Library

Notes: Abstract Background. Kaposi's sarcoma is frequently found in association with acquired immunodeficiency syndrome (AIDS). We report on radiotherapy for patients with AIDS-related Kaposi's sarcoma at Tokyo Metropolitan Komagome Hospital. Methods. Between April 1991 and May 1997, radiotherapy was given to 11 lesions in eight men with AIDS-related Kaposi's sarcoma to relieve their symptoms. The lesions involved the head and neck region, the legs, and the gastrointestinal tract. Radiotherapy was carried out with 4-MV photon through parallel opposed fields or high energy electrons. Total doses ranged from 20 to 38 Gy, with a median of 30 Gy, delivered in 2- to 3-Gy fractions. Four patients were given other treatments prior to the radiotherapy. Acute reaction was evaluated according to the modified acute radiation morbidity scoring criteria of the Radiation Therapy Oncology Group (RTOG). Results. Radiotherapy had relieved the symptoms in all patients at completion of this therapy. Lesions that involved the hard palate and vocal cords had completely disappeared. The lesions that received radiotherapy were controlled without symptoms until the patients died. Patients who had the head and neck region treated exhibited severe acute mucosal reaction (at a dose of 30 Gy, there was grade 2 morbidity by modified RTOG criteria, in two patients, and grade 3 in three patients) although the radiation therapy was completed for these patients. Conclusion. Radiotherapy promises a favorable outcome for symptom relief in AIDS-related Kaposi's sarcoma.

Notes: Abstract There have been two contrasting doctrines concerning learning, more generally about acquisition of knowledge: empiricism and rationalism. The theory of learning in such a field as artificial intelligence seems to fall within the empiricist framework. On the hand, N. Chomsky and his followers have discussed, during the last decade, concerning learning, especially about language learning, from the rationalist point of view (Chomsky, 1965). The main feature in the rationalist approach toward a theory of learning lies in the speculation that in order to acquire knowledge it is indispensable for a learner to be endowed with “innate ideas”, and that “experience” in the external world are merely subsidiary types of information for the learner. If this is acceptable, we can inquire: Under what kind of innate ideas can the learner understand the structure of the external world? In our previous paper (Uesaka, Aizawa, Ebara, and Ozeki, 1973), we formalized this by introducing the mathematical notion of “learnability”, and gave a partial answer to the above inquiry. In this formalization we assumed that the set F of objects to be learned consists of mappings of N to itself, where N is the set of positive integers. Then, constructing a topological space (F, $$\mathcal{O}$$ ) by an appropriate family $$\mathcal{O}$$ of open sets, we observed that the notion of learnability can be well described in terms of topological properties of the learning space (F, $$\mathcal{O}$$ ). Many problems must be solved, however, before we raise the theory to a complete model of the rationalist theory of learning. The topological study of the space (F, $$\mathcal{O}$$ ) is, we believe, the first step toward this approach. In this context, we discuss the topological aspects of this space. Now we define $$\mathcal{O}$$ as follows: By N 2 we mean the direct product of two N's. Let s be a subset of N 2. If, for any (x, y), (x′, y′) in s, x=x′ implies y=y′, then we say that s is single-valued. Let f ∈ F, If, for any (x, y) in s, y=f(x), then f is said to be on s, denoted as $$f\underline \supseteq s$$ . Let $$\pi \left( s \right) = \left\{ {g;g \in F,g\underline \supseteq s} \right\}$$ . A single-valued finite subset of N 2 is called datum. Let D denote the family of all data. Let $$\mathcal{O}* = \left\{ \phi \right\} \cup \left\{ {\pi \left( d \right);d \in D} \right\}$$ , and $$\mathcal{O}$$ denote the family of all subsets of F, each of which is written as $$\mathop \cup \limits_\alpha W_{\alpha }$$ , where W α is in $$\mathcal{O}*$$ . Then, it is easily seen that $$\mathcal{O}$$ satisfies the axiom of the open system of a topological space. It is shown that the learning space (F, $$\mathcal{O}$$ ) has the following properties: (1) It satisfies the first and the second countability axioms. (2) It is separable and is totally disconnected. (3) It is a Hausdorff space and, further, is regular and normal. (4) It is neither compact nor locally compact. (5) It is metrizable, or more precisely there exists a complete but not totally bounded metric space which is homeomorphic to learning space. (6) Any of its subspace can be embedded into its special subspace.