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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 34 (1996), S. 811-842 
    ISSN: 1432-1416
    Keywords: Orientation selection ; Total alignment ; Peak ansatz ; Parallel cells
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The problem of alignment of cells (or other objects) that interact in an angle-dependent way was described in Mogilner and Edelstein-Keshet (1995). In this sequel we consider in detail a special limiting case of nearly complete alignment. This occurs when the rotational diffusion of individual objects becomes very slow. In this case, the motion of the objects is essentially deterministic, and the individuals or objects tend to gather in clusters at various orientations. (Numerical solutions show that the angular distribution develops sharp peaks at various discrete orientations.) To understand the behaviour of the deterministic models with analytic tools, we represent the distribution as a number of δ-like peaks. This approximation of a true solution by a set of (infinitely sharp) peaks will be referred to as thepeak ansatz. For weak but nonzero angular diffusion, the peaks are smoothed out. The analysis of this case leads to a singular perturbation problem which we investigate. We briefly discuss other applications of similar techniques.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 34 (1996), S. 811-842 
    ISSN: 1432-1416
    Keywords: Key words: Orientation selection ; Total alignment ; Peak ansatz ; Parallel cells
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract.  The problem of alignment of cells (or other objects) that interact in an angle-dependent way was described in Mogilner and Edelstein-Keshet (1995). In this sequel we consider in detail a special limiting case of nearly complete alignment. This occurs when the rotational diffusion of individual objects becomes very slow. In this case, the motion of the objects is essentially deterministic, and the individuals or objects tend to gather in clusters at various orientations. (Numerical solutions show that the angular distribution develops sharp peaks at various discrete orientations.) To understand the behaviour of the deterministic models with analytic tools, we represent the distribution as a number of δ-like peaks. This approximation of a true solution by a set of (infinitely sharp) peaks will be referred to as the peak ansatz. For weak but nonzero angular diffusion, the peaks are smoothed out. The analysis of this case leads to a singular perturbation problem which we investigate. We briefly discuss other applications of similar techniques.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Contributions to mineralogy and petrology 28 (1970), S. 117-134 
    ISSN: 1432-0967
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract This paper attempts to illustrate the chemical variations of metamorphic hornblendes regarding host rocks and prograde variations. Changes related to bulk chemistry (orthoamphibolites) mainly concern Si, Al, Mg, Fetot and Ca. The Mg, Fe2+ and Fe3+ contents of hornblendes are, however, not strictly related to host rook compositions and Mg enrichments are correlated with increasing Fe3+ contents in the amphiboles. Thus, variations of oxygen fugacity may control the Mg contents of the Ca amphiboles studied but this does not show clear relations with the prograde metamorphism. The most sensitive but irregular variation related to the metamorphic conditions is the prograde enrichment of the alkalis into the “A” vacant position and an increase of the (Na+K)tot/Na+K+Ca ratios of the amphiboles. Increasing Ti and AlIV contents as well as decreasing AlVI concentrations are also, but much less evidently, related to increasing T and P. A variation trend from tschermakitic to edenitic hornblendes may be drawn using Shido's end members calculation; this tendency and the relative deficiency of AlVI contents in the low-grade members suggests that the amphiboles studied were subjected to conditions of a low-pressure metamorphism type. Such a conclusion is in agreement with the occurrence of andalusite-cordierite/sillimanite-cordierite associations in the metapelitic rocks, and the absence of Fe-rich garnet and epidote from the orthoamphibolites of the amphibolite facies at Aracena. Comparisons with Ca amphiboles from other metamorphic areas show, in agreement with various authors, that “Abukuma” hornblendes are similar to those encountered in high-grade thermal aureoles and tonalitic intrusives but different from the hornblendes of “Barrovian” metamorphism types.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 59 (1997), S. 533-549 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We describe a three-species mechanism for spatial pattern formation in which only one species spatially moves. We show that a bifurcation to traveling or standing waves occurs. We contrast this mechanism for pattern formation with the better known cases where more than one species moves.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 60 (1998), S. 449-475 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We studied mathematical models for the length distributions of actin filaments under the effects of polymerization/depolymerization, and fragmentation. In this paper, we emphasize the effects of these two processes acting alone. In this case, simple discrete and continuous models can be derived and solved explicitly (in several special cases), making the problem interesting from a modeling and pedagogical point of view. In a companion paper (Ermentrout and Edelstein-Keshet, 1998, Bull. Math. Biol. 60, 477–503) we investigate what happens when the processes act together, with particular attention to fragmentation by gelsolin, and with a greater level of biological detail.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 59 (1997), S. 399-406 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 60 (1998), S. 477-503 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In a previous paper, we studied elementary models for polymerization, depolymerization, and fragmentation of actin filaments (Edelstein-Keshet and Ermentrout, 1998, Bull. Math. Biol. 60, 449–475). When these processes act together, more complicated dynamics occur. We concentrate on a particular case study, using the actin-fragmenting protein gelsolin. A set of biological parameter values (drawn from the experimental literature) is used in computer simulations of the kinetics of gelsolin-mediated actin filament fragmentation.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of heuristics 5 (1999), S. 53-70 
    ISSN: 1572-9397
    Keywords: flow shop scheduling ; sequence-dependent setup times ; heuristics ; traveling salesman problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents an enhanced heuristic for minimizing the makespan of the flow shop scheduling problem with sequence-dependent setup times. The procedure transforms an instance of the problem into an instance of the traveling salesman problem by introducing a cost function that penalizes for both large setup times and bad fitness of schedule. This hybrid cost function is an improvement over earlier approaches that penalized for setup times only, ignoring the flow shop aspect of the problem. To establish good parameter values, each component of the heuristic was evaluated computationally over a wide range of problem instances. In the testing stage, an experimental comparison with a greedy randomized adaptive search procedure revealed the conditions and data attributes where the proposed procedure works best.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    International journal of flexible manufacturing systems 9 (1997), S. 251-272 
    ISSN: 1572-9370
    Keywords: approximation ; assembly lines ; NP-completeness ; product sequencing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Mixed-model assembly lines are becoming increasingly interesting as the use of just-in-time principles in manufacturing continues to expand. This paper presents, for the first time, complexity results for the underlying problem of product sequencing. It is shown that the problem is intractable for both the single station and the multiple station case. Nevertheless, efficient 1.5-approximation algorithms are developed for the early- and late-start models associated with the former case. Empirical results demonstrate that these algorithms perform extremely well in practice.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    International journal of primatology 18 (1997), S. 105-114 
    ISSN: 1573-8604
    Keywords: laterality ; infants ; locomotion ; chimpanzees ; reflexes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract We assessed laterality for leading limb in crawling and leading limb in stepping in 13 chimpanzees (Pan troglodytes) during the first 3 months of life. Overall, there is a significant populational right-side bias for crawling but not for stepping. There is a significant negative correlation between laterality in stepping and crawling. The females are more right-sided in lateral bias than the males across both measures. These data suggest that asymmetries in postural organization are present early in life and are specific to the inherent locomotor behavior of a given species.
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