Regular projections of graphs with at most three double points

A generic immersion of a planar graph into the 2-space is said to be knotted if there does not exist a trivial embedding of the graph into the 3-space obtained by lifting the immersion with respect to the natural projection from the 3-space to the 2-space. In this paper we show that if a generic immersion of a planar graph is knotted then the number of double points of the immersion is more than or equal to three. To prove this, we also show that an embedding of a graph obtained from a generic immersion of the graph (does not need to be planar) with at most three double points is totally free if it contains neither a Hopf link nor a trefoil knot.Comment: 16 pages, 31 figure

Fiber amplification of radially and azimuthally polarized laser light

The results on amplifying either radially or azimuthally polarized light with a fiber amplifier are presented. Experimental results reveal that more than 85% polarization purity can be retained at the output even with 40dB amplification, and that efficient conversion of the amplified light to linear polarization can be obtained.Comment: 3 pages, 4 figures, submitted to optics letter

Knots, Braids and BPS States in M-Theory

In previous work we considered M-theory five branes wrapped on elliptic Calabi-Yau threefold near the smooth part of the discriminant curve. In this paper, we extend that work to compute the light states on the worldvolume of five-branes wrapped on fibers near certain singular loci of the discriminant. We regulate the singular behavior near these loci by deforming the discriminant curve and expressing the singularity in terms of knots and their associated braids. There braids allow us to compute the appropriate string junction lattice for the singularity and,hence to determine the spectrum of light BPS states. We find that these techniques are valid near singular points with N=2 supersymmetry.Comment: 38 page

Characteristics of a Microcystin-Degrading Bacterium under Alkaline Environmental Conditions

The pH of the water associated with toxic blooms of cyanobacteria is typically in the alkaline range; however, previously only microcystin-degrading bacteria growing in neutral pH conditions have been isolated. Therefore, we sought to isolate and characterize an alkali-tolerant microcystin-degrading bacterium from a water bloom using microcystin-LR. Analysis of the 16S rRNA gene sequence revealed that the isolated bacterium belonged to the genus Sphingopyxis, and the strain was named C-1. Sphingopyxis sp. C-1 can grow; at pH 11.0; however, the optimum pH for growth was pH 7.0. The microcystin degradation activity of the bacterium was the greatest between pH 6.52 and pH 8.45 but was also detected at pH 10.0. The mlrA homolog encoding the microcystin-degrading enzyme in the C-1 strain was conserved. We concluded that alkali-tolerant microcystin-degrading bacterium played a key role in triggering the rapid degradation of microcystin, leading to the disappearance of toxic water blooms in aquatic environments

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

A specious unlinking strategy

We show that the following unlinking strategy does not always yield an optimal sequence of crossing changes: first split the link with the minimal number of crossing changes, and then unknot the resulting components

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

Adaptation of a distributed controller depending on morphology

In this paper, we investigate the influence of an agent’s morphology on its neural controller. Our model consists of a number of identical modules, each of which comprises two half-wheels for movement and a central pattern generator (CPG) as its own neural control. Based on a series of simulation experiments, we conclude that one single type of CPG can adapt well to different types of morphologies, and that there seems to be a suitable or optimal morphology depending on the environmental givens