Remark on fundamental groups and effective Diophantine methods for hyperbolic curves

In a letter from Grothendieck to Faltings, it was suggested that a positive answer to the section conjecture should imply finiteness of points on hyperbolic curves over number fields. In this paper, we point out instead the analogy between the section conjecture and the finiteness conjecture for the Tate-Shafarevich group of elliptic curves. That is, the section conjecture should provide a terminating algorithm for finding all rational points on a hyperbolic curve equipped with a rational point

Combinatorial Library Enumeration and Lead Hopping using Comparative Interaction Fingerprint Analysis and Classical 2D QSAR Methods for Seeking Novel GABAA r3 Modulators

Selective modulators of GABAA R3 (gamma amino butyric acid R3) receptor are known to alleviate the side effects associated with nonspecific modulators. A follow up study was undertaken on a series of functionally selective phthalazines with an ideological credo of identifying more potent isofunctional chemotypes. A bioisosteric database enumerated using the combichem approach endorsed mining in a lead-like chemical space. Primary screening of the massive library was undertaken using the “Miscreen” toolkit, which uses sophisticated bayesian statistics for calculating bioactivity score. The resulting subset, thus, obtained was mined using a novel proteo-chemometric method that integrates molecular docking and QSAR formalism termed CoIFA (comparative interaction fingerprint analysis). CoIFA encodes protein-ligand interaction terms as propensity values based on a statistical inference to construct categorical QSAR models that assist in decision making during virtual screening. In the absence of an experimentally resolved structure of GABAA R3 receptor, standard comparative modeling techniques were employed to construct a homology model of GABAA R3 receptor. A typical docking study was then carried out on the modeled structure, and the interaction fingerprints generated based on the docked binding mode were used to derive propensity values for the interacting atom pairs that served as pseudo-energy variables to generate a CoIFA model. The classification accuracy of the CoIFA model was validated using different metrics derived from a confusion matrix. Further predictive lead mining was carried out using a consensus two-dimensional QSAR approach, which offers a better predictive protocol compared to the arbitrary choice of a single QSAR model. The predictive ability of the generated model was validated using different statistical metrics, and similarity-based coverage estimation was carried out to define applicability boundaries. Few analogs designed using the concept of bioisosterism were found to be promising and could be considered for synthesis and subsequent screening