Swain: Stata module to correct the SEM chi-square overidentification test in small sample sizes or complex models. Statistical Software Components S457617, Boston College Department of Economics.

Swain corrects the chi-square overidentification test (i.e., likelihood ratio test of fit) for structural equation models whethr with or without latent variables. The chi-square statistic is asymptotically correct; however, it does not behave as expected in small samples and/or when the model is complex (cf. Herzog, Boomsma, & Reinecke, 2007). Thus, particularly in situations where the ratio of sample size (n) to the number of parameters estimated (p) is relatively small (i.e., the p to n ratio is large), the chi-square test will tend to overreject correctly specified models. To obtain a closer approximation to the distribution of the chi-square statistic, Swain (1975) developed a correction; this scaling factor, which converges to 1 asymptotically, is multiplied with the chi-square statistic. The correction better approximates the chi-square distribution resulting in more appropriate Type 1 reject error rates (see Herzog & Boomsma, 2009; Herzog, et al., 2007).

Saint Mathew Law and Bonini Paradox in Textual Theory of Complex Models

The mathematical models of the complex reality are texts belonging to a certain literature that is written in a semi-formal language, denominated L(MT) by the authors whose laws linguistic mathematics have been previously defined. This text possesses linguistic entropy that is the reflection of the physical entropy of the processes of real world that said text describes. Through the temperature of information defined by Mandelbrot, the authors begin a text-reality thermodynamic theory that drives to the existence of information attractors, or highly structured point, settling down a heterogeneity of the space text, the same one that of ontologic space, completing the well-known law of Saint Mathew, of the General Theory of Systems and formulated by Margalef saying: “To the one that has more he will be given, and to the one that doesn't have he will even be removed it little that it possesses.

Simple and complex models for nonlinear seismic response of reinforced concrete structures /

Mode of access: Internet.

Dimensionality reduction in complex models

As a part of the Managing Uncertainty in Complex Models (MUCM) project, research at Aston University will develop methods for dimensionality reduction of the input and/or output spaces of models, as seen within the emulator framework. Towards this end this report describes a framework for generating toy datasets, whose underlying structure is understood, to facilitate early investigations of dimensionality reduction methods and to gain a deeper understanding of the algorithms employed, both in terms of how effective they are for given types of models / situations, and also their speed in applications and how this scales with various factors. The framework, which allows the evaluation of both screening and projection approaches to dimensionality reduction, is described. We also describe the screening and projection methods currently under consideration and present some preliminary results. The aim of this draft of the report is to solicit feedback from the project team on the dataset generation framework, the methods we propose to use, and suggestions for extensions that should be considered.

Introduction to Coding Theory for Flow Equations of Complex Systems Models

The modeling of complex dynamic systems depends on the solution of a differential equations system. Some problems appear because we do not know the mathematical expressions of the said equations. Enough numerical data of the system variables are known. The authors, think that it is very important to establish a code between the different languages to let them codify and decodify information. Coding permits us to reduce the study of some objects to others. Mathematical expressions are used to model certain variables of the system are complex, so it is convenient to define an alphabet code determining the correspondence between these equations and words in the alphabet. In this paper the authors begin with the introduction to the coding and decoding of complex structural systems modeling.

Mathematical models in percutaneous absorption

A number of mathematical models have been used to describe percutaneous absorption kinetics. In general, most of these models have used either diffusion-based or compartmental equations. The object of any mathematical model is to a) be able to represent the processes associated with absorption accurately, b) be able to describe/summarize experimental data with parametric equations or moments, and c) predict kinetics under varying conditions. However, in describing the processes involved, some developed models often suffer from being of too complex a form to be practically useful. In this chapter, we attempt to approach the issue of mathematical modeling in percutaneous absorption from four perspectives. These are to a) describe simple practical models, b) provide an overview of the more complex models, c) summarize some of the more important/useful models used to date, and d) examine sonic practical applications of the models. The range of processes involved in percutaneous absorption and considered in developing the mathematical models in this chapter is shown in Fig. 1. We initially address in vitro skin diffusion models and consider a) constant donor concentration and receptor conditions, b) the corresponding flux, donor, skin, and receptor amount-time profiles for solutions, and c) amount- and flux-time profiles when the donor phase is removed. More complex issues, such as finite-volume donor phase, finite-volume receptor phase, the presence of an efflux. rate constant at the membrane-receptor interphase, and two-layer diffusion, are then considered. We then look at specific models and issues concerned with a) release from topical products, b) use of compartmental models as alternatives to diffusion models, c) concentration-dependent absorption, d) modeling of skin metabolism, e) role of solute-skin-vehicle interactions, f) effects of vehicle loss, a) shunt transport, and h) in vivo diffusion, compartmental, physiological, and deconvolution models. We conclude by examining topics such as a) deep tissue penetration, b) pharmacodynamics, c) iontophoresis, d) sonophoresis, and e) pitfalls in modeling.

A critical evaluation of methods for the reconstruction of tissue-specific models

Under the framework of constraint based modeling, genome-scale metabolic models (GSMMs) have been used for several tasks, such as metabolic engineering and phenotype prediction. More recently, their application in health related research has spanned drug discovery, biomarker identification and host-pathogen interactions, targeting diseases such as cancer, Alzheimer, obesity or diabetes. In the last years, the development of novel techniques for genome sequencing and other high-throughput methods, together with advances in Bioinformatics, allowed the reconstruction of GSMMs for human cells. Considering the diversity of cell types and tissues present in the human body, it is imperative to develop tissue-specific metabolic models. Methods to automatically generate these models, based on generic human metabolic models and a plethora of omics data, have been proposed. However, their results have not yet been adequately and critically evaluated and compared. This work presents a survey of the most important tissue or cell type specific metabolic model reconstruction methods, which use literature, transcriptomics, proteomics and metabolomics data, together with a global template model. As a case study, we analyzed the consistency between several omics data sources and reconstructed distinct metabolic models of hepatocytes using different methods and data sources as inputs. The results show that omics data sources have a poor overlapping and, in some cases, are even contradictory. Additionally, the hepatocyte metabolic models generated are in many cases not able to perform metabolic functions known to be present in the liver tissue. We conclude that reliable methods for a priori omics data integration are required to support the reconstruction of complex models of human cells.

What do we gain from simplicity versus complexity in species distribution models?

Species distribution models (SDMs) are widely used to explain and predict species ranges and environmental niches. They are most commonly constructed by inferring species' occurrence-environment relationships using statistical and machine-learning methods. The variety of methods that can be used to construct SDMs (e.g. generalized linear/additive models, tree-based models, maximum entropy, etc.), and the variety of ways that such models can be implemented, permits substantial flexibility in SDM complexity. Building models with an appropriate amount of complexity for the study objectives is critical for robust inference. We characterize complexity as the shape of the inferred occurrence-environment relationships and the number of parameters used to describe them, and search for insights into whether additional complexity is informative or superfluous. By building 'under fit' models, having insufficient flexibility to describe observed occurrence-environment relationships, we risk misunderstanding the factors shaping species distributions. By building 'over fit' models, with excessive flexibility, we risk inadvertently ascribing pattern to noise or building opaque models. However, model selection can be challenging, especially when comparing models constructed under different modeling approaches. Here we argue for a more pragmatic approach: researchers should constrain the complexity of their models based on study objective, attributes of the data, and an understanding of how these interact with the underlying biological processes. We discuss guidelines for balancing under fitting with over fitting and consequently how complexity affects decisions made during model building. Although some generalities are possible, our discussion reflects differences in opinions that favor simpler versus more complex models. We conclude that combining insights from both simple and complex SDM building approaches best advances our knowledge of current and future species ranges.

CD8+ cytotoxic T lymphocyte activation by soluble major histocompatibility complex-peptide dimers.

CD8+ cytotoxic T lymphocyte (CTL) can recognize and kill target cells that express only a few cognate major histocompatibility complex class I-peptide (pMHC) complexes. To better understand the molecular basis of this sensitive recognition process, we studied dimeric pMHC complexes containing linkers of different lengths. Although dimers containing short (10-30-A) linkers efficiently bound to and triggered intracellular calcium mobilization and phosphorylation in cloned CTL, dimers containing long linkers (> or = 80 A) did not. Based on this and on fluorescence resonance energy transfer experiments, we describe a dimeric binding mode in which two T cell receptors engage in an anti-parallel fashion two pMHC complexes facing each other with their constant domains. This binding mode allows integration of diverse low affinity interactions, which increases the overall binding and, hence, the sensitivity of antigen recognition. In proof of this, we demonstrated that pMHC dimers containing one agonist and one null ligand efficiently activate CTL, corroborating the importance of endogenous pMHC complexes in antigen recognition.

Impact of model complexity on cross-temporal transferability in Maxent species distribution models: An assessment using paleobotanical data

Maximum entropy modeling (Maxent) is a widely used algorithm for predicting species distributions across space and time. Properly assessing the uncertainty in such predictions is non-trivial and requires validation with independent datasets. Notably, model complexity (number of model parameters) remains a major concern in relation to overfitting and, hence, transferability of Maxent models. An emerging approach is to validate the cross-temporal transferability of model predictions using paleoecological data. In this study, we assess the effect of model complexity on the performance of Maxent projections across time using two European plant species (Alnus giutinosa (L.) Gaertn. and Corylus avellana L) with an extensive late Quaternary fossil record in Spain as a study case. We fit 110 models with different levels of complexity under present time and tested model performance using AUC (area under the receiver operating characteristic curve) and AlCc (corrected Akaike Information Criterion) through the standard procedure of randomly partitioning current occurrence data. We then compared these results to an independent validation by projecting the models to mid-Holocene (6000 years before present) climatic conditions in Spain to assess their ability to predict fossil pollen presence-absence and abundance. We find that calibrating Maxent models with default settings result in the generation of overly complex models. While model performance increased with model complexity when predicting current distributions, it was higher with intermediate complexity when predicting mid-Holocene distributions. Hence, models of intermediate complexity resulted in the best trade-off to predict species distributions across time. Reliable temporal model transferability is especially relevant for forecasting species distributions under future climate change. Consequently, species-specific model tuning should be used to find the best modeling settings to control for complexity, notably with paleoecological data to independently validate model projections. For cross-temporal projections of species distributions for which paleoecological data is not available, models of intermediate complexity should be selected.

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Probabilistic Independence Networks for Hidden Markov Probability Models

Graphical techniques for modeling the dependencies of randomvariables have been explored in a variety of different areas includingstatistics, statistical physics, artificial intelligence, speech recognition, image processing, and genetics.Formalisms for manipulating these models have been developedrelatively independently in these research communities. In this paper weexplore hidden Markov models (HMMs) and related structures within the general framework of probabilistic independencenetworks (PINs). The paper contains a self-contained review of the basic principles of PINs.It is shown that the well-known forward-backward (F-B) and Viterbialgorithms for HMMs are special cases of more general inference algorithms forarbitrary PINs. Furthermore, the existence of inference and estimationalgorithms for more general graphical models provides a set of analysistools for HMM practitioners who wish to explore a richer class of HMMstructures.Examples of relatively complex models to handle sensorfusion and coarticulationin speech recognitionare introduced and treated within the graphical model framework toillustrate the advantages of the general approach.

The International Urban Energy Balance Models Comparison Project: First Results from Phase 1

A large number of urban surface energy balance models now exist with different assumptions about the important features of the surface and exchange processes that need to be incorporated. To date, no com- parison of these models has been conducted; in contrast, models for natural surfaces have been compared extensively as part of the Project for Intercomparison of Land-surface Parameterization Schemes. Here, the methods and first results from an extensive international comparison of 33 models are presented. The aim of the comparison overall is to understand the complexity required to model energy and water exchanges in urban areas. The degree of complexity included in the models is outlined and impacts on model performance are discussed. During the comparison there have been significant developments in the models with resulting improvements in performance (root-mean-square error falling by up to two-thirds). Evaluation is based on a dataset containing net all-wave radiation, sensible heat, and latent heat flux observations for an industrial area in Vancouver, British Columbia, Canada. The aim of the comparison is twofold: to identify those modeling ap- proaches that minimize the errors in the simulated fluxes of the urban energy balance and to determine the degree of model complexity required for accurate simulations. There is evidence that some classes of models perform better for individual fluxes but no model performs best or worst for all fluxes. In general, the simpler models perform as well as the more complex models based on all statistical measures. Generally the schemes have best overall capability to model net all-wave radiation and least capability to model latent heat flux.

The METAFOR project: preserving data through metadata standards for climate models and simulations

Climate modeling is a complex process, requiring accurate and complete metadata in order to identify, assess and use climate data stored in digital repositories. The preservation of such data is increasingly important given the development of ever-increasingly complex models to predict the effects of global climate change. The EU METAFOR project has developed a Common Information Model (CIM) to describe climate data and the models and modelling environments that produce this data. There is a wide degree of variability between different climate models and modelling groups. To accommodate this, the CIM has been designed to be highly generic and flexible, with extensibility built in. METAFOR describes the climate modelling process simply as "an activity undertaken using software on computers to produce data." This process has been described as separate UML packages (and, ultimately, XML schemas). This fairly generic structure canbe paired with more specific "controlled vocabularies" in order to restrict the range of valid CIM instances. The CIM will aid digital preservation of climate models as it will provide an accepted standard structure for the model metadata. Tools to write and manage CIM instances, and to allow convenient and powerful searches of CIM databases,. Are also under development. Community buy-in of the CIM has been achieved through a continual process of consultation with the climate modelling community, and through the METAFOR team’s development of a questionnaire that will be used to collect the metadata for the Intergovernmental Panel on Climate Change’s (IPCC) Coupled Model Intercomparison Project Phase 5 (CMIP5) model runs.

GIS linked environmental process models

In recent years there has been a great effort to combine the technologies and techniques of GIS and process models. This project examines the issues of linking a standard current generation 2½d GIS with several existing model codes. The focus for the project has been the Shropshire Groundwater Scheme, which is being developed to augment flow in the River Severn during drought periods by pumping water from the Shropshire Aquifer. Previous authors have demonstrated that under certain circumstances pumping could reduce the soil moisture available for crops. This project follows earlier work at Aston in which the effects of drawdown were delineated and quantified through the development of a software package that implemented a technique which brought together the significant spatially varying parameters. This technique is repeated here, but using a standard GIS called GRASS. The GIS proved adequate for the task and the added functionality provided by the general purpose GIS - the data capture, manipulation and visualisation facilities - were of great benefit. The bulk of the project is concerned with examining the issues of the linkage of GIS and environmental process models. To this end a groundwater model (Modflow) and a soil moisture model (SWMS2D) were linked to the GIS and a crop model was implemented within the GIS. A loose-linked approach was adopted and secondary and surrogate data were used wherever possible. The implications of which relate to; justification of a loose-linked versus a closely integrated approach; how, technically, to achieve the linkage; how to reconcile the different data models used by the GIS and the process models; control of the movement of data between models of environmental subsystems, to model the total system; the advantages and disadvantages of using a current generation GIS as a medium for linking environmental process models; generation of input data, including the use of geostatistic, stochastic simulation, remote sensing, regression equations and mapped data; issues of accuracy, uncertainty and simply providing adequate data for the complex models; how such a modelling system fits into an organisational framework.