EPSILON DICHOTOMY FOR LINEAR MODELS (Analytic, geometric and pp-adic aspects of automorphic forms and LL-functions)

This is an expanded version of my talk at the RIMS conference "Analytic, geometric and p-adic aspects of automorphic forms and L-functions". It surveys some recent work towards a conjecture of Prasad and Takloo-Bighash on epsilon dichotomy for linear models. I thank the organizers of the conference for their hospitality. I am also grateful to Miyu Suzuki for her help during the preparation of this note. This work is partially supported by the NSF grant DMS #1901862

Twisted linear periods and a new relative trace formula

We study the linear periods on $GL_{2n}$ twisted by a character using a new relative trace formula. We establish the relative fundamental lemma and the transfer of orbital integrals. Together with the spectral isolation technique of Beuzart-Plessis--Liu--Zhang--Zhu, we are able to compare the elliptic part of the relative trace formulae and to obtain new results generalizing Waldspurger's theorem in the $n=1$ case

The arithmetic and geometry of genus four curves

We construct a point in the Jacobian of a non-hyperelliptic genus four curve which is defined over a quadratic extension of the base field. We attempt to answer two questions: 1. Is this point torsion? 2. If not, does it generate the Mordell--Weil group of the Jacobian? We show that this point generates the Mordell--Weil group of the Jacobian of the universal genus four curve. We construct some families of genus four curves over the function field of \bP^1 over a finite field and prove that half of the Jacobians in this family are generated by this point via the other half are not. We then turn to the case where the base field is a number field or a function field. We compute the Neron--Tate height of this point in terms of the self-intersection of the relative dualizing sheaf of (the stable model of) the curve and some local invariants depending on the completion of the curve at the places where this curve has bad or smooth hyperelliptic reduction. In the case where the reduction satisfies some certain conditions, we compute these local invariants explicitly

Omega-3 Polyunsaturated Fatty Acids Antagonize Macrophage Inflammation via Activation of AMPK/SIRT1 Pathway

Macrophages play a key role in obesity-induced inflammation. Omega-3 polyunsaturated fatty acids (v-3 PUFAs) eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) exert anti-inflammatory functions in both humans and animal models, but the exact cellular signals mediating the beneficial effects are not completely understood. We previously found that two nutrient sensors AMP-activated protein kinase (AMPK) and SIRT1 interact to regulate macrophage inflammation. Here we aim to determine whether v-3 PUFAs antagonize macrophage inflammation via activation of AMPK/SIRT1 pathway. Treatment of v-3 PUFAs suppresses lipopolysaccharide (LPS)-induced cytokine expression in macrophages. Luciferase reporter assays, electrophoretic mobility shift assays (EMSA) and Chromatin immunoprecipitation (ChIP) assays show that treatment of macrophages with v-3 PUFAs significantly inhibits LPS-induced NF-kB signaling. Interestingly, DHA also increases expression, phosphorylation and activity of the major isoform a1AMPK, which further leads to SIRT1 overexpression. More importantly, DHA mimics the effect of SIRT1 on deacetylation of the NF-kB subunit p65, and the ability of DHA to deacetylate p65 and inhibit its signaling and downstream cytokine expression require SIRT1. In conclusion, v-3 PUFAs negatively regulate macrophage inflammation by deacetylating NF-kB, which acts through activation of AMPK/SIRT1 pathway. Our study defines AMPK/SIRT1 as a novel cellular mediator for the anti-inflammatory effects of v-3 PUFAs

Development of docetaxel and alendronate-loaded chitosan-conjugated polylactide-co-glycolide nanoparticles: In vitro characterization in osteosarcoma cells

Purpose: To develop docetaxel (DTX)- and alendronate (ALN)-loaded, chitosan  (CS)-conjugated polylactide- co-glycolide (PLGA) nanoparticles (NPs) to increase therapeutic efficacy in osteosarcoma cells.Methods: Drug-loaded PLGA NPs were prepared by nanoprecipitation and  chemically conjugated by the carboxylic group of PLGA to the amine-bearing CS polymer. The nanocarrier was characterized by dynamic light scattering, transmission electron microscopy, scanning electron microscopy, and differential scanning calorimetry as well as by in vitro drug release and cell culture studies.Results: NP size was within the tumour targeting range (~200 nm) with an effective positive charge (20 mV), thus increasing cellular uptake efficiency. Morphological analysis revealed clear spherical particles with uniform dispersion. The NPs  exhibited identical sustained release kinetics for both DTX and ALN. CS-conjugated PLGA with dual-drug-loaded (DTX and AL) NPs showed typical time-dependent cellular uptake and also displayed superior cytotoxicity in MG-63 cells compared with blank NPs, which were safe and biocompatible.Conclusion: Combined loading of DTX and ALN in NPs increased the therapeutic efficacy of the formulation for osteosarcoma treatment, thus indicating the potential benefit of a combinatorial drug regimen using nanocarriers for effective treatment of osteosarcoma.Keywords: Chitosan, Docetaxel, Alendronate, Nanocarriers, Sustained-release kinetics, Polylactide-coglycolide, Osteosarcoma, Cellular uptak