The First-Order Genus of a Knot

We introduce a geometric invariant of knots in the three-sphere, called the first-order genus, that is derived from certain 2-complexes called gropes, and we show it is computable for many examples. While computing this invariant, we draw some interesting conclusions about the structure of a general Seifert surface for some knots.Comment: 14 pages, 17 figure

Noncommutative knot theory

The classical abelian invariants of a knot are the Alexander module, which is the first homology group of the the unique infinite cyclic covering space of S^3-K, considered as a module over the (commutative) Laurent polynomial ring, and the Blanchfield linking pairing defined on this module. From the perspective of the knot group, G, these invariants reflect the structure of G^(1)/G^(2) as a module over G/G^(1) (here G^(n) is the n-th term of the derived series of G). Hence any phenomenon associated to G^(2) is invisible to abelian invariants. This paper begins the systematic study of invariants associated to solvable covering spaces of knot exteriors, in particular the study of what we call the n-th higher-order Alexander module, G^(n+1)/G^(n+2), considered as a Z[G/G^(n+1)$-module. We show that these modules share almost all of the properties of the classical Alexander module. They are torsion modules with higher-order Alexander polynomials whose degrees give lower bounds for the knot genus. The modules have presentation matrices derived either from a group presentation or from a Seifert surface. They admit higher-order linking forms exhibiting self-duality. There are applications to estimating knot genus and to detecting fibered, prime and alternating knots. There are also surprising applications to detecting symplectic structures on 4-manifolds. These modules are similar to but different from those considered by the author, Kent Orr and Peter Teichner and are special cases of the modules considered subsequently by Shelly Harvey for arbitrary 3-manifolds.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-19.abs.htm

Characterization of Knots and Links Arising From Site-specific Recombination on Twist Knots

We develop a model characterizing all possible knots and links arising from recombination starting with a twist knot substrate, extending previous work of Buck and Flapan. We show that all knot or link products fall into three well-understood families of knots and links, and prove that given a positive integer $n$, the number of product knots and links with minimal crossing number equal to $n$ grows proportionally to $n^5$. In the (common) case of twist knot substrates whose products have minimal crossing number one more than the substrate, we prove that the types of products are tightly prescribed. Finally, we give two simple examples to illustrate how this model can help determine previously uncharacterized experimental data.Comment: 32 pages, 7 tables, 27 figures, revised: figures re-arranged, and minor corrections. To appear in Journal of Physics

TCO evaluation in physical asset management : benefits and limitations for industrial adoption

Part 1: Knowledge-Based Performance ImprovementInternational audienceNowadays, the evaluation of the total cost of ownership (TCO) of an asset for supporting informed decision-making both for investments and managerial issues within the asset management framework is gaining increasing attention in industry. Nevertheless its application in practice is still limited. The aim of this paper is to analyze the benefits and limitations of the adoption of TCO evaluation in asset management. Based on a literature review, the paper defines a framework that categorizes the benefits and potential applications that a TCO model can have for different stakeholders. Together with that, industry related issues that influence its implementation are also considered. Finally, empirical evidences are analyzed through a multiple case study to understand if those benefits are recognized in practice and which are the limitations for the practical adoption of a TCO model that should allow exploiting such benefits

Cross-species epigenetics identifies a critical role for VAV1 in SHH subgroup medulloblastoma maintenance

The identification of key tumorigenic events in Sonic Hedgehog (SHH) subgroup medulloblastomas (MBSHH) will be essential for the development of individualized therapies and improved outcomes. However, beyond confirmation of characteristic SHH pathway mutations, recent genome-wide sequencing studies have not revealed commonly mutated genes with widespread relevance as potential therapeutic targets. We therefore examined any role for epigenetic DNA methylation events in MBSHH using a cross-species approach to candidate identification, prioritization and validation. MBSHH-associated DNA methylation events were first identified in 216 subgrouped human medulloblastomas (50 MBSHH, 28 Wnt/Wingless, 44 Group 3 and 94 Group 4) and their conservation then assessed in tumors arising from four independent murine models of Shh medulloblastoma, alongside any role in tumorigenesis using functional assessments in mouse and human models. This strategy identified widespread regional CpG hypo-methylation of VAV1, leading to its elevated expression, as a conserved aberrant epigenetic event, which characterizes the majority of MBSHH tumors in both species, and is associated with a poor outcome in MBSHH patients. Moreover, direct modulation of VAV1 in mouse and human models revealed a critical role in tumor maintenance, and its abrogation markedly reduced medulloblastoma growth. Further, Vav1 activity regulated granule neuron precursor germinal zone exit and migration initiation in an ex vivo model of early postnatal cerebellar development. These findings establish VAV1 as a critical epigenetically regulated oncogene with a key role in MBSHH maintenance, and highlight its potential as a validated therapeutic target and prognostic biomarker for the improved therapy of medulloblastoma

Conditional Creation and Rescue of Nipbl-Deficiency in Mice Reveals Multiple Determinants of Risk for Congenital Heart Defects

Elucidating the causes of congenital heart defects is made difficult by the complex morphogenesis of the mammalian heart, which takes place early in development, involves contributions from multiple germ layers, and is controlled by many genes. Here, we use a conditional/invertible genetic strategy to identify the cell lineage(s) responsible for the development of heart defects in a Nipbl-deficient mouse model of Cornelia de Lange Syndrome, in which global yet subtle transcriptional dysregulation leads to development of atrial septal defects (ASDs) at high frequency. Using an approach that allows for recombinase-mediated creation or rescue of Nipbl deficiency in different lineages, we uncover complex interactions between the cardiac mesoderm, endoderm, and the rest of the embryo, whereby the risk conferred by genetic abnormality in any one lineage is modified, in a surprisingly non-additive way, by the status of others. We argue that these results are best understood in the context of a model in which the risk of heart defects is associated with the adequacy of early progenitor cell populations relative to the sizes of the structures they must eventually form

Three Small Planets Transiting a Hyades Star

We present the discovery of three small planets transiting K2-136 (LP 358 348, EPIC 247589423), a late K dwarf in the Hyades. The planets have orbital periods of $7.9757 \pm 0.0011$, $17.30681^{+0.00034}_{-0.00036}$, and $25.5715^{+0.0038}_{-0.0040}$ days, and radii of $1.05 \pm 0.16$, $3.14 \pm 0.36$, and $1.55^{+0.24}_{-0.21}$ $R_\oplus$, respectively. With an age of 600-800 Myr, these planets are some of the smallest and youngest transiting planets known. Due to the relatively bright (J=9.1) host star, the planets are compelling targets for future characterization via radial velocity mass measurements and transmission spectroscopy. As the first known star with multiple transiting planets in a cluster, the system should be helpful for testing theories of planet formation and migration.Comment: Accepted to The Astronomical Journa

Investigating the Bivalve Tree of Life -- an exemplar-based approach combining molecular and novel morphological characters.

To re-evaluate the relationships of the major bivalve lineages, we amassed detailed morpho-anatomical, ultrastructural and molecular sequence data for a targeted selection of exemplar bivalves spanning the phylogenetic diversity of the class. We included molecular data for 103 bivalve species (up to five markers) and also analysed a subset of taxa with four additional nuclear protein-encoding genes. Novel as well as historically employed morphological characters were explored, and we systematically disassembled widely used descriptors such as gill and stomach ‘types’. Phylogenetic analyses, conducted using parsimony direct optimisation and probabilistic methods on static alignments (maximum likelihood and Bayesian inference) of the molecular data, both alone and in combination with morphological characters, offer a robust test of bivalve relationships. A calibrated phylogeny also provided insights into the tempo of bivalve evolution. Finally, an analysis of the informativeness of morphological characters showed that sperm ultrastructure characters are among the best morphological features to diagnose bivalve clades, followed by characters of the shell, including its microstructure. Our study found support for monophyly of most broadly recognised higher bivalve taxa, although support was not uniform for Protobranchia. However, monophyly of the bivalves with protobranchiate gills was the best-supported hypothesis with incremental morphological and/or molecular sequence data. Autobranchia, Pteriomorphia, Heteroconchia, Palaeoheterodonta, Archiheterodonta, Euheterodonta, Anomalodesmata and Imparidentia new clade ( = Euheterodonta excluding Anomalodesmata) were recovered across analyses, irrespective of data treatment or analytical framework. Another clade supported by our analyses but not formally recognised in the literature includes Palaeoheterodonta and Archiheterodonta, which emerged under multiple analytical conditions. The origin and diversification of each of these major clades is Cambrian or Ordovician, except for Archiheterodonta, which diverged from Palaeoheterodonta during the Cambrian, but diversified during the Mesozoic. Although the radiation of some lineages was shifted towards the Palaeozoic (Pteriomorphia, Anomalodesmata), or presented a gap between origin and diversification (Archiheterodonta, Unionida), Imparidentia showed steady diversification through the Palaeozoic and Mesozoic. Finally, a classification system with six major monophyletic lineages is proposed to comprise modern Bivalvia: Protobranchia, Pteriomorphia, Palaeoheterodonta, Archiheterodonta, Anomalodesmata and Imparidentia

Acute Homeostatic Responses to Increased Fat Consumption in MCH1R Knockout Mice

Melanin-concentrating hormone (MCH) is a hypothalamic neuropeptide which has been shown to regulate energy homeostasis. Using genetic knockout mice lacking the MCH1 receptor (MCH1R), we investigated how these mice adapt to metabolic changes caused by excessive caloric consumption. We show that the MCH system is one of the players mediating behavioral and metabolic responses upon increased caloric consumption. MCH1R knockout mice showed decreased tendency of food intake upon exposure to a high-fat diet. They also are resistant to gain weight upon high-fat diet by increasing fat metabolism. Therefore, the MCH system is important in regulating metabolic responses upon various environmental stimuli such as high-fat diet

Describing semigroups with defining relations of the form xy=yz xy and yx=zy and connections with knot theory

We introduce a knot semigroup as a cancellative semigroup whose defining relations are produced from crossings on a knot diagram in a way similar to the Wirtinger presentation of the knot group; to be more precise, a knot semigroup as we define it is closely related to such tools of knot theory as the twofold branched cyclic cover space of a knot and the involutory quandle of a knot. We describe knot semigroups of several standard classes of knot diagrams, including torus knots and torus links T(2, n) and twist knots. The description includes a solution of the word problem. To produce this description, we introduce alternating sum semigroups as certain naturally defined factor semigroups of free semigroups over cyclic groups. We formulate several conjectures for future research