Maximum approximate likelihood estimation of general continuous-time state-space models

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions concerning linearity and Gaussianity to facilitate inference on the model parameters via the Kalman filter. In this contribution, we provide a general continuous-time SSM framework, allowing both the observation and the state process to be non-linear and non-Gaussian. Statistical inference is carried out by maximum approximate likelihood estimation, where multiple numerical integration within the likelihood evaluation is performed via a fine discretization of the state process. The corresponding reframing of the SSM as a continuous-time hidden Markov model, with structured state transitions, enables us to apply the associated efficient algorithms for parameter estimation and state decoding. We illustrate the modelling approach in a case study using data from a longitudinal study on delinquent behaviour of adolescents in Germany, revealing temporal persistence in the deviation of an individual's delinquency level from the population mean.

Designing and Modeling of a Municipal Wastewater Treatment Plant With GPS-X

Wastewater treatment is the process used to remove contaminants from wastewater to produce an effluent suitable for discharge to the environment. Several kinds of wastewater are treated based on the concentration of various parameters. Domestic Wastewater/Municipal Wastewater is treated in Sewage Treatment Plants (STP), which involve various types of processes like physical, chemical and biological to treat the wastewater better. The treatment plant involves five steps of the process – preliminary treatment, primary treatment, secondary treatment, tertiary treatment and sludge treatment to meet the safe disposal guidelines of the department of the environment. In this paper, a municipal wastewater treatment plant for Uttara City is designed and modeled with GPS-X. GPS-X is a wastewater treatment plant modeling software package that is used for verify the treatment process. The design calculation of all unit operations is shown with a specification table. The Process Flow Diagram (PFD), Process Block Diagram (PBD) and mass balance of the process are expressed in the article. The design calculation of the STP is performed with a steady-state process. After each unit operation, the concentration of various parameters – TSS, BOD, VSS, TN is analyzed and the removal efficiency for different equipment is calculated. The STP is designed to maintain the guidelines of the Department of Environment, Bangladesh. At the end of the paper, the designing and modeling steps of a sewage treatment plant will be pursued. Finally, some recommendations are done in the conclusion section.

Performance Evaluation of Adaptive Tracking Techniques with Direct-State Kalman Filter

This paper evaluates the performance of robust adaptive tracking techniques with the direct-state Kalman filter (DSKF) used in modern digital global navigation satellite system (GNSS) receivers. Under the assumption of a well-known Gaussian distributed model of the states and the measurements, the DSKF adapts its coefficients optimally to achieve the minimum mean square error (MMSE). In time-varying scenarios, the measurements’ distribution changes over time due to noise, signal dynamics, multipath, and non-line-of-sight effects. These kinds of scenarios make difficult the search for a suitable measurement and process noise model, leading to a sub-optimal solution of the DSKF. The loop-bandwidth control algorithm (LBCA) can adapt the DSKF according to the time-varying scenario and improve its performance significantly. This study introduces two methods to adapt the DSKF using the LBCA: The LBCA-based DSKF and the LBCA-based lookup table (LUT)-DSKF. The former method adapts the steady-state process noise variance based on the LBCA’s loop bandwidth update. In contrast, the latter directly relates the loop bandwidth with the steady-state Kalman gains. The presented techniques are compared with the well-known state-of-the-art carrier-to-noise density ratio (C/N0)-based DSKF. These adaptive tracking techniques are implemented in an open software interface GNSS hardware receiver. For each implementation, the receiver’s tracking performance and the system performance are evaluated in simulated scenarios with different dynamics and noise cases. Results confirm that the LBCA can be successfully applied to adapt the DSKF. The LBCA-based LUT-DSKF exhibits superior static and dynamic system performance compared to other adaptive tracking techniques using the DSKF while achieving the lowest complexity.

Numerical Solutions of the Hattendorff Differential Equation for Multi-state Markov Insurance Models

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

Investigation on Friction Stir Weldability Characteristics of AA7075-T651 and AA6061-T6 Based Nanocomposites

Friction stir welding (FSW) is an emerging solid-state process and alternative to fusion welding, wherein frictional heat is generated between a nonconsumable rotating steel tool and the work substrate. The present study focuses on the influence of the operating attributes like tool pin contact geometry, welding speed, and tool rotational speed on dissimilar aluminum matrix nanocomposites. AA6061-T6 and AA7075-T651 aluminum alloy plates were joined via double-pass FSW with the inclusion of 5 vol. % of nanoscale h-BN particles. Welding was performed with four rotational speeds (600, 800, 900, and 1000 rpm), three traversing speeds (30, 40, and 60 mm/min), and three distinct tool pin geometry (cylindrical, threaded cylindrical, and square), respectively. Besides, unreinforced and reinforced weldments were analyzed for mechanical properties like tensile strength and microhardness. Microstructural characterization was also carried out using FESEM and XRD techniques. The findings concluded that the reinforced samples welded using a cylindrical tool and double-pass strategy showcased homogenous distribution of nanoparticles with grain refinement, thereby exhibiting improved strength and hardness.

The Demand Supply Steady-State Process-Based Multi-Level Spare Parts Optimization

Spare parts are one of the important components of the equipment comprehensive support system. Spare parts management plays a decisive role in achieving the desired availability with the minimum cost. With the equipment complexity increasing, the price of spare parts has risen sharply. The traditional spare parts management makes the contradiction between fund shortage and spare parts shortage increasingly prominent. Based on the analysis of the multi-echelon and multi-indenture spare parts support model VARI-METRIC (vary multi-echelon technology for recoverable item control, VARI-METRIC), which is widely used by troops and enterprises in various countries, the model is mainly used in high system availability scenarios. However, in the case of low equipment system availability, the accuracy and cost of model inventory prediction are not ideal. This paper proposed the multi-level spare parts optimization model, which is based on the demand-supply steady-state process. It is an analytical model, which is used to solve the low accuracy problem of the VARI-METRIC model in the low equipment system availability. The analytical model is based on the multi-level spare parts support process. The article deduces methods for solving demand rate, demand–supply rate, equipment system availability, and support system availability. The marginal analysis method is used in the model to analyze the spare parts inventory allocation strategy’s current based cost and availability optimal value. Finally, a simulation model is established to evaluate and verify the model. Then, the simulation results show that, when the low availability of equipment systems are 0.4, 0.6, the relative errors of the analytical model are 3.54%, 3.86%, and its costs are 0.52, 1.795 million ¥ RMB. The experiment proves that the inventory prediction accuracy of the analytical model is significantly higher than that of the VARI-METRIC model in low equipment system availability. Finally, the conclusion and future research directions are discussed.

Numerical Solutions of the Hattendorff Differential Equation for Multi-state Markov Insurance Models

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

Structural Characterization of Ectodomain G Protein of Respiratory Syncytial Virus and Its Interaction with Heparan Sulfate: Multi-Spectroscopic and In Silico Studies Elucidating Host-Pathogen Interactions

The global burden of disease caused by a respiratory syncytial virus (RSV) is becoming more widely recognized in young children and adults. Heparan sulfate helps in attaching the virion through G protein with the host cell membrane. In this study, we examined the structural changes of ectodomain G protein (edG) in a wide pH range. The absorbance results revealed that protein maintains its tertiary structure at physiological and highly acidic and alkaline pH. However, visible aggregation of protein was observed in mild acidic pH. The intrinsic fluorescence study shows no significant change in the λmax except at pH 12.0. The ANS fluorescence of edG at pH 2.0 and 3.0 forms an acid-induced molten globule-like state. The denaturation transition curve monitored by fluorescence spectroscopy revealed that urea and GdmCl induced denaturation native (N) ↔ denatured (D) state follows a two-state process. The fluorescence quenching, molecular docking, and 50 ns simulation measurements suggested that heparan sulfate showed excellent binding affinity to edG. Our binding study provides a preliminary insight into the interaction of edG to the host cell membrane via heparan sulfate. This binding can be inhibited using experimental approaches at the molecular level leading to the prevention of effective host–pathogen interaction.

Transcription bursting and epigenetic plasticity: an updated view

The vast majority of eukaryotic transcription occurs in bursts during discrete periods of promoter activity, separated by periods of deep repression and inactivity. Elucidating the factors responsible for triggering transitions between these two states has been extremely challenging, partly due to the difficulties in measuring transcriptional bursting genome-wide, but also due to the vast array of candidate transcriptional and epigenetic factors and their complex and dynamic interactions. Additionally, this long-held view of transcriptional bursting as a two-state process has become increasingly challenged, and a resulting lack in consensus on terminology of the involved events has further complicated our understanding of the molecular mechanisms involved. Here, we review the impact of epigenetics on dynamic gene expression, with a focus on transcription bursting. We summarise current understanding of the epigenetic regulation of transcription bursting and propose new terminology for the interpretation of future results measuring transcription dynamics.