arXiv subjects

Rafayel Petrosyan

Publications and source records attributed to Rafayel Petrosyan.

3 recordsLinked to original sources

arXiv2024

Formulation of probability theory problem with subtle condition

Problems in probability theory prove to be one of the most challenging for students. Here, we formulate and discuss four related problems in probability theory that proved difficult for first to fourth-year undergraduate students whose first language was not English. These examples emphasize how crucial it is to understand the conditions and requirements of the problems precisely before starting to solve them. We discuss the solutions to those problems in detail, complement them with numerical estimations, and link the conditions in the problems to the logical statements in Python programming language. We also tested two widely used chatbots (GPT-4o and Claude 3.5 Sonnet) by checking their responses to these problems.

cs.CL↗

arXiv2019

Unfolding force definition and the unified model for the mean unfolding force dependence on the loading rate

In single-molecule force spectroscopy experiments, the dependence of the mean unfolding force on the loading rate is used for obtaining information about the energetic and dynamic properties of the system under study. However, it is crucial to understand that different dynamic force spectroscopy (DFS) models are applicable in different regimes, and that different definitions of the unfolding force might be used in those models. Here, for the first time, we discuss three definitions of the unfolding force. We carried out Brownian dynamics simulations in order to demonstrate the difference between these definitions and compare DFS models. Importantly, we derive the dependence of the mean unfolding force for the whole range of the loading rates by unifying three previously reported DFS models. Among the currently available models, this unified model shows the best agreement with the simulated data.

physics.bio-ph↗

arXiv2016

Improved Approximations for Some Polymer Extension Models

We propose approximations for force-extension dependencies for the freely jointed chain (FJC) and worm-like chain (WLC) models as well as for extension-force dependence for the WLC model. Proposed expressions show less than 1% relative error in the useful range of the corresponding variables. These results can be applied for fitting force-extension curves obtained in molecular force spectroscopy experiments. Particularly they can be useful for cases where one has geometries of springs in series and/or in parallel where particular combination of expressions should be used for fitting the data. All approximations have been obtained following the same procedure of determining the asymptotes and then reducing the relative error of that expression by adding an appropriate term obtained from fitting its absolute error.

physics.bio-ph↗