3,231 research outputs found

    Orthonormal bases of extreme quantumness

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    Spin anticoherent states acquired recently a lot of attention as the most "quantum" states. Some coherent and anticoherent spin states are known as optimal quantum rotosensors. In this work, we introduce a measure of quantumness for orthonormal bases of spin states, determined by the average anticoherence of individual vectors and the Wehrl entropy. In this way, we identify the most coherent and most quantum states, which lead to orthogonal measurements of extreme quantumness. Their symmetries can be revealed using the Majorana stellar representation, which provides an intuitive geometrical representation of a pure state by points on a sphere. Results obtained lead to maximally (minimally) entangled bases in the 2j+12j+1 dimensional symmetric subspace of the 22j2^{2j} dimensional space of states of multipartite systems composed of 2j2j qubits. Some bases found are iso-coherent as they consist of all states of the same degree of spin-coherence

    Apartment classes of integral symplectic groups

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    In this note we present an alternative proof of a theorem of Gunnells, which states that the Steinberg module of Sp2n(Q)\operatorname{Sp_{2n}}(\mathbb{Q}) is a cyclic Sp2n(Z)\operatorname{Sp_{2n}}(\mathbb{Z})-module, generated by integral apartment classes.Comment: 16 pages. Comments welcome

    On Chevalley group schemes over function fields: quotients of the Bruhat-Tits building by {}\{\wp\}-arithmetic subgroups

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    Let G\mathbf{G} be a reductive Chevalley group scheme (defined over Z\mathbb{Z}). Let C\mathcal{C} be a smooth, projective, geometrically integral curve over a field F\mathbb{F}. Let \wp be a closed point on C\mathcal{C}. Let AA be the ring of functions that are regular outside {}\lbrace \wp \rbrace. The fraction field kk of AA has a discrete valuation ν=ν:k×Z\nu=\nu_{\wp}: k^{\times} \rightarrow \mathbb{Z} associated to \wp. In this work, we study the action of the group G(A) \textbf{G}(A) of AA-points of G\mathbf{G} on the Bruhat-Tits building X=X(G,k,ν)\mathcal{X}=\mathcal{X}(\textbf{G},k,\nu_\wp) in order to describe the structure of the orbit space G(A)\X \textbf{G}(A)\backslash \mathcal{X}. We obtain that this orbit space is the ``gluing'' of a closed connected CW-complex with some sector chambers. The latter are parametrized by a set depending on the Picard group of C{}\mathcal{C} \smallsetminus \{\wp\} and on the rank of G\mathbf{G}. Moreover, we observe that any rational sector face whose tip is a special vertex contains a subsector face that embeds into this orbit space. We deduce, from this description, a writing of G(A)\mathbf{G}(A) as a free product with amalgamation. We also obtain a counting of the Γ\Gamma-conjugacy classes of maximal unipotent subgroups contained in a finite index subgroup ΓG(A)\Gamma \subseteq \mathbf{G}(A), together with a description of these maximal unipotent subgroups.Comment: Comments are welcom

    Modeling horizon absorption in spinning binary black holes using effective worldline theory

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    The mass and spin of black holes (BHs) in binary systems may change due to the infall of gravitational-wave (GW) energy down the horizons. For spinning BHs, this effect enters at 2.5 post-Newtonian (PN) order relative to the leading-order energy flux at infinity. There is currently a discrepancy in the literature in the expressions of these horizon fluxes in the test-body limit at 4PN order (relative 1.5PN order). Here, we model the horizon absorption as tidal heating in an effective worldline theory of a spinning particle equipped with tidally-induced quadrupole and octupole moments. We match the tidal response to analytic solutions of the Teukolsky equation in a scattering scenario, and obtain general formulae for the evolution of mass and spin. We then specialize to the case of aligned-spin--quasi-circular binaries, obtaining the corresponding contributions to the GW phasing through 4PN order. Importantly, we find that the number of GW cycles due to horizon fluxes with masses observed by LIGO-Virgo-KAGRA detectors is about 2-3 orders of magnitude smaller than the other contributions to the phasing at the same PN order. Furthermore, in the test-body limit, we find full agreement with results obtained earlier from BH perturbation theory, with a small mass in an equatorial circular orbit treated as a source perturbing the Kerr metric. Thus, we weigh in on one side of the previous discrepancy.Comment: 29 Pages, 1 figure, 2 table

    Commensurations of Aut(FN){{\rm{Aut}}}(F_N) and its Torelli subgroup

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    For N3N \geq 3, the abstract commensurators of both Aut(FN){{\rm{Aut}}}(F_N) and its Torelli subgroup IAN{{\rm{IA}}}_N are isomorphic to Aut(FN){{\rm{Aut}}}(F_N) itself.Comment: 29 pages, 5 figure

    Simulation of incompressible viscous flow using finite element method

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    This study focused on simulating incompressible viscous flow using the finite element method. This study used velocity and pressure as unknowns known as primitive variable formulations. Simulation of incompressible fluid flow poses numerical challenges due to the presence of nonlinear convective terms in Navier-Stokes equations and the incompressible nature of the fluid. If the connection between velocities and pressure is not discretized correctly, the stable and convergent velocities might be gained, but the obtained pressure will be oscillatory. To avoid these difficulties, continuous quadratic and additional cubic bubble functions will be used for the velocity field and linear functions for the pressure field. This kind of discretization satisfies the Ladyzhenskaya-Babuška-Brezzi (LBB) stability condition. Two cases of different Reynolds numbers were used to test the formulation's effectiveness. In the case of Reynolds number 0.12, no vortices were formed, suggesting that the flow is primarily governed by fluid friction, and fluid inertia has minimal effect. In the case of Reynolds number 120, the vortex formation, which is known as Von Kármán vortex street, appeared. These results concluded that the formulation using the finite element method is correct

    RecolorNeRF: Layer Decomposed Radiance Fields for Efficient Color Editing of 3D Scenes

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    Radiance fields have gradually become a main representation of media. Although its appearance editing has been studied, how to achieve view-consistent recoloring in an efficient manner is still under explored. We present RecolorNeRF, a novel user-friendly color editing approach for the neural radiance fields. Our key idea is to decompose the scene into a set of pure-colored layers, forming a palette. By this means, color manipulation can be conducted by altering the color components of the palette directly. To support efficient palette-based editing, the color of each layer needs to be as representative as possible. In the end, the problem is formulated as an optimization problem, where the layers and their blending weights are jointly optimized with the NeRF itself. Extensive experiments show that our jointly-optimized layer decomposition can be used against multiple backbones and produce photo-realistic recolored novel-view renderings. We demonstrate that RecolorNeRF outperforms baseline methods both quantitatively and qualitatively for color editing even in complex real-world scenes.Comment: To appear in ACM Multimedia 2023. Project website is accessible at https://sites.google.com/view/recolorner

    FLARE: Fast Learning of Animatable and Relightable Mesh Avatars

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    Our goal is to efficiently learn personalized animatable 3D head avatars from videos that are geometrically accurate, realistic, relightable, and compatible with current rendering systems. While 3D meshes enable efficient processing and are highly portable, they lack realism in terms of shape and appearance. Neural representations, on the other hand, are realistic but lack compatibility and are slow to train and render. Our key insight is that it is possible to efficiently learn high-fidelity 3D mesh representations via differentiable rendering by exploiting highly-optimized methods from traditional computer graphics and approximating some of the components with neural networks. To that end, we introduce FLARE, a technique that enables the creation of animatable and relightable mesh avatars from a single monocular video. First, we learn a canonical geometry using a mesh representation, enabling efficient differentiable rasterization and straightforward animation via learned blendshapes and linear blend skinning weights. Second, we follow physically-based rendering and factor observed colors into intrinsic albedo, roughness, and a neural representation of the illumination, allowing the learned avatars to be relit in novel scenes. Since our input videos are captured on a single device with a narrow field of view, modeling the surrounding environment light is non-trivial. Based on the split-sum approximation for modeling specular reflections, we address this by approximating the pre-filtered environment map with a multi-layer perceptron (MLP) modulated by the surface roughness, eliminating the need to explicitly model the light. We demonstrate that our mesh-based avatar formulation, combined with learned deformation, material, and lighting MLPs, produces avatars with high-quality geometry and appearance, while also being efficient to train and render compared to existing approaches.Comment: 15 pages, Accepted: ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia), 202
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