Positivity-preserving H∞ model reduction for positive systems

This is the post-print version of the Article - Copyright @ 2011 ElevierThis paper is concerned with the model reduction of positive systems. For a given stable positive system, our attention is focused on the construction of a reduced-order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed H∞ performance. Based upon a system augmentation approach, a novel characterization on the stability with H∞ performance of the error system is first obtained in terms of linear matrix inequality (LMI). Then, a necessary and sufficient condition for the existence of a desired reduced-order model is derived accordingly. Furthermore, iterative LMI approaches with primal and dual forms are developed to solve the positivity-preserving H∞ model reduction problem. Finally, a compartmental network is provided to show the effectiveness of the proposed techniques.The work was partially supported by GRF HKU 7137/09E

Block type symmetry of bigraded Toda Hierarchy

In this paper, we define Orlov-Schulman's operators $M_L$, $M_R$, and then use them to construct the additional symmetries of the bigraded Toda hierarchy (BTH). We further show that these additional symmetries form an interesting infinite dimensional Lie algebra known as a Block type Lie algebra, whose structure theory and representation theory have recently received much attention in literature. By acting on two different spaces under the weak W-constraints we find in particular two representations of this Block type Lie algebra.Comment: 30 pages, accepted by Journal of Mathematical Physic

The Bloch-Okounkov correlation functions of classical type

Bloch and Okounkov introduced an n-point correlation function on the infinite wedge space and found an elegant closed formula in terms of theta functions. This function has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, etc, and it can also be interpreted as correlation functions on integrable gl_\infty-modules of level one. Such gl_\infty-correlation functions at higher levels were then calculated by Cheng and Wang. In this paper, generalizing the type A results, we formulate and determine the n-point correlation functions in the sense of Bloch-Okounkov on integrable modules over classical Lie subalgebras of gl_\infty of type B,C,D at arbitrary levels. As byproducts, we obtain new q-dimension formulas for integrable modules of type B,C,D and some fermionic type q-identities.Comment: v2, very minor changes, Latex, 41 pages, to appear in Commun. Math. Phy

Growth and properties of few-layer graphene prepared by chemical vapor deposition

The structure, and electrical, mechanical and optical properties of few-layer graphene (FLG) synthesized by chemical vapor deposition (CVD) on a Ni coated substrate were studied. Atomic resolution transmission electron microscope (TEM) images show highly crystalline single layer parts of the sample changing to multilayer domains where crystal boundaries are connected by chemical bonds. This suggests two different growth mechanisms. CVD and carbon segregation participate in the growth process and are responsible for the different structural formations found. Measurements of the electrical and mechanical properties on the centimeter scale provide evidence of a large scale structural continuity: 1) in the temperature dependence of the electrical conductivity, a non-zero value near 0 K indicates the metallic character of electronic transport; 2) the Young's modulus of a pristine polycarbonate film (1.37 GPa) improves significantly when covered with FLG (1.85 GPa). The latter indicates an extraordinary Young modulus value of the FLG-coating of TPa orders of magnitude. Raman and optical spectroscopy support the previous conclusions. The sample can be used as a flexible and transparent electrode and is suitable for special membranes to detect and study individual molecules in high resolution TEM

Building efficient and flexible feature-based indices

If database management systems are to play an important role in CAD/CAM technologies, building engineering indices must be a primary task even though it is beyond conventional database practice. Information regarding design semantics or functionalities is often embedded in the geometric description of design objects, and is therefore not directly available for indexing. Presented in this paper is an efficient and flexible indexing mechanism for retrieving design objects that possess similar design features as described by the user. The underlying database is composed of rotational objects represented by constructive solid geometry (CSG). Although domain-specific representation schemes and algorithms are involved, the main objective of this paper is to emphasize the importance of engineering indices and to illustrate the effort required to build as well as to use such indices.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28912/1/0000749.pd

Poisson-Lie group of pseudodifferential symbols

We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators on the line and the circle (with scalar or matrix coefficients). This defines a Poisson--Lie structure on the dual group of pseudodifferential symbols of an arbitrary real (or complex) order. We show that the usual (second) Benney, KdV (or GL_n--Adler--Gelfand--Dickey) and KP Poisson structures are naturally realized as restrictions of this Poisson structure to submanifolds of this ``universal'' Poisson--Lie group. Moreover, the reduced (=SL_n) versions of these manifolds (W_n-algebras in physical terminology) can be viewed as subspaces of the quotient (or Poisson reduction) of this Poisson--Lie group by the dressing action of the group of functions. Finally, we define an infinite set of functions in involution on the Poisson--Lie group that give the standard families of Hamiltonians when restricted to the submanifolds mentioned above. The Poisson structure and Hamiltonians on the whole group interpolate between the Poisson structures and Hamiltonians of Benney, KP and KdV flows. We also discuss the geometrical meaning of W_\infty as a limit of Poisson algebras W_\epsilon as \epsilon goes to 0.Comment: 64 pages, no figure

KATP channels in the nodose ganglia mediate the orexigenic actions of ghrelin

Ghrelin is the only known hunger signal derived from the peripheral tissues. Ghrelin overcomes the satiety signals evoked by anorexigenic molecules, such as cholecystokinin (CCK) and leptin, to stimulate feeding. The mechanisms by which ghrelin reduces the sensory signals evoked by anorexigenic hormones, which act via the vagus nerve to stimulate feeding, are unknown. Patch clamp recordings of isolated rat vagal neurons show that ghrelin hyperpolarizes neurons by activating K+ conductance. Administering a KATP channel antagonist or silencing Kir6.2, a major subunit of the KATP channel, abolished ghrelin inhibition in vitro and in vivo. Patch clamp studies show that ghrelin inhibits currents evoked by leptin and CCK‐8, which operate through independent ionic channels. The inhibitory actions of ghrelin were abolished by treating the vagal ganglia neurons with pertussis toxin, as well as phosphatidylinositol 3‐kinase (PI3K) or extracellular signal‐regulated kinase 1 and 2 (Erk1/2) small interfering RNA. In vivo gene silencing of PI3K and Erk1/2 in the nodose ganglia prevented ghrelin inhibition of leptin‐ or CCK‐8‐evoked vagal firing. Feeding experiments showed that silencing Kir6.2 in the vagal ganglia abolished the orexigenic actions of ghrelin. These data indicate that ghrelin modulates vagal ganglia neuron excitability by activating KATP conductance via the growth hormone secretagogue receptor subtype 1a–Gαi–PI3K–Erk1/2–KATP pathway. The resulting hyperpolarization renders the neurons less responsive to signals evoked by anorexigenic hormones. This provides a mechanism to explain the actions of ghrelin with respect to overcoming anorexigenic signals that act via the vagal afferent pathways.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/113677/1/tjp6781.pd

Temporal Database Architecture Enhancements

Database systems used in the past were characterized by storing only current valid states., which is not., however., optimal for intelligent systems and applications. Temporal paradigm allows us to delimit the object state with the time validity regarding the modeled granularity. Temporal systems are based on the extension of conventional approaches., which do not provide powerful solutions. Database server architecture is described with emphasis on the optimization options to improve and shorten the data retrieval process. In this paper., we attach significance to the migrated row., which forces the system to load multiple data blocks from the database into the memory. The solution., based on the evolution steps., is implemented using the mapping module inside the memory of the database instance

Carbonylation of Csp3−H Bonds through Oxidative Wittig‐Type Reaction: An Unprecedented Version of Wittig Reaction

A Wittig‐type reaction was achieved by radical cation salt induced aerobic oxidation of Csp3−H bonds. Different from the “standard” version of the Wittig reaction, in which a carbon‐carbon double bond is formed from a carbonyl, carbonyl groups can be installed by similar process.Not from carbonyls but to carbonyls: A Wittig‐type reaction was achieved by radical cation salt induced aerobic oxidation of sp3 C−H bonds. Different from the “standard” version of the Wittig reaction, in which a carbon‐carbon double bond is formed from a carbonyl, carbonyl groups can be installed by similar process.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137437/1/ajoc201600055-sup-0001-misc_information.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137437/2/ajoc201600055.pd