Search

Most neurological diseases are associated with abnormal brain asymmetries. Recent advances in automatic unsupervised techniques model normal brain asymmetries from healthy subjects only and treat anomalies as outliers. Outlier detection is usually done in a common standard coordinate space that limits its usability. To alleviate the problem, we extend a recent fully unsupervised supervoxel-based approach (SAAD) for abnormal asymmetry detection in the native image space of MR brain images. Experimental results using our new method, called N-SAAD, show that it can achieve higher accuracy in detection with considerably less false positives than a method based on unsupervised deep learning for a large set of MR-T1 images.

Computational cytometry methods are now frequently used in flow and mass cytometric data analyses. However, systematic bias-free methodologies to assess inter-sample variability have been lacking, thereby hampering efficient data mining from a large set of samples. Here, we devised a computational method termed LAVENDER (latent axes discovery from multiple cytometry samples with nonparametric divergence estimation and multidimensional scaling reconstruction). It measures the Jensen-Shannon distances between samples using the k-nearest neighbor density estimation and reconstructs samples in a new coordinate space, called the LAVENDER space. The axes of this space can then be compared against other omics measurements to obtain biological information. Application of LAVENDER to multidimensional flow cytometry datasets of 301 Japanese individuals immunized with a seasonal influenza vaccine revealed an axis related to baseline immunological characteristics of each individual. This axis correlated with the proportion of plasma cells and the neutrophil-to-lymphocyte ratio, a clinical marker of the systemic inflammatory response. The same method was also applicable to mass cytometry data with more molecular markers. These results demonstrate that LAVENDER is a useful tool for identifying critical heterogeneity among similar, yet different, single-cell datasets.

Large-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing solvers can become very slow, and their performance dependent on manual fine-tuning of numerical parameters. In addition, convergence can sensitively depend on particularities of the EDF’s parametrisation under consideration. Using the widely-used Skyrme EDF as an example, we investigate the impact of the parametrisation of the EDF, both in terms of the operator structures present and the size of coupling constants, on the convergence of numerical solvers. We focus on two aspects of the self-consistency cycle, which are the diagonalisation of a fixed single-particle Hamiltonian on one hand and the evolution of the mean-field densities and potentials on the other. Throughout the article we use a coordinate-space representation, for which the behaviour of algorithms can be straightforwardly analysed. We propose two algorithmic improvements that are easily implementable in existing solvers, heavy-ball dynamics and potential preconditioning. We demonstrate that these methods can be made virtually parameter-free, requiring no manual fine-tuning to achieve near-optimal performance except for isolated cases. The combination of both methods decreases substantially the CPU time required to obtain converged results. The improvements are illustrated for the MOCCa code that solves the self-consistent HFB problem in a 3d coordinate space representation for parametrisations of the standard Skyrme EDF at next-to-leading order in gradients and its extension to next-to-next-to-leading order., SCOPUS: ar.j, info:eu-repo/semantics/published

Differential cross sections for elastic nucleon–deuteron scattering at intermediate energies are calculated by solving the Faddeev equation in coordinate space using interaction models consisting of a two-nucleon potential and three-nucleon potentials based on the exchange of two pions among three nucleons. Attractive effects of the pion-exchange at medium range region in the three-nucleon potential are taken into account by using a larger cutoff mass parameter and by adding phenomenological repulsive three-nucleon potentials as a counterpart. It is shown that these effects increase the cross sections at backward angles, which tends to reduce discrepancies between theoretical calculations and experimental data.

The accurate evaluation of the Wigner phase space density for multidimensional system remains a challenging task. Path integral Monte Carlo methods offer a numerically exact approach for obtaining the Boltzmann density in coordinate space, but the Fourier-type integral required to construct the Wigner distribution generally leads to poor convergence. This paper describes a path integral method for constructing the Wigner density which substantially mitigates the Monte Carlo sign problem and thus is applicable to systems with many degrees of freedom. The starting point is the path integral representation of the coherent state density, which does not involve a Fourier integral and thus converges rapidly. We then use the relation between the coherent state and Wigner densities to construct the Wigner function, taking advantage of destructive phase cancellation to truncate the infinite series and thus confine the integrand, avoiding highly oscillatory regions. We also describe the use of information-guided noise reduction (IGNoR) to improve the Monte Carlo statistics in the most challenging regimes. The method is applied to strongly anharmonic one-dimensional models, a system-bath Hamiltonian, as well as the formamide molecule within an ab initio quartic potential, and the results are compared to those obtained by various approximate methods. These calculations suggest that the coherent state-based path integral method described in this paper offers an efficient, numerically exact approach for constructing the Wigner phase space density in systems of many degrees of freedom, and thus will be useful for quantizing the initial condition in classical trajectory-based simulations of dynamical properties.

We present the first exploratory lattice QCD calculation of the pion valence quark distribution extracted from spatially separated current-current correlations in coordinate space. We show that an antisymmetric combination of vector and axial-vector currents provides direct information on the pion valence quark distribution. Using the collinear factorization approach, we calculate the perturbative tree-level kernel for this current combination and extract the pion valence distribution. The main goal of this article is to demonstrate the efficacy of this general lattice QCD approach in the reliable extraction of parton distributions. With controllable power corrections and a good understanding of the lattice systematics, this method has the potential to serve as a complementary to the many efforts to extract parton distributions in global analyses from experimentally measured cross sections. We perform our calculation on an ensemble of 2+1 flavor QCD using the isotropic-clover fermion action, with lattice dimensions $32^3\times 96$ at a lattice spacing \mbox{$a=0.127$ fm} and the quark mass equivalent to a pion mass $m_\pi \simeq 416$ MeV., Comment: Version to appear in Physical Review D, 13 pages, 7 figures

We consider higher-order finite-nuclear-size (FNS) contributions to the energy levels of light ordinary and muonic hydrogenlike atoms. Relativistic corrections to the leading FNS term have been known in terms of an integration in coordinate space. The related results are model dependent. In the meantime, if the data on the nuclear structure are obtained from electron-nucleus scattering, it is a representation of the electric charge form factor in momentum space rather than the charge density. An example is the case of a proton as a nucleus. Often the electric form factor is presented in terms of a dispersion integral or a Pad\'e approximation. We present explicit results for such representations for leading finite-nuclear-size higher-order (in $Z\ensuremath{\alpha}$ and in $Z\ensuremath{\alpha}m{R}_{N}$) corrections beyond the leading FNS term.

The Articulated Arm Coordinate Measuring Machine (AACMM) is a kind of coordinate measuring devices in the form of an articulated robot. To improve the accuracy of AACMM, a kinematic identification method is presented in this paper. Firstly, we perform the kinematics modeling and simulation to realize the kinematic transformation from the joint space to the coordinate space. Then, we establish an error model and use least squares method to identify kinematic parameters. And the effectiveness of the least squares method for kinematic parameter identification is studied. Finally, the experiments of single point repeatability accuracy and the standard gauge accuracy are performed. The experimental results show that proposed the kinematic identification method can effectively improve the measurement accuracy of the joint coordinate measuring machine.

Calibrating multiple depth cameras to a common coordinate space can be a laborious and time-consuming task, and often relies on expensive motion capture tracking systems. However, if accuracy constraints can be relaxed then a consumer-grade virtual reality tracking system is sufficient to support the calibration process. In this paper, we present a fast and convenient camera calibration method aimed at such systems. The calibration process can be carried out in about ten minutes and the resulting calibration is sufficiently accurate to achieve spatial coherence when targeting reconstructions on an 8 mm grid over a $\approx 2.2\text{m}^{3}$ capture volume.

Simulating electron-nucleus coupled dynamics poses a non-trivial challenge and an important problem in the investigation of ultrafast processes involving coupled electronic and vibrational dynamics. Because irreversibility of the system dynamics results from thermal activation and dissipation caused by the environment, in dynamical studies, it is necessary to include heat bath degrees of freedom in the total system. When the system dynamics involves high-energy electronic transitions, the environment is regarded to be in a low-temperature regime and we must treat it quantum mechanically. In this paper, we present rigorous and versatile approaches for investigating the dynamics of open systems with coupled electronic and vibrational degrees of freedom within a fully quantum mechanical framework. These approaches are based on a quantum Fokker-Planck equation and a quantum Smoluchowski equation employing a heat bath with an Ohmic spectral density, with non-Markovian low-temperature correction terms, and extensions of these equations to the case of multi-state systems. The accuracy of these equations was numerically examined for a single-state Brownian system, while their applicability was examined for multi-state double-well systems by comparing their results with those of the fewest-switch surface hopping and Ehrenfest methods with a classical Markovian Langevin force. Comparison of the transient absorption spectra obtained using these methods clearly reveals the importance of the quantum low-temperature correction terms. These equations allow us to treat non-adiabatic dynamics in an efficient way, while maintaining numerical accuracy. The C++ source codes that we developed, which allow for the treatment of the phase and coordinate space dynamics with any single-state or multi-state potential forms, are provided as Supporting Information., 21 pages, 10 figures

A feature-based phase retrieval wavefront sensing approach using machine learning is proposed in contrast to the conventional intensity-based approaches. Specifically, the Tchebichef moments which are orthogonal in the discrete domain of the image coordinate space are introduced to represent the features of the point spread functions (PSFs) at the in-focus and defocus image planes. The back-propagation artificial neural network, which is one of most wide applied machine learning tool, is utilized to establish the nonlinear mapping between the Tchebichef moment features and the corresponding aberration coefficients of the optical system. The Tchebichef moments can effectively characterize the intensity distribution of the PSFs. Once well trained, the neural network can directly output the aberration coefficients of the optical system to a good precision with these image features serving as the input. Adequate experiments are implemented to demonstrate the effectiveness and accuracy of proposed approach. This work presents a feasible and easy-implemented way to improve the efficiency and robustness of the phase retrieval wavefront sensing.

The (2+1)-dimensional static magnetic susceptibility in strong-coupling is studied via a Reissner-Nordstr\"{o}m-AdS geometry. The analyticity of the susceptibility on the complex momentum $\mathfrak{q}$-plane in relation to the Friedel-like oscillation in coordinate space is explored. In contrast to the branch-cuts crossing the real momentum-axis for a Fermi liquid, we prove that the holographic magnetic susceptibility remains an analytic function of the complex momentum around the real axis in the limit of zero temperature, At zero temperature, we located analytically two pairs of branch-cuts that are parallel to the imaginary momentum-axis for large $|\text{Im}\ \mathfrak{q}|$ but become warped with the end-points keeping away from the real and imaginary momentum-axes. We conclude that these branch-cuts give rise to the exponential decay behaviour of Friedel-like oscillation of magnetic susceptibility in coordinate space. We also derived the analytical forms of the susceptibility in large and small-momentum, respectively., Comment: 2 figure, big changes from the first version

The exchange of spin-0 or spin-1 bosons between fermions or spin-polarised macroscopic objects gives rise to various spin-dependent potentials. We derive the coordinate-space non-relativistic potentials induced by the exchange of such bosons, including contact terms that can play an important role in atomic-scale phenomena, and correct for errors and omissions in the literature. We summarise the properties of the potentials and their relevance for various types of experiments. These potentials underpin the interpretation of experiments that search for new bosons, including spectroscopy, torsion-pendulum measurements, magnetometry, parity nonconservation and electric dipole moment experiments., 8 pages, 1 figure

An exact solution for the scattering wavefunction from a nonlocal potential in the presence of Coulomb interaction is presented. The approach is based on the construction of a Coulomb Green's function in coordinate space whose associated kernel involves any nonlocal optical potential superposed to the Coulomb-screened interaction. The scattering wavefunction, exact solution of the integro-differential Schr\"odinger's equation, poses no restrictions on the type of nonlocality of the interaction nor on the beam energy., Comment: 17 pages, 1 figure. Published in Physics Letters B

In this chapter, we proposed a pattern regression framework to predict individuals brain ages from the whole-brain resting-state functional connectivity MRI (rs-fcMRI). In the framework, a supervised locality preserving projections (LPP) algorithm was employed to learn a low-dimensional representation of brain development from many individuals at different ages, and locally adjusted support vector regression (LASVR) method was developed in the manifold coordinate space for making continuously valued predictions about the functional development levels of individual brains. We aimed to decode the developmental dynamics of the whole-brain functional network in seven decades (8–79 years) of the human lifespan. We first used parametric curve fitting to examine linear and nonlinear age effect on the resting human brain. We found that age-related changes in interregional functional connectivity exhibited spatially and temporally specific patterns. During brain development from childhood to senescence, functional connections tended to linearly increase in the emotion system and decrease in the sensorimotor system, while quadratic trajectories were observed in functional connections related to higher-order cognitive functions. The complex patterns of age effect on the whole-brain functional network could be effectively represented by a low-dimensional, nonlinear manifold embedded in the functional connectivity space, which uncovered the inherent structure of brain maturation and aging. Regression of manifold coordinates with age further showed that the manifold representation extracted sufficient information from rs-fcMRI data to make prediction about individual brain functional development levels. This study not only gives insights into the neural substrates that underlie behavioral and cognitive changes over age but also provides a possible way to quantitatively describe the typical and atypical developmental progression of human brain function using rs-fcMRI.

The morphology of the stagnated plasma resulting from Magnetized Liner Inertial Fusion (MagLIF) is measured by imaging the self-emission x-rays coming from the multi-keV plasma, and the evolution of the imploding liner is measured by radiographs. Equivalent diagnostic response can be derived from integrated rad-MHD simulations from programs such as Hydra and Gorgon. There have been only limited quantitative ways to compare the image morphology, that is the texture, of simulations and experiments. We have developed a metric of image morphology based on the Mallat Scattering Transformation (MST), a transformation that has proved to be effective at distinguishing textures, sounds, and written characters. This metric has demonstrated excellent performance in classifying ensembles of synthetic stagnation images. We use this metric to quantitatively compare simulations to experimental images, cross experimental images, and to estimate the parameters of the images with uncertainty via a linear regression of the synthetic images to the parameters used to generate them. This coordinate space has proved very adept at doing a sophisticated relative background subtraction in the MST space. This was needed to compare the experimental self emission images to the rad-MHD simulation images. We have also developed theory that connects the transformation to the causal dynamics of physical systems. This has been done from the classical kinetic perspective and from the field theory perspective, where the MST is the generalized Green's function, or S-matrix of the field theory in the scale basis. From both perspectives the first order MST is the current state of the system, and the second order MST are the transition rates from one state to another. An efficient, GPU accelerated, Python implementation of the MST was developed. Future applications are discussed., Comment: 56 pages, 24 figures, Sandia National Laboratories Technical Report

We study coherent diffractive dijet production in electron-hadron and electron-nucleus collisions within the dipole picture. We provide semi-analytic results for the differential cross section and elliptic anisotropy in the angle between dijet transverse momentum and hadron recoil momentum. We demonstrate the direct relation between angular moments of the dipole amplitude in coordinate space and angular moments of the diffractive dijet cross sections. To perform explicit calculations we employ two different saturation models, extended to include the target geometry. In the limit of large photon virtuality or quark masses, we find fully analytic results that allow direct insight into how the differential cross section and elliptic anisotropy depend on the saturation scale, target geometry, and kinematic variables. We further provide numerical results for more general kinematics in collisions at a future electron-ion collider, and study the effects of approaching the saturated regime on diffractive dijet observables., Comment: 22 pages, 18 figures, typos corrected, figures updated to match published version

The time-dependent Skyrme Hartree-Fock calculations have been performed to study $^{24}$Mg +$^{24}$Mg collisions. The twisted boundary conditions, which can avoid finite box-size effects of the employed 3D coordinate space, have been implemented. The prolate deformed $^{24}$Mg has been set to different orientations to study vibrations and rotations of the compound nucleus $^{48}$Cr. Our time evolution results show continuum damping effects associated with the twist-averaged boundary condition play a persistent role after the fusion stage. In particular, a rotational damping in continuum is presented in calculations of both twist-averaged and absorbing boundary conditions, in which damping widths can be clearly extracted. It is unusual that the rotating compound nucleus in continuum evolves towards spherical but still has a considerable angular momentum., Comment: 6 pages, 6 figures, submitted to PRC

Concept Factorization (CF) and its variants may produce inaccurate representation and clustering results due to the sensitivity to noise, hard constraint on the reconstruction error and pre-obtained approximate similarities. To improve the representation ability, a novel unsupervised Robust Flexible Auto-weighted Local-coordinate Concept Factorization (RFA-LCF) framework is proposed for clustering high-dimensional data. Specifically, RFA-LCF integrates the robust flexible CF by clean data space recovery, robust sparse local-coordinate coding and adaptive weighting into a unified model. RFA-LCF improves the representations by enhancing the robustness of CF to noise and errors, providing a flexible constraint on the reconstruction error and optimizing the locality jointly. For robust learning, RFA-LCF clearly learns a sparse projection to recover the underlying clean data space, and then the flexible CF is performed in the projected feature space. RFA-LCF also uses a L2,1-norm based flexible residue to encode the mismatch between the recovered data and its reconstruction, and uses the robust sparse local-coordinate coding to represent data using a few nearby basis concepts. For auto-weighting, RFA-LCF jointly preserves the manifold structures in the basis concept space and new coordinate space in an adaptive manner by minimizing the reconstruction errors on clean data, anchor points and coordinates. By updating the local-coordinate preserving data, basis concepts and new coordinates alternately, the representation abilities can be potentially improved. Extensive results on public databases show that RFA-LCF delivers the state-of-the-art clustering results compared with other related methods., Comment: Accepted by IEEE Transactions on Knowledge and Data Engineering (IEEE TKDE)

We investigate the high-dimensional data clustering problem by proposing a novel and unsupervised representation learning model called Robust Flexible Auto-weighted Local-coordinate Concept Factorization (RFA-LCF). RFA-LCF integrates the robust flexible CF, robust sparse local-coordinate coding and the adaptive reconstruction weighting learning into a unified model. The adaptive weighting is driven by including the joint manifold preserving constraints on the recovered clean data, basis concepts and new representation. Specifically, our RFA-LCF uses a L2,1-norm based flexible residue to encode the mismatch between clean data and its reconstruction, and also applies the robust adaptive sparse local-coordinate coding to represent the data using a few nearby basis concepts, which can make the factorization more accurate and robust to noise. The robust flexible factorization is also performed in the recovered clean data space for enhancing representations. RFA-LCF also considers preserving the local manifold structures of clean data space, basis concept space and the new coordinate space jointly in an adaptive manner way. Extensive comparisons show that RFA-LCF can deliver enhanced clustering results., Comment: Accepted at the 44th IEEE International Conference on Acoustics, Speech, and Signal Processing(ICASSP 2019)

In this work we propose an approach for estimating 3D human poses of multiple people from a set of calibrated cameras. Estimating 3D human poses from multiple views has several compelling properties: human poses are estimated within a global coordinate space and multiple cameras provide an extended field of view which helps in resolving ambiguities, occlusions and motion blur. Our approach builds upon a real-time 2D multi-person pose estimation system and greedily solves the association problem between multiple views. We utilize bipartite matching to track multiple people over multiple frames. This proofs to be especially efficient as problems associated with greedy matching such as occlusion can be easily resolved in 3D. Our approach achieves state-of-the-art results on popular benchmarks and may serve as a baseline for future work.

This project addresses the task of category-level pose estimation for articulated objects from a single depth image. We present a novel category-level approach that correctly accommodates object instances previously unseen during training. We introduce Articulation-aware Normalized Coordinate Space Hierarchy (ANCSH) - a canonical representation for different articulated objects in a given category. As the key to achieve intra-category generalization, the representation constructs a canonical object space as well as a set of canonical part spaces. The canonical object space normalizes the object orientation,scales and articulations (e.g. joint parameters and states) while each canonical part space further normalizes its part pose and scale. We develop a deep network based on PointNet++ that predicts ANCSH from a single depth point cloud, including part segmentation, normalized coordinates, and joint parameters in the canonical object space. By leveraging the canonicalized joints, we demonstrate: 1) improved performance in part pose and scale estimations using the induced kinematic constraints from joints; 2) high accuracy for joint parameter estimation in camera space., Comment: 14 pages, 8 figures

We solve three-nucleon (3N) Faddeev equations with nucleon–nucleon (NN) and three-nucleon forces (3NF) derived consistently in the framework of chiral perturbation theory, taking the semilocal coordinate-space regularized chiral N $$^4$$ LO NN potential supplemented by the chiral N $$^2$$ LO 3NF regularized in the same way. Based on these solutions the nucleon–deuteron (Nd) elastic scattering and deuteron breakup reactions are studied. We checked that the elastic Nd scattering cross section can be used as an alternative observable to the doublet neutron–deuteron (nd) scattering length to fix, together with the $$^3$$ H binding energy, the strengths of the contact terms of the N $$^2$$ LO 3NF. We investigated the predicted 3NF effects in 3N continuum reactions putting an emphasis on the $$A_y$$ puzzle in low energy nd elastic scattering and on cross sections in the symmetrical-space-star and quasi-free-scattering breakup configurations. We found that the N $$^2$$ LO 3NF provides effects comparable to those of standard, (semi-)phenomenological $$2\pi $$ -exchange Tucson-Melbourne 3NF.

We consider one-loop light-by-light-scattering contributions to the Lamb shift of the $1s, 2s, 2p$ states in light muonic hydrogen like atoms at $Z\leq10$. The contributions are of the order $\alpha^5m_\mu$ (with diverse dependence on the nuclear charge $Z$). Those include the contributions of the so-called Wichmann-Kroll potential ($\alpha(Z\alpha)^4m_\mu$), the virtual Delbr\"uck scattering ($\alpha^2(Z\alpha)^3m_\mu$), etc. The results are obtained in a nonrelativistic approximation. For the calculation of the virtual-Delbr\"uck-scattering contribution, we have constructed an effective potential in the coordinate space which may be applied to other calculations in muonic atoms., Comment: 9 pages

We present a theoretical consideration of the radiative two-photon finite-nuclear-size contributions to the Lamb shift in a light muonic atom. They are of the order of $\ensuremath{\alpha}{(Z\ensuremath{\alpha})}^{5}m$ and may depend differently on $m{R}_{N}$. The contributions are due to the electronic and muonic vacuum polarization and the muon self-energy. The consideration is done within the external field approximation. We also found the leading logarithmic finite-nuclear-size contributions in the next order. One of them is of the order $\ensuremath{\alpha}{(Z\ensuremath{\alpha})}^{6}{ln}^{2}(Z\ensuremath{\alpha})\phantom{\rule{0.16em}{0ex}}{(m{R}_{N})}^{2}m$ and the other is of the order ${\ensuremath{\alpha}}^{2}{(Z\ensuremath{\alpha})}^{5}{ln}^{2}({m}_{e}{R}_{N})\phantom{\rule{0.16em}{0ex}}{(m{R}_{N})}^{3}m$. Special attention is paid to higher-order effects in muonic hydrogen and the related applications of various parametrizations of the proton electric form factors. We also consider the general expressions in coordinate space for the finite-size radiative contributions to the Lamb shift in two-body muonic atoms. The numerical results are present for the atoms with $Z\ensuremath{\le}10$.

We derive a high-rank separable potential formula of the atom-atom interaction by using the two-body wave function in the coordinate space as inputs. This high-rank separable potential can be utilized to numerically solve the two-body Lippmann-Schwinger equation and three-body Faddeev equation. By analyzing the convenience and stability of numerical calculations for different kinds of the matrix forms of the Lippmann-Schwinger and Faddeev equations, we can find the optimal forms of the kernal matrices in the two- and three-body scattering equations. We calculate the dimer bound energy, two-body scattering phase shift and off-shell t-matrix, the trimer bound energy, atom-dimer scattering length, and three-body recombination rate using the high-rank separable potentials, taking the identical 4He atoms as an application example. All the calculations converge quickly for the rank number N⩾3. The high-rank separable potential is valid for two-body scattering calculation of 4He atoms, but not accurate enough for reproducing the three-body scattering results by using only two-body s-wave interaction and describing the contributions of two-body high partial-waves to the three-body scattering for the 4He3 system.We derive a high-rank separable potential formula of the atom-atom interaction by using the two-body wave function in the coordinate space as inputs. This high-rank separable potential can be utilized to numerically solve the two-body Lippmann-Schwinger equation and three-body Faddeev equation. By analyzing the convenience and stability of numerical calculations for different kinds of the matrix forms of the Lippmann-Schwinger and Faddeev equations, we can find the optimal forms of the kernal matrices in the two- and three-body scattering equations. We calculate the dimer bound energy, two-body scattering phase shift and off-shell t-matrix, the trimer bound energy, atom-dimer scattering length, and three-body recombination rate using the high-rank separable potentials, taking the identical 4He atoms as an application example. All the calculations converge quickly for the rank number N⩾3. The high-rank separable potential is valid for two-body scattering calculation of 4He atoms, but not accurate enough fo...

Globally modeling and reasoning over relations between regions can be beneficial for many computer vision tasks on both images and videos. Convolutional Neural Networks (CNNs) excel at modeling local relations by convolution operations, but they are typically inefficient at capturing global relations between distant regions and require stacking multiple convolution layers. In this work, we propose a new approach for reasoning globally in which a set of features are globally aggregated over the coordinate space and then projected to an interaction space where relational reasoning can be efficiently computed. After reasoning, relation-aware features are distributed back to the original coordinate space for down-stream tasks. We further present a highly efficient instantiation of the proposed approach and introduce the Global Reasoning unit (GloRe unit) that implements the coordinate-interaction space mapping by weighted global pooling and weighted broadcasting, and the relation reasoning via graph convolution on a small graph in interaction space. The proposed GloRe unit is lightweight, end-to-end trainable and can be easily plugged into existing CNNs for a wide range of tasks. Extensive experiments show our GloRe unit can consistently boost the performance of state-of-the-art backbone architectures, including ResNet, ResNeXt, SE-Net and DPN, for both 2D and 3D CNNs, on image classification, semantic segmentation and video action recognition task.

We present a preliminary study of the leading hadronic contribution to the running of the Weinberg angle $\theta_{\mathrm{W}}$. The running is extracted from the correlation function of the electromagnetic current with the vector part of the weak neutral current using both the standard time-momentum representation method and the Lorentz-covariant coordinate-space method recently introduced by Meyer. Both connected and disconnected contributions have been computed on $N_{\mathrm{f}}=2+1$ non-perturbatively $O(a)$-improved Wilson fermions configurations from the CLS initiative. Similar covariant coordinate-space methods can be used to compute the leading hadronic contribution to the anomalous magnetic moment of the muon $(g-2)_\mu$ and to the running of the QED coupling $\alpha$., Comment: 7 pages, 2 figures, talk presented at The 36th Annual International Symposium on Lattice Field Theory, July 22-28, 2018, East Lansing, MI, USA

A new paradigm of Anderson localization caused by correlations in the long-range hopping along with uncorrelated on-site disorder is considered which requires a more precise formulation of the basic localization-delocalization principles. A new class of random Hamiltonians with translation-invariant hopping integrals is suggested and the localization properties of such models are established both in the coordinate and in the momentum spaces alongside with the corresponding level statistics. Duality of translation-invariant models in the momentum and coordinate space is uncovered and exploited to find a full localization-delocalization phase diagram for such models. The crucial role of the spectral properties of hopping matrix is established and a new matrix inversion trick is suggested to generate a one-parameter family of equivalent localization/delocalization problems. Optimization over the free parameter in such a transformation together with the localization/delocalization principles allows to establish exact bounds for the localized and ergodic states in long-range hopping models. When applied to the random matrix models with deterministic power-law hopping this transformation allows to confirm localization of states at all values of the exponent in power-law hopping and to prove analytically the symmetry of the exponent in the power-law localized wave functions., 14 pages, 8 figures + 5 pages, 2 figures in appendices

Possible observables of baryon number clustering due to the instabilities occurring at a first order QCD phase transition are discussed. The dynamical formation of baryon clusters at a QCD phase transition can be described by numerical fluid dynamics, augmented with a gradient term and an equation of state with a mechanically unstable region. It is shown that the dynamical description of this phase transition, in nuclear collisions, will lead to the formation of dense baryon clusters at the phase boundary. State-of-the-art machine learning methods find that the coordinate space clumping leaves characteristic imprints on the spatial net density distribution in almost every event. On the other hand the momentum distributions do not show any clear event-by-event features. It is shown that the 'third order' cumulant, the skewness, shows a peak at the beam energy where the system, created in the heavy ion collision, reaches the deconfinement phase transition.

We consider the dynamics of the simplest Schrodinger's cat composed by a superposition of two canonical coherent states of the Schrodinger quantum harmonic oscillator. We demonstrate that the interchange of the “alive” and “dead” constituents in the whole Schrodinger's cat wave function opens the possibility to reveal one interesting, but obviously, only formal analogy with the Pauli exclusion principle. We show analytically and computationally that the symmetric cat states will occupy the ground state of the harmonic oscillator, whereas the antisymmetric cat states, vice versa, will never occupy the ground state when these states closely approach in space each other. The antisymmetric overlapping in space and time “alive” and “dead” Schrodinger cat states simply jump onto the first excited energy level of the quantum harmonic oscillator. This effect could be considered as the formal analogy of the Pauli exclusion principle applied to the antisymmetric “jumping off” Schrodinger cats. As the name suggests, the main feature of the “jumping off” Schrodinger cat consists in the transformation of the probability distribution (both in ordinary coordinate space and in the momentum space as well) in such a way that antisymmetric “alive” and “dead” cats are found to be in the first excited energy state of the quantum harmonic oscillator. We conclude that the wave and particle-like analogies in the dynamics of the symmetric and antisymmetric Schrodinger's cat states confirm at least formally the famous Pauli statements that “a symmetric solution can never develop into an antisymmetric one, and vice versa”, and that “for particles with antisymmetric states it can, therefore, never happen that two particles find themselves in the same state”

In this article, a soft s-open set in soft bitopological structures is introduced. With the help of this newly defined soft s-open set, soft separation axioms are regenerated in soft bitopological structures with respect to crisp points. Soft continuity at some certain points, soft bases, soft subbase, soft homeomorphism, soft first-countable and soft second-countable, soft connected, soft disconnected and soft locally connected spaces are defined with respect to crisp points under s-open sets in soft bitopological spaces. The product of two soft axioms with respect crisp points with almost all possibilities in soft bitopological spaces relative to semiopen sets are introduced. In addition to this, soft (countability, base, subbase, finite intersection property, continuity) are addressed with respect to semiopen sets in soft bitopological spaces. Product of soft first and second coordinate spaces are addressed with respect to semiopen sets in soft bitopological spaces. The characterization of soft separation axioms with soft connectedness is addressed with respect to semiopen sets in soft bitopological spaces. In addition to this, the product of two soft topological spaces is ( space if each coordinate space is soft space, product of two sot topological spaces is (S regular and C regular) space if each coordinate space is (S regular and C regular), the product of two soft topological spaces is connected if each coordinate space is soft connected and the product of two soft topological spaces is (first-countable, second-countable) if each coordinate space is (first countable, second-countable).

Enterprise's archives are inevitably affected by the presence of data quality problems (also called glitches). This article proposes the application of a new method to analyze the quality of datasets stored in the tables of a database, with no knowledge of the semantics of the data and without the need to define repositories of rules. The proposed method is based on proper revisions of different approaches for outlier detection that are combined to boost overall performance and accuracy. A novel transformation algorithm is conceived that treats the items in database tables as data points in real coordinate space of n dimensions, so that fields containing dates and fields containing text are processed to calculate distances between those data points. The implementation of an iterative approach ensures that global and local outliers are discovered even if they are subject, primarily in datasets with multiple outliers or clusters of outliers, to masking and swamping effects. The application of the method to a set of archives, some of which have been studied extensively in the literature, provides very promising experimental results and outperforms the application of a single other technique. Finally, a list of future research directions is highlighted.

A new compact combinatorial coordinate system is presented to address not only the voxels (truncated octahedra) of the body-centered cubic grid but also the lower-dimensional cells - faces, edges and vertices. Almost all integer triples address some cell in the grid, and incidence and adjacency relations between cells can easily be captured by the coordinate values. The new coordinate system can effectively and efficiently be applied in topological shape analysis and modeling, image processing and computer graphics applications.

The core of big data is intelligence still. Facing the challenge of big data, AI needs a deep and united theory, especially, a deep and united cognition math. There were three branches of cognition math emerging in 1982. One of them is Factor space theory initiated by the first author. Factor is factor, i.e. the initiator of fact, the quality-root of things, which is the generalization of gene. Factor space is the coordinate space with dimensions named by factors, which is generalization of Cartesian coordination for describing things and thinking. The paper introduces how to emulate cognition functions by factor space and how clear and pertinent the emulation is. Four simple and fast algorithms are presented. Based on factor space, the cognition packet is built as the basic unit in factor databases. Different from the existent data processing, factor databases are built by cultivation, whose target is cultivating the sample S of background relation R to emulate R. With the lapse of time, the background sample S becomes more mature and stable. Once the S equals to R, cognition packet will have the whole correct knowledge. Maintaining such a powerful function for big data, factor databases can employ background base to drastically compress data without information loss. As for the existent data processing frightened by the multi-challenge of big data, factor space theory brings us a sedative. The tide of big data will be tamed in factor databases. The cultivation is easy to be made since the sample of background relation don’t concern about privacy. The bottlenecks caused by big data can be overcome by factor space theory, which is the best framework for cognition math.

The presented enhanced version of Eriksen’s theorem defines an universal transform of the Foldy–Wouthuysen type and in any external static electromagnetic field (ESEMF) reveals a discrete symmetry of Dirac’s equation (DE), responsible for existence of a highly influential conserved quantum number—the charge index distinguishing two branches of DE spectrum. It launches the charge-index formalism (CIF) obeying the charge-index conservation law (CICL). Via its unique ability to manipulate each spectrum branch independently, the CIF creates a perfect charge-symmetric architecture of Dirac’s quantum mechanics (DQM), which resolves all the riddles of the standard DE theory (SDET). Besides the abstract CIF algebra, the paper discusses: (1) the novel accurate charge-symmetric definition of the electric-current density; (2) DE in the true-particle representation, where electrons and positrons coexist on equal footing; (3) flawless “natural” scheme of second quantization; and (4) new physical grounds for the Fermi–Dirac statistics. As a fundamental quantum law, the CICL originates from the kinetic-energy sign conservation and leads to a novel single-particle physics in strong-field situations. Prohibiting Klein’s tunneling (KT) in Klein’s zone via the CICL, the precise CIF algebra defines a new class of weakly singular DE solutions, strictly confined in the coordinate space and experiencing the total reflection from the potential barrier.

We consider a charged quantum particle moving in a two-dimensional plane in the three-dimensional coordinate space and scattering on an immovable Coulomb center in the same plane. We derive and investigate expansions of the wave function and of all radial wave functions of the particle in integer powers of the wave number and in Bessel functions of a real order. We prove that finite sums of such expansions are asymptotic in the low-energy limit.

We solve the Balitsky-Kovchegov small-x evolution equation in coordinate space. We find that the solution to the equation is unstable when using an initial condition relevant for phenomenological applications at leading order. The problematic behavior is shown to be due to a large double logarithmic contribution. The same problem is found when the evolution of the “conformal dipole” is solved, even though the double logarithmic term is then absent from the evolution equation.

This paper attempts to describe the graphical behavior of the distributed lag model in an infinite coordinate space. The “mega distributed lag model” (MDL) is a mathematical framework that can examine the simultaneous interrelationships between all involved variables. The multidimensional graphical setting simultaneously reveals all non-linear exposure — response dependencies and delayed effects between lagged and dependent variables — which two-dimensional figures overwhelmingly fail to capture. Under the Omnia Mobilis assumption, each distribution lag function is indexed with respect to time and space. The Mega distributed lag model observes multiple trends in full motion, the final output (determinant) of which is called “the JIM-coefficient”. Hence, this paper tries to analyze different approaches of lag distribution models that can help in the construction of our new model. The mega distributed lag model (MDL) is moving from the uses of the classic 2-dimensional and 3-dimensional graphical modeling to a multidimensional graphical modeling in Econometrics. Finally, this model is an extension of those explored earlier in the field of Econographicology.

The application of the transformation of phase coordinate system into orthogonal coordinate system to the five phase induction motor with concentrated windings results in mathematical model of the two pairs of alpha-beta components of two vectors rotating in a stationary frame. The first coordinate system corresponds to the third harmonic variables while the second coordinate system corresponds to the third harmonic variables. For each coordinate system there exist a separate set of machine parameters. The components of the vector rotating in one coordinate system do not affect the component derivatives of the vector rotating in the second coordinate system. The application of the nonlinear transformation allows for obtaining two multiscalar models, separately for each of the coordinate systems. The paper proposes novel multiscalar control that allow forcing the command magnitude and phase of third harmonic rotor flux thereby increasing the utilization of the construction material of the five phase machine. (Five Phase Induction Motor Multiscalar Control).

This research aims to describe ann-dimensional line on a parallel coordinate and uses the representation as a display of aircraft motion which flies at a straight line and constant velocity. A parallel coordinate of n-dimensional space depicted in the form of nparallel vertical lines which represent axis.Every two adjacent axes have the same distance. A horizontal line that cutsall axes indicates the initial pointsof each axis. In a parallel coordinate,an 15n"> -dimensional point is represented as a polygonal chainwhere the vertices located on its axis. Based on the representations of some of collinear points, a line is described on a parallel coordinate. On the other hand, one can consider a graph of an aircraft motion as a graph of a 4-dimensional space. At a constant speed with a straight line orbit, the graph of an aircraft movementis a graph of 4-dimensional line. The result shows that, on a parallel coordinate, an n-dimensional line represented as 15n-1"> dots. As a consequence, the graph of an aircraft that moveat a constant speed with a straight line orbitrepresented as3 dots. By this representation, the coordinate and altitude of the aircraft can be observes at anytime. It also shows whether the movement of an aircraft disturb (strike or too close to) another plane or not. Keywords: parallel coordinate, n-dimensional space, aircraft movement display

In this work the high-order moment-conserving method of classes (HMMC) ( Alopaeus et al., 2006 ) is extended to solve the bivariate Population Balance Equation (PBE). The method is capable of guaranteeing the internal consistency of the discretized equations for a generic moment set, including mixed-order moments of the distribution. The construction of the product tables in the case of aggregation, breakage and convection in internal coordinate space are discussed. Eventually, several test cases are considered to assess the accuracy of the method. The application to a realistic mass transfer problems in a liquid–liquid system is preliminarily discussed. The comparison with analytical solutions of pure aggregation problems shows that the proposed method is accurate with only a limited number of categories.

We solve the problem of the propagation of a charged quantum particle in a two-dimensional plane embedded in the three-dimensional coordinate space. We consider scattering of this particle by a stable Coulomb center situated in the same plane. We study the wave function of this particle, its Green’s function, and all radial components of these functions. We derive uniform majorant bounds on absolute values of these functions and find the wave function representation in terms of regular radial Coulomb functions and the scattering amplitude representation via partial phases. We obtain integral representations of the Greens’s function and all its radial components.

The article explains practical aspects of the departmental geodetic control network segment development on the part of the M-4 “Don” highway. It describes procedure and results of the departmental geodetic control network stations association with world, national and local coordinate systems. It also shows a comparative analysis of the elevations transfer precision in the 1977 Baltic height system with GNSS-methods and geometrical levelling.

The purpose of this paper is to present the basic mathematical modeling of a hexacopter, which could be used to develop proper methods for stabilization and trajectory control. A hexacopter consists of six rotors with three pairs of counter-rotating fixed-pitch blades. This mechanism is an under-actuated, dynamically unstable, six-degrees-of-freedom system. The whole motion of this object consists of translational and rotational motion in three dimensions, where the translational motion is created by changing the direction and magnitude of the upward propeller thrust. The hexacopter is controlled by adjusting the angular velocities of the rotors, which are spun by electric motors. It is assumed to be a rigid body; thus, the differential equation of the hexacopter dynamics can be derived from the Newton–Euler equation. The Euler-angle parametrization of the three-dimensional rotations contains singular points in the coordinate space that can cause failure of both the dynamical model and control. In order to avoid singularities, the rotations of the hexacopter are parametrized in terms of quaternions. This choice has been made considering the linearity of the quaternion formulation and their stability and efficiency. Further, control simulation of a hexacopter applying cascaded-PID control is also presented in this paper.

The rationale of Econographicology revolves around the efficacy of multidimensional graphs as the most effective visual tool to understand any economic phenomenon from a multidimensional view. The main motivation behind the creation of Econographicology is to evaluate multidimensional graphs evolved so far in economics and to develop new type of multidimensional graphs to facilitate the study of economics, as well as finance and business. Thereby, the mission of Econographicology is to offer academics, researchers and policy maker’s an alternative multidimensional graphical modeling approach for the research and teaching–learning process of economics, finance and business from a multidimensional perspective. Hence, this alternative multidimensional graphical modeling approach is offer a set of multi-dimensional coordinate spaces to build different types of multidimensional graphs to study any economic phenomenon. The following new types of multi-dimensional coordinate spaces are presented: the 5-dimensional coordinate space (vertical position and horizontal position), the mega-dynamic disks coordinate space (vertical position and horizontal position), and the mega-disks networks mapping.

The registration of point cloud is important for large object measurement. A measurement method for coordinate system transformation based on robot is proposed in this paper. Firstly, for obtaining extrinsic parameters, the robot moves to three different positions to capture the images of three targets. Then the transformation matrix X between camera and tool center point (TCP) coordinate systems can be calculated by using the known parameters of robot and the extrinsic parameters, and finally the multi-view coordinate system can be transformed into robot coordinate system by the transformation matrix X. With the help of robot, the multi-view point cloud can be easily transformed into a unified coordinate system. By using robot, the measurement doesn’t need any mark. Experimental results show that the method is effective.

Effective lambda-proton and lambda-neutron potentials, restored from theoretical scattering phases through Gel'fand-Levitan-Marchenko theory, are tested on a lambda hypertriton through three-body calculations. The lambda hypertriton is treated as a three-body system consisting of lambda-proton, lambda-neutron and proton-neutron subsystems. Binding energy and root-mean-square radius are computed for the ground state of lambda hypertriton ($J^{\pi}=1/2^+$). In coordinate space, the dynamics of the system is described using a set of coupled hyperradial equations obtained from the Differential Faddeev Equations. By solving the eigenvalue problem derived from this set of coupled hyperradial equations, the binding energy and root-mean-square matter radius computed are found to be -2.462 MeV and 7.00 fm, respectively. The potentials are also shown to display a satisfactory convergence behaviour., Comment: 9 pages, 8 figures

This study employs the relativistic mean field theory with the Green's function method to study the single-particle resonant states. In contrast to our previous work [Phys. Rev. C, 90: 054321 (2014)], the resonant states are identified by searching for the poles of Green's function or the extremes of the density of states. This new approach is highly effective for all kinds of resonant states, no matter whether they are broad or narrow. The dependence on the space size for the resonant energies, widths, and the density distributions in the coordinate space has been checked and was found to be very stable. Taking 120Sn as an example, four new broad resonant states , , , and were observed, and the accuracy for the width of the very narrow resonant state was highly improved to MeV. Further, our results are very close to those obtained using the complex momentum representation method and the complex scaling method.

Structure–property relationships play a central role in condensed matter physics, chemistry, and materials science. However, the problem of predicting the structure of a material, given its chemical composition, remains immensely challenging. Here, we review some of the progress that has been made in this area for both crystalline materials and atomic clusters. Early work consisted of heuristic rules-of-thumb or structure maps using descriptors that were obtained largely by inspection. Increasingly, these approaches are being expanded to use descriptors that have been obtained by applying machine learning techniques to big data containing information from the experiment and/or first principles calculations. Improved techniques for global optimization in the multi-dimensional coordinate space have also led to major advances in the field.