Coordinate Space Research Articles

Возможность применения метода Гершберга-Папулиса в задаче реконструкции фазовой структуры по малоракурсным гильбертограммам

The possibility of processing small-view hilbertograms by the Gershberg-Papulis method to restore the refractive index of phase objects is discussed. The method consists in iterative transitions from estimating a function in the Fourier plane to estimating it in a coordinate space with an adjustment using a priori information. The spectrum of the function is determined on the entire frequency plane as an iterative process result Numerical simulation of the refractive index reconstruction for various test functions was performed using the Gershberg-Papulis method using Radon data known for four angles. Experimental studies on the Hilbert diagnostics example of reacting media (flames) in a high-speed shooting mode (up to 2000 frames per second) were performed using a four-angle tomographic complex implemented on the basis of an upgraded IAB-463M shadow device.

Spatial attention-based implicit neural representation for arbitrary reduction of MRI slice spacing

Magnetic resonance (MR) images collected in 2D clinical protocols typically have large inter-slice spacing, resulting in high in-plane resolution and reduced through-plane resolution. Super-resolution technique can enhance the through-plane resolution of MR images to facilitate downstream visualization and computer-aided diagnosis. However, most existing works train the super-resolution network at a fixed scaling factor, which is not friendly to clinical scenes of varying inter-slice spacing in MR scanning. Inspired by the recent progress in implicit neural representation, we propose a Spatial Attention-based Implicit Neural Representation (SA-INR) network for arbitrary reduction of MR inter-slice spacing. The SA-INR aims to represent an MR image as a continuous implicit function of 3D coordinates. In this way, the SA-INR can reconstruct the MR image with arbitrary inter-slice spacing by continuously sampling the coordinates in 3D space. In particular, a local-aware spatial attention operation is introduced to model nearby voxels and their affinity more accurately in a larger receptive field. Meanwhile, to improve the computational efficiency, a gradient-guided gating mask is proposed for applying the local-aware spatial attention to selected areas only. We evaluate our method on the public HCP-1200 dataset and the clinical knee MR dataset to demonstrate its superiority over other existing methods.

Criminalistics and Crime Scene Investigation in Microgravity Space

Addresses the challenges and considerations of criminalistics and crime scene investigation in extraterrestrial gravitational environments. Future space exploration may require the development of protocols for extraterrestrial crime scene investigations. Challenges in microgravity effects, confined space environments, forensic techniques, communication, coordination, and legal jurisdiction are highlighted in this brief. Microgravity effects create difficulties in dis-placing evidence, such as blood spatter patterns, which make interpretation of events difficult. Restricted areas such as spacecraft and stations require special techniques and equipment. Storing and securing evidence in microgravity makes traditional methods impractical. The lack of gravity affects fingerprint development and preservation, requiring the use of alternative methods. Compact and specialized equipment is required to analyze DNA in space. Communication de-lays hinder real-time collaboration between researchers on Earth and those in space. Guidance can be provided to personnel in space with remote technologies and autonomous systems. Determining legal jurisdiction for crimes committed in space or on spacecraft requires complex international cooperation and agreements. The development of space law, technology and international agreements is important to meet the challenges of extraterrestrial crime scene investigations. Future discussions and research will provide a basis for establishing protocols for extraterrestrial crime scene investigations to ensure effective and fair forensic practices. As space exploration progresses, advances need to be made in these areas. As space exploration advances, the development of space law, technology, and international agreements is crucial to meeting the unique challenges of extraterrestrial crime scene investigations. This summary provides a basis for future discussions and research regarding the establishment of protocols to ensure effective and fair forensic practices off Earth.

Quantization of non-Abelian Yang-Mills theories

A non-Abelian theory of fermions interacting with gauge bosons, the constrained system, is studied. The equations of motion for a singular system are obtained as total differential equations in many variables. The integrability conditions are investigated, and the set of equations of motion is integrable. The Senjanovic and the canonical methods are used to quantize the system, and the integration is taken over the canonical phase space coordinates.

Multilevel superposition for deciphering the conformational variability of protein ensembles.

The dynamics and variability of protein conformations are directly linked to their functions. Many comparative studies of X-ray protein structures have been conducted to elucidate the relevant conformational changes, dynamics and heterogeneity. The rapid increase in the number of experimentally determined structures has made comparison an effective tool for investigating protein structures. For example, it is now possible to compare structural ensembles formed by enzyme species, variants or the type of ligands bound to them. In this study, the author developed a multilevel model for estimating two covariance matrices that represent inter- and intra-ensemble variability in the Cartesian coordinate space. Principal component analysis using the two estimated covariance matrices identified the inter-/intra-enzyme variabilities, which seemed to be important for the enzyme functions, with the illustrative examples of cytochrome P450 family 2 enzymes and class A $\beta$-lactamases. In P450, in which each enzyme has its own active site of a distinct size, an active-site motion shared universally between the enzymes was captured as the first principal mode of the intra-enzyme covariance matrix. In this case, the method was useful for understanding the conformational variability after adjusting for the differences between enzyme sizes. The developed method is advantageous in small ensemble-size problems and hence promising for use in comparative studies on experimentally determined structures where ensemble sizes are smaller than those generated, for example, by molecular dynamics simulations.

Рубежность и сущностные характеристики театрального танца в России конца XIX – начала ХХ века

Innovation and experiment as sources that expand and deepen the space of theatrical dance in Russia in the late 19th – early 20th centuries had a complex connection: from “traditional” and “local modern” to “systemic” and “natural”. Unlike Western European ballet theater, in Russia the aesthetic concepts of expressionism, constructivism and abstractionism were the first poetic experiments “with” choreography and “in” choreography, which received reinterpretation not only at the level of off-dance plans and free formative laws of movement, but also at the level of artistic coordinates of space and the semantics of academic ballet art. The paper aims to substantiate the position that after the era of romantic ballets by Marius Ivanovich Petipa (1818-1910), a milestone of the choreographic system begins in Russia, associated with the tasks of rethinking the language of theatrical dance, its architectonic structures (scenic and bodily), as well as the essential characteristics of the content and form of the ballet text. The study is novel in that it develops the following hypothesis: the architectonic space of the stage and architectonic bodily forms become figuratively and expressively evidence-based. The connection between the lexical potential and the creation of tectonic tasks in the system of academic movement is revealed, the verbal, temporal and visual continuum of space is correlated. As a result, the paper systematizes European and Asian theatrical traditions in the study of artistic and physiological processes of movement in order to determine the specifics of the architectonic bodily structures of the period under consideration.

A computationally efficient method for dynamic response analyses of accessory drive systems using harmonic balance method together with alternating frequency/time domain technique

Serpentine belt accessory drive system (SBADS) is a typical coupled vibration system with rigid body vibrations and continuum vibrations. Vibration behaviors of a SBADS consist of rotational vibrations of pulleys and tensioner arm and transverse vibrations of belt spans. In modeling of a SBADS, transverse vibration of a belt span consisting of time and space coordinates is discretized into multiple degrees of freedom with only time variable. As a result, number of degrees of freedom of a SBADS is large, and computational efficiency of dynamic responses of a SBADS is low. To solve this issue, a calculation method for nonlinear dynamic characteristics of a SBADS is proposed based on the harmonic balance method with alternating frequency/time domain technique in the paper. An engine front end accessory drive system is taken as a study example, the coupling vibration model of the SBADS is established, and hysteretic behavior of the tensioner is considered in the model. In addition, a dimensionality reduction method for the dynamic matrix is proposed based on local nonlinearity of the model. A calculation method for nonlinear dynamic responses of the SBADS is subsequently developed by combining the harmonic balance method and alternating frequency/time domain technique. Nonlinear dynamic responses estimated by the proposed method are validated by comparing with numerical simulations. Finally, amplitude-frequency responses of the SBADS are calculated using arc-length continuation method, and influences of nonlinear tensioner on frequency domain responses and internal resonance phenomena of the SBADS are analyzed.

Renovation in St. Petersburg as a field of power-civil relations: Approaches to analysis

The article is focused on the analysis of the reaction of the population of St. Peters burg as a field of power-civic relations. A comprehensive approach is used, including both the tools of sociology of social movements and the model of citizens’ behavior in the space of normative coordinates. Attention is paid to the inconsistency of the adopted legislation. Emphasis is placed on the use of digital platforms to coordinate protest activity and protect their personal space.

Multiple ESIPT and triplet formation pathways in photoexcited 2-mercapto-5-methyl-1,3-benzenedicarboxaldehyde

Simultaneous dynamical events happening upon photoexcitation of 2-mercapto-5-methyl-1,3-benzenedicarboxaldehyde (MMB) are studied using quantum wavepacket simulations. Several crossings among S1, S2, S3, T3, and T4 states are identified using the potential energy profile analyses in vibrational coordinate space. Simulations in the singlet manifold show nonadiabatic population transfer to higher states (S2 and S3) within a few tens of femtoseconds upon initiating the wavepacket on S1. Such population exchange opens up multiple excited-state intramolecular proton transfer (ESIPT) pathways involving all three singlet states, i.e., S1, S2 and S3. The singlet-triplet dynamics using spin-orbit coupling constants reveal that the triplet generation via S1 to T3/T4 is a minor deactivation pathway and can compete with the proton transfer process.

Content Modeling in Multi-Platform Multilingual Social Media Data

An increase in the use of social media as the primary news source for the general population has created an ecosystem in which organic conversation commingles with inorganically seeded and amplified narratives, which can include public relations and marketing activity but also covert and malign influence operations. An efficient and easily understandable analysis of such data is important, as it allows relevant stakeholders to protect online communities and free discussion while better identifying activity and content that may violate social media platform terms of service. To accomplish this, we propose a method of large-scale social media data analysis, which allows for multilingual conversations to be analyzed in depth across any number of social media platforms simultaneously. Our method uses a text embedding model, i.e., a natural language processing model that holds semantic and contextual understandings of language. The model uses an “understanding” of language to represent posts as coordinates in a high-dimensional space, such that posts with similar meanings are assigned coordinates close together. We then cluster and analyze the posts to identify online topics of conversation existing across multiple social media platforms. We explicitly show how our method can be applied to four different datasets, three consisting of Chinese social media posts related to the Belt and Road Initiative and one relating to the Russia-Ukraine war, and we find politically-influenced conversations that contain misleading information relating to the Chinese government and the Russia-Ukraine war.

Topology of Conical Intersection Seams and the Geometric Phase.

In this paper, we demonstrate two topological properties of crossing seams, that is, the sets of points in the N-dimensional space of nuclear coordinates where two electronic eigenstates are degenerate. We shall examine the typical case of states of the same spin with accidental degeneracies, whereby the crossing seam is of dimension N - 2. The first property we demonstrate is that a crossing seam has no boundary, therefore, it must either extend asymptotically to infinite values of one or more coordinates or wrap on itself. The second property is that two (or more) crossing seams can intersect each other but in such a way that neither of them ends at the intersection. When N = 3, the crossing seam is a line in a 3D space; this is so in triatomic molecules but also in reduced dimensionality treatments of larger polyatomics. The above-mentioned rules then mean that the crossing seam is a line of infinite length or a closed loop and can split into three branches but not in two. The example of the first two excited 1A' states of H2Cl+ illustrates these rules and shows their usefulness for computational search and characterization of crossing seams.

Renormalon cancellation and linear power correction to threshold-like asymptotics of space-like parton correlators

In this paper, we show that the common hard kernel of double-log-type or threshold-type factorization for certain space-like parton correlators that arise in the context of lattice parton distributions, the heavy-light Sudakov hard kernel, has linear infrared (IR) renormalon. We explicitly demonstrate how this IR renormalon correlates with ultraviolet (UV) renormalons of next-to-leading power operators in two explicit examples: threshold asymptotics of space-like quark-bilinear coefficient functions and transverse momentum dependent (TMD) factorization of quasi wave function amplitude. Theoretically, the pattern of renormalon cancellation complies with general expectations to marginal asymptotics in the UV limit. Practically, this linear renormalon explains the slow convergence of imaginary parts observed in lattice extraction of the Collins-Soper kernel and signals the relevance of next-to-leading power contributions. Fully factorized, fully controlled threshold asymptotic expansion for space-like quark-bilinear coefficient functions in coordinate and moment space has also been proposed.

STODOLA-VIANELLO ITERATION METHOD FOR FREE TORSIONAL VIBRATION ANALYSIS OF MONOSYMMETRIC BOX-BEAM BRIDGES

Box-beam bridges are used in large spans and wider decks due to their high strength and greater torsional and flexural stiffness. They are usually prone to vibration due to moving vehicular traffic. Their eigenfrequency analysis is a crucial aspect of their design in order to ensure that the natural frequency is not close to the excitation frequency to avert resonance failures. The free torsional vibration equation is a fourth order partial differential equation (PDE) with variable parameters. For prismatic cross-sections, homogeneous and isotropic materials the governing PDE have constant parameters. This paper explores the Stodola-Vianello iteration method (SVIM) for solving the PDE for isotropic, homogeneous prismatic box-beams. Harmonic response is assumed, decoupling the PDE to two equations, one in terms of time and the second an ordinary differential equation (ODE) in terms of space coordinates. The Stodola-Vianello method is used by the method of four successive integrations to express the ODE as an algebraic iteration problem with four constants of integration. The four boundary conditions are used to solve for the four constants of integration, thus making the problem determinate. Application of the boundary conditions results in the full determination of the iteration equations. For simply supported boundaries studied in the work, a trigonometric buckling shape function that satisfies all the boundary conditions is employed in the SVIM formula to obtain the next bucking modal shape function. The requirement for convergence is then used to establish the characteristic buckling equation from which the eigenvalues are obtained. The solution to the characteristic buckling equation gave the exact mathematical expression for the natural torsional frequency at the nth vibration mode. The frequencies are determined for the first eight vibration modes and compared with previously obtained values. It was found that the natural frequencies are identical with previously found values of the exact natural frequencies. The natural frequency obtained is exact because it satisfies the PDE and the boundary conditions at all points in the domain.

Nonlinear ion acoustic waves in dense magnetoplasmas: Analyzing interaction solutions of the KdV equation using Wronskian formalism for electron trapping with Landau diamagnetism and thermal excitations

Nonlinear ion acoustic waves in the presence of electron trapping with Landau quantization and thermal excitations induced smearing effects of the Fermi step function are investigated using the two-fluid theory in the vicinity of white dwarfs. In spite of the fact that the Kortweg de Vries (KdV) equation is derived within the confines of small amplitude approximation used in the reductive perturbation theory (RPT), it is found to admit solutions that exhibit outstanding capability of wave enhancement and have applications in the nonlinear wave propagation. It is found that enhancing the quantizing magnetic field and the electron thermal effects modify the spatial scale of the formation of the novel nonlinear structures reported for our model. Interestingly, it is found that, unlike the solitary and periodic structures, the choice of space and time coordinates affects the structure of these solutions. Interaction of these solutions with a stable nonlinear structure are also studied.

Orthogonal separation of variables for spaces of constant curvature

Abstract We construct all orthogonal separating coordinates in constant curvature spaces of arbitrary signature. Further, we construct explicit transformation between orthogonal separating and flat or generalised flat coordinates, as well as explicit formulas for the corresponding Killing tensors and Stäckel matrices.

A hybrid quantum algorithm to detect conical intersections

Conical intersections are topologically protected crossings between the potential energy surfaces of a molecular Hamiltonian, known to play an important role in chemical processes such as photoisomerization and non-radiative relaxation. They are characterized by a non-zero Berry phase, which is a topological invariant defined on a closed path in atomic coordinate space, taking the value π when the path encircles the intersection manifold. In this work, we show that for real molecular Hamiltonians, the Berry phase can be obtained by tracing a local optimum of a variational ansatz along the chosen path and estimating the overlap between the initial and final state with a control-free Hadamard test. Moreover, by discretizing the path into N points, we can use N single Newton-Raphson steps to update our state non-variationally. Finally, since the Berry phase can only take two discrete values (0 or π), our procedure succeeds even for a cumulative error bounded by a constant; this allows us to bound the total sampling cost and to readily verify the success of the procedure. We demonstrate numerically the application of our algorithm on small toy models of the formaldimine molecule (H2C=NH).

A Vlasov-Fokker-Planck-Landau code for the simulation of colliding supersonic dense plasma flows

A Vlasov-Fokker-Planck-Landau (VFPL) code is developed for the study of colliding supersonic dense plasma flows, in which the VFPL equations for both electrons and ions are solved by the time splitting strategy in the two-dimensional Cartesian coordinate space and the two-dimensional velocity space (2D2V). To accurately handle two colliding supersonic plasma flows with their velocities even much higher than the thermal velocities of ions, the full Fokker-Planck-Landau operator is employed for the collision terms. Using advanced numerical methods such as the fast spectral method and the asymptotic-preserving scheme, the ion-ion and electron-electron collision terms can be properly solved with a relatively large time step so that both high accuracy and efficiency of the developed code can be achieved. Further, the quantum degeneracy effect due to the high density and relatively low initial temperature of the electrons is included in the model. In addition, both the energy and momentum conservation are well satisfied. The developed code provides a unique numerical tool to study the interactions between high-velocity high-density plasma flows, which may be encountered in some advanced schemes of inertial confinement fusion and laser-driven laboratory astrophysics experiments.

Plasma kinetic simulation in Eulerian approach fully respecting f≥0 requirement and total particle number conservation

Abstract Plasma kinetic simulation in Eulerian approach (PKSiEA) can yield a dynamic description on plasmas and hence is a popular method in theoretical plasmas physics. Its mathematical model consists of 8 members: 5 partial differential equations (PDEs), a phase space boundary condition and an initial condition of the distribution function (PDF) f, and a mandatory non-negativity requirement on f. Because Vlasov equation (VE) is a PDE with variable coefficients and the non-negativity requirement is mandatory, when 5 PDEs (4 Maxwell equations and the VE) are treated as an initial-value problem, the temporal evolution of f is difficult to be attacked by existing popular computational mathematics techniques, such as Fourier analysis technique and finite-difference technique, and hence these techniques do not yield efficient and reliable schemes of the PKSiEA. In a universal scheme of the PKSiEA presented here, because the phase space boundary condition f∣ r=∞,∣υ∣=c = 0 causes the VE to yield a conservation of total particle number ∫fd 3 rd 3 υ, we propose an efficient and strict expression of the f-profile in terms of two classes of functions of phase space coordinates r , υ , and the VE displays a universal relation between two classes. By this new expression, we express the initial-value problem of 5 PDEs in terms of allowed deformation modes from an initial f-profile, and ensure the PKSiEA fully respecting the non-negativity requirement on f.

The problem of implementing the concept of maximum integration of heterogeneous data in practical navigation

The topic of the work is the research of the problem of the practical realization of opportunistic navigation, which actually consists in the fact that the “signals of opportunity” are not optimized for global navigation according to their original purpose. A hypothesis about the possibility of strategic application of the navigation concept based on the principles of data integration with the objective existence of tactically surmountable difficulties is put forward. In the conditions of vulnerability of the global satellite system, an approach to use an additional source of combined signals in order to continuously ensure accurate geolocation of water transport vehicles is proposed. The comparative assessment confirms the comparability of the positioning error of alternative navigation with the data of classical satellite observations of mobile objects. An assumption about the effectiveness of spline modeling of the cartographic standard of informativeness for the practical organization of the basic principle of opportunistic positioning by analogy with the paradigm of correlation-extreme navigation is made. A computer visualization of a fixed fragment of the ocean gravitational field based on spline approximation is performed in order to optimize the problem of simultaneous localization and three-dimensional representation of the ship movement in a graphical environment unaffiliated with foreign software. A hybrid algorithm for mathematical synthesis of the navigational isosurface has been tested as a harmonized support for the navigation staff to implement the “terrain-referenced procedure” in the landscape coordinate space. The variants of the “ambiguity resolution” problem implementation in the issue of maximum integration of heterogeneous navigation data are considered. The probability of practical use of the opportunistic navigation postulates in marine applications, taking into account the “navigation gap” factor for leveling local satellite incapacity with a real possibility of countering malicious interception of ship control, is estimated. The expediency of using the factor of observational reckoning of the vessel path as an additional condition for navigation safety in the aspect of packet processing of the “signals of opportunity” slot is substantiated.

A common points selection method based on the uniformity of FLTMMS for pre-alignment of particle accelerators

High-precision pre-alignment of a magnet is a crucial step in the construction of a particle accelerator such as the Hefei Advanced Light Facility (HALF) or High Energy Photon Source (HEPS). To improve the accuracy and efficiency of pre-alignment, there are plans to build a four-station laser tracker multilateration measurement system (FLTMMS) at HALF. In the coordinate conversion and self-calibration processes of a FLTMMS, an unreasonable distribution of common points can lead to a loss of accuracy. A method for selecting common points based on uniformity in the FLTMMS is therefore proposed. In this method, the coordinate transformation space is divided according to the uniformity in different directions. The feasibility of our method is compared and analysed through coordinate conversion and self-calibration experiments. Simulations show that with the same number of common points, this method leads to higher accuracy in coordinate conversion and self-calibration. The proposed method compensates for the loss of accuracy due to aggregation of common points. Comparative analyses show a clear positive relationship between the accuracy improvement effect and the difference in uniformity. The distribution of common points will change the accuracy distribution of FLTMMS. Our approach of providing essential references for pre-aligning HALF magnets has been applied to HEPS with extensive engineering experience, to verify the practicality of this method for engineering applications. In the actual measurements, self-calibration is performed using an edge measurement network, and coordinate conversion is conducted using angle measurements. Based on actual measurements, the self-calibration accuracy is 1.7 μm and a conversion accuracy is 14.8 μm. The results show that under the premise of satisfying precision, the method can reduce the number of common points, thus decreasing the cost of common points construction. Our study provides instructions for pre-alignment at HALF in the future.