(SEMI-)GLOBAL ANALYTIC HYPOELLIPTICITY FOR A CLASS OF "SUMS OF SQUARES" WHICH FAIL TO BE LOCALLY ANALYTIC HYPOELLIPTIC

The global and semi-global analytic hypoellipticity on the torus is proved for two classes of sums of squares operators, introduced by P. Albano, A. Bove, and M. Mughetti, satisfying the Ho spacing diaeresis rmander condition and which fail to be either locally or microlocally analytic hypoelliptic

On the microlocal regularity of the analytic vectors for "sums of squares" of vector fields

We prove via FBI-transform a result concerning the microlocal Gevrey regularity of analytic vectors for operators sums of squares of vector fields with real-valued real analytic coefficients of Hormander type, thus providing a microlocal version, in the analytic category, of a result due to Derridj (Pac J Math 302(2):511-543, 2019) concerning the problem of the local regularity for the Gevrey vectors for sums of squares of vector fields with real-valued real analytic/Gevrey coefficients

An Empirical Study On Text Summarization Techniques By Integrating NLP With Machine And Deep Learning Techniques

From the past few decades, data storage in multiple sources is getting more attention. Due to either time constraints in the current scenario or busy life in the co-operate world irrespective of the age factor, people did attract towards reading the in short news to get acquainted with the national and international news especially in their regional languages. So, the proposed paper has conducted an empirical study on the regional language "Telugu," summarization that generates a brief note of huge texts stored in multiple databases. In the early days, text summarization does perform with traditional NLP approaches, with the advancement of Artificial Intelligence; it has spread its wings to the world of NLP also, to summarize the text smartly. Smart Text Summarization technique can reduce the time and work a lot for any human to understand the exact purpose of that document. However, the real complexity arises while developing such an abstract summary by choosing the required words or phrases that fit the whole document. Some kinds of texts also were used to find its sensitivity which is frequently used in social media texts, reviews, and e-commerce sites to know the exact view of the customer or the person

Analytic and Gevrey Hypoellipticity for Perturbed Sums of Squares Operators

We prove a couple of results concerning pseudodifferential perturbations of differential operators being sums of squares of vector fields and satisfying H\"ormander's condition. The first is on the minimal Gevrey regularity: if a sum of squares with analytic coefficients is perturbed with a pseudodifferential operator of order strictly less than its subelliptic index it still has the Gevrey minimal regularity. We also prove a statement concerning real analytic hypoellipticity for the same type of pseudodifferential perturbations, provided the operator satisfies to some extra conditions (see Theorem 1.2 below) that ensure the analytic hypoellipticity

In search for potential antidiabetic compounds from natural sources: docking, synthesis and biological screening of small molecules from Lycium spp. (Goji)

© 2019 Current clinical antidiabetic drugs, like rosiglitazone 1, have been implicated in some serious side effects like edema, weight gain, and heart failure, making it necessary to find alternative agents. Partial agonists of peroxisome-proliferator activated receptor-gamma (PPARγ) were determined to possess improved insulin sensitivity without undeseirable side-effects when compared to full agonists of PPARγ, like rosiglitazone 1. The traditional Chinese medicine (TCM) plants, Goji (Lycium barbarum and Lycium chinense) are widely used for treating symptoms related to various diseases including diabetes and hypertension. Twenty-seven reported compounds from Goji were docked into both partial- and full-agonist binding sites of PPARγ. Amongst the docked compounds, phenylethylamide-based phytochemicals (5–9) (termed as tyramine-derivatives, TDs) were found to possess good docking scores and binding poses with favorable interactions. Synthesis of 24 TDs, including three naturally occuring amides (6, 8, 9) were synthesized and tested for PPARγ gene induction with cell-based assay. Three compounds showed similar or higher fold induction than the positive control, rosiglitazone. Among these three active TDs, trans-N-feruloyloctopamine (9) and tyramine derivatives-enriched extract (TEE) (21%) of the root bark of L. chinense were further studied in vivo using db/db mice. However, both TEE as well as 9 did not show significant antidiabetic properties in db/db mice. In vivo results suggest that the proposed antidiabetic property of Lycium species may not be due to tyramine derivatives alone. Further studies of tyramine derivatives or enriched extract(s) for other bioactivities like hypocholesterolemic activities, and studies of novel isolated compounds from Goji will enable a more complete understanding of their bioactivities

CXCR4 Expression in Prostate Cancer Progenitor Cells

Tumor progenitor cells represent a population of drug-resistant cells that can survive conventional chemotherapy and lead to tumor relapse. However, little is known of the role of tumor progenitors in prostate cancer metastasis. The studies reported herein show that the CXCR4/CXCL12 axis, a key regulator of tumor dissemination, plays a role in the maintenance of prostate cancer stem-like cells. The CXCL4/CXCR12 pathway is activated in the CD44+/CD133+ prostate progenitor population and affects differentiation potential, cell adhesion, clonal growth and tumorigenicity. Furthermore, prostate tumor xenograft studies in mice showed that a combination of the CXCR4 receptor antagonist AMD3100, which targets prostate cancer stem-like cells, and the conventional chemotherapeutic drug Taxotere, which targets the bulk tumor, is significantly more effective in eradicating tumors as compared to monotherapy

Chemokine Coreceptor Signaling in HIV-1 Infection and Pathogenesis

Binding of the HIV-1 envelope to its chemokine coreceptors mediates two major biological events: membrane fusion and signaling transduction. The fusion process has been well studied, yet the role of chemokine coreceptor signaling in viral infection has remained elusive through the past decade. With the recent demonstration of the signaling requirement for HIV latent infection of resting CD4 T cells, the issue of coreceptor signaling needs to be thoroughly revisited. It is likely that virus-mediated signaling events may facilitate infection in various immunologic settings in vivo where cellular conditions need to be primed; in other words, HIV may exploit the chemokine signaling network shared among immune cells to gain access to downstream cellular components, which can then serve as effective tools to break cellular barriers. This virus-hijacked aberrant signaling process may in turn facilitate pathogenesis. In this review, we summarize past and present studies on HIV coreceptor signaling. We also discuss possible roles of coreceptor signaling in facilitating viral infection and pathogenesis