Fast systematic encoding of multiplicity codes

We present quasi-linear time systematic encoding algorithms for multiplicity codes. The algorithms have their origins in the fast multivariate interpolation and evaluation algorithms of van der Hoeven and Schost (2013), which we generalise to address certain Hermite-type interpolation and evaluation problems. By providing fast encoding algorithms for multiplicity codes, we remove an obstruction on the road to the practical application of the private information retrieval protocol of Augot, Levy-dit-Vehel and Shikfa (2014)

A new Truncated Fourier Transform algorithm

Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in terms of ring operations, is comparable to existing not-in-place TFT methods. We also describe a transformation that maps between two families of TFT algorithms that use different sets of evaluation points.Comment: 8 pages, submitted to the 38th International Symposium on Symbolic and Algebraic Computation (ISSAC 2013

Change of basis for m-primary ideals in one and two variables

Following recent work by van der Hoeven and Lecerf (ISSAC 2017), we discuss the complexity of linear mappings, called untangling and tangling by those authors, that arise in the context of computations with univariate polynomials. We give a slightly faster tangling algorithm and discuss new applications of these techniques. We show how to extend these ideas to bivariate settings, and use them to give bounds on the arithmetic complexity of certain algebras.Comment: In Proceedings ISSAC'19, ACM, New York, USA. See proceedings version for final formattin

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Gustaaf A. van der Hoeven, Energy efficient landscaping, Kansas State University, November 1982

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Gustaaf A. van der Hoeven, Landscaping the farmstead, Kansas State University, December 1983

The role of antiphase boundaries during ion sputtering and solid phase epitaxy of Si(001)

The Si(001) surface morphology during ion sputtering at elevated temperatures and solid phase epitaxy following ion sputtering at room temperature has been investigated using scanning tunneling microscopy. Two types of antiphase boundaries form on Si(001) surfaces during ion sputtering and solid phase epitaxy. One type of antiphase boundary, the AP2 antiphase boundary, contributes to the surface roughening. AP2 antiphase boundaries are stable up to 973K, and ion sputtering and solid phase epitaxy performed at 973K result in atomically flat Si(001) surfaces.Comment: 16 pages, 4 figures, to be published in Surface Scienc

Virulence behavior of uropathogenic Escherichia coli strains in the host model Caenorhabditis elegans

Urinary tract infections (UTIs) are among the most common bacterial infections in humans. Although a number of bacteria can cause UTIs, most cases are due to infection by uropathogenic Escherichia coli (UPEC). UPEC are a genetically heterogeneous group that exhibit several virulence factors associated with colonization and persistence of bacteria in the urinary tract. Caenorhabditis elegans is a tiny, free-living nematode found worldwide. Because many biological pathways are conserved in C. elegans and humans, the nematode has been increasingly used as a model organism to study virulence mechanisms of microbial infections and innate immunity. The virulence of UPEC strains, characterized for antimicrobial resistance, pathogenicity-related genes associated with virulence and phylogenetic group belonging was evaluated by measuring the survival of C. elegans exposed to pure cultures of these strains. Our results showed that urinary strains can kill the nematode and that the clinical isolate ECP110 was able to efficiently colonize the gut and to inhibit the host oxidative response to infection. Our data support that C. elegans, a free-living nematode found worldwide, could serve as an in vivo model to distinguish, among uropathogenic E. coli, different virulence behavior

Towards a Model Theory for Transseries

The differential field of transseries extends the field of real Laurent series, and occurs in various context: asymptotic expansions, analytic vector fields, o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field, and report on our efforts to understand its first-order theory.Comment: Notre Dame J. Form. Log., to appear; 33 p