Fluctuation-stabilized marginal networks and anomalous entropic elasticity

We study the elastic properties of thermal networks of Hookean springs. In the purely mechanical limit, such systems are known to have vanishing rigidity when their connectivity falls below a critical, isostatic value. In this work we show that thermal networks exhibit a non-zero shear modulus $G$ well below the isostatic point, and that this modulus exhibits an anomalous, sublinear dependence on temperature $T$. At the isostatic point, $G$ increases as the square-root of $T$, while we find $G \propto T^{\alpha}$ below the isostatic point, where ${\alpha} \simeq 0.8$. We show that this anomalous $T$ dependence is entropic in origin.Comment: 9 pages, 7 figure

Exact sequence matches in genomic studies

The purpose of this article is to review usage of exact sequence matches in different field of genomic studies. Methods. The presentation is built in the form of a brief review of clearly non-exhaustive list of works in which the authors inferred biological knowledge using statistical properties of exact matches between different genomic texts or self-matches along the same genomic sequence. Results. Often, in genomic studies, different genomic loci exhibit different statistical properties, while their boundaries are not known a priory. In such cases we conclude that studying statistical properties of exact sequence matches is a useful alternative to other methods, for instance, based on arbitrary-size (non-)sliding windowing of the genome. Conclusion. This review demonstrates that exact sequences matches are not only an important auxiliary alignment step, but also helpful in other contexts. Their statistical properties are relatively easy to calculate analytically or numerically under various assumptions and compare to empirical data, validating models and fitting the models’ parameters

Detecting LLM-Generated Text in Computing Education: A Comparative Study for ChatGPT Cases

Due to the recent improvements and wide availability of Large Language Models (LLMs), they have posed a serious threat to academic integrity in education. Modern LLM-generated text detectors attempt to combat the problem by offering educators with services to assess whether some text is LLM-generated. In this work, we have collected 124 submissions from computer science students before the creation of ChatGPT. We then generated 40 ChatGPT submissions. We used this data to evaluate eight publicly-available LLM-generated text detectors through the measures of accuracy, false positives, and resilience. The purpose of this work is to inform the community of what LLM-generated text detectors work and which do not, but also to provide insights for educators to better maintain academic integrity in their courses. Our results find that CopyLeaks is the most accurate LLM-generated text detector, GPTKit is the best LLM-generated text detector to reduce false positives, and GLTR is the most resilient LLM-generated text detector. We also express concerns over 52 false positives (of 114 human written submissions) generated by GPTZero. Finally, we note that all LLM-generated text detectors are less accurate with code, other languages (aside from English), and after the use of paraphrasing tools (like QuillBot). Modern detectors are still in need of improvements so that they can offer a full-proof solution to help maintain academic integrity. Further, their usability can be improved by facilitating a smooth API integration, providing clear documentation of their features and the understandability of their model(s), and supporting more commonly used languages.Comment: 18 pages total (16 pages, 2 reference pages). In submissio

Decay of Quantum Accelerator Modes

Experimentally observable Quantum Accelerator Modes are used as a test case for the study of some general aspects of quantum decay from classical stable islands immersed in a chaotic sea. The modes are shown to correspond to metastable states, analogous to the Wannier-Stark resonances. Different regimes of tunneling, marked by different quantitative dependence of the lifetimes on 1/hbar, are identified, depending on the resolution of KAM substructures that is achieved on the scale of hbar. The theory of Resonance Assisted Tunneling introduced by Brodier, Schlagheck, and Ullmo [9], is revisited, and found to well describe decay whenever applicable.Comment: 16 pages, 11 encapsulated postscript figures (figures with a better resolution are available upon request to the authors); added reference for section

First passage time distribution for a random walker on a random forcing energy landscape

We present an analytical approximation scheme for the first passage time distribution on a finite interval of a random walker on a random forcing energy landscape. The approximation scheme captures the behavior of the distribution over all timescales in the problem. The results are carefully checked against numerical simulations.Comment: 16 page

Molecular motors robustly drive active gels to a critically connected state

Living systems often exhibit internal driving: active, molecular processes drive nonequilibrium phenomena such as metabolism or migration. Active gels constitute a fascinating class of internally driven matter, where molecular motors exert localized stresses inside polymer networks. There is evidence that network crosslinking is required to allow motors to induce macroscopic contraction. Yet a quantitative understanding of how network connectivity enables contraction is lacking. Here we show experimentally that myosin motors contract crosslinked actin polymer networks to clusters with a scale-free size distribution. This critical behavior occurs over an unexpectedly broad range of crosslink concentrations. To understand this robustness, we develop a quantitative model of contractile networks that takes into account network restructuring: motors reduce connectivity by forcing crosslinks to unbind. Paradoxically, to coordinate global contractions, motor activity should be low. Otherwise, motors drive initially well-connected networks to a critical state where ruptures form across the entire network.Comment: Main text: 21 pages, 5 figures. Supplementary Information: 13 pages, 8 figure

Effects of intersegmental transfers on target location by proteins

We study a model for a protein searching for a target, using facilitated diffusion, on a DNA molecule confined in a finite volume. The model includes three distinct pathways for facilitated diffusion: (a) sliding - in which the protein diffuses along the contour of the DNA (b) jumping - where the protein travels between two sites along the DNA by three-dimensional diffusion, and finally (c) intersegmental transfer - which allows the protein to move from one site to another by transiently binding both at the same time. The typical search time is calculated using scaling arguments which are verified numerically. Our results suggest that the inclusion of intersegmental transfer (i) decreases the search time considerably (ii) makes the search time much more robust to variations in the parameters of the model and (iii) that the optimal search time occurs in a regime very different than that found for models which ignore intersegmental transfers. The behavior we find is rich and shows surprising dependencies, for example, on the DNA length.Comment: 40 pages, 14 figure

How evolution of genomes is reflected in exact DNA sequence match statistics

Genome evolution is shaped by a multitude of mutational processes, including point mutations, insertions, and deletions of DNA sequences, as well as segmental duplications. These mutational processes can leave distinctive qualitative marks in the statistical features of genomic DNA sequences. One such feature is the match length distribution (MLD) of exactly matching sequence segments within an individual genome or between the genomes of related species. These have been observed to exhibit characteristic power law decays in many species. Here, we show that simple dynamical models consisting solely of duplication and mutation processes can already explain the characteristic features of MLDs observed in genomic sequences. Surprisingly, we find that these features are largely insensitive to details of the underlying mutational processes and do not necessarily rely on the action of natural selection. Our results demonstrate how analyzing statistical features of DNA sequences can help us reveal and quantify the different mutational processes that underlie genome evolution