Space Model Research Articles

Analyzing factors causing deadlock events of bi-directional pedestrian flow when moving on stairs using a personal space model

Comprehending crowd dynamics on staircases is imperative for preventing accidents, particularly in emergency scenarios. In this context, our study delves into bi-directional pedestrian flow. When confronted with limited staircase space, the occurrence of two distinct lanes—one for upstairs and another for downstairs—is a common observation. However, there has been no quantitative investigation conducted to understand this phenomenon. To facilitate such an analysis, we employ a velocity-based personal space model that accurately reproduces the formation of upstairs and downstairs lanes in bi-directional staircases. The study of lane formation mechanisms and the exploration of factors influencing deadlock are essentially two sides of the same coin. This is due to the fact that, the occurrence of deadlock signifies a disruption in the anticipated lane behavior during counter flow. As a result, we have devised various scenarios to meticulously analyze the factors contributing to both deadlock formation and its subsequent performance. This involves manipulating parameters such as speed, speed dispersion, pedestrian count, initial density, right-hand preference weight, minimum personal space size, same-direction following intensity, and time step. The findings hold the potential to enhance the overall quality of service in stairway movement and offer significant contributions to the understanding and management of pedestrian behavior in such settings.

How can entrepreneurial obstacles improve entrepreneurs’ psychological well-being? The role of emotional ambivalence

ABSTRACT Entrepreneurial obstacles present both threats to survival and opportunities for learning. By integrating the double-edged nature of obstacles into the evaluative space model of emotion, this study examines the effects of entrepreneurial obstacles on entrepreneurs’ emotional ambivalence and their psychological well-being. Through survey among 324 new ventures in China, we find that although entrepreneurial obstacle is directly detrimental to psychological well-being, it can also trigger entrepreneurs’ emotional ambivalence which has a U-shaped relationship with psychological well-being. Moreover, demand uncertainty increases entrepreneurs’ ambivalent emotional response to entrepreneurial obstacles. This study identifies a self-healing path between entrepreneurial obstacles and entrepreneurs’ psychological well-being.

Thermodiffusively unstable laminar hydrogen flame in a sufficiently large 3D computational domain – Part II: NOx formation mechanism and flamelet modeling

In this work, the NOx formation mechanism in three-dimensional (3D) thermodiffusively unstable premixed hydrogen flames is investigated through direct numerical simulations (DNS) and a reaction path analysis based on the DNS dataset. In part I of this study (Wen et al., 2024), the characteristic patterns of the instabilities were studied using the same dataset. Here, first, the effects of the computational setup (2D vs. 3D) and curvature on the flux ratio of nitrogen atom are quantified. In addition, the composition space model (CSM) proposed in previous works is extended to account for the NOx chemical reaction mechanism to predict NOx formation in thermodiffusively unstable premixed hydrogen flames. The flamelet solutions are obtained from the premixed flamelet equations in composition space so that the wide range of curvatures associated with the strongly corrugated flame front can be considered. The performance of the CSM in predicting the NOx species and the important radicals involved in the NOx formation pathways is evaluated through an a priori analysis. To investigate the effects of curvature on the NOx formation pathways and the performance of the composition space model, the positively- and negatively-curved regions in the DNS are studied separately. The results show that different from the 2D simulation, the NNH reaction pathway becomes dominant in the 3D simulation due to the increased range of curvature, which promotes the accumulation of the highly diffusive H radical in the positively-curved regions. The NNH reaction pathway is dominant in the positively-curved regions, while the N2O reaction pathway is more important in the negatively-curved regions. The flamelet model based on the composition space solutions that consider the effects of curvature yields accurate predictions for the radicals that are sensitive to the effects of curvature.Novelty and significance statementThe novelty of the present work includes the following aspects,(i) Analysis of NOx formation mechanism based on the large-scale 3D DNS dataset of a laminar fuel-lean premixed hydrogen flame on a sufficiently large domain;(ii) Quantification of the effects of computational setup (2D and 3D) and curvature on the NOx formation pathways;(iii) Extension of the previous composition space model (CSM) by incorporating the NOx chemical reaction mechanism to consider the effects of curvature on the NOx formation.

Integral Models of Moduli Spaces of Shtukas with Deep Bruhat-Tits Level Structures

Abstract We construct integral models for moduli spaces of shtukas with deeper Bruhat-Tits level structures. We embed the moduli space of global shtukas for a deeper Bruhat-Tits group scheme into the limit of the moduli spaces of shtukas for all associated parahoric group schemes. Its schematic image defines an integral model of the moduli space of shtukas with deeper Bruhat-Tits level with favourable properties. They admit proper, surjective and generically étale level maps as well as a natural Newton stratification. In the Drinfeld case, this general construction of integral models recovers the moduli space of Drinfeld shtukas with Drinfeld level structures.

Quark and lepton modular models from the binary dihedral flavor symmetry

Inspired by the structure of top-down derived models endowed with modular flavor symmetries, we investigate the yet phenomenologically unexplored binary dihedral group 2D3. After building the vector-valued modular forms in the representations of 2D3 with small modular weights, we systematically classify all (Dirac and Majorana) mass textures of fermions with fractional modular weights and all possible 2 + 1-family structures. This allows us to explore the parameter space of fermion models based on 2D3, aiming at a description of both quarks and leptons with a minimal number of parameters and best compatibility with observed data. We consider the separate possibilities of neutrino masses generated by either a type-I seesaw mechanism or the Weinberg operator. We identify a model that, besides fitting all known flavor observables, delivers predictions for six not-yet measured parameters and favors normal-ordered neutrino masses generated by the Weinberg operator. It would be interesting to figure out whether it is possible to embed our model within a top-down scheme, such as \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{T}}^{2}/{\\mathbb{Z}}_{4}$$\\end{document} heterotic orbifold compactifications.

Unsupervised multimodal modeling of cognitive and brain health trajectories for early dementia prediction

Predicting the course of neurodegenerative disorders early has potential to greatly improve clinical management and patient outcomes. A key challenge for early prediction in real-world clinical settings is the lack of labeled data (i.e., clinical diagnosis). In contrast to supervised classification approaches that require labeled data, we propose an unsupervised multimodal trajectory modeling (MTM) approach based on a mixture of state space models that captures changes in longitudinal data (i.e., trajectories) and stratifies individuals without using clinical diagnosis for model training. MTM learns the relationship between states comprising expensive, invasive biomarkers (β-amyloid, grey matter density) and readily obtainable cognitive observations. MTM training on trajectories stratifies individuals into clinically meaningful clusters more reliably than MTM training on baseline data alone and is robust to missing data (i.e., cognitive data alone or single assessments). Extracting an individualized cognitive health index (i.e., MTM-derived cluster membership index) allows us to predict progression to AD more precisely than standard clinical assessments (i.e., cognitive tests or MRI scans alone). Importantly, MTM generalizes successfully from research cohort to real-world clinical data from memory clinic patients with missing data, enhancing the clinical utility of our approach. Thus, our multimodal trajectory modeling approach provides a cost-effective and non-invasive tool for early dementia prediction without labeled data (i.e., clinical diagnosis) with strong potential for translation to clinical practice.

Unveiling Code Pre-Trained Models: Investigating Syntax and Semantics Capacities

Code models have made significant advancements in code intelligence by encoding knowledge about programming languages. While previous studies have explored the capabilities of these models in learning code syntax, there has been limited investigation on their ability to understand code semantics. Additionally, existing analyses assume the number of edges between nodes at the abstract syntax tree (AST) is related to syntax distance, and also often require transforming the high-dimensional space of deep learning models to a low-dimensional one, which may introduce inaccuracies. To study how code models represent code syntax and semantics, we conduct a comprehensive analysis of 7 code models, including four representative code pre-trained models (CodeBERT, GraphCodeBERT, CodeT5, and UnixCoder) and three large language models (StarCoder, CodeLlama and CodeT5+). We design four probing tasks to assess the models’ capacities in learning both code syntax and semantics. These probing tasks reconstruct code syntax and semantics structures (AST, CDG, DDG and CFG) in the representation space. These structures are core concepts for code understanding. We also investigate the syntax token role in each token representation and the long dependency between the code tokens. Additionally, we analyze the distribution of attention weights related to code semantic structures. Through extensive analysis, our findings highlight the strengths and limitations of different code models in learning code syntax and semantics. The results demonstrate that these models excel in learning code syntax, successfully capturing the syntax relationships between tokens and the syntax roles of individual tokens. However, their performance in encoding code semantics varies. CodeT5 and CodeBERT demonstrate proficiency in capturing control and data dependencies, while UnixCoder shows weaker performance in this aspect. We do not observe LLMs generally performing much better than pre-trained models. The shallow layers of LLMs perform better than their deep layers. The investigation of attention weights reveals that different attention heads play distinct roles in encoding code semantics. Our research findings emphasize the need for further enhancements in code models to better learn code semantics. This study contributes to the understanding of code models’ abilities in syntax and semantics analysis. Our findings provide guidance for future improvements in code models, facilitating their effective application in various code-related tasks.

Physics‐constrained symbolic model discovery for polyconvex incompressible hyperelastic materials

AbstractWe present a machine learning framework capable of consistently inferring mathematical expressions of hyperelastic energy functionals for incompressible materials from sparse experimental data and physical laws. To achieve this goal, we propose a polyconvex neural additive model (PNAM) that enables us to express the hyperelastic model in a learnable feature space while enforcing polyconvexity. An upshot of this feature space obtained via the PNAM is that (1) it is spanned by a set of univariate basis functions that can be re‐parametrized with a more complex mathematical form, and (2) the resultant elasticity model is guaranteed to fulfill the polyconvexity, which ensures that the acoustic tensor remains elliptic for any deformation. To further improve the interpretability, we use genetic programming to convert each univariate basis into a compact mathematical expression. The resultant multi‐variable mathematical models obtained from this proposed framework are not only more interpretable but are also proven to fulfill physical laws. By controlling the compactness of the learned symbolic form, the machine learning‐generated mathematical model also requires fewer arithmetic operations than its deep neural network counterparts during deployment. This latter attribute is crucial for scaling large‐scale simulations where the constitutive responses of every integration point must be updated within each incremental time step. We compare our proposed model discovery framework against other state‐of‐the‐art alternatives to assess the robustness and efficiency of the training algorithms and examine the trade‐off between interpretability, accuracy, and precision of the learned symbolic hyperelastic models obtained from different approaches. Our numerical results suggest that our approach extrapolates well outside the training data regime due to the precise incorporation of physics‐based knowledge.

The Construction of the Pedagogical Space from the Narratives of the Early Childhood Education Teachers

Environments or learning spaces in school classrooms contribute to the improvement of educational processes. Specifically, in the Early Childhood Education, teachers can design learning spaces, which fosters an environment of safety and autonomy for the students of the Early Childhood Education. This study explores the teachers' narratives concerning the meanings they assign to the school space, the criteria by which they design and transform it, and its connection to model of educational. We have collected 34 stories of pre-primary education teachers through a semi-structured interview in which they had to reflect on this pedagogical design. As most relevant result we identify a model sustained under constructivist or cognitive criteria, rather than a dialogical one. We conclude that this epistemological perspective of the construction of the school environment should be oriented towards a more participatory and co-constructed model of the educational space.

Rare species of dark matter

I discuss implications of rare species of particles that have larger than commonly assumed interaction and/or annihilation cross sections. Large fractions of the parameter space of such models remain unexplored. I point out a number of the most interesting consequences, such as large accumulation of such particles in the earth, direct annihilation inside large neutrino detectors, possibility to accelerate such particles using particle beams with subsequent detection using the direct detection experiments. I also discuss the de-excitations on nuclear isomers through a recoil on dark matter, as well as in-situ formation of the DM-nucleus bound states.

Bent-half space model problem for Lame equation with surface tension

The study of fluid flow is a very fascinating area of fluid dynamics. Fluid motion has received more and more attention in recent years and numerous researchers have looked into this topic. However, they rarely used a mathematical analysis approach to analyse fluid motion; instead, they used numerical analysis. This serves as a significant justification for the researcher's decision to study fluid flow from the perspective of mathematical analysis. In this paper, we consider the ${\mathcal R}$-boundedness of the solution operator families of the Lam\'e equation with surface tension in bent half-space model problem by taking into account the surface tension in a bounded domain of {\it N}-dimensional Euclidean space ($N \geq 2$). The motion of the model problem can be described by linearizing an equation system of a model problem. This research is a continuation of [13]. They investigated the ${\mathcal R}$-boundedness of the solution operator families in the half-space case for the model problem of the Lam\'e equation with surface tension. First of all, by using Laplace transformation we consider the resolvent of the model problem, then treat the problem in bent half-space case. By using Weis's operator-valued Fourier multiplier theorem, we know that ${\mathcal R}$-boundedness implies the maximal $L_p$-$L_q$ regularity for the initial boundary value. This regularity is an essential tool for the partial differential equation problem.

An automated multi-layer perceptron discriminative neural network based on Bayesian optimization achieves high-precision one-source single-snapshot direction-of-arrival estimation

This paper proposes an innovative global solution which is a pioneering work applying automated machine learning algorithms to remarkable precision sparse underwater direction-of-arrival (DOA) estimation that views the subaquatic sparse-sampling DOA estimation problem as a classification prediction task. The proposed solution, termed automated multi-layer perceptron discriminative neural network (AutoMPDNN), is built upon a Bayesian optimization framework. AutoMPDNN transforms sparsely sampled time-domain signals into the complex domain, preserving essential components in a one-source single-snapshot scenario. Leveraging Bayesian optimization principles, the algorithm embeds necessary hyperparameters into the loss function, effectively defining it as a maximum likelihood problem using the upper confidence bound function and incorporating sparse signal features. We also explore the model space architecture and introduce variants of AutoMPDNN, denoted as AutoMPDNNs_ln (n = 2,3,4). Through a series of plane wave simulation experiments, it is demonstrated that AutoMPDNN achieves the highest prediction performance for one-source single-snapshot scenarios compared to classical DOA estimation algorithms that incorporate sparse representation approaches, as well as contemporary deep learning DOA methods under varying conditions.

The Weighted Least-Squares Approach to State Estimation in Linear State Space Models: The Case of Correlated Noise Terms

In this article, a particular approach to deriving recursive state estimators for linear state space models is generalised, namely the weighted least-squares approach introduced by Duncan and Horn in 1972, for the case of the two noise processes arising in such models being cross-correlated; in this context, the fact that in the available literature two different non-equivalent recursive algorithms are presented for the task of state estimation in the aforementioned case is discussed. Although the origin of the difference between these two algorithms can easily be identified, the issue has only rarely been discussed so far. Then the situations in which each of the two algorithms apply are explored, and a generalised Kalman filter which represents a merger of the two original algorithms is proposed. While, strictly speaking, optimal state estimates can be obtained only through the non-recursive weighted least-squares approach, in examples of modelling simulated and real-world data, the recursive generalised Kalman filter shows almost as good performance as the optimal non-recursive filter.

Joint Inversion of Surface-Wave Dispersions and Receiver Functions Based on Deep Learning

Abstract We proposed a deep learning (DL) method to derive VS models from joint inversion of Rayleigh-wave dispersions and receiver functions, which is based on multilabel convolutional neural network and recurrent neural network. We used a spline-based approach to generate synthetic models instead of directly using existing models to build the training data set, which improves the generalization of the method. Unlike the traditional methods, which usually set a fixed VP/VS ratio, our method makes full use of the powerful data mining ability of DL to invert the VS models assuming different VP/VS ratios. A loss function is specially designed that focuses on key features of the model space, for example, the shape and depth of Moho. Synthetic tests demonstrate that the proposed method is accurate and fast. Application to the southeast margin of the Tibetan Plateau shows results consistent with the previous joint inversion with P constraints, indicating the proposed method is reliable and robust.

Adaptive laterally constrained inversion of time-domain electromagnetic data using hierarchical Bayes

Laterally constrained inversion (LCI) of time-domain electromagnetic (TEM) data is effective in recovering quasi-layered models, particularly in sedimentary environments. By incorporating lateral constraints, LCI enhances the stability of the inverse problem and improves the resolution of stratified interfaces. However, a limitation of the LCI is the recovery of laterally smooth transitions, even in regions unsupported by the available data sets. Therefore, we have developed an adaptive LCI scheme within a Bayesian framework. Our approach introduces user-defined constraints through a multivariate Gaussian prior, wherein the variances serve as hyperparameters in a hierarchical Bayes algorithm. By simultaneously sampling the model parameters and hyperparameters, our scheme allows for varying constraints throughout the model space, selectively preserving lateral constraints that align with the available data sets. We demonstrate the effectiveness of our adaptive LCI scheme through a synthetic example. The inversion results showcase the self-adaptive nature of the strength of the constraints, yielding models with smooth lateral transitions while accurately retaining sharp lateral interfaces. An application to field TEM data collected in Laizhou, China, supports the findings from the synthetic example. The adaptive LCI scheme successfully images quasi-layered environments and formations with well-defined lateral interfaces. Moreover, the Bayesian inversion provides a measure of certainty, allowing for a comprehensive illustration of the confidence in the inversion results.

Research and Development of Digital Work Ticket Information Sharing System Based on Mathematical Differential Improved Vector Space Model

In the traditional production business operation and maintenance maintenance involves the work ticket filled by hand, easy to produce errors, and need to review, approval and other operations, low efficiency. The author proposes a digital work ticket sharing system based on mathematical differential improved vector space model, through the integration with PMS2.0 system and security risk management and control platform, achieve mobile office management away from WEB, in terms of functions, it realizes all the functions of the work ticket module in the PMS2.0 system, and integrates various requirements of the on-site paper work ticket, through the application of digital work ticket, real-time data collection and comprehensive sharing of the whole process and business of work ticket are realized, at the same time, according to the requirements of security management and control, data fusion with the security risk management and control platform is realized to improve work efficiency and security sharing.

Proxy-SU(4) symmetry in A=60-90 region

Abstract Applications of the proxy-SU(3) model of Bonatsos and collaborators to nuclei in A=60-90 region introduces proxy-SU(4) symmetry. Shell model spaces with single particle (sp) orbits 1p3⁄2, 1p1⁄2, 0f5⁄2 and 0g9⁄2 are essential for these nuclei and also protons and neutrons in this region occupy the same sp orbits. With this and applying the ”proxy scheme”, the 0g9⁄2 changes to 0f7⁄2 giving the SGA U(40)have the proxy-⊃ [U(10)SU⊃ G(3) model. It is easy to see that proxy-⊃ SO(3)] ⊗ [SU(4) ⊃ SUS(2) ⊗ SUT(2)]. With G = SU(3), weSU(3) symmetry implies goodness of the SU(4) symmetry appearing above, i.e. proxy-SU(4) symmetry. Shell model calculations pointing out the need for 0g9⁄2 orbit, ground state masses, shape changes and shape co-existence in A=60-90 region and GT distributions clearly show the importance of proxy-SU(4) in this mass region. Besides presenting this evidence, new proxy schemes with G = SU(5), SO(6) and SO(10) that are generated by good proxy-SU(4) symmetry are described in some detail. An important feature is that the four proxy symmetries SU(3), SO(6), SU(5) and SO(10) appear twice.

Underground Diagnosis Based on GPR and Learning in the Model Space.

Ground Penetrating Radar (GPR) has been widely used in pipeline detection and underground diagnosis. In practical applications, the characteristics of the GPR data of the detected area and the likely underground anomalous structures could be rarely acknowledged before fully analyzing the obtained GPR data, causing challenges to identify the underground structures or anomalies automatically. In this article, a GPR B-scan image diagnosis method based on learning in the model space is proposed. The idea of learning in the model space is to use models fitted on parts of data as more stable and parsimonious representations of the data. For the GPR image, 2-Direction Echo State Network (2D-ESN) is proposed to fit the image segments through the next item prediction. By building the connections between the points on the image in both the horizontal and vertical directions, the 2D-ESN regards the GPR image segment as a whole and could effectively capture the dynamic characteristics of the GPR image. And then, semi-supervised and supervised learning methods could be further implemented on the 2D-ESN models for underground diagnosis. Experiments on real-world datasets are conducted, and the results demonstrate the effectiveness of the proposed model.

Measurability of quality characteristics identified in latent spaces of Generative AI Models

Deep Learning can learn complex properties from image datasets, which are difficult to model with traditional machine vision algorithms, inherently in the form of disentangled latent spaces. With latent spaces of Generative AI models, a feature extraction method to access these properties can be implemented. This work evaluates whether the learned properties can be measured in the latent space. Quantity and quantity-value scale properties and the measurability of the dimensional quality characteristic ‘filling degree’ using a linear calibration function are demonstrated for an industrial machine vision application. An uncertainty indicator between 0.4–0.9 mm is estimated for the latent space measurements.

Shift invariant subspaces in growth spaces and sets of finite entropy

AbstractWe investigate shift invariant subspaces within the realm of analytic functions in the unit disc, whose radial growth is determined by a majorant . Our main result offers a complete characterization of the shift invariant subspaces generated by Nevanlinna class functions within the aforementioned class of growth spaces. Our description is expressed in terms of a certain ‐entropy condition, which naturally arises in connection with boundary zero sets for analytic functions in the unit disc, having modulus of continuity not exceeding on the unit circle. Furthermore, we utilize our findings to establish a structural theorem on approximation in model spaces.