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 $N=1$ 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 $s,t$ query computes the corresponding distance from the labels of $s$ and $t$ 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