Comparison of pure and combined search strategies for single and multiple targets

We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with L\'evy search based on long-tailed jump length distributions. We then compare these results with a search process combined of two different long-tailed jump length distributions. Moreover, we study the case of multiple targets located by a L\'evy searcher.Comment: 16 pages, 12 figure

Negative diffusion of excitons in quasi-two-dimensional systems

We show how two different mobile-immobile type models explain the observation of negative diffusion of excitons reported in experimental studies in quasi-two-dimensional semiconductor systems. The main reason for the effect is the initial trapping and a delayed release of free excitons in the area close to the original excitation spot. The density of trapped excitons is not registered experimentally. Hence, the signal from the free excitons alone includes the delayed release of not diffusing trapped particles. This is seen as the narrowing of the exciton density profile or decrease of mean-squared displacement which is then interpreted as a negative diffusion. The effect is enhanced with the increase of recombination intensity as well as the rate of the exciton-exciton binary interactions.Comment: 14 pages, 8 figure

First passage and first hitting times of Lévy flights and Lévy walks

Abstract For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it (‘leapovers’), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms

Search reliability and search efficiency of combined Lévy–Brownian motion: long relocations mingled with thorough local exploration

A combined dynamics consisting of Brownian motion and Levy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and Levy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Levy flights with stable exponent α<1, by itself implying zero probability of hitting a point on a line, lead to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent α of the Levy flight component

Derivatives of 9-phosphorylated acridine as butyrylcholinesterase inhibitors with antioxidant activity and the ability to inhibit β-amyloid self-aggregation: potential therapeutic agents for Alzheimer’s disease

We investigated the inhibitory activities of novel 9-phosphoryl-9,10-dihydroacridines and 9-phosphorylacridines against acetylcholinesterase (AChE), butyrylcholinesterase (BChE), and carboxylesterase (CES). We also studied the abilities of the new compounds to interfere with the self-aggregation of β-amyloid (Aβ42) in the thioflavin test as well as their antioxidant activities in the ABTS and FRAP assays. We used molecular docking, molecular dynamics simulations, and quantum-chemical calculations to explain experimental results. All new compounds weakly inhibited AChE and off-target CES. Dihydroacridines with aryl substituents in the phosphoryl moiety inhibited BChE; the most active were the dibenzyloxy derivative 1d and its diphenethyl bioisostere 1e (IC50 = 2.90 ± 0.23 µM and 3.22 ± 0.25 µM, respectively). Only one acridine, 2d, an analog of dihydroacridine, 1d, was an effective BChE inhibitor (IC50 = 6.90 ± 0.55 μM), consistent with docking results. Dihydroacridines inhibited Aβ42 self-aggregation; 1d and 1e were the most active (58.9% ± 4.7% and 46.9% ± 4.2%, respectively). All dihydroacridines 1 demonstrated high ABTS•+-scavenging and iron-reducing activities comparable to Trolox, but acridines 2 were almost inactive. Observed features were well explained by quantum-chemical calculations. ADMET parameters calculated for all compounds predicted favorable intestinal absorption, good blood–brain barrier permeability, and low cardiac toxicity. Overall, the best results were obtained for two dihydroacridine derivatives 1d and 1e with dibenzyloxy and diphenethyl substituents in the phosphoryl moiety. These compounds displayed high inhibition of BChE activity and Aβ42 self-aggregation, high antioxidant activity, and favorable predicted ADMET profiles. Therefore, we consider 1d and 1e as lead compounds for further in-depth studies as potential anti-AD preparations

Online chemical modeling environment (OCHEM): web platform for data storage, model development and publishing of chemical information

The Online Chemical Modeling Environment is a web-based platform that aims to automate and simplify the typical steps required for QSAR modeling. The platform consists of two major subsystems: the database of experimental measurements and the modeling framework. A user-contributed database contains a set of tools for easy input, search and modification of thousands of records. The OCHEM database is based on the wiki principle and focuses primarily on the quality and verifiability of the data. The database is tightly integrated with the modeling framework, which supports all the steps required to create a predictive model: data search, calculation and selection of a vast variety of molecular descriptors, application of machine learning methods, validation, analysis of the model and assessment of the applicability domain. As compared to other similar systems, OCHEM is not intended to re-implement the existing tools or models but rather to invite the original authors to contribute their results, make them publicly available, share them with other users and to become members of the growing research community. Our intention is to make OCHEM a widely used platform to perform the QSPR/QSAR studies online and share it with other users on the Web. The ultimate goal of OCHEM is collecting all possible chemoinformatics tools within one simple, reliable and user-friendly resource. The OCHEM is free for web users and it is available online at http://www.ochem.eu

Lévy flights do not always optimize random blind search for sparse targets

It is generally believed that random search processes based on scale-free, Lévy stable jump length distributions (Lévy flights) optimize the search for sparse targets. Here we show that this popular search advantage is less universal than commonly assumed. We study the efficiency of a minimalist search model based on Lévy flights in the absence and presence of an external drift (underwater current, atmospheric wind, a preference of the walker owing to prior experience, or a general bias in an abstract search space) based on two different optimization criteria with respect to minimal search time and search reliability (cumulative arrival probability). Although Lévy flights turn out to be efficient search processes when the target is far from the starting point, or when relative to the starting point the target is upstream, we show that for close targets and for downstream target positioning regular Brownian motion turns out to be the advantageous search strategy. Contrary to claims that Lévy flights with a critical exponent α = 1 are optimal for the search of sparse targets in different settings, based on our optimization parameters the optimal α may range in the entire interval (1, 2) and especially include Brownian motion as the overall most efficient search strategy