Exact solution of the zero-range process: fundamental diagram of the corresponding exclusion process

In this paper, we propose a general way of computing expectation values in the zero-range process, using an exact form of the partition function. As an example, we provide the fundamental diagram (the flux-density plot) of the asymmetric exclusion process corresponding to the zero-range process.We express the partition function for the steady state by the Lauricella hypergeometric function, and thereby have two exact fundamental diagrams each for the parallel and random sequential update rules. Meanwhile, from the viewpoint of equilibrium statistical mechanics, we work within the canonical ensemble but the result obtained is certainly in agreement with previous works done in the grand canonical ensemble.Comment: 12 pages, 2 figure

Ultra-discrete Optimal Velocity Model: a Cellular-Automaton Model for Traffic Flow and Linear Instability of High-Flux Traffic

In this paper, we propose the ultra-discrete optimal velocity model, a cellular-automaton model for traffic flow, by applying the ultra-discrete method for the optimal velocity model. The optimal velocity model, defined by a differential equation, is one of the most important models; in particular, it successfully reproduces the instability of high-flux traffic. It is often pointed out that there is a close relation between the optimal velocity model and the mKdV equation, a soliton equation. Meanwhile, the ultra-discrete method enables one to reduce soliton equations to cellular automata which inherit the solitonic nature, such as an infinite number of conservation laws, and soliton solutions. We find that the theory of soliton equations is available for generic differential equations, and the simulation results reveal that the model obtained reproduces both absolutely unstable and convectively unstable flows as well as the optimal velocity model.Comment: 9 pages, 6 figure

Exact solution and asymptotic behaviour of the asymmetric simple exclusion process on a ring

In this paper, we study an exact solution of the asymmetric simple exclusion process on a periodic lattice of finite sites with two typical updates, i.e., random and parallel. Then, we find that the explicit formulas for the partition function and the average velocity are expressed by the Gauss hypergeometric function. In order to obtain these results, we effectively exploit the recursion formula for the partition function for the zero-range process. The zero-range process corresponds to the asymmetric simple exclusion process if one chooses the relevant hop rates of particles, and the recursion gives the partition function, in principle, for any finite system size. Moreover, we reveal the asymptotic behaviour of the average velocity in the thermodynamic limit, expanding the formula as a series in system size.Comment: 10 page

Meta-analysis fine-mapping is often miscalibrated at single-variant resolution

Meta-analysis is pervasively used to combine multiple genome-wide association studies (GWASs). Fine-mapping of meta-analysis studies is typically performed as in a single-cohort study. Here, we first demonstrate that heterogeneity (e.g., of sample size, phenotyping, imputation) hurts calibration of meta-analysis fine-mapping. We propose a summary statistics-based quality-control (QC) method, suspicious loci analysis of meta-analysis summary statistics (SLALOM), that identifies suspicious loci for meta-analysis fine-mapping by detecting outliers in association statistics. We validate SLALOM in simulations and the GWAS Catalog. Applying SLALOM to 14 meta-analyses from the Global Biobank Meta-analysis Initiative (GBMI), we find that 67% of loci show suspicious patterns that call into question fine-mapping accuracy. These predicted suspicious loci are significantly depleted for having nonsynonymous variants as lead variant (2.7×; Fisher's exact p = 7.3 × 10−4). We find limited evidence of fine-mapping improvement in the GBMI meta-analyses compared with individual biobanks. We urge extreme caution when interpreting fine-mapping results from meta-analysis of heterogeneous cohorts.</p

Treatment planning for the layer-stacking irradiation system for three-dimensional conformal heavy-ion radiotherapy

We have upgraded a heavy-ion radiotherapy treatment-planning system to adapt for the layer-stacking irradiation method, which is to conform a variable spread-out Bragg peak to a target volume by means of dynamic control of the conventional beam-modifying devices. The biophysical model, the beam-setup logic, and the dose-calculation algorithm implemented for the layer-stacking method are described and the expected clinical usability is discussed. The layer-stacking method was integrated in perfect accordance with the ongoing conventional treatments so that the established protocols, which are the clinically optimized dose fractionation schemes, will still be valid. On the other hand, a simulation study indicated a substantial improvement of dose distribution with the layer-stacking method though the significance may depend on the size, shape, and location of the tumor. The completed treatment system will provide an option for improved conformal radiotherapy without interfering with the conventional method and we expect a gradual expansion of the clinical cases applicable to the layer-stacking method