Matrix Completion via Max-Norm Constrained Optimization

Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a range of applications and the standard trace-norm relaxation can behave very poorly when the underlying sampling scheme is non-uniform. In this paper we propose and analyze a max-norm constrained empirical risk minimization method for noisy matrix completion under a general sampling model. The optimal rate of convergence is established under the Frobenius norm loss in the context of approximately low-rank matrix reconstruction. It is shown that the max-norm constrained method is minimax rate-optimal and yields a unified and robust approximate recovery guarantee, with respect to the sampling distributions. The computational effectiveness of this method is also discussed, based on first-order algorithms for solving convex optimizations involving max-norm regularization.Comment: 33 page

A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion

We consider in this paper the problem of noisy 1-bit matrix completion under a general non-uniform sampling distribution using the max-norm as a convex relaxation for the rank. A max-norm constrained maximum likelihood estimate is introduced and studied. The rate of convergence for the estimate is obtained. Information-theoretical methods are used to establish a minimax lower bound under the general sampling model. The minimax upper and lower bounds together yield the optimal rate of convergence for the Frobenius norm loss. Computational algorithms and numerical performance are also discussed.Comment: 33 pages, 3 figure

Common power laws for cities and spatial fractal structures

Datasets for "Common power laws for cities and spatial fractal structures" Dataset S1 (distance_computation.zip) A ZIP file including a manual for the computation of bilateral distances and travel time among cities, as well as three associated python codes. Dataset S2 (cities.zip) A ZIP file including six CSV files. For each country, there is a corresponding file containing the population sizes and location information of cities. In each file, there are four columns: city ID (UA), population size (POP), longitude (LON) and latitude (LAT) of the the most densely inhabited location in the city according to the geodetic reference system, WGS1984. Dataset S3 (distances.zip) A ZIP file including six CSV files. For each country, there is a corresponding file containing the shortest bilateral road distance and driving time between each pair of cities. In each file, there are four columns: origin city ID (ORIG), destination city ID (DEST), the shortest-path distance in meters (DISTANCE), and the driving time along the shortest-time path in seconds (DURATION), where only the cases with ORIG<DEST are contained

Equi-Biaxial Fatigue Behaviour of Magnetorheological Elastomers in Magnetic Fields

The equi-biaxial fatigue behaviour of silicone based magnetorheological elastomers (MREs) in external magnetic fields was studied. Wöhler curves relating fatigue life to stress amplitude and dynamic stored energy for MREs with a range of magnetic particle contents were derived. It was found that the fatigue life of MREs in magnetic fields was higher than that without magnetic fields. Under constant stress amplitude conditions, the presence of magnetic fields resulted in longer times for the samples to undergo large deformations and thus complex modulus (E*) decreased at a slower rate during the fatigue process, especially for low stress amplitudes. MRE samples tested in the presence of magnetic fields reached limiting values of E* at failure ranging from 1.28 MPa to 1.44 MPa. The application of magnetic fields was found to have negligible influence on the damping loss factor of MREs containing various volume fractions of carbonyl iron particles

Impact of Packing and Processing Technique on Mechanical Properties of Acrylic Denture Base Materials

The fracture resistance of polymethylmethacrylate (PMMA) as the most popular denture base material is not satisfactory. Different factors can be involved in denture fracture. Among them, flexural fatigue and impact are the most common failure mechanisms of an acrylic denture base. It has been shown that there is a correlation between the static strength and fatigue life of composite resins. Therefore, the transverse strength of the denture base materials can be an important indicator of their service life. In order to improve the fracture resistance of PMMA, extensive studies have been carried out; however, only a few promising results were achieved, which are limited to some mechanical properties of PMMA at the cost of other properties. This study aimed at optimizing the packing and processing condition of heat-cured PMMA as a denture base resin in order to improve its biaxial flexural strength (BFS). The results showed that the plain type of resin with a powder/monomer ratio of 2.5:1 or less, packed conventionally and cured in a water bath for 2 h at 95 °C provides the highest BFS. Also, it was found that the performance of the dry heat processor is inconsistent with the number of flasks being loaded

Kinetic Monte Carlo Simulations

Kinetic Monte Carlo (kMC) is a set of scientific libraries designed to deploy kMC simulations intended to simulate the time evolution of some processes occurring in nature. kMC is currently allows the user to intuitively generate single component crystal lattices to simulate, post process, and visualize the kinetic Monte Carlo-based atomistic evolution of materials. kMC provides an interface to the Stochastic Parallel PARticle Kinetic Simulator (SPPARKS) [1] and is specifically designed to simulate individual atomic deposition (condensation) and dissolution (evaporation) events, while simultaneously tracking the surface and bulk crystallographic anisotropic diffusion. The main goal of this project is to create Graphical User Interfaces for WulffShape and Physical Vapor Deposition (PVD) examples. The Wulff shape is the shape that possesses the lowest surface energy for a fixed volume and Physical Vapor Deposition is a collective set of processes used to deposit thin layers of material. We are trying to offer the user an option to choose a material, specify the material and change environmental parameters. kMC could generate crystal lattices, simulate, and render images according to the user\u27s setting. Moreover, there is an option for users to see three-dimensional structured atoms created by visIt. In conclusion, this application is going to simulate the time evolution of Wulff Shape and PVD

The Effects of Monetary Policy on the Australian Property Market

The use of monetary policy has important implications within an economy as it directly affects the supply and demand of cash itself. One most notable application of monetary policy in Australia is the change in the official cash rate (OCR) and its effects on both domestic as well as at international levels. We attempt to use both effects from foreign investments as well as impacts from domestic sources to measure the influences of the OCR on the Australian housing markets.   This research also draws attention towards the variation in the growth rate of property prices in major Australian cities and how it reacts to the changes in this major economic variable. Our paper also addresses the limitations of the devised models however, at a high level these models gives guidance to general movements in housing prices given monetary policy changes with fixed money supply as determined by the Reserve Bank of Australia (RBA) and with that reinforced by movements in several macroeconomic indicators. Keywords: official cash rate; monetary policy; Australian property market; housing prices