Objective
The aim of this fellowship is to enable Dr Christopher Good, as Scientist in Charge, and Dr Ziqin Feng, as Researcher, to carry out some innovative and mutually beneficial research utilizing their complementary skill sets.
The 13th Problem from Hilbert's famous list asks whether every continuous (respectively smooth) function of three variables can be written as a superposition (or, in modern parlance, composition) of continuous (respectively smooth) functions of two variables. Hilbert conjectured that the answer to this problem was `no.' However, in 1957, Kolmogorov together with his student Arnold gave a positive solution in the continuous case: every continuous function of n variables taken from the closed unit interval can be represented as a linear superposition of one-variable functions and the two-variable function addition. One might expect this result to have applications (for example to data analysis), since it allows for multi-dimensional functions to be expressed as `simpler' functions of one variable and addition. However, whilst being of great theoretical interest, Kolmogorov's result is highly non-constructive and does not obviously allow for this. Together with Professor Paul Gartside, Feng has made highly non-trivial extensions to Kolmogorov's theorem that suggest ways around these restrictions. This project aims to realize potential applications by providing improved algorithms, implementing the extensions in high-level computer code.
Vitushkin gave a negative answer to the smooth (differentiable) version of Hilbert's 13th problem in 1954, proving, in particular, that there are continuously differentiable functions of three variables which can not be written as a superposition of continuously differentiable functions of two variables. The project also aims to investigate just how smooth one can take the functions arising in Kolmogorov's theorem to be. Questions along these lines will be addressed through combinatorical analysis of Vitushkin's work, the topology of critical points, and approximation theory in function spaces.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciences computer and information sciences data science
- natural sciences mathematics pure mathematics topology
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP7-PEOPLE-2011-IIF
See other projects for this call
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
B15 2TT Birmingham
United Kingdom
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.