Cyclotomic expansions for glN knot invariants via interpolation Macdonald polynomials

In this paper we construct a new basis for the cyclotomic completion of the center of the quantum glN in terms of the interpolation Macdonald polynomials. Then we use a result of Okounkov to provide a dual basis with respect to the quantum Killing form (or Hopf pairing). The main applications are: 1) cyclotomic expansions for the glN Reshetikhin--Turaev link invariants and the universal glN knot invariant; 2) an explicit construction of the unified glN invariants for integral homology 3-spheres using universal Kirby colors. These results generalize those of Habiro for sl2. In addition, we give a simple proof of the fact that the universal glN invariant of any evenly framed link and the universal slN invariant of any 0-framed algebraically split link are Γ-invariant, where Γ=Y/2Y with the root lattice Y

Cyclotomic expansions for glN\mathfrak{gl}_N knot invariants via interpolation Macdonald polynomials

In this paper we construct a new basis for the cyclotomic completion of the center of the quantum $\mathfrak{gl}_N$ in terms of the interpolation Macdonald polynomials. Then we use a result of Okounkov to provide a dual basis with respect to the quantum Killing form (or Hopf pairing). The main applications are: 1) cyclotomic expansions for the $\mathfrak{gl}_N$ Reshetikhin--Turaev link invariants and the universal $\mathfrak{gl}_N$ knot invariant; 2) an explicit construction of the unified $\mathfrak{gl}_N$ invariants for integral homology 3-spheres using universal Kirby colors. These results generalize those of Habiro for $\mathfrak{sl}_2$. In addition, we give a simple proof of the fact that the universal $\mathfrak{gl}_N$ invariant of any evenly framed link and the universal $\mathfrak{sl}_N$ invariant of any $0$-framed algebraically split link are $\Gamma$-invariant, where $\Gamma=Y/2Y$ with the root lattice $Y$.Comment: 43 page

3D Mueller-matrix diffusive tomography of polycrystalline blood films for cancer diagnosis

The decomposition of the Mueller matrix of blood films has been carried out using differential matrices with polarized and depolarized parts. The use of a coherent reference wave is applied and the algorithm of digital holographic reconstruction of the field of complex amplitudes is used. On this basis, the 3D Mueller-matrix diffuse tomography method-the reconstruction of distributions of fluctuations of linear and circular birefringence of depolarizing polycrystalline films of human blood is analytically justified and experimentally tested. The dynamics of the change in the magnitude of the statistical moments of the first-fourth order, which characterize layer-by-layer distributions of fluctuations in the phase anisotropy of the blood film, is examined and analyzed. The most sensitive parameters for prostate cancer are the statistical moments of the third and fourth orders, which characterize the asymmetry and kurtosis of fluctuations in the linear and circular birefringence of blood films. The excellent accuracy of differentiation obtained polycrystalline films of blood from healthy donors and patients with cancer patients was achieved

Community-Level Responses to Iron Availability in Open Ocean Plankton Ecosystems

Predicting responses of plankton to variations in essential nutrients is hampered by limited in situ measurements, a poor understanding of community composition, and the lack of reference gene catalogs for key taxa. Iron is a key driver of plankton dynamics and, therefore, of global biogeochemical cycles and climate. To assess the impact of iron availability on plankton communities, we explored the comprehensive bio-oceanographic and bio-omics data sets from Tara Oceans in the context of the iron products from two state-of-the-art global scale biogeochemical models. We obtained novel information about adaptation and acclimation toward iron in a range of phytoplankton, including picocyanobacteria and diatoms, and identified whole subcommunities covarying with iron. Many of the observed global patterns were recapitulated in the Marquesas archipelago, where frequent plankton blooms are believed to be caused by natural iron fertilization, although they are not captured in large-scale biogeochemical models. This work provides a proof of concept that integrative analyses, spanning from genes to ecosystems and viruses to zooplankton, can disentangle the complexity of plankton communities and can lead to more accurate formulations of resource bioavailability in biogeochemical models, thus improving our understanding of plankton resilience in a changing environment

Invasive species alter ontogenetic shifts in the trophic ecology of Lake Sturgeon (Acipenser fulvescens) in the Niagara River and Lake Ontario

Species invasions can alter food web structure and change ecosystem-level functioning, but it is often unclear how these invasions may affect the life history of native species. The Lake Sturgeon (Acipenser fulvescens), a large long-lived native fish species in the Great Lakes, has increased in abundance in the lower Niagara River and nearby Lake Ontario during a period of invasive species-induced ecosystem change precipitated most recently by Dreissenid mussels (Driessena polymorpha and Driessena bugensis) and Round Goby (Neogobius melanostomus). Material taken from cross-sections of archived pectoral spines from Niagara River Lake Sturgeon captured in 1998–2000 and 2010–2012 were analyzed for stable isotopes across discrete growth zones to provide an ontogenetic assessment of diet, and diet analysis of Lake Sturgeon captured in 2014 was conducted to assess the contribution of invasive prey. Round Goby was the most important Lake Sturgeon prey item (86% by weight) in 2014, which corroborated results of δ15N and δ13C. Lake Sturgeon captured after the invasion of Round Goby exhibited ontogenetic changes in δ15N that differed from pre-Round Goby patterns, though this effect was weaker for δ13C. Values of δ15N from spine growth zones indicated non-linear increases in trophic position with age and increased rate of δ15N enrichment after the Round Goby invasion. We conclude that Round Goby establishment in western Lake Ontario changed the feeding ecology of Lake Sturgeon, which may have a positive effect on population growth for this native species

Novel trophic interaction between lake sturgeon (Acipenser fulvescens) and non-native species in an altered food web

Lake sturgeon (Acipenser fulvescens) were once abundantly distributed throughout the Laurentian Great Lakes. However, widespread overharvesting and habitat degradation has diminished their numbers. The lower Niagara River contains one of the few remnant lake sturgeon populations in New York State. This study determined the diet of adult lake sturgeon and quantified their trophic position in a food web dominated by non-native species. Stomach content analysis assessed recent diet, and stable isotope analysis (δ 15 N and δ 13 C) of blood and fin tissue quantified trophic position and carbon source over varying time scales. Two non-native species dominated the diet of lake sturgeon — the amphipod Echinogammarus ischnus (62% by number) and the round goby (Neogobius melanostomus) (44% by mass). Stable isotope analysis revealed that round goby was the primary contributor to the long-term (i.e., fin) average diet, whereas short-term (i.e., blood) diet was more diverse. In contrast with findings from other systems, we found that adult lake sturgeon in the lower Niagara River were primarily piscivorous, actively targeting live fish prey. The recovery of this population is potentially supported by the high availability of energetically rich but non-native food resources

Humble beginnings with big goals: Small molecule soluble epoxide hydrolase inhibitors for treating CNS disorders

Soluble epoxide hydrolase (sEH) degrades epoxides of fatty acids including epoxyeicosatrienoic acid isomers (EETs), which are produced as metabolites of the cytochrome P450 branch of the arachidonic acid pathway. EETs exert a variety of largely beneficial effects in the context of inflammation and vascular regulation. sEH inhibition is shown to be therapeutic in several cardiovascular and renal disorders, as well as in peripheral analgesia, via the increased availability of anti-inflammatory EETs. The success of sEH inhibitors in peripheral systems suggests their potential in targeting inflammation in the central nervous system (CNS) disorders. Here, we describe the current roles of sEH in the pathology and treatment of CNS disorders such as stroke, traumatic brain injury, Parkinson's disease, epilepsy, cognitive impairment, dementia and depression. In view of the robust anti-inflammatory effects of stem cells, we also outlined the potency of stem cell treatment and sEH inhibitors as a combination therapy for these CNS disorders. This review highlights the gaps in current knowledge about the pathologic and therapeutic roles of sEH in CNS disorders, which should guide future basic science research towards translational and clinical applications of sEH inhibitors for treatment of neurological diseases