Related papers: Introducing the ISE Methodology: A Powerful New To…
Motion serves as a powerful cue for scene perception and understanding by separating independently moving surfaces and organizing the physical world into distinct entities. We introduce SIRE, a self-supervised method for motion discovery of…
The systems without symmetries, e.g. the spatial and chiral symmetries, are generally thought to be improper for topological study and no conventional integral topological invariant can be well defined. In this work, with multi-band…
The study of representations is of fundamental importance to any form of communication, and our ability to exploit them effectively is paramount. This article presents a novel theory -- Representational Systems Theory -- that is designed to…
We propose reCSE, a self supervised contrastive learning sentence representation framework based on feature reshaping. This framework is different from the current advanced models that use discrete data augmentation methods, but instead…
We introduce ICE-TIDE, a method for cryogenic electron tomography (cryo-ET) that simultaneously aligns observations and reconstructs a high-resolution volume. The alignment of tilt series in cryo-ET is a major problem limiting the…
Among plenty of applications, low-dimensional homogeneous spaces appear in cosmological models as both, classical factor spaces of multidimensional geometry and minisuperspaces in canonical quantization. Here a new tool to restrict their…
Reconstructing the surfaces of deformable objects from correspondences between a 3D template and a 2D image is well studied under Shape-from-Template (SfT) methods; however, existing approaches break down when topological changes accompany…
In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…
Deep learning models (DLMs) achieve increasingly high performance both on structured and unstructured data. They significantly extended applicability of machine learning to various domains. Their success in making predictions, detecting…
The problem of topology change description in gravitation theory is analized in detailes. It is pointed out that in standard four-dimensional theories the topology of space may be considered as a particular case of boundary conditions (or…
In this letter we discuss the possibility of treating the spacetime by itself as a kind of deformable body for which we can define an fundamental lattice, just like atoms in crystal lattices. We show three signs pointing in that direction.…
The classical fiber product in algebraic geometry provides a powerful tool for studying loci where two morphisms to a base scheme, $\phi: X \to S$ and $\psi: Y \to S$, coincide exactly. This condition of strict equality, however, is…
Tomography has made a revolutionary impact on diverse fields, ranging from macro-/mesoscopic scale studies in biology, radiology, plasma physics to the characterization of 3D atomic structure in material science. The fundamental of…
We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived. Using Information Geometry, we consider geometric properties of statistical models for…
We consider the task of predicting a response Y from a set of covariates X in settings where the conditional distribution of Y given X changes over time. For this to be feasible, assumptions on how the conditional distribution changes over…
We propose a functional description of rewriting systems on topological vector spaces. We introduce the topological confluence property as an approximation of the confluence property. Using a representation of linear topological rewriting…
In previous publications, we have started investigating some possible applications to the retraction theory in gravitational physics and showed that it can be very useful in providing proofs and explaining the topological bases. In the…
Why is the manifold topology in a spacetime taken for granted? Why do we prefer to use Riemann open balls as basic-open sets, while there also exists a Lorentz metric? Which topology is a best candidate for a spacetime; a topology…
Recently, the structural reading comprehension (SRC) task on web pages has attracted increasing research interests. Although previous SRC work has leveraged extra information such as HTML tags or XPaths, the informative topology of web…
The tomographic histories approach is presented. As an inverse problem, we recover in an operational way the effective topology of the extended configuration space of a system. This means that from a series of experiments we get a set of…