563 research outputs found
Suzuki equations and integrals of motion for supersymmetric CFT
Using equations proposed by J. Suzuki we compute numerically the first three
integrals of motion for supersymmetric CFT. Our computation agrees with
the results of ODE-CFT correspondence which was explained in a more general
context by S. Lukyanov.Comment: 11 page
One point functions of fermionic operators in the Super Sine Gordon model
We describe the integrable structure of the space of local operators for the
supersymmetric sine-Gordon model. Namely, we conjecture that this space is
created by acting on the primary fields by fermions and a Kac-Moody current. We
proceed with the computation of the one-point functions. In the UV limit they
are shown to agree with the alternative results obtained by solving the
reflection relations.Comment: 34 pages, two figure
Fermion-current basis and correlation functions for the integrable spin 1 chain
We use the fermion-current basis in the space of local operators for the
computation of the expectation values for the integrable spin chain of spins 1.
Our main tool consists in expressing a given local operators in the
fermion-current basis. For this we use the same method as in the spin 1/2 case
which is based on the arbitrariness of the Matsubara data.Comment: 12 page
Asymptotic description of solutions of the exterior Navier Stokes problem in a half space
We consider the problem of a body moving within an incompressible fluid at
constant speed parallel to a wall, in an otherwise unbounded domain. This
situation is modeled by the incompressible Navier-Stokes equations in an
exterior domain in a half space, with appropriate boundary conditions on the
wall, the body, and at infinity. We focus on the case where the size of the
body is small. We prove in a very general setup that the solution of this
problem is unique and we compute a sharp decay rate of the solution far from
the moving body and the wall
Formulation of the uncertainty relations in terms of the Renyi entropies
Quantum mechanical uncertainty relations for position and momentum are
expressed in the form of inequalities involving the Renyi entropies. The proof
of these inequalities requires the use of the exact expression for the
(p,q)-norm of the Fourier transformation derived by Babenko and Beckner.
Analogous uncertainty relations are derived for angle and angular momentum and
also for a pair of complementary observables in N-level systems. All these
uncertainty relations become more attractive when expressed in terms of the
symmetrized Renyi entropies
The Hilbert-Schmidt Theorem Formulation of the R-Matrix Theory
Using the Hilbert-Schmidt theorem, we reformulate the R-matrix theory in
terms of a uniformly and absolutely convergent expansion. Term by term
differentiation is possible with this expansion in the neighborhood of the
surface. Methods for improving the convergence are discussed when the
R-function series is truncated for practical applications.Comment: 16 pages, Late
Long-Term Visual Object Tracking Benchmark
We propose a new long video dataset (called Track Long and Prosper - TLP) and
benchmark for single object tracking. The dataset consists of 50 HD videos from
real world scenarios, encompassing a duration of over 400 minutes (676K
frames), making it more than 20 folds larger in average duration per sequence
and more than 8 folds larger in terms of total covered duration, as compared to
existing generic datasets for visual tracking. The proposed dataset paves a way
to suitably assess long term tracking performance and train better deep
learning architectures (avoiding/reducing augmentation, which may not reflect
real world behaviour). We benchmark the dataset on 17 state of the art trackers
and rank them according to tracking accuracy and run time speeds. We further
present thorough qualitative and quantitative evaluation highlighting the
importance of long term aspect of tracking. Our most interesting observations
are (a) existing short sequence benchmarks fail to bring out the inherent
differences in tracking algorithms which widen up while tracking on long
sequences and (b) the accuracy of trackers abruptly drops on challenging long
sequences, suggesting the potential need of research efforts in the direction
of long-term tracking.Comment: ACCV 2018 (Oral
PinnerSage: Multi-Modal User Embedding Framework for Recommendations at Pinterest
Latent user representations are widely adopted in the tech industry for
powering personalized recommender systems. Most prior work infers a single high
dimensional embedding to represent a user, which is a good starting point but
falls short in delivering a full understanding of the user's interests. In this
work, we introduce PinnerSage, an end-to-end recommender system that represents
each user via multi-modal embeddings and leverages this rich representation of
users to provides high quality personalized recommendations. PinnerSage
achieves this by clustering users' actions into conceptually coherent clusters
with the help of a hierarchical clustering method (Ward) and summarizes the
clusters via representative pins (Medoids) for efficiency and interpretability.
PinnerSage is deployed in production at Pinterest and we outline the several
design decisions that makes it run seamlessly at a very large scale. We conduct
several offline and online A/B experiments to show that our method
significantly outperforms single embedding methods.Comment: 10 pages, 7 figure
Separating Hierarchical and General Hub Labelings
In the context of distance oracles, a labeling algorithm computes vertex
labels during preprocessing. An query computes the corresponding distance
from the labels of and only, without looking at the input graph. Hub
labels is a class of labels that has been extensively studied. Performance of
the hub label query depends on the label size. Hierarchical labels are a
natural special kind of hub labels. These labels are related to other problems
and can be computed more efficiently. This brings up a natural question of the
quality of hierarchical labels. We show that there is a gap: optimal
hierarchical labels can be polynomially bigger than the general hub labels. To
prove this result, we give tight upper and lower bounds on the size of
hierarchical and general labels for hypercubes.Comment: 11 pages, minor corrections, MFCS 201
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