New bounds on the Lieb-Thirring constants

Improved estimates on the constants $L_{\gamma,d}$, for $1/2<\gamma<3/2$, $d\in N$ in the inequalities for the eigenvalue moments of Schr\"{o}dinger operators are established

Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

We find a Hermite-type basis for which the eigenvalue problem associated to the operator $H_{A,B}:=B(-\partial_x^2)+Ax^2$ acting on $L^2({\bf R};{\bf C}^2)$ becomes a three-terms recurrence. Here $A$ and $B$ are two constant positive definite matrices with no other restriction. Our main result provides an explicit characterization of the eigenvectors of $H_{A,B}$ that lie in the span of the first four elements of this basis when $AB\not= BA$.Comment: 11 pages, 1 figure. Some typos where corrected in this new versio

Many Particle Hardy-Inequalities

In this paper we prove three differenttypes of the so-called many-particle Hardy inequalities. One of them is a "classical type" which is valid in any dimesnion $d\neq 2$. The second type deals with two-dimensional magnetic Dirichlet forms where every particle is supplied with a soplenoid. Finally we show that Hardy inequalities for Fermions hold true in all dimensions.Comment: 20 page

Much Ado About Time: Exhaustive Annotation of Temporal Data

Large-scale annotated datasets allow AI systems to learn from and build upon the knowledge of the crowd. Many crowdsourcing techniques have been developed for collecting image annotations. These techniques often implicitly rely on the fact that a new input image takes a negligible amount of time to perceive. In contrast, we investigate and determine the most cost-effective way of obtaining high-quality multi-label annotations for temporal data such as videos. Watching even a short 30-second video clip requires a significant time investment from a crowd worker; thus, requesting multiple annotations following a single viewing is an important cost-saving strategy. But how many questions should we ask per video? We conclude that the optimal strategy is to ask as many questions as possible in a HIT (up to 52 binary questions after watching a 30-second video clip in our experiments). We demonstrate that while workers may not correctly answer all questions, the cost-benefit analysis nevertheless favors consensus from multiple such cheap-yet-imperfect iterations over more complex alternatives. When compared with a one-question-per-video baseline, our method is able to achieve a 10% improvement in recall 76.7% ours versus 66.7% baseline) at comparable precision (83.8% ours versus 83.0% baseline) in about half the annotation time (3.8 minutes ours compared to 7.1 minutes baseline). We demonstrate the effectiveness of our method by collecting multi-label annotations of 157 human activities on 1,815 videos.Comment: HCOMP 2016 Camera Read

Stability of the magnetic Schr\"odinger operator in a waveguide

The spectrum of the Schr\"odinger operator in a quantum waveguide is known to be unstable in two and three dimensions. Any enlargement of the waveguide produces eigenvalues beneath the continuous spectrum. Also if the waveguide is bent eigenvalues will arise below the continuous spectrum. In this paper a magnetic field is added into the system. The spectrum of the magnetic Schr\"odinger operator is proved to be stable under small local deformations and also under small bending of the waveguide. The proof includes a magnetic Hardy-type inequality in the waveguide, which is interesting in its own