Reformulation Of Models Research Articles

New robust approach for the globally optimal design of fired heaters

Fired heaters are important components of heat exchanger network (HEN) synthesis, especially in view of the existing procedures to simultaneously synthesize the HEN and obtain the basic design of heat exchangers. Existing basic design procedures for fired-heaters are either too simple, or difficult to solve when based on MINLP procedures. In addition, CFD approaches can hardly be used in design optimization and metaheuristics do not guarantee global optimality. We present two novel advances: a reformulation of models from previous optimization literature and we use Partial and Proxy Set Trimming followed by Smart Enumeration, a recently introduced robust technique. The proposed approach does neither needs initial solutions, nor does it have convergence problems and it also guarantees global optimality. The Set Trimming variant, namely Proxy Set Trimming, which was not part of the original Set Trimming version of Set Trimming is also used.

A Single-Variable Zigzag Approach to Model Imperfect Interfaces in Layered Beams

The flexibility of the bonds between the adjacent layers of multi-layered systems and their degradation or the presence of delaminations strongly affect mechanical response and final collapse. The formulation of accurate and efficient models able to capture the complex local distributions of stresses and displacements, which arise due to the layered structure and imperfect bonding, is of great importance for the design and verification of the systems. In this paper a novel and effective “single-variable zigzag” theory is formulated to analyze beams with homogeneous layers made of the same material and imperfect interfaces, which allow sliding between the layers. The primal variable is a fictitious bending displacement, which is derived in order to define all other kinematic and static quantities in terms of it. The “zigzag” technique describes multilayer systems with imperfect interfaces as equivalent single-layers, so that the problem is governed by equations similar to those of the classical theories for homogeneous beams; the “single-variable” formulation facilitates the implementation into numerical schemes and eliminates well-known numerical problems. Explicit solutions are straightforwardly derived for simply supported beams subjected to uniform and sinusoidal transverse loads. The results for some exemplary structural elements confirm the accuracy and efficiency of the approach. The study is preliminary to the single-variable reformulation and numerical implementation of the zigzag models for laminates with elastic mismatch between the layers.

A complementarity‐based vapor‐liquid equilibrium formulation for equation‐oriented simulation and optimization

AbstractVapor‐liquid equilibrium (VLE) is a cornerstone of computer‐aided process engineering (CAPE). Embedded within process system models, VLE calculations are inherently procedural with non‐smooth behavior that frequently requires discrete decisions. Traditionally, these features resist the incorporation of VLE within efficient, large‐scale equation‐oriented (EO) process simulation and optimization strategies. On the other hand, recent reformulation of VLE models through the incorporation of complementarity constraints has broadened its scope to deal seamlessly with phase transitions and even supercritical excursions in process simulation and optimization. In this study, we extend these VLE complementarity models to EO frameworks where procedural thermodynamic property libraries are still required. Here we develop an efficient, non‐intrusive, and intuitive “square‐flash” equation system that has been implemented within the IDAES Integrated Platform (IDAES‐IP). The effectiveness of this modular approach is demonstrated on case studies for non‐ideal flash calculations and distillation optimization, with disappearing phases and supercritical transitions.

Nonlinear programming reformulation of dynamic flux balance analysis models

Dynamic flux balance analysis (dFBA) models are very popular in systems biology because of the many possible applications. dFBA consists of dynamic mass balance equations that describe the concentration of external metabolites and an optimization model to compute the internal flux distribution of the cell. Here, we applied a nonlinear programming formulation for solving dFBA models. The ODE system is discretized using the orthogonal collocation technique and the optimization problem is replaced by its first-order optimality conditions. In addition, an adaptive mesh scheme is applied to improve performance by efficiently handling changes in the active set of constraints. This formulation ensures total differentiability of the model, which can be solved by large-scale solvers and take advantage of automatic differentiation packages. The new approach presents results equivalent to state-of-the-art methods and outperforms them in dynamic optimization problems by avoiding calling an external solver to handle the embedded optimization model.

One-matrix differential reformulation of two-matrix models

Differential reformulations of field theories are often used for explicit computations. We derive a one-matrix differential formulation of two-matrix models, with the help of which it is possible to diagonalize the one- and two-matrix models using a formula by Itzykson and Zuber that allows diagonalizing differential operators with respect to matrix elements of Hermitian matrices. We detail the equivalence between the expressions obtained by diagonalizing the partition function in differential or integral formulation, which is not manifest at first glance. For one-matrix models, this requires transforming certain derivatives to variables. In the case of two-matrix models, the same computation leads to a new determinant formulation of the partition function, and we discuss potential applications to new orthogonal polynomials methods.

LFT-Based Identification of Lateral Vehicle Dynamics

This paper presents a novel estimation and identification approach for lateral vehicle dynamics. The algorithm leverages on a Linear Fraction Transform (LFT) reformulation of vehicle and tyre models, allowing for a simple and computationally efficient inclusion of complex and nonlinear dynamic models, like, for example, two-wheels, four-wheels or single-track as vehicle model, and Pacejka, brush or Fiala as tyre model. As a result, this technique can be easily adopted in the development of an online identification system, able to run on a standard embedded device, implementing a flexible identification procedure that can handle different driving conditions, up to the limits of handling, different vehicle modelling approaches, and different input measurements. Experimental results demonstrate the effectiveness of the proposal, either in a persistent excitation and in a non-persistent excitation scenario.

A Structural Framework for Neuro-Linguistic Programming (NLP) and its Consequence on Leadership Succession Planning Strategy Applying to the Leaders of King Khalid University and Qualified Personnel for Leadership Position

The research paper pursues to know the effect of NLP practices on leadership succession planning strategy by applying to The Leaders of King Khalid University and Qualified Personnel for the Leadership position. After reviewing the literature, the researchers formulated a hypothetical model for the study that includes the central hypothesis from which six sub-hypotheses emerge, including measuring the impact of NLP pillars on leadership succession planning strategy. A sample size of 100 individuals was selected, representing the research population represented by the deans and deans of the university and colleges and heads of departments in colleges at King Khalid University in Saudi Arabia. The response rate was 82%, with 82 valid questionnaires for analysis. The study relied on Structural Equation Modeling (SEM) by AMOS (V.26) and SPSS (V.25) for data analysis and hypotheses. The study found a positive and significant effect between NLP and leadership succession planning strategy. NLP confirmed its re-formulation of standard mental models to understand and facilitate the process of thinking and training, which helps successive leaders understand the ideas and beliefs of current leaders and their ways of thinking in solving problems and facing crises. In addition, NLP plays a vital role in increasing the successive leader’s sense of the need to establish their reputation for outstanding performance after similarity and learning from the model. Finally, the novice leader needs a model and role model to help him control the way he feels, transforming it into positive thinking that stimulates energy and focuses on goals, which the application of NLP practices does. So, this study is recommended the necessity of activating leadership succession planning strategy within universities through establishing a leadership academy in which NLP methods are practiced, as this academy has a significant impact on achieving leadership succession and the continuation of pipelines of leaders.

Efficient and low memory strain-rate independent return mapping algorithm for general yield surfaces and stress states

Structural theories often consider constraints on the stresses, creating a partition into active and fixed components. Sophisticated nonlinear material models are usually described in 3D-continuum form. A reformulation of the material models is then necessary in order to enforce the constraint on the relevant stress components. In this paper, a new strain-rate independent return mapping algorithm is developed in order to deal with arbitrary partitions of the stresses considering general associative elasto-plastic material models. The developed algorithm works directly with the active stress and strain components, satisfying the constraints on the relevant stresses components at each integration point of each element and yielding optimal computational efficiency and memory costs. The tangent operator is obtain in closed-form, providing quadratic convergence to the local iterative process. A comparison of the proposed approach to a previously developed algorithm is made to highlight its properties.

Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise term to the Schrödinger equation, and extract definite measurement outcomes either from the wave function (e.g. mass density ontology) or the noise itself (flash ontology). Bohmian mechanics keeps the Schrödinger equation intact but uses the wave function to guide particles (or fields), which comprise the primitive ontology. Collapse models modify the predictions of orthodox quantum mechanics, whilst Bohmian mechanics can be argued to reproduce them. However, it turns out that collapse models and their primitive ontology can be exactly recast as Bohmian theories. More precisely, considering (i) a system described by a non-Markovian collapse model, and (ii) an extended system where a carefully tailored bath is added and described by Bohmian mechanics, the stochastic wave-function of the collapse model is exactly the wave-function of the original system conditioned on the Bohmian hidden variables of the bath. Further, the noise driving the collapse model is a linear functional of the Bohmian variables. The randomness that seems progressively revealed in the collapse models lies entirely in the initial conditions in the Bohmian-like theory. Our construction of the appropriate bath is not trivial and exploits an old result from the theory of open quantum systems. This reformulation of collapse models as Bohmian theories brings to the fore the question of whether there exists `unromantic' realist interpretations of quantum theory that cannot ultimately be rewritten this way, with some guiding law. It also points to important foundational differences between `true' (Markovian) collapse models and non-Markovian models.

A numerical method for linear Volterra integral equations on infinite intervals and its application to the resolution of metastatic tumor growth models

A Nyström method for linear second kind Volterra integral equations on unbounded intervals, with sufficiently smooth kernels, is described. The procedure is based on the use of a truncated Lagrange interpolation process and of a truncated Gaussian quadrature formula. The stability and the convergence of the method in suitable weighted spaces of functions are studied and some numerical examples showing its reliability are presented. In particular, the proposed method has been tested for the numerical resolution of some Volterra integral equations arising from the reformulation of differential models describing metastatic tumor growth whose unknown solutions represent biological observables as the metastatic mass or the number of metastases.

Bayesian estimation of multidimensional polytomous item response theory models with Q-matrices using Stan

The Q-matrix is commonly used in diagnostic classification models and has recently been incorporated into the multidimensional item response theory (MIRT) models to add information about the relationship between items and dimensions of the latent trait. The reformulation of the MIRT models with Q-matrix (MIRT-Q) has presented to improve the precision of the parameters of these models and to provide a simple and intuitive method for users to define the item-trait relationship. This paper aims to explore the incorporation of the Q-matrix in the formulation of MIRT models for polytomous item responses. Specifically, we introduce the incorporation of the Q-matrix into two of the polytomous MIRT models most known and used: the multidimensional graded response (MGR) model, hereinafter called MGR-Q, and the multidimensional generalized partial credit (MGPC) model, hereinafter called MGPC-Q. We provide readers the code of the MGR-Q and MGPC-Q models in Stan, a Bayesian estimation software, and we conduct a simulation study in order to evaluate the parameter recovery of the estimation method. To illustrate the use of both models in practice, we fit them to an operational dataset from 2400 individuals on 13 items and demonstrate the estimation of MGR-Q and MGPC-Q using the Stan program.

Empirical determination of the covariance of forecast errors: An empirical justification and reformulation of hybrid covariance models

AbstractDuring the last decade, the replacement of static climatological forecast error covariance models with hybrid error covariance models that linearly combine localised ensemble covariances with static climatological error covariances has led to significant forecast improvements at several major forecasting centres. Here, a deeper understanding of why the hybrid's superficially ad hoc mix of ensemble‐based and climatological covariances yields such significant improvements is pursued. In practice, ensemble covariances are not equal to the true flow‐dependent forecast error covariance matrix. Here, the relationship between actual forecast error covariance and the corresponding ensemble covariance is empirically demonstrated. Using a simplified global circulation model and the local ensemble transform Kalman filter (LETKF), the covariance of the set of actual forecast errors corresponding to ensemble covariances close to a fixed target value is computed. By doing this for differing target values, an estimate of the actual forecast error covariance as a function of ensemble covariance is obtained. A demonstration that the hybrid is a much better approximation to this estimate than either the static climatological covariance or the localised ensemble covariance is given. The empirical estimate has two features that current hybrid error covariance models fail to represent: (i) The weight given to the static covariance matrix is an increasing function of the horizontal separation distance of the covarying model variables, and (ii) for small ensemble sizes and ensemble covariances near zero but negative, the actual forecast error covariance is a decreasing function of increasing ensemble covariance. While the first finding has been anticipated by other authors, the second finding has not been anticipated, as far as the authors are aware. Here, (ii) is hypothesised to be a consequence of spurious sample correlations and variances associated with reduced ensembles. Consistent with this hypothesis, the non‐monotonicity of this relationship is almost eliminated by quadrupling the ensemble size.

On the unification of the graph edit distance and graph matching problems

Error-tolerant graph matching gathers an important family of problems. These problems aim at finding correspondences between two graphs while integrating an error model. In the Graph Edit Distance (GED) problem, the insertion/deletion of edges/nodes from one graph to another is explicitly expressed by the error model. At the opposite, the problem commonly referred to as “graph matching” does not explicitly express such operations. For decades, these two problems have split the research community in two separated parts. It resulted in the design of different solvers for the two problems. In this paper, we propose a unification of both problems thanks to a single model. We give the proof that the two problems are equivalent under a reformulation of the error models. This unification makes possible the use on both problems of existing solving methods from the two communities.

Toward a Relational Approach? Common Models of Pious Women's Agency and Pious Feminist Autonomy in Turkey

AbstractThis article reviews the common models of pious women's agency in the literature with respect to pious feminist perceptions in Turkey, and calls for a relational approach to subjectivity and autonomy. After critically assessing individualistic models of pious women's autonomy as well as the main theoretical tenets of Saba Mahmood's landmark study on the women's piety movement in Egypt, I argue that previous models cannot fully explain the second stage of pious subjectivity-formation in the pious feminist narratives in Turkey, which combines habituation with informed choice. In the intersection of applied theory and ethnographic empirical research, my study posits the need for a relational reformulation of these common models that can account for (1) self-constitutive engagement with multiple discursive traditions, and (2) the importance of complex and interrelated webs of relationships. I suggest that Jennifer Nedelsky's relational self and relational autonomy and Kenneth Gergen's relational multi-being might provide a starting point for such an approach.

Appearance model update based on online learning and soft‐biometrics traits for people re‐identification in multi‐camera environments

Intelligent surveillance systems in multi-camera environments pose a hard-open problem for computer vision. The way the people look changes inside and also among cameras, so people re-identification task can be largely improved collecting data about people already identified and take advantage of it as time advances in surveillance video. Furthermore, a camera change or a slight change in the objective traits may require the complete re-formulation of the appearance models. In this paper, we propose several heuristics for updating the appearance model in a multi-camera surveillance environment. Through these heuristics, the subject's appearance model is updated across different time and environmental conditions. The update process is carried out primarily in three different aspects: 1) based on time lapses, 2) based on the change of camera, and 3) based on the automatic selection of the most representative samples selected through decision functions of the classifier. The proposed system focuses on video surveillance environments, that is, the objective is to identify an individual across the set of cameras in the surveillance area, the comparison considers only those people that share time and space. We used four public benchmarks to test our claims; the results confirm the importance of continuous appearance model's updating.

Immunoglobulin G structure and rheumatoid factor epitopes.

Antibodies are important for immunity and exist in several classes (IgM, IgD, IgA, IgG, IgE). They are composed of symmetric dimeric molecules with two antigen binding regions (Fab) and a constant part (Fc), usually depicted as Y-shaped molecules. Rheumatoid factors found in patients with rheumatoid arthritis are autoantibodies binding to IgG and paradoxically appear to circulate in blood alongside with their antigen (IgG) without reacting with it. Here, it is shown that rheumatoid factors do not react with native IgG in solution, and that their epitopes only become accessible upon certain physico-chemical treatments (e.g. heat treatment at 57 °C), by physical adsorption on a hydrophobic surface or by antigen binding. Moreover, chemical cross-linking in combination with mass spectrometry showed that the native state of IgG is a compact (closed) form and that the Fab parts of IgG shield the Fc region and thereby control access of rheumatoid factors and presumably also some effector functions. It can be inferred that antibody binding to pathogen surfaces induces a conformational change, which exposes the Fc part with its effector sites and rheumatoid factor epitopes. This has strong implications for understanding antibody structure and physiology and necessitates a conceptual reformulation of IgG models.

Reducing the complexity of mathematical models for the plant circadian clock by distributed delays

A major bottleneck in the modelling of biological networks is the parameter explosion problem – the exponential increase in the number of parameters that need to be optimised to data as the size of the model increases. Here, we address this problem in the context of the plant circadian clock by applying the method of distributed delays. We show that using this approach, the system architecture can be simplified efficiently – reducing the number of parameters – whilst still preserving the core mechanistic dynamics of the gene regulatory network. Compared to models with discrete time-delays, which are governed by functional differential equations, the distributed delay models can be converted into sets of equivalent ordinary differential equations, enabling the use of standard methods for numerical integration, and for stability and bifurcation analyses. We demonstrate the efficiency of our modelling approach by applying it to three exemplar mathematical models of the Arabidopsis circadian clock of varying complexity, obtaining significant reductions in complexity in each case. Moreover, we revise one of the most up-to-date Arabidopsis models, updating the regulation of the PRR9 and PRR7 genes by LHY in accordance with recent experimental data. The revised model more accurately reproduces the LHY-induction experiments of core clock genes, compared with the original model. Our work thus shows that the method of distributed delays facilitates the optimisation and reformulation of genetic network models.

An improved methodology to evaluate crop salt tolerance from field trials

The salt tolerance of crops is commonly expressed in descriptive parameters such as threshold or 50%-yield soil salinity and shape parameters describing the yield curve. Estimation by visual or simplified ordinary least squares (OLS) regression methods has multiple issues: parameter bias due to uncertainty in soil salinity, lack of independent estimates of the reference yield, questionable robustness of the threshold parameter and missing information about uncertainty and correlation of the parameter estimates. Here, we present a comprehensive OLS method together with an analysis of its statistical properties to alleviate and overcome such issues, on the basis of a numerical experiment that mimics observed yield responses to saline groundwater across a range of salinities in the experimental test facility Salt Farm Texel.The results indicate under which experimental conditions bias is not a major problem. The method allows estimation of the zero-observed-effect yield from the data, which is relevant to agricultural practice. Estimates for zero-observed-effect yield and threshold ECe are negatively correlated, underlining the difficulty of obtaining reliable threshold values. The estimated confidence regions are reliable and robust against soil salinity uncertainty, but large observation error jeopardizes the confidence intervals, especially for the slope parameter. Data uncertainty alone can be responsible for substantial differences from experiment to experiment, providing a partial explanation for the wide variety in reported parameters in the literature, and stressing the need for long-term repetitions.Given the lack of robustness of the threshold parameter, we propose to adopt the 90%-yield EC (ECe90) as tolerance parameter. Its confidence bounds can be obtained from a simple reformulation of the original models. We also present uncertainty ellipses as a suitable tool to unite multiple-year estimates. The method is offered as a solid and generic basis for reliable assessment of the cultivation potential of varieties and crops on salt-affected soils.

Recent advances in and future challenges for mesoscopic hydrodynamic modelling of complex wetting

We highlight some recent developments that widen the scope and reach of mesoscopic thin-film (or long-wave) hydrodynamic models employed to describe the dynamics of thin films, drops and contact lines of simple and complex liquids on solid substrates. The basis of the discussed developments is the reformulation of various mesoscopic thin-film hydrodynamic models as gradient dynamics on underlying energy functionals. After briefly presenting the general approach, the following sections discuss how to improve these models by amending the energy functional and the mobility function, how to obtain gradient dynamics models for some complex liquids, and how to incorporate processes beyond relaxational dynamics.

Reformulation of Network Data Envelopment Analysis models using a common modelling framework

Abstract Network Data Envelopment Analysis (network DEA) is an extension of the conventional Data Envelopment Analysis (DEA) developed to take into account the internal structure of the Decision Making Units (DMUs). In network DEA, the DMU is considered as a network of interconnected sub-processes, where the connections indicate the flow of the intermediate measures. In this paper, we reformulate some of the basic network DEA methodologies in a common modelling framework. We show that the leader-follower approach, the multiplicative and the additive decomposition methods as well as the recently introduced min-max method and the “weak-link” approach, can all be modelled in a multi-objective programming framework, differentiating only in the definition of the overall system efficiency and the solution procedure adopted. Such a common modelling framework makes the direct comparison of the different methodologies possible and enables us to spot and underline their similarities and dissimilarities effectively. We illustrate graphically how the aforementioned methodologies locate their optimal efficiency scores on the Pareto front in the objective functions space, with an example taken from the literature.