The Kitai criterion and backward shifts

It is proved that for any separable infinite dimensional Banach space X, there is a bounded linear operator T on X such that T satisfies the Kitai criterion. The proof is based on a quasisimilarity argument and on showing that I + T satisfies the Kitai criterion for certain backward weighted shifts T.

Shock avoidance by discrimination learning in the shore crab (Carcinus maenas) is consistent with a key criterion for pain

Nociception allows for immediate reflex withdrawal whereas pain allows for longer-term protection via rapid learning. We examine here whether shore crabs placed within a brightly lit chamber learn to avoid one of two dark shelters when that shelter consistently results in shock. Crabs were randomly selected to receive shock or not prior to making their first choice and were tested again over 10 trials. Those that received shock in trial 2, irrespective of shock in trial 1, were more likely to switch shelter choice in the next trial and thus showed rapid discrimination. During trial 1, many crabs emerged from the shock shelter and an increasing proportion emerged in later trials, thus avoiding shock by entering a normally avoided light area. In a final test we switched distinctive visual stimuli positioned above each shelter and/or changed the orientation of the crab when placed in the chamber for the test. The visual stimuli had no effect on choice, but crabs with altered orientation now selected the shock shelter, indicating that they had discriminated between the two shelters on the basis of movement direction. These data, and those of other recent experiments, are consistent with key criteria for pain experience and are broadly similar to those from vertebrate studies. © 2013. Published by The Company of Biologists Ltd.

An optimal algorithm for low power multiplierless FIR filter design using chebychev criterion

In this paper, we propose a novel finite impulse response (FIR) filter design methodology that reduces the number of operations with a motivation to reduce power consumption and enhance performance. The novelty of our approach lies in the generation of filter coefficients such that they conform to a given low-power architecture, while meeting the given filter specifications. The proposed algorithm is formulated as a mixed integer linear programming problem that minimizes chebychev error and synthesizes coefficients which consist of pre-specified alphabets. The new modified coefficients can be used for low-power VLSI implementation of vector scaling operations such as FIR filtering using computation sharing multiplier (CSHM). Simulations in 0.25um technology show that CSHM FIR filter architecture can result in 55% power and 34% speed improvement compared to carry save multiplier (CSAM) based filters.

Existence of disjoint weakly mixing operators that fail to satisfy the Disjoint Hypercyclicity Criterion

Recently, Bès, Martin, and Sanders [11] provided examples of disjoint hypercyclic operators which fail to satisfy the Disjoint Hypercyclicity Criterion. However, their operators also fail to be disjoint weakly mixing. We show that every separable, infinite dimensional Banach space admits operators T1,T2,…,TN with N⩾2 which are disjoint weakly mixing, and still fail to satisfy the Disjoint Hypercyclicity Criterion, answering a question posed in [11]. Moreover, we provide examples of disjoint hypercyclic operators T1, T2 whose corresponding set of disjoint hypercyclic vectors is nowhere dense, answering another question posed in [11]. In fact, we explicitly describe their set of disjoint hypercyclic vectors. Those same disjoint hypercyclic operators fail to be disjoint topologically transitive. Lastly, we create examples of two families of d-hypercyclic operators which fail to have any d-hypercyclic vectors in common.