Characterization of Birkhoff-James orthogonality

The Birkhoff-James orthogonality is a generalization of Hilbert space orthogonality to Banach spaces. We investigate this notion of orthogonality when the Banach space has more structures. We start by doing so for the Banach space of square matrices moving gradually to all bounded operators on any Hilbert space, then to an arbitrary C*-algebra and finally a Hilbert C*-module.

Analysis of the Genome and Transcriptome of Cryptococcus neoformans var. grubii Reveals Complex RNA Expression and Microevolution Leading to Virulence Attenuation

Cryptococcus neoformans is a pathogenic basidiomycetous yeast responsible for more than 600,000 deaths each year. It occurs as two serotypes (A and D) representing two varieties (i.e. grubii and neoformans, respectively). Here, we sequenced the genome and performed an RNA-Seq-based analysis of the C. neoformans var. grubii transcriptome structure. We determined the chromosomal locations, analyzed the sequence/structural features of the centromeres, and identified origins of replication. The genome was annotated based on automated and manual curation. More than 40,000 introns populating more than 99% of the expressed genes were identified. Although most of these introns are located in the coding DNA sequences (CDS), over 2,000 introns in the untranslated regions (UTRs) were also identified. Poly(A)-containing reads were employed to locate the polyadenylation sites of more than 80% of the genes. Examination of the sequences around these sites revealed a new poly(A)-site-associated motif (AUGHAH). In addition, 1,197 miscRNAs were identified. These miscRNAs can be spliced and/or polyadenylated, but do not appear to have obvious coding capacities. Finally, this genome sequence enabled a comparative analysis of strain H99 variants obtained after laboratory passage. The spectrum of mutations identified provides insights into the genetics underlying the micro-evolution of a laboratory strain, and identifies mutations involved in stress responses, mating efficiency, and virulence.

Single network adaptive critic aided dynamic inversion for optimal regulation and command tracking with online adaptation for enhanced robustness

To combine the advantages of both stability and optimality-based designs, a single network adaptive critic (SNAC) aided nonlinear dynamic inversion approach is presented in this paper. Here, the gains of a dynamic inversion controller are selected in such a way that the resulting controller behaves very close to a pre-synthesized SNAC controller in the output regulation sense. Because SNAC is based on optimal control theory, it makes the dynamic inversion controller operate nearly optimal. More important, it retains the two major benefits of dynamic inversion, namely (i) a closed-form expression of the controller and (ii) easy scalability to command tracking applications without knowing the reference commands a priori. An extended architecture is also presented in this paper that adapts online to system modeling and inversion errors, as well as reduced control effectiveness, thereby leading to enhanced robustness. The strengths of this hybrid method of applying SNAC to optimize an nonlinear dynamic inversion controller is demonstrated by considering a benchmark problem in robotics, that is, a two-link robotic manipulator system. Copyright (C) 2013 John Wiley & Sons, Ltd.

Adaptive Flight-Control Design Using Neural-Network-Aided Optimal Nonlinear Dynamic Inversion

A neural-network-aided nonlinear dynamic inversion-based hybrid technique of model reference adaptive control flight-control system design is presented in this paper. Here, the gains of the nonlinear dynamic inversion-based flight-control system are dynamically selected in such a manner that the resulting controller mimics a single network, adaptive control, optimal nonlinear controller for state regulation. Traditional model reference adaptive control methods use a linearized reference model, and the presented control design method employs a nonlinear reference model to compute the nonlinear dynamic inversion gains. This innovation of designing the gain elements after synthesizing the single network adaptive controller maintains the advantages that an optimal controller offers, yet it retains a simple closed-form control expression in state feedback form, which can easily be modified for tracking problems without demanding any a priori knowledge of the reference signals. The strength of the technique is demonstrated by considering the longitudinal motion of a nonlinear aircraft system. An extended single network adaptive control/nonlinear dynamic inversion adaptive control design architecture is also presented, which adapts online to three failure conditions, namely, a thrust failure, an elevator failure, and an inaccuracy in the estimation of C-M alpha. Simulation results demonstrate that the presented adaptive flight controller generates a near-optimal response when compared to a traditional nonlinear dynamic inversion controller.

An estimate of the number of tropical tree species

The high species richness of tropical forests has long been recognized, yet there remains substantial uncertainty regarding the actual number of tropical tree species. Using a pantropical tree inventory database from closed canopy forests, consisting of 657,630 trees belonging to 11,371 species, we use a fitted value of Fisher's alpha and an approximate pantropical stem total to estimate the minimum number of tropical forest tree species to fall between similar to 40,000 and similar to 53,000, i.e., at the high end of previous estimates. Contrary to common assumption, the Indo-Pacific region was found to be as species-rich as the Neotropics, with both regions having a minimum of similar to 19,000-25,000 tree species. Continental Africa is relatively depauperate with a minimum of similar to 4,500-6,000 tree species. Very few species are shared among the African, American, and the Indo-Pacific regions. We provide a methodological framework for estimating species richness in trees that may help refine species richness estimates of tree-dependent taxa.