Dyck Paths, Motzkin Paths and Traffic Jams

It has recently been observed that the normalization of a one-dimensional out-of-equilibrium model, the Asymmetric Exclusion Process (ASEP) with random sequential dynamics, is exactly equivalent to the partition function of a two-dimensional lattice path model of one-transit walks, or equivalently Dyck paths. This explains the applicability of the Lee-Yang theory of partition function zeros to the ASEP normalization. In this paper we consider the exact solution of the parallel-update ASEP, a special case of the Nagel-Schreckenberg model for traffic flow, in which the ASEP phase transitions can be intepreted as jamming transitions, and find that Lee-Yang theory still applies. We show that the parallel-update ASEP normalization can be expressed as one of several equivalent two-dimensional lattice path problems involving weighted Dyck or Motzkin paths. We introduce the notion of thermodynamic equivalence for such paths and show that the robustness of the general form of the ASEP phase diagram under various update dynamics is a consequence of this thermodynamic equivalence.Comment: Version accepted for publicatio

Demagnetization via Nucleation of the Nonequilibrium Metastable Phase in a Model of Disorder

We study both analytically and numerically metastability and nucleation in a two-dimensional nonequilibrium Ising ferromagnet. Canonical equilibrium is dynamically impeded by a weak random perturbation which models homogeneous disorder of undetermined source. We present a simple theoretical description, in perfect agreement with Monte Carlo simulations, assuming that the decay of the nonequilibrium metastable state is due, as in equilibrium, to the competition between the surface and the bulk. This suggests one to accept a nonequilibrium "free-energy" at a mesoscopic/cluster level, and it ensues a nonequilibrium "surface tension" with some peculiar low-T behavior. We illustrate the occurrence of intriguing nonequilibrium phenomena, including: (i) Noise-enhanced stabilization of nonequilibrium metastable states; (ii) reentrance of the limit of metastability under strong nonequilibrium conditions; and (iii) resonant propagation of domain walls. The cooperative behavior of our system may also be understood in terms of a Langevin equation with additive and multiplicative noises. We also studied metastability in the case of open boundaries as it may correspond to a magnetic nanoparticle. We then observe burst-like relaxation at low T, triggered by the additional surface randomness, with scale-free avalanches which closely resemble the type of relaxation reported for many complex systems. We show that this results from the superposition of many demagnetization events, each with a well- defined scale which is determined by the curvature of the domain wall at which it originates. This is an example of (apparent) scale invariance in a nonequilibrium setting which is not to be associated with any familiar kind of criticality.Comment: 26 pages, 22 figure

Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide

We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of this class of driven diffusive systems - which includes exclusion processes - focusing on interesting physical properties, such as shocks and phase transitions. We then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form. In addition to a gentle introduction to this matrix product approach, how it works and how it relates to similar constructions that arise in other physical contexts, we present a unified, pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed. We also review a number of more advanced topics, including nonequilibrium free energy functionals, the classification of exclusion processes involving multiple particle species, existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled. We conclude with a brief discussion of open problems for future research.Comment: 127 pages, 31 figures, invited topical review for J. Phys. A (uses IOP class file

Single-molecule experiments in biological physics: methods and applications

I review single-molecule experiments (SME) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SME it is possible to: manipulate molecules one at a time and measure distributions describing molecular properties; characterize the kinetics of biomolecular reactions and; detect molecular intermediates. SME provide the additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SME it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level emphasizing the importance of SME to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SME from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOT), magnetic tweezers (MT), biomembrane force probe (BFP) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation), proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SME to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.Comment: Latex, 60 pages, 12 figures, Topical Review for J. Phys. C (Cond. Matt

Coaggregation of RNA-Binding Proteins in a Model of TDP-43 Proteinopathy with Selective RGG Motif Methylation and a Role for RRM1 Ubiquitination

TAR DNA-binding protein 43 (TDP-43) is a major component within ubiquitin-positive inclusions of a number of neurodegenerative diseases that increasingly are considered as TDP-43 proteinopathies. Identities of other inclusion proteins associated with TDP-43 aggregation remain poorly defined. In this study, we identify and quantitate 35 co-aggregating proteins in the detergent-resistant fraction of HEK-293 cells in which TDP-43 or a particularly aggregate prone variant, TDP-S6, were enriched following overexpression, using stable isotope-labeled (SILAC) internal standards and liquid chromatography coupled to tandem mass spectrometry (LC-MS/MS). We also searched for differential post-translational modification (PTM) sites of ubiquitination. Four sites of ubiquitin conjugation to TDP-43 or TDP-S6 were confirmed by dialkylated GST-TDP-43 external reference peptides, occurring on or near RNA binding motif (RRM) 1. RRM-containing proteins co-enriched in cytoplasmic granular structures in HEK-293 cells and primary motor neurons with insoluble TDP-S6, including cytoplasmic stress granule associated proteins G3BP, PABPC1, and eIF4A1. Proteomic evidence for TDP-43 co-aggregation with paraspeckle markers RBM14, PSF and NonO was also validated by western blot and by immunocytochemistry in HEK-293 cells. An increase in peptides from methylated arginine-glycine-glycine (RGG) RNA-binding motifs of FUS/TLS and hnRNPs was found in the detergent-insoluble fraction of TDP-overexpressing cells. Finally, TDP-43 and TDP-S6 detergent-insoluble species were reduced by mutagenesis of the identified ubiquitination sites, even following oxidative or proteolytic stress. Together, these findings define some of the aggregation partners of TDP-43, and suggest that TDP-43 ubiquitination influences TDP-43 oligomerization

Uncovering Ubiquitin and Ubiquitin-like Signaling Networks

Microscopic imaging and technolog

Investigating prehistoric pottery from the Gansu-Qinghai region (northwest China): from Andersson's first excavations to contemporary research

Over the past 100 years since J.G. Andersson first brought the prehistoric pottery of Gansu and Qinghai Provinces, China, to the world stage, significant advances have been made in our understanding of Neolithic and Bronze age pottery from that region. From the first typologies produced by Andersson and colleagues to the refinement of chronologies in the 1940s–1990s to the application of modern analytical techniques in the last 20 years, our understanding of both the pottery itself and the people who produced it has been radically transformed. However, up to this point, the history of this research has been scattered across dozens of publications in multiple languages. Here, for the first time, we present a concise history of this work, paired with recent findings from research on newly excavated materials as well as older collections from the Museum of Far Eastern Antiquities (MFEA) and various institutions in China. We hope that this will allow scholars to better understand the trajectory of ceramic research in this field, while also illuminating areas of interest for future research projects