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  • 1
    Electronic Resource
    Electronic Resource
    Two Finiteness Theorems for Periodic Tilings of d -Dimensional Euclidean Space (1998)
    Springer
    Discrete & computational geometry 20 (1998), S. 143-153 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. Consider the d -dimensional euclidean space E d . Two main results are presented: First, for any N∈ N, the number of types of periodic equivariant tilings $({\cal T},\Gamma)$ that have precisely N orbits of (2,4,6, . . . ) -flags with respect to the symmetry group Γ , is finite. Second, for any N∈ N, the number of types of convex, periodic equivariant tilings $({\cal T},\Gamma)$ that have precisely N orbits of tiles with respect to the symmetry group Γ , is finite. The former result (and some generalizations) is proved combinatorially, using Delaney symbols, whereas the proof of the latter result is based on both geometric arguments and Delaney symbols. 〈lsiheader〉 〈onlinepub〉7 August, 1998 〈editor〉Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; 〈pdfname〉20n2p143.pdf 〈pdfexist〉yes 〈htmlexist〉no 〈htmlfexist〉no 〈texexist〉no 〈sectionname〉 〈/lsiheader〉
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009380
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  • 2
    Electronic Resource
    Electronic Resource
    Affine Maps That Induce Polyhedral Complex Isomorphisms (2000)
    Springer
    Discrete & computational geometry 24 (2000), S. 49-60 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. In this paper we show that an affine bijection f : T 1 → T 2 between two polyhedral complexes T 1 ,T 2 , both of which consist of a union of faces of two convex polyhedra P 1 and P 2 , necessarily respects the cell-complex structure of T 1 and T 2 inherited from P 1 and P 2 , respectively, provided f extends to an affine map from P 1 into P 2 . In addition, we present an application of this result within the area of T-theory to obtain a far-reaching generalization of previous results regarding the equivalence of two distinct constructions of the phylogenetic tree associated to ``perfect'' (that is, treelike) distance data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004540010034
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  • 3
    Electronic Resource
    Electronic Resource
    On the cost functions for the control of the human arm movement (1990)
    Springer
    Biological cybernetics 62 (1990), S. 519-528 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract The aim of our investigation is to understand the mechanisms which control the movement of the human arm. The arm is here considered as a redundant system: the shoulder, elbow and wrist joints, which provide three degrees of freedom, combine to move the hand in a horizontal plane, i.e. a two dimensional space. Thus the system has one extra degree of freedom. Earlier investigations of the static situation led to the hypothesis that independent cost functions were attached to each of the three joints and that the configuration chosen for a given target position is that which provides the minimum total cost (Cruse 1986). The aim of the current investigation was to look for measurable values corresponding to the hypothetical cost functions. Experiments using pointers of different lengths attached to the hand showed that the strategy in choosing the joint angles are independent of the limb length. The muscle force necessary to reach a given angle is increased by a spring mounted across a joint. In this situation the angles of the loaded joint are changed for a given target point to give way to the force effect. This leads to the conclusion that the hypothetical cost functions are not independent of the physiological costs necessary to hold the joint at a given angle. The cost functions seem to depend on joint angle and on the force which is necessary to hold the joint in a given position. Cost functions are measured by psychophysical methods. The results showU-shaped curves which can be approximated by parabolas. The position of minimum cost (maximum comfort) for one joint showed no or weak dependency on the angles of the other joints. For each subject these “psychophysical” cost functions are compared with the hypothetical cost functions. The comparison showed reasonable agreement. This supports the assumption that the psychophysically measured “comfort functions” provide a measure for the hypothetical cost functions postulated to explain the targeting movements. Targeting experiments using a four joint arm which has two extra degrees of freedom showed a much larger scatter compared to the three joint arm. Nevertheless, the results still conform to the hypothesis that also in this case the minimum cost principle is applied to solve the redundancy problem. As the cost function for the whole arm shows a large minimum valley, quite a large range of arm positions is possible of about equal total costs. The scatter does not result from pure randomness but seems to be mainly produced by the fact that the angles at the end of the movement depend on the value of the joint angles at the beginning of the movement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00205114
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  • 4
    Electronic Resource
    Electronic Resource
    A comparison between two distinct continuous models in projective cluster theory: The median and the tight-span construction (1998)
    Springer
    Annals of combinatorics 2 (1998), S. 299-311 
    Details
    ISSN: 0219-3094
    Keywords: 04A03 ; 04A20 ; 05C99 ; 52B99 ; 92B99 ; Buneman graph ; cluster theory ; split systems ; split decomposition ; T-theory ; T-construction ; pairwise compatibility ; weak compatibility ; median networks ; hypercube ; phylogenetic trees ; phylogenetic networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is possible to consider two variants of cluster theory: Inaffine cluster theory, one considers collections ofsubsets of a given setX of objects or states, whereas inprojective cluster theory, one considers collections ofsplits (orbipartitions) of that set. In both contexts, it can be desirable to produce acontinuous model, that is, a spaceT encompassing the given setX which represents in a well-specified and more or less parsimonious way all possibleintermediate objects ortransition states compatible with certain restrictions derived from the given collection of subsets or splits. We investigate an interesting and intriguing relationship between two such constructions that appear in the context of projective cluster theory: TheBuneman construction and thetight-span (or justT)construction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01608527
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  • 5
    Electronic Resource
    Electronic Resource
    Formation of morphological differentiation patterns in the ascomycete Neurospora crassa
    Amsterdam : Elsevier
    Mechanisms of Development 44 (1993), S. 17-31 
    Details
    ISSN: 0925-4773
    Keywords: Cellular automaton ; Computer simulation ; Cyclic AMP ; Differentiation process ; Experimental condition ; Hypha ; Morphogen ; Neurospora crassa
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/0925-4773(93)90013-N
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  • 6
    Electronic Resource
    Electronic Resource
    Charged-particle multiplicity distributions in oxygen-nucleus collisions at 60 and 200 GeV per nucleon
    Amsterdam : Elsevier
    Nuclear Physics, Section B 333 (1990), S. 48-65 
    Details
    ISSN: 0550-3213
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0550-3213(90)90222-Y
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  • 7
    Electronic Resource
    Electronic Resource
    Measurement of the transverse energy flow in nucleus-nucleus collisions at 200 GeV per nucleon
    Amsterdam : Elsevier
    Nuclear Physics, Section B 353 (1991), S. 1-19 
    Details
    ISSN: 0550-3213
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0550-3213(91)90498-M
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  • 8
    Electronic Resource
    Electronic Resource
    Weak hierarchies associated with similarity measures—An additive clustering technique (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 133-166 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A new and apparently rather useful and natural concept in cluster analysis is studied: given a similarity measure on a set of objects, a sub-set is regarded as a cluster if any two objectsa, b inside this sub-set have greater similarity than any third object outside has to at least one ofa, b. These clusters then form a closure system which can be described as a hypergraph without triangles. Conversely, given such a system, one may attach some weight to each cluster and then compose a similarity measure additively, by letting the similarity of a pair be the sum of weights of the clusters containing that particular pair. The original clusters can be reconstructed from the obtained similarity measure. This clustering model is thus located between the general additive clustering model of Shepard and Arabie (1979) and the standard hierarchical model. Potential applications include fitting dendrograms with few additional nonnested clusters and simultaneous representation of some families of multiple dendrograms (in particular, two-dendrogram solutions), as well as assisting the search for phylogenetic relationships by proposing a somewhat larger system of possibly relevant “family groups”, from which an appropriate choice (based on additional insight or individual preferences) remains to be made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458841
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  • 9
    Electronic Resource
    Electronic Resource
    The classification of face-transitive periodic three-dimensional tilings (1993)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 49 (1993), S. 806-817 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It has long been known that there exists an infinite number of types of tile-transitive periodic three-dimensional tilings. Here, it is shown that, by contrast, the number of types of face-transitive periodic three-dimensional tilings is finite. The method of Delaney symbols and the properties of the 219 isomorphism classes of crystallographic space groups are used to find exactly 88 equivariant types that fall into seven topological families.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S010876739300354X
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  • 10
    Electronic Resource
    Electronic Resource
    Zur Galoistheorie pythagoreischer Körper (1965)
    Springer
    Archiv der Mathematik 16 (1965), S. 148-152 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01220014
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