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## On Variable-Structure Stochastic Automata

### Pattern Recognition and Machine Learning (1971-01-01): 277-287 , January 01, 1971

A stochastic automaton with a variable structure (SAVS) may be described by the sextuple {X, Φ, α, p, U, G} where X={x_{0}, x_{1},⋯,x_{k}} is the input set, Φ = {Φ_{1}, Φ_{2},⋯,Φ_{s}} is the internal state set, α = {α_{1}, α_{1},⋯,α_{r}} with r ≤ s is the output or action set, p is the state probability vector (i.e., at stage or time instant n, p(n) = (p_{1}(n), p_{2}(n),⋯,p_{s}(n)) governing the choice of the state, U is an updating scheme which generates p(n + 1) from p(n) and G:Φ → α is the output function. In general, G may be a stochastic function. In this paper it is assumed that G is deterministic and one-to-one (i.e., r = s), k = 1 and s < ∞.

## Front Matter - Coding for Markov Sources

### Coding for Markov Sources (1971-01-01): 110 , January 01, 1971

## Presse und Kybernetik

### Automat und Mensch (1971-01-01) 81: 249-258 , January 01, 1971

### Zusammenfassung

Presse und Kybernetik haben manches gemeinsam:

Beide beschäftigen sich mit Information,

beide sind typische Komponenten unserer Kultur,

beide sind oft Ziel überheblicher Kritik, und

beide entwickeln sich trotzdem mit erstaunlicher Vitalität.

## A note on dense and nondense families of complexity classes

### Mathematical systems theory (1971-03-01) 5: 66-70 , March 01, 1971

In a model for a measure of computational complexity, Ф, for a partial recursive function*t*, let*R*_{t}^{Ф}
denote all partial recursive functions having the same domain as*t* and computable within time*t.* Let Σ^{Ф} = {*R*_{t}^{Ф}
|*t* is recursive} and let Ω^{Ф} = {
$$R_{\Phi _i } $$
|Ф_{i} is actually the running time function of a computation}. Σ^{Ф} and Ω^{Ф} are partially ordered under set-theoretic inclusion. These partial orderings have been extensively investigated by Borodin, Constable and Hopcroft in [3]. In this paper we present a simple uniform proof of some of their results. For example, we give a procedure for easily calculating a model of computational complexity Ф for which Σ^{Ф} is not dense while Ω^{Ф} is dense. In our opinion, our technique is so transparent that it indicates that certain questions of density are not intrinsically interesting for general abstract measures of computational complexity, Ф. (This is not to say that similar questions are necessarily uninteresting for specific models.)

## Bedingte Reflexe, die Lernmatrix und andere adaptive Strukturen

### Automat und Mensch (1971-01-01) 81: 151-179 , January 01, 1971

### Zusammenfassung

Bei allen Tieren, die über ein Nervensystem verfügen, kann man unter geeigneten Voraussetzungen angeborene und bedingte Reflexe beobachten. Die angeborenen Reflexe sind unabhängig von der Vorgeschichte. Typische Beispiele solcher angeborener Reflexe sind Sehnenreflexe, Speichelabsonderungsreflexe, Schluckreflexe, Augenreflexe usw.

## Identification of control systems by performance

### Mathematical systems theory (1971-12-01) 5: 349-352 , December 01, 1971

## Advanced Computer Graphics

### Advanced Computer Graphics (1971-01-01) , January 01, 1971

## Computer Graphics in Molecular Biology

### Computer Graphics in Medical Research and Hospital Administration (1971-01-01): 56-70 , January 01, 1971

We are applying computer display techniques to research work on the three-dimensional structure of macromolecules, biologically interesting smaller molecules, and to the three-dimensional neural anatomy of small invertebrates. In order to understand the precise nature of the interactions between molecules and the relationships between structural elements of living organisms, one needs techniques for presenting a description of three-dimensional objects in a convenient form. Since the parameters of interest are often ill defined and sometimes unknown beforehand, visualization of a three-dimensional abstraction of the physical object or system seems to be the most useful technique available to us at present. Construction of three-dimensional physical models has been the traditional method in this approach, although stereoscopic diagrams have also been used. Physical models are severely limited when the molecule or structure becomes highly complex. In that case only a few models are constructed and often only a useful representation of the final stage of the analysis is actually made, while intermediate models are simply not done.

We have constructed a computerized system which makes it psychologically and physically easier to construct pictures for representing three-dimensional structures. The pictures themselves are drawn of successive line segments, and pictures of over five thousand line segments plus alphanumeric characters can be observed as a flicker-free presentation. These images may be rotated, translated and scaled in real time. The real-time user manipulation provides the necessary three-dimensional illusion for perception of complex three-dimensional shapes.

A system for constructing a ‘stick’ model of any arbitrary molecule based on standard geometrical values for the atoms is described below. This presentation of what is essentially a tree-structure conveys information about the chemical inter-relatedness of the several atoms in the structure and often represents the *a priori* knowledge of the investigator. Methods by which the initial conformation of a molecule possessing internal degrees of flexibility can be changed to provide chemically plausible alternative configurations are also discussed. Since the physical extent of the atoms requires that they do not ‘bump’ or occupy the same space at the same time, the user can interactively manipulate his model so as to remove contact violations if they occur.

Construction of surfaces of constant electron density, analagous to standard contour maps of X-ray crystallographers is also described. This is a representation of the experimental information, and portrays the space-occupying aspects of the model. It is especially powerful when chemical groups fail to lie in crystallographically convenient directions. Both the stick model and the density surfaces can have text material added (labels). These labels can be attached to specific lines in the picture, and will rotate along with the image. The interactive system for fitting any proposed stick model of a molecule to the observed positions in three-dimensional space of the density maxima enables the structure solution to be verified and conveys what the molecule ‘looks like’.

The construction and use of an interactive program which enables the user to record and redisplay the three-dimensional geometry and connectivity of any tree-like structure is described. Its application to the recording and mapping of the neural anatomy of a microscopic invertebrate is discussed.

## Learning Processes in a Random Machine

### Pattern Recognition and Machine Learning (1971-01-01): 160-171 , January 01, 1971

A random machine, [1, 2] in which the random pulse frequency is used as the machine variable, may be considered to be somewhere between an analog and a digital computer in speed and accuracy of operation and to perform functions similar to those of the brain. The authors have developed an experimental random machine which can be effectively applied to the analysis of a system governed by algebraic or differential equations.