Dimensional Space Research Articles

Hausdorff dimension of the parameters for (α,β)-shifts with the specification property

In this paper, we consider the specification property for ( α , β ) -shifts. When α = 0 , Schmeling shows that the set of β > 1 for which the β-shift has the specification property has the Lebesgue measure zero but has the full Hausdorff dimension [Schmeling. Symbolic dynamics for β-shifts and self-normal numbers, Ergodic Theory Dyn. Syst. 17 (1997), pp. 675–694]. So it is natural to ask what happens when α > 0 . Buzzi shows that for fixed α the set of β > 1 for which the ( α , β ) -shift has the specification property has Lebesgue measure zero. Hence we consider the Hausdorff dimension of the parameter space of ( α , β ) -shifts.

Forecasting Urban Traffic States with Sparse Data Using Hankel Temporal Matrix Factorization

Forecasting urban traffic states is crucial to transportation network monitoring and management, playing an important role in the decision-making process. Despite the substantial progress that has been made in developing accurate, efficient, and reliable algorithms for traffic forecasting, most existing approaches fail to handle sparsity, high-dimensionality, and nonstationarity in traffic time series and seldom consider the temporal dependence between traffic states. To address these issues, this work presents a Hankel temporal matrix factorization (HTMF) model using the Hankel matrix in the lower dimensional spaces under a matrix factorization framework. In particular, we consider an alternating minimization scheme to optimize the factor matrices in matrix factorization and the Hankel matrix in the lower dimensional spaces simultaneously. To perform traffic state forecasting, we introduce two efficient estimation processes on real-time incremental data, including an online imputation (i.e., reconstruct missing values) and an online forecasting (i.e., estimate future data points). Through extensive experiments on the real-world Uber movement speed data set in Seattle, Washington, we empirically demonstrate the superior forecasting performance of HTMF over several baseline models and highlight the advantages of HTMF for addressing sparsity, nonstationarity, and short time series. History: Accepted by Ram Ramesh, Area Editor for Data Science & Machine Learning. Funding: This research was supported by the Institute for Data Valorisation, the Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation, the National Natural Science Foundation of China [Grants 12371456, 72101049, 72232001], the Sichuan Science and Technology Program [Grant 2024NSFJQ0038], and the Fundamental Research Funds for the Central Universities [Grant DUT23RC(3)045].

A variational approach to stability relative to a set of single-valued and set-valued mappings

Based on the limiting normal cone relative to a set, we present in this paper the novel versions of the limiting coderivative relative to a set and subdifferentials relative to a set of multifunctions and singleton mappings, respectively. In addition to giving the necessary and sufficient conditions for the Aubin property relative to a set of multifunctions, the limiting coderivative relative to a set also provides a coderivative criterion for the metric regularity relative to a set of multifunctions. Besides, our study establishes sudifferential characteristics of the metric regularity and the locally Lipschitz continuity relative to a set for single-valued mappings. In finite dimensional spaces, our results are more general than the previous results. Furthermore, we also give examples to illustrate our results.

Eigenbin compression for reducing photon-counting CT data size.

Photon-counting CT (PCCT) systems acquire multiple spectral measurements at high spatial resolution, providing numerous image quality benefits while also increasing the amount of data that must be transferred through the gantry slip ring. This study proposes a lossy method to compress photon-counting CT data using eigenvector analysis, with the goal of providing image quality sufficient for applications that require a rapid initial reconstruction, such as to confirm anatomical coverage, scan quality, and to support automated advanced applications. The eigenbin compression method was experimentally evaluated on a clinical silicon PCCT prototype system. The proposed eigenbin method performs principal component analysis (PCA) on a set of PCCT calibration measurements. PCA finds the orthogonal axes or eigenvectors, which capture the maximum variance in the N dimensional photon-count data space, where N is the number of acquired energy bins. To reduce the dimensionality of the PCCT data, the data are linearly transformed into a lower dimensional space spanned by the M<N eigenvectors with highest eigenvalues (i.e., the vectors that account for most of the information in the data). Only M coefficients are then transferred per measurement, which we term eigenbin values. After transmission, the original N energy-bin measurements are estimated as a linear combination of the M eigenvectors. Two versions of the eigenbin method were investigated: pixel-specific and pixel-general. The pixel-specific eigenbin method determines eigenvectors for each individual detector pixel, while the more practically realizable pixel-general eigenbin method finds one set of eigenvectors for the entire detector array. The eigenbin method was experimentally evaluated by scanning a 20cm diameter Gammex Multienergy phantom with different material inserts on a clinical silicon-based PCCT prototype. The method was evaluated with the number of eigenbins varied between two and four. In each case, the eigenbins were used to estimate the original 8-bin data, after which material decomposition was performed. The mean, standard deviation, and contrast-to-noise ratio (CNR) of values in the reconstructed basis and virtual monoenergetic images (VMI) were compared for the original 8-bin data and for the eigenbin data. The pixel-specific eigenbin method reduced photon-counting CT data size by a factor of four with<5% change in mean values and a small noise penalty (mean change in noise of<12%, maximum change in noise of 20% for basis images). The pixel-general eigenbin compression method reduced data size by a factor of 2.67 with<5% change in mean values and a less than 10% noise penalty in the basis images (average noise penalty≤5%). The noise penalty and errors were less for the VMIs than for the basis images, resulting in<5% change in CNR in the VMIs. The eigenbin compression method reduced photon-counting CT data size by a factor of two to four with less than 5% change in mean values, noise penalty of less than 10%-20%, and change in CNR ranging from 15% decrease to 24% increase. Eigenbin compression reduces the data transfer time and storage space of photon-counting CT data for applications that require rapid initial reconstructions.

Radiation of the energy-critical wave equation with compact support

We prove exterior energy lower bounds for (nonradial) solutions to the energy-critical nonlinear wave equation in space dimensions 3≤d≤5, with compactly supported initial data. In particular, it is shown that nontrivial global solutions with compact spatial support must be radiative in a sharp sense. In space dimensions 3 and 4, a nontrivial soliton background is also considered. As an application, we obtain partial results on the rigidity conjecture concerning solutions with the compactness property, including a new proof for the global existence of such solutions.

DMMGNet: A Discrimination Mapping and Memory Bank Mean Guidance-based Network for High-performance Few-shot Industrial Anomaly Detection

For deep learning-based industrial anomaly detection, it is still challenging to get adequate images for model training and achieve cold start for cross-product migration, restricting their practical application in real industrial production. Herein, an innovative few-shot anomaly detection network DMMGNet based on discrimination mapping and memory bank mean guidance strategies are demonstrated, which is trained by a new two-branch data augmentation technique. By separating the features stored in memory bank from the features used for training, the two-branch data augmentation method can significantly improve the robustness of few-shot model training and reduce the redundance of memory bank. In the elaborately designed discrimination mapping module, new negative samples are generated by adding dynamic Gaussian noise to normal samples along the channel dimension in feature space to solve the problem of sample imbalance. Meanwhile, the discrimination mapping module also helps to map the feature distribution of positive samples to the target domain more efficiently and reduce the deviation of feature domain, conducive to a more precise separation of positive and negative samples. In addition, a novel mean guidance approach with an optimized loss function is developed to guide the positive sample feature mapping by specifying the local feature space center to form a clear feature domain contour and enhance the detection accuracy. The multiple experimental results validate that our DMMGNet outperforms the most advanced anomaly detection counterparts on image-level AUROC, showing an increase by 0.3-3% on both MVTec AD and MPDD benchmarks under several few-shot scenarios.

Gravitational wave signal extraction against non-stationary instrumental noises with deep neural network

Sapce-borne gravitational wave antennas, such as LISA and LISA-like mission (Taiji and Tianqin), will offer novel perspectives for exploring our Universe while introduce new challenges, especially in data analysis. Aside from the known challenges like high parameter space dimension, superposition of large number of signals etc., gravitational wave detections in space would be more seriously affected by anomalies or non-stationarities in the science measurements. Considering the three types of foreseeable non-stationarities including data gaps, transients (glitches), and time-varying noise auto-correlations, which may come from routine maintenance or unexpected disturbances during science operations, we developed a deep learning model for accurate signal extractions confronted with such anomalous scenarios. Our model exhibits the same performance as the current state-of-the-art models do for the ideal and anomaly free scenario, while shows remarkable adaptability in extractions of coalescing massive black hole binary signal against all three types of non-stationarities and even their mixtures. This also provide new explorations into the robustness studies of deep learning models for data processing in space-borne gravitational wave missions.

Constructing all BPS black hole microstates from the gravitational path integral

Understanding how to prepare and count black hole micro-states by using the gravitational path integral is one of the most important problems in quantum gravity. Nevertheless, a state-by-state count of black hole microstates is difficult because the apparent number of degrees of freedom available in the gravitational effective theory can vastly exceed the entropy of the black hole, even in the special case of BPS black holes. In this paper, we show that we can use the gravitational path integral to prepare a basis for the Hilbert space of all BPS black hole microstates. We find that the dimension of this Hilbert space computed by an explicit state count is in complete agreement with the degeneracy obtained from the Gibbons-Hawking prescription. Specifically, this match includes all non-perturbative corrections in 1/GN. Such corrections are, in turn, necessary in order for this degeneracy of BPS states to match the non-perturbative terms in the 1/GN expansion in the string theory count of such microstates.

Efficient six-dimensional phase space reconstructions from experimental measurements using generative machine learning

Efficient six-dimensional phase space reconstructions from experimental measurements using generative machine learning

An automated convergence diagnostic for phylogenetic MCMC analyses.

Assessing convergence of Markov chain Monte Carlo (MCMC) based analyses is crucial but challenging, especially so in high dimensional and complex spaces such as the space of phylogenetic trees (treespace). In practice, it is assumed that the target distribution is the unique stationary distribution of the MCMC and convergence is achieved when samples appear to be stationary. Here we leverage recent advances in computational geometry of the treespace and introduce a method that combines classical statistical techniques and algorithms with geometric properties of the treespace to automatically evaluate and assess practical convergence of phylogenetic MCMC analyses. Our method monitors convergence across multiple MCMC chains and achieves high accuracy in detecting both practical convergence and convergence issues within treespace. Furthermore, our approach is developed to allow for real-time evaluation during the MCMC algorithm run, eliminating any of the chain post-processing steps that are currently required. Our tool therefore improves reliability and efficiency of MCMC based phylogenetic inference methods and makes analyses easier to reproduce and compare. We demonstrate the efficacy of our diagnostic via a well-calibrated simulation study and provide examples of its performance on real data sets. Although our method performs well in practice, a significant part of the underlying treespace probability theory is still missing, which creates an excellent opportunity for future mathematical research in this area. The open source package for the phylogenetic inference framework BEAST2, called ASM, that implements these methods, making them accessible through a user-friendly GUI, is available from https://github.com/rbouckaert/asm/. The open source Python package, called tetres, that provides an interface for these methods enabling their applications beyond BEAST2 can be accessed at https://github.com/bioDS/tetres/.

China's logistics evolution: A study of development characteristics and catalytic effects on economic growth.

The impact of logistics development on the economy covers many aspects, such as production, cost, employment, international trade, etc. It is an indispensable part of the modern economy, which helps to improve overall economic efficiency and social prosperity. This study studies the spatiotemporal dynamic evolution characteristics of China's logistics development from 2008 to 2018 and explores its impact on economic growth in multiple dimensions of time and space. The research findings indicate the following: (1) From 2008 to 2018, China's logistics development level (LDL) exhibited a clear upward trend. The differences between the eastern, central, and western regions showed fluctuating downward patterns, ultimately converging towards a high-level concentration. Concerning spatial distribution, China's logistics development demonstrated a trend towards the west and south. However, the spatial pattern of "strong in the east and weak in the west " has existed for a long time. Moreover, the "T-shaped" pattern between coastal provinces and those along the Yangtze River Basin deepened, and the LDL in the central and western regions significantly improved. (2) The advancement of China's LDL effectively promotes its economic growth, confirming that the Belt and Road Initiative enhances the role of logistics development in driving economic growth. Regarding regional differences, logistics development positively influences economic growth in the eastern and western regions, with a less significant impact on the central region. Regarding the strength of influence, logistics development has a more substantial effect on promoting high-ranking provinces in the entire country, the eastern region, and the central region, as well as boosting economic growth in low-ranking provinces in the western region.

Aflatoxin contamination level estimation in food using reflectance multispectral imaging based system

This study presents a non-invasive, non-destructive, and rapid method of classifying and estimating aflatoxin levels in food samples using a multispectral imaging. A cost effective, mass deployable in-house built multispectral imaging system, suitable for onsite testing and operating in range from 365 nm to 940 nm, is utilized to capture the multispectral images of the aflatoxin contaminated bread samples. Spatial and spectral corrections are performed to mitigate the imperfections of the multispectral imaging system, followed by image preprocessing steps to mitigate the effect of random noise. Linear discriminant analysis is used to reduce the dimensionality of the feature space. Ensemble classification analysis utilizing classical machine learning classifiers yielded an accuracy of 90 % when classifying samples according to aflatoxin contamination levels. A functional relationship between the Bhattacharyya distance of noncontaminated samples to contaminated samples and aflatoxin contamination levels was modeled as a first order polynomial with an R2 value of 0.9723.

Prior knowledge embedding convolutional autoencoder: A single-source domain generalized fault diagnosis framework under small samples

The proposed transfer learning-based fault diagnosis models have achieved good results in multi-source domain generalization (MDG) tasks. However, research on single-source domain generalization (SDG) is relatively scarce, and the limited availability of small training samples is seldom considered. Therefore, to address the insufficient feature extraction capability and poor generalization performance of existing models on single-source domain small sample data, a novel single-source domain generalization fault diagnosis (SDGFD) framework, the prior knowledge embedded convolutional autoencoder (PKECA), is proposed. During the training phase, first, single-source domain data are used to construct prior features based on the time domain, frequency domain, and time-frequency domain. Second, a prior knowledge embedding structure based on the convolutional autoencoder is built, which compresses the prior knowledge and original vibration data into a high-dimensional space of consistent dimensions, embedding the prior knowledge into the features corresponding to the vibration data using a mean squared error loss function. Subsequently, the proposed centroid-based self-supervised learning (CBSSL) strategy further constrains high-dimensional features, improving the generalization ability. The designed sparse regularized activation (SRA) function significantly enhances the regularization effect on features. During the testing phase, it is only necessary to input the data from the unknown domain to identify the fault types. The experimental results show that the proposed method achieves superior performance in fault diagnosis tasks involving cross-speed, time-varying speed, and small sample data in SDGFD, demonstrating that PKECA has strong generalizability. The code can be found here: https://github.com/John-520/PKECA. © 2024 Elsevier Science. All rights reserved

Two grasses differ in their absorptive root physiological traits and rooting depth under drought in an alpine steppe.

Absorptive root traits play important roles in acquisition of water and nutrients from soil by plants. Despite numerous reports on the changes in species dominance under long-term drought in grassland community, few studies have specifically investigated absorptive root traits of these dominant species in grasslands, especially in the alpine grasslands. Here, two grass species (Leymus secalinus and Stipa purpurea) differing in their responses to drought were selected from an alpine steppe. A series of absorptive root traits were examined under drought in a 3-year glasshouse experiment. We found that drought had no effects on root morphological and architectural traits, whereas root physiological traits and rooting depth differed in their responses to drought. Specifically, drought significantly reduced root respiration and enhanced organ carbon (C) exudation rate, carboxylate exudation rate, acid phosphatase activity and rooting depth of L. secalinus. Particularly, L. secalinus released more citrate into the rhizosphere under drought than S. purpurea. In contrast, these root traits of S. purpurea remained relatively unchanged in response to the drought. These differential responses would render L. secalinus more competitive in acquisition of nutrients and water, thus contributing to its dominance in the community under drought. Moreover, root respiration was negatively correlated with organic C exudation rate, carboxylate exudation rate and acid phosphatase activity, indicating a tradeoff between root respiration and root exudates to acquire nutrients and water by optimizing C allocation under drought. Additionally, all root traits exhibited two independent dimensions in root economic space (RES) for both species under drought. These results indicate that the plant species with great capacity to acquire water and nutrients in soil by optimizing C allocation under drought will be dominant in the community of the alpine grasslands. These findings provide an important insight into species re-ordering under drought on the Tibetan Plateau.

A 5D super-extreme-multistability hyperchaotic map based on parallel-cascaded memristors

A new 5-dimensional discrete memristors-based hyperchaotic map (5DMHM) is constructed by introducing four charge-controlled discrete memristors (DMs, coupled through parallel-cascade mixing operation) into the sine map. This 5DMHM has 4-dimensional space fixed points and its stability distributions are partitioned in coupling strength, memristor initial condition, and parameter planes. The dynamics of the map are investigated by employing 2D dynamical behavior and the first Lyapunov exponent (LE) distribution. The super extreme multistability is discovered through the basin of attraction, the initial-value-dependent LE spectra, bifurcation diagrams, the mean value of state variables, and trajectory plots. Moreover, a high level of complexity can be observed by calculating the spectral entropy complexity for various parameter planes. Subsequently, a microcontroller-based digital circuit is designed to implement the 5DMHM. The security analysis of the pseudorandom number generator (PRNG) designed by the 5DMHM is presented and the PRNG passes the NIST SP800-22 test. The comparison of the 5DMHM with the recent maps indicates a higher performance in secure communication and image encryption.

Semantic redundancy-aware implicit neural compression for multidimensional biomedical image data

The surge in advanced imaging techniques has generated vast biomedical image data with diverse dimensions in space, time and spectrum, posing big challenges to conventional compression techniques in image storage, transmission, and sharing. Here, we propose an intelligent image compression approach with the first-proved semantic redundancy of biomedical data in the implicit neural function domain. This Semantic redundancy based Implicit Neural Compression guided with Saliency map (SINCS) can notably improve the compression efficiency for arbitrary-dimensional image data in terms of compression ratio and fidelity. Moreover, with weight transfer and residual entropy coding strategies, it shows improved compression speed while maintaining high quality. SINCS yields high quality compression with over 2000-fold compression ratio on 2D, 2D-T, 3D, 4D biomedical images of diverse targets ranging from single virus to entire human organs, and ensures reliable downstream tasks, such as object segmentation and quantitative analyses, to be conducted at high efficiency.

Approximation of Classical Two-Phase Flows of Viscous Incompressible Fluids by a Navier–Stokes/Allen–Cahn System

We show convergence of the Navier–Stokes/Allen–Cahn system to a classical sharp interface model for the two-phase flow of two viscous incompressible fluids with same viscosities in a smooth bounded domain in two and three space dimensions as long as a smooth solution of the limit system exists. Moreover, we obtain error estimates with the aid of a relative entropy method. Our results hold provided that the mobility mε>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_\\varepsilon >0$$\\end{document} in the Allen–Cahn equation tends to zero in a subcritical way, i.e., mε=m0εβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_\\varepsilon = m_0 \\varepsilon ^\\beta $$\\end{document} for some β∈(0,2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta \\in (0,2)$$\\end{document} and m0>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_0>0$$\\end{document}. The proof proceeds by showing via a relative entropy argument that the solution to the Navier–Stokes/Allen–Cahn system remains close to the solution of a perturbed version of the two-phase flow problem, augmented by an extra mean curvature flow term mεHΓt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_\\varepsilon H_{\\Gamma _t}$$\\end{document} in the interface motion. In a second step, it is easy to see that the solution to the perturbed problem is close to the original two-phase flow.

Social and environmental dimensions of public spaces of the indigenous territory of the Sierra de Manantlan mountain range, Jalisco state, western Mexico

The social and environmental dimension of the public space occupants of the indigenous territory of the Sierra de Manantlan, Jalisco, has a crucial place in the heritage of Mexico, such is the case of its form of idiosyncrasy, mutual interaction, and coexistence. The cultural, political, and economic organizations the Sierra de Manantlan mark an identity of the native peoples, where their customs, communal life, and solidarity work are preserved. The research objective was to evaluate the social perception and environmental habitability conditions of public space occupants in the towns of Chacala and Telcruz. Therefore, semi-structured interviews were conducted for the primary actors in both study areas and 259 information cards were applied to the inhabitants with data regarding social interaction variables and meteorological conditions in two seasons (summer and winter of a calendar year). Regarding data analysis and statistical purposes, the Pearson and Spearman correlations was used according to the needs of the study. The results revealed that the occupants of public spaces mostly report the pleasure of interacting in said spaces; however, they indicate that they would like an intervention or remodeling in the place that would encourage greater interaction with their neighbors, family, and friends. Another additional fact is that climatic variables, especially in summer, harm the desire to attend or stay in said spaces because of the lack of natural elements or bioclimatic devices that mitigate the environmental impact.

Connected k-Center and k-Diameter Clustering

AbstractMotivated by an application from geodesy, we study the connected k-center problem and the connected k-diameter problem. The former problem has been introduced by Ge et al. (ACM Trans Knowl Discov Data 2(2):1–35, 2008. https://doi.org/10.1145/1376815.1376816) to model clustering of data sets with both attribute and relationship data. These problems arise from the classical k-center and k-diameter problems by adding a side constraint. For the side constraint, we are given an undirected connectivity graphG on the input points, and a clustering is now only feasible if every cluster induces a connected subgraph in G. Usually in clustering problems one assumes that the clusters are pairwise disjoint. We study this case but additionally also the case that clusters are allowed to be non-disjoint. This can help to satisfy the connectivity constraints. Our main result is an $$O(\log ^2k)$$ O ( log 2 k ) -approximation algorithm for the disjoint connected k-center and k-diameter problem. For Euclidean spaces of constant dimension and for metrics with constant doubling dimension, the approximation factor improves to O(1). Our algorithm works by computing a non-disjoint connected clustering first and transforming it into a disjoint connected clustering. We complement these upper bounds by several upper and lower bounds for variations and special cases of the model.

FF-RRT*: A Sampling-Based Planner for Multirobot Global Formation Path Planning

Abstract This article presents a collision-free global path planning approach for multirobot systems called flexible formation—rapidly exploring randomized trees* (FF-RRT*). The algorithm is based on RRT* and provides a flexible and efficient representation of the formation geometry independent of the number of robots. It is designed to generate optimal paths for multirobot systems in a five-dimensional configuration space comprising the formation centroid, orientation, and scaling. An affine transformation is used to convert the path in the configuration space to the workspace of the robots. The proposed method employs a new distance function that eliminates the need for tuning weights and a sampling scheme for scaling factors to avoid inter-robot collisions. FF-RRT* is experimentally demonstrated using nonholonomic wheeled mobile robots and is effective in planning the collective motion of the robots. Robots could collectively reach goals by squeezing through narrow gaps and splitting and merging around large obstacles.