A sequence π1,π2,… of permutations is said to be "quasirandom" if
the induced density of every permutation σ in πn converges to
1/∣σ∣! as n→∞. We prove that π1,π2,… is quasirandom
if and o...
Coarse and bi-Lipschitz embeddability of subspaces of the
Gromov-Hausdorff space into Hilbert spaces
March 8, 2023
Mathematics
Metric Geometry
In this paper, we discuss the embeddability of subspaces of the
Gromov-Hausdorff space, which consists of isometry classes of compact metric
spaces endowed with the Gromov-Hausdorff distance, into Hilbert spaces. These
embeddings are partic...
Einstein metrics on the Ten-Sphere
March 8, 2023
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Mathematics
Differential Geometry
We prove the existence of three non-round, non-isometric Einstein metrics
with positive scalar curvature on the sphere S10. Previously, the only
even-dimensional spheres known to admit non-round Einstein metrics were S6
and S8....
Efficient Visuo-Haptic Object Shape Completion for Robot Manipulation
March 8, 2023
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Computer Science
Robotics
For robot manipulation, a complete and accurate object shape is desirable.
Here, we present a method that combines visual and haptic reconstruction in a
closed-loop pipeline. From an initial viewpoint, the object shape is
reconstructed usin...
A spectral resolution of the large sieve
March 8, 2023
Mathematics
Number Theory
The quadratic form V(\varphi,Q)=\sum_{q\sim Q}\sum_{a\mod^*
q}|S(\varphi,a/q)|^2 and its eigenvalues are well understood when
Q=o(N), while V(φ,Q) is expected to behave like a Riemann sum
when N=o(Q). The behavior in th...
A Host--Kra F2ω-system of order 5 that is not
Abramov of order 5, and non-measurability of the inverse theorem for the
U6(F2n) norm
March 8, 2023
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Mathematics
Dynamical Systems
Combinatorics
It was conjectured by Bergelson, Tao, and Ziegler that every Host--Kra
Fpω-system of order k is an Abramov system of order k.
This conjecture has been verified for k≤p+1. In this paper we show that
the conjectu...
Quantum order by disorder in Frustrated Spin Nanotubes
March 8, 2023
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Physics
Strongly Correlated Electrons
We investigate quantum order by disorder in a frustrated spin nanotube formed
by wrapping a J1-J2 Heisenberg model at 45∘ around a cylinder.
Using Schwinger boson theory and Density Matrix Renormalization Group (DMRG),
we have ...
Time-Dependent Blackwell Approachability and Application to Absorbing
Games
March 8, 2023
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Mathematics
Computer Science
Optimization and Control
Computer Science and Game Theory
Machine Learning
Blackwell's approachability (Blackwell, 1954, 1956) is a very general online
learning framework where a Decision Maker obtains vector-valued outcomes, and
aims at the convergence of the average outcome to a given ``target'' set.
Blackwell g...
Graphically discrete groups and rigidity
March 8, 2023
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Mathematics
Group Theory
Geometric Topology
We introduce the notion of graphical discreteness to group theory. A finitely
generated group is graphically discrete if whenever it acts geometrically on a
locally finite graph, the automorphism group of the graph is
compact-by-discrete. N...
GRADE: Generating Realistic And Dynamic Environments for Robotics
Research with Isaac Sim
March 8, 2023
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Computer Science
Robotics
Synthetic data and novel rendering techniques have greatly influenced
computer vision research in tasks like target tracking and human pose
estimation. However, robotics research has lagged behind in leveraging it due
to the limitations of ...