Arbitrary Density Research Articles

Non-parametric identification of single-lined binary candidates in young clusters using single-epoch spectroscopy

Binarity plays a crucial role in star formation and evolution. Consequently, identifying binary stars is essential to deepening our understanding of these processes. We propose a method to investigate the observed radial velocity distribution of massive stars in young clusters with the goal of identifying binary systems. We reconstruct the radial velocity distribution using a three-layer hierarchical Bayesian non-parametric approach; non-parametric methods are data-driven models able to infer arbitrary probability densities under minimal mathematical assumptions. When applying our statistical framework, it is possible to identify variable stars and binary systems because these deviate significantly from the expected intrinsic Gaussian distribution for radial velocities. We tested our method with the massive star-forming region within the giant H$_ II $ region M17. We are able to confidently identify binaries and variable stars with as little as single-epoch observations. The distinction between variable and binary stars improves significantly when introducing additional epochs.

Feature Enhancement Based Oriented Object Detection in Remote Sensing Images

Since objects in remote sensing imagery often have arbitrary orientations and high densities, the features of small objects are inclined to be contaminated by the background and other instances. To address the issues, we propose a new oriented object detection framework where a series of feature enhancement schemes are implemented so as to improve robustness and accuracy of the detector. Firstly, we design a weighted bidirectional feature pyramid network, which can be used to fuse both high-level semantic features and low-level detail features for effectively handling with multi-scale objects. Accordingly, we apply the convolutional block attention module that exploits both spatial- and channel-wise attention in our detector, and study how to effectively integrate it into the framework for adaptive feature refinement. In the meanwhile, we present a semantic segmentation guided module to generate naive mask, which is used to multiple with pyramid features to filter out background noise and improve feature representation for small objects. The experimental results on two public datasets, i.e., UCAS-AOD and DOTA, validate the effective performance of the proposed method for oriented object detection in remote sensing images.

Structured multi-view k-means clustering

K-means is a very efficient clustering method and many multi-view k-means clustering methods have been proposed for multi-view clustering during the past decade. However, since k-means have trouble uncovering clusters of varying sizes and densities, these methods suffer from the same performance issues as k-means. Improving the clustering performance of multi-view k-means has become a challenging problem. In this paper, we propose a new multi-view k-means clustering method that is able to uncover clusters in arbitrary sizes and densities. The new method simultaneously performs three tasks, i.e., sparse connection probability matrices learning, prototypes aligning, and cluster structure learning. We evaluate the proposed new method by 5 benchmark datasets and compare it with 11 multi-view clustering methods. The experimental results on both synthetic and real-world experiments show the superiority of our proposed method.

The interplay of excitonic delocalization and vibrational localization in optical lineshapes: A variational polaron approach.

The dynamics of molecular excitonic systems are complicated by a competition between electronic coupling (which drives delocalization) and vibrational-electronic (vibronic) interactions (which tend to encourage electronic localization). A particular challenge of molecular systems is that they typically possess a large number of independent vibrations, with frequencies often spanning the entire spectrum of relevant electronic energy gaps. Recent spectroscopic observations and numerical simulations on a water-soluble chlorophyll-binding protein (WSCP) reveal a transition between two regimes of vibronic behavior, a Redfield-like regime in which low-frequency vibrations respond to a delocalized excitonic state, and a Förster-like regime where high-frequency vibrations act as incoherent excitations on individual pigments. Although numerical simulations can reproduce these effects, there is a need for a simple, systematic theory that accurately describes the smooth transition between these two regimes in experimental spectra. Here we address this challenge by generalizing the variational polaron transform approach of [Bloemsma et al., Chem. Phys. 481, 250 (2016)] to include arbitrary bath densities for systems with or without symmetry. We benchmark this theory against both numerical matrix-diagonalization methods and experimental 77K fluorescence spectra for two WSCP variants, obtaining quite satisfactory agreement in both cases. We apply this theory to offer an explanation for the large loss in apparent electronic coupling in the WSCP Q57K mutant and to examine the likely impact of the interplay between excitonic delocalization and vibrational localization on vibrational sideband shapes and apparent coupling strengths in high-resolution optical spectra for chlorophyll-protein complexes such as WSCP.

Spin relaxation dynamics with a continuous spin environment: The dissipaton equation of motion approach.

We investigate the quantum dynamics of a spin coupling to a bath of independent spins via the dissipaton equation of motion (DEOM) approach. The bath, characterized by a continuous spectral density function, is composed of spins that are independent level systems described by the su(2) Lie algebra, representing an environment with a large magnitude of anharmonicity. Based on the previous work by Suarez and Silbey [J. Chem. Phys. 95, 9115 (1991)] and by Makri [J. Chem. Phys. 111, 6164 (1999)] that the spin bath can be mapped to a Gaussian environment under its linear response limit, we use the time-domain Prony fitting decomposition scheme to the bare-bath time correlation function (TCF) given by the bosonic fluctuation-dissipation theorem to generate the exponential decay basis (or pseudo modes) for DEOM construction. The accuracy and efficiency of this strategy have been explored by a variety of numerical results. We envision that this work provides new insights into extending the hierarchical equations of motion and DEOM approach to certain types of anharmonic environments with arbitrary TCF or spectral density.

A unified structure-preserving parametric finite element method for anisotropic surface diffusion

We propose and analyze a unified structure-preserving parametric finite element method (SP-PFEM) for the anisotropic surface diffusion of curves in two dimensions ( d = 2 ) (d=2) and surfaces in three dimensions ( d = 3 ) (d=3) with an arbitrary anisotropic surface energy density γ ( n ) \gamma (\boldsymbol {n}) , where n ∈ S d − 1 \boldsymbol {n}\in \mathbb {S}^{d-1} represents the outward unit vector. By introducing a novel unified surface energy matrix G k ( n ) \boldsymbol {G}_k(\boldsymbol {n}) depending on γ ( n ) \gamma (\boldsymbol {n}) , the Cahn-Hoffman ξ \boldsymbol {\xi } -vector and a stabilizing function k ( n ) : S d − 1 → R k(\boldsymbol {n}):\ \mathbb {S}^{d-1}\to {\mathbb R} , we obtain a unified and conservative variational formulation for the anisotropic surface diffusion via different surface differential operators, including the surface gradient operator, the surface divergence operator and the surface Laplace-Beltrami operator. A SP-PFEM discretization is presented for the variational problem. In order to establish the unconditional energy stability of the proposed SP-PFEM under a very mild condition on γ ( n ) \gamma (\boldsymbol {n}) , we propose a new framework via local energy estimate for proving energy stability/structure-preserving properties of the parametric finite element method for the anisotropic surface diffusion. This framework sheds light on how to prove unconditional energy stability of other numerical methods for geometric partial differential equations. Extensive numerical results are reported to demonstrate the efficiency and accuracy as well as structure-preserving properties of the proposed SP-PFEM for the anisotropic surface diffusion with arbitrary anisotropic surface energy density γ ( n ) \gamma (\boldsymbol {n}) arising from different applications.

Theory for measuring electric charge density of a ring from scanning force microscopy

We consider a ring that carries an arbitrary electric charge density in the presence of a scanning force microscopy tip. We propose an algorithm that predicts this charge density from knowledge of the electrostatic ring-tip contribution to the total scanning force microscopy force–distance curves. We first solve the direct electrostatic problem of finding the electrostatic forces by the ring on a scanning force microscopy conducting probe. These forces are in the pN and nN range and, therefore, measurable with current technologies. Finally, we describe a method based on the least squares minimization method to measure the charge on the ring.

Increasing the Interlayer Fracture Toughness of Polymer Fabric Composites Using Local 3D-Reinforcement (Felting)

Introduction. One of the reasons for undesirable delamination of polymer composites with fabric reinforcement is low transverse shear properties. It is known that the reinforcement of polymer fabric composites in the Z direction reduces the sensitivity to delamination and increases the viscosity of interlayer fracture. Various methods of three-dimensional reinforcement of polymer fabric composites are proposed in the literature. However, they complicate the manufacturing process of the structure. The problem is solved by the method of three-dimensional reinforcement proposed in this article — felting. This is a local reinforcement of the composite in the Z direction with minimal production changes. The degree of Z-reinforcement is determined by the felting density, i.e., the number of needle punches per 1 cm2 of the fabric package. The work is aimed at evaluating the effect of felting on the interlayer crack resistance of a composite material.Materials and Methods. The interlayer fracture toughness GIIc was determined on a cross-woven fiberglass with felting of 10 cm-2. The material was impregnated with Etal-370 resin and Etal-45 hardener. Experiments according to ASTM D7905M–14 and GOST 33685–2015 standards were carried out on an Instron 5900R test machine. The stress state at the crack tip was analyzed with regard to the nonlocal strength theory in the ANSYS Workbench program (option “static strength analysis”). The finite element method (FEM) was used.Results. The “load — displacement” curves were considered for the samples. Values GIIc were calculated. The results of ENF tests for felting density of 0 cm–2 and 10 cm–2 were summarized. Control samples and felting samples were compared. In the latter case, GIIс turned out to be ~33% higher. The stress state at the crack tip was calculated under DCB and ENF loading. The dependences of maximum normal and shear stresses, as well as displacements, were visualized in the form of graphs and color charts. To get the calculated “load — displacement” dependences using FEM, the reverse method of obtaining transverse shear constants was used. DCB loading showed that felting provided increasing the rupture strength in the Z direction to ~18%, by 39 to 46 MPa, and in the planes XZ— to ~16%, by 77 to 89 MPa.Discussion and Conclusion. Felting as a method of local three-dimensional reinforcement enhances the interlayer crack resistance of polymer fabric composites. It provides reducing the area of stratifications after local impacts during the operation of structures. Flexible felting technology makes it possible to create zones with an arbitrary impact density, increasing fracture toughness only in the required places of structures. The FEM analysis of the stress state at the crack tip within the framework of the nonlocal strength theory has shown that in strength calculations, the stratification crack can be considered as a stress concentrator.

An Efficient Algorithm for Gravity Forward Modeling (GFM) with Masses of Arbitrary Shapes and Density Distributions

Summary Currently, gravimetric forward modelling of mass density structures with arbitrary geometries and density distributions typically involves subdividing the mass body into individual geometric elements (such as rectangular prisms), calculating their gravitational contributions that are then summed up to obtain the gravitational attraction of the whole body. To achieve a more accurate approximation of the true geometric shape and density distribution, this rectangular prism model requires fine dividing, which significantly increases computational load and reduces numerical efficiency. To address this issue, we propose the algorithm for gravimetric forward modeling of arbitrary geometric shapes and density distributions in spectral domain that significantly improves numerical efficiency while preserves computational accuracy. The novelty of our proposed algorithm lies in dividing the masses into multiple layers of equal thickness in the vertical direction, providing constant upper and lower bounds. This allows to extended Parker's formulas and apply the Fast Fourier Transform (FFT) to increase numerical efficiency. The algorithm is tested using synthetic models and then used to compute gravitational effects of topography and sediments using real data from Tibet. Results show high accuracy and numerical efficiency than rectangular prism approach.

Feature-Based Interpolation and Geodesics in the Latent Spaces of Generative Models.

Interpolating between points is a problem connected simultaneously with finding geodesics and study of generative models. In the case of geodesics, we search for the curves with the shortest length, while in the case of generative models, we typically apply linear interpolation in the latent space. However, this interpolation uses implicitly the fact that Gaussian is unimodal. Thus, the problem of interpolating in the case when the latent density is non-Gaussian is an open problem. In this article, we present a general and unified approach to interpolation, which simultaneously allows us to search for geodesics and interpolating curves in latent space in the case of arbitrary density. Our results have a strong theoretical background based on the introduced quality measure of an interpolating curve. In particular, we show that maximizing the quality measure of the curve can be equivalently understood as a search of geodesic for a certain redefinition of the Riemannian metric on the space. We provide examples in three important cases. First, we show that our approach can be easily applied to finding geodesics on manifolds. Next, we focus our attention in finding interpolations in pretrained generative models. We show that our model effectively works in the case of arbitrary density. Moreover, we can interpolate in the subset of the space consisting of data possessing a given feature. The last case is focused on finding interpolation in the space of chemical compounds.

A Framework for Constraining Ocean Mixing Rates and Overturning Circulation from Age Tracers

Abstract The age of seawater refers to the amount of time that has elapsed since that water encountered the surface. This age measures the ventilation rate of the ocean, and the spatial distribution of age can be influenced by multiple processes, such as overturning circulation, ocean mixing, and air–sea exchange. In this work, we aim to gain new quantitative insights about how the ocean’s age tracer distribution reflects the strength of the meridional overturning circulation and diapycnal diffusivity. We propose an integral constraint that relates the age tracer flow across an isopycnal surface to the geometry of the surface. With the integral constraint, a relationship between the globally averaged effective diapycnal diffusivity and the meridional overturning strength at an arbitrary density level can be inferred from the age tracer concentration near that level. The theory is tested in a set of idealized single-basin simulations. A key insight from this study is that the age difference between regions of upwelling and downwelling, rather than any single absolute age value, is the best indicator of overturning strength. The framework has also been adapted to estimate the strength of abyssal overturning circulation in the modern North Pacific, and we demonstrate that the age field provides an estimate of the circulation strength consistent with previous studies. This framework could potentially constrain ocean circulation and mixing rates from age-like realistic tracers (e.g., radiocarbon) in both past and present climates. Significance Statement The age of seawater—the local mean time since local water from different pathways was last at the surface—is a valuable indicator of ocean circulation and the transport time scale of heat and carbon. We introduce a novel constraint that relates total age flow across a density surface to its geometry, which provides new insights into constraining ocean circulation and mixing rates from age-like realistic tracers (e.g., radiocarbon).

Techniques for solving static Klein-Gordon equation with self-interaction λϕ4 and arbitrary spherical source terms

The Klein-Gordon equation for a scalar field sourced by a static spherically symmetric background is an interesting second-order differential equation with applications in particle physics, astrophysics, and elsewhere. Here we present static solutions for generic source density profiles in the case where the scalar field has no interactions or a mass term. For a λϕ4 self-interaction term, we develop the techniques that are necessary numerical computation. We also provide code to perform the numerical calculations that can be adapted for arbitrary density profiles. ▪.

Thermodynamics of spin-1/2 fermions on coarse temporal lattices using automated algebra.

Recent advances in automated algebra for dilute Fermi gases in the virial expansion, where coarse temporal lattices were found advantageous, motivate the study of more general computational schemes that could be applied to arbitrary densities, beyond the dilute limit where the virial expansion is physically reasonable. We propose here such an approach by developing what we call the Quantum Thermodynamics Computational Engine (QTCE). In QTCE, the imaginary-time direction is discretized and the interaction is accounted for via a quantum cumulant expansion, where the coefficients are expressed in terms of non-interacting expectation values. The aim of QTCE is to enable the systematic resolution of interaction effects at fixed temporal discretization, as in lattice Monte Carlo calculations, but here in an algebraic rather than numerical fashion. Using this approach, in combination with numerical integration techniques (both known and alternative ones proposed here), we explore the thermodynamics of spin-1/2 fermions across spatial dimensions, focusing on the unitary limit. We find that, remarkably, extremely coarse temporal lattices, when suitably renormalized using known results from the virial expansion, yield stable partial sums for QTCE's cumulant expansion that are qualitatively and quantitatively correct in wide regions (when compared with known experimental results). This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

1-Cocycles of the Witt algebra with coefficients in tensor product of modules

In this paper, we classify 1-cocycles of the Witt algebra with coefficients in the tensor product of two arbitrary tensor density modules. In a special case, we recover a theorem originally established by Ng and Taft in [24]. Furthermore, by these 1-cocycles, we determine Lie bialgebra structures over certain infinite-dimensional Lie algebras containing the Witt algebra.

Variable transformations in combination with wavelets and ANOVA for high-dimensional approximation

We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low-dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet basis on the torus. With a variable transformation, we are able to transform the approximation rates and fast algorithms from the torus to other domains. We perform and analyze scattered data approximation for smooth but arbitrary density functions by using a least squares method. The corresponding system matrix is sparse due to the compact support of the wavelets, which leads to a significant acceleration of the matrix vector multiplication. For non-periodic functions, we propose a new extension method. A proper choice of the extension parameter together with the piecewise polynomial Chui-Wang wavelets extends the functions appropriately. In every case, we are able to bound the approximation error with high probability. Additionally, if the function has a low effective dimension (i.e., only interactions of a few variables), we qualitatively determine the variable interactions and omit ANOVA terms with low variance in a second step in order to decrease the approximation error. This allows us to suggest an adapted model for the approximation. Numerical results show the efficiency of the proposed method.

Dynamical Explanation of the Dark Matter and Baryon Energy Density Coincidence.

The near equality of the dark matter and baryon energy densities is a remarkable coincidence, especially when one realizes that the baryon mass is exponentially sensitive to UV parameters in the form of dimensional transmutation. We explore a new dynamical mechanism, where in the presence of an arbitrary number density of baryons and dark matter, a scalar adjusts the masses of dark matter and baryons until the two energy densities are comparable. In this manner, the coincidence is explained regardless of the microscopic identity of dark matter and how it was produced. This new scalar causes a variety of experimental effects such as a new force and a (dark) matter density-dependent proton mass.

Model expressions for refractive indices of electron waves in cold magnetoactive plasma of arbitrary density

Despite the undoubted importance of having fairly simple analytical expressions for the refractive indices of wave modes in a magnetoactive plasma, such expressions are known only in some particular cases. For electron waves with frequencies much higher than the lower hybrid resonance frequency, such an expression is known only for whistler waves in a dense plasma when the electron plasma frequency significantly exceeds the electron cyclotron frequency. In this Letter, we propose simple operational expressions for the refractive indices of all four electron modes in a magnetoactive plasma, namely, the fast magnetosonic, also called whistler mode, the slow extraordinary mode, the ordinary mode, and the fast extraordinary mode. The form of these expressions does not depend on the value of the ratio of plasma frequency to cyclotron frequency.

Machine-Learned Kohn-Sham Hamiltonian Mapping for Nonadiabatic Molecular Dynamics.

In this work, we report a simple, efficient, and scalable machine-learning (ML) approach for mapping non-self-consistent Kohn-Sham Hamiltonians constructed with one kind of density functional to the nearly self-consistent Hamiltonians constructed with another kind of density functional. This approach is designed as a fast surrogate Hamiltonian calculator for use in long nonadiabatic dynamics simulations of large atomistic systems. In this approach, the input and output features are Hamiltonian matrices computed from different levels of theory. We demonstrate that the developed ML-based Hamiltonian mapping method (1) speeds up the calculations by several orders of magnitude, (2) is conceptually simpler than alternative ML approaches, (3) is applicable to different systems and sizes and can be used for mapping Hamiltonians constructed with arbitrary density functionals, (4) requires a modest training data, learns fast, and generates molecular orbitals and their energies with the accuracy nearly matching that of conventional calculations, and (5) when applied to nonadiabatic dynamics simulation of excitation energy relaxation in large systems yields the corresponding time scales within the margin of error of the conventional calculations. Using this approach, we explore the excitation energy relaxation in C60 fullerene and Si75H64 quantum dot structures and derive qualitative and quantitative insights into dynamics in these systems.

Evidence of evolution of the black hole mass function with redshift

Aims.We investigate the observed distribution of the joint primary mass, mass ratio, and redshift of astrophysical black holes using the gravitational wave events detected by the LIGO-Virgo-KAGRA collaboration and included in the third gravitational wave transient catalogue.Methods.We reconstructed this distribution using Bayesian non-parametric methods, which are data-driven models able to infer arbitrary probability densities under minimal mathematical assumptions.Results.We find evidence that both the primary mass and mass-ratio distribution evolve with redshift: our analysis shows the presence of two distinct subpopulations in the primary mass−redshift plane, with the lighter population, ≲20 M⊙, disappearing at higher redshifts,z > 0.4. The mass-ratio distribution shows no support for symmetric binaries.Conclusions.The observed population of coalescing binary black holes evolves with look-back time, suggesting a trend in metallicity with redshift and/or the presence of multiple redshift-dependent formation channels.

High-speed generation of non-Rayleigh speckle.

Speckle with non-Rayleigh amplitude distribution has significant research value in imaging and measurement using structured illumination. However, existing speckle customizing schemes have been limited in generation speed due to the refresh rate of spatial light modulators (SLMs). In this work, we proposed a method to rapidly generate non-Rayleigh distributed speckle fields using a digital micro-mirror device (DMD). In contrast to SLMs that allow for gray-scale phase modulation, DMD is limited to binary amplitude control. To solve this limitation, we design a Gerchberg-Saxton-like algorithm based on super-pixel method, this algorithm enables the customization of non-Rayleigh speckle with arbitrary intensity probability density function. Statistical analyses of experimental results have demonstrated that the customized speckles exhibit excellent stability in their lateral statistical properties, while also maintaining consistent propagation characteristics with Rayleigh speckle in the longitudinal direction. This method provides a new approach for high-speed and arbitrary intensity speckle customization, holding potential applications in imaging, measurement, and encryption fields.