Walkability Optimization: Formulations, Algorithms, and a Case Study of Toronto

The concept of walkable urban development has gained increased attention due to its public health, economic, and environmental sustainability benefits. Unfortunately, land zoning and historic under-investment have resulted in spatial inequality in walkability and social inequality among residents. We tackle the problem of Walkability Optimization through the lens of combinatorial optimization. The task is to select locations in which additional amenities (e.g., grocery stores, schools, restaurants) can be allocated to improve resident access via walking while taking into account existing amenities and providing multiple options (e.g., for restaurants). To this end, we derive Mixed-Integer Linear Programming (MILP) and Constraint Programming (CP) models. Moreover, we show that the problem's objective function is submodular in special cases, which motivates an efficient greedy heuristic. We conduct a case study on 31 underserved neighborhoods in the City of Toronto, Canada. MILP finds the best solutions in most scenarios but does not scale well with network size. The greedy algorithm scales well and finds near-optimal solutions. Our empirical evaluation shows that neighbourhoods with low walkability have a great potential for transformation into pedestrian-friendly neighbourhoods by strategically placing new amenities. Allocating 3 additional grocery stores, schools, and restaurants can improve the "WalkScore" by more than 50 points (on a scale of 100) for 4 neighbourhoods and reduce the walking distances to amenities for 75% of all residential locations to 10 minutes for all amenity types. Our code and paper appendix are available at https://github.com/khalil-research/walkability

Efficiency comparison between the LLCL and LCL-filters based single-phase grid-tied inverters

An LLCL-filter is becoming more attractive than an LCL-filter as the interface between the grid-tied inverter and the grid due to possibility of reducing the copper and the magnetic materials. The efficiency of the LLCL-filter based single-phase grid-tied inverter also excites interests for many applications. The operation of the switches of the VSI is various with different modulation methods, which lead to different efficiencies for such a single-phase grid-tied inverter system, and therefore important research has been carried out on the effect of the choice of PWM schemes. Then power losses and efficiencies of the LLCL-filter and the LCL-filter based single-phase grid-tied inverters are analyzed and compared under the discontinuous unipolar, the dual-buck and the bipolar modulations. Results show that the efficiency of LLCL-filter based inverter system is higher than the LCL- filter based independent on the modulation method adopted. Experiments on a 2 kW prototype are in good agreement with results of the theoretical analysis

Wave Height Estimation from Shipborne X-Band Nautical Radar Images

A shadowing-analysis-based algorithm is modified to estimate significant wave height from shipborne X-band nautical radar images. Shadowed areas are first extracted from the image through edge detection. Smith’s function fit is then applied to illumination ratios to derive the root mean square (RMS) surface slope. From the RMS surface slope and the mean wave period, the significant wave height is estimated. A data quality control process is implemented to exclude rain-contaminated and low-backscatter images. A smoothing scheme is applied to the gray scale intensity histogram of edge pixels to improve the accuracy of the shadow threshold determination. Rather than a single full shadow image, a time sequence of shadow image subareas surrounding the upwind direction is used to calculate the average RMS surface slope. It has been found that the wave height retrieved from the modified algorithm is underestimated under rain and storm conditions and overestimated for cases with low wind speed. The modified method produces promising results by comparing radar-derived wave heights with buoy data, and the RMS difference is found be 0.59 m

Analysis of some mixed elements for the Stokes problem

AbstractIn this paper we discuss some mixed finite element methods related to the reduced integration penalty method for solving the Stokes problem. We prove optimal order error estimates for bilinear-constant and biquadratic-bilinear velocity-pressure finite element solutions. The result for the biquadratic-bilinear element is new, while that for the bilinear-constant element improves the convergence analysis of Johnson and Pitkäranta (1982). In the degenerate case when the penalty parameter is set to be zero, our results reduce to some related known results proved in by Brezzi and Fortin (1991) for the bilinear-constant element, and Bercovier and Pironneau (1979) for the biquadratic-bilinear element. Our theoretical results are consistent with the numerical results reported by Carey and Krishnan (1982) and Oden et al. (1982)