29,744 research outputs found
A combinatorial non-positive curvature I: weak systolicity
We introduce the notion of weakly systolic complexes and groups, and initiate
regular studies of them. Those are simplicial complexes with
nonpositive-curvature-like properties and groups acting on them geometrically.
We characterize weakly systolic complexes as simply connected simplicial
complexes satisfying some local combinatorial conditions. We provide several
classes of examples --- in particular systolic groups and CAT(-1) cubical
groups are weakly systolic. We present applications of the theory, concerning
Gromov hyperbolic groups, Coxeter groups and systolic groups.Comment: 35 pages, 1 figur
Cycling Through History: Making an American Sport 1880-present, Blog 2
Student blog posts from the Great VCU Bike Race Book
Persistence time of SIS infections in heterogeneous populations and networks
For a susceptible-infectious-susceptible (SIS) infection model in a
heterogeneous population, we present simple formulae giving the leading-order
asymptotic (large population) behaviour of the mean persistence time, from an
endemic state to extinction of infection. Our model may be interpreted as
describing an infection spreading through either (i) a population with
heterogeneity in individuals' susceptibility and/or infectiousness; or (ii) a
heterogeneous directed network. Using our asymptotic formulae, we show that
such heterogeneity can only reduce (to leading order) the mean persistence time
compared to a corresponding homogeneous population, and that the greater the
degree of heterogeneity, the more quickly infection will die out
Analysis of Testing-Based Forward Model Selection
This paper introduces and analyzes a procedure called Testing-based forward
model selection (TBFMS) in linear regression problems. This procedure
inductively selects covariates that add predictive power into a working
statistical model before estimating a final regression. The criterion for
deciding which covariate to include next and when to stop including covariates
is derived from a profile of traditional statistical hypothesis tests. This
paper proves probabilistic bounds, which depend on the quality of the tests,
for prediction error and the number of selected covariates. As an example, the
bounds are then specialized to a case with heteroskedastic data, with tests
constructed with the help of Huber-Eicker-White standard errors. Under the
assumed regularity conditions, these tests lead to estimation convergence rates
matching other common high-dimensional estimators including Lasso
Track-Down Operations on Bilattices
This paper discusses a dualization of Fitting's notion of a "cut-down" operation on a bilattice, rendering a "track-down" operation, later used to represent the idea that a consistent opinion cannot arise from a set including an inconsistent opinion. The logic of track-down operations on bilattices is proved equivalent to the logic d_Sfde, dual to Deutsch's system S_fde. Furthermore, track-down operations are employed to provide an epistemic interpretation for paraconsistent weak Kleene logic. Finally, two logics of sequential combinations of cut-and track-down operations allow settling positively the question of whether bilattice-based semantics are available for subsystems of S_fde
A note on the Manin-Mumford conjecture
In the article [PR1] {\it On Hrushovski's proof of the Manin-Mumford
conjecture} (Proceedings of the ICM 2002), R. Pink and the author gave a short
proof of the Manin-Mumford conjecture, which was inspired by an earlier
model-theoretic proof by Hrushovski. The proof given in [PR1] uses a difficult
unpublished ramification-theoretic result of Serre. It is the purpose of this
note to show how the proof given in [PR1] can be modified so as to circumvent
the reference to Serre's result. J. Oesterl\'e and R. Pink contributed several
simplifications and shortcuts to this note.Comment: 11 page
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