Man and machine thinking about the smooth 4-dimensional Poincar\'e conjecture

While topologists have had possession of possible counterexamples to the smooth 4-dimensional Poincar\'{e} conjecture (SPC4) for over 30 years, until recently no invariant has existed which could potentially distinguish these examples from the standard 4-sphere. Rasmussen's s-invariant, a slice obstruction within the general framework of Khovanov homology, changes this state of affairs. We studied a class of knots K for which nonzero s(K) would yield a counterexample to SPC4. Computations are extremely costly and we had only completed two tests for those K, with the computations showing that s was 0, when a landmark posting of Akbulut (arXiv:0907.0136) altered the terrain. His posting, appearing only six days after our initial posting, proved that the family of ``Cappell--Shaneson'' homotopy spheres that we had geared up to study were in fact all standard. The method we describe remains viable but will have to be applied to other examples. Akbulut's work makes SPC4 seem more plausible, and in another section of this paper we explain that SPC4 is equivalent to an appropriate generalization of Property R (``in S^3, only an unknot can yield S^1 x S^2 under surgery''). We hope that this observation, and the rich relations between Property R and ideas such as taut foliations, contact geometry, and Heegaard Floer homology, will encourage 3-manifold topologists to look at SPC4.Comment: 37 pages; changes reflecting that the integer family of Cappell-Shaneson spheres are now known to be standard (arXiv:0907.0136

Representing model inadequacy: A stochastic operator approach

Mathematical models of physical systems are subject to many uncertainties such as measurement errors and uncertain initial and boundary conditions. After accounting for these uncertainties, it is often revealed that discrepancies between the model output and the observations remain; if so, the model is said to be inadequate. In practice, the inadequate model may be the best that is available or tractable, and so despite its inadequacy the model may be used to make predictions of unobserved quantities. In this case, a representation of the inadequacy is necessary, so the impact of the observed discrepancy can be determined. We investigate this problem in the context of chemical kinetics and propose a new technique to account for model inadequacy that is both probabilistic and physically meaningful. A stochastic inadequacy operator $\mathcal{S}$ is introduced which is embedded in the ODEs describing the evolution of chemical species concentrations and which respects certain physical constraints such as conservation laws. The parameters of $\mathcal{S}$ are governed by probability distributions, which in turn are characterized by a set of hyperparameters. The model parameters and hyperparameters are calibrated using high-dimensional hierarchical Bayesian inference. We apply the method to a typical problem in chemical kinetics---the reaction mechanism of hydrogen combustion

Canada's Nuclear Crossroads: Steps to a Viable Nuclear Energy Industry

Canada is at an energy and environmental crossroad. Fossil fuels cause environmental damage and the growth potential of large-scale hydroelectricity is limited. Policymakers are reconsidering the merits of nuclear power as both a low-carbon emitting and low-cost base load electricity source. While nuclear power may look like an attractive option, nuclear power must overcome problems such as the high and uncertain cost of construction, dealing with nuclear waste, reactor licensing and regulation, and the future of Canada’s nuclear reactor builder, Atomic Energy of Canada Limited (AECL), a federal Crown corporation.economic growth and innovation, energy and environmental policy

The process of user-innovation: A case study on user innovation in a consumer goods setting

Manufacturers usually benefit by dividing their innovation processes into distinct phases in order to ensure that the development activities are performed efficiently in an appropriate sequence. Users usually do not apply such structured processes. They follow a more intuition-driven approach. In this paper we analyze the way users improve or develop novel products. The field of our research is a new and rapidly evolving consumer market, the sport of kite surfing. We identified a sequence that underlies the approaches of user inventors. This sequence consists of two major stages, (1) idea generation and (2) idea realization, each again subdivided. We propose that a manufacturer in the relevant product field can significantly profit from more closely observing such user activities: Better understanding of tacit needs which cannot be derived by applying classical market research methods. Learn about the adequacy of solutions from the user. This may guide their development activities and prevent development of inadequate solutions. Collect user ideas as well as corresponding solution knowledge at very low tariffs and increase reputation as a customer-close organization. --Produktinnovation,Produktentwicklung,Benutzer / Beteiligung

Comments on diffraction processes and total cross sections

Some controversial aspects of diffraction dissociation are discussed in the light of some recent results. Evidence is presented that the $A_1$ , $A_3$ , $Q$ and $L$ mass enhancements are not single resonant states and that an N* (l400) is not required. It is suggested that the cross section for diffraction dissociation is almost equal to that for diffraction elastic scattering and both are slowly rising as does the total inelastic cross section, i.e., as $s^+$ 0.04 or (log s)$^+$ 0.4. The Reggeon exchange part of pp elastic scattering then falls as $s^l$

Loss Aversion and Intertemporal Choice: A Laboratory Investigation

We present results from a laboratory study of loss aversion in the context of intertemporal choice. We investigate whether the provision of (windfall) endowments results in different elicited discount rates relative to subjects who earn income or earn and retain the income for a period before making intertemporal decisions. We hypothesize that loss aversion in an intertemporal choice yields higher discount rates among subjects earning and retaining. Our results support this hypothesis: among subjects who earn and retain their income we elicit substantially higher discount rates relative to those experiencing a windfall gain.intertemporal choice, discount rates, experiments

Loss aversion and intertemporal choice: A laboratory investigation

We present results from a laboratory study of loss aversion in the context of intertemporal choice. We investigate whether the provision of (windfall) endowments results in different elicited discount rates relative to subjects who earn income or earn and retain the income for a period before making intertemporal decisions. We hypothesize that loss aversion in an intertemporal choice yields higher discount rates among subjects earning and retaining. Our results support this hypothesis: among subjects who earn and retain their income we elicit substantially higher discount rates relative to those experiencing a windfall gain