A vision architecture for unconstrained and incremental learning of multiple categories

We present an integrated vision architecture capable of incrementally learning several visual categories based on natural hand-held objects. Additionally we focus on interactive learning, which requires real-time image processing methods and a fast learning algorithm. The overall system is composed of a figure-ground segregation part, several feature extraction methods and a life-long learning approach combining incremental learning with category-specific feature selection. In contrast to most visual categorization approaches, where typically each view is assigned to a single category, we allow labeling with an arbitrary number of shape and color categories. We also impose no restrictions on the viewing angle of presented objects, relaxing the common constraint on canonical views.     

On the Lifetime of Quasi-Stationary States in Non-Relativistic QED

We consider resonances in the Pauli–Fierz model of non-relativistic QED. We use and slightly modify the analysis developed by Bach, Fr?hlich, and Sigal [3, 4] to obtain an upper and lower bound on the lifetime of quasistationary states. Submitted: September 30, 2007. Accepted: March 28, 2008.     

Ground States in the Spin Boson Model

We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant λ. We show that the ground-state energy is an analytic function of λ and that the corresponding ground state can also be chosen to be an analytic function of λ. No infrared regularization is imposed. Our proof is based on a modified version of the BFS operator theoretic renormalization analysis. Moreover, using a positivity argument we prove that the ground state of the spin-boson model is unique. We show that the expansion coefficients of the ground state and the ground-state energy can be calculated using regular analytic perturbation theory.     

Anderson Localization at Band Edges for Random Magnetic Fields

We consider a magnetic Schrödinger operator in two dimensions. The magnetic field is given as the sum of a large and constant magnetic field and a random magnetic field. Moreover, we allow for an additional deterministic potential as well as a magnetic field which are both periodic. We show that the spectrum of this operator is contained in broadened bands around the Landau levels and that the edges of these bands consist of pure point spectrum with exponentially decaying eigenfunctions. The proof is based on a recent Wegner estimate obtained in Erd?s and Hasler (Commun. Math. Phys., preprint, arXiv:1012.5185) and a multiscale analysis.