14,046 research outputs found
Combed 3-Manifolds with Concave Boundary, Framed Links, and Pseudo-Legendrian Links
We provide combinatorial realizations, according to the usual objects/moves
scheme, of the following three topological categories: (1) pairs (M,v) where M
is a 3-manifold (up to diffeomorphism) and v is a (non-singular vector) field,
up to homotopy; here possibly the boundary of M is non-empty and v may be
tangent to the boundary, but only in a concave fashion, and homotopy should
preserve tangency type; (2) framed links L in M, up to framed isotopy; (3)
triples (M,v,L), with (M,v) as above and L transversal to v, up to
pseudo-Legendrian isotopy (transversality-preserving simultaneous homotopy of v
and isotopy of L). All realizations are based on the notion of branched
standard spine, and build on results previously obtained. Links are encoded by
means of diagrams on branched spines, where the diagram is smooth with respect
to the branching. Several motivations for being interested in combinatorial
realizations of the topological categories considered in this paper are given
in the introduction. The encoding of links is suitable for the comparison of
the framed and the pseudo-Legendrian categories, and some applications are
given in connection with contact structures, torsion and finite-order
invariants. An estension of Trace's notion of winding number of a knot diagram
is introduced and discussed.Comment: 38 pages, 33 figure
Problem-formulation in a South African organization. Executive summary
Complex Problem Solving is an area of cognitive science that has received a good amount of
attention, but theories in the field have not progressed accordingly. In general, research of
problem solving has focussed on identifying preferable methods rather than on what happens
when human beings confront problems in an organizational context
Queseda, Kirtsch and Gomez (2005)
Existing literature recognises that most organizational problems are ill-defined. Some problems
can become well-defined whereas others are and remain ill-structured. For problems that can
become well-defined, failure to pay attention to the area of problem definition has the potential to
jeopardise the effectiveness of problem-formulation and thus the entire problem solving activity.
Problem defining, a fundamental part of the problem-formulation process, is seen as the best
defence against a Type III Error (trying to solve the wrong problem). Existing literature addresses
possible processes for problem-formulation and recognises the importance of applying problem
domain knowledge within them. However, inadequate attention is given to the possible
circumstances that, within an organization, the participants do not know enough about the
problem domain and do not recognise the importance of applying adequate problem domain
knowledge or experience to the problem-formulation process. A case study is conducted into
exactly these circumstances as they occurred and were successfully addressed within Eskom
Holdings Ltd (Eskom), the national electricity utility in South Africa. The case study is a
fundamental part of this research project, which explores the gap in the existing body of
knowledge related to the circumstances described above and specifically to problems that can
become well-defined, and provides the basis for the innovation developed herein that addresses
that gap
The chemistry of comets An annotated bibliography
Annotated bibliography on chemistry of comets - free radicals, photochemistry, photolysis, and spectral analysi
Stochastic Gradient Hamiltonian Monte Carlo
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for
defining distant proposals with high acceptance probabilities in a
Metropolis-Hastings framework, enabling more efficient exploration of the state
space than standard random-walk proposals. The popularity of such methods has
grown significantly in recent years. However, a limitation of HMC methods is
the required gradient computation for simulation of the Hamiltonian dynamical
system-such computation is infeasible in problems involving a large sample size
or streaming data. Instead, we must rely on a noisy gradient estimate computed
from a subset of the data. In this paper, we explore the properties of such a
stochastic gradient HMC approach. Surprisingly, the natural implementation of
the stochastic approximation can be arbitrarily bad. To address this problem we
introduce a variant that uses second-order Langevin dynamics with a friction
term that counteracts the effects of the noisy gradient, maintaining the
desired target distribution as the invariant distribution. Results on simulated
data validate our theory. We also provide an application of our methods to a
classification task using neural networks and to online Bayesian matrix
factorization.Comment: ICML 2014 versio
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