Blogs

COST Action INDEPTH Approved !

The European COST Action entitled Impact of Nuclear Domains On Gene Expression and Plant Traits (INDEPTH for short, summary on page 14) borne by my University and my biologist friends has been approved!
More news about that coming soon!

I'll consider job offers

I'll consider serious job offers which show good prospects to move forward quickly my main Research Project. Please drop me an e-mail...

A Theory for Integer Only Numerical Analysis

A draft of our Theory for Integer Only Numerical Analysis is now online. Summary:
  1. Generic notion of an anlyzable space (algebraic structure)
  2. Generic nD notion of a differentiation mask and convolution based differentiation operators.
  3. New ??? version for the famous Taylor Theorem with multiple integreal remainder
  4. Multigrid convergence of nD differential estimators of any order under various noise models
  5. Multidiemensional Generalized B-Spline families, analytical functions, and piecewise Besier surfaces
  6. Explicit expression of B-splines using piecewise Bernstein Polynomials
  7. Basic idea for linear PDE intheger only solutions
The PDF of the draft is available here

Sparse convolution-based digital derivatives (TCS paper)

Our paper on 1D integer only numerical analysis has been published as: Henri-Alex Esbelin, Rémy Malgouyres, Sparse convolution-based digital derivatives, fast estimation for noisy signals and approximation results, Journal of Theoretical Computer Science (TCS), Elsevier, 2016. Summary:
  1. Notion of a Digital Derivative and main properties
  2. Different families of masks
  3. Multigrid convergence for derivative estimation for any order and from possibly noisy signal
  4. Explicit expression of uniform B-splines as piecewise Bernstein polynomials
  5. Multidiemensional Generalized B-Spline families, analytical functions, and piecewise Besier surfaces
  6. Interpretation of Digital Derivatives as derivatives of B-splines
The PDF of the paper available here
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