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1. Theoretical investigations of asymmetric simple exclusion processes for interacting oligomers

   https://doi.org/https://doi.org/10.1088/1742-5468/aac139  

   Tripti Midha, Luiza V (May 2018, Journal of statistical mechanics)

   Motivated by biological transport phenomena that involve the motion of interacting molecular motors along linear filaments, we developed a theoretical framework to analyze the dynamics of interacting oligomers (extended size particles) on one-dimensional lattices. Our method extends the asymmetric simple exclusion processes for interacting monomers to particles of arbitrary size, and it utilizes cluster mean-field calculations supplemented by extensive Monte Carlo computer simulations. Interactions between particles are accounted for by a thermodynamically consistent method that views the formation and breaking bonds between particles as a chemical process. The dynamics of the system are analyzed for both periodic and open boundary conditions. It is found that the nature of the current-density relation depends on the strength of interactions, on the size of oligomers and on the way interactions influence particles transition rates. Stationary phase diagram is also fully evaluated, and it is shown how the dynamic properties depend on the interactions and on the sizes of the particles. To explain the dynamic behavior of the system particles density correlations are explicitly analyzed for different ranges of parameters. Theoretical calculations generally agree well with the results from the computer simulations, suggesting that our method correctly describes the main features of the molecular mechanisms of the transport of interacting oligomers. 

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2. Effect of interactions for one-dimensional asymmetric exclusion processes under periodic and bath-adapted coupling environment

   https://doi.org/https://doi.org/10.1088/1742-5468/aab022  

   Tripti Midha, Anatoly B (April 2018, Journal of statistical mechanics)

   Stimulated by the effect of the nearest neighbor interactions in vehicular traffic and motor proteins, we study a 1D driven lattice gas model, in which the nearest neighbor particle interactions are taken in accordance with the thermodynamic concepts. The non-equilibrium steady-state properties of the system are analyzed under both open and periodic boundary conditions using a combination of cluster mean-field analysis and Monte Carlo simulations. Interestingly, the fundamental diagram of current versus density shows a complex behavior with a unimodal dependence for attractions and weak repulsions that turns into the bimodal behavior for stronger repulsive interactions. Specific details of system-reservoir coupling for the open system have a strong effect on the stationary phases. We produce the steady-state phase diagrams for the bulk-adapted coupling to the reservoir using the minimum and maximum current principles. The strength and nature of interaction energy has a striking influence on the number of stationary phases. We observe that interactions lead to correlations having a strong impact on the system dynamical properties. The correlation between any two sites decays exponentially as the distance between the sites increases. Moreover, they are found to be short-range for repulsions and long-range for attractions. Our results also suggest that repulsions and attractions asymmetrically modify the dynamics of interacting particles in exclusion processes. 

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3. Thermodynamic non-ideality in charge regulation of weak polyelectrolytes

   https://doi.org/10.1039/D1SM00848J  

   Gallegos, Alejandro; Ong, Gary M.; Wu, Jianzhong (October 2021, Soft Matter)

   Polymer ionization differs from that for their monomeric counterparts due to intramolecular correlations. Such effects are conventionally described in terms of the site-binding model that accounts for short-range interactions between neighboring sites. With an apparent equilibrium constant for each ionizable group and the nearest-neighbor energy as adjustable parameters, the site-binding method is useful to correlate experimental titration curves when the site–site interactions are insignificant at long ranges. This work aims to describe the electrostatic behavior of weak polyelectrolytes in aqueous solutions on the basis of the intrinsic equilibrium constants of the individual ionizable groups and solution conditions underlying the thermodynamic non-ideality. A molecular thermodynamic model is proposed for the protonation of weak polyelectrolytes by incorporating classical density functional theory into the site-binding model to account for the effects of the local ionic environment on both inter-chain and intra-chain correlations. By an extensive comparison of theoretical predictions with experimental titration curves, we demonstrate that the thermodynamic model is able to quantify the ionization behavior of weak polyelectrolytes over a broad range of molecular architectures and solution conditions. 

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4. Large time behavior, bi-Hamiltonian structure, and kinetic formulation for a complex Burgers equation

   https://doi.org/10.1090/qam/1573  

   Gao, Yu; Gao, Yuan; Liu, Jian-Guo (March 2021, Quarterly of Applied Mathematics)

   We prove the existence and uniqueness of positive analytical solutions with positive initial data to the mean field equation (the Dyson equation) of the Dyson Brownian motion through the complex Burgers equation with a force term on the upper half complex plane. These solutions converge to a steady state given by Wigner’s semicircle law. A unique global weak solution with nonnegative initial data to the Dyson equation is obtained, and some explicit solutions are given by Wigner’s semicircle laws. We also construct a bi-Hamiltonian structure for the system of real and imaginary components of the complex Burgers equation (coupled Burgers system). We establish a kinetic formulation for the coupled Burgers system and prove the existence and uniqueness of entropy solutions. The coupled Burgers system in Lagrangian variable naturally leads to two interacting particle systems, the Fermi–Pasta–Ulam–Tsingou model with nearest-neighbor interactions, and the Calogero–Moser model. These two particle systems yield the same Lagrangian dynamics in the continuum limit. 

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5. KNN-DBSCAN: a DBSCAN in high dimensions

   https://doi.org/10.1145/3701624  

   Chen, Youguang; Ruys, William; Biros, George (March 2025, ACM Transactions on Parallel Computing)

   Clustering is a fundamental task in machine learning. One of the most successful and broadly used algorithms is DBSCAN, a density-based clustering algorithm. DBSCAN requires ϵ-nearest neighbor graphs of the input dataset, which are computed with range-search algorithms and spatial data structures like KD-trees. Despite many efforts to design scalable implementations for DBSCAN, existing work is limited to low-dimensional datasets, as constructing ϵ-nearest neighbor graphs can be expensive in high-dimensions. This article introduces a modified DBSCAN, usingk-nearest neighbor (kNN) graphs to improve efficiency. We outline conditions forkNN-DBSCAN to match DBSCAN’s results and present a parallel implementation using OpenMP and MPI for shared and distributed memory systems. Testing on datasets up to 32 dimensions, we achieve remarkable scalability. Our implementation clusters one billion 3D points in under one second on 28K cores at TACC’s Frontera system. In a larger run, we cluster 65 billion points in 20 dimensions in under 40 seconds using 114,688 cores. Our method is up to 37× faster than state-of-the-art parallel DBSCAN on a 20-dimensional dataset with 4 million points. Code is available athttps://github.com/ut-padas/knndbscan. 

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