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

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

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

Development of CRISPR-Cas13a-based antimicrobials capable of sequence-specific killing of target bacteria

The emergence of antimicrobial-resistant bacteria is an increasingly serious threat to global health, necessitating the development of innovative antimicrobials. Here we report the development of a series of CRISPR-Cas13a-based antibacterial nucleocapsids, termed CapsidCas13a(s), capable of sequence-specific killing of carbapenem-resistant Escherichia coli and methicillin-resistant Staphylococcus aureus by recognizing corresponding antimicrobial resistance genes. CapsidCas13a constructs are generated by packaging programmed CRISPR-Cas13a into a bacteriophage capsid to target antimicrobial resistance genes. Contrary to Cas9-based antimicrobials that lack bacterial killing capacity when the target genes are located on a plasmid, the CapsidCas13a(s) exhibit strong bacterial killing activities upon recognizing target genes regardless of their location. Moreover, we also demonstrate that the CapsidCas13a(s) can be applied to detect bacterial genes through gene-specific depletion of bacteria without employing nucleic acid manipulation and optical visualization devices. Our data underscore the potential of CapsidCas13a(s) as both therapeutic agents against antimicrobial-resistant bacteria and nonchemical agents for detection of bacterial genes

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

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

Correction to: Compartments in medulloblastoma with extensive nodularity are connected through differentiation along the granular precursor lineage (Nature Communications, (2024), 15, 1, (269), 10.1038/s41467-023-44117-x)

\ua9 The Author(s) 2024.Correction to: Nature Communications https://doi.org/10.1038/s41467-023-44117-x, published online 08 January 2024 In the Acknowledgements section, the following sentence ‘The development of spatial transcriptomics protocol was supported by the START-HD project within the HMLS Explorer program of the University of Heidelberg’ should have read ‘The development of spatial transcriptomics protocols was supported by the Baden- W\ufcrttemberg Stiftung (project MET-ID41-STARFISH) and by the HMLS Explorer program of the University of Heidelberg (project START-HD). The original article has been corrected