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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 27 (1982), S. 457-472 
    ISSN: 1572-9613
    Keywords: Cayley tree ; iteration ; fixed point ; spin glass ; Gaussian distribution ; local mean-field theory ; SK equations ; TAP equations.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we study rigorously the random Ising model on a Cayley tree in the limit of infinite coordination numberz → 8. An iterative scheme is developed relating mean magnetizations and mean square magnetizations of successive shells far removed from the surface of the lattice. In this way we obtain local properties of the model in the (thermodynamic) limit of an infinite number of shells. When the coupling constants are independent Gaussian random variables the SK expressions emerge as stable fixed points of our scheme and provide a valid local mean-field theory of spin glasses in which negative local entropy (at low temperatures) while perfectly possible mathematically may still perhaps be physically undesirable. Finally we examine the TAP equations and show that if the average over bond disorder and the limitz → 8 are actually performed, one recovers our iterative scheme and hence the SK equations also in the thermodynamic limit.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 27 (1982), S. 441-456 
    ISSN: 1572-9613
    Keywords: Ising model ; Cayley tree ; phase transition ; iteration ; fixed point ; bifurcation ; ferromagnetic ; antiferromagnetic.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Ising model on a Cayley tree displays a peculiar (continuous order) phase transition with zero long-range order at all finite temperatures. When one studies expection values of spins far removed from the surface (which contains a finite fraction of the total number of spins in the thermodynamic limit), however, one obtains the so-called Bethe approximation. Here we study such a local description by setting up a simple recurrence relation for successive shell magnetizations far removed from the surface. In the ferromagnetic case the local magnetization is a fixed point of the iterative transformation, while in the antiferromagnetic case the fixed point bifurcates to a two-cycle of the transformation (for low temperatures and fields) giving rise to local sublattice magnetizations. In both cases, local thermodynamical properties are obtained by integration.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 33 (1983), S. 419-436 
    ISSN: 1572-9613
    Keywords: Cayley tree ; iteration ; fixed points ; cycles ; attractors ; chaos ; spin glass ; frequency locking ; devil's staircase
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An iterative scheme is developed for a renormalized effective nearest-neighbor couplingK r and effective field per siteK r for spins in therth shell of a Cayley tree with nearest neighborJ, and next nearest neighborJ′, interactions between Ising spins on the lattice. In addition to the expected paramagnetic, ferromagnetic, and antiferromagnetic phases, we find an intermediate range ofJ'/J 〈 0 values whereX r, and Kr iterate to a continuous or quasicontinuous attractor in theX-K plane. In this range the local magnetization is mainly chaotic with oscillatory glasslike behavior. Embedded in the chaos, however, are regions of periodic and commensurate phases.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Cell & tissue research 281 (1995), S. 413-419 
    ISSN: 1432-0878
    Keywords: Key words: Apoptosis ; Mammary gland ; Lactation ; Involution ; DNA laddering ; Mouse
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Abstract. Mammary involution after cessation of milk removal is associated with extensive loss of secretory epithelial cells. Ultrastructural changes and the appearance of oligonucleosomal DNA laddering in ethidium bromide-stained gels indicates that cell loss during involution occurs by apoptosis. In this study, a technique for nick end-labelling of genomic DNA with radiolabelled deoxynucleotide has been used to monitor the induction of programmed cell death in mice after litter removal at peak lactation. This technique proved more sensitive than conventional ethidium bromide staining, and results suggested that apoptosis was induced rapidly by milk stasis, before extensive tissue re-modelling had begun. Oligonucleosomal DNA laddering on agarose gels was detected within 24 h of milk stasis, and increased progressively for at least 4 days. Nick-end labelling also detected laddering before litter removal, suggesting that programmed cell death is a normal feature of the lactating tissue. The DNA end-labelling technique was also adapted for in situ visualisation of apoptotic cells in tissue sections. By this criterion, apoptotic cells were identified in both the secretory epithelium lining the alveoli of the gland and, increasingly with prolonged milk stasis, amongst those sloughed into the alveolar lumen. The results demonstrate the utility of these techniques for study of mammary cell death and suggest that, whilst apoptosis is rapidly induced by milk stasis, it is also a normal physiological event in the lactating mammary gland.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Cell & tissue research 281 (1995), S. 413-419 
    ISSN: 1432-0878
    Keywords: Apoptosis ; Mammary gland ; Lactation ; Involution ; DNA laddering ; Mouse
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Abstract Mammary involution after cessation of milk removal is associated with extensive loss of secretory epithelial cells. Ultrastructural changes and the appearance of oligonucleosomal DNA laddering in ethidium bromide-stained gels indicates that cell loss during involution occurs by apoptosis. In this study, a technique for nick end-labelling of genomic DNA with radiolabelled deoxynucleotide has been used to monitor the induction of programmed cell death in mice after litter removal at peak lactation. This technique proved more sensitive than conventional ethidium bromide staining, and results suggested that apoptosis was induced rapidly by milk stasis, before extensive tissue re-modelling had begun. Oligonucleosomal DNA laddering on agarose gels was detected within 24 h of milk stasis, and increased progressively for at least 4 days. Nick-end labelling also detected laddering before litter removal, suggesting that programmed cell death is a normal feature of the lactating tissue. The DNA end-labelling technique was also adapted for in situ visualisation of apoptotic cells in tissue sections. By this criterion, apoptotic cells were identified in both the secretory epithelium lining the alveoli of the gland and, increasingly with prolonged milk stasis, amongst those sloughed into the alveolar lumen. The results demonstrate the utility of these techniques for study of mammary cell death and suggest that, whilst apoptosis is rapidly induced by milk stasis, it is also a normal physiological event in the lactating mammary gland.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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