22,823 research outputs found
Topological finiteness properties of monoids. Part 1: Foundations
We initiate the study of higher dimensional topological finiteness properties
of monoids. This is done by developing the theory of monoids acting on CW
complexes. For this we establish the foundations of -equivariant homotopy
theory where is a discrete monoid. For projective -CW complexes we prove
several fundamental results such as the homotopy extension and lifting
property, which we use to prove the -equivariant Whitehead theorems. We
define a left equivariant classifying space as a contractible projective -CW
complex. We prove that such a space is unique up to -homotopy equivalence
and give a canonical model for such a space via the nerve of the right Cayley
graph category of the monoid. The topological finiteness conditions
left- and left geometric dimension are then defined for monoids
in terms of existence of a left equivariant classifying space satisfying
appropriate finiteness properties. We also introduce the bilateral notion of
-equivariant classifying space, proving uniqueness and giving a canonical
model via the nerve of the two-sided Cayley graph category, and we define the
associated finiteness properties bi- and geometric dimension. We
explore the connections between all of the these topological finiteness
properties and several well-studied homological finiteness properties of
monoids which are important in the theory of string rewriting systems,
including , cohomological dimension, and Hochschild
cohomological dimension. We also develop the corresponding theory of
-equivariant collapsing schemes (that is, -equivariant discrete Morse
theory), and among other things apply it to give topological proofs of results
of Anick, Squier and Kobayashi that monoids which admit presentations by
complete rewriting systems are left-, right- and bi-.Comment: 59 pages, 1 figur
Speeding up neighborhood search in local Gaussian process prediction
Recent implementations of local approximate Gaussian process models have
pushed computational boundaries for non-linear, non-parametric prediction
problems, particularly when deployed as emulators for computer experiments.
Their flavor of spatially independent computation accommodates massive
parallelization, meaning that they can handle designs two or more orders of
magnitude larger than previously. However, accomplishing that feat can still
require massive supercomputing resources. Here we aim to ease that burden. We
study how predictive variance is reduced as local designs are built up for
prediction. We then observe how the exhaustive and discrete nature of an
important search subroutine involved in building such local designs may be
overly conservative. Rather, we suggest that searching the space radially,
i.e., continuously along rays emanating from the predictive location of
interest, is a far thriftier alternative. Our empirical work demonstrates that
ray-based search yields predictors with accuracy comparable to exhaustive
search, but in a fraction of the time - bringing a supercomputer implementation
back onto the desktop.Comment: 24 pages, 5 figures, 4 table
The Laws of Unintended Consequence: The Effect of Labour Legislation on Wages and Strikes
When politicians consider intervening in labour disputes, they should also consider the long-term, potentially unintended results of such action. In this study, the authors investigate the lessons from previous government legislative interventions, whether through compulsory arbitration, “back-to-work” legislation or bans on replacement workers during strikes, and find these actions have unintended results that give reason for sober second thought.Economic Growth and Innovation, Canadian federal and provincial governments, labour relations, compulsory arbitration, back-to-work legislation
- …