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Many high-dimensional practical data sets have hierarchical structures induced by graphs or time series. Such data sets are hard to process in Euclidean spaces and one often seeks low-dimensional embeddings in other space forms to perform…
A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and…
The rapidly increasing size of deep-learning models has caused renewed and growing interest in alternatives to digital computers to dramatically reduce the energy cost of running state-of-the-art neural networks. Optical matrix-vector…
Optical aberrations of optical systems cause significant degradation of imaging quality. Aberration correction by sophisticated lens designs and special glass materials generally incurs high cost of manufacturing and the increase in the…
We present a framework to use recently introduced Capsule Networks for solving the problem of Optical Flow, one of the fundamental computer vision tasks. Most of the existing state of the art deep architectures either uses a correlation…
Unidirectional optical systems enable selective control of light through asymmetric processing of radiation, effectively transmitting light in one direction while blocking unwanted propagation in the opposite direction. Here, we introduce a…
The Fourier transform operation is an important conceptual as well as computational tool in the arsenal of every practitioner of physical and mathematical sciences. We discuss some of its applications in optical science and engineering,…
A new theoretical technique for understanding, analyzing and developing optical systems is presented. The approach is statistical in nature, where information about an object under investigation is discovered, by examining deviations from a…
The combinatorial interpretation of the persistence diagram as a M\"obius inversion was recently shown to be functorial. We employ this discovery to recast the Persistent Homology Transform of a geometric complex as a representation of a…
The most common methods in explainable artificial intelligence are post-hoc techniques which identify the most relevant features used by pretrained opaque models. Some of the most advanced post hoc methods can generate explanations that…
We reconsider the basic properties of ray-transfer matrices for first-order optical systems from a geometrical viewpoint. In the paraxial regime of scalar wave optics, there is a wide family of beams for which the action of a ray-transfer…
Image Classification is a fundamental task in the field of computer vision that frequently serves as a benchmark for gauging advancements in Computer Vision. Over the past few years, significant progress has been made in image…
Neural networks transform data through learned representations whose geometry affects separation, contraction, and generalization. Recent work studies this geometry using discrete curvature on neighborhood graphs, suggesting Ricci-flow-like…
Hyperspectral object tracking using snapshot mosaic cameras is emerging as it provides enhanced spectral information alongside spatial data, contributing to a more comprehensive understanding of material properties. Using transformers,…
Open-vocabulary multiple object tracking aims to generalize trackers to unseen categories during training, enabling their application across a variety of real-world scenarios. However, the existing open-vocabulary tracker is constrained by…
Given a DG-category A we introduce the bar category of modules Modbar(A). It is a DG-enhancement of the derived category D(A) of A which is isomorphic to the category of DG A-modules with A-infinity morphisms between them. However, it is…
Haskell provides type-class-bounded and parametric polymorphism as opposed to subtype polymorphism of object-oriented languages such as Java and OCaml. It is a contentious question whether Haskell 98 without extensions, or with common…
We describe the structure of bimodules (over finite dimensional algebras) which have the property that the functor of tensoring with such a bimodule sends any module to a projective module. The main result is that all such bimodules are…
We introduce a new class of extensions of terms that consists in navigation strategies and insertion of contexts. We introduce an operation of combination on this class which is associative, admits a neutral element and so that each…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…