Bounds for the genus of a normal surface

This paper gives sharp linear bounds on the genus of a normal surface in a triangulated compact, orientable 3--manifold in terms of the quadrilaterals in its cell decomposition---different bounds arise from varying hypotheses on the surface or triangulation. Two applications of these bounds are given. First, the minimal triangulations of the product of a closed surface and the closed interval are determined. Second, an alternative approach to the realisation problem using normal surface theory is shown to be less powerful than its dual method using subcomplexes of polytopes.Comment: 38 pages, 25 figure

Valuing Options in Water Markets: A Laboratory Investigation

Risk and reliability dominate water supply discussions in the arid western United States in light of increasing demand and finite, weather-dependant supply. Thus water agencies increasingly turn to contractual mechanisms such as dry-year options to manage supply risk in advance of need. Although a few water agencies across the West have implemented dry-year options, sufficient data for conventional econometric analysis do not yet exist. We thus utilize experimental economics to analyze the effect of annual dry-year options on water markets. We consider how market structure (competitive versus monopsony power) and option contract availability affect water price and allocation within a market and find that realized gains from trade are on average higher when options can be traded, by 46% in competitive markets and by 63% in dominant buyer markets. Important for the political feasibility of such markets, we also find that gains from trade, once an options market is available, are much more evenly distributed between the single buyer and the many sellers in the case of monopsony.Resource /Energy Economics and Policy, D23, L22, Q25,

fMRI in Translation: The Challenges Facing Real-World Applications

Functional neuroimaging has increased our understanding of human brain function tremendously and has become a standard tool in clinical and cognitive neuroscience research. We briefly review its methodological foundations and describe remaining challenges for translational research. The application of neuroimaging results to individual subjects, for example in predicting treatment response or determining the veracity of a statement, is limited by these challenges, in particular by the anatomical and statistical procedures commonly employed. We thus argue for sincere caution in the translation of functional neuroimaging to real-world applications

The Trisection Genus of Standard Simply Connected PL 4-Manifolds

Gay and Kirby recently introduced the concept of a trisection for arbitrary smooth, oriented closed 4-manifolds, and with it a new topological invariant, called the trisection genus. In this note we show that the K3 surface has trisection genus 22. This implies that the trisection genus of all standard simply connected PL 4-manifolds is known. We show that the trisection genus of each of these manifolds is realised by a trisection that is supported by a singular triangulation. Moreover, we explicitly give the building blocks to construct these triangulations

What absent switch costs and mixing costs during bilingual language comprehension can tell us about language control.

Epub 2019 Mar 28.In the current study, we set out to investigate language control, which is the process that minimizes cross-language interference, during bilingual language comprehension. According to current theories of bilingual language comprehension, language-switch costs, which are a marker for reactive language control, should be observed. However, a closer look at the literature shows that this is not always the case. Furthermore, little to no evidence for language-mixing costs, which are a marker for proactive language control, has been observed in the bilingual language comprehension literature. This is in line with current theories of bilingual language comprehension, as they do not explicitly account for proactive language control. In the current study, we further investigated these two markers of language control and found no evidence for comprehension-based language-switch costs in six experiments, even though other types of switch costs were observed with the exact same setup (i.e., task-switch costs, stimulus modality-switch costs, and production-based language-switch costs). Furthermore, only one out of three experiments showed comprehension-based language-mixing costs, providing the first tentative evidence for proactive language control during bilingual language comprehension. The implications of the absence and occurrence of these costs are discussed in terms of processing speed and parallel language activation. (PsycINFO Database Record (c) 2019 APA, all rights reserved)This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 706128. This research was also supported by grants ANR-11-LABX-0036 (BLRI), ANR-16-CONV-0002 (ILCB), and ANR-11-IDEX-0001-02 from the French National Research Council (ANR)

Valuing Options in California Water Markets: A Laboratory Investigation

Risk and reliability dominate water supply discussions in the arid western United States. In the past, water managers built additional storage to mitigate supply risk. The optimal, least expensive storage sites have now been taken, and there are strong, environmental objections to new facilities. Reliability of existing supplies is further diminished due to concerns about endangered species and global climate change. Thus water agencies increasingly turn to contractual mechanisms such as dry-year options to manage supply risk in advance of need. However, although a few water agencies across the West have implemented dry-year options, sufficient data for conventional econometric analysis do not yet exist. We thus utilize experimental economics to analyze the effect of annual dry-year options on water markets. How do market structure (competitive versus market power) and option contract availability affect water price and allocation within a market? Experiment participants trade stochastic realizations of water in a non-uniform double auction parameterized to resemble the California water market. We find that realized gains from trade are on average higher when options can be traded, by 11% in competitive markets and by 21% in dominant buyer markets. Findings in this analysis may assist policymakers in preparing for the next multi-year drought in California.Resource /Energy Economics and Policy,

A qualitative difference between gradient flows of convex functions in finite- and infinite-dimensional Hilbert spaces

We consider gradient flow/gradient descent and heavy ball/accelerated gradient descent optimization for convex objective functions. In the gradient flow case, we prove the following: 1. If $f$ does not have a minimizer, the convergence $f(x_t)\to \inf f$ can be arbitrarily slow. 2. If $f$ does have a minimizer, the excess energy $f(x_t) - \inf f$ is integrable/summable in time. In particular, $f(x_t) - \inf f = o(1/t)$ as $t\to\infty$. 3. In Hilbert spaces, this is optimal: $f(x_t) - \inf f$ can decay to $0$ as slowly as any given function which is monotone decreasing and integrable at $\infty$, even for a fixed quadratic objective. 4. In finite dimension (or more generally, for all gradient flow curves of finite length), this is not optimal: We prove that there are convex monotone decreasing integrable functions $g(t)$ which decrease to zero slower than $f(x_t)-\inf f$ for the gradient flow of any convex function on $\mathbb R^d$. For instance, we show that any gradient flow $x_t$ of a convex function $f$ in finite dimension satisfies $\liminf_{t\to\infty} \big(t\cdot \log^2(t)\cdot \big\{f(x_t) -\inf f\big\}\big)=0$. This improves on the commonly reported $O(1/t)$ rate and provides a sharp characterization of the energy decay law. We also note that it is impossible to establish a rate $O(1/(t\phi(t))$ for any function $\phi$ which satisfies $\lim_{t\to\infty}\phi(t) = \infty$, even asymptotically. Similar results are obtained in related settings for (1) discrete time gradient descent, (2) stochastic gradient descent with multiplicative noise and (3) the heavy ball ODE. In the case of stochastic gradient descent, the summability of $\mathbb E[f(x_n) - \inf f]$ is used to prove that $f(x_n)\to \inf f$ almost surely - an improvement on the convergence almost surely up to a subsequence which follows from the $O(1/n)$ decay estimate

A nonlinear model for rotationally constrained convection with Ekman pumping

It is a well established result of linear theory that the influence of differing mechanical boundary conditions, i.e., stress-free or no-slip, on the primary instability in rotating convection becomes asymptotically small in the limit of rapid rotation. This is accounted for by the diminishing impact of the viscous stresses exerted within Ekman boundary layers and the associated vertical momentum transport by Ekman pumping. By contrast, in the nonlinear regime recent experiments and supporting simulations are now providing evidence that the efficiency of heat transport remains strongly influenced by Ekman pumping in the rapidly rotating limit. In this paper, a reduced model is developed for the case of low Rossby number convection in a plane layer geometry with no-slip upper and lower boundaries held at fixed temperatures. A complete description of the dynamics requires the existence of three distinct regions within the fluid layer: a geostrophically balanced interior where fluid motions are predominately aligned with the axis of rotation, Ekman boundary layers immediately adjacent to the bounding plates, and thermal wind layers driven by Ekman pumping in between. The reduced model uses a classical Ekman pumping parameterization to alleviate the need for spatially resolving the Ekman boundary layers. Results are presented for both linear stability theory and a special class of nonlinear solutions described by a single horizontal spatial wavenumber. It is shown that Ekman pumping allows for significant enhancement in the heat transport relative to that observed in simulations with stress-free boundaries. Without the intermediate thermal wind layer the nonlinear feedback from Ekman pumping would be able to generate a heat transport that diverges to infinity. This layer arrests this blowup resulting in finite heat transport at a significantly enhanced value.Comment: 38 pages, 14 figure