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