Markov Chain Monte Carlo Research Articles

Mapping soil moisture across the UK: assimilating cosmic-ray neutron sensors, remotely sensed indices, rainfall radar and catchment water balance data in a Bayesian hierarchical model

Abstract. Soil moisture is important in many hydrological and ecological processes. However, data sets which are currently available have issues with accuracy and resolution. To translate remotely sensed data to an absolute measure of soil moisture requires mapped estimates of soil hydrological properties and estimates of vegetation properties, and this introduces considerable uncertainty. We present an alternative methodology for producing daily maps of soil moisture over the UK at 2 km resolution (“SMUK”). The method is based on a simple linear statistical model, calibrated with 5 years of daily data from cosmic-ray neutron sensors at ∼ 40 sites across the country. The model is driven by precipitation, humidity, a remotely sensed “soil water index” satellite product and soil porosity. The spatial variation in the parameter describing the soil water retention (and thereby the response to precipitation) was estimated using daily water balance data from ∼ 1200 catchments with good coverage across the country. The model parameters were estimated by Bayesian calibration using a Markov chain–Monte Carlo method, so as to characterise the posterior uncertainty in the parameters and predictions. The approach reduces uncertainty by integrating multiple data sources, all of which have weaknesses but together act as a better constraint on the true soil moisture. The model explains around 70 % of the variance in the daily observations with a root-mean-square error of 0.05 m3 m−3, better than results from more complex process-based models. Given the high resolution of the inputs in time and space, the model can predict the very detailed variation in soil moisture which arises from the sporadic nature of precipitation events, including the small-scale and short-term variations associated with orographic and convective rainfall. Predictions over the period 2016 to 2023 demonstrated realistic patterns following the passage of weather fronts and prolonged droughts. The model has negligible computation time, and inputs and predictions are updated daily, lagging approximately 1 week behind real time.

Predictive model of spatial nematic order in confined cell populations

AbstractTwo-dimensional tissues made of spindle-shaped cells have many applications in the fields of tissue engineering and biotechnology. The uniformity of the tissues is critically affected by topological defects, which are singular points of cell alignment. For systematic control and analysis of defect distributions, this paper proposes a numerical method to predict and quantify spatial distributions of defects in two-dimensional domains. In the proposed method, spindle-shaped cells are modeled as nematic liquid crystals, whose alignment and Frank elastic energy are explicitly expressed. The equilibrium distributions of the defects can then be calculated using a Markov chain Monte Carlo method. The proposed method was experimentally verified by culturing mouse myoblast (C2C12) cells on microwells. The order of the defect scattering was almost the same as for the proposed estimation method, indicating that the proposed method can be used for the systematic design of topographical guides for controlling defect distributions.

Optimal Estimation of Reliability Parameters for Modified Frechet-Exponential Distribution Using Progressive Type-II Censored Samples with Mechanical and Medical Data

The aim of this research is to estimate the parameters of the modified Frechet-exponential (MFE) distribution using different methods when applied to progressive type-II censored samples. These methods include using the maximum likelihood technique and the Bayesian approach, which were used to determine the values of parameters in addition to calculating the reliability and failure functions at time t. The approximate confidence intervals (ACIs) and credible intervals (CRIs) are derived for these parameters. Two bootstrap techniques of parametric type are provided to compute the bootstrap confidence intervals. Both symmetric loss functions such as the squared error loss (SEL) and asymmetric loss functions such as the linear-exponential (LINEX) loss are used in the Bayesian method to obtain the estimates. The Markov Chain Monte Carlo (MCMC) technique is utilized in the Metropolis–Hasting sampler approach to obtain the unknown parameters using the Bayes approach. Two actual datasets are utilized to examine the various progressive schemes and different estimation methods considered in this paper. Additionally, a simulation study is performed to compare the schemes and estimation techniques.

BSN: The First Photometric Analysis of Contact Binary Systems V1961 Cyg and V0890 Lyr

Abstract We presented the first photometric analysis of the V1961 Cyg and V0890 Lyr binary systems. We observed and analyzed these systems at an observatory in France as part of the Binary Systems of South and North (BSN) Project. We extracted and collected the times of minima from the observations and literature and presented a new ephemeris for each system. Due to the few observations about these systems over the years, both O-C diagrams were fitted linearly. The PHysics Of Eclipsing BinariEs (PHOEBE) Python code and the Markov Chain Monte Carlo (MCMC) method were used to light curve solutions. The light curve solution required a cold starspot on the hotter component in the V1961 Cyg binary system. We compared and have close agreements between our mass ratios' results from the light curve analysis processes and a new method based on the light curve derivative. We estimated the absolute parameters using an empirical relationship between the semi-major axis and orbital period for contact binary systems. The results show that V1961 Cyg and V0890 Lyr are W-type contact binary systems. We displayed stars and systems' positions in the $M-L$, $M-R$, and $logM_{tot}-logJ_0$ diagrams. We also presented a new relationship between mass ratio and luminosity ratio.

Variational inference for acceleration of SN Ia photometric distance estimation with BayeSN

Abstract Type Ia supernovae (SNe Ia) are standarizable candles whose observed light curves can be used to infer their distances, which can in turn be used in cosmological analyses. As the quantity of observed SNe Ia grows with current and upcoming surveys, increasingly scalable analyses are necessary to take full advantage of these new datasets for precise estimation of cosmological parameters. Bayesian inference methods enable fitting SN Ia light curves with robust uncertainty quantification, but traditional posterior sampling using Markov Chain Monte Carlo (MCMC) is computationally expensive. We present an implementation of variational inference (VI) to accelerate the fitting of SN Ia light curves using the BayeSN hierarchical Bayesian model for time-varying SN Ia spectral energy distributions (SEDs). We demonstrate and evaluate its performance on both simulated light curves and data from the Foundation Supernova Survey with two different forms of surrogate posterior – a multivariate normal and a custom multivariate zero-lower-truncated normal distribution – and compare them with the Laplace Approximation and full MCMC analysis. To validate of our variational approximation, we calculate the pareto-smoothed importance sampling (PSIS) diagnostic, and perform variational simulation-based calibration (VSBC). The VI approximation achieves similar results to MCMC but with an order-of-magnitude speedup for the inference of the photometric distance moduli. Overall, we show that VI is a promising method for scalable parameter inference that enables analysis of larger datasets for precision cosmology.

Control of probability flow in Markov chain Monte Carlo-Nonreversibility and lifting.

The Markov chain Monte Carlo (MCMC) method is widely used in various fields as a powerful numerical integration technique for systems with many degrees of freedom. In MCMC methods, probabilistic state transitions can be considered as a random walk in state space, and random walks allow for sampling from complex distributions. However, paradoxically, it is necessary to carefully suppress the randomness of the random walk to improve computational efficiency. By breaking detailed balance, we can create a probability flow in the state space and perform more efficient sampling along this flow. Motivated by this idea, practical and efficient nonreversible MCMC methods have been developed over the past ten years. In particular, the lifting technique, which introduces probability flows in an extended state space, has been applied to various systems and has proven more efficient than conventional reversible updates. We review and discuss several practical approaches to implementing nonreversible MCMC methods, including the shift method in the cumulative distribution and the directed-worm algorithm.

Bayesian inversion of bacterial physiology and dissolved organic carbon biodegradability on water incubation data

In aquatic ecosystems, dissolved organic carbon (DOC) plays a significant role in the global carbon cycle. Microorganisms mineralize biodegradable DOC, releasing greenhouse gases (carbon dioxide, methane) into the atmosphere. Extensive research has focused on the concentrations and biodegradability of DOC in aquatic systems worldwide. However, little attention has been given to uncertainties regarding the physiological characteristics of heterotrophic bacteria, which are crucial for biogeochemical modeling. In this study, the physiological properties of heterotrophic bacteria and the properties of DOC biodegradability in water are inferred through a Bayesian inversion approach. To achieve this, treated and natural water samples collected from the Seine River basin, were inoculated and incubated in laboratory. During incubation, the concentrations of DOC and heterotrophic bacteria biomass were measured. Then, a multiple Monte Carlo Markov Chains method and the HSB model (High-weight polymers, Substrate, heterotrophic Bacteria) are applied on the water incubation data. The results indicate a higher biodegradable fraction of DOC in natural water compared to treated water and significant variability in the fraction of fast biodegradable DOC within 5 days in both water samples. The significant variability highlights the uncertainties/challenges in the HSB model parameterization. The seven water samples used in the paper serve as a proof of concept. They are from various origins and display the potential of the method to identify parameter values in a large range of values. Because mortality rate of heterotrophic bacteria at 20 ∘C (kd20) showed a remarkable stability at 0.013 h−1, we considered that this parameter can be fixed at this value. The maximum growth rates at 20 ∘C (μmax20) was 0.061 h−1 while optimal growth yield (Y) estimated at 0.34 for treated water and at 0.25 for natural water. All these parameter values are well in accordance with previous determinations.

Real-time modeling of transient crustal deformation through the quantification of uncertainty deduced from GNSS data

We propose a new method for real-time uncertainty monitoring of earthquake and volcano source models using data from the global navigation satellite system (GNSS) and explore its application concerning observation station placement. The Geospatial Information Authority of Japan operates two main types of GNSS earth observation network system (GEONET) coordinates for crustal deformation monitoring on different time scales: post-processing analysis values and real-time GEONET analysis system for rapid deformation monitoring (REGARD). REGARD uses the Markov Chain Monte Carlo (MCMC) method termed real-time automatic uncertainty estimation of a coseismic single rectangular model using GNSS data (RUNE) for single rectangular fault model estimation to handle uncertainty. Thus far, no GNSS monitoring system can automatically detect transient crustal deformation events, such as volcanic activity and earthquake swarms, on timescales of a day or less. We extended RUNE and developed a core program for a new monitoring system for earthquake and volcanic source models and their uncertainties. Our program achieved automatic and stable MCMC utilization for rectangular fault, dike, Mogi, and spheroid models by increasing the computational speed, improving search efficiency, and adjusting hyperparameters. The program automatically determines the standard deviation of the likelihood function assuming a normal distribution with weights for each observation station. The calculation time was within 15 s for 1 × 106 samples on a standard 1U server. We assessed the reliability of the developed method using synthetic and observed GNSS data from the 2015 Sakurajima volcanic event. The results were consistent with the assumed model and previous studies and indicated an advantage in automatically quantifying uncertainty in a short computation time. Based on MCMC samples, we developed a new visualization algorithm to indicate areas on a map in which the number of observation stations should be expanded. We assessed the reliability using data from the 2023 Noto Peninsula earthquake [Mj 6.5]. The results indicate that the algorithm is helpful in studying the placement of stations. The above model extensions and their application are essential to achieve a rapid quantitative understanding of disaster events near urban areas and for utilizing this information in emergency response activities.Graphical

Forecasting Constraint on the f(R) Theory with the CSST SN Ia and BAO Surveys

The f(R) modified gravity theory can explain the accelerating expansion of the late Universe without introducing dark energy. In this study, we predict the constraint strength on the f(R) theory using the mock data generated from the Chinese Space Station Telescope (CSST) Ultra-Deep Field Type Ia supernova (SN Ia) survey and wide-field slitless spectroscopic baryon acoustic oscillation (BAO) survey. We explore three popular f(R) models and introduce a parameter b to characterize the deviation of the f(R) theory from the ΛCDM theory. The Markov Chain Monte Carlo method is employed to constrain the parameters in the f(R) models, and the nuisance parameters and systematic uncertainties are also considered in the model fitting process. Besides, we also perform model comparisons between the f(R) models and the ΛCDM model. We find that the constraint accuracy using the CSST SN Ia+BAO data set alone is comparable to or even better than the result given by the combination of the current relevant observations, and the CSST SN Ia+BAO survey can distinguish the f(R) models from the ΛCDM model. This indicates that the CSST SN Ia and BAO surveys can effectively constrain and test the f(R) theory.

An Efficient Method for Batch Derivation of Detached Eclipsing Binary Parameters: Analysis of 34,907 OGLE Systems

Detached eclipsing binary (EB) systems are crucial for measuring the physical properties of stars that evolve independently. Large-scale time-domain surveys have released a substantial number of light curves for detached EBs. Utilizing the Physics of Eclipsing Binaries package in conjunction with Markov Chain Monte Carlo (MCMC) methods for batch parameter derivation poses significant computational challenges, primarily due to the high computational cost and time demands. Therefore, this paper develops an efficient method based on the neural network model and the stochastic variational inference method (denoted NNSVI) for the rapid derivation of parameters for detached EBs. For studies involving more than three systems, the NNSVI method significantly outperforms techniques that combine MCMC methods in terms of parameter inference speed, making it highly suitable for the batch derivation of large numbers of light curves. We efficiently derived parameters for 34,907 detached EBs, selected from the Optical Gravitational Lensing Experiment catalog and located in the Galactic bulge, using the NNSVI method. A catalog detailing the parameters of these systems is provided. Additionally, we compared the parameters of two double-lined detached EBs with those from previous studies and found the estimated parameters to be essentially identical.

Treatment for essential tremor: a systematic review and Bayesian Model-based Network Meta-analysis of RCTs

Essential tremor (ET) significantly impacts patients' daily lives and quality of life, presenting a considerable challenge in clinical practice. In recent years, novel therapeutic regimens have been investigated in randomized controlled trials (RCTs). This study aims to investigate and evaluate the relative efficacy and safety of various therapeutic interventions for ET. We did a systematic review and Bayesian Model-based Network Meta-analysis (NMA) of RCTs. Following PRISMA-NMA guidelines, a comprehensive database search was conducted up to April 1, 2024 to identify RCTs focused on ET treatments. The Bayesian Markov Chain Monte Carlo (MCMC) method was utilized for the analysis, evaluating the relative efficacy and safety of treatments using standardized mean difference (SMD) and log odds ratios (log ORs), respectively. Additionally, the Surface Under the Cumulative Ranking Curve (SUCRA) was applied to assess the relative efficacy of the treatment modalities. PROSPERO registration: CRD42023415752. This study included 33 RCTs involving 1251 patients, covering 19 oral medication treatments and six non-oral medication treatments. NMA showed that deep brain stimulation (DBS) (SMD=-4.93; 95% CI: [-7.73,-2.13]), CX-8998 (SMD=-2.69; 95% CI: [-5.26,-0.14]), atenolol (SMD=-2.36; 95% CI: [-4.70,-0.10]), and propranolol (SMD=-1.59; 95% CI: [-2.25,-0.67]) showed relative efficacy compared to placebo, with DBS demonstrating relative efficacy compared to 15 other treatment methods. However, GRADE assessment indicated that the evidence level for these conclusions was "low" or "very low." According to SUCRA rankings, DBS (0.97) ranked first in relative efficacy, followed by CX-8998 (0.80), thalamotomy (0.79), atenolol (0.76), metoprolol (0.66), propranolol (0.64), magnetic resonance guided focus ultrasound (MR-FUS) (0.624), ICI-118551 (0.620), nimodipine (0.61) and phenobarbitone (0.59). In terms of safety, as a network graph could not be constructed, DBS and thalamotomy were excluded from the NMA, while other effective treatments showed no significant differences in safety compared to placebo. Our study results indicate that CX-8998, propranolol, and atenolol demonstrate relative efficacy and safety in treating ET. DBS is effective for medication-resistant ET and ranks first in relative efficacy, though our NMA lacks safety data for DBS. Given the low overall grade of evidence, these results should be applied cautiously in clinical practice. Further large-scale, head-to-head RCTs are needed. This work was supported by grants from the National Nature Science Foundation of China (Grant No. 82271459).

A mathematical model for the study of HIV/AIDS transmission with PrEP coverage increase and parameter estimation using MCMC with a Bayesian approach

In this article, we present a mathematical model for the study of HIV/AIDS considering the implementation of Pre-Exposure Prophylaxis (PrEP). As a novel element in the construction of the model, we consider the diagnosis of cases for attempting to enter the PrEP program, which allows us to study different forms of PrEP. The diagnosis of new infections helps to reduce transmission in the population because these patients are incorporated into the therapy and can achieve an undetectable viral load in blood which prevents them from infecting others. The model contains a compartment of infected persons with undetectable viral load in blood that is reached by adherence to treatment which is separated from those simply infected with the virus as they do not transmit it. Considering the structure of the model, we propose a method to study the effect of increased PrEP use and HIV incidence in a population. In the case of incidence, we took into account the stochasticity of the behavior. Besides, we find the basic reproduction number and present results that allow us to obtain the impact of the parameters associated with transmission, treatment and diagnosis on the basic reproduction number. We perform computational simulations, using demographic and HIV/AIDS data from Brazil, and utilize the Markov Chain Monte Carlo (MCMC) method with a Bayesian approach to estimate model parameters. We study two coverage increases at 25% and 35% that were selected according to the size of the Brazilian population and the daily use of PrEP. We compare the increases in coverage focused on HIV incidence, which is the number of new HIV cases infected and the number of HIV cases avoided, we conclude that by increasing PrEP coverage the incidence of HIV is reduced and the number of cases avoided increases.

Spatially resolved plasma composition evolution in a solar flare – The effect of reconnection outflow

Context. Solar flares exhibit complex variations in elemental abundances compared to photospheric values. These abundance variations, characterized by the first ionization potential (FIP) bias, remain challenging to interpret. Aims. We aim to (1) examine the spatial and temporal evolution of coronal abundances in the X8.2 flare on 2017 September 10, and (2) provide a new scenario to interpret the often observed high FIP bias loop top, and provide further insight into differences between spatially resolved and Sun-as-a-star flare composition measurements. Methods. We analyzed 12 Hinode/Extreme-ultraviolet Imaging Spectrometer (EIS) raster scans spanning 3.5 hours, employing both Ca XIV 193.87 Å/Ar XIV 194.40 Å and Fe XVI 262.98 Å/S XIII 256.69 Å composition diagnostics to derive FIP bias values. We used the Markov Chain Monte Carlo (MCMC) differential emission measure (DEM) method to obtain the distribution of plasma temperatures, which forms the basis for the FIP bias calculations. Results. Both the Ca/Ar and Fe/S composition diagnostics consistently show that flare loop tops maintain high FIP bias values of > 2–6, with peak phase values exceeding 4, over the extended duration, while footpoints exhibit photospheric FIP bias of ∼1. The consistency between these two diagnostics forms the basis for our interpretation of the abundance variations. Conclusions. We propose that this variation arises from a combination of two distinct processes: high FIP bias plasma downflows from the plasma sheet confined to loop tops, and chromospheric evaporation filling the loop footpoints with low FIP bias plasma. Mixing between these two sources produces the observed gradient. Our observations show that the localized high FIP bias signature at loop tops is likely diluted by the bright footpoint emission in spatially averaged measurements. The spatially resolved spectroscopic observations enabled by EIS prove critical for revealing this complex abundance variation in loops. Furthermore, our observations show clear evidence that the origin of hot flare plasma in flaring loops consists of a combination of both directly heated plasma in the corona and from ablated chromospheric material; and our results provide valuable insights into the formation and composition of loop top brightenings, also known as EUV knots, which are a common feature at the tops of flare loops.

Bayesian Modeling of INGARCHX Models for Cellulitis Related to Meteorological Factors in Mahasarakham and Roi-Et HospitalsMahasarakham and Roi-Et Hospitals

The objective of this research is to develop integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models to represent the weekly incidence of cellulitis cases in relation to two exogenous variables: seasonality and the weekly average of either relative humidity or maximum temperature. The key to the proposed model is its capacity to explain overdispersion and lag dependence. For predictions and model parameters, we employ the Bayesian Markov Chain Monte Carlo (MCMC) approach, as supported by both a simulation study and an empirical study. To assess different models, we apply the deviance information criterion (DIC) criterion to the weekly cellulitis case sample data with two independent variables. In addition, we offer a one-week prediction to help Mahasarakham and Roi-Et Hospitals manage the increasing volume of hospital admissions by estimating the weekly cellulitis case incidence rate.

Probabilistic geophysical inversion of complex resistivity measurements using the Hamiltonian Monte Carlo method

Summary In this work, we introduce the probabilistic inversion of tomographic complex resistivity (CR) measurements using the Hamiltonian Monte Carlo (HMC) method. The posterior model distribution on which our approach operates accounts for the underlying complex-valued nature of the CR imaging problem accurately by including the individual errors of the measured impedance magnitude and phase, allowing for the application of independent regularization on the inferred subsurface conductivity magnitude and phase, and incorporating the effects of cross-sensitivities. As the tomographic CR inverse problem is non-linear, of high dimension and features strong correlations between model parameters, efficiently sampling from the posterior model distribution is challenging. To meet this challenge we use HMC, a Markov-chain Monte Carlo method that incorporates gradient information to achieve efficient model updates. To maximize the benefit of a given number of forward calculations, we use the No-U-Turn sampler (NUTS) as a variant of HMC. We demonstrate the probabilistic inversion approach on a synthetic CR tomography measurement. The NUTS succeeds in creating a sample of the posterior model distribution that provides us with the ability to analyze correlations between model parameters and to calculate statistical estimators of interest, such as the mean model and the covariance matrix. Our results provide a strong basis for the characterization of the posterior model distribution and uncertainty quantification in the context of the tomographic CR inverse problem.

Within-chain parallelization-Giving Stan Jet Fuel for population modeling in pharmacometrics.

Stan is a powerful probabilistic programming language designed mainly for Bayesian data analysis. Torsten is a collection of Stan functions that handles the events (e.g., dosing events) and solves the ODE systems that are frequently present in pharmacometric models. To perform a Bayesian data analysis, most models in pharmacometrics require Markov Chain Monte Carlo (MCMC) methods to sample from the posterior distribution. However, MCMC is computationally expensive and can be time-consuming, enough so that people will often forgo Bayesian methods for a more traditional approach. This paper shows how to speed up the sampling process in Stan by within-chain parallelization through both multi-threading using Stan's reduce_sum() function and multi-processing using Torsten's group ODE solver. Both methods show substantial reductions in the time necessary to sufficiently sample from the posterior distribution compared with a basic approach with no within-chain parallelization.

QPOs from charged particles around magnetized black holes in braneworlds

Quasiperiodic oscillations (QPOs) are a powerful tool for testing gravity theories, probing gravitational and electromagnetic field properties, and obtaining constraints on the black hole and field parameters. This work considers charged particle dynamics near uniformly magnetized black holes in braneworlds. First, we obtain the solution of the Maxwell equation for magnetic fields and calculate the radial and angular magnetic field components. We derive and analyze the effective potential of charged particles for circular orbits and investigate the energy and angular momentum for the circular orbits. We also analyze the combined effects of magnetic interaction and braneworlds on the charged particles’ innermost stable circular orbits (ISCOs). We calculate the angular momentum of charged particles in Keplerian orbits in the presence of an external magnetic field and braneworlds. Also, we investigate frequencies of the particle oscillations along vertical and angular directions. We applied our studies on particle oscillations to the QPO studies in the relativistic precession model. Finally, we obtain constraints on magnetic interaction and braneworld parameters together with the black hole mass and QPO orbits using Monte Carlo Markov Chain (MCMC) simulation in the four-dimensional parameter space for the QPOs observed in the microquasars XTE J1550-564, GRO J1655-40 & GRS 1915-105, and at the center of galaxies M82 and Milky Way.

Evaluating MCMC Convergence in a Bayesian Model of ST-Elevation Myocardial Infarction Female Patients in Malaysia

The majority of research that looked at the Bayesian Markov Chain Monte Carlo (MCMC) approach for prognostic modelling of cardiovascular disease only focused on the use of the Bayesian approach in variable selection, model selection, and prior distribution selection. But very few of this research has looked at the Markov chains' convergence in the model. In this study, convergence diagnostics were carried out to evaluate the convergence of Markov chains using both visual inspection and additional diagnostics. The National Cardiovascular Disease Database-Acute Coronary Syndrome (NCVD-ACS) registry, which included 1248 female patients with ST-Elevation Myocardial Infarction (STEMI) between 2006 and 2013, was used for this study's analysis. The multivariate Bayesian model identified six significant variables: dyslipidaemia, myocardial infarction, smoking, renal disease, Killip class, and age group. The trace plots did not reveal any distinctive patterns based on these significant variables, and the model's MCMC mixing is typically good. While for the autocorrelation plots, mild autocorrelations for age group, Killip IV, as well as the intercept term in the model. Since there were only mild autocorrelations, no thinning is needed. Also, the Geweke diagnostic showed that the chain is divided into two windows containing a set fraction of the first and last iterations which produced standard Z-scores. The Geweke diagnostic did not provide evidence of non-convergence, as none of the Z-scores fell in the extreme tails of the N (0,1). In this study, a number of plots and additional diagnostic tools showed that the Markov chains have reached convergence, which is relevant to the general use of the MCMC approach.

Sampling random graphs with specified degree sequences

The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network’s structure can be explained by its degree structure alone. A Markov chain Monte Carlo (MCMC) algorithm, based on a degree-preserving double-edge swap, provides an asymptotic solution to sample from the configuration model. However, accurately and efficiently detecting when this Markov chain is sufficiently close to its stationary distribution remains an unsolved problem. Here, we provide a solution to sample from the configuration model using this standard MCMC algorithm. We develop an algorithm, based on the assortativity of the sampled graphs, for estimating the gap between effectively independent MCMC states, and a computationally efficient gap-estimation heuristic derived from analyzing a corpus of 509 empirical networks. We provide a convergence detection method based on the Dickey-Fuller Generalized Least Squares test, which we show is more accurate and efficient than three alternative Markov chain convergence tests. Supplementary materials for the proposed methods can be found here.

Reaction kinetics for catalytic hydrogenation of quinoline to decahydroquinoline as liquid organic hydrogen carrier

The catalytic hydrogenation of quinoline to decahydroquinoline (DHQ) formation is studied for various parameters such as temperature, hydrogen pressure, reaction time, solvents, reactant-to-solvent ratio, and catalyst loading over 5%Pd loaded on alumina (Pd/Al2O3) to obtain optimal reaction conditions. The hydrogen uptake of quinoline in the liquid phase reaction using isopropylalcohol (IPA) is studied in an autoclave reactor. The optimum reaction parameters of 50 bar H2 pressure and 175oC with reactant to solvent ratio of 1:9 for reaction time of 5 h are observed. The effect of IPA solvent showed that hydrogen uptake of 6.91 wt% with complete hydrogenation of quinoline and DHQ yield of more than 99% is observed. The reaction kinetic model is developed for a simplified reaction mechanism and is simulated using the Markov Chain Monte Carlo (MCMC) simulation tool to predict the rate constants and the experimental observations are validated with the model predictions. The activation energy for quinoline hydrogenation to py-THQ formation is estimated to be 136.57 kJ/mol. It is envisaged that quinoline hydrogenation to pz-THQ is the rate-limiting step in the DHQ formation.