Family of Commuting Operators for the Totally Asymmetric Exclusion Process

The algebraic structure underlying the totally asymmetric exclusion process is studied by using the Bethe Ansatz technique. From the properties of the algebra generated by the local jump operators, we explicitly construct the hierarchy of operators (called generalized hamiltonians) that commute with the Markov operator. The transfer matrix, which is the generating function of these operators, is shown to represent a discrete Markov process with long-range jumps. We give a general combinatorial formula for the connected hamiltonians obtained by taking the logarithm of the transfer matrix. This formula is proved using a symbolic calculation program for the first ten connected operators. Keywords: ASEP, Algebraic Bethe Ansatz. Pacs numbers: 02.30.Ik, 02.50.-r, 75.10.Pq.Comment: 26 pages, 1 figure; v2: published version with minor changes, revised title, 4 refs adde

Spectral gap of the totally asymmetric exclusion process at arbitrary filling

We calculate the spectral gap of the Markov matrix of the totally asymmetric simple exclusion process (TASEP) on a ring of L sites with N particles. Our derivation is simple and self-contained and extends a previous calculation that was valid only for half-filling. We use a special property of the Bethe equations for TASEP to reformulate them as a one-body problem. Our method is closely related to the one used to derive exact large deviation functions of the TASEP

Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz

We derive, using the algebraic Bethe Ansatz, a generalized Matrix Product Ansatz for the asymmetric exclusion process (ASEP) on a one-dimensional periodic lattice. In this Matrix Product Ansatz, the components of the eigenvectors of the ASEP Markov matrix can be expressed as traces of products of non-commuting operators. We derive the relations between the operators involved and show that they generate a quadratic algebra. Our construction provides explicit finite dimensional representations for the generators of this algebra.Comment: 16 page

Sustainability, stakeholders and business. Editorial

Over the past 20 years, there has been an increasing attention on the drivers of value in organizations. Both the strategic management literature and practice have remarked the importance for managers to be aware of the impact of firm activities, products and services on either the external and internal environment and, more generally, on all firm stakeholders. The emergence of the notions of “sustainable development” and “sustainability” reflects a profound change in global thinking, which forces firms to move beyond trade-offs between business and society

Hidden symmetries in the asymmetric exclusion process

We present a spectral study of the evolution matrix of the totally asymmetric exclusion process on a ring at half filling. The natural symmetries (translation, charge conjugation combined with reflection) predict only two fold degeneracies. However, we have found that degeneracies of higher order also exist and, as the system size increases, higher and higher orders appear. These degeneracies become generic in the limit of very large systems. This behaviour can be explained by the Bethe Ansatz and suggests the presence of hidden symmetries in the model. Keywords: ASEP, Markov matrix, symmetries, spectral degeneracies, Bethe Ansatz.Comment: 16 page

The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics

The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by Bethe ansatz and put emphasis on the algebraic properties of this model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP are derived from the algebraic Bethe ansatz. Using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted. An extension of the Bethe ansatz leads to an analytic expression for the large deviation function of the current in the ASEP that satisfies the Gallavotti-Cohen relation. Finally, we describe some variants of the ASEP that are also solvable by Bethe ansatz. Keywords: ASEP, integrable models, Bethe ansatz, large deviations.Comment: 24 pages, 5 figures, published in the "special issue on recent advances in low-dimensional quantum field theories", P. Dorey, G. Dunne and J. Feinberg editor

Power Spectra of a Constrained Totally Asymmetric Simple Exclusion Process

To synthesize proteins in a cell, an mRNA has to work with a finite pool of ribosomes. When this constraint is included in the modeling by a totally asymmetric simple exclusion process (TASEP), non-trivial consequences emerge. Here, we consider its effects on the power spectrum of the total occupancy, through Monte Carlo simulations and analytical methods. New features, such as dramatic suppressions at low frequencies, are discovered. We formulate a theory based on a linearized Langevin equation with discrete space and time. The good agreement between its predictions and simulation results provides some insight into the effects of finite resoures on a TASEP.Comment: 4 pages, 2 figures v2: formatting change

Global, regional, and national burden of hepatitis B, 1990-2019: a systematic analysis for the Global Burden of Disease Study 2019

Background: Combating viral hepatitis is part of the UN Sustainable Development Goals (SDGs), and WHO has put forth hepatitis B elimination targets in its Global Health Sector Strategy on Viral Hepatitis (WHO-GHSS) and Interim Guidance for Country Validation of Viral Hepatitis Elimination (WHO Interim Guidance). We estimated the global, regional, and national prevalence of hepatitis B virus (HBV), as well as mortality and disability-adjusted life-years (DALYs) due to HBV, as part of the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019. This included estimates for 194 WHO member states, for which we compared our estimates to WHO elimination targets. Methods: The primary data sources were population-based serosurveys, claims and hospital discharges, cancer registries, vital registration systems, and published case series. We estimated chronic HBV infection and the burden of HBV-related diseases, defined as an aggregate of cirrhosis due to hepatitis B, liver cancer due to hepatitis B, and acute hepatitis B. We used DisMod-MR 2.1, a Bayesian mixed-effects meta-regression tool, to estimate the prevalence of chronic HBV infection, cirrhosis, and aetiological proportions of cirrhosis. We used mortality-to-incidence ratios modelled with spatiotemporal Gaussian process regression to estimate the incidence of liver cancer. We used the Cause of Death Ensemble modelling (CODEm) model, a tool that selects models and covariates on the basis of out-of-sample performance, to estimate mortality due to cirrhosis, liver cancer, and acute hepatitis B. Findings: In 2019, the estimated global, all-age prevalence of chronic HBV infection was 4·1% (95% uncertainty interval [UI] 3·7 to 4·5), corresponding to 316 million (284 to 351) infected people. There was a 31·3% (29·0 to 33·9) decline in all-age prevalence between 1990 and 2019, with a more marked decline of 76·8% (76·2 to 77·5) in prevalence in children younger than 5 years. HBV-related diseases resulted in 555 000 global deaths (487 000 to 630 000) in 2019. The number of HBV-related deaths increased between 1990 and 2019 (by 5·9% [-5·6 to 19·2]) and between 2015 and 2019 (by 2·9% [-5·9 to 11·3]). By contrast, all-age and age-standardised death rates due to HBV-related diseases decreased during these periods. We compared estimates for 2019 in 194 WHO locations to WHO-GHSS 2020 targets, and found that four countries achieved a 10% reduction in deaths, 15 countries achieved a 30% reduction in new cases, and 147 countries achieved a 1% prevalence in children younger than 5 years. As of 2019, 68 of 194 countries had already achieved the 2030 target proposed in WHO Interim Guidance of an all-age HBV-related death rate of four per 100 000. Interpretation: The prevalence of chronic HBV infection declined over time, particularly in children younger than 5 years, since the introduction of hepatitis B vaccination. HBV-related death rates also decreased, but HBV-related death counts increased as a result of population growth, ageing, and cohort effects. By 2019, many countries had met the interim seroprevalence target for children younger than 5 years, but few countries had met the WHO-GHSS interim targets for deaths and new cases. Progress according to all indicators must be accelerated to meet 2030 targets, and there are marked disparities in burden and progress across the world. HBV interventions, such as vaccination, testing, and treatment, must be strategically supported and scaled up to achieve elimination. Funding: Bill & Melinda Gates Foundation

Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion Process with Finite Resources

We revisit a totally asymmetric simple exclusion process (TASEP) with open boundaries and a global constraint on the total number of particles [Adams, et. al. 2008 J. Stat. Mech. P06009]. In this model, the entry rate of particles into the lattice depends on the number available in the reservoir. Thus, the total occupation on the lattice feeds back into its filling process. Although a simple domain wall theory provided reasonably good predictions for Monte Carlo simulation results for certain quantities, it did not account for the fluctuations of this feedback. We generalize the previous study and find dramatically improved predictions for, e.g., the density profile on the lattice and provide a better understanding of the phenomenon of "shock localization."Comment: 11 pages, 3 figures, v2: Minor change