Strong Converse Results for Linking Operators and Convex Functions

We consider a family B n , ρ c of operators which is a link between classical Baskakov operators (for ρ = ∞ ) and their genuine Durrmeyer type modification (for ρ = 1 ). First, we prove that for fixed n , c and a fixed convex function f , B n , ρ c f is decreasing with respect to ρ . We give two proofs, using various probabilistic considerations. Then, we combine this property with some existing direct and strong converse results for classical operators, in order to get such results for the operators B n , ρ c applied to convex functions.

Multilevel Diversity Coding with Secure Regeneration: Separate Coding Achieves the MBR Point

The problem of multilevel diversity coding with secure regeneration (MDC-SR) is considered, which includes the problems of multilevel diversity coding with regeneration (MDC-R) and secure regenerating code (SRC) as special cases. Two outer bounds are established, showing that separate coding can achieve the minimum-bandwidth-regeneration (MBR) point of the achievable normalized storage-capacity repair-bandwidth trade-off regions for the general MDC-SR problem. The core of the new converse results is an exchange lemma, which can be established using Han’s subset inequality.

Interference in memory for pitch-only and rhythm-only sequences

In human memory, the ability to recognize a previously encountered stimulus often undergoes cumulative interference when the number of intervening items between its first and second presentation increases. Although this is a common effect in many domains, melodies composed in tuning systems familiar to participants (e.g., Western tonal music) do not seem to suffer such cumulative decrements in recognition performance. Interestingly, melodies in unfamiliar tuning systems do show cumulative decrements. This finding has been predicted by a novel Regenerative Multiple Representations (RMR) conjecture. The present study further explores this phenomenon and the conjecture by investigating pitch-only (isochronous rhythm) and rhythm-only (monotone pitch) sequences of melodies in an unfamiliar tuning system that previously showed cumulative disruptive effects. Experiment 1 replicated previous studies reporting significant interference effects from the number of intervening items when melodies use uncommon rhythms and are composed in an unfamiliar tuning system. Furthermore, as predicted by the RMR conjecture, when rhythmic information was neutralized (Experiment 2), the cumulative interference related to the number of intervening items was retained. This was also the case when the original pitch information of each melody was neutralized, leaving variation only in the rhythmic information (Experiment 3). Results are discussed in the context of the RMR conjecture: given converse results, the conjecture would have been falsified. However, it currently remains plausible and appears to be a useful tool for precise predictions about the link between prior experience, perception, and formation of new memories.

Left-right fredholm and left-right browder linear relations

In this paper we introduce the notions of left (resp. right) Fredholm and left (resp. right) Browder linear relations. We construct a Kato-type decomposition of such linear relations. The results are then applied to give another decomposition of a left (resp. right) Browder linear relation T in a Banach space as an operator-like sum T = A + B, where A is an injective left (resp. a surjective right) Fredholm linear relation and B is a bounded finite rank operator with certain properties of commutativity. The converse results remain valid with certain conditions of commutativity. As a consequence, we infer the characterization of left (resp. right) Browder spectrum under finite rank operator.