Current moments of 1D ASEP by duality

We consider the exponential moments of integrated currents of 1D asymmetric simple exclusion process using the duality found by Sch\"utz. For the ASEP on the infinite lattice we show that the $n$th moment is reduced to the problem of the ASEP with less than or equal to $n$ particles.Comment: 13 pages, no figur

Determinant representation for some transition probabilities in the TASEP with second class particles

We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an explicit expression of these quantities in terms of the Bethe wave function. In a next step it is proved rigorously that this expression can be written in a compact determinantal form for the case where the order of the first and second class particles does not change in time. An independent geometrical approach provides insight into these results and enables us to generalize the determinantal solution to the multi-class TASEP.Comment: Minor revision; journal reference adde

A Fredholm Determinant Representation in ASEP

In previous work the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice. The dynamics are uniquely determined once the initial state is specified. In this note we restrict our attention to the case of step initial condition with particles at the positive integers, and consider the distribution function for the m'th particle from the left. In the previous work an infinite series of multiple integrals was derived for this distribution. In this note we show that the series can be summed to give a single integral whose integrand involves a Fredholm determinant. We use this determinant representation to derive (non-rigorously, at this writing) a scaling limit.Comment: 12 Pages. Version 3 includes a scaling conjectur

From Vicious Walkers to TASEP

We propose a model of semi-vicious walkers, which interpolates between the totally asymmetric simple exclusion process and the vicious walkers model, having the two as limiting cases. For this model we calculate the asymptotics of the survival probability for $m$ particles and obtain a scaling function, which describes the transition from one limiting case to another. Then, we use a fluctuation-dissipation relation allowing us to reinterpret the result as the particle current generating function in the totally asymmetric simple exclusion process. Thus we obtain the particle current distribution asymptotically in the large time limit as the number of particles is fixed. The results apply to the large deviation scale as well as to the diffusive scale. In the latter we obtain a new universal distribution, which has a skew non-Gaussian form. For $m$ particles its asymptotic behavior is shown to be $e^{-\frac{y^{2}}{2m^{2}}}$ as $y\to -\infty$ and $e^{-\frac{y^{2}}{2m}}y^{-\frac{m(m-1)}{2}}$ as $y\to \infty$.Comment: 37 pages, 4 figures, Corrected reference

Differential stress reaction of human colon cells to oleic-acid-stabilized and unstabilized ultrasmall iron oxide nanoparticles.

Therapeutic engineered nanoparticles (NPs), including ultrasmall superparamagnetic iron oxide (USPIO) NPs, may accumulate in the lower digestive tract following ingestion or injection. In order to evaluate the reaction of human colon cells to USPIO NPs, the effects of non-stabilized USPIO NPs (NS-USPIO NPs), oleic-acid-stabilized USPIO NPs (OA-USPIO NPs), and free oleic acid (OA) were compared in human HT29 and CaCo2 colon epithelial cancer cells. First the biophysical characteristics of NS-USPIO NPs and OA-USPIO NPs in water, in cell culture medium supplemented with fetal calf serum, and in cell culture medium preconditioned by HT29 and CaCo₂ cells were determined. Then, stress responses of the cells were evaluated following exposure to NS-USPIO NPs, OA-USPIO NPs, and free OA. No modification of the cytoskeletal actin network was observed. Cell response to stress, including markers of apoptosis and DNA repair, oxidative stress and degradative/autophagic stress, induction of heat shock protein, or lipid metabolism was determined in cells exposed to the two NPs. Induction of an autophagic response was observed in the two cell lines for both NPs but not free OA, while the other stress responses were cell- and NP-specific. The formation of lipid vacuoles/droplets was demonstrated in HT29 and CaCo₂ cells exposed to OA-USPIO NPs but not to NS-USPIO NPs, and to a much lower level in cells exposed to equimolar concentrations of free OA. Therefore, the induction of lipid vacuoles in colon cells exposed to OA utilized as a stabilizer for USPIO NPs is higly amplified compared to free OA, and is not observed in the absence of this lipid in NS-USPIO NPs

Fluctuation properties of the TASEP with periodic initial configuration

We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a kernel defining a signed determinantal point process. We then consider certain periodic initial conditions and determine the kernel in the scaling limit. This result has been announced first in a letter by one of us and here we provide a self-contained derivation. Connections to last passage directed percolation and random matrices are also briefly discussed.Comment: 33 pages, 4 figure, LaTeX; We added several references to the general framework and techniques use

Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition

For the symmetric simple exclusion process on an infinite line, we calculate exactly the fluctuations of the integrated current $Q_t$ during time $t$ through the origin when, in the initial condition, the sites are occupied with density $\rho_a$ on the negative axis and with density $\rho_b$ on the positive axis. All the cumulants of $Q_t$ grow like $\sqrt{t}$. In the range where $Q_t \sim \sqrt{t}$, the decay $\exp [-Q_t^3/t]$ of the distribution of $Q_t$ is non-Gaussian. Our results are obtained using the Bethe ansatz and several identities recently derived by Tracy and Widom for exclusion processes on the infinite line.Comment: 2 figure

Leaf nutrients, not specific leaf area, are consistent indicators of elevated nutrient inputs

Leaf traits are frequently measured in ecology to provide a ‘common currency’ for predicting how anthropogenic pressures impact ecosystem function. Here, we test whether leaf traits consistently respond to experimental treatments across 27 globally distributed grassland sites across 4 continents. We find that specific leaf area (leaf area per unit mass)—a commonly measured morphological trait inferring shifts between plant growth strategies—did not respond to up to four years of soil nutrient additions. Leaf nitrogen, phosphorus and potassium concentrations increased in response to the addition of each respective soil nutrient. We found few significant changes in leaf traits when vertebrate herbivores were excluded in the short-term. Leaf nitrogen and potassium concentrations were positively correlated with species turnover, suggesting that interspecific trait variation was a significant predictor of leaf nitrogen and potassium, but not of leaf phosphorus concentration. Climatic conditions and pretreatment soil nutrient levels also accounted for significant amounts of variation in the leaf traits measured. Overall, we find that leaf morphological traits, such as specific leaf area, are not appropriate indicators of plant response to anthropogenic perturbations in grasslands

Distribution of a Particle’s Position in the ASEP with the Alternating Initial Condition

In this paper we give the distribution of the position of the particle in the asymmetric simple exclusion process (ASEP) with the alternating initial condition. That is, we find $\mathbb{P}(X_m(t) \leq x)$ where $X_m(t)$ is the position of the particle at time $t$ which was at $m =2k-1, k \in \mathbb{Z}$ at $t=0.$ As in the ASEP with the step initial condition, there arises a new combinatorial identity for the alternating initial condition, and this identity relates the integrand to a determinantal form together with an extra product.Comment: Version 3 expands the introduction and adds more references. Published versio