Homotopy techniques for multiplication modulo triangular sets

International audienceWe study the cost of multiplication modulo triangular families of polynomials. Following previous work by Li et al. (2007), we propose an algorithm that relies on homotopy and fast evaluation-interpolation techniques. We obtain a quasi-linear time complexity for substantial families of examples, for which no such result was known before. Applications are given notably to additions of algebraic numbers in small characteristic

Algorithms for zero-dimensional ideals using linear recurrent sequences

Inspired by Faug\`ere and Mou's sparse FGLM algorithm, we show how using linear recurrent multi-dimensional sequences can allow one to perform operations such as the primary decomposition of an ideal, by computing the annihilator of one or several such sequences.Comment: LNCS, Computer Algebra in Scientific Computing CASC 201

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page

A Cluster of MYB Transcription Factors Regulates Anthocyanin Biosynthesis in Carrot (Daucus carota L.) Root and Petiole

Purple carrots can accumulate large quantities of anthocyanins in their roots and –in some genetic backgrounds- petioles, and therefore they represent an excellent dietary source of antioxidant phytonutrients. In a previous study, using linkage analysis in a carrot F2 mapping population segregating for root and petiole anthocyanin pigmentation, we identified a region in chromosome 3 with co-localized QTL for all anthocyanin pigments of the carrot root, whereas petiole pigmentation segregated as a single dominant gene and mapped to one of these “root pigmentation” regions conditioning anthocyanin biosynthesis. In the present study, we performed fine mapping combined with gene expression analyses (RNA-Seq and RT-qPCR) to identify candidate genes controlling anthocyanin pigmentation in the carrot root and petiole. Fine mapping was performed in four carrot populations with different genetic backgrounds and patterns of pigmentation. The regions controlling root and petiole pigmentation in chromosome 3 were delimited to 541 and 535 kb, respectively. Genome wide prediction of transcription factor families known to regulate the anthocyanin biosynthetic pathway coupled with orthologous and phylogenetic analyses enabled the identification of a cluster of six MYB transcription factors, denominated DcMYB6 to DcMYB11, associated with the regulation of anthocyanin biosynthesis. No anthocyanin biosynthetic genes were present in this region. Comparative transcriptome analysis indicated that upregulation of DcMYB7 was always associated with anthocyanin pigmentation in both root and petiole tissues, whereas DcMYB11 was only upregulated with pigmentation in petioles. In the petiole, the level of expression of DcMYB11 was higher than DcMYB7. DcMYB6, a gene previously suggested as a key regulator of carrot anthocyanin biosynthesis, was not consistently associated with pigmentation in either tissue. These results strongly suggest that DcMYB7 is a candidate gene for root anthocyanin pigmentation in all the genetic backgrounds included in this study. DcMYB11 is a candidate gene for petiole pigmentation in all the purple carrot sources in this study. Since DcMYB7 is co-expressed with DcMYB11 in purple petioles, the latter gene may act also as a co-regulator of anthocyanin pigmentation in the petioles. This study provides linkage-mapping and functional evidence for the candidacy of these genes for the regulation of carrot anthocyanin biosynthesis

Symphytum Species: A Comprehensive Review on Chemical Composition, Food Applications and Phytopharmacology

Symphytum species belongs to the Boraginaceae family and have been used for centuries for bone breakages, sprains and rheumatism, liver problems, gastritis, ulcers, skin problems, joint pain and contusions, wounds, gout, hematomas and thrombophlebitis. Considering the innumerable potentialities of the Symphytum species and their widespread use in the world, it is extremely important to provide data compiling the available literature to identify the areas of intense research and the main gaps in order to design future studies. The present review aims at summarizing the main data on the therapeutic indications of the Symphytum species based on the current evidence, also emphasizing data on both the e cacy and adverse e ects. The present review was carried out by consulting PubMed (Medline), Web of Science, Embase, Scopus, Cochrane Database, Science Direct and Google Scholar (as a search engine) databases to retrieve the most updated articles on this topic. All articles were carefully analyzed by the authors to assess their strengths and weaknesses, and to select the most useful ones for the purpose of review, prioritizing articles published from 1956 to 2018. The pharmacological e ects of the Symphytum species are attributed to several chemical compounds, among them allantoin, phenolic compounds, glycopeptides, polysaccharides and some toxic pyrrolizidine alkaloids. Not less important to highlight are the risks associated with its use. In fact, there is increasing consumption of over-the-counter drugs, which when associated with conventional drugs can cause serious and even fatal adverse events. Although clinical trials sustain the folk topical application of Symphytum species in musculoskeletal and blunt injuries, with minor adverse e ects, its antimicrobial potency was still poorly investigated. Further studies are needed to assess the antimicrobial spectrum of Symphytum species and to characterize the active molecules both in vitro and in vivo

Collisionless kinetic theory of rolling molecules

We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of statistical physics. In particular, we show that even though the energy of the system is conserved, and the system is closed in the thermodynamic sense, some fundamental features of statistical physics such as invariant measure do not hold for such nonholonomic systems. Nevertheless, we are able to construct a consistent kinetic theory using Hamilton's variational principle in Lagrangian variables, by regarding the kinetic solution as being concentrated on the constraint distribution. A cold fluid closure for the kinetic system is also presented, along with a particular class of exact solutions of the kinetic equations.Comment: Revised version; 31 pages, 1 figur

Autopolyploid inheritance and a heterozygous reciprocal translocation shape chromosome genetic behavior in tetraploid blueberry (Vaccinium corymbosum)

Understanding chromosome recombination behavior in polyploidy species is key to advancing genetic discoveries. In blueberry, a tetraploid species, the line of evidences about its genetic behavior still remain poorly understood, owing to the inter-specific, and inter-ploidy admixture of its genome and lack of in depth genome-wide inheritance and comparative structural studies. Here we describe a new high-quality, phased, chromosome-scale genome of a diploid blueberry, clone W85. The genome was integrated with cytogenetics and high-density, genetic maps representing six tetraploid blueberry cultivars, harboring different levels of wild genome admixture, to uncover recombination behavior and structural genome divergence across tetraploid and wild diploid species. Analysis of chromosome inheritance and pairing demonstrated that tetraploid blueberry behaves as an autotetraploid with tetrasomic inheritance. Comparative analysis demonstrated the presence of a reciprocal, heterozygous, translocation spanning one homolog of chr-6 and one of chr-10 in the cultivar Draper. The translocation affects pairing and recombination of chromosomes 6 and 10. Besides the translocation detected in Draper, no other structural genomic divergences were detected across tetraploid cultivars and highly inter-crossable wild diploid species. These findings and resources will facilitate new genetic and comparative genomic studies in Vaccinium and the development of genomic assisted selection strategy for this cro

New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain

In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair-correlations in the Ising chain in a transverse field. The results are seen to match extremely well long large-time asymptotic expansions newly derived here. For our initial conditions we use new long asymptotic expansions for the equal-time pair correlation functions of the transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising model. Using this one can also study the equal-time wavevector-dependent correlation function of the quantum chain, a.k.a. the q-dependent diagonal susceptibility in the 2d Ising model, in great detail with very little computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references added and minor changes of style. vs3: Corrections made and reference adde

High-spin States in \u3csup\u3e191, 193\u3c/sup\u3eAu and \u3csup\u3e192\u3c/sup\u3ePt: Evidence for Oblate Deformation and Triaxial Shapes

High-spin states of 191, 193Au and 192Pt have been populated in the 186W(11B, xn) and 186W(11B, p4n) reactions, respectively, at a beam energy of 68 MeV and their γ decay was studied using the YRAST Ball detector array at the Wright Nuclear Structure Laboratory at Yale University. The level scheme of 193Au has been extended up to Iπ = 55/2+. New transitions were observed also in 191Au and 192Pt. Particle-plus-Triaxial-Rotor (PTR) and Total Routhian Surface (TRS) calculations were performed to determine the equilibrium deformations of the Au isotopes. The predictions for oblate deformations in these nuclei are in agreement with the experimental data. Development of nonaxial shapes is discussed within the framework of the PTR model