub-problems, and automation making the actual implementation. Preferably, the process iterates in cycles, i.e., the analysis feeds back such data that assists in optimizing and evaluating the efficiency and elegance of the solution. Thus, the process largely resembles the DBR design cycles. Test-driven development is also recommended in order to instill good coding practices.The CS fundamentals are function, variable, and type. In addition, the control flow of execution necessitates control structures, such as selection and iteration. These structures are positioned in the learning trajectories of the corresponding mathematics syllabus areas of algebra, arithmetic, or geometry. During the transition phase to the new syllabus, in-service mathematics teachers can utilize their prior mathematical knowledge to reap the benefits of ‘near transfer’. Successful transfer requires close conceptual analogies, such as those that exist between algebra and the functional programming paradigm.However, the integration with mathematics and the utilization of the functional paradigm are far from being the only approaches to teaching computing, and it might turn out that they are perhaps too exclusive. Instead of the grounded mathematics metaphor, computing may be perceived as basic literacy for the 21st century, and as such it could be taught as a separate subject in its own right
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