搜索结果：Maps

DUSt3R has recently shown that one can reduce many tasks in multi-view geometry, including estimating camera intrinsics and extrinsics, reconstructing the scene in 3D, and establishing image correspondences, to the prediction of a pair of viewpoint-invariant point maps, i.e., pixel-aligned point clouds defined in a common reference frame. This formulation is elegant and powerful, but unable to tackle dynamic scenes. To address this challenge, we introduce the concept of Dynamic Point Maps (DPM), extending standard point maps to support 4D tasks such as motion segmentation, scene flow estimation, 3D object tracking, and 2D correspondence. Our key intuition is that, when time is introduced, there are several possible spatial and time references that can be used to define the point maps. We identify a minimal subset of such combinations that can be regressed by a network to solve the sub tasks mentioned above. We train a DPM predictor on a mixture of synthetic and real data and evaluate it across diverse benchmarks for video depth prediction, dynamic point cloud reconstruction, 3D scene flow and object pose tracking, achieving state-of-the-art performance. Code, models and additional

We study proper holomorphic maps of annuli in complex Euclidean spaces, that is, domains with $U(n)$ as the automorphism group. By the Hartogs phenomenon and a result of Forstnerič, such maps are always rational and extend to proper maps of balls. We first prove that a proper map of annuli from $n$ dimensions to $N$ dimensions where $N < \binom{n+1}{2}$ is always an affine embedding. This inequality is sharp as the homogeneous map of degree 2 satisfies $N=\binom{n+1}{2}$. Next we find a necessary and sufficient condition for a map to be homogeneous: A proper map of annuli is homogeneous if and only if its general hyperplane rank, the affine dimension of the image of a general hyperplane, is exactly $N-1$. As a corollary, we obtain a classification of homogeneous proper maps of balls. A homogeneous proper ball map takes all spheres centered at the origin to spheres centered at the origin. We show that if a proper ball map has general hyperplane rank $N-1$ and takes one sphere centered at the origin to a sphere centered at the origin, then it is homogeneous. Another corollary of this result is a complete classification of proper maps of annuli from dimension 2 to dimension 3. Fina

Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these limitations, we propose a fundamentally new approach to shape correspondence based on denoising diffusion models. In our method, a diffusion model learns to directly predict the functional map, a low-dimensional representation of a point-wise map between shapes. We use a large dataset of synthetic human meshes for training and employ two steps to reduce the number of functional maps that need to be learned. First, the maps refer to a template rather than shape pairs. Second, the functional map is defined in a basis of eigenvectors of the Laplacian, which is not unique due to sign ambiguity. Therefore, we introduce an unsupervised approach to select a specific basis by correcting the signs of eigenvectors based on surface features. Our model achieves competitive performance on standard human datasets, meshes with anisotropic connectivity, non-isometric humanoid shapes, as well as animals compared to existing descriptor-based and large-scale shape

We present a new two-dimensional (2D) map of total Galactic extinction, $A_\mathrm{V}$, across the entire dust half-layer from the Sun to extragalactic space for Galactic latitudes $|b|>13$ deg, as well as a three-dimensional (3D) map of $A_\mathrm{V}$ within 2~kpc of the Sun. These maps are based on $A_\mathrm{V}$ and distance estimates derived from a dataset, which utilizes {\it Gaia} Data Release 3 parallaxes and multi-band photometry for nearly 100 million dwarf stars. We apply our own corrections to account for significant systematics in this dataset. Our 2D map achieves an angular resolution of 6.1~arcmin, while the 3D map offers a transverse resolution of 3.56~pc -- corresponding to variable angular resolution depending on distance -- and a radial resolution of 50~pc. In constructing these maps, we pay particular attention to the solar neighborhood (within 200~pc) and to high Galactic latitudes. The 3D map predicts $A_\mathrm{V}$ from the Sun to any extended object within the Galactic dust layer with an accuracy of $σ(A_\mathrm{V}) = 0.1$~mag. The 2D map provides $A_\mathrm{V}$ estimates for the entire dust half-layer up to extragalactic distances with an accuracy of $σ(A

This paper studies the diameter of the numerical range of bounded operators on Hilbert space and the induced seminorm, called the numerical diameter, on bounded linear maps between operator systems which is sensible in the case of unital maps and their scalar multiples. It is shown that the completely bounded numerical diameter is a norm that is comparable but not equal to the completely bounded norm. This norm is particularly interesting in the case of unital completely positive maps and their sections.

This paper focuses on distinguishing classes of dynamical behavior for one- and two-dimensional torus maps, in particular between orbits that are incommensurate, resonant, periodic, or chaotic. We first consider Arnold's circle map, for which there is a universal power law for the fraction of nonresonant orbits as a function of the amplitude of the nonlinearity. Our methods give a more precise calculation of the coefficients for this power law. For two-dimensional torus maps, we show that there is no such universal law for any of the classes of orbits. However, we find different categories of maps with qualitatively similar behavior. Our results are obtained using three fast and high precision numerical methods: weighted Birkhoff averages, Farey trees, and resonance orders.

We consider the perturbative renormalisation of the $Φ^4_d$ model from Euclidean Quantum Field Theory for any, possibly non-integer dimension $d<4$. The so-called BPHZ renormalisation, named after Bogoliubov, Parasiuk, Hepp and Zimmermann, is usually encoded into extraction-contraction operations on Feynman diagrams, which have a complicated combinatorics. We show that the same procedure can be encoded in the much simpler algebra of polynomials in two unknowns $X$ and $Y$, which represent the fourth and second Wick power of the field. In this setting, renormalisation takes the form of a \lq\lq Wick map\rq\rq\ which maps monomials into Bell polynomials. The construction makes use of recent results by Bruned and Hou on multiindices, which are algebraic objects of intermediate complexity between Feynman diagrams and polynomials.

The use of highly sensitive pixelated direct detectors has dramatically improved the performance of high energy instrumentation such as transmission electron microscopy. Here, we describe a recently developed monolithic active pixel sensor designed for low energy scanning electron microscopy applications. This detector enables electron backscatter diffraction (EBSD) at lower energies and dose than are accessible with existing scintillator-coupled detectors, expanding grain orientation mapping capabilities to materials such as ceramics that are poor electron conductors. The high detector sensitivity allows collection of rich diffraction information - providing dislocation defect contrast that is otherwise not accessible via EBSD. Indeed, even the energy of single electron interaction events can be measured with this detector, which we demonstrate to energy filter diffraction patterns revealing details of how diffraction occurs at low energy.

This article presents new bijections on planar maps. At first a bijection is established between bipolar orientations on planar maps and specific "transversal structures" on triangulations of the 4-gon with no separating 3-cycle, which are called irreducible triangulations. This bijection specializes to a bijection between rooted non-separable maps and rooted irreducible triangulations. This yields in turn a bijection between rooted loopless maps and rooted triangulations, based on the observation that loopless maps and triangulations are decomposed in a similar way into components that are respectively non-separable maps and irreducible triangulations. This gives another bijective proof (after Wormald's construction published in 1980) of the fact that rooted loopless maps with $n$ edges are equinumerous to rooted triangulations with $n$ inner vertices.

Two infinite families of Cremona maps depending on one real parameter are given. For all integers $n \ge 1$ the first family of Cremona maps consists of group elements in $Bir \left( \mathbb{P}^{n} \right)$ with bidegree $(n, n)$, the second family of Cremona maps consists of group elements in $Bir \left( \mathbb{P}^{2n} \right)$ with bidegree $(2 n, 2 n)$. For the first family and $n \ge 5$, for the second family and $n \ge 3$ the existence of this group elements and the properties depend on a conjecture. But computational results suggest that the conjecture is true for all $n$.

In this paper, we focus on a numerical technique, the weighted Birkhoff average (WBA) to distinguish between four categories of dynamics for quasiperiodically-forced circle maps. Regular dynamics can be classified by rotation vectors, and these can be rapidly computed to machine precision using the WBA. Regular orbits can be resonant or incommensurate and we distinguish between these by computing their "resonance order." When the dynamics is chaotic the WBA converges slowly. Such orbits can be strongly chaotic, when they have a positive Lyapunov exponent or weakly chaotic, when the maximal Lyapunov exponent is zero. The latter correspond to the strange nonchaotic attractors (SNA) that have been observed in quasiperiodically-forced circle maps beginning with the models introduced by Ding, Grebogi, and Ott. The WBA provides a new technique to find SNAs, and allows us to accurately compute the proportions of each of the four orbit types as a function of map parameters.

Signal maps are essential for the planning and operation of cellular networks. However, the measurements needed to create such maps are expensive, often biased, not always reflecting the metrics of interest, and posing privacy risks. In this paper, we develop a unified framework for predicting cellular signal maps from limited measurements. Our framework builds on a state-of-the-art random-forest predictor, or any other base predictor. We propose and combine three mechanisms that deal with the fact that not all measurements are equally important for a particular prediction task. First, we design quality-of-service functions ($Q$), including signal strength (RSRP) but also other metrics of interest to operators, i.e., coverage and call drop probability. By implicitly altering the loss function employed in learning, quality functions can also improve prediction for RSRP itself where it matters (e.g., MSE reduction up to 27% in the low signal strength regime, where errors are critical). Second, we introduce weight functions ($W$) to specify the relative importance of prediction at different locations and other parts of the feature space. We propose re-weighting based on importance sam

In the 1998-99 flight, BOOMERanG has produced maps of $\sim 4 %$ of the sky at high Galactic latitudes, at frequencies of 90, 150, 240 and 410 GHz, with resolution $\simgt 10'$. The faint structure of the Cosmic Microwave Background at horizon and sub-horizon scales is evident in these maps. These maps compare well to the maps recently obtained at lower frequencies by the WMAP experiment. Here we compare the amplitude and morphology of the structures observed in the two sets of maps. We also outline the polarization sensitive version of BOOMERanG, which was flown early this year to measure the linear polarization of the microwave sky at 150, 240 and 350 GHz.

We provide a complete combinatorial classification of critically fixed anti-Thurston maps, i.e., orientation-reversing branched covers of the 2-sphere that fix every critical point. The first step in the proof, and an interesting result in its own right, is a combinatorial classification of critically fixed anti-rational maps as "Schottky maps" associated to certain plane graphs. Both of these classification results heavily rely on an orientation-reversing version of Thurstons's theory, including the canonical decomposition of anti-Thurston maps, which we develop in this paper. Lastly, we give some applications to the global curve attractor and twisting problems, as well as to anti-rational maps with symmetries and to critically fixed anti-polynomials.

In this article, we investigate the cobordism maps on periodic Floer homology (PFH). In the first part of the paper, we define the cobordism maps on PFH via Seiberg Witten theory as well as the isomorphism between PFH and Seiberg Witten cohomology. Furthermore, we show that the maps satisfy the holomorphic curve axiom. In the second part of the paper, we give an alternative definition of these maps by using holomorphic curve method, provided that the symplectic cobordisms are Lefschetz fibration satisfying certain nice conditions. Under additionally certain monotonicity assumptions, we show that these two definitions are equivalent.

This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that appear in the realm of special holonomy as well as some of the topological and analytic considerations that are essential to pseudoholomorphic invariants. The first part presents the geometric framework of compatible $n$-triads, from which follows naturally the definition of a multiholomorphic mapping. Some of the general analytic and differential-geometric properties of these maps are derived, including an energy identity which expresses a multiholomorphic map as a minimizer in its homotopy class of the appropriate $L^p$-energy. Some theorems confining the critical loci of such maps are obtained as well as some Liouville-type theorems for maps with sufficient regularity in the presence of curvature hypotheses. Finally, attention is focused onto a special case of the theory which pertains to the calibrated geometry of $\Gtwo$-manifolds.

We use results of Auroux arXiv:1001.4323 and Zemke arXiv:1801.09270 to prove that, in the morphism spaces formulation of Heegaard Floer homology given in arXiv:1005.1248, the opposite composition map agrees up to homotopy with the map on Heegaard Floer complexes induced by a pair-of-pants cobordism. As an application, we give an algorithm for computing arbitrary cobordism maps on hat Heegaard Floer homology.

This paper is concerned with the construction of new solutions in terms of birational maps to the functional tetrahedron equation and parametric tetrahedron equation. We present a method for constructing solutions to the parametric tetrahedron equation via Darboux transformations. In particular, we study matrix refactorisation problems for Darboux transformations associated with the nonlinear Schrödinger (NLS) and the derivative nonlinear Schrödinger (DNLS) equation, and we construct novel nine-dimensional tetrahedron maps. We show that the latter can be restricted to six-dimensional parametric tetrahedron maps on invariant leaves. Finally, we construct parametric tetrahedron maps employing degenerated Darboux transformations of NLS and DNLS type.

We initiate a study of linear maps on $M_n(\mathbb{C})$ that have the property that they factor through a tracial von Neumann algebra $(\mathcal{A,τ})$ via operators $Z\in M_n(\mathcal{A})$ whose entries consist of positive elements from the von-Neumann algebra. These maps often arise in the context of non-local games, especially in the synchronous case. We establish a connection with the convex sets in $\mathbb{R}^n$ containing self-dual cones and the existence of these maps. The Choi matrix of a map of this kind which factors through an abelian von-Neumann algebra turns out to be a completely positive (CP) matrix. We fully characterize positively factorizable maps whose Choi rank is 2. We also provide some applications of this analysis in finding doubly nonnegative matrices which are not CPSD. A special class of these examples is found from the concept of Unextendible Product Bases in quantum information theory.