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Key Points Question Is it more effective to disburse fixed total financial incentives at a constant, increasing, or decreasing rate to encourage physical activity? Findings In this randomized clinical trial, financial incentives for physical activity were significantly more effective at motivating activity during and immediately after a payment period if they were offered at a constant rate rather than an increasing or decreasing rate. Meaning This finding has implications for the design and delivery of incentive programs to promote healthy behaviors.

Let f:N→N be a function. Let A n =(a ij) be the n×n matrix defined by a ij =1 if i=f(j) for some i and j and a ij =0 otherwise. We describe the Jordan canonical form of the matrix A n in terms of the directed graph for which A n is the adjacency matrix. We discuss several examples including a connection with the Collatz 3n+1 conjecture.

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Stocks occupy a vital position in the financial market. Over the years, scholars have made unremitting efforts in forecasting the stock market. Because the more accurate the prediction, the more people will profit from the stock market. Machine learning has achieved excellent results in stock prediction. Nowadays, with the rise of deep learning, the stock prediction methods used by people are beginning to lean towards deep learning, and many results have been achieved. This paper will use news rather than traditional stock structured data for stock prediction, and we will use machine learning and deep learning methods in contrast. Moreover, we use natural language processing to process the news. The objects of prediction are stock indexes (DJIA, S & P500) and individual stocks (IBM, JPM). We find that deep learning performs at least 4.5% better than machine learning on prediction tasks related to stock indexes, and at least 3% better in the prediction of individual stocks. We discuss the implications of this result.

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