Equivalence of concentration inequalities for linear and non-linear functions

We consider a random variable $X$ that takes values in a (possibly infinite-dimensional) topological vector space $\mathcal{X}$. We show that, with respect to an appropriate "normal distance" on $\mathcal{X}$, concentration inequalities for linear and non-linear functions of $X$ are equivalent. This normal distance corresponds naturally to the concentration rate in classical concentration results such as Gaussian concentration and concentration on the Euclidean and Hamming cubes. Under suitable assumptions on the roundness of the sets of interest, the concentration inequalities so obtained are asymptotically optimal in the high-dimensional limit.Comment: 19 pages, 5 figure

Teaching College Economics in a High School Setting: Lessons Learned and Implementation Strategies

Interest in exposing high school seniors to college level economics has risen in recent years. Under one delivery option, a dual-enrollment program, students are concurrently enrolled in college and high school, and receive credit at both institutions for the same course. These programs benefit high schools by increasing the academic rigor in the senior year, and may also aid colleges' external relations and recruitment. Colleges and universities considering such a program must recognize important administrative and student body differences between the university and high school settings. This paper summarizes the experiences of Southern Illinois University, where a dual-enrollment program was implemented in the mid 1990s, and uses this case to illustrate key differences between the two classroom environments. Suggested strategies for coping with these differences are described.

Analysis of gradient descents in random energies and heat baths

This thesis concerns the mathematical analysis of random gradient descent evolutions as models for rate-independent dissipative systems under the influence of thermal effects. The basic notions of the theory of gradient descents (especially rate-independent evolutions) are reviewed in chapter 2. Chapters 3 and 4 focus on the scaling regime in which the microstructure dominates the thermal effects and comprise a rigorous justification of rateindependent processes in smooth, convex energies as scaling limits of ratedependent gradient descents in energies that have rapidly-oscillating random microstructure: chapter 3 treats the one-dimensional case with quite a broad class of random microstructures; chapter 4 treats a case in which the microstructure is modeled by a sum of “dent functions” that are scattered in Rn using a suitable point process. Chapters 5 and 6 focus on the opposite scaling regime: a gradient descent system (typically a rate-independent process) is placed in contact with a heat bath. The method used to “thermalize” a gradient descent is an interior-point regularization of the Moreau–Yosida incremental problem for the original gradient descent. Chapter 5 treats the heuristics and generalities; chapter 6 treats the case of 1-homogeneous dissipation (rate independence) and shows that the heat bath destroys the rate independence in a controlled and deterministic way, and that the effective dynamics are a gradient descent in the original energetic potential but with respect to a different and non-trivial effective dissipation potential. The appendices contain some auxiliary definitions and results, most of them standard in the literature, that are used in the main text

Analysis of gradient descents in random energies and heat baths

This thesis concerns the mathematical analysis of random gradient descent evolutions as models for rate-independent dissipative systems under the influence of thermal effects. The basic notions of the theory of gradient descents (especially rate-independent evolutions) are reviewed in chapter 2. Chapters 3 and 4 focus on the scaling regime in which the microstructure dominates the thermal effects and comprise a rigorous justification of rateindependent processes in smooth, convex energies as scaling limits of ratedependent gradient descents in energies that have rapidly-oscillating random microstructure: chapter 3 treats the one-dimensional case with quite a broad class of random microstructures; chapter 4 treats a case in which the microstructure is modeled by a sum of “dent functions” that are scattered in Rn using a suitable point process. Chapters 5 and 6 focus on the opposite scaling regime: a gradient descent system (typically a rate-independent process) is placed in contact with a heat bath. The method used to “thermalize” a gradient descent is an interior-point regularization of the Moreau–Yosida incremental problem for the original gradient descent. Chapter 5 treats the heuristics and generalities; chapter 6 treats the case of 1-homogeneous dissipation (rate independence) and shows that the heat bath destroys the rate independence in a controlled and deterministic way, and that the effective dynamics are a gradient descent in the original energetic potential but with respect to a different and non-trivial effective dissipation potential. The appendices contain some auxiliary definitions and results, most of them standard in the literature, that are used in the main text.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research Council (Great Britain) (EPSRC)University of Warwick (UoW)GBUnited Kingdo

Investigating the impact of design criteria on the expected seismic losses of an office building

Low Damage Seismic Design (LDSD) guidance material being developed by Engineering NZ is considering a design drift limit for multi-storey buildings of 0.5% at a new damage control limit state (DCLS). The impact of this new design requirement on the expected annual loss due to repair costs is investigated for a four-storey office building with reinforced concrete walls located in Christchurch. The LDSD guidance material aims to reduce the expected annual loss of complying buildings to below 0.1% of building replacement cost. The research tested this expectation. Losses were estimated in accordance with FEMA P58, using building responses from non-linear time history analyses (performed with OpenSees using lumped plasticity models). The equivalent static method, in line with NZS 1170.5 and NZS 3101, was used to design the building to LDSD specifications, representing a future state-of-practice design. The building designed to low-damage specification returned an expected annual loss of 0.10%, and the building designed conventionally returned an expected annual loss of 0.13%. Limitations with the NZS 3101 method for determining wall stiffness were identified, and a different method acknowledging the relationship between strength and stiffness was used to redesign the building. Along with improving this design assumption, the study finds that LDSD design criteria could be an effective way of limiting damage and losses

Supporting reasoning with different types of evidence in intelligence analysis

The aim of intelligence analysis is to make sense of information that is often conflicting or incomplete, and to weigh competing hypotheses that may explain a situation. This imposes a high cognitive load on analysts, and there are few automated tools to aid them in their task. In this paper, we present an agent-based tool to help analysts in acquiring, evaluating and interpreting information in collaboration with others. Agents assist analysts in reasoning with different types of evidence to identify what happened and why, what is credible, and how to obtain further evidence. Argumentation schemes lie at the heart of the tool, and sense-making agents assist analysts in structuring evidence and identifying plausible hypotheses. A crowdsourcing agent is used to reason about structured information explicitly obtained from groups of contributors, and provenance is used to assess the credibility of hypotheses based on the origins of the supporting information

Emissions of CO 2 , CO, NO x , HC, PM, HFC-134a, N 2 O and CH 4 from the global light duty vehicle fleet

Abstract Vehicle

Multicolor Observations of a Planetary Transit of HD 209458

We present B, V, R, I and Z-band photometric observations of HD 209458 during the transit by its planetary companion on UT 1999 November 15 with the University of Hawaii 0.6m and 2.2m telescopes and the High Altitude Observatory STARE telescope. The detailed shape of the transit curve is predicted to vary with color due primarily to the color-dependent limb-darkening of the star, but potentially due as well to the effect of color-dependent opacity in the planetary atmosphere. We model the light curves and present refined values for the transit timing and orbital period, useful for planning future observations of the planetary transit. We also derive significantly improved measurements of the planetary radius, R_p = 1.55 +/- 0.10 R_Jup, stellar radius, R_s = 1.27 +/- 0.05 R_Sun, and orbital inclination, i = 85.9 +/- 0.5 deg. The derived planetary radius favors evolutionary models in which the planet has a low albedo.Comment: 6 pages, 3 figures, accepted for publication in ApJ Letter

Comparative bioavailability: A new type of in vitro-in vivo correlation exemplified by prednisone

The average time to reach half-maximal plasma concentration of prednisolone and the average plasma concentrations of prednisolone at 0.5 and 1 hr obtained from three crossover bioavailability studies, involving testing of commercially available 5-mg prednisone tablets, were highly correlated (r⪖ 0.88) with parameters derived from in vitro tablet dissolution rates performed in the spin filter apparatus of Shah. The in vitro parameters were the times to dissolve 16% or 50% of the labeled amount of prednisone or the percent of the labeled amount of prednisone dissolved in 20 min in water at 37‡C. Such correlations may be useful in the setting of in vitro dissolution rate specifications for commencal prednisone tablets .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45065/1/10928_2005_Article_BF01086152.pd