A reusable knowledge acquisition shell: KASH

KASH (Knowledge Acquisition SHell) is proposed to assist a knowledge engineer by providing a set of utilities for constructing knowledge acquisition sessions based on interviewing techniques. The information elicited from domain experts during the sessions is guided by a question dependency graph (QDG). The QDG defined by the knowledge engineer, consists of a series of control questions about the domain that are used to organize the knowledge of an expert. The content information supplies by the expert, in response to the questions, is represented in the form of a concept map. These maps can be constructed in a top-down or bottom-up manner by the QDG and used by KASH to generate the rules for a large class of expert system domains. Additionally, the concept maps can support the representation of temporal knowledge. The high degree of reusability encountered in the QDG and concept maps can vastly reduce the development times and costs associated with producing intelligent decision aids, training programs, and process control functions

Hochschild (co)homology of the second kind I

We define and study the Hochschild (co)homology of the second kind (known also as the Borel-Moore Hochschild homology and the compactly supported Hochschild cohomology) for curved DG-categories. An isomorphism between the Hochschild (co)homology of the second kind of a CDG-category B and the same of the DG-category C of right CDG-modules over B, projective and finitely generated as graded B-modules, is constructed. Sufficient conditions for an isomorphism of the two kinds of Hochschild (co)homology of a DG-category are formulated in terms of the two kinds of derived categories of DG-modules over it. In particular, a kind of "resolution of the diagonal" condition for the diagonal CDG-bimodule B over a CDG-category B guarantees an isomorphism of the two kinds of Hochschild (co)homology of the corresponding DG-category C. Several classes of examples are discussed.Comment: LaTeX 2e, 67 pages. v.2: The case of matrix factorizations discussed in detail in the new subsections 4.8 and 4.1

Maximal L2L^2 regularity for Dirichlet problems in Hilbert spaces

We consider the Dirichlet problem $\lambda U - {\mathcal{L}}U= F$ in \mathcal{O}, U=0 on $\partial \mathcal{O}$. Here $F\in L^2(\mathcal{O}, \mu)$ where $\mu$ is a nondegenerate centered Gaussian measure in a Hilbert space $X$, $\mathcal{L}$ is an Ornstein-Uhlenbeck operator, and $\mathcal{O}$ is an open set in $X$ with good boundary. We address the problem whether the weak solution $U$ belongs to the Sobolev space $W^{2,2}(\mathcal{O}, \mu)$. It is well known that the question has positive answer if $\mathcal{O} = X$; if $\mathcal{O} \neq X$ we give a sufficient condition in terms of geometric properties of the boundary $\partial \mathcal{O}$. The results are quite different with respect to the finite dimensional case, for instance if \mathcal{O} is the ball centered at the origin with radius $r$ we prove that $U\in W^{2,2}(\mathcal{O}, \mu)$ only for small $r$

Computation in Finitary Stochastic and Quantum Processes

We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process's behaviors, are recognized and generated by suitable specializations. We characterize and compare deterministic and nondeterministic versions, summarizing their relative computational power in a hierarchy of finitary process languages. Quantum finite-state transducers and generators are a first step toward a computation-theoretic analysis of individual, repeatedly measured quantum dynamical systems. They are explored via several physical systems, including an iterated beam splitter, an atom in a magnetic field, and atoms in an ion trap--a special case of which implements the Deutsch quantum algorithm. We show that these systems' behaviors, and so their information processing capacity, depends sensitively on the measurement protocol.Comment: 25 pages, 16 figures, 1 table; http://cse.ucdavis.edu/~cmg; numerous corrections and update

Internal Partitions of Regular Graphs

An internal partition of an $n$-vertex graph $G=(V,E)$ is a partition of $V$ such that every vertex has at least as many neighbors in its own part as in the other part. It has been conjectured that every $d$-regular graph with $n>N(d)$ vertices has an internal partition. Here we prove this for $d=6$. The case $d=n-4$ is of particular interest and leads to interesting new open problems on cubic graphs. We also provide new lower bounds on $N(d)$ and find new families of graphs with no internal partitions. Weighted versions of these problems are considered as well

Accessibility of Slovak towns

Two simple topological and one metric measures were used to characterize the accessibility of 136 Slovak towns. The network of Slovakia with green-line buss stops was conceptualized as a graph. The first measure is defined as number of edges ending in the vertice, the second as a number of edges between selected vertice and all other vertices of the graph using the shortest path. The third measure represents the metric version of the second. According to the first measure Bratislava, the capital of Slovakia, takes the first position. It is followed by Ko?ice, the second largest town of Slovakia. According to the second measure the town of Nitra located in the south-west of Slovakia, takes the first position. According to the third measure the town of ?iar nad Hronom located in central Slovakia, takes the first position. The authors try also to consider possible associations between accessibility and regional development.