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Different frameworks exist to describe the flat-space limit of AdS/CFT, include momentum space, Mellin space, coordinate space, and partial-wave expansion. We explain the origin of momentum space as the smearing kernel in Poincare AdS, while the origin of latter three is the smearing kernel in global AdS. In Mellin space, we find a Mellin formula that unifies massless and massive flat-space limit, which can be transformed to coordinate space and partial-wave expansion. Furthermore, we also manage to transform momentum space to smearing kernel in global AdS, connecting all existed frameworks. Finally, we go beyond scalar and verify that $\langle VV\mathcal{O}\rangle$ maps to photon-photon-massive amplitudes., 57 pages, 12 figures, latex; comments added, refs added; the version to appear on JHEP

A method is proposed for the synthesis of a closed-loop system with controls that ensure the movement of an object with minimal deviations from a given trajectory of the output coordinate and its higher derivatives and a transition to this set. To solve the problem, the Pontryagin maximum principle is used to study special situations without analysis of auxiliary variables, supplemented by the apparatus of general position conditions for nonlinear systems in an extended coordinate space, taking into account the object, a functional that is nonlinear regarding deviations of the output coordinate and the explicit occurrence of time. The combined use of these methods allows us, firstly, to find special trajectories of coordinates that are higher derivatives of the output coordinate, and after excluding time, a special phase trajectory is found, which is a switching line for reaching the final state, a given programmed motion along which in a closed system is carried out by special control. Secondly, access to a special phase trajectory from the initial state is carried out for linear objects by relay control, and for nonlinear objects, under certain boundary conditions, relay control is supplemented by a special control of the speed problem. Examples of control of programmed motion with oscillatory and aperiodic processes of a given duration for linear and nonlinear objects are given. Taking into account the nature of equilibrium states, determined by the methods of the qualitative theory of differential equations, and restrictions on control and coordinates, topologies of trajectories are obtained for the implementation of a continuous special control or sliding mode. New algorithms and structures of control systems are obtained. The results are accompanied by modeling, illustrating the effectiveness of algorithms and structures of control systems according to the proposed synthesis method and confirming analytical materials. The results of the work can be used to control linear and nonlinear objects in mechatronics, robotics, thermal processes and other industries.

In the space of square integrable functions on a Hilbert space with a translation invariant measure, we study unitary groups of operators of shift by vectors of the momentum space. Analyzing the averaging of functionals of Gaussian random processes in the momentum space, we obtain a semigroup of self-adjoint contractions; we establish conditions for the strong continuity of this semigroup and study its generator, which is the operator of multiplication by a quadratic form of a nonpositive trace-class operator in the Hilbert space. We compare the properties of the groups of shift operators in the coordinate and momentum spaces, as well as the properties of semigroups of self-adjoint contractions generated by diffusion in the coordinate and momentum spaces. In addition, we show that one cannot define the Fourier transform as a unitary map that would provide a unitary equivalence of these contraction semigroups.

We obtain an analytic description of the excitation front propagation in a medium during nonstationary superdiffusive (nonlocal) transport in the case of a finite fixed velocity of perturbation carriers (so-called Levy walks with stops). This problem embraces phenomena such as resonance radiation transport in astrophysical gases and plasma, biological migration, and energy transfer by waves in a plasma. In this approach, the result obtained by integrating the exact solution to the kinetic equation for the Green function is independent of the coordinate space dimensionality. The results are compared with data obtained using another more exact method of determining the front and with the results of numerical calculations of the statistics of trajectories using the Monte Carlo method. Comparison demonstrates the applicability of our results in a wide range of parameters of the problem. We propose a universal description of the perturbation front dynamics in the medium for an arbitrary (including infinitely high) fixed velocity of perturbation carriers. This corresponds to the combination of expressions for the front in the case of transport by Levy flights and by Levy walks. We consider the criteria of transition between these regimes of the superdiffusive transport, which corresponds, in particular, to the account for the finite velocity of light in the superdiffusive transport of resonance radiation in gases and plasmas. For Levy walks, we have obtained a relation between the integral characteristic of perturbation of the medium and its carriers.

A criterion for the total coordinate space of a trinomial hypersurface to be a hypersurface is found. An algorithm for calculating the Cox ring in explicit form is proposed, and criteria for the total coordinate space to be rational and factorial are obtained.

Most category-level object pose estimation methods are multi-tasking, including instance segmentation, Normalized Object Coordinate Space (NOCS) map estimation and classification. However, previous approaches overlooked the connection between multiple tasks. In this work, we propose an efficient network to make better use of the complementarity between different tasks. Specifically, we propose an external sharing unit (ESU) to promote instance segmentation and NOCS map estimation. In addition, we propose an internal sharing unit (ISU) to improve the NOCS map estimation. The NOCS map head has three branches. And the estimated coordinates of each branch have strong correlation. Extensive experiments on the CAMERA and REAL dataset demonstrate the effectiveness of joint optimization in multi-tasking category-level object estimation. Experimental results also show that the proposed method can improve not only accuracy but also efficiency on several benchmarks.

This article models the interconnection between the public transfer payment policy in Malaysia and the overall Malaysian economy using an inter-linkage coordinate space. This space is represented graphically, with the public transfer payment distribution in the centre and the number of periods plotted along rays (axes) that are drawn from the centre, each of which can have as many windows as required at the predetermined perimeter levels. Using this model, this article evaluates whether and how the implementation of public transfer payment policy in Malaysia can simultaneously affect the overall Malaysian economy through selected macroeconomic indicators. Finally, this article proposes the use of computer graphical animation when sufficient data are available to provide a more accurate measurement and visual representation of the economic ripple effect in the same graphical space.JEL: C00, E60, H53

The search procedure, as a part of the Modified Ambiguity Function Approach (MAFA), is conducted in the coordinate space. The main advantage of searching for a fixed solution in the coordinate doma...

The rank of the sparse signals brought by multiple measurement vectors (MMV) augments the performance of joint sparse recovery. In general, suppose the sparsity level $ k$ is less than or equal to $ [rank(\boldsymbol{X})+spark(\boldsymbol{A})-1]/2$ , the sparsest solution of the MMV problem is unique and recoverable via various methods. It is shown in this letter that the unique solution of the sparsity level $ k$ up to $ spark(\boldsymbol{A})-1$ actually exists in a measure theoretical point of view. More specifically, even when $ [rank(\boldsymbol{X})+spark(\boldsymbol{A})-1]/2\leq k , the sparsest solution to $ \boldsymbol{A}\boldsymbol{X}=\boldsymbol{Y}$ is still unique with full Lebesgue measure in every $ k$ -sparse coordinate space. This phenomenon is fully confirmed by the MMV tail- $ \ell _{2,1}$ minimization technique. Furthermore, the phenomenon that the traditional $ \ell _{2,1}$ minimization actually fails to recover $ \boldsymbol{X}$ with $ k \geq [spark(\boldsymbol{A})-1]/2$ is investigated from the same perspective of measure theory. Extensive numerical tests conducted by the MMV tail- $ \ell _{2,1}$ minimization and $ \ell _{2,1}$ minimization are demonstrated to confirm the findings. The tail minimization procedure exhibits the most prominent effectiveness for the larger sparsity levels among all known techniques.

To date, 3-D radar imaging of moving objects in a multipath coordinate space close to antennas remains a technical challenge. In this work, we demonstrate the implementation of such 3-D motion imaging based on a continuous-wave, multiple-input multiple-output (MIMO) Doppler radar sensor (DRS). Working with a time-division-multiplex (TDM) scheme, this portable, cost-effective DRS is a bistatic system with one transmitting and one receiving channels, and a radio frequency (RF) switch in each channel toggling between two antennas. Assisted by algorithms specifically derived for the TDM-MIMO architecture, highly sensitive 3-D imaging performed in a multipath indoor environment was experimentally implemented. Numerical simulations and experimental demonstrations verified the effectiveness and accuracy of the proposed approach.

Bearing fault diagnosis based on the classification of patterns of permutation entropy is presented in this paper. Patterns of permutation entropy are constructed by using non-uniform embedding of the vibration signal into a delay coordinate space with variable time lags. These patterns are interpreted, processed and classified by employing deep learning techniques based on convolutional neural networks. Computational experiments are used to compare the accuracy of classification with other methods and to demonstrate the efficacy of the presented early defect detection and classification method.

Electrically charged particles are trapped by the Earth’s magnetic field, forming the Van Allen radiation belts. Observations show that electrons in this region can have energies in excess of 7 MeV. However, whether electrons at these ultra-relativistic energies are locally accelerated, arise from betatron and Fermi acceleration due to transport across the magnetic field, or if a combination of both mechanisms is required, has remained an unanswered question in radiation belt physics. Here, we present a unique way of analyzing satellite observations which demonstrates that local acceleration is capable of heating electrons up to 7 MeV. By considering the evolution of phase space density peaks in magnetic coordinate space, we observe distinct signatures of local acceleration and the subsequent outward radial diffusion of ultra-relativistic electron populations. The results have important implications for understanding the origin of ultra-relativistic electrons in Earth’s radiation belts, as well as in magnetized plasmas throughout the solar system., Electrons in the Van Allen radiation belts can have energies in excess of 7 MeV, however, the energization mechanism is debated. Here, the authors show phase space density peaks in magnetic coordinate space as a way of analyzing satellite observations which demonstrates that local acceleration is capable of heating electrons up to 7 MeV.

The problems of speed and accuracy are typical in the theory and practice of optimal control, and the requirement for the technology of minimum deviation from a given motion is often more important than speed. The search for controls that ensure the accuracy of reproducing the trajectory of motion for a given time of the transient process is considered. The Pontryagin maximum principle is used as the main method. It is supplemented for the study of special situations without analyzing auxiliary variables by the state commonness conditions (SCC) for nonlinear systems in extended coordinate space, taking into account an object, a criterion nonlinear in coordinate deviations, and an explicit occurrence of time. To expand the control algorithms, the elements of the vectors that affect the execution of the SCC are investigated. The transition time is determined by the parameter introduced into the integral criterion of accuracy, which characterizes the rate of change of coordinates. An example of a transition to the origin of coordinates of an object with two series-connected integrators with a criterion that takes into account the accuracy and time of the transition is considered. With the help of SCC, new control algorithms and structures of closed systems are obtained. Relationships between the regulation time parameter and the initial conditions for coordinates are determined. Taking into account the constraint on the control, the conditions for realizing the continuous special control and / or sliding mode are obtained. Analytical materials are confirmed by the results of system modeling. The results of the work can be used for control, including nonlinear objects, in robotics, thermal processes (furnaces, autoclaves, intermittent heating control in buildings).

We employ another approach to quantize electromagnetic fields in the coordinate space, instead of the mode (or Fourier) space, such that local features of photons can be efficiently, physically, and more intuitively described. To do this, coordinate-ladder operators are defined from mode-ladder operators via the unitary transformation of systems involved in arbitrary inhomogeneous dielectric media. Then, one can expand electromagnetic field operators through the coordinate-ladder operators weighted by non-orthogonal and spatially-localized bases, which are propagators of initial quantum electromagnetic (complex-valued) field operators. Here, we call them QEM-CV-propagators. However, there are no general closed form solutions available for them. This inspires us to develop a quantum finite-difference time-domain (Q-FDTD) scheme to numerically time evolve QEM-CV-propagators. In order to check the validity of the proposed Q-FDTD scheme, we perform computer simulations to observe the Hong-Ou-Mandel effect resulting from the destructive interference of two photons in a 50/50 quantum beam splitter.

Intermediate states in protein folding are associated with formation of amyloid fibrils, which are responsible for a number of neurodegenerative diseases. Therefore, prevention of the aggregation of folding intermediates is one of the most important problems to overcome. Recently, we studied the origins and prevention of formation of intermediate states with the example of the Formin binding protein 28 (FBP28) WW domain. We demonstrated that the replacement of Leu26 by Asp26 or Trp26 (in ∼15% of the folding trajectories) can alter the folding scenario from three-state folding, a major folding scenario for the FBP28 WW domain (WT) and its mutants, toward two-state or downhill folding at temperatures below the melting point. Here, for a better understanding of the physics of the formation/elimination of intermediates, (i) the dynamics and energetics of formation of β-strands in folding, misfolding, and nonfolding trajectories of these mutants (L26D and L26W) is investigated; (ii) the experimental structures of WT, L26D, and L26W are analyzed in terms of a kink (heteroclinic standing wave solution) of a generalized discrete nonlinear Schrodinger equation. We show that the formation of each β-strand in folding trajectories is accompanied by the emergence of kinks in internal coordinate space as well as a decrease in local free energy. In particular, the decrease in downhill folding trajectory is ∼7 kcal/mol, while it varies between 31 and 48 kcal/mol for the three-state folding trajectory. The kink analyses of the experimental structures give new insights into formation of intermediates, which may become a useful tool for preventing aggregation.

Einstein-Podolsky-Rosen (EPR) entanglement involving a pair of particles entangled in their positions and momenta is of special interest in the field of quantum information. Previously, EPR entanglement has been studied in different physical systems but in fixed coordinate spaces. Here, we demonstrate an experiment of ghost imaging and ghost interference in rotated position-momentum spaces by using position-momentum entangled photons generated from a hot atomic ensemble. By using different image objects, the measured position-momentum correlations exhibit intriguing dynamics, including gradual decrease and axis-independent EPR entanglement. The reported results on manipulating the EPR entanglement in rotating coordinate spaces hold promise in quantum communication and distant quantum image processing.

A four-state diabatic potential energy matrix (DPEM), Hd, for the description of the nonadiabatic quenching of OH(A2Σ+) by collisions with H2 is reported. The DPEM is constructed as a fit to adiabatic energies, energy gradients, and derivative couplings obtained exclusively from multireference configuration interaction wave functions. A four-adiabatic-electronic-state representation is used in order to describe all energetically accessible regions of the nuclear coordinate space. Partial permutation-inversion symmetry is incorporated into the representation. The fit is based on electronic structure data at 42 882 points, described by over 1.6 million least squares equations with a root mean square (mean unsigned) error of 178(83) cm−1. Comparison of ab initio and Hd determined minima, saddle points, and energy minimized points on C2v, Cs, C∞v, and C1 (noncoplanar) portions of two conical intersection seams are used to establish the accuracy of the Hd.

We present a new strain-rate dependent elasto-viscoplastic damage constitutive model for cementitious materials by incorporating Duvaut-Lions viscoplasticity generalized to multi-surface plasticity (c.f. Simo et al., 1988b; Simo and Hughes, 1998) followed by strain-rate-dependent damage initiation and evolution under multiaxial loading, to our previous inviscid elastoplastic-damage model (Paliwal et al., 2017). We also present a unique numerical scheme in which the integration algorithm for modeling elastoplastic response utilizes fully implicit, backward Euler method in which the governing system of non-linear equations are solved in the space of invariants based on Haigh-Westergaard coordinate system, hardening parameter and discretized plastic multiplier. It uses the framework by (Matzenmiller and Taylor, 1994), which is modified in this work. This is particularly useful as the yield criteria, flow rule, and the non-linear hardening utilize functions that are dependent on the pressure, effective shear stress, and Lode angle components of the stress tensor. To the best of authors’ knowledge, such integration algorithm in Haigh-Westergaard coordinate space has never been developed for Lode angle dependent yield criteria and the flow rule, and non-linear hardening plasticity. Furthermore, we also develop an accurate form for the algorithmic elastoplastic-damage tangent modulus consistent with the proposed return mapping technique. Numerical simulations of uniaxial tension and compression cases demonstrate that both the local integration point algorithm as well as the global algorithm using the algorithmic elastoplastic-damage tangent modulus exhibit quadratic convergence. Finally, the predictive capability of the proposed model is demonstrated by virtue of several numerical examples under various loading conditions covering different stress paths and different dynamic strain-rates. These predictions are also compared against experimental results and experimentally observed features from tests on various concrete specimens, and demonstrate excellent agreement.

With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various structures and formations such as waves, vortices, turbulent pulsations and others. Such properties of the mathematical physics equations, which are hidden (they appear only in the process of solving these equations), depend on the consistency of derivatives in partial differential equations and on the consistency of equations, if the equations of mathematical physics are a set of equations. This is due to the integrability of mathematical physics equations. It is shown that the equations of mathematical physics can have double solutions, namely, the solutions on the original coordinate space and the solutions on integrable structures that are realized discretely (due to any degrees of freedom). The transition from the solutions of the first type to one of the second type describes discrete transitions and the processes of origin of various structures and observable formations. Only mathematical physics equations, on what no additional conditions such as the integrability conditions are imposed, can possess such properties. The results of the present paper were obtained with the help of skew-symmetric differential forms.

We explore the importance of global relation reasoning in Human Pose Estimation (HPE). Global relation reasoning aims to globally learn relations among regions of images or videos. For HPE, if we can globally model the relations among different body joints, we may mitigate some challenges such as occlusion. Most existing human pose estimation methods rely on building Convolutional Neural Networks (CNNs). Because convolution operations can only model local relations, in order to capture global relations, they must inefficiently stack multiple convolution layers to enlarge the receptive fields to cover all the body joints in the image. In this paper, we propose to utilize Global Relation Reasoning Graph Convolutional Networks (GRR-GCN) to efficiently capture the global relations among different body joints. GRR-GCN projects all the features in the original coordinate space to a graph space. In the graph space, these features are represented by a set of nodes to form a fully-connected graph, on which global relation reasoning is performed by graph convolution. After reasoning, node features are projected back to the coordinate space for further processing. GRR-GCN is a plug-and-play module, and can be integrated into current state-of-the-art networks. Experiments on human pose estimation benchmark, MPII and COCO keypoint detection dataset, show that GRR-GCN can boost the performance of state-of-the-art human pose estimation networks including SimpleBaseline and HRNet (High-Resolution Net).

There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincar\'{e} gauge theory and metric-affine gauge theory adopt the first approach. This paper adopts the second. In this approach: (i) Gauge field and gravitational field can both be represented by affine connection; they can be described by a unified spatial frame. (ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space and external coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as a geometric theory of distribution of gradient directions. Hence, gauge theory, gravitational theory, and quantum theory all reflect intrinsic geometric properties of manifold. (iii) Coupling constants, chiral asymmetry, PMNS mixing and CKM mixing arise spontaneously as geometric properties in affine connection representation, so they are not necessary to be regarded as direct postulates in the Lagrangian anymore. (iv) The unification theory of gauge fields that are represented by affine connection can avoid the problem that a proton decays into a lepton in theories such as SU(5). (v) There exists a geometric interpretation to the color confinement of quarks. In the affine connection representation, we can get better interpretations to the above physical properties, therefore, to represent gauge fields by affine connection is probably a necessary step towards the ultimate theory of physics., Comment: 36 pages

In this work, an anisotropic and time-dependent continuum damage-coupled plasticity model is written under a finite strain formulation in arbitrary coordinate space to describe the mechanical behavior of ductile materials. The model accommodates the simulation of proportional and non-proportional 3D loadings. A phenomenological continuum damage mechanics approach is suggested to model the anisotropic damage in the mechanical behavior, including the post-necking region, up to failure. The mathematical model scheme captures the strain rate effect on the material's mechanical response and precisely approximates the yield stress, ultimate tensile strength, and strain to fracture. This paper also presents an implicit time integration method for the anisotropic time-dependent continuum damage-coupled plasticity model under finite strains. The prediction capability of the proposed model is validated by comparing the numerical results to uniaxial tensile experiments on TRC sheets of Mg AZ31B alloy. Magnesium alloys are the lightest engineering metals and therefore are potential candidates for use in stamped automotive panels. Comparisons between the numerical predictions and the experimental results show fair agreement over a wide range of strain rates and temperatures.

Symmetry deepens our insight into a physical system and its interplay with topology enables the discovery of topological phases. Symmetry analysis is conventionally performed either in the physical space of interest, or in the corresponding reciprocal space. Here we borrow the concept of virtual space from transformation optics to demonstrate how a certain class of symmetries can be visualised in a transformed, spectrally related coordinate space, illuminating the underlying topological transitions. By projecting a plasmonic system in a higher-dimensional virtual space onto a lower-dimensional system in real space, we show how transformation optics allows us to construct a topologically non-trivial system by inspecting its modes in the virtual space. Interestingly, we find that the topological invariant can be controlled via the singularities in the conformal mapping, enabling the intuitive engineering of edge states. The confluence of transformation optics and topology here can be generalized to other wave realms beyond photonics., Visualizing and studying topological features is becoming crucial to develop new generation topological systems. Here the authors provide the theoretical and numerical demonstration of the potential of transformation optics connecting the virtual space to the physical space of lower dimension via conformal mapping.

The use of an autonomous underwater vehicle (AUV) to inspect underwater industrial infrastructure requires the precise, coordinated movement of the AUV relative to subsea objects. One significant underwater infrastructure system is the subsea production system (SPS), which includes wells for oil and gas production, located on the seabed. The present paper suggests a method for the accurate navigation of AUVs in a distributed SPS to coordinate space using video information. This method is based on the object recognition and computation of the AUV coordinate references to SPS objects. Stable high accuracy during the continuous movement of the AUV in SPS space is realized through the regular updating of the coordinate references to SPS objects. Stereo images, a predefined geometric SPS model, and measurements of the absolute coordinates of a limited number of feature points of objects are used as initial data. The matrix of AUV coordinate references to the SPS object coordinate system is computed using 3D object points matched with the model. The effectiveness of the proposed method is estimated based on the results of computational experiments with virtual scenes generated in the simulator for AUV, and with real data obtained by the Karmin2 stereo camera (Nerian Vision, Stuttgart, Germany) in laboratory conditions.

The problem of finding a compact natural representation of brain dynamics and connectivity is addressed using an expansion in terms of physical spatial eigenmodes and their frequency resonances. It is demonstrated that this discrete expansion via the system transfer function enables linear and nonlinear dynamics to be analyzed in compact form in terms of natural dynamic ``atoms,'' each of which is a frequency resonance of an eigenmode. Because these modal resonances are determined by the system dynamics, not the investigator, they are privileged over widely used phenomenological patterns, and obviate the need for artificial discretizations and thresholding in coordinate space. It is shown that modal resonances participate as nodes of a discrete spectral network, are noninteracting in the linear regime, but are linked nonlinearly by wave-wave coalescence and decay processes. The modal resonance formulation is shown to be capable of speeding numerical calculations of strongly nonlinear interactions. Recent work in brain dynamics, especially based on neural field theory (NFT) approaches, allows eigenmodes and their resonances to be estimated from data without assuming a specific brain model. This means that dynamic equations can be inferred using system identification methods from control theory, rather than being assumed, and resonances can be interpreted as control-systems data filters. The results link brain activity and connectivity with control-systems functions such as prediction and attention via gain control and can also be linked to specific NFT predictions if desired, thereby providing a convenient bridge between physiologically based theories and experiment. Amplitudes of modes and resonances can also be tracked to provide a more direct and temporally localized representation of the dynamics than correlations and covariances, which are widely used in the field. By synthesizing many different lines of research, this work provides a way to link quantitative electrophysiological and imaging measurements, connectivity, brain dynamics, and function. This underlines the need to move between coordinate and spectral representations as required. Moreover, standard theoretical-physics approaches and mathematical methods can be used in place of ad hoc statistical measures such as those based on graph theory of artificially discretized and decimated networks, which are highly prone to selection effects and artifacts.

We present a novel but simple physics-based method to interactively manipulate surface shapes of 3D models with $$ C^1 $$ C 1 continuity in real time. A fourth-order partial differential equation involving a sculpting force originating from elastic bending of thin plates is proposed to define physics-based deformations and achieve $$ C^1 $$ C 1 continuity at the boundary of deformation regions. In order to obtain real-time physics-based surface manipulation, we construct a mapping relationship between a deformation region in a 3D coordinate space and a unit circle on a 2D parametric plane, formulate corresponding $$ C^1 $$ C 1 continuous boundary conditions for the unit circle, and obtain a simple analytical solution to describe the physics-based deformation in the unit circle caused by a sculpting force. After that, the obtained physics-based deformation is mapped back to the 3D coordinate space, and added to the original surface to create a new surface shape with $$ C^1 $$ C 1 continuity at the boundary of the deformation region. We also develop an interactive user interface as a plug-in of the 3D modelling software package Maya to achieve real-time surface manipulation. The effectiveness, easiness, real-time performance, and better realism of our proposed method is demonstrated by testing surface deformations on several 3D models and comparing with other methods and ground-truth deformations.

Algorithms for black-box optimization need considering numerous properties of objective functions in advance. The covariance matrix adaptation evolution strategy (CMA-ES) is known as one of the state-of-the-art algorithms for black-box optimization. Despite its achievement, the CMA-ES fails to minimize the objective function which is high-dimensional and ill-conditioned such as 100,000-dimensional Ellipsoid function. This fact is a serious problem to apply the CMA-ES to recent high-dimensional machine learning models. We confirm that the "single" step-size for all coordinates is one of the hindrances to the adaptation of the variance-covariance matrix. To solve this, we propose a CMA-ES with coordinate selection. Coordinate selection enables us to vectorize the step-size and adapt each component of the vector to the scale of selected coordinates. Furthermore, coordinate selection based on estimated curvature reduces the condition number during updating variables in selected coordinate space. Our method is enough simple to easily apply to most of variations of CMA-ES: only execute conventional algorithms in the selected coordinate space. The experimental results show that our method applied to the CMA-ES, the sep-CMA-ES and the VD-CMA outperforms the conventional variations of CMA-ES in terms of function evaluations and an objective value in the optimization of high-dimensional and ill-conditioned functions.

Purpose Automated segmentation of brain structures (objects) in MR three-dimensional (3D) images for quantitative analysis has been a challenge and probabilistic atlases (PAs) are among the most well-succeeded approaches. However, the existing models do not adapt to possible object anomalies due to the presence of a disease or a surgical procedure. Post-processing operation does not solve the problem, for example, tissue classification to detect and remove such anomalies inside the resulting segmentation mask, because segmentation errors on healthy tissues cannot be fixed. Such anomalies very often alter the shape and texture of the brain structures, making them different from the appearance of the model. In this paper, we present an effective and efficient adaptive probabilistic atlas, named AdaPro, to circumvent the problem and evaluate it on a challenging task - the segmentation of the left hemisphere, right hemisphere, and cerebellum, without pons and medulla, in 3D MR-T1 brain images of Epilepsy patients. This task is challenging due to temporal lobe resections, artifacts, and the absence of contrast in some parts between the structures of interest. Methods In AdaPro, we first build one probabilistic atlas per object of interest from a training set with normal 3D images and the corresponding 3D object masks. Second, we incorporate a texture classifier based on convex optimization which dynamically indicates the regions of the target 3D image where the PAs (shape constraints) should be further adapted. This strategy is mathematically more elegant and avoids problems with post-processing. Third, we add a new object-based delineation algorithm based on combinatorial optimization and diffusion filtering. AdaPro can then be used to locate and delineate the objects in the coordinate space of the atlas or of the test image. We also compare AdaPro with three other state-of-the-art methods: an statistical shape model based on synergistic object search and delineation, and two methods based on multi-atlas label fusion (MALF). Results We evaluate the methods quantitatively on 3D MR-T1 brain images of 2T and 3T from epilepsy patients, before and after temporal lobe resections, and on the template and native coordinate spaces. The results show that AdaPro is considerably faster and consistently more accurate than the baselines with statistical significance in both coordinate spaces. Conclusion AdaPro can be used as a fast and effective step for brain tissue segmentation and it can also be easily extended to segment subcortical brain structures. By choice of its components, probabilistic atlas, texture classifier, and delineation algorithm, it can also be extended to other organs and imaging modalities.

We perform canonical analysis of a model in which gravity is coupled to a spherically symmetric dust shell in 2+1 spacetime dimensions. The result is a reduced action depending on a finite number of degrees of freedom. The emphasis is made on finding canonical variables providing the global chart for the entire phase space of the model. It turns out that all the distinct pieces of momentum space could be assembled into a single manifold which has ADS^{2}-geometry, and the global chart for it is provided by the Euler angles. This results in both non-commutativity and discreteness in coordinate space, which allows to resolve the central singularity. We also find the map between ADS^{2} momentum space obtained here and momentum space in Kuchar variables, which could be helpful in extending the present results to 3+1 dimensions., 19 pages, 3 figures, conference

We study random walks in a Hilbert space H and their applications to representations of solutions to Cauchy problems for differential equations whose initial conditions are number-valued functions on the Hilbert space H. Examples of such representations of solutions to various evolution equations in the case of a finite-dimensional space H are given. Measures on a Hilbert space that are invariant with respect to shifts are considered for constructing such representations in infinite-dimensional Hilbert spaces. According to a theorem of A. Weil, there is no Lebesgue measure on an infinite-dimensional Hilbert space. We study a finitely additive analog of the Lebesgue measure, namely, a nonnegative, finitely additive measure λ defined on the minimal ring of subsets of an infinite-dimensional Hilbert space H containing all infinite-dimensional rectangles whose products of sides converge absolutely; this measure is invariant with respect to shifts and rotations in the Hilbert space H. We also consider finitely additive analogs of the Lebesgue measure on the spaces lp, 1 ≤ p ≤ ∞, and introduce the Hilbert space \( \mathcal{H} \) of complex-valued functions on the Hilbert space H that are square integrable with respect to a shift-invariant measure λ. We also obtain representations of solutions to the Cauchy problem for the diffusion equation in the space H and the Schrodinger equation with the coordinate space H by means of iterations of the mathematical expectations of random shift operators in the Hilbert space \( \mathcal{H} \).

We examine skyrmionic field configurations on a spherical ferromagnet with large normal anisotropy. Exploiting variational concepts of angular momentum, we find a new family of localized solutions to the Landau–Lifshitz equation that are topologically distinct from the ground state and not equivariant. Significantly, we observe an emergent spin–orbit coupling on the level of magnetization dynamics in a simple system without individual rotational invariance in spin and coordinate space.

The equation of state of neutron and symmetric matter is calculated within the lowest order constrained variational (LOCV) method using the Argonne V18 (AV18) nucleon–nucleon interaction supplemented by the local, coordinate space versions of the chiral three-nucleon force (TNF) at next-to-next-to-leading order (N2LOL). We present the first results of studying the nuclear equation of state in the LOCV framework by employing a chiral TNF. It is shown that although some calculated values of saturation properties lie well in the empirically determined ranges, all of the saturation quantities can not be predicted simultaneously. We also study other possible parametrizations of the N2LOL TNF by fitting the low-energy constants (LECs) to nuclear saturation point. It is found that by employing the proposed sets of LECs, LOCV method is able to successfully produce the equilibrium properties of symmetric nuclear matter.

We study a puzzle raised recently regarding the running coupling prescription used in the calculation of forward particle production in proton-nucleus collisions at next-to-leading order: using a coordinate space prescription which is consistent with the one used in the high energy evolution of the target leads to results which can be two orders of magnitude larger than the ones obtained with a momentum space prescription. We show that this is an artefact of the Fourier transform involved when passing between coordinate and momentum space and propose a new coordinate space prescription which avoids this problem., Comment: 4 pages, 1 figure. Quark Matter 2018 proceedings

Generators of the Poincar\'e group, for a free massive scalar field, are usually expressed in the momentum space. In this work we perform a transformation of these generators into the coordinate space. This (spatial)-position space is spanned by eigenvectors of the Newton-Wigner-Pryce operator. The motivation is a deeper understanding of the commutative spatial coordinate space in QFT, in order to investigate the non-commutative version thereof., Comment: added a new Theorem

We present a general study of 3-point functions of conformal field theory in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWI' s), introduced in recent works by Bzowski, McFadden and Skenderis (BMS). We investigate and detail the structure of the CWI's, their non-perturbative solutions and the transition to momentum space, comparing them to perturbation theory by taking QED as an example. We then proceed with an analysis of the $TJJ$ correlator, presenting independent and detailed re-derivations of the conformal equations in the reconstruction method of BMS, originally formulated using a minimal tensor basis in the transverse traceless sector. A careful comparison with a second basis introduced in previous studies shows that this correlator is affected by one anomaly pole in the graviton (T) line, induced by renormalization. The result shows that the origin of the anomaly, in this correlator, should be necessarily attributed to the exchange of a massless effective degree of freedom. Our results are then exemplified in massless QED at one-loop in $d$-dimensions, expressed in terms of perturbative master integrals. An independent analysis of the Fuchsian character of the solutions, which bypasses the 3K integrals, is also presented. We show that the combination of field theories at one-loop - with a specific field content of degenerate massless scalar and fermions - is sufficient to generate the complete non-perturbative solution, in agreement with a previous study in coordinate space. The result shows that free conformal field theories, in specific dimensions, arrested at one-loop, reproduce the general result for the $TJJ$. Analytical checks of this correspondence are presented in $d=3,4$ and $5$ spacetime dimensions[..]., 79 pages, 3 Figures. Final version, with changes in section 8. Accepted for publication in Nuclear Physics B

Modern processes of air traffic control are realized on a single information platform called globally-localized information clusters, which are united in a single information environment. The main information component for such a system is navigation information about the location of each aircraft, containing dynamically updated data on its current coordinates and motion parameters. Under such conditions, there is the task of integrating navigation information obtained from various information sources that make up the aircraft avionics. Traditional approaches do not provide joint smoothing of coordinate information invariant to synchronization of measurements; therefore, the statistical analysis of experimental samples of navigation parameters is determined by the object of research. The paper deals with a mathematical apparatus for providing multidimensional smoothing of the navigation parameters of an aircraft using the least squares method. To implement the proposed approach, the method of affine mapping of the coordinate space is used. This provides independent functional dependencies of the coordinate field of the aircraft for their joint processing by the method of least squares. The developed software for multidimensional smoothing of the navigation parameters of the aircraft can be used to study the processes of evolution and maintenance of the software of the on-board computer complex of the aircraft. A feature of the approach is the time coordination of the obtained measurements at the model level, reduces the requirements for synchronization of the primary navigation parameters and expands the possibilities in the list of parameters that are processed together. This provides an increase in the accuracy of determining the current position of the aircraft compared to traditional approaches by attracting additional data redundancy. The proposed approach can be extended to a wide range of applied industries related to the measurement, evaluation and prediction of changes over time in interrelated processes.

The human body has a complex shape requiring a control structure of matching complexity. This involves keeping track of several body parts that are best represented in different frames of reference (coordinate systems). In performing a complex action, representations in more than one system are active at a time, and switches from one set of coordinate systems to another are performed. During a simple act of grasping, for example, an object is represented in a purely visual, retina-centered coordinate system and is transformed into headand body-centered representations. On the control side, 3-dimensional movement fields, found in the motor cortex, surround the body and determine the goal position of a reaching movement. A conceptual, object-centered coordinate space representing the difference between target object and hand position may be used for movement corrections near the end of grasping. As a guideline for the development of more sophisticated robotic actions, we take inspiration from the brain. A cortical area represents information about an object or an actuator in a specific coordinate system. This view is generalized in the light of population coding and distributed object representations. In the motor system, neurons represent motor "affordances" which code for certain configurations of objectand effector positions, while mirror neurons code actions in an abstract fashion. One challenge to the technological development of a robotic / humanoid action control system is – besides vision – its complexity, another is learning. One must explain the cortical mechanisms which support the several processing stages that transform retinal stimulation into the mirror neuron and motor neuron responses (Oztop et al., 2006). Recently, we have trained a frame of reference transformation network by unsupervised learning (Weber & Wermter, 2006). It transforms between representations in two reference frames which may dynamically change their position to each other. For example the mapping between retinal and body-centered coordinates while the eyes may move. We will briefly but concisely present this self-organizing network in the context of grasping. We will also discuss mechanisms required for unsupervised learning such as requested slowness of neuronal response changes in those frames of reference that tend to remain constant during a task. This book chapter shall guide and inspire the development of sensory-motor control strategies for humanoids. This book chapter is organized as follows. Section 2 reviews neurobiological findings; Section 3 reviews robotic research. Then, after motivating learning in Section 4, we will

Internet Coordinate Systems, shortly ICS, (e.g. [9] [8]) have been proposed to allow for distance (Round-Trip Time, shortly RTT) estimation between nodes, in order to reduce the measurement overhead of many applications and overlay networks. Indeed, by embedding the Internet delay space into a metric space – an operation that only requires each node in the system to measure delays to a small set of other nodes (its neighbors), nodes are attributed coordinates that can then be used to estimate the RTT between any two nodes, without further measurements, simply by applying the distance function associated with the chosen metric space to the nodes’ coordinates. Recent works have shown how coordinate-embedding services could be vulnerable to malicious attacks, providing a potentially attractive fertile ground for the disruption or collapse of the many applications and overlays that would use these services [2]. There are actually two obvious ways to disrupt the operation of a coordinate based system. First when requested to give its coordinate for a distance estimation at the application-level, a malicious node could simply and blatantly lie. Second, a malicious node, or even a colluding group, may aim at disrupting the embedding process itself. This latter strategy is very insidious and effective as it can result in important distortions of the coordinate space which then spoils the coordinate computations of many nodes (malicious and honest alike) [2]. This chapter focuses on developing and studying generic Kalman filter-based methods to secure the coordinate embedding process. More precisely, the embedding process, regardless of the actual coordinate-based positioning system, works on the premise that nodes adjust their coordinate based on some comparison between measured and estimated distances to some other nodes. Malicious nodes can interfere with this embedding process by, amongst other things, lying about their real coordinate and/or tampering with measurement probes, to create a discrepancy between measured and estimated latencies, so that unsuspecting nodes would wrongly adjust their own coordinate in a bid to reduce the difference [1]. Because the load on the network naturally varies in time, so does latency between pair of nodes, and as a Source: Kalman Filter, Book edited by: Vedran Kordic, ISBN 978-953-307-094-0, pp. 390, May 2010, INTECH, Croatia, downloaded from SCIYO.COM

To interpret in vivo experiments designed to understand brain function, high-resolution whole-brain microscopy provides a means for post hoc determination of the location of implanted devices and recorded cells in three dimensional brain space that is a critical step for data interrogation. Here we have developed Python-based tools (brainreg and brainreg-segment) to accurately map, in a common coordinate space, the position of dye-labelled probe tracks and two-photon imaged cell populations expressing fluorescent protein. The precise location of probes and cells were validated using physiological recordings and human raters that indicate accuracy levels to less than 70µm. These flexible, open-source methodologies are expected to further evolve with need and to deliver the anatomical precision that is necessary for understanding the functional architecture of the brain.

The Madelung-de Broglie-Bohm formulation of the Schrodinger equation casts the time-evolution of a wave function as dynamics of an ensemble of quantum, or Bohmian, trajectories, interacting via the nonlocal quantum potential. This trajectory perspective gives insight into the quantumness (or classicality) of a given system due to clear partitioning of the energy into classical and quantum components. Here, we propose a system-independent measure of the quantumness of dynamics, based on the energy time-change, referred to as "quantum power". This measure is local in the coordinate space. Based on applications to model chemical systems, we argue that during the transition from the quantum to classical regime, defined as compression of quantization, the quantum features in dynamics do not "disappear" but are pushed forward in time. This feature may be used to gauge the validity of the semiclassical and other approximate dynamics approaches in applications to anharmonic systems.

Background: Recently, the researches of cluster structure have attracted considerable attention. Many microscopic structure models have been applied to describe the cluster configurations.Purpose: To better analyze the cluster structure and associate with the experimental observations, comparative studies are carried out in this paper by combining the nuclear structure model with the electron scattering theory.Method: The density distributions for candidate nuclei of normal and cluster states are obtained from the deformed relativistic Hartree-Bogoliubov (RHB) model. Using some moderate approximations, the corresponding Coulomb form factors $|{F}_{C}{(q)|}^{2}$ and inclusive cross sections for different configurations are calculated by the distorted wave Born approximation (DWBA) and coherent density fluctuation model (CDFM), respectively.Results: Comparing the $|{F}_{C}{(q)|}^{2}$ and inclusive cross sections of different configurations, the effects of nuclear cluster structure can be revealed, due to the differences of nuclear charge radii ${R}_{C}$ in coordinate space and the discrepancies of Fermi momentum ${k}_{F}$ in momentum space.Conclusions: Results illustrate that the cluster structure can be reflected from the elastic and inclusive electron scattering. The studies conducted in this paper provide a new approach to analyze the cluster configurations, and are also helpful to guide future electron scattering experiments.

Multi-configurational time-dependent Hartree (MCTDH) calculations using time-dependent grid representations can be used to accurately simulate high-dimensional quantum dynamics on general ab initio potential energy surfaces. Employing the correlation discrete variable representation, sets of direct product type grids are employed in the calculation of the required potential energy matrix elements. This direct product structure can be a problem if the coordinate system includes polar and azimuthal angles that result in singularities in the kinetic energy operator. In the present work, a new direct product-type discrete variable representation (DVR) for arbitrary sets of polar and azimuthal angles is introduced. It employs an extended coordinate space where the range of the polar angles is taken to be [-pi, pi]. The resulting extended space DVR resolves problems caused by the singularities in the kinetic energy operator without generating a very large spectral width. MCTDH calculations studying the F·CH4 complex are used to investigate important properties of the new scheme. The scheme is found to allow for more efficient integration of the equations of motion compared to the previously employed cot-DVR approach [G. Schiffel and U. Manthe, Chem. Phys. 374, 118 (2010)] and decreases the required central processing unit times by about an order of magnitude.

We study the Post-Minkowskian (PM) and Post-Newtonian (PN) expansions of the gravitational three-body effective potential. At order 2PM a formal result is given in terms of a differential operator acting on the maximal generalized cut of the one-loop triangle integral. We compute the integral in all kinematic regions and show that the leading terms in the PN expansion are reproduced. We then perform the PN expansion unambiguously at the level of the integrand. Finding agreement with the 2PN three-body potential after integration, we explicitly present new $G^2v^4$-contributions at order 3PN and outline the generalization to $G^2v^{2n}$. The integrals that represent the essential input for these results are obtained by applying the recent Yangian bootstrap directly to their $\epsilon$-expansion around three dimensions. The coordinate space Yangian generator that we employ to obtain these integrals can be understood as a special conformal symmetry in a dual momentum space., Comment: 15 pages, 5 figures, 1 ancillary machine-readable file, v2: minor improvements and additions, title adapted to journal title

We investigate the prospects of combining a standard momentum space approach for ultracold three-body scattering with efficient coordinate space schemes to solve the underlying two-body problem. In many of those schemes, the two-body problem is numerically restricted up to a finite interparticle distance ${r}_{\mathrm{b}}$. We analyze the effects of this two-body restriction on the two- and three-body level using pairwise square-well potentials that allow for analytic two-body solutions and more realistic Lennard-Jones van der Waals potentials to model atomic interactions. We find that the two-body $t$ operator converges exponentially in ${r}_{\mathrm{b}}$ for the square-well interaction. Setting ${r}_{\mathrm{b}}$ to 2000 times the range of the interaction, the three-body recombination rate can be determined accurately up to a few percent when the magnitude of the scattering length is small compared to ${r}_{\mathrm{b}}$, while the position of the lowest Efimov features is accurate up to the percent level. In addition, we find that with the introduction of a momentum cutoff, it is possible to determine the three-body parameter in good approximation even for deep van der Waals potentials.

In large-momentum effective theory (LaMET), calculating parton physics starts from calculating coordinate-space-$z$ correlation functions $\tilde h(z, a,P^z)$ in a hadron of momentum $P^z$ in lattice QCD. Such correlation functions involve both linear and logarithmic divergences in lattice spacing $a$, and thus need to be properly renormalized. We introduce a hybrid renormalization procedure to match these lattice correlations to those in the continuum $\overline{\rm MS}$ scheme, without introducing extra non-perturbative effects at large $z$. We analyze the effect of ${\cal O}(\Lambda_{\rm QCD})$ ambiguity in the Wilson line self-energy subtraction involved in this hybrid scheme. To obtain the momentum-space distributions, we recommend to extrapolate the lattice data to the asymptotic $z$-region using the generic properties of the coordinate space correlations at moderate and large $P^z$, respectively., Comment: Text revised, version to appear in NPB

We apply a recently developed momentum-space semilocally regularized chiral potential to the $^{2}\mathrm{H}$ and $^{3}\mathrm{He}$ photodisintegration processes and to the (anti)neutrino induced deuteron breakup reactions. Specifically, the differential cross section, the photon analyzing power, and the final proton polarization have been calculated for deuteron photodisintegration at photon energies of 30 and 100 MeV. For $^{3}\mathrm{He}$ photodisintegration, predictions for the semi-inclusive and exclusive differential cross sections are presented for photon energies up to 120 MeV. The total cross section is calculated for (anti)neutrino disintegration of the deuteron for (anti)neutrino energies below 200 MeV. Predictions based on the Argonne V18 potential and on an older chiral force with regularization applied in coordinate space are used for comparison. Using the fifth-order chiral nucleon-nucleon potential supplemented with dominant contributions from the sixth order allows us to obtain converged predictions for observables in the investigated reactions. Our results based on the newest semilocal chiral potentials show even smaller cutoff dependence and a somewhat faster convergence for the considered electroweak observables than the previously reported ones with a coordinate-space regulator, which make them a promising tool to study electroweak processes.

Despite the rapid technical advancement of augmented reality (AR) and mixed reality (MR) in minimally invasive surgery (MIS) in recent years, monocular-based 2D/3D reconstruction still remains technically challenging in AR/MR guided surgery navigation nowadays. In principle, soft tissue surface is smooth and watery with sparse texture, specular reflection, and frequent deformation. As a result, we frequently obtain only sparse feature points that give rise to incorrect matching results with conventional image processing methods. To ameliorate, in this paper we enunciate an accurate and robust description and matching method for dense feature points in endoscopic videos. Our new method first extracts contours of the low-rank image sequences based on the adaptive robust principal component analysis (RPCA) decomposition. Then we propose a multi-scale dense geometric feature description approach, which simultaneously extracts dense feature descriptors of the contours in the original Euclidean coordinate space, the accompanying 3D color coordinate space, and the derived curvature-gradient coordinate space. Finally, we devise a new algorithm for both global and local point-wise matching based on feature fusion. For global matching, we employ the fast Fourier transform (FFT) to reduce the dimension of the dense feature descriptors. For local feature point matching, in order to enhance the robustness and accuracy of the matching, we cluster multiple contour points to form “super-point” based on dense feature descriptors and their spatio-temporal continuity. The comprehensive experimental results confirm that our novel approach can overcome the highlight influence, and robustly describe contours from image sequences of soft tissue surfaces. Compared with the state-of-the-art feature point description and matching methods, our analysis framework shows the key advantages of both robustness and accuracy in dense point-wise matching, even when the severe soft tissue deformation occurs. Our new approach is expected to have high potential in 2D/3D reconstruction in endoscopy.

The proposed system is a pick and place algorithm for a robotic arm using multirate event triggered sliding mode controller. The robotic arm in three dimensional coordinate space is analysed for the work. The arm is modeled as a switched system divided into individual subsystems which are dependent on the angular positions of the arm in the coordinate space. Event triggering is found to be efficient when compared to time triggered control as the control update is done only at instants when a triggering rule is violated. And the triggering rule is chosen such that it takes into account the stability conditions of the system. The multirate control employed is the fast output sampling based sliding mode control. The three dimensional arm system is thus controlled on an event triggering basis such that one can pick and place an object in the defined coordinate space with minimum control updates and thus help in efficient utilization of resources.

We present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space from lattice QCD. We investigate the degree of universality of the extracted PDFs when the lattice and experimental data are treated under the same conditions within the Bayesian likelihood analysis. For the unpolarized sector, we find rather weak constraints from the current lattice data on the phenomenological PDFs, and difficulties in describing the lattice matrix elements at large spatial distances. In contrast, for the polarized PDFs we find good agreement between experiment and lattice data, with the latter providing significant constraints on the spin-dependent isovector quark and antiquark distributions., Comment: 23 pages, 4 figures