Fast Conical Hull Algorithms for Near-separable Non-negative Matrix Factorization

The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012) turns non-negative matrix factorization (NMF) into a tractable problem. Recently, a new class of provably-correct NMF algorithms have emerged under this assumption. In this paper, we reformulate the separable NMF problem as that of finding the extreme rays of the conical hull of a finite set of vectors. From this geometric perspective, we derive new separable NMF algorithms that are highly scalable and empirically noise robust, and have several other favorable properties in relation to existing methods. A parallel implementation of our algorithm demonstrates high scalability on shared- and distributed-memory machines.Comment: 15 pages, 6 figure

The Potential of Servicizing as a Green Business Model

It has been argued that servicizing business models, under which a firm sells the use of a product rather than the product itself, are environmentally beneficial. The main arguments are: First, under servicizing the firm charges customers based on the product usage. Second, the quantity of products required to meet customer needs may be smaller because the firm may be able to pool customer needs. Third, the firm may have an incentive to offer products with higher efficiency. Motivated by these arguments, we investigate the economic and environmental potential of servicizing business models. We endogenize the firm's choice between a pure sales, a pure servicizing, and a hybrid model with both sales and servicizing options, the pricing decisions and, the resulting customer usage. We consider two extremes of pooling efficacy, viz., no versus strong pooling. We find that under no pooling servicizing leads to higher environmental impact due to production but lower environmental impact due to use. In contrast, under strong pooling, when a hybrid business model is more profitable, it is also environmentally superior. However, a pure servicizing model is environmentally inferior for high production costs as it leads to a larger production quantity even under strong pooling. We also examine the product efficiency choice and find that the firm offers higher efficiency products only under servicizing models with strong pooling

A Comparative Study of Some Pseudorandom Number Generators

We present results of an extensive test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations. The generators include public domain programs, manufacturer installed routines and a random number sequence produced from physical noise. We start by traditional statistical tests, followed by detailed bit level and visual tests. The computational speed of various algorithms is also scrutinized. Our results allow direct comparisons between the properties of different generators, as well as an assessment of the efficiency of the various test methods. This information provides the best available criterion to choose the best possible generator for a given problem. However, in light of recent problems reported with some of these generators, we also discuss the importance of developing more refined physical tests to find possible correlations not revealed by the present test methods.Comment: University of Helsinki preprint HU-TFT-93-22 (minor changes in Tables 2 and 7, and in the text, correspondingly