521,423 research outputs found
A general model of the public goods dilemma
An individually costly act that benefits all group members is a public good.
Natural selection favors individual contribution to public goods only when some
benefit to the individual offsets the cost of contribution. Problems of sex
ratio, parasite virulence, microbial metabolism, punishment of noncooperators,
and nearly all aspects of sociality have been analyzed as public goods shaped
by kin and group selection. Here, I develop two general aspects of the public
goods problem that have received relatively little attention. First, variation
in individual resources favors selfish individuals to vary their allocation to
public goods. Those individuals better endowed contribute their excess
resources to public benefit, whereas those individuals with fewer resources
contribute less to the public good. Thus, purely selfish behavior causes
individuals to stratify into upper classes that contribute greatly to public
benefit and social cohesion and to lower classes that contribute little to the
public good. Second, if group success absolutely requires production of the
public good, then the pressure favoring production is relatively high. By
contrast, if group success depends weakly on the public good, then the pressure
favoring production is relatively weak. Stated in this way, it is obvious that
the role of baseline success is important. However, discussions of public goods
problems sometimes fail to emphasize this point sufficiently. The models here
suggest simple tests for the roles of resource variation and baseline success.
Given the widespread importance of public goods, better models and tests would
greatly deepen our understanding of many processes in biology and sociality
Real Rational Curves in Grassmannians
Fulton asked how many solutions to a problem of enumerative geometry can be
real, when that problem is one of counting geometric figures of some kind
having specified position with respect to some general fixed figures. For the
problem of plane conics tangent to five general conics, the (surprising) answer
is that all 3264 may be real. Similarly, given any problem of enumerating
p-planes incident on some general fixed subspaces, there are real fixed
subspaces such that each of the (finitely many) incident p-planes are real. We
show that the problem of enumerating parameterized rational curves in a
Grassmannian satisfying simple (codimension 1) conditions may have all of its
solutions be real.Comment: 9 pages, 1 eps figure, uses epsf.sty. Below the LaTeX source is a
MAPLE V.5 file which computes an example in the paper, and its outpu
Some real and unreal enumerative geometry for flag manifolds
We present a general method for constructing real solutions to some problems
in enumerative geometry which gives lower bounds on the maximum number of real
solutions. We apply this method to show that two new classes of enumerative
geometric problems on flag manifolds may have all their solutions be real and
modify this method to show that another class may have no real solutions, which
is a new phenomenon. This method originated in a numerical homotopy
continuation algorithm adapted to the special Schubert calculus on
Grassmannians and in principle gives optimal numerical homotopy algorithms for
finding explicit solutions to these other enumerative problems.Comment: 19 pages, LaTeX-2e; Updated and final version. To appear in the issue
of Michigan Mathematical Journal dedicated to Bill Fulto
SUSY Before the Next Lepton Collider
After a brief review of the Minimal Supersymmetric Standard Model (MSSM) and
specifically the Minimal Supergravity Model (SUGRA), the prospects for
discovering and studying SUSY at the CERN Large Hadron Collider are reviewed.
The possible role for a future Lepton Collider --- whether or
--- is also discussed.Comment: LaTeX with included aipproc.sty, 17 pages, 12 figures. To appear in
Workshop on Physics at the First Muon Collide
Preventing extinction and outbreaks in chaotic populations
Interactions in ecological communities are inherently nonlinear and can lead
to complex population dynamics including irregular fluctuations induced by
chaos. Chaotic population dynamics can exhibit violent oscillations with
extremely small or large population abundances that might cause extinction and
recurrent outbreaks, respectively. We present a simple method that can guide
management efforts to prevent crashes, peaks, or any other undesirable state.
At the same time, the irregularity of the dynamics can be preserved when chaos
is desirable for the population. The control scheme is easy to implement
because it relies on time series information only. The method is illustrated by
two examples: control of crashes in the Ricker map and control of outbreaks in
a stage-structured model of the flour beetle Tribolium. It turns out to be
effective even with few available data and in the presence of noise, as is
typical for ecological settings.Comment: 10 pages, 6 figure
The hadron-quark transition with a lattice of nonlocal confining solitons
We use a lattice of nonlocal confining solitons to describe nuclear matter in
the Wigner-Seitz approximation. The average density is varied by changing the
size of the Wigner-Seitz cell. At sufficiently large density quark energy bands
develop. The intersection of the filled valence band with the next empty band
at a few times standard nuclear density signals a transition from a color
insulator to a color conductor and is identified with the critical density for
quark deconfinement.Comment: 12 pages Latex with one PS figur
Exploring the utility of joint morphological and syntactic learning from child-directed speech
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