Dimensional Space Research Articles

Leveraging multi-output modelling for CIELAB using colour difference formula towards sustainable textile dyeing

Textile dyeing requires optimizing combinations of ingredients and process parameters to achieve target colour properties. Modelling the complex relationships between these factors and the resulting colour is challenging. In this case, a physics-informed approach for multi-output regression to model CIELAB colour values from dyeing ingredient and process inputs is proposed. Leveraging attention mechanisms and multi-task learning, the model outperforms baseline methods at predicting multiple colour outputs jointly. Specifically, the Transformer model’s attention mechanism captures the complex interactions between dyeing ingredients and process parameters, while the multi-task learning framework exploits the intrinsic correlations among the L*, a*, and b* dimensions of the CIELAB colour space. In addition, the incorporation of physical knowledge through a physics-informed loss function integrates the CMC colour difference formula. This loss function, along with the attention mechanisms, enables the model to learn the nuanced relationships between the dyeing process variables and the final colour output, thereby improving the overall prediction accuracy. This reduces trial-and-error costs and resource waste, contributing to environmental sustainability by minimizing water and energy consumption and chemical emissions.

On a Simple Characterization of Conformally Flat 4-Dimensional Spaces of Neutral Signature

In this work, the full characterization of 4-dimensional conformally flat spaces of neutral signature is given by using methods based on holonomy structure. Possible holonomy types are obtained for the spaces in question and several remarks are made. Various examples are presented related to this investigation.

Greedy trial subspace selection in meshfree time-stepping scheme with applications in coupled bulk-surface pattern formations

Combining kernel-based collocation methods with time-stepping methods to solve parabolic partial differential equations can potentially introduce challenges in balancing temporal and spatial discretization errors. Typically, using kernels with high orders of smoothness on some sufficiently dense set of trial centers provides high spatial approximation accuracy that can exceed the accuracy of finite difference methods in time. The paper proposes a greedy approach for selecting trial subspaces in the kernel-based collocation method applied to time-stepping to balance errors in both well-conditioned and ill-conditioned scenarios. The approach involves selecting trial centers using a fast block-greedy algorithm with new stopping criteria that aim to balance temporal and spatial errors. Numerical simulations of coupled bulk-surface pattern formations, a system involving two functions in the domain and two on the boundary, illustrate the effectiveness of the proposed method in reducing trial space dimensions while maintaining accuracy.

W‐schemes in spectral methods for reaction‐diffusion equations

AbstractWe consider reaction‐diffusion equations, which are parabolic systems of partial differential equations. Assuming periodic boundary conditions in space, a multidimensional Fourier transform can be used. A spectral method yields an initial value problem of a stiff system of ordinary differential equations for time‐dependent Fourier coefficients. We investigate the application of Rosenbrock‐Wanner W‐schemes in the time integration of the ordinary differential equations including step size selection. Results of numerical computations are presented using a Turing system in two space dimensions.

The maximum principle for lumped-distributed control systems.

This paper concerns the optimal control of lumped-distributed systems, an examplar of which is a mechanical system with rotating components connected by flexible rods. The underlying mathematical model is a controlled semilinear evolution equation, in which nonlinear terms involve a projection of the full state onto a finite dimensional subspace. We derive necessary conditions of optimality in the form of a maximum principle, for a problem formulation which involves pathwise and end-point constraints on the lumped components of the state variable. Perturbational methods are employed in the derivation, which allow for non-smooth data. A key step in the analysis is the reduction of the optimization problem with an infinite dimensional state space, to one with finite dimensional aspects. The computational implications of this reduction will be explored in future work. Necessary conditions for problems with state constraints and end-point constraints can only be achieved under rather strict compatibility hypotheses on the way the dynamics interact with the state constraint and end-point constraint sets, due the infinite dimensionality of the state space. This paper identifies a class of infinite dimensional problems, of engineering significance, for which necessary conditions of optimality can be derived, in the absence of any additional compatibility hypotheses.

Three Ellipsoids for External Approximation of the Half-Ball

Introduction. Ellipsoids that approximate the half-ball in Rn (n≥2) and their volume is smaller than the volume of the ball can be used to construct algorithms for solving the problem of minimization of a convex (smooth or non-smooth) function, the problem of minimization of a convex function on a sphere, a general problem convex programming, saddle point problems of convex-concave functions and others. The speed of convergence of such algorithms will be determined by the ratio of the volume of the approximating ellipsoid to the volume of the ball. The purpose of the work is to describe properties of three ellipsoids for approximation of a n-dimensional half-ball, the volume reduction factor of which depends only on n - dimension of space. The first is the well-known ellipsoid of minimum volume, which is used in the classical Yudin-Nemirovsky-Shor ellipsoid method. It provides a minimum volume reduction factor and can be used if n≥2. If n=1, then the classical ellipsoid method replaces the dichotomy method. The other two ellipsoids are close to the minimum volume ellipsoid and at large n guarantee volume reduction coefficients close to the minimum. The results. It is shown that when n=1 the first approximate ellipsoid provides a coefficient of reduction of the segment length equal to 2–√2 ≈ 0.5858. The second approximate ellipsoid is new and the volume reduction factor for it is slightly larger than the factor for the first approximate ellipsoid. If n=1, then it provides a coefficient of reduction of the segment length equal to (√5–1)/2 ≈ 0.6180. For three ellipsoids, comparative results are given in terms of volume reduction coefficients (n=1/20) and the number of iterations for solving problems with relative accuracy 1e-10 (n=1/30). Conclusions. A new ellipsoid has been constructed to approximate the n-dimensional half-ball, which is close in volume to the minimal ellipsoid. The volume reduction factor of the proposed ellipsoid is approximated by an asymptotic formula 1–1/(2n)+1/n², which differs little from the formula 1–1/(2n) for an ellipsoid of minimum volume.

A new approach on constitutive modeling for quasi-brittle materials under multiaxial loading

Abstract This work introduces a new method for expanding unidimensional models to predict material behavior under multiaxial loading. The concept of six-dimensional mechanical space is adopted, and in each basis direction of the space, there is one fiber-bundle model (FBM), so these six FBMs are independent amongst one another but follow the same damage evolution rule. Under triaxial loading, these FBMs have different stress and strain states, so six corresponding damage variables have different values. The anisotropic damage is thus represented by the six damage variables. When it is under uniaxial loading, the six-dimensional space reduces to one-dimensional space, so the proposed model can be calibrated using uniaxial loading test data, and the calibrated model can predict the material behavior under multiaxial loading conditions. Biaxial loading and triaxial loading test data are used to verify the proposed model, and parametric analyses are performed to analyze model predictions under different loading conditions. It shows that model predictions agree well with the test data and are consistent with experimental observations.

The relativistic Vlasov–Maxwell system: Local smooth solvability for a weak topology

This article is devoted to the relativistic Vlasov–Maxwell system in space dimension three. We prove the local well-posedness (existence and uniqueness) for initial data (\mathrm{f}_{0}, \mathrm{E}_{0},\mathrm{B}_{0}) \in L^{\infty} \times H^{1} \times H^{1} , with \mathrm{f}_{0} compactly supported in momentum. As a byproduct, we obtain the uniqueness of weak solutions to the 3D relativistic Vlasov–Maxwell system. This result is at the interface of the classical solutions in the sense of Glassey–Strauss, and the weak solutions in the sense of DiPerna–Lions. It is the consequence of the local smooth solvability for the weak topology associated with L^{\infty} \times H^{1} \times H^{1} . We derive our result from a representation formula decoding how the momentum spreads and revealing that the domain of influence in momentum is controlled by mild information. We do so by developing a Radon Fourier analysis on the RVM system, leading to the study of a class of singular weighted integrals. In parallel, we implement our method to construct smooth solutions to the RVM system in the regime of dense, hot and strongly magnetized plasmas.

Derivation of Bose–Einstein statistics from the uncertainty principle

Abstract The microstate of any degree of freedom of any classical dynamical system can be represented by a point in its two dimensional phase space. Since infinitely precise measurements are impossible, a measurement can, at best, constrain the location of this point to a region of phase space whose area is finite. This paper explores the implications of assuming that this finite area is bounded from below. I prove that if the same lower bound applied to every degree of freedom of a sufficiently-cold classical dynamical system, the distribution of the system’s energy among its degrees of freedom would be a Bose–Einstein distribution.

The Multiple Dimensions of Space: Spatial Narrative Types and Socio-Cultural Mapping in New Century Chinese Novels

This study explores how spatial narratives in new-century Chinese novels reflect and engage with China's rapidly changing socio-cultural landscape. Since the mid-1990s, China's accelerated marketization and globalization have profoundly altered traditional lifestyles and public aesthetics, significantly influencing literary creation. How do contemporary Chinese novelists employ spatial narratives to represent these changes, and what insights do these narratives offer into modern Chinese society? Employing textual analysis grounded in Lefebvre's spatial theory and Soja's Thirdspace concept, this paper examines the manifestations and functions of physical, psychological, and social spaces in new-century Chinese novels. Findings reveal diverse and complex spatial narratives: fragmented physical spaces reflecting globalization's impact, psychological spaces highlighting identity recognition anxiety, and social spaces exposing modern society's alienation and class disparities. This study contributes to a deeper application of spatial narrative theory in Chinese literary research, offering new analytical tools for understanding modern literature and its reflection of social changes. It provides insights into the characteristics and trends of new-century Chinese social culture, promoting further research and theoretical development in related fields.

A translation of “classification of four-vectors of an 8-dimensional space”, by Antonyan, L. V., with an appendix by the translator

We give a translation of the entitled paper by Antonyan [Trudy Sem. Vektor. Tenzor. Anal. 20 (1981), pp. 144–161]. We include an appendix that shows how to produce normal forms for each nilpotent orbit.

Heritage Value Assessment and Landscape Preservation of Traditional Chinese Villages Based on the Daily Lives of Local Residents: A Study of Tangfang Village in China and the UNESCO HUL Approach

Traditional Chinese villages, recognized as national heritage sites, are invaluable cultural assets. Since 2012, efforts have focused on their preservation, though issues remain such as prioritizing authenticity over usability and material over cultural elements. This paper adopts the Historic Urban Landscape (HUL) approach, emphasizing the integration of physical heritage with daily life to shift value assessment. The fundamental argument of this paper is that the HUL method can serve as a new tool for preserving the historical heritage and landscape of rural areas, particularly in the context of assessing and formulating preservation frameworks for traditional Chinese villages. Through the case study of Tangfang village’s new conservation plan, the research demonstrates that the value of traditional villages lies in the continuous interaction between daily activities and physical space, including landscape, functional, and spiritual dimensions. The study concludes that a preservation framework based on local residents’ daily lives ensures more effective heritage conservation and landscape preservation by addressing both material and human values.

Multi-population differential evolution approach for feature selection with mutual information ranking

Feature selection is a crucial aspect of data preprocessing because of the significant effect of redundant features on classification performance and the extensive computational resources required. Evolutionary algorithm-based feature-selection methods have shown remarkable results in determining the optimal feature subset. To further enhance classification performance, this paper proposes a novel multi-population differential evolution approach for feature selection with mutual information ranking (MI-MPODE). Firstly, population preprocessing guided by mutual information is employed to reduce the dimensionality of the initial feature space. Then, the feature subset obtained from mutual information serves as the initial population for MI-MPODE. MI-MPODE incorporates a novel multi-population information-sharing mechanism, with common individuals from three layers contributing to inter-subpopulation information sharing. Additionally, an individual enhancement strategy is proposed to handle the variations of individuals in the population, and a Lens imaging opposition-based learning method is adopted to improve the algorithm’s optimization capability. MI-MPODE is compared with several state-of-the-art evolutionary algorithm-based feature selection methods through experimental comparisons. The results show that MI-MPODE outperforms all comparison algorithms on more than half of the datasets, with a significant reduction in the number of features used, demonstrating a significant advantage over competitors.

On the Inference of Original Graph Information from Graph Embeddings

Graph embedding converts a graph data into a low dimensional space to preserve the original graph information. However, graph data can be reconstructed by malicious adversaries to train machine learning models from graph embeddings. This paper studies to what extent an adversary (without the original graph data) can recover the original graph data from graph embeddings. To quantify the original graph information leakage from graph embeddings, we develop a deep neural network model InferNet that can be used by adversaries to infer the original graph information from an adversary-accessible graph embedding database. More specifically, we propose the data-free reversed knowledge distillation technique to support the InferNet training even if the original graph dataset is absent. To ensure the performance of InferNet, we design two cycle-consistency loss functions to have an interactive training of InferNet over three series of datasets. To further enhance the performance of InferNet, we provide a joint training algorithm that simultaneously trains the pseudo-sample generator and InferNet, which significantly reduces the storage space. We evaluate the performance of InferNet on three datasets, and the intensive experiments demonstrate that InferNet can infer the original graph information from the graph embedding dataset with high accuracy.

Dimensionality reduction of neuronal degeneracy reveals two interfering physiological mechanisms.

Neuronal systems maintain stable functions despite large variability in their physiological components. Ion channel expression, in particular, is highly variable in neurons exhibiting similar electrophysiological phenotypes, which raises questions regarding how specific ion channel subsets reliably shape intrinsic properties of neurons. Here, we use detailed conductance-based modeling to explore how stable neuronal function is achieved despite variability in channel composition among neurons. Using dimensionality reduction, we uncover two principal dimensions in the channel conductance space that capture most of the variance of the observed variability. These two dimensions correspond to two sources of variability that originate from distinct physiologically relevant mechanisms underlying the regulation of neuronal activity, providing quantitative insights into how channel composition is linked to the electrophysiological activity of neurons. These insights allow us to understand and design a model-independent, reliable neuromodulation rule for variable neuronal populations.

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.

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 datasets, 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. Supplementary materials for this article are available online.

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].

Projected state ensemble of a generic model of many-body quantum chaos

Abstract The projected ensemble is based on the study of the quantum state of a subsystem A conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design, i.e. a system thermalizes when it becomes indistinguishable, up to the kth moment, from a Haar ensemble of uniformly distributed pure states. Here we consider a random unitary circuit with the brick-wall geometry and analyze its convergence to the Haar ensemble through the frame potential and its mapping to a statistical mechanical problem. This approach allows us to highlight a geometric interpretation of the frame potential based on the existence of a fluctuating membrane, similar to those appearing in the study of entanglement entropies. At large local Hilbert space dimension q, we find that all moments converge simultaneously with a time scaling linearly in the size of region A, a feature previously observed in dual unitary models. However, based on the geometric interpretation, we argue that the scaling at finite q on the basis of rare membrane fluctuations, finding the logarithmic scaling of design times t k = O ( log ⁡ k ) . Our results are supported with numerical simulations performed at q = 2.

Irreversible Boltzmann samplers in dense liquids: Weak-coupling approximation and mode-coupling theory.

Exerting a nonequilibrium drive on an otherwise equilibrium Langevin process brings the dynamics out of equilibrium but can also speed up the approach to the Boltzmann steady state. Transverse forces are a minimal framework to achieve dynamical acceleration of the Boltzmann sampling. We consider a simple liquid in three space dimensions subjected to additional transverse pairwise forces, and quantify the extent to which transverse forces accelerate the dynamics. We first explore the dynamics of a tracer in a weak coupling regime describing high temperatures. The resulting acceleration is correlated with a monotonous increase of the magnitude of odd transport coefficients (mobility and diffusivity) with the amplitude of the transverse drive. We then develop a nonequilibrium version of the mode-coupling theory able to capture the effect of transverse forces, and more generally of forces created by additional degrees of freedom. Based on an analysis of transport coefficients, both odd and longitudinal, both for the collective modes and for a tracer particle, we find a systematic acceleration of the dynamics. Quantitatively, the gain, which is guaranteed throughout the ergodic phase, turns out to be a decreasing function of temperature beyond a temperature crossover, in particular as the glass transition is approached. Our theoretical results are in good agreement with available numerical results.