Remark on algorithm 705

Remark on Hsu-Du New Algorithm for the LCS Problem

One of the time bounds claimed by Hsu and Du for the modification of Hirschberg's strategy set up by them is not correct. This is of some consequence, notably, it voids the claim, made else~ where in the same paper, that the proposed algorithm performs better than the Hunt-Szymanski's strategy in cases of sparse matches. In fact it is pointed out here tbat just the opposite is true. In addition...

A remark about orthogonal matching pursuit algorithm

In this note, we investigate the theoretical properties of Orthogonal Matching Pursuit (OMP), a class of decoder to recover sparse signal in compressed sensing. In particular, we show that the OMP decoder can give (p, q) instance optimality for a large class of encoders with 1 ≤ p ≤ q ≤ 2 and (p, q) 6= (2, 2). We also show that, if the encoding matrix is drawn from an appropriate distribution, ...

705 Grunfeld.qxd

Background. Routine follow-up of breast cancer patients in specialist clinics is standard practice in most countries. Follow-up involves regularly scheduled breast cancer check-ups during the disease-free period. The aims of follow-up are to detect breast cancer recurrence and to provide psychosocial support to the patient; however, little is known about patients’ views on breast cancer follow-...

Remark on Taylor's Formula

does not contain any point of Er other than p. Cp(r]) is defined as in (5). From this it can be shown that Er has finite (n —1)-dimensional measure. Let us not assume now that r is large. We then write E = UjLxE^ where the E's are closed and their diameter is less than €. Then, by what has been shown before, if e is small enough Ef* has finite (w —1)-dimensional measure. Clearly ErCUjLxE?^'. Bu...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem