The paper is concerned with two-class active learning. While the common approach for collecting data in active learning is to select samples close to the classification boundary, better performance can be achieved by taking into account the prior data distribution. The main contribution of the paper is a formal framework that incorporates clustering into active learning. The algorithm first constructs a classifier on the set of the cluster representatives, and then propagates the classification decision to the other samples via a local noise model. The proposed model allows to select the most representative samples as well as to avoid repeatedly labeling samples in the same cluster. During the active learning process, the clustering is adjusted using the coarse-to-fine strategy in order to balance between the advantage of large clusters and the accuracy of the data representation. The results of experiments in image databases show a better performance of our algorithm compared to the current methods.

Derivation of effective zero-range one-dimensional (1D) interactions between atoms in tight waveguides is reviewed, as is the Fermi-Bose mapping method for determination of exact and stronglycorrelated many-body ground states of ultracold bosonic and fermionic atomic vapors in such waveguides, including spin degrees of freedom. Odd-wave 1D interactions derived from 3D p-wave scattering are included as well as the usual even-wave interactions derived from 3D s-wave scattering, with emphasis on the role of 3D Feshbach resonances for selectively enhancing s-wave or p-wave scattering so as to reach 1D confinement-induced resonances of the even and odd-wave interactions. A duality between 1D fermions and bosons with zero-range interactions suggested by Cheon and Shigehara is shown to hold for the effective 1D dynamics of a spinor Fermi gas with both even and odd-wave interactions and that of a spinor Bose gas with even and odd-wave interactions, with even(odd)-wave Bose coupling constants inversely related to odd(even)-wave Fermi coupling constants. Some recent applications of Fermi-Bose mapping to determination of many-body ground states of Bose gases and of both magnetically trapped, spin-aligned and optically trapped, spin-free Fermi gases are described, and a new generalized Fermi-Bose mapping is used to determine the phase diagram of ground-state total spin of the spinor Fermi gas as a function of its even and odd-wave coupling constants.

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We propose a new method for object tracking in image sequences using template matching. To update the template, appearance features are smoothed temporally by robust Kalman filters, one to each pixel. The resistance of the resulting template to partial occlusions enables the accurate detection and handling of more severe occlusions. Abrupt changes of lighting conditions can also be handled, especially when photometric invariant color features are used. The method has only a few parameters and is computationally fast enough to track objects in real time.

This paper conceives of tracking as the developing distinction of a foreground against the background. In this manner, fast changes in the object or background appearance can be dealt with. When modelling the target alone (and not its distinction from the background), changes of lighting or changes of viewpoint can invalidate the internal target model. As the main contribution, we propose a new model for the detection of the target using foreground/background texture discrimination. The background is represented as a set of texture patterns. During tracking, the algorithm maintains a set of discriminant functions each distinguishing one pattern in the object region from background patterns in the neighborhood of the object. The idea is to train the foreground/background discrimination dynamically, that is while the tracking develops. In our case, the discriminant functions are efficiently trained online using a differential version of Linear Discriminant Analysis (LDA). Object detection is performed by maximizing the sum of all discriminant functions. The method employs two complementary sources of information: it searches for the image region similar to the target object, and simultaneously it seeks to avoid background patterns seen before. The detection result is therefore less sensitive to sudden changes in the appearance of the object than in methods relying solely on similarity to the target. The experiments show robust performance under severe changes of viewpoint or abrupt changes of lighting.