An incremental approach to MSE-based feature selection

Feature selection plays an important role in classification systems. Using classifier error rate as the evaluation function, feature selection is integrated with incremental training. A neural network classifier is implemented with an incremental training approach to detect and discard irrelevant features. By learning attributes one after another, our classifier can find directly the attributes that make no contribution to classification. These attributes are marked and considered for removal. Incorporated with a Minimum Squared Error (MSE) based feature ranking scheme, four batch removal methods based on classifier error rate have been developed to discard irrelevant features. These feature selection methods reduce the computational complexity involved in searching among a large number of possible solutions significantly. Experimental results show that our feature selection methods work well on several benchmark problems compared with other feature selection methods. The selected subsets are further validated by a Constructive Backpropagation (CBP) classifier, which confirms increased classification accuracy and reduced training cost

Critical behaviours of contact near phase transitions

A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. It appears in universal relations among thermodynamic quantities, such as large momentum tails, energy, and dynamic structure factors, through the renowned Tan relations. However, a conceptual question remains open as to whether or not contact can signify phase transitions that are insensitive to short-range physics. Here we show that, near a continuous classical or quantum phase transition, contact exhibits a variety of critical behaviors, including scaling laws and critical exponents that are uniquely determined by the universality class of the phase transition and a constant contact per particle. We also use a prototypical exactly solvable model to demonstrate these critical behaviors in one-dimensional strongly interacting fermions. Our work establishes an intrinsic connection between the universality of dilute many-body systems and universal critical phenomena near a phase transition.Comment: Final version published in Nat. Commun. 5:5140 doi: 10.1038/ncomms6140 (2014

Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature

We study minimal hypersurfaces in manifolds of non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay at infinity. By comparison with capped spherical cones, we identify a precise borderline for the Ricci curvature decay. Above this value, no complete area-minimizing hypersurfaces exist. Below this value, in contrast, we construct examples.Comment: 31 pages. Comments are welcome