8,931 research outputs found
A combinatorial proof that Schubert vs. Schur coefficients are nonnegative
We give a combinatorial proof that the product of a Schubert polynomial by a
Schur polynomial is a nonnegative sum of Schubert polynomials. Our proof uses
Assaf's theory of dual equivalence to show that a quasisymmetric function of
Bergeron and Sottile is Schur-positive. By a geometric comparison theorem of
Buch and Mihalcea, this implies the nonnegativity of Gromov-Witten invariants
of the Grassmannian.Comment: 26 pages, several colored figure
PI-BA Bundle Adjustment Acceleration on Embedded FPGAs with Co-observation Optimization
Bundle adjustment (BA) is a fundamental optimization technique used in many
crucial applications, including 3D scene reconstruction, robotic localization,
camera calibration, autonomous driving, space exploration, street view map
generation etc. Essentially, BA is a joint non-linear optimization problem, and
one which can consume a significant amount of time and power, especially for
large optimization problems. Previous approaches of optimizing BA performance
heavily rely on parallel processing or distributed computing, which trade
higher power consumption for higher performance. In this paper we propose
{\pi}-BA, the first hardware-software co-designed BA engine on an embedded
FPGA-SoC that exploits custom hardware for higher performance and power
efficiency. Specifically, based on our key observation that not all points
appear on all images in a BA problem, we designed and implemented a
Co-Observation Optimization technique to accelerate BA operations with
optimized usage of memory and computation resources. Experimental results
confirm that {\pi}-BA outperforms the existing software implementations in
terms of performance and power consumption.Comment: in Proceedings of IEEE FCCM 201
Interpolated Schur multiple zeta values
Inspired by a recent work of M. Nakasuji, O. Phuksuwan and Y. Yamasaki we
combine interpolated multiple zeta values and Schur multiple zeta values into
one object, which we call interpolated Schur multiple zeta values. Our main
result will be a Jacobi-Trudi formula for a certain class of these new objects.
This generalizes an analogous result for Schur multiple zeta values and implies
algebraic relations between interpolated multiple zeta values.Comment: 21 page
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