Related papers: Virtual Manifolds and Localization
By double ideal quotient, we mean $(I:(I:J))$ where ideals $I$ and $J$. In our previous work [11], double ideal quotient and its variants are shown to be very useful for checking prime divisor and generating primary component. Combining…
We present a new method to construct Virtual Element spaces on polygons with curved edges.
This paper is concerned with the theory and applications of varifolds to the representation, approximation and diffeomorphic registration of shapes. One of its purpose is to synthesize and extend several prior works which, so far, have made…
We describe a method for performing active localization of objects in instances of visual situations. A visual situation is an abstract concept---e.g., "a boxing match", "a birthday party", "walking the dog", "waiting for a bus"---whose…
This note is about invariants of moduli spaces of curves. It includes their intersection theory and cohomology. Our main focus in on the distinguished piece containing the so called tautological classes. These are the most natural classes…
This paper presents an immersive virtual reality environment that can be used to develop collaborative educational applications. Multiple users can collaborate within the virtual shared space and communicate with each other through voice.…
Let $({\bf X},\omega_{\bf X}^*)$ be a separated, $-2$-shifted symplectic derived $\mathbb C$-scheme, in the sense of Pantev, Toen, Vezzosi and Vaquie arXiv:1111.3209, of complex virtual dimension ${\rm vdim}_{\mathbb C}{\bf X}=n\in\mathbb…
We describe new explicit examples of moduli spaces of Bridgeland semistable objects on surfaces, parametrizing objects whose numerical class agrees with the class of a point. This follows ideas of Tramel and Xia, using stability conditions…
This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital…
We apply virtual localization to the problem of finding blowup formulae for virtual sheaf-theoretic invariants on a smooth projective surface. This leads to a general procedure that can be used to express virtual enumerative invariants on…
Visual localization is the problem of estimating a camera within a scene and a key component in computer vision applications such as self-driving cars and Mixed Reality. State-of-the-art approaches for accurate visual localization use…
We provide an account of the construction of the moduli stack of elliptic curves as an analytic orbifold. While intimately linked to Thurston's point of view on the subject (discrete groups acting properly and effectively on differentiable…
Density estimation is an important technique for characterizing distributions given observations. Much existing research on density estimation has focused on cases wherein the data lies in a Euclidean space. However, some kinds of data are…
We construct a moduli space of stable pairs over a smooth projective variety, parametrizing morphisms from a fixed coherent sheaf to a varying sheaf of fixed topological type, subject to a stability condition. This generalizes the notion…
We introduce a higher rank analog of the Pandharipande-Thomas theory of stable pairs on a Calabi-Yau threefold $X$. More precisely, we develop a moduli theory for frozen triples given by the data $O^r(-n)\rightarrow F$ where $F$ is a sheaf…
In this paper, we give an accessible introduction to the theory of orbispaces via groupoids. We define a certain class of topological groupoids, which we call orbigroupoids. Each orbigroupoid represents an orbispace, but just as with…
Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of…
Visual localization and mapping is a crucial capability to address many challenges in mobile robotics. It constitutes a robust, accurate and cost-effective approach for local and global pose estimation within prior maps. Yet, in highly…
Since its introduction in 1995 by Li-Tian and Behrend-Fantechi, the theory of virtual fundamental class has played a key role in algebraic geometry, defining important invariants such as the Gromov-Witten invariant and the Donaldson-Thomas…
One key challenge in Augmented Reality is the placement of virtual content in natural locations. Most existing automated techniques can only work with a closed-vocabulary, fixed set of objects. In this paper, we introduce and evaluate…