Space Model Research Articles

A geometric model for cadential forces

When describing tonal attraction, metaphors referring to physical forces can be powerful tools, leading to so called cadential forces. Apart from that, Hilbert space models for tonal attraction have found their way into music theory recently. The paper at hand takes up two approaches: A group around Daniel Harrison has developed a theory of cadence that can be embedded into the concept of cadential forces. The present paper moreover contributes to a previous attempt to model tonal attraction using a qubit system by extending this model, in view of Harrison's theory, to a two-component system in which the relevant forces for a minimal cadence consisting of two chords only are considered adequately. As a result, numerical values for cadential forces can be computed so that various types of authentic and plagal cadences can be compared quantitatively. The resulting scale of cadential forces is finally used to discuss and evaluate the proposed model.

Efficient Importance Variational Approximations for State Space Models

Variational methods are a potentially scalable estimation approach for state space models. However, existing methods are inaccurate or computationally infeasible for many state space models. This article proposes a variational approximation that is accurate and fast for any model with a closed-form measurement density function and a state transition distribution within the exponential family of distributions. Our approach constructs a variational approximation to the states that is close to the exact conditional posterior distribution of the states using insights from the efficient importance sampling literature. We show that our method can accurately and quickly estimate a multivariate Skellam stochastic volatility model with high-frequency tick-by-tick discrete price changes of four stocks.

Diffusion-based generation of gene regulatory networks from scRNA-seq data with DigNet.

A gene regulatory network (GRN) intricately encodes the interconnectedness of identities and functionalities of genes within cells, ultimately shaping cellular specificity. Despite decades of endeavors, reverse engineering of GRNs from gene expression profiling data remains a profound challenge, particularly when it comes to reconstructing cell-specific GRNs that are tailored to precise cellular and genetic contexts. Here, we propose a discrete diffusion generation model, called DigNet, capable of generating corresponding GRNs from high-throughput single-cell RNA sequencing (scRNA-seq) data. DigNet embeds the network generation process into a multistep recovery procedure with Markov properties. Each intermediate step has a specific model to recover a portion of the gene regulatory architectures. It thus can ensure compatibility between global network structures and regulatory modules through the unique multistep diffusion procedure. Furthermore, through iMetacell integration and non-Euclidean discrete space modeling, DigNet is robust to the presence of noise in scRNA-seq data and the sparsity of GRNs. Benchmark evaluation results against more than a dozen state-of-the-art network inference methods demonstrate that DigNet achieves superior performance across various single-cell GRN reconstruction experiments. Furthermore, DigNet provides unique insights into the immune response in breast cancer, derived from differential gene regulation identified in T cells. As an open-source software, DigNet offers a powerful and effective tool for generating cell-specific GRNs from scRNA-seq data.

Stabilisation in an infinite time horizon by homomorphically encrypted first-order controllers with regular Pisot poles

It has been previously found that partially homomorphic encryption based controllers cannot operate in an infinite time horizon, unless all elements of their state matrices are integer numbers. Considering this fact and the results of a recent research revealing the role of Pisot numbers to act as the poles of integer state matrix based state space models involving no unstable pole-zero cancellation, the present paper aims to introduce some classes of realisations implementing first-order discrete-time controllers, which can be used in an infinite time horizon in encrypted control systems. These classes of controller realisations are obtained based on sequences approaching to limit points of positive Pisot numbers settled in the range ( 1 , 2 ) . An analytical procedure is also suggested to find the exact range of the controller gain for ensuring the closed-loop stability.

Robust Hedging GANs: Towards Automated Robustification of Hedging Strategies

The availability of deep hedging has opened new horizons for solving hedging problems under a large variety of realistic market conditions. At the same time, any model – be it a traditional stochastic model or a market generator – is at best an approximation of market reality, prone to model-misspecification and estimation errors. This raises the question, how to address the risk of discrepancy between anticipated distribution and market reality, in an automated way. This paper presents a natural extension of the original deep hedging framework to address uncertainty in the data generating process via an adversarial approach inspired by GANs. This is achieved through an interplay of three modular components: (i) a (deep) hedging engine, (ii) a data-generating process (that is model agnostic permitting a large variety of classical models as well as machine learning-based market generators), and (iii) a notion of distance on model space to measure deviations between our market prognosis and reality. We do not restrict the ambiguity set to a region around a reference model, but instead penalize deviations from the anticipated distribution. We demonstrate this in numerical experiments to benchmark our framework against other existing results.

Research on a Bearing Fault Diagnosis Method Based on a CNN-LSTM-GRU Model

In view of the problem of the insufficient performance of deep learning models in time series prediction and poor comprehensive space–time feature extraction, this paper proposes a diagnostic method (CNN-LSTM-GRU) that integrates convolutional neural network (CNN), long short-term memory (LSTM) network, and gated recurrent unit (GRU) models. In this study, a convolutional neural network (CNN) model is used to process two-dimensional image data in both time and frequency domains, and a convolutional core attention mechanism is introduced to extract spatial features, such as peaks, cliffs, and waveforms, from the samples. A long short-term memory (LSTM) network is embedded in the output processing of the convolutional neural network (CNN) to analyze the long-sequence variation characteristics of rolling bearing vibration signals and enable long-term time series prediction by capturing long-term dependencies in the sequence. In addition, a gated recurrent unit (GRU) is used to refine long-term time series predictions, providing local fine-tuning and improving the accuracy of fault diagnosis. Using a dataset obtained from Case Western Reserve University (CWRU), the average accuracy of CNN-LSTM-GRU fault vibration is greater than 99%, and its superior performance in a noisy environment is demonstrated.

A Model for the Development of Learning in a Virtual Geological Field Trip as a Modified Novelty Space

Abstract The purpose of this study is to propose a “modified novelty space” model for learning in virtual geological field trips. To do so, three field sites in Busan National Geopark were selected to explore geological characteristics. VR-based virtual field trips (VFTs) were developed for participation. These VFTs consisted of basic, plus, and advanced steps. The modified novelty space model redefines the novelty space for the context of virtual learning environments (VLEs) by subdividing it into cognitive, geographic, psychological, technical, and social factors. The cognitive domain refers to the curriculum content in geology. The geographic domain involves contextual interpretations of places. The psychological domain increases familiarity based on methods to provide stability. The technical domain refers to the ability to handle skills. The social domain refers to emotional sharing among people in relationships. This model proposes five elements with the aim of decrease in modified novelty space ultimately contributing positively to virtual learning.

Training for Students of Pedagogical Specialties “Modeling of Subjective Space”

Introduction. The article presents a scientific problem of modeling the subjective space of students, which is due to a number of factors: the need to monitor the process of developing personal competencies of the student; the primacy of studying and optimizing the relationship between teachers and students; insufficient theoretical and practical study of issues related to the phenomenon of the personal space of a student-future teacher. The purpose of the publication is to theoretically study the subjective space of students of pedagogical specialties and experimental testing of training as a means of working with students along seven vectors of objective movement: knowledge, skills, abilities, intellectual abilities, value-semantic awareness, spiritual and moral potential and metacognitive thinking. Methodology. The study was facilitated by the methods of theoretical (analysis, synthesis, induction, deduction, formalization) and empirical knowledge (observation, questionnaires, comparison). Results. The scientific results obtained during the study fully confirm the effectiveness of the study. The pedagogical innovation of the problem study is concentrated in the modeling of the subjective space and the development of training for studying the vectors of the subjective movement of students in the context of forming their readiness for strategic activity. As part of the training work, the process of student diagnostics is presented. The author has developed nine questions for each vector. Conclusions. Based on the conducted research, conclusions are formulated that in the professional training of future teachers it is advisable to use the training “Modeling of Subjective Space”, the task of which is the individualization of professional and pedagogical education, which is required with the growth of the educational load, when students need a reflexive assessment of the results of their achievements for successful strategic activity in the future.

Дополнительное соотношение неопределенностей Гейзенберга в (1+3) пространстве Минковского и в (1+4)D модели расширенного пространства

The article considers the introducing possibility an additional Heisenberg uncertainty relation, which can be introduced in the (1+3)D Minkowski space and in the (1+4)D 5-dimensional extended space model (ESM). In the ESM (1+4)D formalism, in addition to the usual coordinates T;X,Y,Z, the interval S already existing in Minkowski space is considered as the fifth coordinate. The fifth coordinate S in the ESM has a action physical meaning. The work shows that it is possible to introduce one more additional Heisenberg uncertainty relation connecting mass and interval.

Early Prediction of Remaining Useful Life for Lithium-Ion Batteries with the State Space Model

In the realm of lithium-ion batteries (LIBs), issues like material aging and capacity decline contribute to performance degradation or potential safety hazards. Predicting remaining useful life (RUL) serves as a crucial method of assessing the health of batteries, thereby enhancing reliability and safety. To reduce the complexity and improve the accuracy and applicability of early RUL predictions for LIBs, we proposed a Mamba-based state space model for early RUL prediction. Due to the impacts of abnormal data, we first use the interquartile range (IQR) method with a sliding window for data cleansing. Subsequently, the top three highest correlated features are selected, and only the first 300 cycling data are used for training. The model has the ability to make forecasts using these few historical data. Extensive experiments are conducted using CALCE CS2 datasets. The MAE, RMSE, and RE are less than 0.015, 0.019, and 0.0261; meanwhile, R2 is higher than 0.99. Compared to the baseline approaches (CNN, BiLSTM, and CNN-BiLSTM), the average MAE, RMSE, and RE of the proposed approach are reduced by at least 29%, 21%, and 36%, respectively. According to the experimental results, the proposed approach performs better in terms of accuracy, robustness, and efficiency.

Data-Driven Voltage Control Method of Active Distribution Networks Based on Koopman Operator Theory

The advent of large-scale distributed generation (DG) has introduced several challenges to the voltage control of active distribution networks (ADNs). These challenges include the heterogeneity of control devices, the complexity of models, and their inherent fluctuations. To maintain ADN voltage stability more economically and quickly, a data-driven ADN voltage control scheme is proposed in this paper. Firstly, based on the multi-run state sensitivity matrix, buses with similar voltage responses are clustered, and critical buses are selected to downsize the scale of the model. Secondly, a linear voltage-to-power dynamics model in high-dimensional state space is trained based on the offline data of critical bus voltages, DGs, and energy storage system (ESS) outputs, utilizing the Koopman theory and the Extended Dynamic Mode Decomposition (EDMD) method. A linear model predictive voltage controller, which takes ADN stability and control cost into account, is also proposed. Finally, the effectiveness and applicability of the method are verified by applying it to an improved 33-bus ADN system. The proposed control method can respond more quickly and accurately to the voltage fluctuation problems caused by source-load disturbances and short-circuit faults.

Social Intervention and Cultural Strategy Integration of Cultural Heritage Elements in Glass Product Innovation

With the vigorous development of the cultural and creative industry, glass products, as an important carrier, have received increasing attention in their innovative design. This study aims to explore the social intervention and cultural strategy integration of cultural heritage elements in glass product innovation. Through the analysis of the Hazel Clark cultural space model, it seeks to find a path to effectively integrate cultural heritage elements into glass product design. This study adopts comparative analysis and case study methods to deeply analyze the inherent relationship between cultural spatial patterns and product attributes, and verify their feasibility in practical applications. The results indicate that cultural heritage spatial analysis and application have significant social intervention effects in glass product innovation, which can enrich the cultural connotation of products and enhance their market competitiveness. Meanwhile, this study also reveals the transformation patterns and value enhancement strategies of cultural heritage elements in glass product innovation.

An Introduction to Quantitative Text Analysis for Linguistics: Reproducible Research Using R

Jerid Francom’s book An Introduction to Quantitative Text Analysis for Linguistics: Reproducible Research Using R is an essential textbook for researchers and students alike, who are exploring quantitative text analysis. This book is designed with beginners in mind, it emphasizes reproducible research, offering a structured approach to text analysis through the programming language R. Spanning five interconnected parts, beginning with foundational concepts like the Data-Information-Knowledge-Insight (DIKI) hierarchy, corpus creation, and data curation, advancing to topics like tokenization, dimensionality reduction, vector space modeling, and hypothesis testing with the {infer} package. This book contains practical exercises alongside detailed explanations that guide readers through the entire process of text analysis, starting from data acquisition to predictive modeling and statistical designs. Computational methods including readability measures, sentiment analysis, semantic modeling, and topic modeling are highlighted within this book, ensuring that readers are equipped to extract meaningful insights from linguistic data. Through the incorporation of Tidyverse tools and additional resources like GitHub repositories, Francom successfully bridges theoretical understanding with hands-on application. Transparency and reproducibility have been prioritized within the text, and meticulous data documentation and open-source methodologies have been meticulously advocated by the author. Although the book is an accessible resource for English-language data, readers might be challenged due to its focus on breadth over depth when their focus might be on seeking advanced exploration or on the other hand for those without basic programming experience. Regardless of this, Francom’s pedagogical approach combines clarity with practical guidance, making this book a valuable resource for students, researchers, and professionals who aim to integrate quantitative methods into their linguistic research.

Neural Network Identification-Based Model Predictive Heading Control for Wave Gliders

This paper deals with the neural network identification-based model predictive heading control problem in a wave glider. First, based on a kinematic model of the wave glider subjected to external disturbance and system uncertainty, a state space model of the wave glider is established. Then, a neural network identification-based model predictive heading controller (NNI-MPHC) is designed for the wave glider. The heading controller mainly includes three components: a model predictive controller, a neural network-based model identifier, and a linear reduced-order extended state observer. Third, a design algorithm of the NNI-MPHC is presented. The algorithm is demonstrated through simulation, where the results show the following: (i) The designed NNI-MPHC is remarkably capable of guaranteeing the tracing effects of the wave glider. (ii) Comparing the NNI-MPHC and existing heading controllers, the former is better than the latter in terms of tracking accuracy and rapidity and robustness to model uncertainty and/or external disturbances.

State space model: a magical tool for state prediction in Nonlinear systems

State space model: a magical tool for state prediction in Nonlinear systems

A new mixed split feasibility problem model in Hilbert spaces

We study a generalized model of a split problem which is a combination of a split feasibility problem with multiple output sets and a split equality problem in real Hilbert spaces. Employing an unconstrained optimization approach, we propose two new iterative algorithms for solving such split problems. Our algorithms do not depend on the norms of the transfer mappings.

Accuracy of Reaction Coordinate Based Rate Theories for Modelling Chemical Reactions: Insights From the Thermal Isomerization in Retinal.

Modern potential energy surfaces have shifted attention to molecular simulations of chemical reactions. While various methods can estimate rate constants for conformational transitions in molecular dynamics simulations, their applicability to studying chemical reactions remains uncertain due to the high and sharp energy barriers and complex reaction coordinates involved. This study focuses on the thermal cis-trans isomerization in retinal, employing molecular simulations and comparing rate constant estimates based on one-dimensional rate theories with those based on sampling transitions and grid-based models for low-dimensional collective variable spaces. Even though each individual method to estimate the rate passes its quality tests, the rate constant estimates exhibit considerable disparities. Rate constant estimates based on one-dimensional reaction coordinates prove challenging to converge, even if the reaction coordinate is optimized. However, consistent estimates of the rate constant are achieved by sampling transitions and by multi-dimensional grid-based models.

Signatures and Mechanism Analysis of Converter-Grid Subsynchronous Oscillations

In the last decade, a rather new phenomenon related to subsynchronous oscillations (SSO) in a wide frequency range has emerged in modern power grids with power converters. The consequences of these oscillations can be severe system accidents, which have already occurred in various power systems. Taking into account the importance of studying such oscillations for effective mitigation and the existing gaps in understanding the mechanisms of SSO occurrence due to different combinations of used controllers in the inverter control system, as well as the grid parameters, a frequency analysis of simplified grid inverter models is performed. As a result, five different mechanisms of SSO occurrence, the affecting factors and the level of inverter model detail required for the adequate study of SSO are justified. The developed detailed state–space model allowed for verifying the obtained results, as well as identifying an additional sixth mechanism of SSO occurrence. The common condition for the occurrence of all the identified SSO mechanisms is a weak grid with a short-circuit ratio of less than two. The results of control hardware-in-the-loop testing confirmed the conclusions drawn. As a result, a classification of SSO occurrence mechanisms was formed, reflecting their causes and distinctive features.

Periodic solutions for nonlinear deformation waves based on new Boussinesq-type equation within strain gradient elasticity and reductive perturbation technique

In this article, we present a detailed variational formulation to study and analyze the geometrically nonlinear behavior of elastic materials at small scales, where the classical theory of elasticity becomes inadequate. The presented technique is based on the variation of the internal energy of the elastic material and the virtual work of the external forces for the dynamical system in the framework of the first strain gradient theory of elasticity. This approach simultaneously determines the equilibrium equations in nonlinear form and the complete set of nonlinear boundary conditions. A new hyperbolic Boussinesq-type equation is derived based on the presented model in one-dimensional space and time to examine the impact of geometrical nonlinearity on wave propagation in an isotropic elastic material. The exponential reductive perturbation technique (ERPT) is employed to obtain an approximate and hierarchical solution for the new nonlinear partial differential equation (NPDE). The obtained results are plotted and analyzed, moreover, the results reveal that geometric nonlinearity significantly influences wave propagation in polycrystalline silicon.

Constructing Predictive Implicit Solvent Models: Insights from Exploring Potential Parameter Space and Property Predictions.

Implicit solvent (IS) models enhance the efficiency of simulating liquid systems, but those based on the potential of mean force calculations using explicit solvent (ES) models often fail to capture the solute structure and assembly dynamics under various conditions. This study examines the relationships between the parameter space of IS models and their predictive capabilities regarding solute structure and assembly dynamics, focusing on NaCl solutions and protein-bound silica colloidal nanoparticles. For NaCl solutions, models developed using concentration-dependent dielectric constants generally lack efficacy, and their effectiveness in predicting high-concentration liquid structures varies based on the ES model used. Adjusting the dielectric constant value or the shape of the short-range potentials can improve the accuracy of these models in predicting liquid structures. For protein-bound silica colloidal nanoparticles, we find that interaction site size and model resolution significantly influence the prediction of nanoparticle assembly dynamics, with different resolutions producing aggregates with distinct structures and connection modes. This study elucidates the complex relationship between parameter space in IS models and liquid structure and assembly kinetics, providing crucial insights for developing more accurate and predictive models.