K-Theory of non-linear projective toric varieties

We define a category of quasi-coherent sheaves of topological spaces on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.

A comprehensive comparison between generalized incidence calculus and Dempster-Shafer theory of evidence.

Dealing with uncertainty problems in intelligent systems has attracted a lot of attention in the AI community. Quite a few techniques have been proposed. Among them, the Dempster-Shafer theory of evidence (DS theory) has been widely appreciated. In DS theory, Dempster's combination rule plays a major role. However, it has been pointed out that the application domains of the rule are rather limited and the application of the theory sometimes gives unexpected results. We have previously explored the problem with Dempster's combination rule and proposed an alternative combination mechanism in generalized incidence calculus. In this paper we give a comprehensive comparison between generalized incidence calculus and the Dempster-Shafer theory of evidence. We first prove that these two theories have the same ability in representing evidence and combining DS-independent evidence. We then show that the new approach can deal with some dependent situations while Dempster's combination rule cannot. Various examples in the paper show the ways of using generalized incidence calculus in expert systems.

Imitation and 'theory of mind' competencies in discrimination of autism from other neurodevelopmental disorders

Several studies have reported imitative deficits in autism spectrum disorder (ASD). However, it is still debated if imitative deficits are specific to ASD or shared with clinical groups with similar mental impairment and motor difficulties. We investigated whether imitative tasks can be used to discriminate ASD children from typically developing children (TD) and children with general developmental delay (GDD). We applied discriminant function analyses to the performance of these groups on three imitation tasks and tests of dexterity, motor planning, verbal skills, theory of mind (ToM). Analyses revealed two significant dimensions. The first represented impairment of dexterity and verbal ability, and discriminated TD from GDD children. Once these differences were accounted for, differences in ToM and the three imitation tasks accounted for a significant proportion of the remaining intergroup variance and discriminated the ASD group from other groups. Further analyses revealed that inclusion of imitative tasks increased the specificity and sensitivity of ASD classification and that imitative tasks considered alone were able to reliably discriminate ASD, TD and GDD. The results suggest that imitation and theory of mind impairment in autism may stem from a common domain of origin separate from general cognitive and motor skill.

Electro-thermal theory of intermodulation distortion in lossy microwave components

An analytic formulation of dynamic electro-thermally induced nonlinearity is developed for a general resistive element, yielding a self-heating circuit model based on a fractional derivative. The model explains the 10 dB/decade slope of the intermodulation products observed in two-tone testing. Two-tone testing at 400 MHz of attenuators, microwave chip terminations, and coaxial terminations is reported with tone spacing ranging from 1 to 100 Hz.