We introduce a new method for calculating the O(α3) hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment from ab initio lattice QCD. We first derive expressions suitable ...for computing the higher-order contributions either from the renormalized vacuum polarization function Π^(q2) or directly from the lattice vector-current correlator in Euclidean space. We then demonstrate the approach using previously published results for the Taylor coefficients of Π^(q2) that were obtained on four-flavor QCD gauge-field configurations with physical light-quark masses. We obtain 1010aμHVP,HO=−9.3(1.3) in agreement with, but with a larger uncertainty than, determinations from e+e−→hadrons data plus dispersion relations.
•Graphs arc routing problems with one drone and one mothership.•First mathematical formalization of the problem via MINLP formulations.•Matheuristic algorithm to deal with large instances.•Extensive ...experimental analysis on instances involving planar graphs.
This paper addresses the optimization of routing problems with drones. It analyzes the coordination of one mothership with one drone to obtain optimal routes that have to visit some target objects modeled as general graphs. The goal is to minimize the overall weighted distance traveled by both vehicles while satisfying the requirements in terms of percentages of visits to targets. We discuss different approaches depending on the assumption made on the route followed by the mothership: i) the mothership can move on a continuous framework (the Euclidean plane), ii) on a connected piecewise linear polygonal chain or iii) on a general graph. In all cases, we develop exact formulations resorting to mixed integer second order cone programs that are compared on a testbed of instances to assess their performance. The high complexity of the exact methods makes it difficult to find optimal solutions in short computing time. For that reason, besides the exact formulations we also provide a tailored matheuristic algorithm that allows one to obtain high quality solutions in reasonable time. Computational experiments show the usefulness of our methods in different scenarios.
We study Kähler-Dirac fermions on Euclidean dynamical triangulations. This fermion formulation furnishes a natural extension of staggered fermions to random geometries without requiring vielbeins and ...spin connections. We work in the quenched approximation where the geometry is allowed to fluctuate but there is no backreaction from the matter on the geometry. By examining the eigenvalue spectrum and the masses of scalar mesons we find evidence for a fourfold degeneracy in the fermion spectrum in the large-volume, continuum limit. It is natural to associate this degeneracy with the well-known equivalence in continuum flat space between the Kähler-Dirac fermion and four copies of a Dirac fermion. Lattice effects then lift this degeneracy in a manner similar to staggered fermions on regular lattices. The evidence that these discretization effects vanish in the continuum limit suggests both that lattice continuum Kähler-Dirac fermions are recovered at that point, and that this limit truly corresponds to smooth continuum geometries. One additional advantage of the Kähler-Dirac action is that it respects an exact U(1) symmetry on any random triangulation. This U(1) symmetry is related to continuum chiral symmetry. By examining fermion bilinear condensates we find strong evidence that this U(1) symmetry is not spontaneously broken in the model at order the Planck scale. This is a necessary requirement if models based on dynamical triangulations are to provide a valid ultraviolet-complete formulation of quantum gravity.
Display omitted
•A methodology for conditioned human motion generation.•A novel multimodal dataset that will be available for the community.•Our method shows that the use of GCN provides a more ...coherent approach for the data structure inherent to the problem.•Our approach generates realistic samples, achieving similar benchmarks to real motions on a perceptual study.
Synthesizing human motion through learning techniques is becoming an increasingly popular approach to alleviating the requirement of new data capture to produce animations. Learning to move naturally from music, i.e., to dance, is one of the more complex motions humans often perform effortlessly. Each dance movement is unique, yet such movements maintain the core characteristics of the dance style. Most approaches addressing this problem with classical convolutional and recursive neural models undergo training and variability issues due to the non-Euclidean geometry of the motion manifold structure. In this paper, we design a novel method based on graph convolutional networks to tackle the problem of automatic dance generation from audio information. Our method uses an adversarial learning scheme conditioned on the input music audios to create natural motions preserving the key movements of different music styles. We evaluate our method with three quantitative metrics of generative methods and a user study. The results suggest that the proposed GCN model outperforms the state-of-the-art dance generation method conditioned on music in different experiments. Moreover, our graph-convolutional approach is simpler, easier to be trained, and capable of generating more realistic motion styles regarding qualitative and different quantitative metrics. It also presented a visual movement perceptual quality comparable to real motion data. The dataset and project are publicly available at: https://www.verlab.dcc.ufmg.br/motion-analysis/cag2020.
Exploring non-Euclidean geometries is a common way for College Geometry instructors to highlight subtleties in Euclidean geometry. The concept of congruence, going undefined or informally defined in ...multiple axiomatic systems, is particularly susceptible to conflation with the idea of "same measure." Taxicab geometry provides a context in which congruence (defined as a relationship between figures that can be isometrically mapped to each other) and measure can be disambiguated by investigating the effects of transformations in both Euclidean and Taxicab geometry. This paper describes episodes from our classrooms in which students grappled with their understandings of congruence in Euclidean geometry while completing tasks involving Taxicab geometry.
Timely and reliable information sharing among autonomous vehicles (AVs) provides a promising approach for reducing traffic congestion and improving traffic efficiency in future intelligent ...transportation systems. In this paper, we consider millimeter-wave (mmWave) based multi-hop vehicle-to-vehicle (V2V) communications to facilitate ultra-reliable low-latency information sharing among AVs. We propose a novel framework for performance analysis and design of relay selection schemes in mmWave multi-hop V2V communications, while taking into account the mmWave signal propagation characteristics, road topology, and traffic conditions. In particular, considering the minimum tracking distance requirement of road traffic, the headway, i.e., the distance between adjacent AVs, is modeled as shifted-exponential distribution. Moreover, we model the communication path losses using the Manhattan distance metric in the taxicab geometry, which can more accurately capture the characteristics of mmWave signal propagation in urban grid roads than conventional Euclidean distance geometry. Based on the proposed model, we investigate the latency and reliability of mmWave multi-hop V2V communications for three widely adopted relay selection schemes, i.e., random with forward progress (RFP), most forward with fixed radius (MFR), and nearest with forward progress (NFP), respectively. Furthermore, we propose a novel relay selection scheme for joint optimization of the single-hop forward progress (FP) and single-hop latency according to the AVs' instantaneous locations and an estimate of the residual multi-hop latency. Simulation results show that, by balancing the current single-hop latency and the residual multi-hop latency for the multi-hop V2V network, the proposed relay selection scheme significantly outperforms the MFR, NFP and RFP in both multi-hop transmission latency and reliability of mmWave V2V communications.
Ramsey had shown that $\omega \longrightarrow (\omega )^m_n$ for all natural numbers m and n and Klein and Szekeres had shown in 1935 that among any five points in general position in the Euclidean ...plane there are four which are the corners of a convex quadrilateral. ...partition relations with infinite exponents as above only have content in absence of full $\mathsf {AC}$ . For the discussion the article will be quartered roughly into parts consisting of consecutive sections each which slightly deviates from the disection the author proposes; according to him, the whole article (minus its introduction) is divided in two parts, Sections 2–6 of the paper being concerned with the subject matter proper alluded to in the title whereas the penultimate and final section deal with $\infty $ -Borel-codes in $L(\mathbb {R})$ and results on the Vopénka-forcing by Woodin. Here a good coding system consists of a pointclass $\Gamma $ closed under both projection and continuous substitution and a decoding function d assigning to every real a subset of $\lambda \times \kappa $ and succeeding in decoding every function from $\lambda $ to $\kappa $ from some real. ...letting $\Delta := \{X \subset \mathbb {R} | \{X, \mathbb {R} \setminus X\} \subset \Gamma \}$ , the following shall be satisfied:
We study nonlocal operators acting on functions in the Euclidean space. The operators under consideration generate anisotropic jump processes, e.g., a jump process that behaves like a stable process ...in each direction but with a different index of stability. Its generator is the sum of one-dimensional fractional Laplace operators with different orders of differentiability. We study such operators in the general framework of bounded measurable coefficients. We prove a weak Harnack inequality and Hölder regularity results for solutions to corresponding integro-differential equations.
Compositional measurements from species assemblages define a high dimensional dataspace in which the data can form complex structures, termed manifolds. Comparing assemblages in this dataspace is ...difficult because the data is often sparse relative to its dimensionality and the complex structure of the manifold introduces bias and error in measurements of distance. Here, we apply diffusion maps, a manifold learning method, to find and characterize manifolds in high‐dimensional compositional data. We show that diffusion maps embed the data in reduced dimensions in which the Euclidean distance between data points approximates the distance between them along the manifold. This is especially useful when species turnover is high, as it provides a way to measure meaningful distances between assemblages even when they harbor disjoint sets of species. We anticipate diffusion maps will therefore be particularly useful for characterizing community change over large spatial and temporal scales.
PDF
