Dimensional Space Research Articles

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.

Critical dimension for hydrodynamic turbulence.

Hydrodynamic turbulence exhibits nonequilibrium behavior with k^{-5/3} energy spectrum, and equilibrium behavior with k^{d-1} energy spectrum and zero viscosity, where d is the space dimension. Using recursive renormalization group in Craya-Herring basis, we show that the nonequilibrium solution is valid only for d<6, whereas equilibrium solution with zero viscosity is the only solution for d>6. Thus, d=6 is the critical dimension for hydrodynamic turbulence. In addition, we show that the energy flux changes sign from positive to negative near d=2.15. We also compute the energy flux and Kolmogorov's constants for various d's, and observe that our results are in good agreement with past numerical results.

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.

Study on the thermo-mechanical properties of adaptive thermal control anchoring materials in high-geothermal tunnels

The heat conduction of the rock in high-geothermal tunnels can damage the grout during the initial hardening process, which directly affects the effectiveness of the anchoring support of the surrounding rock. This paper proposed the incorporation of phase change materials in grout to provide the new modified grouting material with the ability to control temperature by exploiting the phase change absorption and exothermic properties of the material. The changes in thermomechanical parameters of anchoring grout containing microencapsulated phase change material (m-PCM) under high geothermal environment were investigated. The influences of m-PCM content on the temperature control effect and mechanical properties of modified grout under different high geothermal environments were explored through macro-mechanical, micro-structural, and thermo-physical property tests on the specimens. The results indicated that m-PCM can effectively control the early hydration temperature of the grout in a high temperature environment, which can slow down the rate of change of the hydration temperature and reduce the peak temperature. The temperature control performance of modified grouts improved as the phase-change content increased, but the mechanical properties showed a significant decline after the initial increase. The results of the scanning electron microscope (SEM) analysis indicated that the high curing temperature had a negative impact on the internal structural integrity of the grout. The addition of a small amount of m-PCM reduced the fractal dimension and irregularity of the pore space in the grouting material, ultimately improving the strength of the grout body. The addition of a certain amount of m-PCM could significantly reduce the thermal conductivity of the grout, with the thermal conductivity of the specimens decreasing as the temperature increased. These study results provided valuable experimental data and theoretical support for the design of cement-based grouting materials in high-geothermal tunnels.

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

Motivated 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(log2k)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(\\log ^2k)$$\\end{document}-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.

Exploring the dual nature of time as a form of energy and a dimension of space

Exploring the dual nature of time as a form of energy and a dimension of space

A new Approach to Hyper Dual Split Quaternions with Different Polar Representation

Hamilton first introduced quaternions in 1843 as a way to represent rotations in three dimensional space, and since then, they have become the important tool in many fields. One advantage of quaternions over other methods of representing rotations is their ability to avoid the problem of gimbal lock, which can occur when using Euler angles. Quaternions also have a relatively simple algebraic structure and can be efficiently implemented in computer algorithms. In recent years, quaternions have been used in the development of virtual reality systems and computer games, where they are used to represent orientations of objects in three-dimensional space. They have also been applied in robotics, control theory, and signal processing. Overall, quaternions have become the valuable tools in many areas of mathematics and engineering, and their usage continue to expand. Sangwine and Bihan introduced a quaternion polar representation that draws inspiration from the Cayley-Dickson form. In their formulation, they express quaternions using a complex modulus and argument. The Cayley-Dickson construction is a mathematical procedure that extends the concept of complex numbers to higher dimensions, paving the way for the development of quaternions. On the other hand, the complex argument represents the direction or orientation of the quaternion in a manner analogous to the argument of a complex number. This approach provides a concise and insightful way to represent quaternions, offering a geometric interpretation that aligns with the principles of complex analysis.

Virtual Reality as an Adjunct to Traditional Patient Counseling in Patients With Newly Diagnosed Localized Prostate Cancer

ObjectivesTo determine the utility of a virtual reality (VR) model constructed using patient-derived clinical imaging to improve patient understanding of localized prostate cancer (PCa) diagnosis and surgical plan. MethodsPatients undergoing robotic radical prostatectomy were selected and demographic data recorded. Patients completed a questionnaire to assess baseline knowledge of their diagnosis after consultation and shared-decision making with their surgeon. A trained non-clinical staff member then guided the patient through a VR experience to view patient-specific anatomy in a 3-dimensional space. Patients then completed the same questionnaire, followed by an additional post-VR questionnaire evaluating patient satisfaction. Questions 1-7 (patient understanding of prostate cancer and treatment plan) and 11-17 (patient opinion of VR) used a standard Likert scale and Questions 8-10 were multiple choice with 1 correct answer. ResultsIn total, 15 patients were included with an average age of 64.1 years. 6 of 7 questions showed an improvement after VR (p<0.001). The percentage of correct responses on Questions 8-10 were higher after VR but not statistically significant (p>0.13). Mean responses range from 4.3 to 4.8 (Likert scale, 1 through 5) for the post-VR questionnaire, with a mean total of 31.9 out of 35. ConclusionThis small preliminary investigation of a novel technology to improve the patient experience showed potential as an adjunct to traditional patient counseling. However, due the small sample size and study design, further research is needed to determine the value VR adds to prostate cancer surgical counselling.

A bound preserving cut discontinuous Galerkin method for one dimensional hyperbolic conservation laws

In this paper we present a family of high order cut finite element methods with bound preserving properties for hyperbolic conservation laws in one space dimension. The methods are based on the discontinuous Galerkin framework and use a regular background mesh, where interior boundaries are allowed to cut through the mesh arbitrarily. Our methods include ghost penalty stabilization to handle small cut elements and a new reconstruction of the approximation on macro-elements, which are local patches consisting of cut and un-cut neighboring elements that are connected by stabilization. We show that the reconstructed solution retains conservation and order of convergence. Our lowest order scheme results in a piecewise constant solution that satisfies a maximum principle for scalar hyperbolic conservation laws. When the lowest order scheme is applied to the Euler equations, the scheme is positivity preserving in the sense that positivity of pressure and density are retained. For the high order schemes, suitable bound preserving limiters are applied to the reconstructed solution on macro-elements. In the scalar case, a maximum principle limiter is applied, which ensures that the limited approximation satisfies the maximum principle. Correspondingly, we use a positivity preserving limiter for the Euler equations, and show that our scheme is positivity preserving. In the presence of shocks additional limiting is needed to avoid oscillations, hence we apply a standard TVB limiter to the reconstructed solution. The time step restrictions are of the same order as for the corresponding discontinuous Galerkin methods on the background mesh. Numerical computations illustrate accuracy, bound preservation, and shock capturing capabilities of the proposed schemes.

Finite element modelling of linear rolling contact problems

The present work is devoted to the finite element modelling of linear hyperbolic rolling contact problems. The main equations encountered in rolling contact mechanics are reviewed in the first part of the paper, with particular emphasis on applications from automotive and vehicle engineering. In contrast to the common hyperbolic systems found in the literature, such equations include integral and boundary terms, as well as time-varying transport velocities, that require special treatment. In this context, existence and uniqueness properties are discussed within the theoretical framework offered by the semigroup theory. The second part of the paper is then dedicated to recovering approximated solutions to the considered problems, by combining discontinuous Galerkin finite element methods (DGMs) with explicit Runge–Kutta (RK) schemes of the first and second order for time discretisation. Under opportune assumptions on the smoothness of the sought solutions, and owing to certain generalised Courant–Friedrichs–Lewy (CFL) conditions, quasi-optimal error bounds are derived for the complete discrete schemes. The proposed algorithms are then tested on simple scalar equations in one space dimension. Numerical experiments seem to suggest the theoretical error estimates to be sharp.

Complex Pseudo 3D Auto-Correlation Network for High-Quality Single-Angle Plane Wave Imaging

Abstract Deep learning has shown potential as an effective beamformer for improving the image quality of plane wave imaging (PWI). But most existing deep learning methods cannot directly handle the complex in-phase and quadrature (IQ) data. And noise in ultrasound signals would significantly damage the performance of regular convolution networks. To address these challenges, we proposed the Complex Pseudo 3D Auto-Correlation Network (CP3AN) which combined complex convolution and pseudo 3D auto-correlation blocks (P3AB) to directly map delayed IQ data from 0° plane wave into PWI pixels. The complex convolution could fully utilize the envelope and phase information of IQ data, while the P3AB used 1D convolution to extract noise in channel and space dimensions, allowing the network to prioritize valid signals with extremely low computational cost. We evaluated the performance of CP3AN through numerical simulations, phantom experiments, and in-vivo experiments, which showed comparable metrics with minimum variance (MV), including contrast (CR), contrast-to-noise ratio (CNR), generalized contrast-to-noise ratio (GCNR), lateral, and axial full-width half maximum (FWHM) at -9.60 dB, 1.12, 0.65, 319 um, and 344 um, respectively. The CP3AN achieved a low computational cost of 0.11 M floating-point operations (FLOPs), significantly lower than the MV or other compared deep learning-based methods. Our proposed method provided a promising solution for improving single-angle PWI imaging, particularly in situations where high frame rates are necessary.

Spin-dependent Goos-Hänchen shift for electron in single-layered semiconductor microstructure modulated by Rashba spin–orbit coupling

We theoretically investigate Goos-Hänchen effect for electron in single-layered semiconductor microstructure (SLSM) modulated by Rashba spin–orbit coupling (SOC). Due to the SOC effect, GH displacement is obviously dependent on spins, which allows electron spins to be separated in space dimension and results in spin polarization of electrons in semiconductors. Spin polarization ratio is associated with incident energy, incident direction and in-plane wave vector, e.g., it reaches maximum at resonance, but no spin polarization effect appears at normal incidence. In particular, both magnitude and sign of spin polarization ratio are controlled by external electric field or semiconductor-layer thickness, therefore, a manipulable spatial electron-spin splitter is obtained for semiconductor spintronics device applications.

Public space and everyday heritage: An inquiry into children's and adults' perception

This paper examines how the spatial environment and the activities within these spaces contribute to their social value in turn informing the concept of everyday heritage within urban public spaces. We develop a novel methodological framework that combines visual representation and narrative analysis to provide insights into how the physical, emotional and perceptual dimensions of a public open space translate into associative social values. By including both adults and children in our study, we capture a comprehensive range of perceptions, highlighting the diverse ways in which different user groups give meaning to everyday heritage. Children and their guardians showed agreement on natural elements and personal representations, but differed on the garden's spatial layout and activities. While they shared values like childhood memories and family time, children prioritized play, forming new friendships, and connecting with nature, whereas parents emphasized children's happiness and personal space. Notably, both groups indicate that childhood – both lived and remembered – is that which gives this public urban space its everyday heritage status. The findings advocate for an expanded understanding of urban public spaces, recognizing the significance of everyday heritage in shaping collective cultural identity.

Task scheduling in cloud computing based on grey wolf optimization with a new encoding mechanism

Task scheduling in the cloud computing still remains challenging in terms of performance. Several evolutionary-derived algorithms have been proposed to solve or alleviate this problem. However, evolutionary algorithms have good exploration ability, but the performance drops significantly in high dimensions. To address this issue, considering the characteristic of task scheduling in cloud computing (i.e. all task-VM mappings are 1-dimensional and have the same search range), we propose a task scheduling algorithm based on grey wolf optimization using a new encoding mechanism (GWOEM) in this work. Through this new encoding mechanism, greedy and evolutionary algorithms are rationally integrated in GWOEM. Besides, based on the new mechanism, the dimension of search space is reduced to 1 and the key parameter (i.e., the population size) is eliminated. We apply the proposed GWOEM to the Google Cloud Jobs dataset (GoCJ) and demonstrate better performance than the prior state of the art in terms of makespan.

Coincidence of the Dimensions of First Countable Spaces with a Countable Network

Coincidence of the Dimensions of First Countable Spaces with a Countable Network

Influence of sinusoidal forcing on the master FitzHugh–Nagumo neuron model and global dynamics of a unidirectionally coupled two-neuron system

In this paper, we investigate a seven-parameter, five-dimensional dynamical system, specifically a unidirectional coupling of two FitzHugh–Nagumo neuron models, with one neuron being sinusoidally driven. This master–slave configuration features neuron N1 as the master, subjected to an external sinusoidal electrical current, and neuron N2 as the slave, interacting with N1 through an electrical force. We report numerical results for three distinct scenarios where N1 operates in (i) periodic, (ii) quasiperiodic, and (iii) chaotic regimes. The primary objective is to explore how the dynamics of the master neuron N1 influence the coupled system’s behavior. To achieve this, we generated cross sections of the seven-dimensional parameter space, known as parameter planes. Our findings reveal that in the periodic regime of N1, the coupled system exhibits period-adding sequences of Arnold tongue-like structures in the parameter planes. Furthermore, regions of multistability can also be identified in these parameter planes of the coupled system. In the quasiperiodic regime, regions of periodic motion are absent, with only regions of quasiperiodic and chaotic dynamics present. In the chaotic regime of N1, the parameter planes display regions of chaos, hyperchaos, and transient hyperchaos.

Some Results about Acts over Monoid and Bounded Linear Operators

الأثر V بالنسبة إلى sinshT و خواصه قد تم دراسته في هذا البحث حيث تم دراسة علاقة الأثر المخلص والاثر المنتهى التولد والاثر المنفصل وربطها بالمؤثرات المتباينة حيث تم بهنة العلاقات التالية ان الاثر اذا وفقط اذا مقاس في حالة كون المؤثر هو عديم القوة وكذلك في حالة كون المؤثر شامل فان الاثر هو منتهي التولد اي ان الغضاء هو منتهي التولد وايضا تم برهن ان الاثر مخلص لكل مؤثر مقيد وك\لك قد تم التحقق من انه لاي مؤثر مقيد فان الاثر منفصل وفي حالة كون الاثر منفصل فان المؤثر سوف يكون متباين وايضا تم برهنة انه في حالة كون الفضاء يمتلك قاعدة فان الاثر سوف يكون كل عنصر فيه يمكن كتابته كتركيبة خطية ومن العلاقات المهمة التي قد تم برهانها انه اذا كان المؤثر مشابه لمؤثر اخر فان الاثر سوف يكون نوثيرين بوجد شرط على الفضاء .