Assignment methods for incidence calculus

Incidence calculus is a mechanism for probabilistic reasoning in which sets of possible worlds, called incidences, are associated with axioms, and probabilities are then associated with these sets. Inference rules are used to deduce bounds on the incidence of formulae which are not axioms, and bounds for the probability of such a formula can then be obtained. In practice an assignment of probabilities directly to axioms may be given, and it is then necessary to find an assignment of incidence which will reproduce these probabilities. We show that this task of assigning incidences can be viewed as a tree searching problem, and two techniques for performing this research are discussed. One of these is a new proposal involving a depth first search, while the other incorporates a random element. A Prolog implementation of these methods has been developed. The two approaches are compared for efficiency and the significance of their results are discussed. Finally we discuss a new proposal for applying techniques from linear programming to incidence calculus.

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.

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.

Model categories for orthogonal calculus

We restate the notion of orthogonal calculus in terms of model categories. This provides a cleaner set of results and makes the role of O(n)-equivariance clearer. Thus we develop model structures for the category of n-polynomial and n-homogeneous functors, along with Quillen pairs relating them. We then classify n-homogeneous functors, via a zig-zag of Quillen equivalences, in terms of spectra with an O(n)-action. This improves upon the classification theorem of Weiss. As an application, we develop a variant of orthogonal calculus by replacing topological spaces with orthogonal spectra.

Belief change with noisy sensing in the situation calculus

Situation calculus has been applied widely in arti?cial intelligence to model and reason about actions and changes in dynamic systems. Since actions carried out by agents will cause constant changes of the agents’ beliefs, how to manage
these changes is a very important issue. Shapiro et al. [22] is one of the studies that considered this issue. However, in this framework, the problem of noisy sensing, which often presents in real-world applications, is not considered. As a
consequence, noisy sensing actions in this framework will lead to an agent facing inconsistent situation and subsequently the agent cannot proceed further. In this paper, we investigate how noisy sensing actions can be handled in iterated
belief change within the situation calculus formalism. We extend the framework proposed in [22] with the capability of managing noisy sensings. We demonstrate that an agent can still detect the actual situation when the ratio of noisy sensing actions vs. accurate sensing actions is limited. We prove that our framework subsumes the iterated belief change strategy in [22] when all sensing actions are accurate. Furthermore, we prove that our framework can adequately handle belief introspection, mistaken beliefs, belief revision and belief update even with noisy sensing, as done in [22] with accurate sensing actions only.

Review of A Guerra e as Igrejas: Angola 1961-1991 by Benedict Schubert

Book review of A GUERRA E AS IGREJAS: ANGOLA 1961-1991. By Benedict Schubert.
Basel, Switzerland: P. Schlettwein Publishing, 2000. Pp. vii; 251; Introduction
by Christine Messiant. CHF. 30, NAM 70, ZAR 70 paper.

Reduced K-theory for Azumaya algebras

Abstract In the theory of central simple algebras, often we are dealing with abelian groups which arise from the kernel or co-kernel of functors which respect transfer maps (for example K-functors). Since a central simple algebra splits and the functors above are “trivial” in the split case, one can prove certain calculus on these functors. The common examples are kernel or co-kernel of the maps Ki(F)?Ki(D), where Ki are Quillen K-groups, D is a division algebra and F its center, or the homotopy fiber arising from the long exact sequence of above map, or the reduced Whitehead group SK1. In this note we introduce an abstract functor over the category of Azumaya algebras which covers all the functors mentioned above and prove the usual calculus for it. This, for example, immediately shows that K-theory of an Azumaya algebra over a local ring is “almost” the same as K-theory of the base ring. The main result is to prove that reduced K-theory of an Azumaya algebra over a Henselian ring coincides with reduced K-theory of its residue central simple algebra. The note ends with some calculation trying to determine the homotopy fibers mentioned above.

Insulin receptor substrate-2 deficiency impairs brain growth and promotes tau phosphorylation

Insulin resistance and diabetes might promote neurodegenerative disease, but a molecular link between these disorders is unknown. Many factors are responsible for brain growth, patterning, and survival, including the insulin-insulin-like growth factor (IGF)-signaling cascades that are mediated by tyrosine phosphorylation of insulin receptor substrate (IRS) proteins. Irs2 signaling mediates peripheral insulin action and pancreatic beta-cell function, and its failure causes diabetes in mice. In this study, we reveal two important roles for Irs2 signaling in the mouse brain. First, disruption of the Irs2 gene reduced neuronal proliferation during development by 50%, which dissociated brain growth from Irs1-dependent body growth. Second, neurofibrillary tangles containing phosphorylated tau accumulated in the hippocampus of old Irs2 knock-out mice, suggesting that Irs2 signaling is neuroprotective. Thus, dysregulation of the Irs2 branch of the insulin-Igf-signaling cascade reveals a molecular link between diabetes and neurodegenerative disease.

Two-stage mixed discrete-continuous identification of radial basis function (RBF) neural models for nonlinear systems

The identification of nonlinear dynamic systems using radial basis function (RBF) neural models is studied in this paper. Given a model selection criterion, the main objective is to effectively and efficiently build a parsimonious compact neural model that generalizes well over unseen data. This is achieved by simultaneous model structure selection and optimization of the parameters over the continuous parameter space. It is a mixed-integer hard problem, and a unified analytic framework is proposed to enable an effective and efficient two-stage mixed discrete-continuous; identification procedure. This novel framework combines the advantages of an iterative discrete two-stage subset selection technique for model structure determination and the calculus-based continuous optimization of the model parameters. Computational complexity analysis and simulation studies confirm the efficacy of the proposed algorithm.

Decisional responsibility for mechanical ventilation and weaning: an international survey

Introduction: Optimal management of mechanical ventilation and weaning requires dynamic and collaborative decision making to minimize complications and avoid delays in the transition to extubation. In the absence of collaboration, ventilation decision making may be fragmented, inconsistent, and delayed. Our objective was to describe the professional group with responsibility for key ventilation and weaning decisions and to examine organizational characteristics associated with nurse involvement.

Methods: A multi-center, cross-sectional, self-administered survey was sent to nurse managers of adult intensive care units (ICUs) in Denmark, Germany, Greece, Italy, Norway, Switzerland, Netherlands and United Kingdom (UK). We summarized data as proportions (95% confidence intervals (CIs)) and calculated odds ratios (OR) to examine ICU organizational variables associated with collaborative decision making.

Results: Response rates ranged from 39% (UK) to 92% (Switzerland), providing surveys from 586 ICUs. Interprofessional collaboration (nurses and physicians) was the most common approach to initial selection of ventilator settings (63% (95% CI 59 to 66)), determination of extubation readiness (71% (67 to 75)), weaning method (73% (69 to 76)), recognition of weaning failure (84% (81 to 87)) and weaning readiness (85% (82 to 87)), and titration of ventilator settings (88% (86 to 91)). A nurse-to-patient ratio other than 1:1 was associated with decreased interprofessional collaboration during titration of ventilator settings (OR 0.2, 95% CI 0.1 to 0.6), weaning method (0.4 (0.2 to 0.9)), determination of extubation readiness (0.5 (0.2 to 0.9)) and weaning failure (0.4 (0.1 to 1.0)). Use of a weaning protocol was associated with increased collaborative decision making for determining weaning (1.8 (1.0 to 3.3)) and extubation readiness (1.9 (1.2 to 3.0)), and weaning method (1.8 (1.1 to 3.0)). Country of ICU location influenced the profile of responsibility for all decisions. Automated weaning modes were used in 55% of ICUs.

Conclusions: Collaborative decision making for ventilation and weaning was employed in most ICUs in all countries although this was influenced by nurse-to-patient ratio, presence of a protocol, and varied across countries. Potential clinical implications of a lack of collaboration include delayed adaptation of ventilation to changing physiological parameters, and delayed recognition of weaning and extubation readiness resulting in unnecessary prolongation of ventilation.

Adsorption-controlled molecular-beam epitaxial growth of BiFeO3

BiFeO3 thin films have been deposited on (111) SrTiO3 single crystal substrates by reactive molecular-beam epitaxy in an adsorption-controlled growth regime. This is achieved by supplying a bismuth overpressure and utilizing the differential vapor pressures between bismuth oxides and BiFeO3 to control stoichiometry. Four-circle x-ray diffraction reveals phase-pure, untwinned, epitaxial, (0001)-oriented films with rocking curve full width at half maximum values as narrow as 25 arc sec (0.007 degrees). Second harmonic generation polar plots combined with diffraction establish the crystallographic point group of these untwinned epitaxial films to be 3m at room temperature. (C) 2007 American Institute of Physics.