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a b s t r a c tWe develop computational bounds on performance for causal state feedback stochastic control with linear dynamics, arbitrary noise distribution, and arbitrary input constraint set. This can be very useful as a comparison with the performance of suboptimal control policies, which we can evaluate using Monte Carlo simulation. Our method involves solving a semidefinite program (a linear optimization problem with linear matrix inequality constraints), a convex optimization problem which can be efficiently solved. Numerical experiments show that the lower bound obtained by our method is often close to the performance achieved by several widely-used suboptimal control policies, which shows that both are nearly optimal. As a by-product, our performance bound yields approximate value functions that can be used as control Lyapunov functions for suboptimal control policies.

This study investigated whether video lectures instructed by a heightened level of expressiveness instructor were better than those instructed by a conventional level of expressiveness instructor or audio-only in promoting students' online learning, and what kind of effects do instructor's facial expressions have on students' learning. Three different types of video lectures (one with a heightened level of expressiveness instructor, one with a conventional level of expressiveness instructor and one with the instructor' audio only) were used to study the effects of instructor's facial expressions. Sixty-nine participants from Chinese Normal University were selected to learn with these video lectures. Results of this study indicated that video lectures with a heightened level of expressiveness instructor were better than those with a conventional level of expressiveness instructor and audio-only ones with regard to improving students' arousal level and learning satisfaction. Instructor's facial expressions had no significant influence on participants' short-term recall (p 5 .90), while instructor's facial expressions did influence students' medium-term recall (p 5 .03). Instructor's facial expressions played a key role in students' online learning.

This paper extends the semi-parametric identification and estimation method for dynamic discrete choice models using Hotz and Miller's (1993) conditional choice probability (CCP) approach to the setting where individuals may have hyperbolic discounting time preferences and may be naive about their time inconsistency. We implement the proposed estimation method to the decisions of undertaking mammography to evaluate the importance of present bias and naivety in the under-utilization of mammography. Preliminary results show evidence for both present bias and naivety.

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Abstract. Biomass burning emits vapors and aerosols into the atmosphere that can rapidly evolve as smoke plumes travel downwind and dilute, affecting climate- and health-relevant properties of the smoke. To date, theory has been unable to explain observed variability in smoke evolution. Here, we use observational data from the Biomass Burning Observation Project (BBOP) field campaign and show that initial smoke organic aerosol mass concentrations can help predict changes in smoke aerosol aging markers, number concentration, and number mean diameter between 40–262 nm. Because initial field measurements of plumes are generally >10 min downwind, smaller plumes will have already undergone substantial dilution relative to larger plumes and have lower concentrations of smoke species at these observations closest to the fire. The extent to which dilution has occurred prior to the first observation is not a directly measurable quantity. We show that initial observed plume concentrations can serve as a rough indicator of the extent of dilution prior to the first measurement, which impacts photochemistry, aerosol evaporation, and coagulation. Cores of plumes have higher concentrations than edges. By segregating the observed plumes into cores and edges, we find evidence that particle aging, evaporation, and coagulation occurred before the first measurement. We further find that on the plume edges, the organic aerosol is more oxygenated, while a marker for primary biomass burning aerosol emissions has decreased in relative abundance compared to the plume cores. Finally, we attempt to decouple the roles of the initial concentrations and physical age since emission by performing multivariate linear regression of various aerosol properties (composition, size) on these two factors.

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A subset $\Omega$ of $\mathbf{R}^d$ with finite positive Lebesgue measure is called a spectral set if there exists a subset $\Lambda\subset\mathbf{R}$ such that ${\mathcal E}_\Lambda :=\{e^{i2\pi \langle\lambda, x\rangle}: \lambda\in\Lambda\}$ form an orthogonal basis of $L^2(\Omega)$. The set $\Lambda$ is called a spectrum of the set $\Omega$. The Spectral Set Conjecture states that $\Omega$ is a spectral set if and only if $\Omega$ tiles $\mathbf{R}^d$ by translation. In this paper we prove the Spectral Set Conjecture for a class of sets $\Omega \subset \mathbf{R}$. Specifically we show that a spectral set possessing a spectrum that is a strongly periodic set must tile $\mathbf{R}$ by translates of a strongly periodic set depending only on the spectrum, and vice versa.