Current research directions in the development of expert systems based on belief networks

An expert system is a computer program that is designed to solve problems at a level comparable to that of a human expert in a given domain. Often expert systems require a representation of uncertainty. This paper highlights some of the key developments in the history of representing uncertainty in expert systems. An uncertainty representation called belief networks is then introduced and its use in expert systems is motivated. The paper concludes with a discussion of current directions in belief network research.     

The ionic distribution in Mn2+ and Zn2+ β″-alumina

The ionic distributions in Mn²⁺ and Zn²⁺ β″-alumina (idealized formula: $\text{X}{}_{\mathrm{<mtext>5</mtext><mtext>6</mtext>}}\text{Mg}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{Al}{}_{\mathrm{<mtext>31</mtext><mtext>3</mtext>}}\text{O}{}_{17}\text{;}\text{X}\text{=}\text{Mn}\text{and}\text{Zn}\text{)}$ at 296 K are reported from single-crystal X-ray diffraction studies. Mn²⁺ β″-alumina exhibits the shortest c-axis found so far in any divalent β″-alumina: 33.141(3) Å;Zn²⁺ β″-alumina, which involves the smallest divalent ion studied in the frame-work, has a considerably longer c-axis: 33.517(3) Å. Both compounds show clear evidence of short-range correlation effects in the X²⁺ ion arrangement by way of departures from the centrosymmetric space-group $\text{R}\text{3}\text{m}$ of the β″-skeleton. Both 6c end-sites and 9d mO-sites ($\text{R}\text{3}\text{m}$ notation) are occupied for both ion-types, a significantly larger occupation (60% compared to 28% of the total) lying at or near the 9d mid-oxygen sites in Mn²⁺ β″-alumina compared to Zn²⁺ β″-alumina. Disorder is also found in the column-oxygen O(5) in both cases; the O(5) displacement from the 3b site in Mn²⁺ β″-alumina (0.59 Å) is the largest found in any divalent β″-alumina. The formula-unit/cell-layer, deduced on the basis of the amounts of X²⁺ ions refined, and assuming charge compensation through Mg substitution alone, are: Mn_0.79Mg_0.57Al_10.43O₁₇ and Zn_0.87Mg_0.74Al_10.26O₁₇.     

Clinical correlations with hippocampal atrophy

There is now a consensus that magnetic resonance imaging (MRI) is a sensitive and specific indicator of mesial temporal sclerosis (MTS) in patients with partial epilepsy. MTS is the most common pathological finding underlying the epileptogenic zone in patients undergoing temporal lobe surgery for medically refractory partial seizures. MRI-based hippocampal volumetric studies (i.e., quantitative MRI), has been shown to provide objective evidence for hippocampal atrophy in patients with MTS. The hippocampal volume in the epileptic temporal lobe has correlated with the neuronal cell densities in selected hippocampal subfields. A history of febrile seizures in childhood and age of unprovoked seizure onset have been associated with MRI-based hippocampal volumetry. There is conflicting evidence regarding the relationship between the duration of the seizure disorder and volumetry. Quantitative MRI has compared favorably to other noninvasive techniques (e.g., scalp-recorded EEG), in indicating the diagnosis of medical temporal lobe epilepsy (MTLE). MRI-identified hippocampal atrophy has also been a favorable prognostic indicator of seizure outcome after temporal lobe surgery. The presence of hippocampal atrophy appears to serve an in vivo surrogate for the presence of MTS.     

NMR spectra of carotenoporphyrins. Computer-assisted conformational analysis

A computer-assisted method of conformational analysis for porphyrin molecules bearing flexible side-chains has been developed. The method utilizes the ring current-induced chemical shift changes of the side-chain protons which arise from the porphyrin macrocycle and any attached aryl rings. The treatment has been applied to a series of carotenoporphyrin molecules, which are important as models for a variety of photophysical processes in biological systems. Chemical shift data of sufficient accuracy for the conformational analysis were obtained from 500 MHz NMR experiments. The conformations of the carotenoporphyrins varied from extended ones with the carotenoid well away from the porphyrin ring to tightly folded species, depending on molecular constitution. The analytical method can be extended to other porphyrin-based systems.     

Large N 2D Yang-Mills Theory and Topological String Theory

We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU(N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A= 0) limit. The string theory is a modified version of topological gravity coupled to a topological sigma model with spacetime as target. The derivation of the string theory relies on a new interpretation of Gross and Taylor's “Ω^-1 points ”. We describe how inclusion of the area, coupling of chiral sectors, and Wilson loop expectation values can be incorporated in the topological string approach. Received: 3 March 1994 / Accepted: 2 February 1995     

The Axisymmetric Deformation of a Thin,or Moderately Thick,Elastic Spherical Cap

A refined shell theory is developed for the elastostatics of a moderately thick spherical cap in axisymmetric deformation. This is a two-term asymptotic theory, valid as the dimensionless shell thickness tends to zero.The theory is more accurate than “thin shell” theory, but is still much more tractable than the full three-dimensional theory. A fundamental difficulty encountered in the formulation of shell (and plate) theories is the determination of correct two-dimensional boundary conditions, applicable to the shell solution, from edge data prescribed for the three-dimensional problem. A major contribution of this article is the derivation of such boundary conditions for our refined theory of the spherical cap. These conditions are more difficult to obtain than those already known for the semi-infinite cylindrical shell, since they depend on the cap angle as well as the dimensionless thickness. For the stress boundary value problem, we find that a Saint-Venant-type principle does not apply in the refined theory, although it does hold in thin shell theory. We also obtain correct boundary conditions for pure displacement and mixed boundary data. In these cases, conventional formulations do not generally provide even the first approximation solution correctly. As an illustration of the refined theory, we obtain two-term asymptotic solutions to two problems, (i) a complete spherical shell subjected to a normally directed equatorial line loading and (ii) an unloaded spherical cap rotating about its axis of symmetry.