The switch operators and push-the-button games: a sequential compound over rulesets

We study operators that combine combinatorial games. This field was initiated by Sprague-Grundy (1930s), Milnor (1950s) and Berlekamp-Conway-Guy (1970-80s) via the now classical disjunctive sum operator on (abstract) games. The new class consists in operators for rulesets, dubbed the switch-operators. The ordered pair of rulesets (R 1 , R 2) is compatible if, given any position in R 1 , there is a description of how to move in R 2. Given compatible (R 1 , R 2), we build the push-the-button game R 1 R 2 , where players start by playing according to the rules R 1 , but at some point during play, one of the players must switch the rules to R 2 , by pushing the button ". Thus, the game ends according to the terminal condition of ruleset R 2. We study the pairwise combinations of the classical rulesets Nim, Wythoff and Euclid. In addition, we prove that standard periodicity results for Subtraction games transfer to this setting, and we give partial results for a variation of Domineering, where R 1 is the game where the players put the domino tiles horizontally and R 2 the game where they play vertically (thus generalizing the octal game 0.07).Comment: Journal of Theoretical Computer Science (TCS), Elsevier, A Para{\^i}tr

Partition games

We introduce CUT, the class of 2-player partition games. These are NIM type games, played on a finite number of heaps of beans. The rules are given by a set of positive integers, which specifies the number of allowed splits a player can perform on a single heap. In normal play, the player with the last move wins, and the famous Sprague-Grundy theory provides a solution. We prove that several rulesets have a periodic or an arithmetic periodic Sprague-Grundy sequence (i.e. they can be partitioned into a finite number of arithmetic progressions of the same common difference). This is achieved directly for some infinite classes of games, and moreover we develop a computational testing condition, demonstrated to solve a variety of additional games. Similar results have previously appeared for various classes of games of take-and-break, for example octal and hexadecimal; see e.g. Winning Ways by Berlekamp, Conway and Guy (1982). In this context, our contribution consists of a systematic study of the subclass `break-without-take'

HABILITATION A DIRIGER DES RECHERCHES Graphes et jeux combinatoires

On considère généralement que la théorie des graphes est née au 18e siècle, et qu'elle connaît un essor significatif depuis les années 1960. L'avènement de la théorie des jeux combinatoires est quant à lui plus récent (fin des années 1970). Ce domaine reste alors moins exploré dans la littérature, et de nombreuses études sur des techniques générales de résolution sont toujours actuellement en cours de construction. Dans ce mémoire, je propose plusieurs tours d'horizons à propos de problématiques bien ciblées de ces deux domaines.Dans un premier temps, je m'interroge sur la complexité des règles de jeux de suppression de tas. Il s'avère que dans la littérature, la complexité d'un jeu est souvent définie comme la complexité algorithmique d'une stratégie gagnante. Cependant, il peut aussi avoir du sens de s'interroger sur la nature des règles de jeu. Un premier pas dans cette direction a été fait avec l'introduction du concept de jeu dit invariant. On notera au passage que certains résultats obtenus ont mis en exergue des liens entre combinatoire des mots et stratégie gagnante d'un jeu. Dans un deuxième chapitre, j'aborde les jeux sous l'angle des graphes. Deux aspects sont considérés:* Un graphe peut être vu comme un support de jeu. Le cas du jeu de Nim et ses variantes sur les graphes y est examiné.* Certaines problématiques standard de théorie des graphes peuvent être transformées dans une version ludique. C'est d'ailleurs un objet d'étude de plus en plus prisé par la communauté. Nous détaillerons le cas des jeux de coloration sommet.Enfin, le dernier chapitre se concentre sur deux nouvelles variantes de problématiques issues de la théorie des graphes: le placement de graphes et les colorations distinguantes. J'en profite pour faire un état de l'art des principaux résultats sur ces deux domaines

Molecular Tools for Adapting Viticulture to Climate Change

Adaptation of viticulture to climate change includes exploration of new geographical areas, new training systems, new management practices, or new varieties, both for rootstocks and scions. Molecular tools can be defined as molecular approaches used to study DNAs, RNAs, and proteins in all living organisms. We present here the current knowledge about molecular tools and their potential usefulness in three aspects of grapevine adaptation to the ongoing climate change. (i) Molecular tools for understanding grapevine response to environmental stresses. A fine description of the regulation of gene expression is a powerful tool to understand the physiological mechanisms set up by the grapevine to respond to abiotic stress such as high temperatures or drought. The current knowledge on gene expression is continuously evolving with increasing evidence of the role of alternative splicing, small RNAs, long non-coding RNAs, DNA methylation, or chromatin activity. (ii) Genetics and genomics of grapevine stress tolerance. The description of the grapevine genome is more and more precise. The genetic variations among genotypes are now revealed with new technologies with the sequencing of very long DNA molecules. High throughput technologies for DNA sequencing also allow now the genetic characterization at the same time of hundreds of genotypes for thousands of points in the genome, which provides unprecedented datasets for genotype-phenotype associations studies. We review the current knowledge on the genetic determinism of traits for the adaptation to climate change. We focus on quantitative trait loci and molecular markers available for developmental stages, tolerance to water stress/water use efficiency, sugar content, acidity, and secondary metabolism of the berries. (iii) Controlling the genome and its expression to allow breeding of better-adapted genotypes. High-density DNA genotyping can be used to select genotypes with specific interesting alleles but genomic selection is also a powerful method able to take into account the genetic information along the whole genome to predict a phenotype. Modern technologies are also able to generate mutations that are possibly interesting for generating new phenotypes but the most promising one is the direct editing of the genome at a precise location

Wythoff Wisdom

International audienceSix authors tell their stories from their encounters with the famous combinatorial game Wythoff Nim and its sequences, including a short survey on exactly covering systems

Orbits for the Impatient: A Bayesian Rejection Sampling Method for Quickly Fitting the Orbits of Long-Period Exoplanets

We describe a Bayesian rejection sampling algorithm designed to efficiently compute posterior distributions of orbital elements for data covering short fractions of long-period exoplanet orbits. Our implementation of this method, Orbits for the Impatient (OFTI), converges up to several orders of magnitude faster than two implementations of MCMC in this regime. We illustrate the efficiency of our approach by showing that OFTI calculates accurate posteriors for all existing astrometry of the exoplanet 51 Eri b up to 100 times faster than a Metropolis-Hastings MCMC. We demonstrate the accuracy of OFTI by comparing our results for several orbiting systems with those of various MCMC implementations, finding the output posteriors to be identical within shot noise. We also describe how our algorithm was used to successfully predict the location of 51 Eri b six months in the future based on less than three months of astrometry. Finally, we apply OFTI to ten long-period exoplanets and brown dwarfs, all but one of which have been monitored over less than 3% of their orbits, producing fits to their orbits from astrometric records in the literature.Comment: 32 pages, 28 figures, Accepted to A

Phase Referencing in Optical Interferometry

One of the aims of next generation optical interferometric instrumentation is to be able to make use of information contained in the visibility phase to construct high dynamic range images. Radio and optical interferometry are at the two extremes of phase corruption by the atmosphere. While in radio it is possible to obtain calibrated phases for the science objects, in the optical this is currently not possible. Instead, optical interferometry has relied on closure phase techniques to produce images. Such techniques allow only to achieve modest dynamic ranges. However, with high contrast objects, for faint targets or when structure detail is needed, phase referencing techniques as used in radio interferometry, should theoretically achieve higher dynamic ranges for the same number of telescopes. Our approach is not to provide evidence either for or against the hypothesis that phase referenced imaging gives better dynamic range than closure phase imaging. Instead we wish to explore the potential of this technique for future optical interferometry and also because image reconstruction in the optical using phase referencing techniques has only been performed with limited success. We have generated simulated, noisy, complex visibility data, analogous to the signal produced in radio interferometers, using the VLTI as a template. We proceeded with image reconstruction using the radio image reconstruction algorithms contained in AIPS IMAGR (CLEAN algorithm). Our results show that image reconstruction is successful in most of our science cases, yielding images with a 4 milliarcsecond resolution in K band. (abridged)Comment: 11 pages, 36 figure

Bringing "The Moth" to Light: A Planet-Sculpting Scenario for the HD 61005 Debris Disk

The HD 61005 debris disk ("The Moth") stands out from the growing collection of spatially resolved circumstellar disks by virtue of its unusual swept-back morphology, brightness asymmetries, and dust ring offset. Despite several suggestions for the physical mechanisms creating these features, no definitive answer has been found. In this work, we demonstrate the plausibility of a scenario in which the disk material is shaped dynamically by an eccentric, inclined planet. We present new Keck NIRC2 scattered-light angular differential imaging of the disk at 1.2-2.3 microns that further constrains its outer morphology (projected separations of 27-135 AU). We also present complementary Gemini Planet Imager 1.6 micron total intensity and polarized light detections that probe down to projected separations less than 10 AU. To test our planet-sculpting hypothesis, we employed secular perturbation theory to construct parent body and dust distributions that informed scattered-light models. We found that this method produced models with morphological and photometric features similar to those seen in the data, supporting the premise of a planet-perturbed disk. Briefly, our results indicate a disk parent body population with a semimajor axis of 40-52 AU and an interior planet with an eccentricity of at least 0.2. Many permutations of planet mass and semimajor axis are allowed, ranging from an Earth mass at 35 AU to a Jupiter mass at 5 AU.Comment: Accepted to AJ; added Figure 5 and minor text edit

An improved reference of the grapevine genome supports reasserting the origin of the PN40024 highly-homozygous genotype

The genome sequence assembly of the diploid and highly homozygous V. vinifera genotype PN40024 serves as the reference for many grapevine studies. Despite several improvements of the PN40024 genome assembly, its current version PN12X.v2 is quite fragmented and only represents the haploid state of the genome with mixed haplotypes. In fact, despite the PN40024 genome is nearly homozygous, it still contains various heterozygous regions. Taking the opportunity of the improvements that long-read sequencing technologies offer to fully discriminate haplotype sequences and considering that several Vitis sp. genomes have recently been assembled with these approaches, an improved version of the reference, called PN40024.v4, was generated. Through incorporating long genomic sequencing reads to the assembly, the continuity of the 12X.v2 scaffolds was highly increased. The number of scaffolds decreased from 2,059 to 640 and the number of N bases was reduced by 88%. Additionally, the full alternative haplotype sequence was built for the first time, the chromosome anchoring was improved and the amount of unplaced scaffolds were reduced by half. To obtain a high-quality gene annotation that outperforms previous versions, a liftover approach was complemented with an optimized annotation workflow for Vitis. Integration of the gene reference catalogue and its manual curation have also assisted in improving the annotation, while defining the most reliable estimation to date of 35,230 genes. Finally, we demonstrate that PN40024 resulted from selfings of cv. ‘Helfensteiner’ (cross of cv. ‘Pinot noir’ and ‘Schiava grossa’) instead of a single ‘Pinot noir’. These advances will help maintaining the PN40024 genome as a gold-standard reference also contributing in the eventual elaboration of the grapevine pangenome.Unpublishe

A Multi-Year Photometric Study of IC 348

The extremely young cluster IC 348 has been monitored photometrically over 5 observing seasons from Dec 1998 to March 2003 in Cousins I with a 0.6 m telescope at Van Vleck Observatory. Twenty-eight periodic variables and 16 irregular variables have been identified. Among the brighter stars, 14 of the 16 known K or M-type WTTS were found to be periodic variables, while all 5 of the known CTTS were found to be irregular variables. In the full sample, which includes 150 stars with I mag as faint as 18, we find that 40% of the 63 WTTS are detected as variables, nearly all of them periodic, while 55% of the 20 CTTS are also detected as variable, with none of them periodic. Our study suggests that 80-90% of all WTTS in young clusters will be detected as periodic variables given sufficiently precise and extended monitoring, whereas CTTS will reveal themselves primarily or solely as irregular variables. This has clear consequences for PMS rotational studies based on photometric periods. We examine the stability of the periodic light curves from season to season. All periodic stars show modulations of their amplitude, mean brightness and light curve shape on time scales of less than 1 yr, presumably due to changes in spot configurations and/or physical characteristics. In no case, however, can we find definitive evidence of a change in period, indicating that differential rotation is probably much less on WTTS than it is on the Sun. Among the non-periodic stars, we report the detection of two possible UXors as well as a pre-main sequence star, HMW 15, which apparently undergoes an eclipse with a duration exceeding three years