The Average Sensitivity of an Intersection of Half Spaces

We prove new bounds on the average sensitivity of the indicator function of an intersection of $k$ halfspaces. In particular, we prove the optimal bound of $O(\sqrt{n\log(k)})$. This generalizes a result of Nazarov, who proved the analogous result in the Gaussian case, and improves upon a result of Harsha, Klivans and Meka. Furthermore, our result has implications for the runtime required to learn intersections of halfspaces

On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages

We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches that are appropriate for higher dimensions. The framework explores the configuration space by taking samples that are entire low-dimensional manifolds of the configuration space capturing its connectivity much better than isolated point samples. The contributions of this paper are as follows: (i) We present a recursive application of MMS in a six-dimensional configuration space, enabling the coordination of two polygonal robots translating and rotating amidst polygonal obstacles. In the adduced experiments for the more demanding test cases MMS clearly outperforms PRM, with over 20-fold speedup in a coordination-tight setting. (ii) A probabilistic completeness proof for the most prevalent case, namely MMS with samples that are affine subspaces. (iii) A closer examination of the test cases reveals that MMS has, in comparison to standard sampling-based algorithms, a significant advantage in scenarios containing high-dimensional narrow passages. This provokes a novel characterization of narrow passages which attempts to capture their dimensionality, an attribute that had been (to a large extent) unattended in previous definitions.Comment: 20 page

Measuring segregation using patterns of daily travel behavior : a social interaction based model of exposure

Recent advances in transportation geography demonstrate the ability to compute a metropolitan scale metric of social interaction opportunities based on the time-geographic concept of joint accessibility. The method we put forward in this article decomposes the social interaction potential (SIP) metric into interactions within and between social groups, such as people of different race, income level, and occupation. This provides a novel metric of exposure, one of the fundamental spatial dimensions of segregation. In particular, the SIP metric is disaggregated into measures of inter-group and intra-group exposure. While activity spaces have been used to measure exposure in the geographic literature, these approaches do not adequately represent the dynamic nature of the target populations. We make the next step by representing both the source and target population groups by space-time prisms, thus more accurately representing spatial and temporal dynamics and constraints. Additionally, decomposition of the SIP metric means that each of the group-wise components of the SIP metric can be represented at zones of residence, workplace, and specific origin-destination pairs. Consequently, the spatial variation in segregation can be explored and hotspots of segregation and integration potential can be identified. The proposed approach is demonstrated for synthetic cities with different population distributions and daily commute flow characteristics, as well as for a case study of the Detroit-Warren-Livonia MSA

Greenhouse Gas Reduction Opportunities for Local Governments: A Quantification and Prioritization Framework

Local governments have steadily increased their initiative to address global climate change, and many present their proposed strategies through climate action plans (CAPs). This study conducts a literature review on current local approaches to greenhouse gas (GHG) reduction strategies by assessing CAPs in California and presents common strategies in the transportation sector along with useful tools. One identified limitation of many CAPs is the omission of quantitative economic cost and emissions data for decision-making on the basis of cost-effectiveness. Therefore, this study proposes a framework for comparing strategies based on their life cycle emissions mitigation potential and costs. The results data can be presented in a marginal abatement cost curve (MACC) to allow for side-by-side comparison of considered strategies. Researchers partnered with Yolo and Unincorporated Los Angeles Counties to analyze 7 strategies in the transportation and energy sectors (five and two, respectively). A MACC was subsequently developed for each county. Applying the life cycle approach revealed strategies that had net cost savings over their life cycle, indicating there are opportunities for reducing emissions and costs. The MACC also revealed that some emissions reduction strategies in fact increased emissions on a life cycle basis. Applying the MACC framework to two case study jurisdictions illustrated both the feasibility and challenges of including quantitative analysis in their decision-making process. An additional barrier to using the MACC framework in the context of CAPs, is the mismatch between a life cycle and annual accounting basis for GHG emissions. Future work could explore more efficient data collection, alternative scopes of emissions for reporting, and environmental justice concerns.View the NCST Project Webpag