Dimensional Space Research Articles

A Hidden Convexity of Nonlinear Elasticity

AbstractA technique for developing convex dual variational principles for the governing PDE of nonlinear elastostatics and elastodynamics is presented. This allows the definition of notions of a variational dual solution and a dual solution corresponding to the PDEs of nonlinear elasticity, even when the latter arise as formal Euler–Lagrange equations corresponding to non-quasiconvex elastic energy functionals whose energy minimizers do not exist. This is demonstrated rigorously in the case of elastostatics for the Saint-Venant Kirchhoff material (in all dimensions), where the existence of variational dual solutions is also proven. The existence of a variational dual solution for the incompressible neo-Hookean material in 2-d is also shown. Stressed and unstressed elastostatic and elastodynamic solutions in 1 space dimension corresponding to a non-convex, double-well energy are computed using the dual methodology. In particular, we show the stability of a dual elastodynamic equilibrium solution for which there are regions of non-vanishing length with negative elastic stiffness, i.e. non-hyperbolic regions, for which the corresponding primal problem is ill-posed and demonstrates an explosive ‘Hadamard instability;’ this appears to have implications for the modeling of physically observed softening behavior in macroscopic mechanical response.

A new diagonalization based method for parallel-in-time solution of linear-quadratic optimal control problems

A new diagonalization technique for the parallel-in-time solution of linear-quadratic optimal control problems with time-invariant system matrices is introduced. The target problems are often derived from a semi-discretization of a Partial Differential Equation (PDE)-constrained optimization problem. The solution of large-scale time dependent optimal control problems is computationally challenging as the states, controls, and adjoints are coupled to each other throughout the whole time domain. This computational difficulty motivates the use of parallel-in-time methods. For time-periodic problems our diagonalization efficiently transforms the discretized optimality system into K (=number of time steps) decoupled complex valued 2n y by 2n y systems, where n y is the dimension of the state space. These systems resemble optimality systems corresponding to a steady-state version of the optimal control problem and they can be solved in parallel across the time steps, but are complex valued. For optimal control problems with initial value state equations a direct solution via diagonalization is not possible, but an efficient preconditioner can be constructed from the corresponding time periodic optimal control problem. The preconditioner can be efficiently applied parallel-in-time using the diagonalization technique. The observed number of preconditioned GMRES iterations is small and insensitive to the size of the problem discretization.

An approach to modeling the spatial interaction of point sets on integer regular grids

The paper demonstrates a generalized approach to modeling the interaction of points and point sets on integer regular grids in metric spaces. The modeling process is based on the definition of spatial relations in "Point-Set" and "Set-Set" pairs, which allows to determine the spatial interaction between arbitrary geometric objects, defined as grid-based geometric models (GGM), which represent point sets on regular grids, generalized schemes of spatial interaction are developed in the work. As a result of the work, software was developed for conducting computer experiments on simulation of interaction in metric spaces of arbitrary dimensions and visualization of their results. The developed approach was tested on data sets of different dimensions. Figs.: 10. Refs.: 11 titles.

Pattern Recognition of Alkaloids by Inhibiting the Catalytic Activity of Dopzymes for Dopamine.

Exploiting the specific recognition probe for all of the biomolecules is difficult in "lock-and-key" biosensors. The cross-reaction or the semispecific probe in pattern recognition mode is an alternative strategy through extracting a multidimensional signal array from recognition elements. Here, we design a pattern recognition sensor array based on the alkaloid-inhibited catalytic activity of dopzymes for the discrimination and determination of six alkaloids. In this sensor array, three different G-rich sequences, i.e., G-triplex (G3), G-quadruplex (GQ1), and the G-quadruplex dimer (2GQ1) possessing various peroxidase activities, conjugated with a dopamine aptamer and the dopzymes (G3-d-apt, GQ1-d-apt, and 2GQ1-d-apt) were obtained with an enhanced catalytic performance for the substrate. Through the interactions between six target alkaloids and G3, GQ1, and 2GQ1 regions, the pattern signal (6 alkaloids × 3 dopzymes × 5 replicates) was obtained from the diverse inhibited effect for the dopzyme activity. In virtue of the statistical method principal component analysis (PCA), the data array was projected into a new dimensional space to acquire the three-dimensional (3D) canonical scores and grouped into their respective clusters. The sensor array exhibited an outstanding discrimination and classification capability for six alkaloids with different concentrations with 100% accuracy. In addition, the nonspecific recognition elements of the sensor array showed high selectivity even though other alkaloids with similar structures to targets existed in the samples. Importantly, the levels of the six targets can be analyzed by the most influential discrimination factor, which represented the vector with the highest variance, evidencing that the sensor array has potential in drug screening and clinical treatment.

A Scalar Measure of Acoustic Hazard Assessment

The article addresses the problem of assessing the impact of road modernization on improving the acoustic environment. It formulates a hypothesis about the advisability of adopting the scalar dimension of the decibel space to describe acoustic hazards. It is proposed to reduce the analysis of changes in sound levels to the analysis of changes in the coefficient of exceedance of the recommended noise levels. Its value is determined by the decibel relation of dividing sound levels. The basis for the assessment of the effectiveness of the adopted solution was the analysis of the statistical characteristics of monitored exceedances of recommended noise levels, considered through the prism of the current and proposed measure. They showed greater sensitivity of the proposed coefficient in the assessment of the improvement of the acoustic climate caused by road modernization. For example, the median noise level for nights before the road modernization was 66.9 dB(A), and after the modernization 65.6 dB(A). However, the coefficient of exceedances decreased by approximately 25 %. Numerical simulations, in accordance with the Cnossos noise model, showed that reducing the speed by 10 km/h will reduce the coefficient of exceedances by approximately 20 %.

Virtual Reality Application for the Safety Improvement of Intralogistics Systems

Immersive technologies from the spectrum of Industry 4.0, such as Virtual Reality (VR), are increasingly used in research and safety analysis in industrial and intralogistics systems, including distribution warehouses and production plants. Safety in intralogistics systems is influenced by design and management processes, human behavior, and device performance. In all these areas, VR can serve as a supportive technology for visualization, testing, and employee training. However, this requires the development of principles for integrating VR into standard procedures for the design, modernization, and analysis of intralogistics and production systems. This article discusses the use of VR to analyze the occupational and functional safety of intralogistics systems. It reviews the literature and VR implementations aimed at examining and improving safety in industrial systems. The article explores the integration of VR into the design and analysis procedures for intralogistics and production systems. The authors present a five-dimensional decision space for assessing the use of VR, including identifying subjects of safety analysis, threats and hazards specific to intralogistics, countermeasures for these threats, factors affecting safety, and mechanisms by which VR can improve safety in intralogistics systems. As a subsequent step, the authors discuss using universal simulation environments that support VR technology to study and enhance safety in intralogistics systems, providing a framework example based on the FlexSim (2023 update 2) environment. Finally, this article addresses the threats and limitations of VR technology, along with the challenges and future prospects of VR in the context of Industry 4.0. The article concludes that VR can be an essential tool for increasing safety in the future, albeit with some reservations about certain features of this technology.

Hybrid genetic optimization for quantum feature map design

Kernel methods are an import class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be linearly separable in feature space. Previous work has shown that quantum feature map design can be automated for a given dataset using NSGA-II, a genetic algorithm, while both minimizing circuit size and maximizing classification accuracy. However, the evaluation of the accuracy achieved by a candidate feature map is costly. In this work, we demonstrate the suitability of kernel-target alignment as a substitute for accuracy in genetic algorithm-based quantum feature map design. Kernel-target alignment is faster to evaluate than accuracy and does not require some data points to be reserved for its evaluation. To further accelerate the evaluation of genetic fitness, we provide a method to approximate kernel-target alignment. To improve kernel-target alignment and root mean squared error, the final trainable parameters of the generated circuits are further trained using COBYLA to determine whether a hybrid approach applying conventional circuit parameter training can easily complement the genetic structure optimization approach. A total of eight new approaches are compared to the original across nine varied binary classification problems from the UCI machine learning repository, showing that kernel-target alignment and its approximation produce feature map circuits enabling comparable accuracy to the previous work but with larger margins on training data (in excess of 20% larger) that improve further with circuit parameter training.

Bayesian Federated Learning with Hamiltonian Monte Carlo: Algorithm and Theory

This work introduces a novel and efficient Bayesian federated learning algorithm, namely, the Federated Averaging stochastic Hamiltonian Monte Carlo (FA-HMC), for parameter estimation and uncertainty quantification. We establish rigorous convergence guarantees of FA-HMC on non-iid distributed data sets, under the strong convexity and Hessian smoothness assumptions. Our analysis investigates the effects of parameter space dimension, noise on gradients and momentum, and the frequency of communication (between the central node and local nodes) on the convergence and communication costs of FA-HMC. Beyond that, we establish the tightness of our analysis by showing that the convergence rate cannot be improved even for continuous FA-HMC process. Moreover, extensive empirical studies demonstrate that FA-HMC outperforms the existing Federated Averaging-Langevin Monte Carlo (FA-LD) algorithm.

Semigroups of linear transformations whose restrictions belong to a general linear group

Let V be a vector space and U a fixed subspace of V. We denote the semigroup of all linear transformations on V under composition of functions by L(V). In this paper, we study the semigroup of all linear transformations on V whose restrictions belong to the general linear group GL(U), denoted by L GL ( U ) ( V ) . More precisely, we consider the subsemigroup L GL ( U ) ( V ) = { α ∈ L ( V ) : α | U ∈ GL ( U ) } of L(V). In this work, Green’s relations and ideals of this semigroup are described. Then we also determine the minimal ideal and the set of all minimal idempotents of it. Moreover, we establish an isomorphism theorem when V is a finite dimensional vector space over a finite field. Finally, we find its generating set.

Reconstruction of OFDM Signals Using a Dual Discriminator CGAN with BiLSTM and Transformer

Communication signal reconstruction technology represents a critical area of research within communication countermeasures and signal processing. Considering traditional OFDM signal reconstruction methods’ intricacy and suboptimal reconstruction performance, a dual discriminator CGAN model incorporating LSTM and Transformer is proposed. When reconstructing OFDM signals using the traditional CNN network, it becomes challenging to extract intricate temporal information. Therefore, the BiLSTM network is incorporated into the first discriminator to capture timing details of the IQ (In-phase and Quadrature-phase) sequence and constellation map information of the AP (Amplitude and Phase) sequence. Subsequently, following the addition of fixed position coding, these data are fed into the core network constructed based on the Transformer Encoder for further learning. Simultaneously, to capture the correlation between the two IQ signals, the VIT (Vision in Transformer) concept is incorporated into the second discriminator. The IQ sequence is treated as a single-channel two-dimensional image and segmented into pixel blocks containing IQ sequence through Conv2d. Fixed position coding is added and sent to the Transformer core network for learning. The generator network transforms input noise data into a dimensional space aligned with the IQ signal and embedding vector dimensions. It appends identical position encoding information to the IQ sequence before sending it to the Transformer network. The experimental results demonstrate that, under commonly utilized OFDM modulation formats such as BPSK, QPSK, and 16QAM, the time series waveform, constellation diagram, and spectral diagram exhibit high-quality reconstruction. Our algorithm achieves improved signal quality while managing complexity compared to other reconstruction methods.

Leisure reimagined: mapping the enablers of restorative servicescapes

ABSTRACT Servicescapes play a crucial role in the marketing strategies of contact-based service businesses, significantly influencing consumer experiences and well-being. Researchers have explored their potential impact on stress levels and attention restoration from various perspectives, including environmental psychology, perceived sensory dimensions and evidence-based design. This study builds upon existing knowledge by employing Interpretive Structural Modelling and MICMAC Analysis to identify the enablers that contribute to the restorative quality of a leisure servicescape. The current research reveals that enhancing servicescape restorativeness involves integrating elements such as refuge, culture, complexity, typicality, accessibility, familiarity, hygiene, space, calmness, legibility, biophilic designs and social dimension. Additionally, the investigation into the interrelationships among these factors highlights the pivotal roles of refuge and culture, influencing the efficacy of most other enablers. Servicescape typicality, however, relies heavily on the operationalization of other enablers. Notably, none of these enablers operates independently in promoting a restorative servicescape. Their interconnected associations underscore the importance for marketers in the leisure service industry to comprehend and leverage the interplay of these factors to achieve optimal results in enhancing the restorative property of their servicescapes. The study concludes by offering recommendations for marketers and policymakers to improve consumer and citizen well-being in a sustainable manner.

A Property that Characterizes the Enneper Surface and Helix Surfaces

The main goal of this paper is to show that helix surfaces and the Enneper surface are the only surfaces in the 3-dimensional Euclidean space R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^{3}$$\\end{document} whose isogonal lines are generalized helices and pseudo-geodesic lines.

Structure-preserving semi-convex-splitting numerical scheme for a Cahn–Hilliard cross-diffusion system in lymphangiogenesis

A fully discrete semi-convex-splitting finite-element scheme with stabilization for a Cahn–Hilliard cross-diffusion system is analyzed. The system consists of parabolic fourth-order equations for the volume fraction of the fiber phase and solute concentration, modeling pre-patterning of lymphatic vessel morphology. The existence of discrete solutions is proved, and it is shown that the numerical scheme is energy stable up to stabilization, conserves the solute mass, and preserves the lower and upper bounds of the fiber phase fraction. Numerical experiments in two space dimensions using FreeFem illustrate the phase segregation and pattern formation.

Fixed-Point Theorems for Fuzzy Mappings

Since the 1970s and 1980s, significant contributions have been made by Weiss, Butnariu, Heilpern, Chitra, Subrahmanyam, and others, extending fixed-point theorems to fuzzy mappings and topological spaces. This paper provides two generalizations of two important fixed-point theorems, one provided by Butnariu and the other provided by Chitra. The first generalization ensures that, under certain conditions, an acyclic fuzzy mapping has a fixed point. The second result ensures the existence of a point in the intersection of two or more fuzzy mappings considering contractible finite dimensional ANR spaces, which is a generalization of the statement provided by Chitra.

Exploration-Exploitation and Suicidal Behavior in Borderline Personality Disorder and Depression

Clinical theory and behavioral studies suggest that people experiencing suicidal crisis are often unable to find constructive solutions or incorporate useful information into their decisions, resulting in premature convergence on suicide and neglect of better alternatives. However, prior studies of suicidal behavior have not formally examined how individuals resolve the tradeoffs between exploiting familiar options and exploring potentially superior alternatives. To investigate exploration and exploitation in suicidal behavior from the formal perspective of reinforcement learning. Two case-control behavioral studies of exploration-exploitation of a large 1-dimensional continuous space and a 21-day prospective ambulatory study of suicidal ideation were conducted between April 2016 and March 2022. Participants were recruited from inpatient psychiatric units, outpatient clinics, and the community in Pittsburgh, Pennsylvania, and underwent laboratory and ambulatory assessments. Adults diagnosed with borderline personality disorder (BPD) and midlife and late-life major depressive disorder (MDD) were included, with each sample including demographically equated groups with a history of high-lethality suicide attempts, low-lethality suicide attempts, individuals with BPD or MDD but no suicide attempts, and control individuals without psychiatric disorders. The MDD sample also included a subgroup with serious suicidal ideation. Behavioral (model-free and model-derived) indices of exploration and exploitation, suicide attempt lethality (Beck Lethality Scale), and prospectively assessed suicidal ideation. The BPD group included 171 adults (mean [SD] age, 30.55 [9.13] years; 135 [79%] female). The MDD group included 143 adults (mean [SD] age, 62.03 [6.82] years; 81 [57%] female). Across the BPD (χ23 = 50.68; P < .001) and MDD (χ24 = 36.34; P < .001) samples, individuals with high-lethality suicide attempts discovered fewer options than other groups as they were unable to shift away from unrewarded options. In contrast, those with low-lethality attempts were prone to excessive behavioral shifts after rewarded and unrewarded actions. No differences were seen in strategic early exploration or in exploitation. Among 84 participants with BPD in the ambulatory study, 56 reported suicidal ideation. Underexploration also predicted incident suicidal ideation (χ21 = 30.16; P < .001), validating the case-control results prospectively. The findings were robust to confounds, including medication exposure, affective state, and behavioral heterogeneity. The findings suggest that narrow exploration and inability to abandon inferior options are associated with serious suicidal behavior and chronic suicidal thoughts. By contrast, individuals in this study who engaged in low-lethality suicidal behavior displayed a low threshold for taking potentially disadvantageous actions.

Community childhood obesity assessment in elementary school, anthropometric indices as screening tools: a community cross-sectional study in Indonesia

BackgroundRepresentative anthropometric epidemiological data are needed to formulate screening and intervention methods to prevent obesity in children. This study aims to conduct community childhood obesity assessment in elementary school based...

Separation and Extraction of Compound-Fault Signal Based on Multi-Constraint Non-Negative Matrix Factorization

To solve the separation of multi-source signals and detect their features from a single channel, a signal separation method using multi-constraint non-negative matrix factorization (NMF) is proposed. In view of the existing NMF algorithm not performing well in the underdetermined blind source separation, the β-divergence constraints and determinant constraints are introduced in the NMF algorithm, which can enhance local feature information and reduce redundant components by constraining the objective function. In addition, the Sine-bell window function is selected as the processing method for short-time Fourier transform (STFT), and it can preserve the overall feature distribution of the original signal. The original vibration signal is first transformed into time–frequency domain with the STFT, which describes the local characteristic of the signal from the time–frequency distribution. Then, the multi-constraint NMF is applied to reduce the dimensionality of the data and separate feature components in the low dimensional space. Meanwhile, the parameter WK is constructed to filter the reconstructed signal that recombined with the feature component in the time domain. Ultimately, the separated signals will be subjected to envelope spectrum analysis to detect fault features. The simulated and experimental results indicate the effectiveness of the proposed approach, which can realize the separation of multi-source signals and their fault diagnosis of bearings. In addition, it is also confirmed that the proposed method, juxtaposed with the NMF algorithm of the traditional objective function, is more applicable for compound fault diagnosis of the rotating machinery.

Separation and Extraction of Compound-Fault Signal Based on Multi-Constraint Non-Negative Matrix Factorization

To solve the separation of multi-source signals and detect their features from a single channel, a signal separation method using multi-constraint non-negative matrix factorization (NMF) is proposed. In view of the existing NMF algorithm not performing well in the underdetermined blind source separation, the β-divergence constraints and determinant constraints are introduced in the NMF algorithm, which can enhance local feature information and reduce redundant components by constraining the objective function. In addition, the Sine-bell window function is selected as the processing method for short-time Fourier transform (STFT), and it can preserve the overall feature distribution of the original signal. The original vibration signal is first transformed into time–frequency domain with the STFT, which describes the local characteristic of the signal from the time–frequency distribution. Then, the multi-constraint NMF is applied to reduce the dimensionality of the data and separate feature components in the low dimensional space. Meanwhile, the parameter WK is constructed to filter the reconstructed signal that recombined with the feature component in the time domain. Ultimately, the separated signals will be subjected to envelope spectrum analysis to detect fault features. The simulated and experimental results indicate the effectiveness of the proposed approach, which can realize the separation of multi-source signals and their fault diagnosis of bearings. In addition, it is also confirmed that the proposed method, juxtaposed with the NMF algorithm of the traditional objective function, is more applicable for compound fault diagnosis of the rotating machinery.

Exponentially improved efficient machine learning for quantum many-body states with provable guarantees

Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an m-dimensional space of physical parameters, the ground state and its properties at an arbitrary parameter configuration can be predicted via a machine learning protocol up to a prescribed prediction error ɛ, provided that a sample set (of size N) of the states can be efficiently prepared and measured. In a recent work [Huang , ], a rigorous guarantee for such a generalization was proved. Unfortunately, an exponential scaling for the provable sample complexity, N=mO(1ɛ), was found to be universal for generic gapped Hamiltonians. This result applies to the situation where the dimension of the parameter space is large, while the scaling with the accuracy is not an urgent factor, not entering the realm of more precise learning and prediction. In this work, we consider an alternative relevant scenario, where the effective dimension m is a finite, not necessarily large constant, while the scaling with the prediction error becomes the central concern. By jointly preserving the fundamental properties of density matrices in the learning protocol and utilizing the continuity of quantum states in the parameter range of interest, we rigorously obtain a polynomial sample complexity for predicting quantum many-body states and their properties, with respect to the prediction error ɛ and the number of qubits, n, with N=poly(ɛ−1,n,ln1δ), where poly denotes a polynomial function, and (1−δ) is the probability of success. Moreover, if restricted to learning local quantum-state properties, the number of samples can be further reduced to N=poly(ɛ−1,lnnδ). Numerical demonstrations confirm our findings, and an alternative approach utilizing statistical learning theory with reproducing kernel Hilbert space achieves consistent results. The mere continuity assumption indicates that our results are not restricted to gapped Hamiltonian systems and properties within the same phase. Published by the American Physical Society 2024

Research on the Effective Sheltering Rates of Public Buildings in Villages in Western Sichuan, China—A Case Study of Ganbao Tibetan Village

The western region of Sichuan Province, located in the Hengduan Mountains, is one of China’s most seismically active zones. Due to limited land resources, many villages in western Sichuan Province are situated in mountainous and valley areas, facing harsh climatic conditions, lagging economic development, and insufficient infrastructure. After experiencing seismic disasters, these villages often encounter challenges, such as cut-off mountain roads, difficulties in delivering relief supplies, and sharply a significant drop in nighttime temperatures due to the high-altitude climate. Consequently, in the case of the economic underdevelopment and limited resources, how to repurpose existing buildings for disaster relief has become a crucial issue for disaster prevention and mitigation in these villages. This paper takes Ganbao Tibetan Village, located in the alpine gorge regions of western Sichuan Province, as a case study. It evaluates the interior space utilization status of different types of existing public buildings during disasters, calculates the effective utilization rate of interior space disaster reduction conversion based on the spatial layout model, and extracts the typical interior space dimensions that are conducive to disaster relief and conversion of public buildings based on the interior space utilization characteristics of disaster relief. This study provides a reference for the design of public service buildings considering the requirements of disaster resilience transformation.