Compact operators without extended eigenvalues

A complex number lambda is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT = lambda TX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

Extended electrochemical windows made accessible by room temperature ionic liquid/organic solvent electrolyte systems

The electrochemical windows of acetonitrile solutions doped with 0.1 m concentrations of several ionic liquids were examined by cyclic voltammetry at gold and platinum microelectrodes. These results were compared with those observed in the commonly used 0.1 m tetrabutylammonium perchlorate/acetonitrile system as well as with neat ionic liquids. The use of a trifluorotris(pentofluoroethyl)phosphate-based ionic liquid, specifically, as supporting electrolyte in acetonitrile solutions affords a wider anodic window, which is attributed to the high stability of the anionic component of these intrinsically conductive and thermally robust compounds.

Hoxa6 potentiates short-term hemopoietic cell proliferation and extended self-renewal.

Hemopoietic progenitor cells express clustered homeobox (Hox) genes in a pattern characteristic of their lineage and stage of differentiation. In general, HOX expression tends to be higher in more primitive and lower in lineage-committed cells. These trends have led to the hypothesis that self-renewal of hemopoietic stem/progenitor cells is HOX-dependent and that dysregulated HOX expression underlies maintenance of the leukemia-initiating cell. Gene expression profile studies support this hypothesis and specifically highlight the importance of the HOXA cluster in hemopoiesis and leukemogenesis. Within this cluster HOXA6 and HOXA9 are highly expressed in patients with acute myeloid leukemia and form part of the "Hox code" identified in murine models of this disease. We have examined endogenous expression of Hoxa6 and Hoxa9 in purified primary progenitors as well as four growth factor-dependent cell lines FDCP-Mix, EML, 32Dcl3, and Ba/F3, representative of early multipotential and later committed precursor cells respectively. Hoxa6 was consistently higher expressed than Hoxa9, preferentially expressed in primitive cells and was both growth-factor and cell-cycle regulated. Enforced overexpression of HOXA6 or HOXA9 in FDCP-Mix resulted in increased proliferation and colony formation but had negligible effect on differentiation. In both FDCP-Mix and the more committed Ba/F3 precursor cells overexpression of HOXA6 potentiated factor-independent proliferation. These findings demonstrate that Hoxa6 is directly involved in fundamental processes of hemopoietic progenitor cell development.

An extended framework for evidential reasoning systems.

Use of the Dempster-Shafer (D-S) theory of evidence to deal with uncertainty in knowledge-based systems has been widely addressed. Several AI implementations have been undertaken based on the D-S theory of evidence or the extended theory. But the representation of uncertain relationships between evidence and hypothesis groups (heuristic knowledge) is still a major problem. This paper presents an approach to representing such knowledge, in which Yen’s probabilistic multi-set mappings have been extended to evidential mappings, and Shafer’s partition technique is used to get the mass function in a complex evidence space. Then, a new graphic method for describing the knowledge is introduced which is an extension of the graphic model by Lowrance et al. Finally, an extended framework for evidential reasoning systems is specified.

Constructing probabilistic ATMS using extended incidence calculus

This paper discusses the relations between extended incidence calculus and assumption-based truth maintenance systems (ATMSs). We first prove that managing labels for statements (nodes) in an ATMS is equivalent to producing incidence sets of these statements in extended incidence calculus. We then demonstrate that the justification set for a node is functionally equivalent to the implication relation set for the same node in extended incidence calculus. As a consequence, extended incidence calculus can provide justifications for an ATMS, because implication relation sets are discovered by the system automatically. We also show that extended incidence calculus provides a theoretical basis for constructing a probabilistic ATMS by associating proper probability distributions on assumptions. In this way, we can not only produce labels for all nodes in the system, but also calculate the probability of any of such nodes in it. The nogood environments can also be obtained automatically. Therefore, extended incidence calculus and the ATMS are equivalent in carrying out inferences at both the symbolic level and the numerical level. This extends a result due to Laskey and Lehner.