Problem Domain Research Articles

Parallelizing process model integration for model predictive control through oracle design and analysis for a Grover’s algorithm-inspired optimization strategy

In model predictive control (MPC), a process dynamic model is utilized to make predictions of the value of the objective function and constraints throughout a prediction horizon. In one method of solving this problem, the time required to find the optimal values of the decision variables depends on the time required to perform the arithmetic operations involved in computing the model predictions. Methods for attempting to reduce the computation time of an MPC could then include developing approximate (reduced-order or data-driven) models for a system that take less time to solve, or to parallelize the computations using, for example, multiple cores or CPU’s. However, an observation in all of these cases is that the values of the process states across the prediction horizon are not the values returned by the optimization problem; the manipulated input trajectory is the desired decision variable. An optimization strategy that cannot explicitly return the process states but can generate some representation of them that then leads to computation of the desired process input would thus be suitable for MPC. Quantum computers achieve their parallelism through creating values that cannot all be returned. They can then operate on this set of values to return a number that is meaningful with respect to that set of values that could not all be returned. Motivated by this, we wish to investigate an idea for utilizing quantum parallelism in developing a representation of an objective function that depends on the solution of a process dynamic model, but then only returning the control actions that minimize the objective function value dependent on those solutions. To do this, several steps are necessary. The first is to locate a quantum algorithm which has the desired characteristics for achieving the goals. In this work, we perform these steps using an amplitude amplification strategy based on Grover’s algorithm on a quantum computer. The second is to analyze the algorithm with respect to its ability to translate across problems in the MPC domain, with respect to both its ability to handle nonlinear systems and to handle a variety of different structures of the set of all possible objective function values given the allowable values of the decision variables. We thus evaluate the benefits and limitations of the algorithm from this perspective. We do not wish to imply that this algorithm is more computationally-tractable for use with MPC than classical optimization techniques traditionally applied in an MPC context. Rather, we wish to understand the manner in which such an algorithm would be designed and when it is appropriate for MPC problems (in the sense of returning the correct answers to the optimization problem), as a step toward better understanding the interactions of the quantum properties of quantum algorithms with control goals. We also see this as forming an important first step in algorithm design/analysis, which can then translate to future works in comparing this technique computationally with classical “competitor” algorithms to guide further work in searching for relevant quantum algorithms for control applications.

Pre-Processing of Categorical Features Within Medical Analysis Systems.

The complexity of the cancer problem domain presents challenges not only to the medical analysis systems tasked with its analysis, but also to the users of such systems. While it is desirable to assist users in operating these medical analysis systems, prior groundwork is required before this can be achieved, such as recognising patterns in the way users create certain analyses within these systems. In this paper, we use machine learning algorithms to analyse user behaviour patterns and attempt to predict the next user interaction within the CARESS medical analysis system. Since an appropriate pre-processing scheme is essential for the performance of these algorithms, we propose the usage of a Natural Language Processing (NLP)- inspired approach to preserve some semantic cohesion of the mostly categorical features of these user interactions. Furthermore, we propose to use a sliding window that contains information about the latest user interactions in combination with Latent Dirichlet Allocation (LDA) to extract a latent topic from these last interactions and use it as additional input to the machine learning models. We compare this pre-processing scheme with other approaches that utilise one-hot encoding and feature hashing. The results of our experiments show that the sliding window LDA scheme is a promising solution, that performs better for our use case than the other evaluated pre-processing schemes. Overall, our results provide an important piece for further research and development in the area of assisting users in operating analysis systems in complex problem domains.

Multi–level method of fundamental solutions for solving polyharmonic problems

We consider a multi–level method of fundamental solutions for solving polyharmonic problems governed by ΔNu=0,N∈N∖{1} in both two and three dimensions. Instead of approximating the solution with linear combinations of N fundamental solutions, we show that, with appropriate deployments of the source points, it is possible to employ an approximation involving only the fundamental solution of the operator ΔN. To determine the optimal position of the source points, we apply the recently developed effective condition number method. In addition, we show that when the proposed technique is applied to boundary value problems in circular or axisymmetric domains, with appropriate distributions of boundary and source points, it lends itself to the application of matrix decomposition algorithms. The results of several numerical tests are presented and analysed.

An ensemble learning framework for snail trail fault detection and diagnosis in photovoltaic modules

This research proposes a method for detecting subtle faults named snail trails for their visual similarity with the trail of a snail in photovoltaic modules. Snail trails do not significantly reduce panel performance but they are the main cause of serious panel deterioration such as microcracks and delamination and can go so far as to set the panel on fire. To detect these faults, this research uses an ensemble learning framework, named ensemble learning for diagnosis, which combines several complementary learning algorithms, namely Support Vector Machines, K-Nearest Neighbors, and Decision Trees. A set of features is obtained by extracting the time–frequency characteristics and statistics from the photovoltaic current signal of the photovoltaic panel. This is followed by a feature selection and dimensionality reduction step that delivers the input to the learning algorithms. The approach presented in this study is experimentally validated, independently for the 4 seasons of the year, with data from a real photovoltaic string of 16 panels. The results demonstrate that the proposed approach can efficiently classify healthy panels and panels with snail trails efficiently. Interestingly, the method only requires the electrical current signal, measured on panels with data acquisition systems that are standard in the photovoltaic industry. The genericity of the approach makes it a good candidate for detecting other photovoltaic faults and for solving diagnosis problems in other domains.

Digital Twins Verification and Validation Approach through the Quintuple Helix Conceptual Framework

The concept of digital twins has been in the field for a long time, constantly challenging the specification, modeling, design, implementation, and exploitation of complex cyber–physical systems. Despite the various foundations, standards, and platforms in systems engineering, there are ongoing challenges with verification and validation methodology. This study aims to establish a generic framework that addresses the various aspects of digital twinning. The multifaceted nature of the problem requires raising the abstraction level in both the real (actual) and virtual domains, effective dissemination of information resources, and a design inspired by verification and validation. The proposed framework combines the quintuple helix model with the problem and operational domains of a real (actual) twin, the solution and implementation domains of a virtual twin, and the execution domain as the bridge that links them. Verification and validation dimensions follow the meta object facility abstraction layers (instance, model, meta-model, and meta-meta-model) mapping over five helices. Embedding the complexity reduction mechanisms in the proposed framework builds a suite for extendible and verifiable digital twinning in simulation and real-time scenarios. The application of main conceptual framework mechanisms in a real-world example study aids the verification of this research’s intentions. The validation is a matter of further research endeavors.

The Political Side of Social Enterprises: A Phenomenon‐Based Study of Sociocultural and Policy Advocacy

AbstractThis study explores the often‐overlooked political dimension of social enterprises, particularly their advocacy activities aimed at influencing public policy, legislation, norms, attitudes, and behaviour. While traditional management research has focused on commercial activity and the beneficiary‐oriented aspects of social enterprises, this paper considers their upstream political activity. Using a phenomenon‐based approach, we analyse original survey data from 718 social enterprises across seven countries and six problem domains to identify factors associated with their engagement in advocacy. Our findings reveal that public spending and competition in social enterprises’ problem domains, as well as their governance choices – legal form, sources of income, and collaborations – are significantly associated with advocacy activities. We propose a new theoretical framework to understand these dynamics, positioning social enterprises as key players in markets for public purpose. This research underscores the importance of recognizing the political activities of social enterprises and offers new insights for studying hybrid organizing and organizations that address complex societal challenges. By highlighting the integral role of advocacy, our study contributes to a more comprehensive understanding of how social enterprises drive social change, not only through direct service provision but also by shaping the broader sociopolitical environment.

Efficient Hyperdimensional Computing With Spiking Phasors.

Hyperdimensional (HD) computing (also referred to as vector symbolic architectures, VSAs) offers a method for encoding symbols into vectors, allowing for those symbols to be combined in different ways to form other vectors in the same vector space. The vectors and operators form a compositional algebra, such that composite vectors can be decomposed back to their constituent vectors. Many useful algorithms have implementations in HD computing, such as classification, spatial navigation, language modeling, and logic. In this letter, we propose a spiking implementation of Fourier holographic reduced representation (FHRR), one of the most versatile VSAs. The phase of each complex number of an FHRR vector is encoded as a spike time within a cycle. Neuron models derived from these spiking phasors can perform the requisite vector operations to implement an FHRR. We demonstrate the power and versatility of our spiking networks in a number of foundational problem domains, including symbol binding and unbinding, spatial representation, function representation, function integration, and memory (i.e., signal delay).

Direct simulation of vortex dynamics of multi-cellular Taylor–Green vortex by pseudo-spectral method

This study investigates the long-time vorticity dynamics of the multi-cellular configurations of the two-dimensional (2D) Taylor–Green vortex (TGV). The pseudo-spectral method is used to solve the incompressible Navier–Stokes equation to analyze the evolution of TGV arrays. The focus is on understanding vortex interactions leading to vortex filamentation and stripping (forward cascade) during primary instability; merger and reconnection (inverse cascade) among the TGV vortical cells subsequently. Here, consideration of multiple cells avoids imposing symmetries at the smallest periodic length scale, and thereby affecting disturbance growth. The initial condition is taken from the analytic solution of the TGV, and Fourier spectral method is employed to track the interactions of the initial doubly-periodic vortices. The full sequence of evolution from one equilibrium state to another for the TGV is not addressed before, as reported here to fill this gap for multiple TGV cells in both directions. By studying various vortical interactions in the ensemble, here we report the enstrophy and energy spectra for different number of TGV cells. This is crucial in understanding the very long-time evolution process, at post-critical Reynolds numbers for the 2D TGV problem in the same physical domain, (0≤(x,y)≤4π) having (4×4) and (6×6) cells. Reported results show the evolution of these vortical cells from original configurations to finally a (1×1) vortical cells — the universal state not demonstrated before.

Explainability of deep reinforcement learning algorithms in robotic domains by using Layer-wise Relevance Propagation

A key component to the recent success of reinforcement learning is the introduction of neural networks for representation learning. Doing so allows for solving challenging problems in several domains, one of which is robotics. However, a major criticism of deep reinforcement learning (DRL) algorithms is their lack of explainability and interpretability. This problem is even exacerbated in robotics as they oftentimes cohabitate space with humans, making it imperative to be able to reason about their behavior. In this paper, we propose to analyze the learned representation in a robotic setting by utilizing Graph Networks (GNs). Using the GN and Layer-wise Relevance Propagation (LRP), we represent the observations as an entity-relationship to allow us to interpret the learned policy. We evaluate our approach in two environments in MuJoCo. These two environments were delicately designed to effectively measure the value of knowledge gained by our approach to analyzing learned representations. This approach allows us to analyze not only how different parts of the observation space contribute to the decision-making process but also differentiate between policies and their differences in performance. This difference in performance also allows for reasoning about the agent’s recovery from faults. These insights are key contributions to explainable deep reinforcement learning in robotic settings.

Comparison of finite element and discrete exterior calculus in computation of time-harmonic wave propagation with controllability

This paper discusses computation of time-harmonic wave problems using a mixed formulation and the controllability method introduced by Roland Glowinski. As an example, a scattering problem (in an exterior domain) is considered, and the continuous problem is first formulated in terms of differential forms. Based on the continuous formulation, we write the discrete problem and the controllability algorithm for methods based on both the finite element exterior calculus (FEEC) and the discrete exterior calculus (DEC). As the discrete exterior calculus method provides us with a diagonal “mass matrix”, time-stepping in the DEC approach is remarkably more efficient than in the FEEC approach. For the computations in this paper, we choose the lowest order Whitney elements (a.k.a. Raviart–Thomas elements) for the FEEC approach, and in the DEC discretization we use different diagonal approximations for the Hodge star. Especially, in the DEC approach, a “harmonic Hodge” approximation is used, the derivation of which is based on the time-harmonicity of the problem. Different type of grids are used to study the sensitivity of the solution to the quality of the grid. Putting an effort on meshes regular enough, the computed DEC-solution is as accurate as the FEEC-solution, but reached in the fraction of the time. Both methods seem to be able to keep the solution accuracy rather well in computations with a high wave number (corresponding to a high frequency and a small wave length).

Analysis of some dynamical systems by combination of two different methods

In this study, we introduce a novel iterative method combined with the Elzaki transformation to address a system of partial differential equations involving the Caputo derivative. The Elzaki transformation, known for its effectiveness in solving differential equations, is incorporated into the proposed iterative approach to enhance its efficiency. The system of partial differential equations under consideration is characterized by the presence of Caputo derivatives, which capture fractional order dynamics. The developed method aims to provide accurate and efficient solutions to this complex mathematical system, contributing to the broader understanding of fractional calculus applications in the context of partial differential equations. Through numerical experiments and comparisons, we demonstrate the efficacy of the proposed Elzaki-transform-based iterative method in handling the intricate dynamics inherent in the given system. The study not only showcases the versatility of the Elzaki transformation but also highlights the potential of the developed iterative technique for addressing similar problems in various scientific and engineering domains.

Separating harmonics in the ground-force signal of a seismic vibratory source

The ground-force signal of a Vibroseis truck is unavoidably contaminated by harmonics. To better characterize the subsurface, the fundamental mode in the ground-force signal is the preferred choice for crosscorrelation with the raw seismic data measured in the field. We develop a novel, efficient, and effective harmonics decomposition method to separate the different orders of harmonics in the ground-force signal. Our method first builds a mathematical model to describe the different orders of harmonics in the ground-force signal by honoring the physical mechanism behind the harmonics generation and then retrieves the different orders of harmonics by solving overdetermined linear problems in the analytic signal domain. The success of our method is demonstrated using synthetic and field data examples.

Uniqueness, regularity, continuity, and stability of solutions of integral equations in irregular domains

This study explores the uniqueness, regularity, continuity, and stability of solutions to integral equations related to elliptical boundary value problems in irregular domains. Traditional methods usually consider soft boundaries, but this work extends these results to include domains with rough boundaries. By employing Sobolev spaces, especially fractional Sobolev spaces, we develop a comprehensive theoretical framework. Under appropriate conditions, the studied integral equation has a unique solution in fractional Sobolev spaces, maintaining the regularity properties of the input function. Two new theorems are introduced to strengthen the findings. The first theorem establishes that solutions are continuous with respect to perturbations in the input data. This means small changes in the input do not cause significant deviations in the solution, ensuring robustness in practical applications. The second theorem demonstrates the stability of the solutions when the domain geometry undergoes small changes. This stability is crucial for real-world scenarios where the exact shapes of domains may not be perfectly known or may vary slightly. These results significantly improve the mathematical understanding of boundary value problems in non-smooth domains. The proposed extended framework allows for more generalized applications, addressing challenges in various fields of physics and engineering. The ability to handle irregular domains with rough boundaries opens up new possibilities for modeling and solving complex problems where traditional soft boundary assumptions are not valid. This research provides a robust basis for future studies and applications, highlighting the importance of considering fractional Sobolev spaces in the analysis of integral equations.

Multimodal Religiously Hateful Social Media Memes Classification Based on Textual and Image Data

Multimodal hateful social media meme detection is an important and challenging problem in the vision-language domain. Recent studies show high accuracy for such multimodal tasks due to datasets that provide better joint multimodal embedding to narrow the semantic gap. Religiously hateful meme detection is not extensively explored among published datasets. While there is a need for higher accuracy on religiously hateful memes, deep learning–based models often suffer from inductive bias. This issue is addressed in this work with the following contributions. First, a religiously hateful memes dataset is created and published publicly to advance hateful religious memes detection research. Over 2000 meme images are collected with their corresponding text. The proposed approach compares and fine-tunes VisualBERT pre-trained on the Conceptual Caption (CC) dataset for the downstream classification task. We also extend the dataset with the Facebook hateful memes dataset. We extract visual features using ResNeXT-152 Aggregated Residual Transformations–based Masked Regions with Convolutional Neural Networks (R-CNN) and Bidirectional Encoder Representations from Transformers (BERT) uncased for textual encoding for the early fusion model. We use the primary evaluation metric of an Area Under the Operator Characters Curve (AUROC) to measure model separability. Results show that the proposed approach has a higher AUROC score of 78%, proving the model’s higher separability performance and an accuracy of 70%. It shows comparatively superior performance considering dataset size and against ensemble-based machine learning approaches.

Comparative Analysis of Nature-Inspired Metaheuristic Techniques for Optimizing Phishing Website Detection

The increasing number, frequency, and sophistication of phishing website-based attacks necessitate the development of robust solutions for detecting phishing websites to enhance the overall security of cyberspace. Drawing inspiration from natural processes, nature-inspired metaheuristic techniques have been proven to be efficient in solving complex optimization problems in diverse domains. Following these successes, this research paper aims to investigate the effectiveness of metaheuristic techniques, particularly Genetic Algorithms (GAs), Differential Evolution (DE), and Particle Swarm Optimization (PSO), in optimizing the hyperparameters of machine learning (ML) algorithms for detecting phishing websites. Using multiple datasets, six ensemble classifiers were trained on each dataset and their hyperparameters were optimized using each metaheuristic technique. As a baseline for assessing performance improvement, the classifiers were also trained with the default hyperparameters. To validate the genuine impact of the techniques over the use of default hyperparameters, we conducted statistical tests on the accuracy scores of all the optimized classifiers. The results show that the GA is the most effective technique, by improving the accuracy scores of all the classifiers, followed by DE, which improved four of the six classifiers. PSO was the least effective, improving only one classifier. It was also found that GA-optimized Gradient Boosting, LGBM and XGBoost were the best classifiers across all the metrics in predicting phishing websites, achieving peak accuracy scores of 98.98%, 99.24%, and 99.47%, respectively.

Are We All in This Together? Examining Nonprofits’ Perceptions of Governmental Actors in the Management of the U.S. Refugee Crisis

Abstract U.S. federal policy has created, at best, a gap and, at worst, a hostile environment for nonprofits serving refugees. We rely on frameworks of nonprofit-government relationships (institutional voids, structural holes, instrumental/expressive support) to explore government-nonprofit interactions in the refugee domain, and their impact on 34 refugee-serving nonprofits in the U.S. Findings indicate limited expressive and instrumental support for nonprofits and suggest nonprofits must navigate complex, multilevel, environments. Contributions include the suggestion of “intentional” rather than institutional voids, and a new typology of forms (zero, unclaimed, symbolic, or comprehensive) of government support for nonprofits in a problem domain based on whether government’s instrumental and expressive support for nonprofits is high or low.

Complete Solutions in the Dilatation Theory of Elasticity with a Representation for Axisymmetry

In this paper, we present certain complete solutions in the dilatation theory of elasticity. This model can be derived as a special case of Eringen’s linear theory of microstretched elastic solids when microrotations are absent. It is also a version of the theory of materials with voids. The dilatation theory can be considered the simplest theoretical model of microstructured materials and is suitable for investigating various phenomena that occur in engineering, geomechanics, and biomechanics. We establish three complete solutions to the displacement equations of equilibrium that are the counterpart of the Green–Lamé (GL), Boussinesq–Papkovich–Neuber (BPN), and Cauchy–Kowalevski–Somigliana (CKS) solutions of classical elasticity. The links between these BPN and CKS solutions are established. Then, we present a representation of the BPN solution in the case of axisymmetry. The results presented here are useful for solving axisymmetric problems in semi-infinite and infinite domains.

Tempered fractional Sobolev spaces

The fractional Laplacian operator Δs is the infinitesimal generator of the isotropic (2s)-stable Lévy process on Rn, which is the scaling limit of the Lévy flight with isotropic power law measure |x|−n−2s. However, their second and higher moments are divergent, leading to the difficulty in the modeling of practical physical processes. Replacing |x|−n−2s by the measure of an isotropic tempered power law with the tempering exponent λ (i.e., e−λ|x||x|−n−2s), the tempered fractional Laplacian operator (Δ+λ)s was introduced in [17] as the infinitesimal generator of the tempered Lévy process. In this paper, guided by the fractional Sobolev spaces Ws,p corresponding to the fractional Laplacian operator Δs, we deal with the tempered fractional Sobolev spaces Ws,λ,p associated with the tempered fractional Laplacian (Δ+λ)s. First, the definition of the tempered fractional Sobolev spaces Ws,λ,p is given via the Gagliardo approach, and some of their basic properties were studied. Subsequently, we focus on the Hilbert case Hs,λ based on the Fourier transform. In particular, we deal with its relation with the tempered fractional Sobolev space Ws,λ,2 and analyze their role in the trace theory, overcoming the challenges posed by the tempering exponent λ. Then we investigate the asymptotic behavior of λ→0+,s→1− and s→0+ that appear in the definition of the tempered fractional Laplacian operator (Δ+λ)s. Moreover, we show continuous and compact embeddings investigating the problem of the extension domains and the generalized Hölder regularity results. As an application of the tempered fractional Sobolev spaces, we prove that the process defined by the tempered Lévy process is a solution of some PDE with tempered fractional Lapalcian operator.

Existence of optimal domains for the helicity maximisation problem among domains satisfying a uniform ball condition

In the present work we present a general framework which guarantees the existence of optimal domains for isoperimetric problems within the class of C1,1-regular domains satisfying a uniform ball condition as long as the desired objective function satisfies certain properties. We then verify that the helicity isoperimetric problem studied in [Cantarella et al., J. Math. Phys. 41, 5615 (2000)] satisfies the conditions of our framework and hence establish the existence of optimal domains within the given class of domains. We additionally use the same framework to prove the existence of optimal domains among uniform C1,1-domains for a first curl eigenvalue problem which has been studied recently for other classes of domains in [Enciso et al., Trans. Am. Math. Soc. 377, 4519–4540 (2024)].

Enhancement of cooling process of hot blocks mounted inside a horizontal channel using flexible baffles — Alternative arrangement

In this paper, two heated blocks and three flexible baffles that are alternately placed on the upper and bottom sides of a rectangular channel are used to replicate the transient heat and air movement. The novelty of this research is the use of flexible baffles to destruct the thermal boundary layer with maintaining little pressure drop, and thus reducing the required pumping capacity. The finite thickness blocks are subject to a constant heat flux, while the baffles are very thin and deforms depending on the strength of the flow of coolant (air). Finite element method with arbitrary Lagrangian–Eulerian approach is used for solving such deforming domain problem. The problem is inspected transiently by varying the dimensionless time (τ=0.0 to 10) and two salient parameters which are Reynolds number Re=10−500, and baffle elasticity parameter E=105−108. Results show that the flexibility feature of the baffles contributes not only in directing the coolant towards the hot blocks, but also contributes in reducing the skin friction and pressure drop through the channel. At Re=150, the skin friction and pressure drop of the flexible baffles are 13.2% and 16.5%, respectively lesser than the rigid baffles. The improvement of Nusselt number with flexibility parameter is marginal and within a limited low Reynolds number, where the maximal improvement is about 3.4% at Re=150.