Objective
The starting point of this research proposal is a recent result by the PI, making progress in a half century old,
notoriously open problem. In the mid 1960’s, Tukey and Cooley discovered the Fast Fourier Transform, an
algorithm for performing one of the most important linear transformations in science and engineering, the
(discrete) Fourier transform, in time complexity O(n log n).
In spite of its importance, a super-linear lower bound has been elusive for many years, with only very limited
results. Very recently the PI managed to show that, roughly speaking, a faster Fourier transform must result
in information loss, in the form of numerical accuracy. The result can be seen as a type of computational
uncertainty principle, whereby faster computation increases uncertainty in data. The mathematical argument
is established by defining a type of matrix quasi-entropy, generalizing Shannon’s measure of information
(entropy) to “quasi-probabilities” (which can be negative, more than 1, or even complex).
This result, which is not believed to be tight, does not close the book on Fourier complexity. More importantly,
the vision proposed by the PI here reaches far beyond Fourier computation. The computation-information
tradeoff underlying the result suggests a novel view of complexity theory as a whole. We can now revisit
some classic complexity theoretical problems with a fresh view. Examples of these problems include better
understanding of the complexity of polynomial multiplication, integer multiplication, auto-correlation and
cross-correlation computation, dimensionality reduction via the Fast Johnson-Linednstrauss Transform (FJLT;
also discovered and developed by the PI), large scale linear algebra (linear regression, Principal Component
Analysis - PCA, compressed sensing, matrix multiplication) as well as binary functions such as integer multiplication.
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 mathematics pure mathematics algebra linear algebra
- natural sciences mathematics pure mathematics mathematical analysis
- natural sciences computer and information sciences computational science
- natural sciences computer and information sciences artificial intelligence machine learning
- natural sciences computer and information sciences artificial intelligence computational intelligence
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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.
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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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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.
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.
ERC-COG - Consolidator Grant
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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.
(opens in new window) ERC-2015-CoG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
32000 Haifa
Israel
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.