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

Funding Information: We acknowledge all the participants and researchers of the 23 biobanks that have contributed to the GBMI. Biobank-specific acknowledgments are included in the Data S3 . We thank H. Huang, A.R. Martin, B.M. Neale, Y. Okada, K. Tsuo, J.C. Ulirsch, Y. Wang, and all the members of Finucane and Daly labs for their helpful feedback. M.K. was supported by a Nakajima Foundation Fellowship and the Masason Foundation . H.K.F. was funded by NIH grant DP5 OD024582 . Publisher Copyright: © 2022 The Author(s)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.Peer reviewe

Multi-ancestry meta-analysis of asthma identifies novel associations and highlights the value of increased power and diversity

Publisher Copyright: © 2022 The Author(s)Asthma is a complex disease that varies widely in prevalence across populations. The extent to which genetic variation contributes to these disparities is unclear, as the genetics underlying asthma have been investigated primarily in populations of European descent. As part of the Global Biobank Meta-analysis Initiative, we conducted a large-scale genome-wide association study of asthma (153,763 cases and 1,647,022 controls) via meta-analysis across 22 biobanks spanning multiple ancestries. We discovered 179 asthma-associated loci, 49 of which were not previously reported. Despite the wide range in asthma prevalence among biobanks, we found largely consistent genetic effects across biobanks and ancestries. The meta-analysis also improved polygenic risk prediction in non-European populations compared with previous studies. Additionally, we found considerable genetic overlap between age-of-onset subtypes and between asthma and comorbid diseases. Our work underscores the multi-factorial nature of asthma development and offers insight into its shared genetic architecture.Peer reviewe

Polygenic burden in focal and generalized epilepsies.

Rare genetic variants can cause epilepsy, and genetic testing has been widely adopted for severe, paediatric-onset epilepsies. The phenotypic consequences of common genetic risk burden for epilepsies and their potential future clinical applications have not yet been determined. Using polygenic risk scores (PRS) from a European-ancestry genome-wide association study in generalized and focal epilepsy, we quantified common genetic burden in patients with generalized epilepsy (GE-PRS) or focal epilepsy (FE-PRS) from two independent non-Finnish European cohorts (Epi25 Consortium, n = 5705; Cleveland Clinic Epilepsy Center, n = 620; both compared to 20 435 controls). One Finnish-ancestry population isolate (Finnish-ancestry Epi25, n = 449; compared to 1559 controls), two European-ancestry biobanks (UK Biobank, n = 383 656; Vanderbilt biorepository, n = 49 494), and one Japanese-ancestry biobank (BioBank Japan, n = 168 680) were used for additional replications. Across 8386 patients with epilepsy and 622 212 population controls, we found and replicated significantly higher GE-PRS in patients with generalized epilepsy of European-ancestry compared to patients with focal epilepsy (Epi25: P = 1.64×10-15; Cleveland: P = 2.85×10-4; Finnish-ancestry Epi25: P = 1.80×10-4) or population controls (Epi25: P = 2.35×10-70; Cleveland: P = 1.43×10-7; Finnish-ancestry Epi25: P = 3.11×10-4; UK Biobank and Vanderbilt biorepository meta-analysis: P = 7.99×10-4). FE-PRS were significantly higher in patients with focal epilepsy compared to controls in the non-Finnish, non-biobank cohorts (Epi25: P = 5.74×10-19; Cleveland: P = 1.69×10-6). European ancestry-derived PRS did not predict generalized epilepsy or focal epilepsy in Japanese-ancestry individuals. Finally, we observed a significant 4.6-fold and a 4.5-fold enrichment of patients with generalized epilepsy compared to controls in the top 0.5% highest GE-PRS of the two non-Finnish European cohorts (Epi25: P = 2.60×10-15; Cleveland: P = 1.39×10-2). We conclude that common variant risk associated with epilepsy is significantly enriched in multiple cohorts of patients with epilepsy compared to controls-in particular for generalized epilepsy. As sample sizes and PRS accuracy continue to increase with further common variant discovery, PRS could complement established clinical biomarkers and augment genetic testing for patient classification, comorbidity research, and potentially targeted treatment

Genome-wide risk prediction of common diseases across ancestries in one million people

Peer reviewe

Preoperative biliary drainage for biliary tract and ampullary carcinomas

We posed six clinical questions (CQ) on preoperative biliary drainage and organized all pertinent evidence regarding these questions. CQ 1. Is preoperative biliary drainage necessary for patients with jaundice? The indications for preoperative drainage for jaundiced patients are changing greatly. Many reports state that, excluding conditions such as cholangitis and liver dysfunction, biliary drainage is not necessary before pancreatoduodenectomy or less invasive surgery. However, the morbidity and mortality of extended hepatectomy for biliary cancer is still high, and the most common cause of death is hepatic failure; therefore, preoperative biliary drainage is desirable in patients who are to undergo extended hepatectomy. CQ 2. What procedures are appropriate for preoperative biliary drainage? There are three methods of biliary drainage: percutaneous transhepatic biliary drainage (PTBD), endoscopic nasobiliary drainage (ENBD) or endoscopic retrograde biliary drainage (ERBD), and surgical drainage. ERBD is an internal drainage method, and PTBD and ENBD are external methods. However, there are no reports of comparisons of preoperative biliary drainage methods using randomized controlled trials (RCTs). Thus, at this point, a method should be used that can be safely performed with the equipment and techniques available at each facility. CQ 3. Which is better, unilateral or bilateral biliary drainage, in malignant hilar obstruction? Unilateral biliary drainage of the future remnant hepatic lobe is usually enough even when intrahepatic bile ducts are separated into multiple units due to hilar malignancy. Bilateral biliary drainage should be considered in the following cases: those in which the operative procedure is difficult to determine before biliary drainage; those in which cholangitis has developed after unilateral drainage; and those in which the decrease in serum bilirubin after unilateral drainage is very slow. CQ 4. What is the best treatment for postdrainage fever? The most likely cause of high fever in patients with biliary drainage is cholangitis due to problems with the existing drainage catheter or segmental cholangitis if an undrained segment is left. In the latter case, urgent drainage is required. CQ 5. Is bile culture necessary in patients with biliary drainage who are to undergo surgery? Monitoring of bile cultures is necessary for patients with biliary drainage to determine the appropriate use of antibiotics during the perioperative period. CQ 6. Is bile replacement useful for patients with external biliary drainage? Maintenance of the enterohepatic bile circulation is vitally important. Thus, preoperative bile replacement in patients with external biliary drainage is very likely to be effective when highly invasive surgery (e.g., extended hepatectomy for hilar cholangiocarcinoma) is planned