On the reconstruction via Urysohn-Chlodovsky operators

The main first goal of this work is to introduce an Urysohn type Chlodovsky operators defined on positive real axis by using the Urysohn type interpolation of the given function f and bounded on every finite subinterval. The basis used in this construction are the Fréchet and Prenter Density Theorems together with Urysohn type operator values instead of the rational sampling values of the function. Afterwards, we will state some convergence results, which are generalization and extension of the theory of classical interpolation of functions to operators.

Can rational sampling maximise isolation and fix distribution measure of entomopathogenic nematodes?

Summary Entomopathogenic nematodes (EPN) can infect and kill a wide range of insect pests and are used as safe alternatives to chemical insecticides. Hence, a hypothesis was tested for obtaining EPN with high recovery frequency value and accurate distribution pattern based on combining four factors: favourable sampling method, time and site targeting and use of multiple extraction technique. As the extreme diversity of EPN sampling makes any generalisation from a given case study difficult, this functional sampling was limited to recovering EPN from citrus trees only in Egypt. It could both detect more EPN isolates and allow the application of different indices of dispersion to study their spatial distribution pattern. Therefore, stratified random and systematic sampling from weed-infested soil under tree canopy during the season of abundant insect pests was done, followed by multiple cycles of Galleria-baiting technique. Consequently, the nematodes were recovered from the seven surveyed groves (100%) and from 37 of 60 (61.7%) soil samples. The spatial distribution of these EPN isolates, previously identified as Heterorhabditis indica, was characterised using five dispersion indices, which were mainly a random rather than an over-dispersed distribution.

Complete reconstruction of the unbinding pathway of an anticancer drug by conventional unbiased molecular dynamics simulation

Understanding the details of unbinding mechanism of small molecule drugs is an inseparable part of rational drug design. Reconstruction of the unbinding pathway of small molecule drugs, todays, can be achieved through molecular dynamics simulations. Nonetheless, simulating a process in which a drug unbinds from its receptor demands lots of time, mostly up to several milliseconds. This amount of time is neither reasonable nor affordable; therefore, many researchers utilize various biases that there are still many doubts about their trustworthiness. In this work we have utilized short-run simulations, replicas, to make such time-consuming process cost effective. By replicating those snapshots of the trajectories which, after careful analyses, were selected as potential candidates we increased our system’s efficiency considerably. As a matter of fact, we have implemented a sort of human bias, inspecting trajectories visually, to achieve multiple unbinding events. We would like to call this stratagem, replicating of potent snapshots, “rational sampling” as it is, in fact, benefiting from human logic. In our case, an anticancer drug, the dasatinib, completely unbounded from its target protein, c-Src kinase, in only 392.6 ns, and this was gained without applying any internal biases and potentials which can increase error level. Thus, we achieved important structural details that can alter our viewpoint as well as assist drug designers.