Ergodicity and Conservativity of products of infinite transformations and their inverses

We construct a class of rank-one infinite measure-preserving transformations such that for each transformation $T$ in the class, the cartesian product $T\times T$ of the transformation with itself is ergodic, but the product $T\times T^{-1}$ of the transformation with its inverse is not ergodic. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.Comment: Added references and revised some arguments; removed old section 6; main results unchange

Large genus bounds for the distribution of triangulated surfaces in moduli space

Triangulated surfaces are compact Riemann surfaces equipped with a conformal triangulation by equilateral triangles. In 2004, Brooks and Makover asked how triangulated surfaces are distributed in the moduli space of Riemann surfaces as the genus tends to infinity. Mirzakhani raised this question in her 2010 ICM address. We show that in the large genus case, triangulated surfaces are well distributed in moduli space in a fairly strong sense. We do this by proving upper and lower bounds for the number of triangulated surfaces lying in a Teichmüller ball in moduli space. In particular, we show that the number of triangulated surfaces lying in a Teichmüller unit ball is at most exponential in the number of triangles, independent of the genus.Ph.D

Size Distribution ;Quorum Quenching Assays from Photophysical studies on curcumin-sophorolipid nanostructures: applications in quorum quenching and imaging

Zeta Potential (-38.41mV) and DLS (100nm, polydispersity index: 0.27) of CUASL (5w/v %);Bioluminescence reduction by CUASL (5w/v %

Modulating the Global Response Regulator, LuxO of V. cholerae Quorum Sensing System Using a Pyrazine Dicarboxylic Acid Derivative (PDCApy): An Antivirulence Approach

Vibrio cholerae is a Gram-negative pathogen which causes acute diarrhoeal disease, cholera by the expression of virulence genes through quorum sensing (QS) mechanism. The QS circuit of V. cholerae is controlled by the global quorum regulator, LuxO, which at low cell density (LCD) state produces major virulence factors such as, toxin co-regulated pilus (TCP) and cholera toxin (CT) to mediate infection. On the contrary, at the high cell density (HCD) state the virulent genes are downregulated and the vibrios are detached from the host intestinal epithelial cells, promoted by HapA protease. Hence, targeting the global regulator LuxO would be a promising approach to modulate the QS to curtail V. cholerae pathogenesis. In our earlier studies, LuxO targeted ligand, 2,3 pyrazine dicarboxylic acid (PDCA) and its derivatives having desired pharmacophore properties were chemically synthesized and were shown to have biofilm inhibition as well as synergistic activity with the conventionally used antibiotics. In the present study, the QS modulatory effect of the PDCA derivative with pyrrolidine moiety designated as PDCApy against the V. cholerae virulence gene expression was analyzed at various growth phases. The data significantly showed a several fold reduction in the expression of the genes, tcp and ct whereas the expression of hapR was upregulated at the LCD state. In addition, PDCApy reduced the adhesion and invasion of the vibrios onto the INT407 intestinal cell lines. Collectively, our data suggest that PDCApy could be a potential QS modulator (QSM) for the antivirulence therapeutic approach

Antimicrobial and Antibiofilm Potential of Acyclic Amines and Diamines against Multi-Drug Resistant Staphylococcus aureus

Multi-drug resistant Staphylococcus aureus (MDRSA) remains a great challenge despite a decade of research on antimicrobial compounds against their infections. In the present study, various acyclic amines and diamines were chemically synthesized and tested for their antimicrobial as well as antibiofilm activity against MDRSA. Among all the synthesized compounds, an acyclic diamine, (2,2′-((butane-1,4-diylbis(azanediyl)bis(methylene))diphenol) designated as ADM 3, showed better antimicrobial activity (minimum inhibitory concentration at 50 μg/mL) and antibiofilm activity (MBIC50 at 5 μg/mL). In addition, ADM 3 was capable of reducing the virulence factors expression (anti-virulence). Confocal laser scanning microscope analysis of the in vitro tested urinary catheters showed biofilm reduction as well as bacterial killing by ADM 3. On the whole, our data suggest that acyclic diamines, especially ADM 3 can be a potent lead for the further studies in alternative therapeutic approaches