2,068 research outputs found
On the Survival of Some Unstable Two-Sided Matching Mechanisms
In the 1960s, three types of matching mechanisms were adopted in regional entry-level British medical labor markets to prevent unraveling of contract dates. One of these categories of matching mechanisms failed to prevent unraveling. Roth (1991) showed the instability of that failing category. One of the surviving categories was unstable as well, and Roth concluded that features of the environments of these mechanisms are responsible for their survival. However, Ünver (2001) demonstrated that the successful yet unstable mechanisms performed better in preventing unraveling than the unsuccessful and unstable category in an artificial-adaptive-agent-based economy. In this paper, we conduct a human subject experiment in addition to short- and long-run artificial agent simulations to understand this puzzle. We find that both the unsuccessful and unstable mechanism and the successful and unstable mechanism perform poorly in preventing unraveling in the experiment and in short-run simulations, while long-run simulations support the previous Ünver finding.
Holonomy reduced dynamics of triatomic molecular systems
Whereas it is easy to reduce the translational symmetry of a molecular system
by using, e.g., Jacobi coordinates the situation is much more involved for the
rotational symmetry. In this paper we address the latter problem using {\it
holonomy reduction}. We suggest that the configuration space may be considered
as the reduced holonomy bundle with a connection induced by the mechanical
connection. Using the fact that for the special case of the three-body problem,
the holonomy group is SO(2) (as opposed to SO(3) like in systems with more than
three bodies) we obtain a holonomy reduced configuration space of topology . The dynamics then takes place on the cotangent
bundle over the holonomy reduced configuration space. On this phase space there
is an symmetry action coming from the conserved reduced angular momentum
which can be reduced using the standard symplectic reduction method. Using a
theorem by Arnold it follows that the resulting symmetry reduced phase space is
again a natural mechanical phase space, i.e. a cotangent bundle. This is
different from what is obtained from the usual approach where symplectic
reduction is used from the outset. This difference is discussed in some detail,
and a connection between the reduced dynamics of a triatomic molecule and the
motion of a charged particle in a magnetic field is established.Comment: 11 pages, submitted to J. Phys.
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