A characterization of Schauder frames which are near-Schauder bases

A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we give a solution to this problem using the notion of the minimal-associated sequence spaces and the minimal-associated reconstruction operators for Schauder frames. We prove that a Schauder frame is a near-Schauder basis if and only if the kernel of the minimal-associated reconstruction operator contains no copy of $c_0$. In particular, a Schauder frame of a Banach space with no copy of $c_0$ is a near-Schauder basis if and only if the minimal-associated sequence space contains no copy of $c_0$. In these cases, the minimal-associated reconstruction operator has a finite dimensional kernel and the dimension of the kernel is exactly the excess of the near-Schauder basis. Using these results, we make related applications on Besselian frames and near-Riesz bases.Comment: 12 page

Critical angles in angular dependent magnetization reversal of exchange biased Co/FeMn bilayers

Magnetization reversal behavior in the exchange biased Co/FeMn bilayers with collinearly aligned ferromagnetic (FM) intrinsic anisotropy and induced interfacial anisotropy was investigated by angular resolved magnetic hysteresis loops measurements, and special attention was paid to the magnetization signals recorded perpendicular to the external magnetic field direction (My). During the angular magnetization reversal process, two critical angles were clearly observed. Around the easy axis, the magnetization reverses in a full circle, i.e., two My peaks appear with opposite signs. In contrast, above a certain critical angle αc1, the magnetization reverses only in one semicircle, i.e., My always remains positive or negative. Above another critical angle αc2, the heights of the two My peaks becomes equivalent. The angular dependence of exchange bias (ADEB) was also carefully investigated. In order to understand the experimental reversal behaviors clearly, numerical simulations were performed based on a modified Stoner-Wohlfarth (S-W) model considering the collinear anisotropies in current samples. The calculated results unambiguously show that the angular dependent reversal behavior as well as the occurrence of two critical angles is originated from the strength competition between the FM intrinsic anisotropy and the field cool induced interfacial exchange anisotropy

Speed up interactive image retrieval

In multimedia retrieval, a query is typically interactively refined towards the “optimal” answers by exploiting user feedback. However, in existing work, in each iteration, the refined query is re-evaluated. This is not only inefficient but fails to exploit the answers that may be common between iterations. Furthermore, it may also take too many iterations to get the “optimal” answers. In this paper, we introduce a new approach called OptRFS (optimizing relevance feedback search by query prediction) for iterative relevance feedback search. OptRFS aims to take users to view the “optimal” results as fast as possible. It optimizes relevance feedback search by both shortening the searching time during each iteration and reducing the number of iterations. OptRFS predicts the potential candidates for the next iteration and maintains this small set for efficient sequential scan. By doing so, repeated candidate accesses (i.e., random accesses) can be saved, hence reducing the searching time for the next iteration. In addition, efficient scan on the overlap before the next search starts also tightens the search space with smaller pruning radius. As a step forward, OptRFS also predicts the “optimal” query, which corresponds to “optimal” answers, based on the early executed iterations’ queries. By doing so, some intermediate iterations can be saved, hence reducing the total number of iterations. By taking the correlations among the early executed iterations into consideration, OptRFS investigates linear regression, exponential smoothing and linear exponential smoothing to predict the next refined query so as to decide the overlap of candidates between two consecutive iterations. Considering the special features of relevance feedback, OptRFS further introduces adaptive linear exponential smoothing to self-adjust the parameters for more accurate prediction. We implemented OptRFS and our experimental study on real life data sets show that it can reduce the total cost of relevance feedback search significantly. Some interesting features of relevance feedback search are also discovered and discussed