Dimensional Space Research Articles

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 .

HEnsem_DTIs: A heterogeneous ensemble learning model for drug-target interactions prediction

Drug discovery is the process by which a drug is discovered. Drug-target interactions prediction is a major part of drug discovery. Unfortunately, producing new drugs is time-consuming and expensive; Because it requires a lot of human and laboratory resources. Recently, predictions have been made using computational methods to solve these problems and prevent blindly examining all interactions. Various experiences using computational methods show that no single algorithm can be suitable for all applications; Hence, ensemble learning is expressed. Although various ensemble methods have been proposed, it is still not easy to find a suitable ensemble method for a particular dataset. In general, the existing algorithms in aggregation and combination method are selected manually based on experience. Reinforcement learning can be one way to meet this challenge. High-dimensional feature space and class imbalance are among the challenges of drug-target interactions prediction. This paper proposes HEnsem_DTIs, a heterogeneous ensemble model, for predicting drug-target interactions using dimensionality reduction and concepts of recommender systems to address these challenges. HEnsem_DTIs is configured with reinforcement learning. Dimensionality reduction is applied to handle the challenge of high-dimensional feature space and recommender systems to improve under-sampling and solve the class imbalance challenge. Six datasets are used to evaluate the proposed model; Results of the evaluation on datasets show that HEnsem_DTIs works better than other models in this field. Results of evaluation of the proposed model on the first dataset using 10-fold cross-validation experiments show the amount of sensitivity 0.896, specificity 0.954, GM 0.924, AUC 0.930 and AUPR 0.935.

A Proposed Framework for integrating IVR Technology in Architectural Design courses; Application on architectural schools in Egypt

Abstract Visual communication has a vital role in the architecture. Virtual reality (VR) is one of the various methods of visual communication and interaction, especially during pandemics. Although it has many benefits such as improved space perception and dimension visualization etc., it’s not commonly used in Egyptian architectural schools. This research aims to investigate the integration of Immersive Virtual Reality (IVR) into the design curriculums in Egyptian architectural schools and to propose a framework for its integration. A mixed method approach was used in this study along with the literature data that was reviewed to identify the benefits, limitations and different IVR setups. First, an interview was conducted with one of the VRCAVE founders in an Egyptian private university to understand the effect of IVR and whether it has affected the students’ outcome. This was followed by conducting an experiment including an IVR setup along with a 3D Virtual model, to conduct semi-structured interview with the participants to analyse the use of IVR in the design modules and whether its integration in the architecture schools design curriculum would be beneficial

Asteroid pairs: Survey of the inner main belt

Context. An asteroid pair forms when an asteroid splits into two unbound fragments because of collision, rotational fission, or binary system decay. The two components of the asteroid pair share similar physical properties and their orbits converge when integrated into the past. Currently, 268 asteroid pairs are known, and new pairs are discovered alongside the continuous discovery of new asteroids. Aims. We conducted a survey in the inner asteroid belt to find new asteroid pairs, estimated their age, and classified their physical properties. As presently no M-type asteroid pairs are known, we also conducted a specialized survey of them. Methods. We preselected asteroid pair candidates based on their distances in the five-dimensional space of osculating orbital elements. We created multiple clones within the uncertainties of their orbital elements and conducted their backtrack integration into the past. We searched for convergence of their clones at close spatial points with small relative velocities, the distribution of which determines the pair formation age. Results. We find 40 new asteroid pairs, thus increasing the total number of known pairs by 15%. One of the newly discovered pairs, 469759 - 2016 QZ 123, with an age of 2.6−0.2+0.7 kyr is now the third-youngest known asteroid pair. We studied the influence of the mutual gravitation of pair components on the process of their evolution and successfully observed the gravitational catching of the two pair members in the past. As a byproduct of pair search, we find eight asteroids connected in a cluster with an age of 76−25+15 kyr that belongs to the Phocaea family and incorporates one previously known asteroid pair. We confirm the convergence of ten asteroid pairs discovered in our previous research and improve their age estimates. We observed a deficiency of M-type asteroid pairs, and therefore conducted a dedicated search for M-type pairs, but found none.

Relative controllability for [formula omitted]Caputo fractional delay control system

This paper resolves around relative controllability of ψ−fractional delayed differential equations in finite dimensional space. The Mittag Leffler type of ψ−delayed perturbation matrix function with two parameters exhibits the Grammian matrix of fractional delay system. Based on this Grammian matrix we derived the necessary and sufficient conditions for the linear system which is relatively controllable. The fixed point approach is applied for obtaining a controllability result for semilinear system. This concept can be applied to some examples in order to illustrate the efficacy of our results.

UAV data link anti-interference via SLHS-SVM-AdaBoost algorithm: Classification prediction and route planning

The ability to predict the anti-interference communications performance of unmanned aerial vehicle (UAV) data links is critical for intelligent route planning of UAVs in real combat scenarios. Previous research in this area has encountered several limitations: Classifiers exhibit low training efficiency, their precision is notably reduced when dealing with imbalanced samples, and they cannot be applied to the condition where the UAV’s flight altitude and the antenna bearing vary. This paper proposes the sequential Latin hypercube sampling (SLHS)-support vector machine (SVM)-AdaBoost algorithm, which enhances the training efficiency of the base classifier and circumvents local optima during the search process through SLHS optimization. Additionally, it mitigates the bottleneck of sample imbalance by adjusting the sample weight distribution using the AdaBoost algorithm. Through comparison, the modeling efficiency, prediction accuracy on the test set, and macro-averaged values of Precision, Recall, and F1-score for SLHS-SVM-AdaBoost are improved by 22.7%, 5.7%, 36.0%, 25.0%, and 34.2%, respectively, compared with Grid-SVM. Additionally, these values are improved by 22.2%, 2.1%, 11.3%, 2.8%, and 7.4%, respectively, compared with particle swarm optimization (PSO)-SVM-AdaBoost. Combining Latin hypercube sampling with the SLHS-SVM-AdaBoost algorithm, the classification prediction model of anti-interference performance of UAV data links, which took factors like three-dimensional space position of UAV and antenna bearing into consideration, is established and used to assess the safety of the classical flying path and optimize the flying route. It was found that the risk of loss of communications could not be completely avoided by adjusting the flying altitude based on the classical path, and that intelligent path planning based on the classification prediction model of anti-interference performance can realize complete avoidance of being interfered while reducing the route length by at least 2.3%, thus benefiting both safety and operation efficiency.

The mean field limit for the Vlasov–Poisson system with a point charge

In this paper, we are concerned with the validity problem for the repulsive Vlasov–Poisson system when the initial datum is the sum of a diffuse density and a point charge in the three dimensional space. Our result leads to a derivation of this system from the regularized microscopic N-plasma particle and one point charge system when the Coulomb force between plasma particles needs to be modified with the modified size N − 1 3 + ϵ while the Coulomb force between plasma and point charge does not need to be modified. More precisely, we obtain the convergence rate between the empirical measure associated to the regularized particle system and the solution of the Vlasov–Poisson system with a point charge in terms of the Wasserstein distance.

VEMcomp: a Virtual Elements MATLAB package for bulk-surface PDEs in 2D and 3D

AbstractWe present a Virtual Element MATLAB solver for elliptic and parabolic, linear and semilinear Partial Differential Equations (PDEs) in two and three space dimensions, which is coined VEMcomp. Such PDEs are widely applicable to describing problems in material sciences, engineering, cellular and developmental biology, among many other applications. The library covers linear and nonlinear models posed on different simple and complex geometries, involving time-dependent bulk, surface, and bulk-surface PDEs. The solver employs the Virtual Element Method (VEM) of lowest polynomial order $${k=1}$$ k = 1 on general polygonal and polyhedral meshes, including the Finite Element Method (FEM) of order $${k=1}$$ k = 1 as a special case when the considered mesh is simplicial. VEMcomp has three main purposes. First, VEMcomp generates polygonal and polyhedral meshes optimized for fast matrix assembly. Triangular and tetrahedral meshes are encompassed as special cases. For surface PDEs, VEMcomp is compatible with the well-known Matlab package DistMesh for mesh generation. Second, given a mesh for the considered geometry, possibly generated with an external package, VEMcomp computes all the matrices (mass and stiffness) required by the VEM or FEM method. Third, for multiple classes of stationary and time-dependent bulk, surface and bulk-surface PDEs, VEMcomp solves the considered PDE problem with the VEM or FEM in space and IMEX Euler in time, through a user-friendly interface. As an optional post-processing, VEMcomp comes with its own functions for plotting the numerical solutions and evaluating the error when possible. An extensive set of examples illustrates the usage of the library.

The 4-Dimensional Spacetime World Line Image Representation and the Law of Existence of Objects Inferred from it

MINKOWSKI defined the four-dimensional spacetime model (x, y, z, t) used to represent world-point and world in [1]. The spacetime light cone is an intuitive diagram, compacted one space component and replaced it by time axis, thus the spacetime light cone was based on (x, y, t). In such a way, although it made the visual expression is possible, but also the spacetime light cone exposed shortages as follows • The spacetime light cone has limited expressive ability • The relationship between two or more world lines or events cannot be expressed • Can't express different world lines correctly • Most images of spacetime light cones are wrong and no use • The image of spacetime light cone is not intuitive and is obscure in application. Because of this, we designed the 4-dimensional Spacetime World Line image representation. This new 4-dimensional Spacetime diagram presents the complete 3 space dimensions and 1 time dimension. It overcomes the weakness of spacetime light cone, gives clear and precise visual expression of the world line, is able to display multi-world lines in one figure, can clearly present the interface and development process of each of the world line, and display the interaction among them. From the 4-dimensional spacetime diagram, we deducted and proved the Law of Existence of Object, which is as such: From its birth, through its past, to the present, and into the future, an object only exists at the "present" moment.

Continuous finite elements satisfying a strong discrete Miranda–Talenti identity

Abstract This article introduces continuous $H^{2}$-nonconforming finite elements in two and three space dimensions that satisfy a strong discrete Miranda–Talenti inequality in the sense that the global $L^{2}$ norm of the piecewise Hessian is bounded by the $L^{2}$ norm of the piecewise Laplacian. The construction is based on globally continuous finite element functions with $C^{1}$ continuity on the vertices (2D) or edges (3D). As an application, these finite elements are used to approximate uniformly elliptic equations in nondivergence form under the Cordes condition without additional stabilization terms. For the biharmonic equation in three dimensions, the proposed methods has less degrees of freedom than existing nonconforming schemes of the same order. Numerical results in two and three dimensions confirm the practical feasibility of the proposed schemes.

Neuronal firing rate diversity lowers the dimension of population covariability.

Populations of neurons produce activity with two central features. First, neuronal responses are very diverse - specific stimuli or behaviors prompt some neurons to emit many action potentials, while other neurons remain relatively silent. Second, the trial-to-trial fluctuations of neuronal response occupy a low dimensional space, owing to significant correlations between the activity of neurons. These two features define the quality of neuronal representation. We link these two aspects of population response using a recurrent circuit model and derive the following relation: the more diverse the firing rates of neurons in a population, the lower the effective dimension of population trial-to-trial covariability. This surprising prediction is tested and validated using simultaneously recorded neuronal populations from numerous brain areas in mice, non-human primates, and in the motor cortex of human participants. Using our relation we present a theory where a more diverse neuronal code leads to better fine discrimination performance from population activity. In line with this theory, we show that neuronal populations across the brain exhibit both more diverse mean responses and lower-dimensional fluctuations when the brain is in more heightened states of information processing. In sum, we present a key organizational principle of neuronal population response that is widely observed across the nervous system and acts to synergistically improve population representation.

Asymmetry index for data and its verification in dimensionality reduction and data visualization

We propose an asymmetry index as a measure of degree of asymmetry of a given dataset. It provides an additional information on a dataset allowing to guide and improve any further analysis. The index reflects the intensity of the asymmetric relationships among data resulting from hierarchical data structure. Using the information retrieved by our asymmetry index, one obtains a justification and explanation of the effectiveness of the subsequent asymmetric data analysis methods, as well as helpful preparation to asymmetrizing the tools for the further analysis. The asymmetry index is based on the k-nearest neighbors graph representing the considered data. Therefore, it uses the intrinsic geometry-based information on the data, in this way, providing an insight into the data structure. Our experiments on real data are designed to verify the usefulness of the asymmetry index and the correctness of its theoretical fundamentals. In our empirical validation, we employ the symmetric and asymmetric dimensionality reduction algorithms and evaluate their results on the basis of clustering in the 2-dimensional visualization space. We test, whether our index indeed predicts the level of superiority of the asymmetric methods over their symmetric counterparts.

A stochastic averaging mathematical framework for design and optimization of nonlinear energy harvesters with several electrical DOFs

Energy harvesters for mechanical vibrations are electro-mechanical systems designed to capture ambient dispersed kinetic energy, and to convert it into usable electrical power. The random nature of mechanical vibrations, combined with the intrinsic non-linearity of the harvester, implies that long, time domain Monte-Carlo simulations are required to assess the device performance, making the analysis burdensome when a large parameter space must be explored. Therefore a simplified, albeit approximate, semi-analytical analysis technique is of paramount importance. In this work we present a methodology for the analysis and design of nonlinear piezoelectric energy harvesters for random mechanical vibrations. The methodology is based on the combined application of model order reduction, to project the dynamics onto a lower dimensional space, and of stochastic averaging, to calculate the stationary probability density function of the reduced variables. The probability distribution is used to calculate expectations of the most relevant quantities, like output voltage, harvested power and power efficiency. Based on our previous works, we consider an energy harvester with a matching network, interposed between the harvester and the load, that reduces the impedance mismatch between the two stages. The methodology is applied to the optimization of the matching network, allowing to maximize the global harvested power and the conversion efficiency. We show that the proposed methodology gives accurate predictions of the harvester’s performance, and that it can be used to significantly simplify the analysis, design and optimization of the device.

On Finite Parts of Divergent Complex Geometric Integrals and Their Dependence on a Choice of Hermitian Metric

Let X be a reduced complex space of pure dimension. We consider divergent integrals of certain forms on X that are singular along a subvariety defined by the zero set of a holomorphic section of some holomorphic vector bundle E→X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E \\rightarrow X$$\\end{document}. Given a choice of Hermitian metric on E we define a finite part of the divergent integral. Our main result is an explicit formula for the dependence on the choice of metric of the finite part.

Single molecule dynamics in a virtual cell combining a 3-dimensional matrix model with random walks

Recent advances in light microscopy have enabled single molecules to be imaged and tracked within living cells and this approach is impacting our understanding of cell biology. Computer modeling and simulation are important adjuncts to the experimental cycle since they aid interpretation of experimental results and help refine, test and generate hypotheses. Object-oriented computer modeling is particularly well-suited for simulating random, thermal, movements of individual molecules as they interact with other molecules and subcellular structures, but current models are often limited to idealized systems consisting of unit volumes or planar surfaces. Here, a simulation tool is described that combines a 3-dimensional, voxelated, representation of the cell consisting of subcellular structures (e.g. nucleus, endoplasmic reticulum, cytoskeleton, vesicles, and filopodia) combined with numerical floating-point precision simulation of thousands of individual molecules moving and interacting within the 3-dimensional space. Simulations produce realistic time-series video sequences comprising single fluorophore intensities and realistic background noise which can be directly compared to experimental fluorescence video microscopy data sets.

Asymptotic profiles for Choquard equations with combined attractive nonlinearities

We study asymptotic behaviour of positive ground state solutions of the nonlinear Choquard equation(Pε)−Δu+εu=(Iα⁎|u|p)|u|p−2u+|u|q−2u,inRN,where N≥3 is an integer, p∈[N+αN,N+αN−2], q∈(2,2NN−2), Iα is the Riesz potential of order α∈(0,N) and ε>0 is a parameter. We show that as ε→0 (resp. ε→∞), the ground state solutions of (Pε), after appropriate rescalings dependent on parameter regimes, converge in H1(RN) to particular solutions of five different limit equations. We also establish a sharp asymptotic characterisation of such rescalings, and the precise asymptotic behaviour of uε(0), ‖∇uε‖22, ‖uε‖22, ∫RN(Iα⁎|uε|p)|uε|p and ‖uε‖qq, which depend in a non-trivial way on the exponents p, q and the space dimension N. Further, we discuss a connection of our results with a mass constrained problem, associated to (Pε) with normalization constraint ∫RN|u|2=c2. As a consequence of the main results, we obtain the existence, multiplicity and precise asymptotic behaviour of positive normalized solutions of such a problem as c→0 and c→∞.