Mixing times of lozenge tiling and card shuffling Markov chains

We show how to combine Fourier analysis with coupling arguments to bound the mixing times of a variety of Markov chains. The mixing time is the number of steps a Markov chain takes to approach its equilibrium distribution. One application is to a class of Markov chains introduced by Luby, Randall, and Sinclair to generate random tilings of regions by lozenges. For an L X L region we bound the mixing time by O(L^4 log L), which improves on the previous bound of O(L^7), and we show the new bound to be essentially tight. In another application we resolve a few questions raised by Diaconis and Saloff-Coste, by lower bounding the mixing time of various card-shuffling Markov chains. Our lower bounds are within a constant factor of their upper bounds. When we use our methods to modify a path-coupling analysis of Bubley and Dyer, we obtain an O(n^3 log n) upper bound on the mixing time of the Karzanov-Khachiyan Markov chain for linear extensions.Comment: 39 pages, 8 figure

Mixing Time of the Rudvalis Shuffle

We extend a technique for lower-bounding the mixing time of card-shuffling Markov chains, and use it to bound the mixing time of the Rudvalis Markov chain, as well as two variants considered by Diaconis and Saloff-Coste. We show that in each case Theta(n^3 log n) shuffles are required for the permutation to randomize, which matches (up to constants) previously known upper bounds. In contrast, for the two variants, the mixing time of an individual card is only Theta(n^2) shuffles.Comment: 9 page

Exact sampling with Markov chains

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.Includes bibliographical references (p. 79-83).by David Bruce Wilson.Ph.D

Disproportionality as a Framework to Target Pollution Reduction from Urban Landscapes

New federal water quality regulations regarding impaired waters and urban stormwater alongside a growing need to reverse eutrophication of urban lakes are creating demand to decrease nutrient export from urban landscapes, particularly lawns. We propose that Nowak’s disproportionality framework could be used to target specific households likely to generate disproportionate levels of nutrient export. The biophysical dimension would be based on landscape vulnerability (slope; soil type; proximity to lakes); the social dimension would target “inappropriate” lawn management behaviors leading to high nutrient export on these vulnerable landscapes. Understanding of lawn nutrient cycling (biophysical dimension) and homeowner beliefs and attitudes (social dimension) would be used to develop targeted, specific messages for homeowners with inappropriate management practices. A lawn management program developed with this disproportionality framework would probably be very effective, highly economical and fair, targeting only homeowners who are creating a disproportionate impact

Centrifuge Model Tests to Identify Dynamic Properties of Dense Sand for Site Response Calculations

Four centrifuge models, tested on the large centrifuge at UC Davis, are described in this paper. These four experiments involved dense profiles of Nevada Sand (Dr = 90 to 100%) tested in two different model containers. The purpose of the experiments was to evaluate numerical site response procedures by comparison with model test data. In this paper we focus on determining basic material properties of one of the models by using in-flight measurements of shear wave velocity and calculations of stress-strain relationships using data from an extensive array of accelerometers. Shear wave velocity profiles were measured at centrifuge accelerations of approximately 10, 20, and 40 g; and before, during, and after the models were subject to base shaking using the servo-hydraulic shaker in an attempt to identify any influence of shaking history on shear wave velocity. The base shaking included realistic earthquake time histories scaled in frequency and amplitude to simulate motions with low, medium, and high intensity, and motions that included sinusoidal sweeps of different frequencies. A new windowing procedure to compute shear modulus and shear strain amplitude time histories from accelerometer array data is briefly described

Feeding the Coffee Habit: A Longitudinal Study of a Robo-Barista

Studying Human-Robot Interaction over time can provide insights into what really happens when a robot becomes part of people's everyday lives. "In the Wild" studies inform the design of social robots, such as for the service industry, to enable them to remain engaging and useful beyond the novelty effect and initial adoption. This paper presents an "In the Wild" experiment where we explored the evolution of interaction between users and a Robo-Barista. We show that perceived trust and prior attitudes are both important factors associated with the usefulness, adaptability and likeability of the Robo-Barista. A combination of interaction features and user attributes are used to predict user satisfaction. Qualitative insights illuminated users' Robo-Barista experience and contribute to a number of lessons learned for future long-term studies.Comment: Author Accepted Manuscript, 8 pages, RO-MAN'23, 32nd IEEE International Conference on Robot and Human Interactive Communication (RO-MAN), August 2023, Busan, South Kore

Bionomics of the sweet potato weevil, Cylas puncticollis (Coleoptera: Brentidae) on four different sweet potato varieties in sub-Saharan Africa

Sweet potato (Ipomoea batatas (L.) Lam.) is an important staple food crop in sub-Saharan Africa. A limiting production factor is infestation by the sweet potato weevil Cylas puncticollis (Boheman) (Coleoptera: Brentidae). The use of host plant resistance is an essential component of Integrated Pest Management (IPM). Therefore, the bionomic parameters of C. puncticollis were studied under laboratory conditions (30 ± 1 °C and 75 ± 5 % RH) on four sweet potato varieties commonly grown in Ghana (Apumoden, Ligri, Bohye, and Okumkom) to determine their susceptibility to the pest. There were significant varietal differences between some of the parameters. Egg to adult development time was highest on Okumkom while larval survival, emergence rate, intrinsic rate of increase, and the net reproductive rate were lowest on Bohye. The results of this study indicate that Bohye was the least susceptible variety compared to the other varieties tested and can be used in host plant resistance as part of an IPM programme against C. puncticollis in Ghana

Electrostatic Solitary Waves in the Solar Wind: Evidence for Instability at Solar Wind Current Sheets

A strong spatial association between bipolar electrostatic solitary waves (ESWs) and magnetic current sheets (CSs) in the solar wind is reported here for the first time. This association requires that the plasma instabilities (e.g., Buneman, electron two stream) which generate ESWs are preferentially localized to solar wind CSs. Distributions of CS properties (including shear angle, thickness, solar wind speed, and vector magnetic field change) are examined for differences between CSs associated with ESWs and randomly chosen CSs. Possible mechanisms for producing ESW-generating instabilities at solar wind CSs are considered, including magnetic reconnection

Do Students Value On-Campus Field-Based Education? A Case Study of Science Educational Initiatives in the Jock Marshall Reserve

Fieldwork, known for fostering more engaging and authentic learning experiences, is an established tradition in higher education which is changing; increasingly run on-campus for financial and logistical reasons and enhanced through education technologies to reflect industry practices. Here we examine student perceptions of on-campus fieldwork with the aim of understanding if on-campus fieldwork was valued and why, to be able to compare against literature on off-campus fieldwork. We explore student views on activities at the Jock Marshall Reserve, an on-campus nature reserve of Monash University, Australia using mixed-methods approach. An online survey targeted students undertaking four subjects across first to third year and received 116 responses. In alignment with off-campus fieldwork studies, we found that overwhelmingly respondents highly valued fieldwork with dominant reasons being; 1) developed skills relevant to ‘real-world’ science, 2) reinforced theoretical learning, and 3) was more engaging than traditional study, with some benefits to their wellbeing. The novel perceptions related to increased convenience and authenticity. Since a majority of respondents wished to undertake on-campus fieldwork more frequently, this study suggests that the inclusion of on-campus fieldwork should be considered within science curriculum in higher education