Affine Model Research Articles

Dynamics of the surface growth resulted from sedimentation of spheres in a Hele–Shaw cell containing a low-viscosity fluid

In this paper, we investigate the dynamics of surface growth resulting from sedimentation of spherical granular particles in a fluid environment, using experiments and simulations. In the experimental part, spherical polystyrene particles are poured down from the top of a vertical Hele–Shaw cell and form a 1 + 1-dimensional growing surface. The surface roughness is obtained from the images, and the growth and roughness exponents are measured. In the numerical simulation part, the surface growth process is simulated using the discrete element method, considering the interactions between the grains, and the exponents are calculated. In this method, unlike conventional simulation models, instead of a discrete deposition law, the dynamics of the individual particles throughout the process are obtained, considering different forces acting on the particles. Finally, the simulation results are compared with the experiment, and we see a very good agreement between them. We find different values for the exponents using different methods, indicating that the system is multi-affine and does not obey the scaling laws of affine models.

The Impact of GCP Chip Distribution on Kompsat-3A RPC Bias Compensation

The vast potential of high-resolution satellite images, including Kompsat-3A, has been demonstrated across diverse applications, such as mapping and disaster monitoring. However, these images can only be utilized as reliable GIS (geographic information system) data when they possess precise geographical information. To achieve this, sensor model information, represented by RPCs (rational polynomial coefficients), requires bias compensation through GCPs (ground control points). Though having a substantial number of well-distributed GCPs across satellite images is ideal, the acquisition process is often restricted due to cost and inaccessibility. The uniform distribution of GCP chips is not guaranteed, necessitating an investigation into the impact of GCP distribution on the bias compensation process, which is the focus of this study. Experiments were meticulously conducted using Kompsat-3A data using dense GCP information. The dense GCP information was automatically generated from aerial orthoimages through a three-step process. Firstly, the GCP chips were extracted from the aerial images, focusing on feature points. Secondly, these chips were projected onto the target Kompsat-3A data to align them accurately. Lastly, precise satellite image coordinates of the chips were obtained through image matching between the chips and the target Kompsat-3A image. The dense GCPs enabled detailed bias analysis that exhibited skewness in most Kompsat-3A data. This necessitates the implementation of an affine model for proper bias compensation over the entire image space. Next, the study delved into the influence of GCP distribution on RPC bias compensation. To this end, each target satellite image space was divided into nine zones, with the dense GCPs assigned accordingly. The accuracy of bias compensation was analyzed across nine experimental cases, ranging from GCPs occupying only one zone to GCPs covering all nine zones. It was observed that GCPs covering at least four or five zones should be utilized for reliable RPC bias compensation of Kompsat-3A, especially when aiming for a high level of accuracy with an RMSE of one pixel. Finally, it was concluded that GCPs covering three zones yielded satisfactory results as a minimum GCP requirement, but this was contingent upon their distribution not following a straight zone pattern.

Prediction of PM2.5 with a piecewise affine model considering spatial-temporal correlation

Over the past several decades, several air pollution prevention measures have been developed in response to the growing concern over air pollution. Using models to anticipate air pollution accurately aids in the timely prevention and management of air pollution. However, the spatial-temporal air quality aspects were not properly taken into account during the prior model construction. In this study, the distance correlation coefficient (DC) between measurements made in various monitoring stations is used to identify appropriate correlated monitoring stations. To derive spatial-temporal correlations for modeling, the causality relationship between measurements made in various monitoring stations is analyzed using Transfer Entropy (TE). This work explores the process of identifying a piecewise affine (PWA) model using a larger dataset and suggests a unique hierarchical clustering-based identification technique with model structure selection. This work improves the BIRCH (Balanced Iterative Reducing and Clustering using Hierarchies) by introducing Kullback-Leibler (KL) Divergence as the dissimilarity between clusters for handling clusters with arbitrary shapes. The number of clusters is automatically determined using a cluster validity metric. The task is formulated as a sparse optimization problem, and the model structure is selected using parameter estimations. Beijing air quality data is used to demonstrate the method, and the results show that the proposed strategy may produce acceptable forecast performance.

A Robust Switching Control Strategy for Three-Phase Voltage Source Converters with Uncertain Circuit Parameters

This study proposes a novel double closed-loop robust control strategy based on a power switching affine model of three-phase voltage source converters (VSCs). The aim is to overcome the challenges posed by inaccurate mathematical models, complex controller configurations, indirect switching control, and performance degradation under circuit parameters uncertainty or load variation in conventional methods. These conventional methods rely on linearization models, duty ratio regulation, and pulse width modulation (PWM) technologies. The contributions of work are the following: (1) A two-dimensional (2D) power switching affine model is constructed without any approximation or averaging. (2) The proposed approach achieves direct switching control of three-phase VSCs, eliminating the need for complex rotation coordinate transformation, PWM, and phase locking loop (PLL), which are utilized in traditional control methods. (3) The rigor of the system stability analysis is enhanced based on the 2D power switching model compared to the existing three-dimensional (3D) current switching model. (4) A simple control structure with only two control parameters is employed to address circuit parameter uncertainties. The effectiveness and superiority of the proposed method is validated through simulation and experimental comparison results.

Kinetics model of crystal nucleation and growth in supercooled water for designing ice-templating soft matter scaffold

Ice-templating technology has recently attracted extensive attention to achieve programed structure-property relationships in porous soft matter scaffolds. However, there is a huge gap existed between theoretical understanding and practical applications of nucleation kinetics and growth of ice crystals in supercooled water. This paper establishes a nucleation kinetics model of crystal growth in supercooled water, for designing ice-templating soft matter scaffolds with programmable structure-property relationship. A phase transition model was firstly formulated to characterize liquid-liquid phase transition of supercooled water, based on a two-state model and free-volume theory. Effects of diffusion coefficient and density of the supercooled water on ice nucleation kinetics and crystal growth were investigated, based on the classic nucleation theory. Analytical results showed excellent agreement with experimental data, with correlation indices of R2=90.7 % for diffusion coefficients and R2=94.0 % for densities, respectively. The model predicted a nucleation rate of 31.7 m−3∙s−1 at 200 K and peak nucleation rate and crystal growth rates appearing at 183 K and 227 K. Constitutive relationships among mechanical behaviors, ice nucleus radius, nucleation ratio, and crystallization growth rate, were developed for the ice-templating scaffolds, based on the affine model theory and verified with finite element analysis results (R2= 99.9 %) and experimental results (R2 = 95.8 %). Finally, the prediction results using the proposed model were further verified using the experimental data reported in the literature. This study provides a new methodology to describe the nucleation kinetics and growth of ice crystals in supercooled water and programmable structure-property relationships in ice-templating soft matter scaffolds.

An affine term structure model with Fed chairs’ speeches

I analyze the impact of the sentiment expressed in speeches by Fed chairs on Treasury bond yields, using an affine term structure model. The speeches by Fed chairs are numerically evaluated to generate three sentiment factors: negative, neutral, and positive. The variance decomposition analysis indicates that sentiment factors account for a considerable portion of the variance in yield forecasts.

Option valuation via nonaffine dynamics with realized volatility

This paper evaluates the improvement in option pricing brought about by realized volatility (RV) through nonaffine dynamics as advocated by Christoffersen et al. (2014). We complement their studies by developing a closed-form approximation of option pricing for the nonaffine models with RV, and then study the trade-off between the degradation in data fitting and the computational convenience offered by the analytical formula. Our studies confirm the literature that the nonaffine dynamics consistently outperform the affine in option pricing. In particular, we find that RV can significantly improve return fitting and option pricing through both affine and nonaffine models. For the affine models, we find strong evidence in favor of the RV information for both returns and options; for the nonaffine models, the evidence is less convincing for option pricing. We also provide additional new evidence that RV and nonaffine structures are equally competent at improving option pricing; moreover, these two features are complements rather than substitutes for GARCH option pricing, and the importance of one feature for option pricing is further enhanced when the other is present. All of these results are robust across moneyness, maturity, and volatility levels, and point to the necessity of including RV in nonaffine option pricing models.

Complex affine arithmetic based uncertain sensitivity analysis of voltage fluctuations in active distribution networks

The uncertainties of distribution generations (DGs) and loads lead to severe voltage fluctuations in active distribution networks (ADNs). Meanwhile, energy storage systems (ESSs) and static var compensators (SVCs) can mitigate the uncertainties of power injections by regulating the active and reactive power. Considering the variations of multiple uncertain factors, this paper proposes a complex affine arithmetic (CAA) based uncertain sensitivity analysis method of voltage fluctuations in ADNs. First, affine models of active and reactive power injections are established. The correlations of noisy symbols are used to reflect the mitigation effects of ESSs and SVCs on the uncertainties introduced by DGs and loads. Next, sensitivity indicators of voltage fluctuations are defined based on the transitivity of noisy symbols. Then, a calculation method for sensitivity indicators based on the micro-increments of coefficients is proposed. Combined with the obtained indicators, a fast sensitivity method for calculating interval values of voltages is further proposed. The modified IEEE 33-bus system is tested to validate the accuracy and efficiency of the proposed method by comparison with the continuous utilization of power flow method. Moreover, the 292-bus system is tested to validate its applicability in a large distribution system. Facts have proved that this method improves the efficiency and reliability of calculations, and in different scenarios, it can achieve fast calculation of nodes and online analysis of the voltage fluctuation range in uncertain environments, provides an effective tool for voltage quality management in active distribution networks.

Conjugation-Based Approach to the ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\varepsilon $\\end{document}-Subdifferential of Convex Suprema

We provide new characterizations of the ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\varepsilon $\\end{document}-subdifferential of the supremum of an arbitrary family of convex functions. The resulting formulas only involve approximate subdifferentials of adequate convex combinations of the data functions. Families of convex functions with a concavity-like property are introduced and their relationship with affine models is studied. The role of the lower semi-continuity of the data functions is also analyzed.

Target-specific novel molecules with their recipe: Incorporating synthesizability in the design process

Application of Artificial intelligence (AI) in drug discovery has led to several success stories in recent times. While traditional methods mostly relied upon screening large chemical libraries for early-stage drug-design, de novo design can help identify novel target-specific molecules by sampling from a much larger chemical space. Although this has increased the possibility of finding diverse and novel molecules from previously unexplored chemical space, this has also posed a great challenge for medicinal chemists to synthesize at least some of the de novo designed novel molecules for experimental validation. To address this challenge, in this work, we propose a novel forward synthesis-based generative AI method, which is used to explore the synthesizable chemical space. The method uses a structure-based drug design framework, where the target protein structure and a target-specific seed fragment from co-crystal structures can be the initial inputs. A random fragment from a purchasable fragment library can also be the input if a target-specific fragment is unavailable. Then a template-based forward synthesis route prediction and molecule generation is performed in parallel using the Monte Carlo Tree Search (MCTS) method where, the subsequent fragments for molecule growth can again be obtained from a purchasable fragment library. The rewards for each iteration of MCTS are computed using a drug-target affinity (DTA) model based on the docking pose of the generated reaction intermediates at the binding site of the target protein of interest. With the help of the proposed method, it is now possible to overcome one of the major obstacles posed to the AI-based drug design approaches through the ability of the method to design novel target-specific synthesizable molecules.

A static replication approach for callable interest rate derivatives: mathematical foundations and efficient estimation of SIMM–MVA

The computation of credit risk measures such as exposure and Credit Value Adjustments (CVA) requires the simulation of future portfolio prices. Recent metrics, such as dynamic Initial Margin (IM) and Margin Value Adjustments (MVA) additionally require the simulation of future conditional sensitivities. For portfolios with non-linear instruments that do not admit closed-form valuation formulas, this poses a significant computational challenge. This problem is addressed by proposing a static replication algorithm for interest rate options with early-exercise features under an affine term-structure model. Under the appropriate conditions, we can find an equivalent portfolio of vanilla options that replicate these products. Specifically, we decompose the product into a portfolio of European swaptions. The weights and strikes of the portfolio are obtained by regressing the target option value with interpretable, feed-forward neural networks. Once an equivalent portfolio of European swaptions is determined, we can leverage on closed-form expressions to obtain the conditional prices and sensitivities, which serve as an input to exposure and SIMM-driven MVA quantification. For a consistent forward sensitivity estimation, this involves the differentiation of the portfolio-weights. The accuracy and convergence of the method is demonstrated through several representative numerical examples, benchmarked against the established least-square Monte Carlo method.

Drug-target Affinity Prediction by Molecule Secondary Structure Representation Network.

Identification of drug-target interactions (DTI) is a crucial step in drug development with high specificity and low toxicity. To accelerate the process, computer-aided DTI prediction algorithms have been used to screen compounds or targets rapidly. Furthermore, DTI prediction can be used to identify potential targets for existing drugs, thus uncovering new indications and repositioning them. Therefore, it is of great importance to develop efficient and accurate DTI prediction algorithms. Current algorithms usually represent drugs as extracted features, which are learned by convolutional neural networks (CNNs) from its linear representation, or utilize graph neural networks (GNNs) to learn its graph representation. However, these methods either lose information or fail to capture the structural information of the drug. To address this issue, a novel molecule secondary structure representation network (MSSRN) is proposed to learn drug characterization more accurately. Firstly, the network performs relational graph convolutional networks (R-GCNs) on the drug's molecular graph and integrates drug sequence convolutions to learn the sequential information. Secondly, inspired by the attention mechanism, spatial importance weights of the drug sequence are calculated to guide R-GCNs to learn the topological information of the drug. A drug-target affinity model, called MSSRN-DTA, was then constructed by using MSSRN to learn drug structure and CNN to learn protein sequence. The effectiveness of the proposed method is verified by comparing it with other alternative methods and baseline models on two benchmark datasets.

Piecewise non-linear model predictive control with bounded disturbance

This work addresses the problem of robust [Formula: see text] model predictive control for constrained piecewise non-linear systems corrupted by norm-bounded disturbances for the first time. In this approach, the system can have different operating points with different subregions. In each subregion, the system is made up of an affine model disturbed by an additive non-linear term that is locally Lipschitz. The employment of the piecewise non-linear model leads to a non-convex optimization problem, which is far more difficult to solve. It is also much more challenging to develop the [Formula: see text] model predictive control for piecewise non-linear systems. The proposed method introduces a control strategy in the form of a convex optimization problem subject to linear matrix inequality constraints, with the ability to minimize the L2 gain between the disturbance input and the controlled output. The proposed controller guarantees system stability with a prescribed [Formula: see text] disturbance attenuation level under switching between subregions. Simulations on a highly non-linear chemical process are conducted to demonstrate the efficacy of the proposed approach.

Deformable 3D/3D CT-to-digital-tomosynthesis image registration in image-guided bronchoscopy interventions

Traditional navigational bronchoscopy procedures rely on preprocedural computed tomography (CT) and intraoperative chest radiography and cone-beam CT (CBCT) to biopsy peripheral lung lesions. This navigational approach is challenging due to the projective nature of radiography, and the high radiation dose, long imaging time, and large footprints of CBCT. Digital tomosynthesis (DTS) is considered an attractive alternative combining the advantages of radiography and CBCT. Only the depth resolution cannot match a full CBCT image due to the limited angle acquisition. To address this issue, preoperative CT is a good auxiliary in guiding bronchoscopy interventions. Nevertheless, CT-to-body divergence caused by anatomic changes and respiratory motion, hinders the effective use of CT imaging. To mitigate CT-to-body divergence, we propose a novel deformable 3D/3D CT-to-DTS registration algorithm employing a multistage, multiresolution approach and using affine and elastic B-spline transformation models with bone and lung mask images. A multiresolution strategy with a Gaussian image pyramid and a multigrid strategy within the B-spline model are applied. The normalized correlation coefficient is included in the cost function for the affine model and a multimetric weighted cost function is used for the B-spline model, with weights determined heuristically. Tested on simulated and real patient bronchoscopy data, the algorithm yields promising results. Assessed qualitatively by visual inspection and quantitatively by computing the Dice coefficient (DC) and the average symmetric surface distance (ASSD), the algorithm achieves mean DC of 0.82±0.05 and 0.74±0.05, and mean ASSD of 0.65±0.29mm and 0.93±0.43mm for simulated and real data, respectively. This algorithm lays the groundwork for CT-aided intraoperative DTS imaging in image-guided bronchoscopy interventions with future studies focusing on automated metric weight setting.

Neural Network Based Adaptive Inverse Optimal Control for Non-Affine Nonlinear Systems

In this paper, a novel methodology is introduced for the inverse optimal control of non-affine, nonlinear and discrete-time systems. Although inverse optimal control of affine systems is studied in detail in technical literature, there is no adequate research about its implementation on non-affine systems. here are two main contributions of this work. Firstly using the input–output data of the system to be controlled its NARMA-L2 model is obtained using a multi-layer feedforward neural network, this step provides a conversion from a non-affine to affine system model. After the affine system model is obtained, the inverse optimal control law is applied. The second contribution of this paper is the computation of the inverse optimal control signal. The selection of the P matrix in the control law is crucial since its value directly affects the control performance. Here a novel method is proposed where an adaptive and optimal P matrix is computed online using a recurrent neural network to minimize a predefined cost function. The performance of the proposed control method is evaluated by simulations performed on benchmark problems. The robustness of the method is also tested by additional simulations where noise and disturbance is imposed on the system. The obtained results justify the applicability of the proposed approach.

Population affinity estimation using pelvic measurements based on computed tomographic data acquired from Japanese and Western Australian populations

The present study analyzes morphological differences in the pelvis of Japanese and Western Australian individuals and investigates the feasibility of population affinity classification based on computed tomography (CT) data. The Japanese and Western Australian samples comprise CT scans of 207 (103 females; 104 males) and 158 (78 females; 80 males) adult individuals, respectively. Following volumetric reconstruction, a total of 19 pelvic landmarks were obtained on each sample, and 11 measurements, including two angles, were calculated. Machine learning methods (random forest modeling [RFM] and support vector machine [SVM]) were used to classify population affinity. Classification accuracy of the two-way models was approximately 80% for RFM: the two-way sex-specific and sex-mixed models for SVM achieved > 90% and > 85%, respectively. The sex-specific models had higher accurate classification rates than the sex-mixed models, except for the Japanese male sample. The classification accuracy of the four-way sex and population affinity model had an overall classification accuracy of 76.71% for RFM and 87.67% for SVM. All the correct classification rates were higher in the Japanese relative to the Western Australian sample. Our data suggest that pelvic morphology is sufficiently distinct between Japanese and Western Australian individuals to facilitate the accurate classification of population affinity based on measurements acquired in CT images. To the best of our knowledge, this is the first study investigating the feasibility of population affinity estimation based on CT images of the pelvis, which appears as a viable supplement to traditional approaches based on cranio-facial morphology.

Efficient Identification of Error-in-Variables Switched Systems Using a Riemannian Embedding

This paper considers the problem of error in variables identification for switched affine models. Since it is well known that this problem is generically NP hard, several relaxations have been proposed in the literature. However, while these approaches work well for low dimensional systems with few subsystems, they scale poorly with both the number of subsystems and their memory. To address this difficulty, we propose a computationally efficient alternative, based on embedding the data in the manifold of positive semidefinite matrices, and using a manifold metric there to perform the identification. Our main result shows that, under dwell-time assumptions, the proposed algorithm is convergent, in the sense that it is guaranteed to identify the system for suitably low noise. In scenarios with larger noise levels, we provide experimental results showing that the proposed method outperforms existing ones. The paper concludes by illustrating these results with academic examples and a non-trivial application: action video segmentation.

Improved modeling of RNA-binding protein motifs in an interpretable neural model of RNA splicing

Sequence-specific RNA-binding proteins (RBPs) play central roles in splicing decisions. Here, we describe a modular splicing architecture that leverages in vitro-derived RNA affinity models for 79 human RBPs and the annotated human genome to produce improved models of RBP binding and activity. Binding and activity are modeled by separate Motif and Aggregator components that can be mixed and matched, enforcing sparsity to improve interpretability. Training a new Adjusted Motif (AM) architecture on the splicing task not only yields better splicing predictions but also improves prediction of RBP-binding sites in vivo and of splicing activity, assessed using independent data.

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real-time and many-query evaluations of parametric Partial Differential Equations (PDEs). Linear techniques such as Proper Orthogonal Decomposition (POD) and Greedy algorithms have been analyzed thoroughly, but they are more suitable when dealing with linear and affine models showing a fast decay of the Kolmogorov n-width. On one hand, the autoencoder architecture represents a nonlinear generalization of the POD compression procedure, allowing one to encode the main information in a latent set of variables while extracting their main features. On the other hand, Graph Neural Networks (GNNs) constitute a natural framework for studying PDE solutions defined on unstructured meshes. Here, we develop a non-intrusive and data-driven nonlinear reduction approach, exploiting GNNs to encode the reduced manifold and enable fast evaluations of parametrized PDEs. We show the capabilities of the methodology for several models: linear/nonlinear and scalar/vector problems with fast/slow decay in the physically and geometrically parametrized setting. The main properties of our approach consist of (i) high generalizability in the low-data regime even for complex behaviors, (ii) physical compliance with general unstructured grids, and (iii) exploitation of pooling and un-pooling operations to learn from scattered data.

Modeling methyl-sensitive transcription factor motifs with an expanded epigenetic alphabet

BackgroundTranscription factors bind DNA in specific sequence contexts. In addition to distinguishing one nucleobase from another, some transcription factors can distinguish between unmodified and modified bases. Current models of transcription factor binding tend not to take DNA modifications into account, while the recent few that do often have limitations. This makes a comprehensive and accurate profiling of transcription factor affinities difficult.ResultsHere, we develop methods to identify transcription factor binding sites in modified DNA. Our models expand the standard A/C/G/T DNA alphabet to include cytosine modifications. We develop Cytomod to create modified genomic sequences and we also enhance the MEME Suite, adding the capacity to handle custom alphabets. We adapt the well-established position weight matrix (PWM) model of transcription factor binding affinity to this expanded DNA alphabet. Using these methods, we identify modification-sensitive transcription factor binding motifs. We confirm established binding preferences, such as the preference of ZFP57 and C/EBPβ for methylated motifs and the preference of c-Myc for unmethylated E-box motifs.ConclusionsUsing known binding preferences to tune model parameters, we discover novel modified motifs for a wide array of transcription factors. Finally, we validate our binding preference predictions for OCT4 using cleavage under targets and release using nuclease (CUT&RUN) experiments across conventional, methylation-, and hydroxymethylation-enriched sequences. Our approach readily extends to other DNA modifications. As more genome-wide single-base resolution modification data becomes available, we expect that our method will yield insights into altered transcription factor binding affinities across many different modifications.