Simpler Submodels Research Articles

Mitigation Strategies for COVID-19: Lessons from the K-SEIR Model Calibrated to the Observable Data

This article develops a detailed epidemiological multi-factor model, the K-susceptible–exposed–infected–removed (K-SEIR) model, and several simpler sub-models as its building blocks. The general model enables us to account for all the relevant COVID-19 features, its disparate impact on different population groups, and interactions within and between the groups. It also includes the availability (or lack thereof) of spare hospital beds and intensive care units (ICU) to accommodate the pent-up demand due to the pandemic. We use the most recent hospitalization and mortality data to calibrate the model. Since our model is multi-factor, we can use it to simulate and analyze the consequences of the sheltering-in-place for each specific group and compare the lives saved and lost due to this measure. We show that in countries with well-developed healthcare systems and a population willing to abide by suitable containment and mitigation procedures, the sheltering in place of the entire community is excessive and harmful when considered holistically. At the same time, sealing nursing homes as thoroughly as possible to avoid high infection and mortality rates is an absolute necessity.

Visual question answering in the medical domain based on deep learning approaches: A comprehensive study

Visual Question Answering (VQA) in the medical domain has attracted more attention from research communities in the last few years due to its various applications. This paper investigates several deep learning approaches in building a medical VQA system based on ImageCLEF’s VQA-Med dataset, which consists of about 4K images with about 15K question-answer pairs. Due to the wide variety of the images and questions included in this dataset, the proposed model is a hierarchical one consisting of many sub-models, each tailored to handle certain questions. For that, a special model is built to classify the questions into four categories, where each category is handled by a separate sub-model. At their core, all of these models consist of pre-trained Convolution Neural Networks (CNN). In order to get the best results, extensive experiments are performed and various techniques are employed including Data Augmentation (DA), Multi-Task Learning (MTL), Global Average Pooling (GAP), Ensembling, and Sequence to Sequence (Seq2Seq) models. Overall, the final model achieves 60.8 accuracy and 63.4 BLEU score, which are competitive with the state-of-the-art results despite using less demanding and simpler sub-models.

Mitigation Strategies for COVID-19: Lessons from the K-SEIR Model

We develop a detailed epidemiological multi-factor model, the K-Susceptible-Exposed-Infected-Removed (K-SEIR) model, as well as several simpler sub-models, as its building blocks. The general model enables us to account for all the relevant COVID-19 features, its disparate impact on different population groups, and interactions within and between the groups. It also includes the availability (or lack thereof) of spare hospital beds and intensive care units (ICU) to accommodate the pent-up demand due to the pandemic. We use the most recent hospitalization and mortality data to calibrate the model. Since our model is multi-factor, it can be used to simulate and analyze the consequences of the sheltering-in-place for each specific group, as well as compare lives saved and lost due to this measure. We show that in countries with well-developed healthcare systems and a population willing to abide by sensible containment and mitigation procedures, the sheltering-in-place of the entire community is excessive and harmful when considered holistically. At the same time, sealing nursing homes as best as possible to avoid high infection and mortality rates is an absolute must.

Hypothesis testing for tail dependence parameters on the boundary of the parameter space

Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter space. Hypothesis tests are proposed for tail dependence parameters that, under the null hypothesis, are on the boundary of the alternative hypothesis. The asymptotic distribution of the weighted least squares estimator is given when the true parameter vector is on the boundary of the parameter space, and two test statistics are proposed. The performance of these test statistics is evaluated for the Brown–Resnick model and the max-linear model. In particular, simulations show that it is possible to recover the optimal number of factors for a max-linear model. Finally, the methods are applied to characterize the dependence structure of two major stock market indices, the DAX and the CAC40.

A Quantitative Model of Early Atherosclerotic Plaques Parameterized Using In Vitro Experiments.

There are a growing number of studies that model immunological processes in the artery wall that lead to the development of atherosclerotic plaques. However, few of these models use parameters that are obtained from experimental data even though data-driven models are vital if mathematical models are to become clinically relevant. We present the development and analysis of a quantitative mathematical model for the coupled inflammatory, lipid and macrophage dynamics in early atherosclerotic plaques. Our modeling approach is similar to the biologists' experimental approach where the bigger picture of atherosclerosis is put together from many smaller observations and findings from in vitro experiments. We first develop a series of three simpler submodels which are least-squares fitted to various in vitro experimental results from the literature. Subsequently, we use these three submodels to construct a quantitative model of the development of early atherosclerotic plaques. We perform a local sensitivity analysis of the model with respect to its parameters that identifies critical parameters and processes. Further, we present a systematic analysis of the long-term outcome of the model which produces a characterization of the stability of model plaques based on the rates of recruitment of low-density lipoproteins, high-density lipoproteins and macrophages. The analysis of the model suggests that further experimental work quantifying the different fates of macrophages as a function of cholesterol load and the balance between free cholesterol and cholesterol ester inside macrophages may give valuable insight into long-term atherosclerotic plaque outcomes. This model is an important step toward models applicable in a clinical setting.

Designing Biological Simulation Models Using Formalism-Based Functional and Spatial Decompositions

One of the most daunting challenges confronting computational biologists is a problem that simulation developers in all disciplines face: the design of simulation code that can be easily understood and modified despite the complexity of the systems being modeled. To meet this challenge, the authors apply the discrete event system specification (DEVS), a general modeling formalism invented for the formal description of a wide range of systems that vary in time. Using DEVS, developers can address the complexity of a biological model by subdividing it into a hierarchy of simpler submodels. Hierarchical design is a well-known strategy for software development in general. But the question remains, what type of decomposition should be used? The authors use the upper levels of a hierarchy to separate different functions or algorithms, and then dedicate lower levels to the partitioning of space. To illustrate the approach, they present a DEVS-based model that captures the 3D self-assembly of vesicle clusters and their role in the propagation of information between nerve cells.

An Efficient Slicing Algorithm for Asynchronous Linear Hotwire Cutting System of Expandable Polystyrene Foam

The asynchronous linear hotwire cutting (ALHC) system of expandable polystyrene (EPS) foam is a new rapid prototyping (RP) technology, which uses the asynchronous linear hotwire cutter and EPS foam to fabricate the part. The efficiency and capacity of ALHC system depends significantly on the pre-process of STL model. This paper presents an original algorithm for adaptively decomposing a STL model into a set of variable slices, which can be efficiently fabricated by ALHC system. A large complex model is first partitioned into several smaller and simpler sub-models by using the curvature-based partitioning. Then, these sub-models are sliced into layers with different thickness based on feature facets. Several experimental results demonstrate the reliability and efficiency of the slicing algorithm.

A New Design of Scientific Software Using Python and XML

In this paper we advance the development of our python-based package for the solution of partial differential equations using spatial discretization techniques such as the finite element method (FEM) via two approaches. First we define a Model class object which makes it easy to break down a complex simulation into simpler sub-models, which then can be linked together into a highly efficient whole. Second, we implement an XML schema in which we can save an entire simulation. This allows implemention of check-pointing in addition to graphical user interfaces which enables non-programmers to use models developed for their research. These features are built upon our escript module, a software package designed to develop numerical models in a very abstract way while still allowing the use of computational components implemented in C and C++ to achieve extreme high-performance for time-intensive calculations.

Inferring cellular networks using probabilistic graphical models.

High-throughput genome-wide molecular assays, which probe cellular networks from different perspectives, have become central to molecular biology. Probabilistic graphical models are useful for extracting meaningful biological insights from the resulting data sets. These models provide a concise representation of complex cellular networks by composing simpler submodels. Procedures based on well-understood principles for inferring such models from data facilitate a model-based methodology for analysis and discovery. This methodology and its capabilities are illustrated by several recent applications to gene expression data.

Comparison of two construction algorithms for local model networks

The divide-and-conquer approach of local model (LM) networks is a common engineering approach to the identification of a complex nonlinear dynamical system. The global representation is obtained from the weighted sum of locally valid, simpler submodels defined over small regions of the operating space. Constructing such networks requires the determination of appropriate partitioning and the parameters of the LMs. This paper focuses on the structural aspect of LM networks. It compares the computational requirements and performances of the Johansen and Foss (J&F) and LOLIMOT tree-construction algorithms. Several useful and important modifications to each algorithm are proposed. The modelling performances are evaluated using real data from a pilot plant of a pH neutralization process. Results show that while J&F achieves a more accurate nonlinear representation of the pH process, LOLIMOT requires significantly less computational effort.

Optimal Construction of Local Model Networks Using Genetic Algorithm

ABSTRACT Local Model (LM) networks represent a complex nonlinear dynamical system by a weighted sum of locally valid, simpler sub-models defined over small regimes of the operating space. Constructing such networks requires the determination of the appropriate regimes and the local model parameters. This paper describes a new soft computing approach to simultaneously determine the local model parameters and the appropriate operating regimes. Structured genetic coding is used to obtain the optimal number of ARX local models and their parameters. Centres and covariances of Gaussian interpolation functions are found through genetic evolution with fuzzy logic used to dynamically evolve the genetic algorithm. Several modifications to the classical genetic algorithm are proposed to detemline the locally valid sub-models. The parallel model prediction error is minimized to produce good generalization from the identified LM network. The modelling potential of the resultant LM network is investigated on practical data from an experimental pH neutralisation process. The same data was also used in a recent comparative study of a hybrid training algorithm and tree type construction (McGinnity and Irwin, 1999) for LM networks. It is concluded that the LM network from the new GA based construction formed a significantly better non linear dynamical model of the pH process.

Parameter Estimation Strategies for Large-Scale Urban Models

Large-scale urban models often are subdivided into simpler submodels. The parameters of these models can be estimated using approaches that differ in regard to whether the full modeling system is run during an estimation procedure or whether that overall estimation is performed simultaneously with the estimation of the individual submodels. There are also ways in which extra data or extra models can be used to further inform parameter values. Five different techniques are presented (“limited view,” “piecewise” “simultaneous,” “sequential,” and “Bayesian sequential”), and the statistical theory necessary to justify each technique concurrently is described. The practical advantages and disadvantages are discussed, and each technique is illustrated using a simple nested logit model example. The concepts then are further illustrated by describing the sequential parameter estimation process for a land use/transport interaction model of the Sacramento, California, region. The ideas and examples should help modelers place more of an emphasis on overall calibration, allow them to follow a more rigorous approach in establishing the parameters of large-scale urban models, and help them understand the theory and assumptions that they are implicitly adopting. Two techniques in particular are noted as worthy of future research in large-scale urban modeling: ( a) establishing the likelihood function based directly on the structural equations of the model, eliminating or reducing the need to “solve” for the model outputs during parameter estimation; and ( b) using Bayesian techniques to adjust parameters in an overall estimation without discarding what is already known about those parameters.

Bayesian computation for the superposition of nonhomogeneous poisson processes

AbstractBayesian inference for the superposition of nonhomogeneous Poisson processes is studied. A Markov‐chain Monte Carlo method with data augmentation is developed to compute the features of the posterior distribution. For each observed failure epoch, a latent variable is introduced that indicates which component of the superposition model gives rise to the failure. This data‐augmentation approach facilitates specification of the transitional kernel in the Markov chain. Moreover, new Bayesian tests are developed for the full superposition model against simpler submodels. Model determination by a predictive likelihood approach is studied. A numerical example based on a real data set is given.

Comparison of CropSyst performance for water management in southwestern France using submodels of different levels of complexity

A comparison of the performance of the CropSyst model when using evapotranspiration (ET) and soil water transport submodels of different levels of complexity was conducted. ET submodels included Penman-Monteith, Priestley Taylor, and a temperature-based submodel. Soil water transport submodels included a finite difference numerical method and a simple cascading method. Simulations of biomass production, yield, and water use of irrigated maize, soybean, and sorghum were compared with experimental data collected at Auzeville, southwestern France. Experimental data for growing seasons 1986, 1989, and 1990 (dry years) were used, including three irrigation levels (full, deficit, and no irrigation) each year. Calibration of a small number of crop parameters was conducted using the most complex submodels. Using these most complex submodels, simulations compared well with measurements. with the Wilmott index of agreement fluctuating from 0.956 to 0.997 (an index of 1.0 indicating perfect agreement). The model appeared suitable for applications over a wide range of water availability and stress conditions. Using simpler submodels, the performance of CropSyst tended to decrease, but generally not significantly. A simple cascading method for soil water transport (non-constrained drainage) appeared to be a valid alternative to more complex numerical methods. All ET submodels predicted similar seasonal ET, but differences in vapor pressure deficit estimation led to growth overprediction in some cases. Simpler submodels would have performed similarly to the most complex submodels if used during calibration. Successful applications of the CropSyst model appear feasible for sites with limited weather and soil data.

Aerosol depletion and deposition in forests—A model analysis

A system of partial differential equations is developed to describe an aerosol entering from an open field into a downwind forest, where deposition and turbulent transfer affect particle concentration. The model considers the interplay between forest structure, open field and forest aerodynamics and aerosol characteristics. The modelling problem is broken down into a set of simpler submodels which can be refined or simplified individually. Model results suggest, basically, significant horizontal (vertical) depletion of super-μm particles downwind from the forest edge (downwards from the canopy top). Distinct edge effects in deposition rates are common. In certain cases vertical exchange processes predominate, leading to enrichment of the aerosol. Sub-μm particles (unless extremely small) are subject to almost negligible depletion and edge effects. Deposition of super-μm particle oriented aerosols are governed by a complex interaction between particle size, forest structure and aerodynamics whereas deposition of sub-μm particles is simply controlled by particle concentration and forest structure. Under certain conditions (dense homogenous forests) aerosol particle concentration across the open field to forest roughness transition increases again after initial depletion.

A noninvasive in vivo method of assessing the kinetics of halothane metabolism in humans.

The authors describe a noninvasive method of estimating the kinetic constants that characterize metabolism of inhaled anesthetics in humans. Ten healthy male volunteers breathed subanesthetic concentrations of halothane and isoflurane in a fixed inspired ratio of 20:1. Isoflurane served as a marker that identified changes in uptake in nonmetabolizing depots. Each study progressed through nine 30-min levels (numbered 0-8). At each level, inspired concentrations of both halothane and isoflurane were doubled, and alveolar concentrations and uptakes were determined. Clearance (uptake/alveolar concentration) of isoflurane remained constant over a range of concentrations of 0.00006 to 0.008%. In contrast, clearance of halothane decreased as the alveolar concentration increased from 0.0007 to 0.13%. On this basis, the authors assumed that the clearance of halothane was a combination of linear clearance to depots and saturable metabolism, the former proportional to the clearance of isoflurane, and the latter attributable to a Michaelis-Menten process. Applying such a model to halothane, they estimated the mean (+/- SE) Vmax (the composite maximum rate of metabolism) to be 0.79 +/- 0.09 ml . min-1 . individual-1, and the Km (the composite concentration at which half-saturation of enzymes occurs) to be 0.029 +/- 0.003%. This model provides a significantly better data fit than that provided by two simpler submodels, one of which assumes that all clearance is linear, and the other of which allows a part of clearance to be saturable but ignores the isoflurane marker data. The value of 0.029% for Km indicates that a wide range of clinical anesthetic concentrations will produce similar rates of metabolism; that metabolism will proceed at near maximum rates during the first several minutes of recovery; and that most metabolism probably occurs after, rather than during, anesthesia.

A systematic computerized method for building enzyme kinetic models

A systematic method for modelling enzyme kinetic mechanisms is presented. It involves the decomposition of a general model into simpler submodels. The submodels with large residual values or slow rates of convergence are eliminated. Hybrid models may be formed from the best submodels. With this method, the initial values of the rate constants of the hybrid models can be obtained from the submodels. Possible models for uricase and xanthine oxidase have been obtained using the proposed method. The residual of the resulting uricase model is smaller than that of the existing one.