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

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

Solar Module Integrated Converters as Power Generator in Small Spacecrafts: Design and Verification Approach

As small satellites are becoming more widespread for new businesses and applications, the development time, failure rate and cost of the spacecraft must be reduced. One of the systems with the highest cost and the most frequent failure in the satellite is the Electrical Power System (EPS). One approach to achieve rapid development times while reducing the cost and failure rate is using scalable modules. We propose a solar module integrated converter (SMIC) and its verification process as a key component for power generation in EPS. SMIC integrates the solar array, its regulators and the telemetry acquisition unit. This paper details the design and verification process of the SMIC and presents the in-orbit results of 12 SMICs used in Ten-Koh satellite, which was developed in less than 1.5 years. The in-orbit data received since the launch reveal that solar module withstands not only the launching environment of H-IIA rocket but also more than 1500 orbits in LEO. The modular approach allowed the design, implementation and qualification of only one module, followed by manufacturing and integration of 12 subsequent flight units. The approach with the solar module can be followed in other components of the EPS such as battery and power regulators

Visual Algebraic proofs for Unknot Detection

A knot diagram looks like a two-dimensional drawing of aknotted rubberband. Proving that a given knot diagram can be untangled(that is, is a trivial knot, called an unknot) is one of the most famousproblems of knot theory. For a small knot diagram, one can try to finda sequence of untangling moves explicitly, but for a larger knot diagramproducing such a proof is difficult, and the produced proofs are hardto inspect and understand. Advanced approaches use algebra, with anadvantage that since the proofs are algebraic, a computer can be usedto produce the proofs, and, therefore, a proof can be produced evenfor large knot diagrams. However, such produced proofs are not easy toread and, for larger diagrams, not likely to be human readable at all.We propose a new approach combining advantages of these: the proofsare algebraic and can be produced by a computer, whilst each part ofthe proof can be represented as a reasonably small knot-like diagram(a new representation as a labeled tangle diagram), which can be easilyinspected by a human for the purposes of checking the proof and findingout interesting facts about the knot diagram

Comparative genomics approach to detecting split-coding regions in a low-coverage genome: lessons from the chimaera Callorhinchus milii (Holocephali, Chondrichthyes)

Recent development of deep sequencing technologies has facilitated de novo genome sequencing projects, now conducted even by individual laboratories. However, this will yield more and more genome sequences that are not well assembled, and will hinder thorough annotation when no closely related reference genome is available. One of the challenging issues is the identification of protein-coding sequences split into multiple unassembled genomic segments, which can confound orthology assignment and various laboratory experiments requiring the identification of individual genes. In this study, using the genome of a cartilaginous fish, Callorhinchus milii, as test case, we performed gene prediction using a model specifically trained for this genome. We implemented an algorithm, designated ESPRIT, to identify possible linkages between multiple protein-coding portions derived from a single genomic locus split into multiple unassembled genomic segments. We developed a validation framework based on an artificially fragmented human genome, improvements between early and recent mouse genome assemblies, comparison with experimentally validated sequences from GenBank, and phylogenetic analyses. Our strategy provided insights into practical solutions for efficient annotation of only partially sequenced (low-coverage) genomes. To our knowledge, our study is the first formulation of a method to link unassembled genomic segments based on proteomes of relatively distantly related species as references

4-Hydroxy-1-naphthaldehydes: proton transfer or deprotonation

A series of naphthaldehydes, including a Mannich base, have been investigated by UV-Vis spectroscopy, NMR and theoretical methods to explore their potential tautomerism. In the case of 4-hydroxy-1-naphthaldehyde concentration dependent deprotonation has been detected in methanol and acetonitrile. For 4-hydroxy-3-(piperidin-1-ylmethyl)-1-naphthaldehyde (a Mannich base) an intramolecular proton transfer involving the OH group and the piperidine nitrogen occurs. In acetonitrile the equilibrium is predominantly at the OH-form, whereas in methanol the proton transferred tautomer is the preferred form. In chloroform and toluene, the OH form is completely dominant. Both 4-hydroxy-1-naphthaldehyde and 4-methoxy-1-naphthaldehyde (fixed enol form) show dimerization in the investigated solvents and the crystallographic data, obtained for the latter, confirm the existence of a cyclic dimer

Dihedral semigroups, their defining relations and an application to describing knot semigroups of rational links

It is known that a knot (link) is rational if and only if its π-orbifold group is dihedral. A semigroup version of this result has been formulated as a conjecture. Working towards proving the conjecture, we describe certain semigroups associated with twist links, clarify how these semigroups are related to dihedral groups and find defining relations of these semigroups

Tilt Angle and Theoretical Target Strength of the Japanese Sandeel, Ammodytes personatus Captured on the Northern Coast of Hokkaido, Japan.

The tilt angle, i.e., the angle from horizontal made by the fish body as its head dives down or up, affects the readings on fish echo soundings. We measured the tilt angle of Japanese sandeels (Ammodytes personatus Girard) in a water tank, and calculated the acoustic target strength (TS) using a theoretical scattering model. This study examined the TS of sandeels from the northern coast of Hokkaido, which have a larger body size than those in other regions in Japan. TS values for sandeels, a swimbladderless fish, were estimated using a distorted-wave Born approximation (DWBA) model at two frequencies: 38 and 120 kHz. The mean tilt angle was 20.4?? (S.D. = 18.5??), which differed slightly from that of the lesser sandeel, Ammodytes marinus. The regression equations of the average TS values were TS38kHz = 8.2 log10SL ??? 74.2 and TS120kHz = 20.9 log10SL ??? 92.6, respectively. At 120 kHz, the slope was close to 20, suggesting that the acoustic backscattering strength was proportional to the square of the body length. This value was smaller at 38 kHz, suggesting that the acoustic backscattering strength was stable to differences in body length. We obtained a small discrepancy for both frequencies (??TS = TS120kHz???TS38kHz) were TS120kHz < TS38kHz. Discrepancies of ???1.3 dB for the maximum TS, and ???1.8 dB for averaged TS were found in 72 fish samples, which would be useful for identifying sandeel schools in practical analysis using TS differences