Examples of CM curves of genus two defined over the reflex field

In "Proving that a genus 2 curve has complex multiplication", van Wamelen lists 19 curves of genus two over $\mathbf{Q}$ with complex multiplication (CM). For each of the 19 curves, the CM-field turns out to be cyclic Galois over $\mathbf{Q}$. The generic case of non-Galois quartic CM-fields did not feature in this list, as the field of definition in that case always contains a real quadratic field, known as the real quadratic subfield of the reflex field. We extend van Wamelen's list to include curves of genus two defined over this real quadratic field. Our list therefore contains the smallest "generic" examples of CM curves of genus two. We explain our methods for obtaining this list, including a new height-reduction algorithm for arbitrary hyperelliptic curves over totally real number fields. Unlike Van Wamelen, we also give a proof of our list, which is made possible by our implementation of denominator bounds of Lauter and Viray for Igusa class polynomials.Comment: 31 pages; Updated some reference

On the arithmetic of a family of degree-two K3 surfaces

Let $\mathbb{P}$ denote the weighted projective space with weights $(1,1,1,3)$ over the rationals, with coordinates $x,y,z,$ and $w$; let $\mathcal{X}$ be the generic element of the family of surfaces in $\mathbb{P}$ given by \begin{equation*} X\colon w^2=x^6+y^6+z^6+tx^2y^2z^2. \end{equation*} The surface $\mathcal{X}$ is a K3 surface over the function field $\mathbb{Q}(t)$. In this paper, we explicitly compute the geometric Picard lattice of $\mathcal{X}$, together with its Galois module structure, as well as derive more results on the arithmetic of $\mathcal{X}$ and other elements of the family $X$.Comment: 20 pages; v2 with some all additions and clarifications suggested by the refere

A study of quartic K3 surfaces with a (Z/2Z)4 action

The main focus of this thesis is to study the equation A(x4+y4+z4+w4)+Bxyzw+C(x2y2+z2w2)+D(x2z2+y2w2)+E(x2w2+y2z2) = 0. To do so, we view this equation as a family of quartic K3 surfaces in P3[x,y,z,w], parametrised by points [A,B,C,D,E] E P4. We pursue two directions. First we look at 320 conics that such a K3 surface contains. In particular, we explore the field of definition of these 320 conics and the Monodromy group linked to these conics. In the other direction we explore the quartic K3 surfaces which contain lines. We list all subfamilies of K3 surfaces for which a very general member contains 8, 16, 24, 32 or 48 lines. We combine the two directions, by using the lines and conics found, to explore the Picard group of the various families found. In particular, not only do we work out the Picard rank of a very general member of a family, but we also decompose the Picard lattice into known lattices. This thesis has a secondary focus on hyperelliptic curves of genus two with complex multiplication (CM). At the end of the thesis, we design an algorithm to find CM curves of genus two which are defined over quadratic extensions of the rationals. To do so we also develop an algorithm which makes the coefficients of a curve smaller

Real-time embedded video denoiser prototype

International audienceLow light or other poor visibility conditions often generate noise on any vision system. However, video denoising requires a lot of computational effort and most of the state-of-the-art algorithms cannot be run in real-time at camera framerate. Noisy video is thus a major issue especially for embedded systems that provide low computational power. This article presents a new real-time video denoising algorithm for embedded platforms called RTE-VD [1]. We first compare its denoising capabilities with other online and offline algorithms. We show that RTE-VD can achieve real-time performance (25 frames per second) for qHD video (960x540 pixels) on embedded CPUs with an output image quality comparable to state-of-the-art algorithms. In order to reach real-time denoising, we applied several high-level transforms and optimizations. We study the relation between computation time and power consumption on several embedded CPUs and show that it is possible to determine find out frequency and core configurations in order to minimize either the computation time or the energy. Finally, we introduce VIRTANS our embedded real-time video denoiser based on RTE-VD

A New Real-Time Embedded Video Denoising Algorithm

International audienceMany embedded applications rely on video processing or on video visualization. Noisy video is thus a major issue for such applications. However, video denoising requires a lot of computational effort and most of the state-of-the-art algorithms cannot be run in real-time at camera framerate. This article introduces a new real-time video denoising algorithm for embedded platforms called RTE-VD. We first compare its denoising capabilities with other online and offline algorithms. We show that RTE-VD can achieve real-time performance (25 frames per second) for qHD video (960×540 pixels) on embedded CPUs and the output image quality is comparable to state-of-the-art algorithms. In order to reach real-time denoising, we applied several high-level transforms and optimizations (SIMDization, multi-core parallelization, operator fusion and pipelining). We study the relation between computation time and power consumption on several embedded CPUs and show that it is possible to determine different frequency and core configurations in order to minimize either the computation time or the energy

Two-Dimensional Patterning by a Trapping/Depletion Mechanism: The Role of TTG1 and GL3 in Arabidopsis Trichome Formation

Trichome patterning in Arabidopsis serves as a model system to study how single cells are selected within a field of initially equivalent cells. Current models explain this pattern by an activator–inhibitor feedback loop. Here, we report that also a newly discovered mechanism is involved by which patterning is governed by the removal of the trichome-promoting factor TRANSPARENT TESTA GLABRA1 (TTG1) from non-trichome cells. We demonstrate by clonal analysis and misexpression studies that Arabidopsis TTG1 can act non-cell-autonomously and by microinjection experiments that TTG1 protein moves between cells. While TTG1 is expressed ubiquitously, TTG1–YFP protein accumulates in trichomes and is depleted in the surrounding cells. TTG1–YFP depletion depends on GLABRA3 (GL3), suggesting that the depletion is governed by a trapping mechanism. To study the potential of the observed trapping/depletion mechanism, we formulated a mathematical model enabling us to evaluate the relevance of each parameter and to identify parameters explaining the paradoxical genetic finding that strong ttg1 alleles are glabrous, while weak alleles exhibit trichome clusters

iSense: a technology platform for cold atom based quantum technologies

A breakthrough in cold atom quantum technology is hindered by a bottleneck in the supporting technologies. We discuss a cold atom technology platform developed within the European iSense project, aiming at a gravimeter as demonstrator