Symmetric Objects Research Articles

Two-fluid stellar objects in general relativity: The covariant formulation

We apply the 1+1+2 covariant approach to describe a general static and spherically symmetric relativistic stellar object which contains two interacting fluids. We then use the 1+1+2 equations to derive the corresponding Tolman-Oppenheimer-Volkoff (TOV) equations in covariant form in the isotropic, non-interacting case. These equations are used to obtain new exact solutions by means of direct resolution and reconstruction techniques. Finally, we show that the generating theorem known for the single fluid case can also be used to obtain two-fluid solutions from single fluid ones.

Microscopic impedance cytometry for quantifying single cell shape

In this work, we investigated the ability of impedance flow cytometry to measure the shape of single cells/particles. We found that the impedance pulses triggered by micro-objects that are asymmetric in morphology show a tilting trend, and there is no such a tilting trend for symmetric ones. Therefore, we proposed a new metric, tilt index, to quantify the tilt level of the impedance pulses. Through simulation, we found that the value of tilt index tends to be zero for perfectly symmetrical objects, while the value is greater than zero for asymmetrical ones. Also, this metric was found to be independent on the trajectories (i.e., lateral, and z-direction shift) of the target micro-object. In experiments, we adopted a home-made lock-in amplifier and performed experiments on 10 μm polystyrene beads and Euglena gracilis (E. gracilis) cells with varying shapes. The experimental results coincided with the simulation results and demonstrated that the new metric (tilt index) enables the impedance cytometry to characterize the shape single cells/particles without microscopy or other optical setups.

Electrically charged string-like axially symmetric object composition in [formula omitted] gravity

Our paper is devoted for the study of a highly compact string-like axially symmetric object in the presence of electromagnetic field which is generated by the existence of electric charge in the model. The basic formulism of one of the alternative theories i.e, f(R,G) theory has been used for this purpose. We have considered the irrotational cylindrical geometry, influence of charge, isotropic pressure and the perfect fluid for the derivation of field equations and the laws of conservation corresponding to f(R,G) theory. Junction conditions suggested by Darmois-Israel will be used for the smooth matching between inner and outer regions of gravastar-like structure. The impact of electric charge on distinct physical features of the model such as proper length, energy, thickness and entropy of shell will also be observed and will be elaborated with the help of graphs. We shall also analyze the vital role of f(R,G) theory for the stability of the model.

Template-based imitation learning for manipulating symmetric objects

With the rise of small batch production, the need to shorten the development cycle has become urgent. This work aims to allow people without expert knowledge to program the robot in a single demonstration to reduce development costs. The idea of this work is to record frame relations between objects during the demonstration as templates. Then the robot is programmed by the template sequence to simplify the programming process and shorten the development time. Since symmetry will cause uncertainty in pose estimation during execution, a symmetry detection module is developed to detect the rotational symmetry of the objects through inertia tensor and all the rotation matrices are acquired using group theory. After that, a template matching module is designed to measure the distance between the current pose and possible target poses to choose the proper target pose which matches the template to avoid unreachable robot poses and accelerate the executing process. Two pick-and-place tasks, a stacking test, and a sorting task are carried out to verify our system and the results show that our method is feasible and efficient.

Bilateral Symmetry Has No Effect on Stereoscopic Shape Judgments.

A single experiment is reported that measured the apparent stereoscopic shapes of symmetric and asymmetric objects at different viewing distances. The symmetric stimuli were specifically designed to satisfy the minimal conditions for computing veridical shape from symmetry. That is to say, they depicted complex, bilaterally symmetric, plane-faced polyhedra whose symmetry planes were oriented at an angle of 45° relative to the line of sight. The asymmetric stimuli were distorted versions of the symmetric ones in which the 3D position of each vertex was randomly displaced. Prior theoretical analyses have shown that it is mathematically possible to compute the 3D shapes of symmetric stimuli under these conditions, but those algorithms are useless for asymmetric objects. The results revealed that the apparent shapes of both types of objects were expanded or compressed in depth as a function of viewing distance, in exactly the same way as has been reported in many other studies, and that the presence or absence of symmetry had no detectable effect on performance.

Симметричные системы управления

The paper focuses on the properties of symmetric control systems, whose distinctive feature is that the solution of the optimal control problem for an object, the mathematical model of which belongs to the class of symmetric control systems, leads to the solution of two problems. The first optimal control problem is the initial one; the result of its solution is a function that ensures the optimal movement of the object from the initial state to the terminal one. In the second problem, the terminal state is the initial state, and the initial state is the terminal state. The complexity of the problem being solved is due to the increase in dimension when the models of all objects of the group are included in the mathematical model of the object, as well as the emerging dynamic phase constraints. The presence of phase constraints in some cases leads to the target functional having several local extrema. A theorem is proved that under certain conditions the functional is not unimodal when controlling a group of objects belonging to the class of symmetric systems. A numerical example of solving the optimal control problem with phase constraints by the Adam gradient method and the evolutionary particle swarm method is given. In the example, a group of two symmetrical objects is used as a control object

CONSTRUCTION OF A PHYSICAL AND MATHEMATICAL MODEL OF THE GRAVITATIONAL FIELD

The problem of gravitational field physics is to identify the relationship between the gravitational field and the expansion of the space-time continuum. Therefore, the creation of models, the study of which makes it possible to identify these relationships and express them in formulas, is relevant. In the modern theory of the gravitational field, small quantities appear, which are neglected in the derivation of formulas of practical application. This paper presents a model of the gravitational field that combines quantum properties with the expansion of the space-time continuum. Also, using a simplified model of the coordinate system, the gravitational field of a stationary centrally symmetric object is studied and the limiting distance of the test particle capture by the gravitational field is calculated. Calculations made without neglecting small quantities gave interesting results: the limiting radius of capture by the gravitational field of the test particle; the formula for the mass defect of the black hole Schwarzschild; relations expressing the dependence of the quantities of quantum physics on the Hubble constant.

Improving linac integrated cone beam computed tomography image quality using tube current modulation.

Linac integrated cone beam CT (CBCT) scanners have become widespread tool for image guidance in radiotherapy. The current implementation uses constant imaging fluence across all the projection angles, which leads to anisotropic noise properties and suboptimal image quality for noncircular symmetric objects. Tube current modulation (TCM) is widely used in conventional CT. The purpose of this work was to implement TCM on a linac integrated CBCT scanner and evaluate its impact on image quality under varying scatter conditions and scatter correction strategies. We have implemented TCM on a nonclinical Elekta Versa HD linear accelerator with enhanced x-ray generator functionality including pulse width modulation. The pulse width was modulated using two Arduino programmable microcontrollers: one placed on the kV arm to measure the projection angle and the other connected to the kV generator control board to vary x-ray pulse width as function of gantry angle and precalculated transmission. An in-house developed phantom with a ratio of the left-right to anterior-posterior path length of 1.85:1 was scanned. Image quality was determined using the anisotropicity of the 2D noise power spectra (NPS) in the transverse plane and the contrast-to-noise ratio (CNR). In addition, to determine the impact of scatter on the applicability of the TCM method we have modified the generated scatter using three different collimators in the cranio-caudal direction as well as with and without an antiscatter grid (ASG). Application of the TCM led to 30-78% reduction of the angular anisotropicity of the NPS in the transverse plane. The amount of reduction depended on the scatter conditions, with lower values corresponding to higher scatter conditions. The same was true for the CNR: when scatter contribution was low (presence of an ASG or very aggressive collimation) the CNR was improved by about 30%, while in high scatter conditions the CNR was improved by about 12%. TCM has the potential to improve CBCT image quality, but this depends on the amount of detected x-ray scatter.

DRNet: A Depth-Based Regression Network for 6D Object Pose Estimation.

This paper focuses on 6Dof object pose estimation from a single RGB image. We tackle this challenging problem with a two-stage optimization framework. More specifically, we first introduce a translation estimation module to provide an initial translation based on an estimated depth map. Then, a pose regression module combines the ROI (Region of Interest) and the original image to predict the rotation and refine the translation. Compared with previous end-to-end methods that directly predict rotations and translations, our method can utilize depth information as weak guidance and significantly reduce the searching space for the subsequent module. Furthermore, we design a new loss function function for symmetric objects, an approach that has handled such exceptionally difficult cases in prior works. Experiments show that our model achieves state-of-the-art object pose estimation for the YCB- video dataset (Yale-CMU-Berkeley).

The Relativistic Jet Orientation and Host Galaxy of the Peculiar Blazar PKS 1413+135

Abstract PKS 1413+135 is one of the most peculiar blazars known. Its strange properties led to the hypothesis almost four decades ago that it is gravitationally lensed by a mass concentration associated with an intervening galaxy. It exhibits symmetric achromatic variability, a rare form of variability that has been attributed to gravitational milli-lensing. It has been classified as a BL Lac object, and is one of the rare objects in this class with a visible counterjet. BL Lac objects have jet axes aligned close to the line of sight. It has also been classified as a compact symmetric object—objects that have jet axes not aligned close to the line of sight. Intensive efforts to understand this blazar have hitherto failed to resolve even the questions of the orientation of the relativistic jet and the host galaxy. Answering these two questions is important because they challenge our understanding of jets in active galactic nuclei and the classification schemes we use to describe them. We show that the jet axis is aligned close to the line of sight and PKS 1413+135 is almost certainly not located in the apparent host galaxy, but is a background object in the redshift range 0.247 < z < 0.5. The intervening spiral galaxy at z = 0.247 provides a natural host for the putative lens responsible for symmetric achromatic variability and is shown to be a Seyfert 2 galaxy. We also show that, as for the radio emission, a “multizone” model is needed to account for the high-energy emission.

Robust, fast and flexible symmetry plane detection based on differentiable symmetry measure

Reflectional symmetry is a potentially very useful feature which many real-world objects exhibit. It is instrumental in a variety of applications such as object alignment, compression, symmetrical editing or reconstruction of incomplete objects. In this paper, we propose a novel differentiable symmetry measure, which allows using gradient-based optimization to find symmetry in geometric objects. We further propose a new method for symmetry plane detection in 3D objects based on this idea. The method performs well on perfectly as well as approximately symmetrical objects, it is robust to noise and to missing parts. Furthermore, it works on discrete point sets and therefore puts virtually no constraints on the input data. Due to flexibility of the symmetry measure, the method is also easily extensible, e.g., by adding more information about the input object and using it to further improve its performance. The proposed method was tested with very good results on many objects, including incomplete objects and noisy objects, and was compared to other state-of-the-art methods which it outperformed in most aspects.

Unsupervised Learning of Probably Symmetric Deformable 3D Objects From Images in the Wild (Invited Paper).

We propose a method to learn 3D deformable object categories from raw single-view images, without external supervision. The method is based on an autoencoder that factors each input image into depth, albedo, viewpoint and illumination. In order to disentangle these components without supervision, we use the fact that many object categories have, at least approximately, a symmetric structure. We show that reasoning about illumination allows us to exploit the underlying object symmetry even if the appearance is not symmetric due to shading. Furthermore, we model objects that are probably, but not certainly, symmetric by predicting a symmetry probability map, learned end-to-end with the other components of the model. Our experiments show that this method can recover very accurately the 3D shape of human faces, cat faces and cars from single-view images, without any supervision or a prior shape model. On benchmarks, we demonstrate superior accuracy compared to another method that uses supervision at the level of 2D image correspondences.

Color–flavor locked strange stars in 4D Einstein–Gauss–Bonnet gravity

This work is devoted to the recently introduced Einstein–Gauss–Bonnet gravity in four dimensions. This theory can bypass Lovelock’s theorem and avoids Ostrogradsky instability. The integrated part of this theory is the GB term which gives rise to a non-trivial contribution to the gravitational dynamics in the limit D→4. Our main interest is to explore a class of static, spherically symmetric compact objects made of strange matter. It is believed that at ultra-high densities, quark matter may exist in a variety of superconducting states, namely, the Color–Flavor-Locked (CFL) phase. With these equations of state (EoS) we explore the conditions under which compact stars are stable under extreme conditions in the context of 4D EGB gravity. In addition, the mass–radius relation is examined and the effects of the coupling constant ‘α’ on the stellar model, energy conditions, speed of sound and adiabatic stability are studied. With the aim to find observational constraints on the GB constant of 4D EGB gravity, the mass–radius curve is determined satisfying the maximum mass constraint of M∼2M⊙ for neutron stars. This feature may be relevant in view of recent observations claiming the existence of stable compact quark stars (hybrid neutron stars or strange stars).

Structure scalars and their evolution for massive objects in f(R) gravity

In this manuscript, the Riemann tensor is split orthogonally to get five scalar functions known as structure scalars which have significance to gain insight into the composition and structure of spherically symmetric self-gravitating objects. Certain stellar equations are then evaluated to gather information about physical characteristics of such astrophysical objects. These stellar equations are further written in terms of acquired structure scalars so that the basic properties such as pressure anisotropy and energy density inhomogeneity of the fluid under consideration can be explored. Also, we have explored few static spherically symmetric solutions to show significance of structure scalars in the background of f(R) gravity.

Combining Appearance and Gradient Information for Image Symmetry Detection.

This work addresses the challenging problem of reflection symmetry detection in unconstrained environments. Starting from the understanding on how the visual cortex manages planar symmetry detection, it is proposed to treat the problem in two stages: i) the design of a stable metric that extracts subsets of consistently oriented candidate segments, whenever the underlying 2D signal appearance exhibits definite near symmetric correspondences; ii) the ranking of such segments on the basis of the surrounding gradient orientation specularity, in order to reflect real symmetric object boundaries. Since these operations are related to the way the human brain performs planar symmetry detection, a better correspondence can be established between the outcomes of the proposed algorithm and a human-constructed ground truth. When compared to the testing sets used in recent symmetry detection competitions, a remarkable performance gain can be observed. In additional, further validation has been achieved by conducting perceptual validation experiments with users on a newly built dataset.

3D point‐cloud spatial expansion by total least‐squares line fitting

AbstractPoint‐cloud spatial expansion (PCSE) allows the creation of a new point‐cloud form that presents an alternative geometry of an entire object in a single spatial view. Spatial expansion facilitates the analysis process and introduces an additional spatial parameter describing the point cloud. An important element of the PCSE method is determining the position of the axis of symmetry of a symmetrical object: the procedure for determining the parameters of this axis (set of cross‐sectional centres) of the object’s point cloud by the total least‐squares method is presented. The estimation results were used to create a spatial expansion of the point cloud of a cylindrical object, demonstrating the usefulness of total least‐squares fitting to the PCSE method.

Object Sorting using Faster R-CNN

In a factory production line, different industry parts need to be quickly differentiated and sorted for further process. Parts can be of different colors and shapes. It is tedious for humans to differentiate and sort these objects in appropriate categories. Automating this process would save more time and cost. In the automation process, choosing an appropriate model to detect and classify different objects based on specific features is more challenging. In this paper, three different neural network models are compared to the object sorting system. They are namely CNN, Fast R-CNN, and Faster R-CNN. These models are tested, and their performance is analyzed. Moreover, for the object sorting system, an Arduino-controlled 5 DoF (degree of freedom) robot arm is programmed to grab and drop symmetrical objects to the targeted zone. Objects are categorized into classes based on color, defective and non-defective objects.

Emergence of low-symmetry foldamers from single monomers.

Self-assembly is a powerful method to obtain large discrete functional molecular architectures. When using a single building block, self-assembly generally yields symmetrical objects in which all the subunits relate similarly to their neighbours. Here we report the discovery of a family of self-constructing cyclic macromolecules with stable folded conformations of low symmetry, which include some with a prime number (13, 17 and 23) of units, despite being formed from a single component. The formation of these objects amounts to the production of polymers with a perfectly uniform length. Design rules for the spontaneous emergence of such macromolecules include endowing monomers with a strong potential for non-covalent interactions that remain frustrated in competing entropically favoured yet conformationally restrained smaller cycles. The process can also be templated by a guest molecule that itself has an asymmetrical structure, which paves the way to molecular imprinting techniques at the level of single polymer chains.

A multiwavelength study of the dual nuclei in Mrk 212

ABSTRACT We present radio observations of the galaxy merger remnant Mrk 212 with the Karl G. Jansky Very Large Array (VLA) and the upgraded Giant Meter Radio Telescope (uGMRT). Mrk 212 has two previously known radio sources associated with the two optical nuclei, S1 and S2, with a projected separation of ∼6 kpc, making it a dual active galactic nuclei (AGN) candidate. Our new 15-GHz VLA observations reveal that S1 is a double radio source centred around the optical nucleus; its total extent is ∼750 pc its average 1.4−8.5 GHz spectral index is −0.81 ± 0.06. S1 therefore resembles a compact symmetric object. The 15-GHz VLA image identifies the radio source at S2 to be a compact core. Our radio observations therefore strongly support the presence of a dual AGN in Mrk 212. The optical emission line flux ratios obtained from the Himalayan Chandra Telescope (HCT) observations however, show that S1 and S2 both fall in the AGN + star formation (SF) region of the Baldwin, Philips and Terlevich (BPT) diagram. Weak AGN lying in the SF or AGN + SF intermediate regions in the BPT diagram have indeed been reported in the literature; our sources clearly fall in the same category. We find an extended radio structure in our newly reduced 8.5-GHz-VLA data, that is offset by ∼1 arcsec from the optical nucleus S2. New deep FUV and NUV observations with the Ultraviolet Imaging Telescope aboard AstroSat reveal SF knots around S2 as well as kpc-scale tidal tails; the SF knots around S2 coincide with the extended radio structure detected at 8.5 GHz. The radio spectral indices are consistent with SF. Any possible association with the AGN in S2 is unclear at this stage.

Symmetry-Aware 6D Object Pose Estimation via Multitask Learning

Although 6D object pose estimation has been intensively explored in the past decades, the performance is still not fully satisfactory, especially when it comes to symmetric objects. In this paper, we study the problem of 6D object pose estimation by leveraging the information of object symmetry. To this end, a network is proposed that predicts 6D object pose and object reflectional symmetry as well as the key points simultaneously via a multitask learning scheme. Consequently, the pose estimation is aware of and regulated by the symmetry axis and the key points of the to-be-estimated objects. Moreover, we devise an optimization function to refine the predicted 6D object pose by considering the predicted symmetry. Experiments on two datasets demonstrate that the proposed symmetry-aware approach outperforms the existing methods in terms of predicting 6D pose estimation of symmetric objects.