Dimensional Space Research Articles

$k$-rational homotopy fixed points, $k\in \Bbb N$

For $k\in \Bbb N$, we introduce the notion of $k$-rational homotopy fixed points and we prove, under a certain assumption, that if $X$ is a rational elliptic space of formal dimension $n$, then $X$ admits an $(n -1)$-rational homotopy fixed point.

Bent-half space model problem for Lame equation with surface tension

The study of fluid flow is a very fascinating area of fluid dynamics. Fluid motion has received more and more attention in recent years and numerous researchers have looked into this topic. However, they rarely used a mathematical analysis approach to analyse fluid motion; instead, they used numerical analysis. This serves as a significant justification for the researcher's decision to study fluid flow from the perspective of mathematical analysis. In this paper, we consider the ${\mathcal R}$-boundedness of the solution operator families of the Lam\'e equation with surface tension in bent half-space model problem by taking into account the surface tension in a bounded domain of {\it N}-dimensional Euclidean space ($N \geq 2$). The motion of the model problem can be described by linearizing an equation system of a model problem. This research is a continuation of [13]. They investigated the ${\mathcal R}$-boundedness of the solution operator families in the half-space case for the model problem of the Lam\'e equation with surface tension. First of all, by using Laplace transformation we consider the resolvent of the model problem, then treat the problem in bent half-space case. By using Weis's operator-valued Fourier multiplier theorem, we know that ${\mathcal R}$-boundedness implies the maximal $L_p$-$L_q$ regularity for the initial boundary value. This regularity is an essential tool for the partial differential equation problem.

A domain knowledge-informed design space exploration methodology for mechanical layout design

Layout designs have a large number of design variables and various physical constraints. Conventional design exploration approaches are time-consuming and may require human intervention. A unique feature about physical layout designs is the availability of domain knowledge, which can be utilised to speed up the design process. In this paper, we propose a generative deep learning-based design space exploration (DSE) methodology that is capable of learning design constraints in the layout design without explicit supervision. Moreover, it can incorporate domain knowledge in the generated layouts, thereby speeding up the design process. This is realised by constructing a layout generation variational autoencoder (LGVAE) model, which uses a latent space as an interface to generate the layouts. By training the LGVAE model, significantly lower-dimensional representations can be learned compared to the original dimensionality of the design space. Therefore, the number of design variables is greatly reduced. We showcase the performance of the proposed DSE approach by solving the heat source layout design problem encountered in thermal management of chips. Experiments demonstrate that the LGVAE model is capable of generating compressed latent representations that capture the characteristics of the input samples, which makes the DSE cost-effective.

Finite dimension of the ion pathway networks in conducting glasses

Abstract In disordered materials, the ordinary understanding is that charge carriers tend to occupy energetically favorable sites known as ion-conducting channels. Many studies have revealed that the inherent fractal properties of such pathways lead to a sub-diffusive behavior. The linearity or branching of these pathways is crucial for determining how the charge carriers move. It can be thought that as the space dimensionality decreases, the average distance between the highest energy barriers along the conduction paths increases. 
 In this study the finite dimension of those pathways is computed using an extended version of the classical Hausdorff dimension. Also, the Arrhenius behavior of the most mobile lithium ions is proved, confirming that such are responsible for conductivity behavior. The lithium ions mobility behavior in response to temperature changes and the finite dimension allowed to identify the ion diffusion regions fractal features. The reported results demonstrate that as the temperature increases the conducting channels become broadener, facilitating the transfer of electrical charge through the glassy matrix, below the transition temperature. The pathways behavior confirms the increase of the ionic conductivity when the temperature increases as it is experimentally observed.




The theory of screws derived from a module over the dual numbers

AbstractThe theory of screws clarifies many analogies between apparently unrelated notions in mechanics, including the duality between forces and angular velocities. It is known that the real 6-dimensional space of screws can be endowed with an operator $$\mathcal {E}$$ E , $$\mathcal {E}^2=0$$ E 2 = 0 , that converts it into a rank 3 free module over the dual numbers. In this paper we prove the converse, namely, given a rank 3 free module over the dual numbers, endowed with orientation and a suitable scalar product ($$\mathbb {D}$$ D -module geometry), we show that it is possible to define, in a canonical way, a Euclidean space so that each element of the module is represented by a screw vector field over it. The new approach has the effectiveness of motor calculus while being independent of any reduction point. It gives insights into the transference principle by showing that affine space geometry is basically vector space geometry over the dual numbers. The main results of screw theory are then recovered by using this point of view.

Cephalometric Screening Assessment for Superior Airway Space Narrowing—Added Value of Three-Dimensional Imaging

Assessing the morphology of the superior airway space is a crucial diagnostic step in the treatment planning of patients with obstructive sleep apnea syndrome (OSAS) or prior to orthognathic surgery. The aim of this study is to evaluate the necessary scope of a two-dimensional cephalometric assessment and the necessity of three-dimensional imaging in the identification of superior airway space narrowing (SASN). Methods: The computed tomography studies of 100 non-obese, non-OSAS patients were evaluated and analyzed retrospectively. Multiplanar reconstructions were created and underwent cephalometric evaluation. The three-dimensional superior airway morphology was segmented and measured for the minimal cross-sectional area (Amin) and volume (V0). Patients were grouped according to Amin < 80 mm2 and V0 < 12 cm3. Cephalometric parameters (CPs) were analyzed according to Amin and V0 with an unpaired t-test, Pearson correlation, and ROC-curve analysis. Results: The CPs regarding sagittal airway space dimensions (IPAS, MPAS, SPAS) and mandibular body length (GoGn) show the strongest correlation to the three-dimensional minimal cross-sectional area (Amin). The ROC-curve analysis classifying for SASN led to an AUC of 0.86 for IPAS, 0.87 for MPAS, 0.88 for SPAS, and 0.63 for GoGn. Three-dimensional imaging may further improve the diagnostic accuracy in the identification of SASN for IPAS below 13.5 mm, MPAS below 10.2 mm, SPAS below 12.5 mm, and GoGn below 90.2 mm. Conclusions: Two-dimensional cephalometric sagittal airway space diameters and mandibular body length are useful initial screening parameters in the identification of superior airway space narrowing. Nevertheless, as the correlation of two-dimensional cephalometric parameters with three-dimensional upper airway space narrowing is varying and highly dependent on acquisition circumstances, indications for three-dimensional imaging, if possible, in the supine position to evaluate upper airway space morphology should be provided generously, especially in patients with low but normal airway space parameters in two-dimensional cephalometry.

Physics-informed neural networks in groundwater flow modeling: Advantages and future directions

In recent years, there has been enormous development in soft computing, especially artificial intelligence (AI), which has developed robust methods for solving complex engineering problems. Researchers in the field of water resources engineering have applied these AI methods to solve a variety of hydrological problems. Despite their widespread use in the surface and atmospheric hydrology fields, groundwater hydrologists have not widely used AI methods in their routine field-scale modeling efforts. This is because AI models have been primarily considered black box models that lack physical meaning. Furthermore, using AI models to generate the space-time distribution of transient groundwater level variations is challenging and requires further flux balance and mass transport analyses. More recently, a new type of physics-informed neural network (PINN) model has been developed to address several limitations by integrating governing physics (groundwater flow equations) into the AI tools. This study presents the systematic advantages of the PINN algorithm for solving groundwater problems using a set of classic test problems. As discussed in detail in the article, these advantages and potentials are associated with the meshless nature of PINN, its continuous time and space dimensions, its independence from time-stepping and incremental marching in space, and its efficiency in running time. However, despite PINN's promising attributes, it is important to acknowledge its nascent stage of development and the inherent limitations of all neural network models, such as training challenges and hyperparameter selection. Thus, collaborative efforts between groundwater modelers and computer scientists are imperative to explore and exploit the full potential of PINN in tackling increasingly complex groundwater problems and nurturing PINN into a dependable modeling tool in industry and academia.

Sea Anemone-Inspired Slippery Liquid-Infused Porous Surface (SLIPS) with Bionic Cilia for Responsive 4D Antifouling.

The formation process of biofouling is actually a 4D process with both spatial and temporal dimensions. However, most traditional antifouling coatings, including slippery liquid-infused porous surface (SLIPS), are limited to performing antifouling process in the 2D coating plane. Herein, inspired by the defensive behavior of sea anemones' wielding toxic tentacles, a "4D SLIPS" (FSLIPS) is constructed with biomimetic cilia via a magnetic field self-assembly method for antifouling. The bionic cilia move in 3D space driven by an external magnetic field, thereby preventing the attachment of microorganisms. The FSLIPS releases the gaseous antifoulant (nitric oxide) at 1D time in response to light, thereby achieving a controllable biocide effect on microorganisms. The FSLIPS regulates the movement of cilia via the external magnetic field, and controls the release of NO overtime via the light response, so as to adjust the antifouling modes on demand during the day or night. The light/magnetic response mechanism endow the FSLIPS with the ability to adjust the antifouling effect in the 4D dimension of 1D time and 3D space, effectively realizing the intelligence, multi-dimensionality and precision of the antifouling process.

Urban vitality and built environment from the perspective of spatiotemporal heterogeneity

ABSTRACT The spatiotemporal heterogeneity of the built environment’s effects on urban vitality is analysed through geographically and temporally weighted regression models. It is found that residents’ travel time and patterns lead to temporal heterogeneity, which is manifested by the fluctuation of the environmental effect of the peak in the morning and evening and the difference between weekdays and weekends. This is especially evident in the business district. Spatial heterogeneity is mainly reflected in the difference between the new urban area and the old city area. Single-function green spaces in areas with high functional complexity still have a weak attraction to people. Land use mix, scale and location are rather nonstationary in the dimensions of time and space.

Flexwork and flextravel

Flexwork—flexible work arrangements that depart from the standard in-office, nine-to-five schedule—has become a staple in the post-pandemic era. The inherent flexibility of place and time in flexwork has significant implications for the travel and tourism sectors. This flexibility gives rise to adaptable travel/tourism arrangements, further blurring the boundaries between work and travel/tourism. Consequently, it creates a potential state where productivity and leisure are seamlessly interwoven. A theoretical framework is developed to encapsulate the temporality, spatiality, and liminality of this flexwork–flextravel state. This conceptualization, as a response to the increasingly indistinct demarcation of time–space dimensions and work–travel domains, carries implications for emerging travel patterns and the potential transformation of tourism landscapes and travel-related activities.

Hypergraph Isomorphism Computation.

The isomorphism problem, crucial in network analysis, involves analyzing both low-order and high-order structural information. Graph isomorphism algorithms focus on structural equivalence to simplify solver space, aiding applications like protein design, chemical pathways, and community detection. However, they fall short in capturing complex high-order relationships, unlike hypergraph isomorphism methods. Traditional hypergraph methods face challenges like high memory use and inaccurate identification, leading to poor performance. To overcome these, we introduce a hypergraph Weisfeiler-Lehman (WL) test algorithm, extending the WL test from graphs to hypergraphs, and develop a hypergraph WL kernel framework with two variants: the Hypergraph WL Subtree Kernel and Hypergraph WL Hyperedge Kernel. The Hypergraph WL Subtree Kernel counts different types of rooted subtrees and generates the final feature vector for a given hypergraph by comparing the number of different types of rooted subtrees. The Subtree Kernel identifies different rooted subtrees, while the Hyperedge Kernel focuses on hyperedges' vertex labels, enhancing feature vector generation. In order to fulfill our research objectives, a comprehensive set of experiments was meticulously designed, including seven graph classification datasets and 12 hypergraph classification datasets. Results on graph classification datasets indicate that the Hypergraph WL Subtree Kernel can achieve the same performance compared with the classical Graph Weisfeiler-Lehman Subtree Kernel. Results on hypergraph classification datasets show significant improvements compared to other typical kernel-based methods, which demonstrates the effectiveness of the proposed methods. In our evaluation, our proposed methods outperform the second-best method in terms of runtime, running over 80 times faster when handling complex hypergraph structures. This significant speed advantage highlights the great potential of our methods in real-world applications.

Linear Spectral Method for Simulating the Generation of Regular Waves by a Moving Bottom in a 3-dimensional Space

In this study, we introduce a linear spectral method capable of simulating wave generation and transformation caused by a moving bottom in a 3-dimensional space. The governing equations are linear dynamic free-surface boundary conditions and linear kinematic free-surface boundary conditions, which are solved in Fourier space. Solved velocity potential and free-surface displacement should satisfy continuity equation and kinematic bottom boundary condition. For numerical analysis, a 4th order Runge-Kutta method was utilized to analyze the time integral. The results obtained in Fourier space can be converted into velocity potential and free-surface displacement in a real space using inverse Fourier transform. Regular waves generated by various types of moving bottoms were simulated with the linear spectral method. Additionally, obliquely generated regular waves using specified bottom movements were simulated. The results obtained from the spectral method were compared to analytical solutions, showing good agreement between the two.

Hidden variable model for quantum computation with magic states on qudits of any dimension

It was recently shown that a hidden variable model can be constructed for universal quantum computation with magic states on qubits. Here we show that this result can be extended, and a hidden variable model can be defined for quantum computation with magic states on qudits with any Hilbert space dimension. This model leads to a classical simulation algorithm for universal quantum computation.

Multisolitons for the cubic NLS in 1-d and their stability

AbstractFor both the cubic Nonlinear Schrödinger Equation (NLS) as well as the modified Korteweg-de Vries (mKdV) equation in one space dimension we consider the set $\mathbf {M}_{N}$ M N of pure $N$ N -soliton states, and their associated multisoliton solutions. We prove that (i) the set $\mathbf {M}_{N}$ M N is a uniformly smooth manifold, and (ii) the $\mathbf {M}_{N}$ M N states are uniformly stable in $H^{s}$ H s , for each $s>-\frac{1}{2}$ s > − 1 2 .One main tool in our analysis is an iterated Bäcklund transform, which allows us to nonlinearly add a multisoliton to an existing soliton free state (the soliton addition map) or alternatively to remove a multisoliton from a multisoliton state (the soliton removal map). The properties and the regularity of these maps are extensively studied.

Review and experimental benchmarking of machine learning algorithms for efficient optimization of cold atom experiments

The generation of cold atom clouds is a complex process which involves the optimization of noisy data in high dimensional parameter spaces. Optimization can be challenging both in and especially outside of the lab due to lack of time, expertise, or access for lengthy manual optimization. In recent years, it was demonstrated that machine learning offers a solution since it can optimize high dimensional problems quickly, without knowledge of the experiment itself. In this paper we present results showing the benchmarking of nine different optimization techniques and implementations, alongside their ability to optimize a rubidium (Rb) cold atom experiment. The investigations are performed on a 3D 87Rb molasses with 10 and 18 adjustable parameters, respectively, where the atom number obtained by absorption imaging was chosen as the test problem. We further compare the best performing optimizers under different effective noise conditions by reducing the signal-to-noise ratio of the images via adapting the atomic vapor pressure in the 2D+ magneto-optical trap and the detection laser frequency stability.

TACO: A Turkish database for abstract concepts.

The organization of abstract concepts reflects different dimensions, grounded in the brain regions coding for the corresponding experience. Normative measures of linguistic stimuli offer noteworthy insights into the organization of conceptual knowledge, but studies differ in the dimensions and classes of concepts considered. Additionally, most of the available information has been collected in English, without considering possible linguistic and cultural differences. Here, we aimed to create a comprehensive Turkish database for abstract concepts (TACO), including rarely investigated classes such as political concepts. We included 503 words-78 concrete (fruits, animals, tools) and 425 abstract (emotions, social, mental states, theoretical, quantity, space, political)-rated by 134 Turkish speakers for familiarity, imageability, age of acquisition, valence, arousal, quantity, space, theoretical, social, mental state, and political dimensions. We calculated dominance and exclusivity, indicating the dimension receiving the highest mean score for each word, and the position of the word along the unidimensional-multidimensional continuum, respectively. A principal component analysis (PCA) was conducted on the semantic dimensions. The results showed that mental state was the dominant dimension for most concepts. Moderate to low levels of exclusivity indicated that the concepts were multidimensional. PCA revealed three components: Component 1 captured the juxtaposition between social/mental state and magnitude polarities, Component 2 highlighted affective components, and Component 3 grouped together political and theoretical dimensions. The introduction of political concepts provided insights into the multidimensional nature of this unexplored class, closely intertwined with the theoretical dimension. TACO constitutes the first comprehensive Turkish database covering several abstract dimensions, paving the way for cross-linguistic and cross-cultural studies of semantic representations.

KAJIAN KEBUTUHAN DAN PENDAPATAN PARKIR PADA KAWASAN OBJEK WISATA PANTAI KELAN KABUPATEN BADUNG BALI

Badung Regency is one of the largest contributors to regional economic income, namely in the world of tourism, especially the South Badung area which is famous for its many beach tourism objects which attract many foreign and local tourists. Availability of parking spaces, of course, must have good parking services in order to optimally utilize the available parking space capacity. This research focuses on planning the need for parking space and parking revenue for two-wheeled vehicles and four-wheeled vehicles in the Kelan Beach tourist area, because parking is one of the supports for tourism so that visitors can feel comfortable and can realize an adequate parking pattern. The planned land area for parking two and four-wheeled vehicles at Kelan Beach is 2097.30 m² in total. The survey method used is the cordon count and patrol method. Characteristics of parking for two-wheeled vehicles include the highest volume, namely 461, accumulation of 141 vehicles, duration of 1.63 hours, capacity of 173, turnover rate of 0.18, index of 0.68 less than (<) 1.00, which means the need for parking is below capacity/sufficient, and four-wheeled characteristics include volume maximum of 163, accumulation of 33 vehicles, duration of 1.48 hours, capacity of 49, turnover rate of 0.23, index of 0.57 less than (<) 1.00 which means parking needs are below capacity and do not need expansion. The parking space requirements for two-wheeled and four-wheeled vehicles are 63 and 20 slots respectively. The parking layout at Kelan Beach tourist destination adopts a 90° angle pattern for both two-wheeled and four-wheeled vehicles, with respective parking space dimensions of 0.75 m x 2.00 m and 2.50 m x 5.00 m. The projected annual parking revenue is estimated at IDR.499,441,667.00, calculated based on fixed rates. Paving blocks are chosen for the parking surface, with a cost of IDR.441,345,000.00.

Numerical workspace optimization for a 3-DOF delta parallel robot on constrained geometric solid models

For the workspace optimization of Delta Parallel Robot (DPR), this paper employs Geometric Modeling Kernel (GMK) to construct DPR’s solid workspace model constrained by two categories of angles with non-toroidal boundaries. Leveraging slicing and interpolating techniques, the maximal inscribed regular space within the DPR’s workspace is obtained in conjunction with numerical optimization methods. With the objective of maximizing effective volume utilization (the volume ratio between the prescribed regular space to the DPR’s workspace) and a prescribed regular space dimension, the Hook-Jeeves direct search method is coupled with the Interior-Point method to attain the optimal geometric DPR parameters on the constrained solid model of workspace. The effectiveness of the algorithm is validated through a design case. This numerical optimization methodology possesses generality, intuitiveness, precision, and high efficiency, theoretically applicable to the workspace optimization for other parallel mechanisms.

Patients' Representations of Perceived Distance and Proximity to Telehealth in France: Qualitative Study.

In the last 2 decades, new technologies have emerged in health care. The COVID-19 pandemic further accelerated the adoption of technology by both health care professionals and patients. These technologies create remote care practices that bring several benefits to the health care system: easier access to care, improved communication with physicians, and greater continuity of care. However, disparities in the acceptance and use of telehealth tools still exist among patients. These tools also disrupt conventional medical practices and prompt a new reassessment of the perceptions of distance and proximity as physical (ie, time and space dimensions) and nonphysical (ie, behavioral dimensions) concepts. The reasons why patients do or do not adopt telehealth tools for their care and therefore their perspectives on telehealth remain unanswered questions. We explored the barriers as well as the motivations for patients to adopt telehealth tools. We specifically focused on the social representations of telehealth to establish a comprehensive conceptual framework to get a better understanding of how telehealth is perceived by patients. This study uses a qualitative design through in-depth individual interviews. Participants were recruited using a convenience sampling method with balanced consideration of gender, age, location (urban/rural), and socioeconomic background. After collecting informed consent, interviews were transcribed and analyzed using the thematic analysis methodology. We conducted 14 interviews, with which data saturation was reached. The 2 main opposed dimensions, perceived proximity and distance, emerged as an essential structure for understanding the social representations of telehealth. A logic of engagement versus hostility emerged as the main tension in adopting telehealth, almost ideological. Interestingly, practical issues emerged regarding the adoption of telehealth: A logic of integration was opposed to a logic of constraints. Altogether, those dimensions enabled us to conceptualize a semiotic square, providing 4 categories with a coherent body of social representations. Due to the dynamic nature of these representations, we proposed 2 "paths" through which adherence to telehealth may improve. Our semiotic square illustrating patients' adherence to telehealth differentiates socially beneficial versus socially dangerous considerations and pragmatic from ideological postures. It shows how crucial it is to consider perceived distance and proximity to better understand barriers and motivations to adopting telehealth. These representations can also be considered as leverage that could be modified to encourage the step-by-step adhesion process. Even if reducing the perceived temporal distance to in-person meeting and enhancing the perceived proximity of access to care may be seen as efficient ways to adopt telehealth tools, telehealth can also be perceived as a care practice that threatens the patient-physician relationship. The patient-oriented perceived value turns out to be critical in the future development of and adherence to telehealth tools.

Two-dimensional and absolutely entanglement-breaking subspaces

Abstract Entanglement-breaking (EB) subspaces help determine the additivity of entanglement of formation (EOF), which is a long-standing issue in quantum information. We explicitly construct the
two-dimensional EB subspaces of any bipartite systems when system dimensions are equal, and we
apply the subspaces to construct EB spaces of arbitrary dimensions. We also present the partial
construction when system dimensions are different. Then we present the notion and properties of
EB subspaces for some systems, and in particular the absolute EB subspaces. We construct some
examples of absolute EB subspaces, as well as EB subspaces for some systems by using multiqubit
Dicke states.