Reviews for Quantitative Sociodynamics Stochastic Methods And Models Of Social Interaction Processes

The average rating for Quantitative Sociodynamics Stochastic Methods And Models Of Social Interaction Processes based on 2 reviews is 4 stars.

Review # 1 was written on 2015-02-08 00:00:00 Thomas Badgett It is a fact oft-repeated amongst shape theorists that while standard notions of homotopy theory may give us good information for studying global properties of spaces with nice local behaviour, they are often inadequate when it comes to analysing global properties of spaces with bad local behaviour. The prototypical example is that of the Warsaw Circle, which in some sense "looks like" S^1 (insofar as they both split the plane into two components), yet is not homotopically equivalent to it. The best we have is that the Warsaw Circle is weakly homotopically equivalent to S^0, which it (globally) resembles far less than S^1. So how do we remedy this? This is the main motivation behind shape theory, or shape equivalence, which gives us a precise way of articulating how the Warsaw Circle and S^1 'look the same'. In light of this, this book gives us two refinements of standard topological ideas - one is the refinement of shape theory to strong shape theory, the other is the refinement of Cech homology to strong homology - and the relationship between the two (in particular, strong homology is a strong shape invariant). There are several technical advantages of strong shape over shape, e.g. when studying the complements of Z-Sets in Hilbert cubes, strong shape allows us to work with the proper homotopy category (of Z-Sets in Hilbert cubes) whereas ordinary shape forces us to work with the less natural weakly homotopy category (of Z-Sets in Hilbert cubes). As for Cech homology - one of the reasons why Cech homology is less widely used than Cech cohomology is because it fails to satisfy the exactness axiom. Strong homology, however does, and is closely linked to the former. More precisely, the strong homology group can be approximated by a sequence of specific homology groups, H^r, where r is indexed by the natural numbers, where we regard the strong homology group as r=∞. The homology group H^0 coincides with the Cech homology group and gives the coarsest approximation of the strong homology group. Overall, this was a fairly self-contained book. All the relevant results were proved in detail and backed by a sea of lemmas and lengthy equational reasoning - which is understandable since this book aimed to fill a gap in the literature by providing a good comprehensive reference for these ideas. Still, while I confessed I skimmed most of the material, the text was sufficiently well-organised so I was always fairly clear on what the main/important results of the chapter were, which was enough to give me a decent (if rough) understanding of what was going on, and to sieve out what could be useful to me.

Review # 2 was written on 2017-02-04 00:00:00 Luke Veitch Recommended by Claus Diem