Tail Inference for a Law in a Max-Semistable Domain of Attraction

2000 Mathematics Subject Classification: 62G32, 62G05.

On a Second Order Condition for Max-Semistable Laws

2000 Mathematics Subject Classification: 62G32, 62G20.

Stable MPC for tracking with maximal domain of attraction

In this work, a stable MPC that maximizes the domain of attraction of the closed-loop system is proposed. The proposed approach is suitable to real applications in the sense that it accounts for the case of output tracking, it is offset free if the output target is reachable and minimizes the offset if some of the constraints are active at steady state. The new approach is based on the definition of a Minkowski functional related to the input and terminal constraints of the stable infinite horizon MPC. It is also shown that the domain of attraction is defined by the system model and the constraints, and it does not depend on the controller tuning parameters. The proposed controller is illustrated with small order examples of the control literature. (C) 2011 Elsevier Ltd. All rights reserved.

Enlarging the domain of attraction of stable MPC controllers, maintaining the output performance

This work presents an alternative way to formulate the stable Model Predictive Control (MPC) optimization problem that allows the enlargement of the domain of attraction, while preserving the controller performance. Based on the dual MPC that uses the null local controller, it proposed the inclusion of an appropriate set of slacked terminal constraints into the control problem. As a result, the domain of attraction is unlimited for the stable modes of the system, and the largest possible for the non-stable modes. Although this controller does not achieve local optimality, simulations show that the input and output performances may be comparable to the ones obtained with the dual MPC that uses the LQR as a local controller. (C) 2009 Elsevier Ltd. All rights reserved.

An Extension of Estimation of Domain of Attraction for Fractional Order Linear System Subject to Saturation Control

This paper employs the Lyapunov direct method for the stability analysis of fractional order linear systems subject to input saturation. A new stability condition based on saturation function is adopted for estimating the domain of attraction via ellipsoid approach. To further improve this estimation, the auxiliary feedback is also supported by the concept of stability region. The advantages of the proposed method are twofold: (1) it is straightforward to handle the problem both in analysis and design because of using Lyapunov method, (2) the estimation leads to less conservative results. A numerical example illustrates the feasibility of the proposed method.

The Max Schling book of indoor gardening,

Mode of access: Internet.

A history of the mathematical theories of attraction and the figure of the earth from the time of Newton to that of Laplace.

Available on demand as hard copy or computer file from Cornell University Library.

Thought vibration; or, The law of attraction in the thought world,

Mode of access: Internet.

Functional Transfer Theorems for Maxima of Stationary Processes

2000 Mathematics Subject Classification: 60G70, 60F12, 60G10.

Structure of the N-terminal oligomerization domain of DnaD reveals a unique tetramerization motif and provides insights into scaffold formation

DnaD is a primosomal protein that remodels supercoiled plasmids. It binds to supercoiled forms and converts them to open forms without nicking. During this remodeling process, all the writhe is converted to twist and the plasmids are held around the periphery of large scaffolds made up of DnaD molecules. This DNA-remodeling function is the sum of a scaffold-forming activity on the N-terminal domain and a DNA-dependent oligomerization activity on the C-terminal domain. We have determined the crystal structure of the scaffold-forming N-terminal domain, which reveals a winged-helix architecture, with additional structural elements extending from both N- and C-termini. Four monomers form dimers that join into a tetramer. The N-terminal extension mediates dimerization and tetramerization, with extensive interactions and distinct interfaces. The wings and helices of the winged-helix domains remain exposed on the surface of the tetramer. Structure-guided mutagenesis and atomic force microscopy imaging indicate that these elements, together with the C-terminal extension, are involved in scaffold formation. Based upon our data, we propose a model for the DnaD-mediated scaffold formation.

Genetic variability and natural selection at the ligand domain of the Duffy binding protein in brazilian Plasmodium vivax populations

Background: Plasmodium vivax malaria is a major public health challenge in Latin America, Asia and Oceania, with 130-435 million clinical cases per year worldwide. Invasion of host blood cells by P. vivax mainly depends on a type I membrane protein called Duffy binding protein (PvDBP). The erythrocyte-binding motif of PvDBP is a 170 amino-acid stretch located in its cysteine-rich region II (PvDBP(II)), which is the most variable segment of the protein. Methods: To test whether diversifying natural selection has shaped the nucleotide diversity of PvDBP(II) in Brazilian populations, this region was sequenced in 122 isolates from six different geographic areas. A Bayesian method was applied to test for the action of natural selection under a population genetic model that incorporates recombination. The analysis was integrated with a structural model of PvDBP(II), and T-and B-cell epitopes were localized on the 3-D structure. Results: The results suggest that: (i) recombination plays an important role in determining the haplotype structure of PvDBP(II), and (ii) PvDBP(II) appears to contain neutrally evolving codons as well as codons evolving under natural selection. Diversifying selection preferentially acts on sites identified as epitopes, particularly on amino acid residues 417, 419, and 424, which show strong linkage disequilibrium. Conclusions: This study shows that some polymorphisms of PvDBP(II) are present near the erythrocyte-binding domain and might serve to elude antibodies that inhibit cell invasion. Therefore, these polymorphisms should be taken into account when designing vaccines aimed at eliciting antibodies to inhibit erythrocyte invasion.

Periodic-orbit analysis and scaling laws of intermingled basins of attraction in an ecological dynamical system

Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins of the other attractors. In order to investigate the occurrence of such phenomenon in dynamical systems of ecological interest (two-species competition with extinction) we have characterized quantitatively the intermingled basins using periodic-orbit theory and scaling laws. The latter results agree with a theoretical prediction from a stochastic model, and also with an exact result for the scaling exponent we derived for the specific class of models investigated. We discuss the consequences of the scaling laws in terms of the predictability of a final state (extinction of either species) in an ecological experiment.