Dimensional Space Research Articles

Moduli Spaces of (Co)Closed G2-Structures on Nilmanifolds

ABSTRACT We compute the dimensions of some moduli spaces of left-invariant closed and coclosed $\mathrm{G}_2$-structures on 7-dimensional nilmanifolds, showing that they are not related to the third Betti number. We also prove that, in contrast to the case of closed $\mathrm{G}_2$-structures, the group of automorphisms of a coclosed $\mathrm{G}_2$-structure is not necessarily abelian.

Formulating approximation error as noise in surrogate-assisted multi-objective evolutionary algorithm

Many real multi-objective optimization problems with 20-50 decision variables often have only a small number of function evaluations available, because of their heavy time/money burden. Therefore, surrogate models are often utilized as alternatives for expensive function evaluations. However, the approximation error of the surrogate model is inevitable compared to the real function evaluation. The approximation error has a similar impact on the algorithm as noise, i.e., different optimization stages suffer from various impacts. Therefore, the current optimization stage can be indirectly detected via measuring the impact of the noise formulated by the approximation error. In addition, the rising dimension of the search space leads to an increase in the approximation errors of the surrogate models, which poses a huge challenge for existing surrogate-assisted multi-objective evolutionary algorithms. In this work, we propose a stage-adaptive surrogate-assisted multi-objective evolutionary algorithm to solve the medium-scale optimization problems. In the proposed algorithm, the ensemble model consisting of the latest and historical models is used as the surrogate model, on the basis of which a set of potential candidates can be discovered. Then, a stage-adaptive infill sampling strategy selects the most suitable sampling strategy by analyzing the demand of the current optimization stage on convergence, diversity, model accuracy to sample from the candidates. As for the current optimization stage, it is detected by a noise impact indicator, where the approximation errors of surrogate models are formulated as noise. The experimental results on a series of medium-scale expensive test problems demonstrate the superiority of the proposed algorithm over six state-of-the-art compared algorithms.

Space jam: how retail technologies are influencing store space production

PurposeTechnologies are dramatically reshaping various aspects of the store space, modifying design, services and usage. Accordingly, several studies tackled technology impact on each of these aspects, investigating design, service and usage singularly, but lacking a holistic viewpoint. Thus, this paper aims to identify the different dimensions of the store space (levels) and assess the impact of technology introduction on store space dimensions (levels).Design/methodology/approachThe research employs a qualitative approach based on direct observations of apparel brand stores located in London between March and April 2023. Data collection followed a structured observation protocol covering store information, adopted technologies and their effects across various store space levels, i.e. consumption activities, service environment and customer experience.FindingsResults show that the store space can be defined as the sum of different dimensions consisting of consumption activities, service environment and customer experience. Accordingly, technology introduction holistically influences each of the three store space levels as follows: (1) first, technologies redefine how activities are performed or alters the location where certain activities are consumed; (2) within the service environment, technologies replace traditional elements, fill empty spaces and enhance the atmospherics; finally, (3) customer experience is enhanced in hedonic and/or utilitarian terms due to technology adoption.Originality/valueThis paper defines the space as a dynamic entity, providing a deeper understanding of how the store space is produced, from a holistic point of view and the role of retail technology in this process.

Two-dimensional and absolutely entanglement-breaking subspaces

Entanglement-breaking (EB) subspaces 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 system, when system dimensions are equal, and we apply the subspaces to construct EB spaces of arbitrary dimensions. We also present 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.

A finite difference scheme for (2+1)D cubic-quintic nonlinear Schrödinger equations with nonlinear damping

Solitons of the purely cubic nonlinear Schrödinger equation in a space dimension of n≥2 suffer critical and supercritical collapses. These solitons can be stabilized in a cubic-quintic nonlinear medium. In this paper, we analyze the Crank-Nicolson finite difference scheme for the (2+1)D cubic-quintic nonlinear Schrödinger equation with cubic damping. We show that both the discrete solution, in the discrete L2-norm, and discrete energy are bounded. By using appropriate settings and estimations, the existence and the uniqueness of the numerical solution are proved. In addition, the error estimations are established in terms of second order for both space and time in discrete L2-norm and H1-norm. Numerical simulations for the (2+1)D cubic-quintic nonlinear Schrödinger equation with cubic damping are conducted to validate the convergence.

Genetically synthesized supergain broadband wire-bundle antenna

High-gain antennas are essential hardware devices, powering numerous daily applications, including distant point-to-point communications, safety radars, and many others. While a common approach to elevate gain is to enlarge an antenna aperture, highly resonant subwavelength structures can potentially grant high gain performances. The Chu-Harrington limit is a standard criterion to assess electrically small structures and those surpassing it are called superdirective. Supergain is obtained in a case when internal losses are mitigated, and an antenna is matched to radiation, though typically in a very narrow frequency band. Here we develop a concept of a spectrally overlapping resonant cascading, where tailored multipole hierarchy grants both high gain and sufficient operational bandwidth. Our architecture is based on a near-field coupled wire bundle. Genetic optimization, constraining both gain and bandwidth, is applied on a 24-dimensional space and predicts 8.81 dBi realized gain within a half-wavelength in a cube volume. The experimental gain is 8.22 dBi with 13% fractional bandwidth. The developed approach can be applied across other frequency bands, where miniaturization of wireless devices is highly demanded.

Spatiotemporal characteristics of ecological resilience and its influencing factors in the Yellow River Basin of China

Maintaining and improving ecological resilience is of great practical significance for the Yellow River Basin to reduce potential ecological risks and deliver sustainable development. Based on the essential characteristics of evolutionary resilience, this paper developed an ecological resilience index system of “resistance-recovery-reconstruction-renewal” and calculated the ecological resilience of 75 prefecture-level cities in the Yellow River Basin from 2007 to 2021 with the improved TOPSIS method. Then the spatiotemporal evolution characteristics of ecological resilience were analyzed using the gravity center-standard deviation ellipse, Dagum Gini coefficient decomposition, and spatial autocorrelation analysis. Furthermore, the dynamic spatial Durbin model (DSDM) was used to investigate the influencing factors of ecological resilience. The main results are as follows: (1) The ecological resilience of the Yellow River Basin showed an overall fluctuating upward trend, and the average annual growth rate in the downstream region was larger than in the upstream and midstream regions. (2) Cities with similar levels of ecological resilience were distributed in a “large settlement, small scattered” pattern. The center of gravity shifted to the southeast, and the spatial distribution exhibited a “northwest-southeast” pattern and a trend towards an “east–west” pattern. The primary source of spatial differences was the intensity of transvariation. (3) The ecological resilience in the Yellow River Basin showed significant spatial clustering, with the H–H clustering area shifting from the Hubao-Eyu urban agglomeration to the Shandong Peninsula urban agglomeration, and the L–L clustering area mainly distributed around the Central Plains city cluster. (4) The ecological resilience of the Yellow River Basin exhibited significant snowball, spillover, and siphon effects in time, space, and space-time dimensions, respectively. In the short and long term, population density and openness significantly positively affected the ecological resilience of local and surrounding cities. Urbanization had a long-term effect on ecological resilience without a short-term effect. GDP per capita and industrial structure only imparted a significant positive influence on local ecological resilience. The negative spatial spillover of the intensity of financial investment in technological innovation gradually turned into a positive effect.

Finite element approximation of unique continuation of functions with finite dimensional trace

We consider a unique continuation problem where the Dirichlet trace of the solution is known to have finite dimension. We prove Lipschitz stability of the unique continuation problem and design a finite element method that exploits the finite dimensionality to enhance stability. Optimal a priori and a posteriori error estimates are shown for the method. The extension to problems where the trace is not in a finite dimensional space, but can be approximated to high accuracy using finite dimensional functions is discussed. Finally, the theory is illustrated in some numerical examples.

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We consider the stability of the global weak solution of the Quantum Euler system in two space dimensions. More precisely, we establish compactness properties of global finite energy weak solution for large initial data provided that these are axisymmetric. The main novelty is that the initial velocity is not necessary irrotational when the density is not vanishing, our main argument is based on the Madelung transform which enables us to prove new Kato estimates on the irrotational part of the velocity.

Datacube segmentation via deep spectral clustering

Extended vision techniques are ubiquitous in physics. However, the data cubes steaming from such analysis often pose a challenge in their interpretation, due to the intrinsic difficulty in discerning the relevant information from the spectra composing the data cube. Furthermore, the huge dimensionality of data cube spectra poses a complex task in its statistical interpretation; nevertheless, this complexity contains a massive amount of statistical information that can be exploited in an unsupervised manner to outline some essential properties of the case study at hand, e.g. it is possible to obtain an image segmentation via (deep) clustering of data-cube’s spectra, performed in a suitably defined low-dimensional embedding space. To tackle this topic, we explore the possibility of applying unsupervised clustering methods in encoded space, i.e. perform deep clustering on the spectral properties of datacube pixels. A statistical dimensional reduction is performed by an ad hoc trained (variational) AutoEncoder, in charge of mapping spectra into lower dimensional metric spaces, while the clustering process is performed by a (learnable) iterative K-means clustering algorithm. We apply this technique to two different use cases, of different physical origins: a set of macro mapping x-ray fluorescence (MA-XRF) synthetic data on pictorial artworks, and a dataset of simulated astrophysical observations.

Recurrence formula for some higher order evolution equations

Riccati’s differential equation is formulated as abstract equation in finite or infinite dimensional Banach spaces. Since the Riccati’s differential equation with the Cole–Hopf transform shows a relation between the first order evolution equations and the second order evolution equations, its generalization suggests the existence of recurrence formula leading to a sequence of differential equations with different order. In conclusion, by means of the logarithmic representation of operators, a transform between the first order evolution equations and the higher order evolution equation is presented. Several classes of evolution equations with different orders are given, and some of them are shown as examples.

Application of Social Space as a Tool for Physical Planning: Case Study of Mymensingh Town

Space has a social dimension. Social space consists of physical space and mental space. Physical and mental perspectives are only able to achieve partial description or cross-sections of space. The general approach of physical planning is concentrated only on physical dimension of space. Most city planners deal with essentially static concepts with land use maps and plans they prepare. They tend to view the city as a static arrangement of physical objects which lacks in mental space. Again, mind is spatially oriented. Hence, there is a gap between the ways our cities have been built and the way people perceive them. Above all, neither the plan nor their underlying studies have successfully depicted the city as a social process operating in space. In the course of time, every section and part of the city takes on something of the character and qualities of its inhabitants. In current (urban) planning process, space is dealt to offer on facilities and services people require to have a better life. It is ignored to explore how they perceive their surrounding and every day’s space domain. This paper explores ‘social space’ as a planning tool and examines its potential application in the physical planning process.

The cubic-quintic nonlinear Schrödinger equation with inverse-square potential

We consider the nonlinear Schrödinger equation in three space dimensions with a focusing cubic nonlinearity and defocusing quintic nonlinearity and in the presence of an external inverse-square potential. We establish scattering in the region of the mass-energy plane where the virial functional is guaranteed to be positive. Our result parallels the scattering result of [11] in the setting of the standard cubic-quintic NLS.

FSBOA: feature selection using bat optimization algorithm for software fault detection

Feature selection (FS) plays a crucial role in software fault prediction (SFP), aiming to identify a subset of relevant and discriminative features from a large pool of software metrics. It serves as a critical preprocessing step in building accurate fault prediction models, enabling the identification of potential software faults early in the development life cycle and facilitating effective resource allocation for testing and maintenance activities. The study's objective is to determine how well the bat optimization algorithm (BOA) can extract the features that are most important for correctly predicting software flaws, improve the accuracy of fault prediction, reduce the dimensionality of the feature space, and mitigate the risk of overfitting, thereby enabling more effective resource utilization and better allocation of testing efforts. The forecasting models underwent testing and training utilizing a collection of software metrics, with the datasets undergoing evaluation using several different FS algorithms. An assessment was conducted by contrasting the effectiveness of multiple optimization algorithms, including evolutionary methods such as FS employing genetic algorithm (FSGA), FS employing differential evolution (FSDE), and swarm-based techniques such as FS employing ant colony optimization (FSACO), FS employing particle swarm optimization (FSPSO), FS employing firefly algorithm (FSFA), and FS employing binary grey wolf optimization algorithm (FSBGWO) in relation to FS employing bat optimization algorithm (FSBAO). The results obtained from FSBAO approach demonstrate the effectiveness in solving FS optimization problems with at most accuracy of 98.92%. Furthermore, the experimental results have been statistically validated for the greater efficiency of the proposed FSBAO algorithm. This study's findings have crucial implications for developing a software failure prediction models that is more accurate and efficient.

A Hidden Convexity of Nonlinear Elasticity

A technique for developing convex dual variational principles for the governing PDE of nonlinear elastostatics and elastodynamics is presented. This allows the definition of notions of a variational dual solution and a dual solution corresponding to the PDEs of nonlinear elasticity, even when the latter arise as formal Euler–Lagrange equations corresponding to non-quasiconvex elastic energy functionals whose energy minimizers do not exist. This is demonstrated rigorously in the case of elastostatics for the Saint-Venant Kirchhoff material (in all dimensions), where the existence of variational dual solutions is also proven. The existence of a variational dual solution for the incompressible neo-Hookean material in 2-d is also shown. Stressed and unstressed elastostatic and elastodynamic solutions in 1 space dimension corresponding to a non-convex, double-well energy are computed using the dual methodology. In particular, we show the stability of a dual elastodynamic equilibrium solution for which there are regions of non-vanishing length with negative elastic stiffness, i.e. non-hyperbolic regions, for which the corresponding primal problem is ill-posed and demonstrates an explosive ‘Hadamard instability;’ this appears to have implications for the modeling of physically observed softening behavior in macroscopic mechanical response.

Near-term quantum algorithm for solving the MaxCut problem with fewer quantum resources

MaxCut is an NP-hard combinatorial optimization problem in graph theory. The quantum approximate optimization algorithms (QAOAs) offer new methods for solving such problems, which are potentially better than classical schemes. However, the requirement of N qubits for solving graphs with N-vertex in QAOA, coupled with the large-N trainability issue due to barren plateaus, poses a substantial challenge for noisy intermediate-scale quantum (NISQ) devices. Recently, a hybrid quantum–classical algorithm has been proposed for solving semidefinite programs (SDPs), named NISQ SDP Solver (NSS). In this paper, we study the performance of the NSS for solving MaxCut problem via the introduction of a near-term quantum algorithm and execution of experimental simulations. Since the MaxCut problem admits a relaxation into an SDP formulation, the SDP can be solved using NSS, with a subsequent classical post-processing step converting the hybrid density matrix into a MaxCut solution. After performing these steps, the near-term quantum algorithm will also inherit the advantages of NSS. We analyze the algorithm as compared to QAOAs and find that the depth of the quantum circuit is independent of the number of edges on the graph. Our algorithm requires logN qubits and has O(1) circuit depth. This implies that it uses exponentially fewer qubits compared to QAOAs while also requiring a significantly reduced circuit depth to solve the MaxCut problem. To demonstrate the effectiveness of the NSS, we focused on 3-regular graphs, 9-regular graphs, and ER graphs. Numerical results indicate that the quantum algorithm achieves a comparable approximation ratio with classical methods by solving the original high dimensional problem within a lower dimensional ansatz space. Analysis under various initial states shows that the algorithm exhibits a remarkably stable performance.

Pattern Recognition of Alkaloids by Inhibiting the Catalytic Activity of Dopzymes for Dopamine.

Exploiting the specific recognition probe for all of the biomolecules is difficult in "lock-and-key" biosensors. The cross-reaction or the semispecific probe in pattern recognition mode is an alternative strategy through extracting a multidimensional signal array from recognition elements. Here, we design a pattern recognition sensor array based on the alkaloid-inhibited catalytic activity of dopzymes for the discrimination and determination of six alkaloids. In this sensor array, three different G-rich sequences, i.e., G-triplex (G3), G-quadruplex (GQ1), and the G-quadruplex dimer (2GQ1) possessing various peroxidase activities, conjugated with a dopamine aptamer and the dopzymes (G3-d-apt, GQ1-d-apt, and 2GQ1-d-apt) were obtained with an enhanced catalytic performance for the substrate. Through the interactions between six target alkaloids and G3, GQ1, and 2GQ1 regions, the pattern signal (6 alkaloids × 3 dopzymes × 5 replicates) was obtained from the diverse inhibited effect for the dopzyme activity. In virtue of the statistical method principal component analysis (PCA), the data array was projected into a new dimensional space to acquire the three-dimensional (3D) canonical scores and grouped into their respective clusters. The sensor array exhibited an outstanding discrimination and classification capability for six alkaloids with different concentrations with 100% accuracy. In addition, the nonspecific recognition elements of the sensor array showed high selectivity even though other alkaloids with similar structures to targets existed in the samples. Importantly, the levels of the six targets can be analyzed by the most influential discrimination factor, which represented the vector with the highest variance, evidencing that the sensor array has potential in drug screening and clinical treatment.

A Scalar Measure of Acoustic Hazard Assessment

The article addresses the problem of assessing the impact of road modernization on improving the acoustic environment. It formulates a hypothesis about the advisability of adopting the scalar dimension of the decibel space to describe acoustic hazards. It is proposed to reduce the analysis of changes in sound levels to the analysis of changes in the coefficient of exceedance of the recommended noise levels. Its value is determined by the decibel relation of dividing sound levels. The basis for the assessment of the effectiveness of the adopted solution was the analysis of the statistical characteristics of monitored exceedances of recommended noise levels, considered through the prism of the current and proposed measure. They showed greater sensitivity of the proposed coefficient in the assessment of the improvement of the acoustic climate caused by road modernization. For example, the median noise level for nights before the road modernization was 66.9 dB(A), and after the modernization 65.6 dB(A). However, the coefficient of exceedances decreased by approximately 25 %. Numerical simulations, in accordance with the Cnossos noise model, showed that reducing the speed by 10 km/h will reduce the coefficient of exceedances by approximately 20 %.

Virtual Reality Application for the Safety Improvement of Intralogistics Systems

Immersive technologies from the spectrum of Industry 4.0, such as Virtual Reality (VR), are increasingly used in research and safety analysis in industrial and intralogistics systems, including distribution warehouses and production plants. Safety in intralogistics systems is influenced by design and management processes, human behavior, and device performance. In all these areas, VR can serve as a supportive technology for visualization, testing, and employee training. However, this requires the development of principles for integrating VR into standard procedures for the design, modernization, and analysis of intralogistics and production systems. This article discusses the use of VR to analyze the occupational and functional safety of intralogistics systems. It reviews the literature and VR implementations aimed at examining and improving safety in industrial systems. The article explores the integration of VR into the design and analysis procedures for intralogistics and production systems. The authors present a five-dimensional decision space for assessing the use of VR, including identifying subjects of safety analysis, threats and hazards specific to intralogistics, countermeasures for these threats, factors affecting safety, and mechanisms by which VR can improve safety in intralogistics systems. As a subsequent step, the authors discuss using universal simulation environments that support VR technology to study and enhance safety in intralogistics systems, providing a framework example based on the FlexSim (2023 update 2) environment. Finally, this article addresses the threats and limitations of VR technology, along with the challenges and future prospects of VR in the context of Industry 4.0. The article concludes that VR can be an essential tool for increasing safety in the future, albeit with some reservations about certain features of this technology.

Hybrid genetic optimization for quantum feature map design

Kernel methods are an import class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be linearly separable in feature space. Previous work has shown that quantum feature map design can be automated for a given dataset using NSGA-II, a genetic algorithm, while both minimizing circuit size and maximizing classification accuracy. However, the evaluation of the accuracy achieved by a candidate feature map is costly. In this work, we demonstrate the suitability of kernel-target alignment as a substitute for accuracy in genetic algorithm-based quantum feature map design. Kernel-target alignment is faster to evaluate than accuracy and does not require some data points to be reserved for its evaluation. To further accelerate the evaluation of genetic fitness, we provide a method to approximate kernel-target alignment. To improve kernel-target alignment and root mean squared error, the final trainable parameters of the generated circuits are further trained using COBYLA to determine whether a hybrid approach applying conventional circuit parameter training can easily complement the genetic structure optimization approach. A total of eight new approaches are compared to the original across nine varied binary classification problems from the UCI machine learning repository, showing that kernel-target alignment and its approximation produce feature map circuits enabling comparable accuracy to the previous work but with larger margins on training data (in excess of 20% larger) that improve further with circuit parameter training.