3D Subspace Research Articles

High-precision two- and three- dimensional atom localization in a microwave and radio-frequency driven Δ∇ system

We introduce a new approach for precise and high-resolution two-dimensional (2D) and three-dimensional (3D) atom localization in a four-level Δ∇ atomic system driven by microwave (M) and radio frequency (R) fields. In the proposed work, additional microwave and radio-frequency fields are utilized for an efficient control of the localization precision. Due to the spatially varying atom-field interaction, the probe susceptibility become position dependent and therefore, one can directly ascertain the position probability distribution of an atom by analyzing the probe spectra. The phase-sensitive property of the atomic system plays a significant role in substantially reducing the uncertainty associated with atom position measurements. We have studied the system behavior through the analysis of dressed states, which forms the basis for its physical interpretation. The increase in precision for measuring the atom’s position is a result of interference between one-photon excitation and the phase-dependent three-photon excitation arising from the closed interacting contour within the laser-driven atomic system, as demonstrated through both numerical calculations and qualitative analyses. The findings indicate that precise sub-wavelength atom localization can be attained by appropriately adjusting the system parameters. Also, the optimal adjustment of these parameters can lead to 100% probability of locating the atom at a particular position within 2D and 3D subspaces.

The Evolution of the Phase Space Structure Along Pitchfork and Period-Doubling Bifurcations in a 3D-Galactic Bar Potential

We investigate how the phase space structure of a Three-Dimensional (3D) autonomous Hamiltonian system evolves across a series of successive Two-Dimensional (2D) and 3D pitchfork and period-doubling bifurcations, as the transition of the parent families of Periodic Orbits (POs) from stability to simple instability leads to the creation of new stable POs. Our research illustrates the consecutive alterations in the phase space structure near POs as the stability of the main family of POs changes. This process gives rise to new families of POs within the system, either maintaining the same or exhibiting higher multiplicity compared to their parent families. Tracking such a phase space transformation is challenging in a 3D system. By utilizing the color and rotation technique to visualize the Four-Dimensional (4D) Poincaré surfaces of section of the system, i.e. projecting them onto a 3D subspace and employing color to represent the fourth dimension, we can identify distinct structural patterns. Perturbations of parent and bifurcating stable POs result in the creation of tori characterized by a smooth color variation on their surface. Furthermore, perturbations of simple unstable parent POs beyond the bifurcation point, which lead to the birth of new stable families of POs, result in the formation of figure-8 structures of smooth color variations. These figure-8 formations surround well-shaped tori around the bifurcated stable POs, losing their well-defined forms for energies further away from the bifurcation point. We also observe that even slight perturbations of highly unstable POs create a cloud of mixed color points, which rapidly move away from the location of the PO. Our study introduces, for the first time, a systematic visualization of 4D surfaces of section within the vicinity of higher multiplicity POs. It elucidates how, in these cases, the coexistence of regular and chaotic orbits contributes to shaping the phase space landscape.

Determining a musculoskeletal system’s pre-stretched state using continuum–mechanical forward modelling and joint range optimization

The subject-specific range of motion (RoM) of a musculoskeletal joint system is balanced by pre-tension levels of individual muscles, which affects their contraction capability. Such an inherent pre-tension or pre-stretch of muscles is not measureable with in vivo experiments. Using a 3D continuum mechanical forward simulation approach for motion analysis of the musculoskeletal system of the forearm with 3 flexor and 2 extensor muscles, we developed an optimization process to determine the muscle fibre pre-stretches for an initial arm position, which is given human dataset. We used RoM values of a healthy person to balance the motion in extension and flexion. The performed sensitivity study shows that the fibre pre-stretches of the m. brachialis, m. biceps brachii and m. triceps brachii with 91%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$91\\%$$\\end{document} dominate the objective flexion ratio, while m. brachiradialis and m. anconeus amount 7.8%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$7.8\\%$$\\end{document} and 1.2%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.2\\%$$\\end{document}. Within the multi-dimensional space of the surrogate model, 3D sub-spaces of primary variables, namely the dominant muscles and the global objective, flexion ratio, exhibit a path of optimal solutions. Within this optimal path, the muscle fibre pre-stretch of two flexors demonstrate a negative correlation, while, in contrast, the primary extensor, m. triceps brachii correlates positively to each of the flexors. Comparing the global optimum with four other designs along the optimal path, we saw large deviations, e.g., up to 15∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }$$\\end{document} in motion and up to 40% in muscle force. This underlines the importance of accurate determination of fibre pre-stretch in muscles, especially, their role in pathological muscular disorders and surgical applications such as free muscle or tendon transfer.

Weyl singularities in polaritonic multiterminal Josephson junctions

We study theoretically analog multi-terminal Josephson junctions formed by gapped superfluids created upon resonant pumping of cavity exciton-polaritons. We study the $p$-like bands of a 5-terminal junction in the 4D parameter space created by the superfluid phases acting as quasi-momenta. We find 4/6 Weyl points in 3D subspaces with preserved/broken time-reversal symmetry. We link the real space topology (vortices) to the parameter space one (Weyl points). We derive an effective Hamiltonian encoding the creation, motion, and annihilation of Weyl nodes in 4D. Our work paves the way to the study of exotic topological phases in a platform allowing direct measurement of eigenstates and band topology.

Cosmological Constant from Boundary Condition and Its Implications beyond the Standard Model

Standard cosmology has long been plagued by a number of persistent problems. The origin of the apparent acceleration of the cosmic expansion remains enigmatic. The cosmological constant has been reintroduced as a free parameter with a value in energy density units that “happens” to be of the same order as the present matter energy density. There is an internal inconsistency with regards to the Hubble constant, the so-called H0 tension. The derived value of H0 depends on the type of data that is used. With supernovae as standard candles, one gets a H0 that is 4–5 σ larger than the value that one gets from CMB (Cosmic Microwave Background) data for the early universe. Here we show that these problems are related and can be solved if the cosmological constant represents a covariant integration constant that arises from a spatial boundary condition, instead of being a new type of hypothetical physical field, “dark energy”, as assumed by standard cosmology. The boundary condition only applies to the bounded 3D subspace that represents the observable universe, the hypersurface of the past light cone.

Density Matrix via Few Dominant Observables for the Ultrafast Non-Radiative Decay in Pyrazine.

Unraveling the density matrix of a non-stationary quantum state as an explicit function of a few observables provides a complementary view of quantum dynamics. We have recently developed a practical way to identify the minimal set of the dominant observables that govern the quantal dynamics even in the case of strong non-adiabatic effects and large anharmonicity [Komarova et al., J. Chem. Phys. 155, 204110 (2021)]. Fast convergence in the number of the dominant contributions is achieved when instead of the density matrix we describe the time-evolution of the surprisal, the logarithm of the density operator. In the present work, we illustrate the efficiency of the proposed approach using an example of the early time dynamics in pyrazine in a Hilbert space accounting for up to four vibrational normal modes, {Q10a, Q6a, Q1, and Q9a}, and two coupled electronic states, the optically dark and the bright states. Dynamics in four-dimensional (4D) configurational space involve 19,600 vibronic eigenstates. Our results reveal that the rate of the ultrafast population decay as well as the shape of the nuclear wave packets in 2D, accounting only for {Q10a,Q6a} normal modes, are accurately captured with only six dominant time-independent observables in the surprisal. Extension of the dynamics to 3D and 4D vibrational subspace requires only five additional constraints. The time-evolution of a quantum state in 4D vibrational space on two electronic states is thus compacted to only 11 time-dependent coefficients of these observables.

Clustering information-constrained 3D U-Net subspace clustering for hyperspectral image

ABSTRACT Hyperspectral image (HSI) clustering is a challenging task due to the complex spatial-spectral structure and high-dimensional property in HSI data. In this letter, a novel clustering information-constrained 3D U-Net subspace clustering network is proposed for HSI clustering. Considering the spatial-spectral information, the proposed network takes the 3D pixel cubes around the pixels as the input. Based on the 3D pixel cubes, a 3D U-Net subspace clustering network is introduced to extract spatial-spectral features from 3D pixel cubes and learn self-representation subspace property among pixels. In order to learn features more suitable for clustering, a clustering information constraint is introduced to explore useful information gain in the existing clustering result. Experiments conducted on three public HSI datasets illustrate the superior performance of the proposed method.

A Framework for the Comparison of Agent-based Models.

We develop a methodology for comparing agent-based models that are developed for the same domain, but may differ in the data sets (e.g., geographical regions) to which they are applied, and in the structure of the model. Our approach is to learn a response surface in the common parameter space of the models and compare the regions corresponding to qualitatively different behaviors in the models. As an example, we develop an active learning algorithm to learn phase shift boundaries in contagion processes in order to compare two agent-based models of rooftop solar panel adoption developed for different regions. We present results for 2D and 3D subspaces of the parameter space, though the approach scales to higher dimensions as well.

3D Compressed Spectrum Mapping With Sampling Locations Optimization in Spectrum-Heterogeneous Environment

Spectrum mapping has emerged as an important problem in wireless communications, which generates a spectrum map for the spectrum resource analysis and management. Given the constrained transceiver volume and the limited energy consumption, how to effectively reconstruct the spectrum situation by the limited sampling data is a pressing challenge for spectrum mapping. In this paper, by exploiting the sparse nature of spectrum situation, we firstly attempt to solve the three-dimensional (3D) compressed spectrum mapping problem in the way of compressed sensing. Then, we develop a quadrature and right-triangular (QR) pivoting based measurement matrix optimization algorithm. By iteratively selecting new dominant sampling locations, it promotes the recovery accuracy compared to random measurement. After that, we propose a 3D spatial subspace based orthogonal matching pursuit (OMP) algorithm to recover spectrum situation for 3D compressed spectrum mapping. Finally, simulations are presented to show the comparisons in terms of localization, source signal strength recovery, recovery success rate and situation recovery. Results show our proposed 3D spectrum mapping scheme not only effectively reduces the sampling number, but also achieves a high level of spectrum mapping accuracy.

Variational Formulation of Linear Equations of Coupled Thermohydrodynamics and Heat Conductivity

We consider the coupled processes of thermohydrodynamics and heat conduction and construct a variational model of such coupled problems using four-dimensional space-time continuum where time is an equal coordinate along with spatial coordinates. In this consideration 3D subspace of generalized four-dimensional pseudo-continuum is associated with three-dimension deformed media. In the general case we consider irreversible processes and use the variational principle of possible displacements and the variational Sedov’s principle to construct variation model. It is assumed that the 4D pseudo-continuum considered below is transversely isotropic in the direction of the unit vector of time. Thus, an asymmetric 4D stress tensor preserves the symmetry properties with respect to spatial tangential stresses in 3D subspaces. It is shown that the proposed version of the model allows us to formulate the full range of consistent thermomechanical and thermodynamic physical relations, and the system of governing equations includes, as special cases, the equations of thermoelasticity, thermohydrodynamics, the linear Navier–Stokes equations for compressible and incompressible media, the equations of heat balance with the laws of thermal conductivity of Fourier, Maxwell–Cattaneo.

Intoxicated person identification using Markov chains and neural networks

In this work, Markov chains are used to model the statistical behavior of the pixels on the image of the forehead of a person in order to detect intoxication. It is the first time that second-order statistics are used for this purpose. The images were obtained in the thermal infrared region. Intoxication affects blood vessels activity and thus the temperature distribution on the face having a significant effect on the corresponding pixels statistics. The pixels of the forehead images are quantized to 32 Gy levels so that Markov chain models are structured using 32 states. The feature vectors used are the eigenvalues obtained from the first-order transition matrices of the Markov chain models. Since for each person a frame sequence of 50 views is acquired, a cluster of 50 vectors is formed in the 32-dimensional feature space. The feature space is firstly analyzed using projections of the clusters in 3D subspaces of the original 32D feature space. After that, the capability of a simple feed forward neural network to separate the clusters belonging to sober persons from those corresponding to intoxicated persons is investigated. A simple three-layer neural structure has a 98% vector separability success and a 100% cluster separability if the majority voting is considered. Furthermore, the classification problem is faced by excluding from the training procedure either one or five persons and using them in the testing phase. Accordingly, a neural network is trained using all except the excluded data. The obtained neural structure tested with the features of the persons in which it was not trained presents high drunk identification success if the majority voting is considered.

Model and observation of dispatchable region for flexible distribution network

Soft open points (SOPs), defined as the power electronic devices installed to replace normally open points in distribution network, can improve the flexibility of power control and thus further enhance the reliability and economy of power grids. Flexible distribution network (FDN) is a system-level concept to describe the distribution network equipped with multiple SOPs. Region method is to describe the secure range of the system operating in a geometric view. This paper adopts the region method to observe FDN for the first time. Firstly, the model of dispatchable region of FDN is proposed. The constraints of region space are formulated, considering SOPs, power flow, thermal capacity and voltage profile. Secondly, a simulation-based observation approach is also proposed to obtain the region projections on 2D and 3D sub-space. To illustrate the approach clearly, 2 small cases are given preceding a 7-feeders IEEE RBTS case. The region projections of case grids are observed and their topological characteristics are compared with those of traditional distribution network (TDN). The results indicate that FDN has advantages over traditional distribution network in operation security. For example, the region projections of FDN on 2-dimensional sub-space are about 2–4 times larger than those of TDN with the same network topology. The dispatchable region can be further developed into a useful tool for the secure and high-efficient operation of FDN in the future.

Static object imaging features recognition algorithm in dynamic scene mapping

In dynamic scene monocular visual SLAM, it is important to recognize static object imaging features for mapping. The optical flow of noise and the object moving in the same orientations would have the same orientations of static feature for two frames image, that would disturb static feature point recognition. Because the translational motion optical flow orientations method judges with optical flow of single feature point and translational motion orientations, it is not reliable for static feature point recognition. Therefore, a 3D motion segmentation combined for static object imaging features recognition is proposed, which clusters the same optical flow of feature points in 3D motion subspace, including orientations and amplitude of translation and rotation. The simulation results show that the proposed static object imaging features recognition method improves the recognition correct rate and reliability of static features. So, it is effective for static object imaging features recognition in dynamic scene mapping.

Examples of 4D, 𝒩 = 2 holoraumy

We provide an introduction to the concepts of holoraumy tensors, Lorentz covariant four-dimensional “Gadgets,” and Gadget angles within the context of minimal off-shell 4D, [Formula: see text] supermultiplets. This is followed by the calculation of the holoraumy tensors, Gadgets, and Gadget angles for minimal off-shell supermultiplets. Four tetrahedrons in four 3D subspaces of the holoraumy lattice space are found.

Sentinel lymph node fingerprinting

Background. When locating the sentinel lymph node (SLN), surgeons use state-of-the-art imaging devices, such as a 1D gamma probe or less widely spread a 2D gamma camera. These devices project the 3D subspace onto a 1D respectively 2D space, hence loosing accuracy and the depth of the SLN which is very important, especially in the head and neck area with many critical structures in close vicinity. Recent methods which use a multi-pinhole collimator and a single gamma detector image try to gain a depth estimation of the SLN. The low intensity of the sources together with the computational cost of the optimization process make the reconstruction in real-time, however, very challenging.Results. In this paper, we use an optimal design approach to improve the classical pinhole design, resulting in a non-symmetric distribution of the pinholes of the collimator. This new design shows a great improvement of the accuracy when reconstructing the position and depth of the radioactive tracer. Then, we introduce our Sentinel lymph node fingerprinting (SLNF) algorithm, inspired by MR-fingerprinting, for fast and accurate reconstruction of the tracer distribution in 3D space using a single gamma detector image. As a further advantage, the method requires no pre-processing, i.e. filtering of the detector image. The method is very stable in its performance even for low exposure times. In our ex vivo experiments, we successfully located multiple Technetium 99m (Tc-99m) sources with an exposure time of only one second and still, with a very small L2-error.Conclusion. These promising results under short exposure time are very encouraging for SLN biopsy. Although, this device has not been tested on patients yet, we believe: that this approach will give the surgeon accurate 3D positions of the SLN and hence, can potentially reduce the trauma for the patient.

Single‐ended travelling wave protection algorithm based on full waveform in the time and frequency domains

Single-ended travelling-wave-based protection has been available for several years, providing the advantages of low cost and no requirement for communication and synchronisation with the remote end. However, conventional single-ended travelling-wave-based protection has low reliability due to its use of only partial fault information, and it has high dependence on extracting a second reflected wavefront. A new single-ended travelling-wave-based protection algorithm using the 2 ms full-waveform post-fault signal in the time–frequency domain, which avoids the discrimination of the reflected wavefront, is presented. First, the full-waveform representation of the travelling wave in 3D subspace is proposed. The fault characteristics of the wideband travelling wave are analysed at different scales. Second, for faults that occur within one line or on adjacent lines, the propagation characteristics and reflection and refraction process are analysed in detail. Then, the correlation and difference of the full waveform are presented qualitatively and quantitatively. Finally, a time–frequency spectrum matrix is established based on the full waveform, and the protection algorithm is developed by using a time–frequency spectrum matrix and wave matching technology. Extensive simulations under different conditions verify the wide applicability and high reliability of the proposed algorithm.

Noninvasive Assessment of Atrial Fibrillation Complexity in Relation to Ablation Characteristics and Outcome.

Background: The use of surface recordings to assess atrial fibrillation (AF) complexity is still limited in clinical practice. We propose a noninvasive tool to quantify AF complexity from body surface potential maps (BSPMs) that could be used to choose patients who are eligible for AF ablation and assess therapy impact.Methods: BSPMs (mean duration: 7 ± 4 s) were recorded with a 252-lead vest in 97 persistent AF patients (80 male, 64 ± 11 years, duration 9.6 ± 10.4 months) before undergoing catheter ablation. Baseline cycle length (CL) was measured in the left atrial appendage. The procedural endpoint was AF termination. The ablation strategy impact was defined in terms of number of regions ablated, radiofrequency delivery time to achieve AF termination, and acute outcome. The atrial fibrillatory wave signal extracted from BSPMs was divided in 0.5-s consecutive segments, each projected on a 3D subspace determined through principal component analysis (PCA) in the current frame. We introduced the nondipolar component index (NDI) that quantifies the fraction of energy retained after subtracting an equivalent PCA dipolar approximation of heart electrical activity. AF complexity was assessed by the NDI averaged over the entire recording and compared to ablation strategy.Results: AF terminated in 77 patients (79%), whose baseline AF CL was 177 ± 40 ms, whereas it was 157 ± 26 ms in patients with unsuccessful ablation outcome (p = 0.0586). Mean radiofrequency emission duration was 35 ± 21 min; 4 ± 2 regions were targeted. Long-lasting AF patients (≥12 months) exhibited higher complexity, with higher NDI values (≥12 months: 0.12 ± 0.04 vs. <12 months: 0.09 ± 0.03, p < 0.01) and short CLs (<160 ms: 0.12 ± 0.03 vs. between 160 and 180 ms: 0.10 ± 0.03 vs. >180 ms: 0.09 ± 0.03, p < 0.01). More organized AF as measured by lower NDI was associated with successful ablation outcome (termination: 0.10 ± 0.03 vs. no termination: 0.12 ± 0.04, p < 0.01), shorter procedures (<30 min: 0.09 ± 0.04 vs. ≥30 min: 0.11 ± 0.03, p < 0.001) and fewer ablation targets (<4: 0.09 ± 0.03 vs. ≥4: 0.11 ± 0.04, p < 0.01).Conclusions: AF complexity can be noninvasively quantified by PCA in BSPMs and correlates with ablation outcome and AF pathophysiology.

Stable exponential cosmological solutions with zero variation of G and three different Hubble-like parameters in the Einstein\u2013Gauss\u2013Bonnet model with a Lambda -term

We consider a D-dimensional gravitational model with a Gauss–Bonnet term and the cosmological term Lambda . We restrict the metrics to diagonal cosmological ones and find for certain Lambda a class of solutions with exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters H >0, h_1 and h_2, corresponding to factor spaces of dimensions m > 2, k_1 > 1 and k_2 > 1, respectively, with k_1 ne k_2 and D = 1 + m + k_1 + k_2. Any of these solutions describes an exponential expansion of 3d subspace with Hubble parameter H and zero variation of the effective gravitational constant G. We prove the stability of these solutions in a class of cosmological solutions with diagonal metrics.

The Subspace Voyager: Exploring High-Dimensional Data along a Continuum of Salient 3D Subspaces.

Analyzing high-dimensional data and finding hidden patterns is a difficult problem and has attracted numerous research efforts. Automated methods can be useful to some extent but bringing the data analyst into the loop via interactive visual tools can help the discovery process tremendously. An inherent problem in this effort is that humans lack the mental capacity to truly understand spaces exceeding three spatial dimensions. To keep within this limitation, we describe a framework that decomposes a high-dimensional data space into a continuum of generalized 3D subspaces. Analysts can then explore these 3D subspaces individually via the familiar trackball interface while using additional facilities to smoothly transition to adjacent subspaces for expanded space comprehension. Since the number of such subspaces suffers from combinatorial explosion, we provide a set of data-driven subspace selection and navigation tools which can guide users to interesting subspaces and views. A subspace trail map allows users to manage the explored subspaces, keep their bearings, and return to interesting subspaces and views. Both trackball and trail map are each embedded into a word cloud of attribute labels which aid in navigation. We demonstrate our system via several use cases in a diverse set of application areas-cluster analysis and refinement, information discovery, and supervised training of classifiers. We also report on a user study that evaluates the usability of the various interactions our system provides.

An eccentricity-based data routing protocol for 3D wireless sensor networks

Wireless sensor networks (WSNs) are facing many challenges due to the limited resources. Thus, routing cost minimisation is one of the major issues in order to design a feasible network topology. This paper presents a simple and efficient data routing protocol of constructing three-dimensional (3D) WSN. It points to minimise the routing cost which includes the data gathering from deployed sensor nodes and the data forwarding to the sink(s). For this, the network is divided into 3D subspaces, and a routing centroid (RC) node is elected in the eccentricity region from any node in a subspace. In data forwarding, it selects an intermediate node in such a way that minimises the number of hops towards the sink. The simulation results show that, with benefit of RC node concept, our scheme can significantly reduce the overall data routing cost and then results in prolonging the network lifetime of a 3D WSN.