A semidefinite relaxation procedure for fault-tolerant observer design

A fault-tolerant observer design methodology is proposed. The aim is to guarantee a minimum level of closed-loop performance under all possible sensor fault combinations while optimizing performance under the nominal, fault-free condition. A novel approach is proposed to tackle the combinatorial nature of the problem, which is computationally intractable even for a moderate number of sensors, by recasting the problem as a robust performance problem, where the uncertainty set is composed of all combinations of a set of binary variables. A procedure based on an elimination lemma and an extension of a semidefinite relaxation procedure for binary variables is then used to derive sufficient conditions (necessary and sufficient in the case of one binary variable) for the solution of the problem which significantly reduces the number of matrix inequalities needed to solve the problem. The procedure is illustrated by considering a fault-tolerant observer switching scheme in which the observer outputs track the actual sensor fault condition. A numerical example from an electric power application is presented to illustrate the effectiveness of the design

Lyckliga Jim

For voice and piano. Plate number 541.https://scholarexchange.furman.edu/krohn-album3/1024/thumbnail.jp

Building invitro 3D human multicellular models of high-grade serous ovarian cancer.

Three-dimensional (3D), multicellular invitro models provide a useful platform for studying human cancer biology, particularly through deconvolution of the tumor microenvironment, or where animal models do not recapitulate the human condition. Here, we detail a protocol for building human multicellular models made of patient-derived primary cells and malignant cell lines, which recapitulate features of the tumor microenvironment. This protocol is optimized for building 3D models of high-grade serous ovarian cancer omental metastasis but can be adapted for modeling other cancers. For complete details on the use and execution of this profile, please refer to Delaine-Smith et al. (2021) and Malacrida et al. (2021)

Dynamical age differences among coeval star clusters as revealed by blue stragglers

Globular star clusters that formed at the same cosmic time may have evolved rather differently from a dynamical point of view (because that evolution depends on the internal environment) through a variety of processes that tend progressively to segregate stars more massive than the average towards the cluster centre. Therefore clusters with the same chronological age may have reached quite different stages of their dynamical history (that is, they may have different dynamical ages). Blue straggler stars have masses greater than those at the turn-off point on the main sequence and therefore must be the result of either a collision or a mass-transfer event. Because they are among the most massive and luminous objects in old clusters, they can be used as test particles with which to probe dynamical evolution. Here we report that globular clusters can be grouped into a few distinct families on the basis of the radial distribution of blue stragglers. This grouping corresponds well to an effective ranking of the dynamical stage reached by stellar systems, thereby permitting a direct measure of the cluster dynamical age purely from observed properties.Comment: Published on the 20 December 2012 issue of Natur

Two distinct sequences of blue straggler stars in the globular cluster M30

Stars in globular clusters are generally believed to have all formed at the same time, early in the Galaxy's history. 'Blue stragglers' are stars massive enough that they should have evolved into white dwarfs long ago. Two possible mechanisms have been proposed for their formation: mass transfer between binary companions and stellar mergers resulting from direct collisions between two stars. Recently, the binary explanation was claimed to be dominant. Here we report that there are two distinct parallel sequences of blue stragglers in M30. This globular cluster is thought to have undergone 'core collapse', during which both the collision rate and the mass transfer activity in binary systems would have been enhanced. We suggest that the two observed sequences arise from the cluster core collapse, with the bluer population arising from direct stellar collisions and the redder one arising from the evolution of close binaries that are probably still experiencing an active phase of mass transfer.Comment: Published on the 24th December 2009 issue of Natur

Ullemar's formula for the Jacobian of the complex moment mapping

The complex moment sequence m(P) is assigned to a univalent polynomial P by the Cauchy transform of the P(D), where D is the unit disk. We establish the representation of the Jacobian det dm(P) in terms of roots of the derivative P'. Combining this result with the special decomposition for the Hurwitz determinants, we prove a formula for the Jacobian which was previously conjectured by C. Ullemar. As a consequence, we show that the boundary of the class of all locally univalent polynomials in $U$ is contained in the union of three irreducible algebraic surfaces.Comment: 14 pages, submitted for "Complex Variables. Theory and Application