Knot Theory: from Fox 3-colorings of links to Yang-Baxter homology and Khovanov homology

This paper is an extended account of my "Introductory Plenary talk at Knots in Hellas 2016" conference We start from the short introduction to Knot Theory from the historical perspective, starting from Heraclas text (the first century AD), mentioning R.Llull (1232-1315), A.Kircher (1602-1680), Leibniz idea of Geometria Situs (1679), and J.B.Listing (student of Gauss) work of 1847. We spend some space on Ralph H. Fox (1913-1973) elementary introduction to diagram colorings (1956). In the second section we describe how Fox work was generalized to distributive colorings (racks and quandles) and eventually in the work of Jones and Turaev to link invariants via Yang-Baxter operators, here the importance of statistical mechanics to topology will be mentioned. Finally we describe recent developments which started with Mikhail Khovanov work on categorification of the Jones polynomial. By analogy to Khovanov homology we build homology of distributive structures (including homology of Fox colorings) and generalize it to homology of Yang-Baxter operators. We speculate, with supporting evidence, on co-cycle invariants of knots coming from Yang-Baxter homology. Here the work of Fenn-Rourke-Sanderson (geometric realization of pre-cubic sets of link diagrams) and Carter-Kamada-Saito (co-cycle invariants of links) will be discussed and expanded. Dedicated to Lou Kauffman for his 70th birthday.Comment: 35 pages, 31 figures, for Knots in Hellas II Proceedings, Springer, part of the series Proceedings in Mathematics & Statistics (PROMS

The immunobiology of primary sclerosing cholangitis

Primary sclerosing cholangitis (PSC) is a chronic cholestatic liver disease histologically characterized by the presence of intrahepatic and/or extrahepatic biliary duct concentric, obliterative fibrosis, eventually leading to cirrhosis. Approximately 75% of patients with PSC have inflammatory bowel disease. The male predominance of PSC, the lack of a defined, pathogenic autoantigen, and the potential role of the innate immune system suggest that it may be due to dysregulation of immunity rather than a classic autoimmune disease. However, PSC is associated with several classic autoimmune diseases, and the strongest genetic link to PSC identified to date is with the human leukocyte antigen DRB01*03 haplotype. The precise immunopathogenesis of PSC is largely unknown but likely involves activation of the innate immune system by bacterial components delivered to the liver via the portal vein. Induction of adhesion molecules and chemokines leads to the recruitment of intestinal lymphocytes. Bile duct injury results from the sustained inflammation and production of inflammatory cytokines. Biliary strictures may cause further damage as a result of bile stasis and recurrent secondary bacterial cholangitis. Currently, there is no effective therapy for PSC and developing a rational therapeutic strategy demands a better understanding of the disease

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta

Seaweeds and their communities in polar regions

Polar seaweeds typically begin to grow in late winter-spring, around the time of sea-ice break up. They can grow under very low light enabling distributions to depths of ≥40 m. Moreover, they are physiologically adapted to low temperatures. Intertidal species exhibit a remarkable stress tolerance against freezing, desiccation and salinity changes. Endemism is much greater in the Antarctic compared to the Arctic species. On rocky shores of the Antarctic Peninsula and of Spitsbergen >80% of the bottom can be covered by seaweeds with standing biomass levels ≥20 kg wet wt m-2. Species richness and biomass declines, however, towards higher latitudes. Seaweeds are the dominant organisms in coastal waters and thus play important roles in benthic food webs and are likely to be of particular importance to benthic detrital food chains. Chemical defenses against herbivores are common in Antarctic, but not in Arctic seaweeds. More research is needed especially to study the effects of global climate changes

Carbon balance under a changing light environment

The natural environment of Antarctic seaweeds is characterized by changing seasonal light conditions. The ability to adapt to this light regime is one of the most important prerequisites for their ecological success. Thus, the persistence of seaweeds depends on their capacity to maintain a positive carbon balance (CB)for buildup of biomass over the course of the year. A positive CB in Antarctica occurs only during the ice-free period in spring and summer, when photosynthetically active radiation (PAR, 400–700 nm) penetrates deeply into the water column. The accumulated carbon compounds during this period are stored and remobilized to support metabolism for the rest of the year. Over the last decades climate warming has induced a severe glacial retreat in Antarctica and has opened newly ice-free areas. Increased sediment runoff, and reduced light penetration due to melting during the warmer months, may lead to a negative CB with changes in the vertical distribution of seaweeds. Furthermore, warmer winters and springs result in earlier sea-ice melt, causing an abrupt increase in light, compensating the reduction in PAR in summer or increasing the annual light budget. Studies performed in Potter Cove, Isla 25 de Mayo/King George Island, reveal that algae growing in newly ice-free areas did not acclimate to the changing light conditions. Lower or even negative CB values in areas close to the glacier runoff seem to be primarily dependent on the incoming PAR that finally determines the lower distribution limit of seaweeds. The present chapter discusses how carbon balance respond to the changing Antarctic light environment and its potential implications for the fate of benthic algal communities