Related papers: Topological Lensing in Spherical Spaces
Recent microscopy imaging techniques allow to precisely analyze cell morphology in 3D image data. To process the vast amount of image data generated by current digitized imaging techniques, automated approaches are demanded more than ever.…
Most camera lens systems are designed in isolation, separately from downstream computer vision methods. Recently, joint optimization approaches that design lenses alongside other components of the image acquisition and processing pipeline…
Sky coverage is one of the most important pieces of information about astronomical observations. We discuss possible representations, and present algorithms to create and manipulate shapes consisting of generalized spherical polygons with…
Strong lensing by an isolated spherically symmetric mass distribution is considered in presence of a positive cosmological constant. Deflection angles and time delay are computed and compared to the multiple image of the quasar SDSS…
We present a method to constrain cosmic topology from the distribution of astronomical objects projected on the celestial sphere. This is an extension of the 3D method introduced in Fujii & Yoshii (2011) that is to search for a pair of…
Topological properties of photonic structures described by Hamiltonian matrices have been extensively studied in recent years. Photonic systems are often open systems, and their coupling with the environment is characterized by scattering…
A flat Universe model supported by recent observations has 18 possible choices for its overall topology. To detect or exclude these possibilities is one of the most important tasks in modern cosmology, but it has been very difficult for…
The chaotical dynamics is studied in different Friedmann-Robertson- Walker cosmological models with scalar (inflaton) field and hydrodynamical matter. The topological entropy is calculated for some particular cases. Suggested scheme can be…
We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subcategory, in which the object is spherical. This general…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
Galactic microlensing has the capability to determine the position angle of the detected planets in a sky reference frame. By a broad enough statistics, it is possible to investigate possible anisotropies in the distribution of the orbital…
We present an analysis of the line-of-sight structure toward a sample of ten strong lensing cluster cores. Structure is traced by groups that are identified spectroscopically in the redshift range, 0.1 $\leq$ z $\leq$ 0.9, and we measure…
We put the theory of interacting topological crystalline phases on a systematic footing. These are topological phases protected by space-group symmetries. Our central tool is an elucidation of what it means to "gauge" such symmetries. We…
A more realistic object detection paradigm, Open-World Object Detection, has arisen increasing research interests in the community recently. A qualified open-world object detector can not only identify objects of known categories, but also…
We derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…
Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…
We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition space of a topological space consisting of the infinite product…
Observations suggest that our universe is spatially flat on the largest observable scales. Exactly six different compact orientable three-dimensional manifolds admit flat metrics. These six manifolds are therefore the most natural choices…
Creating spherical initial conditions in smoothed particle hydrodynamics simulations that are spherically conformal is a difficult task. Here, we describe two algorithmic methods for evenly distributing points on surfaces, that when paired…
The crease set of an event horizon is studied in a spacetime with discrete or continuous symmetry. It determines possible topologies on spatial sections of an event horizon. We thereby investigate the classification of stable topological…