9,761 research outputs found

    Sub-computable Boundedness Randomness

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    This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for PSPACE functions. These new notions are robust in that there are equivalent formulations in terms of (1) Martin-L\"of tests, (2) Kolmogorov complexity, and (3) martingales. We show these notions can be equivalently defined with prefix-free Kolmogorov complexity. We prove that one direction of van Lambalgen's theorem holds for relative computability, but the other direction fails. We discuss statistical properties of these notions of randomness

    ROLLOVER HEDGING

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    Both market advisors and researchers have often suggested rollover hedging as a way of increasing producer returns. This study tests whether rollover hedging can increase expected returns for producers. For rollover hedging to increase expected returns, futures prices must follow a mean-reverting process. Using both the return predictability test based on long-horizon regression and the variance ratio test, we find that mean reversion does not exist in futures prices for corn, wheat, soybeans, soybean oil and soybean meal. The findings are consistent with the weak form of market efficiency. The results of the study imply that rollover hedging should not be seriously considered as a marketing alternative. As long as the commodity markets are efficient, the efforts of producers to improve returns through market timing strategies will meet limited success over time.Rollover hedging, mean reversion, market efficiency, Marketing,

    MARKET INVERSION IN COMMODITY FUTURES PRICES

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    As opposed to a normal market, an inverted market has a negative price of storage or spread. Market inversions in nearby spreads rarely occur during early months of the crop year since stocks are usually abundant after harvest. However, market inversions frequently occur when the spreads are observed across crop years near the end of the crop year. The regressions of spreads on the logarithm of U.S. quarterly stocks show that there exists a positive relationship between the spread and the level of stocks, and further implies that when stocks are scarce, markets will be inverted. Simulations are conducted to determine whether a market inversion is a signal to sell the stocks. The results of the paired-difference tests reveal that as the crop cycle advances towards the end of the crop year, market inversions clearly reflect the market's signal to release stocks in anticipation of new crop supplies. The regressions of actual returns to storage on predicted returns to storage clearly show that a market inversion is a signal to sell. The results support the behavioral finance hypothesis that producers are choosing to hold excess stocks because of some type of biased expectations.Demand and Price Analysis,

    Correlation functions of the One-Dimensional Random Field Ising Model at Zero Temperature

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    We consider the one-dimensional random field Ising model, where the spin-spin coupling, JJ, is ferromagnetic and the external field is chosen to be +h+h with probability pp and h-h with probability 1p1-p. At zero temperature, we calculate an exact expression for the correlation length of the quenched average of the correlation function s0sns0sn\langle s_0 s_n \rangle - \langle s_0 \rangle \langle s_n \rangle in the case that 2J/h2J/h is not an integer. The result is a discontinuous function of 2J/h2J/h. When p=12p = {1 \over 2}, we also place a bound on the correlation length of the quenched average of the correlation function s0sn\langle s_0 s_n \rangle.Comment: 12 pages (Plain TeX with one PostScript figure appended at end), MIT CTP #220

    Dimensionality Reduction for k-Means Clustering and Low Rank Approximation

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    We show how to approximate a data matrix A\mathbf{A} with a much smaller sketch A~\mathbf{\tilde A} that can be used to solve a general class of constrained k-rank approximation problems to within (1+ϵ)(1+\epsilon) error. Importantly, this class of problems includes kk-means clustering and unconstrained low rank approximation (i.e. principal component analysis). By reducing data points to just O(k)O(k) dimensions, our methods generically accelerate any exact, approximate, or heuristic algorithm for these ubiquitous problems. For kk-means dimensionality reduction, we provide (1+ϵ)(1+\epsilon) relative error results for many common sketching techniques, including random row projection, column selection, and approximate SVD. For approximate principal component analysis, we give a simple alternative to known algorithms that has applications in the streaming setting. Additionally, we extend recent work on column-based matrix reconstruction, giving column subsets that not only `cover' a good subspace for \bv{A}, but can be used directly to compute this subspace. Finally, for kk-means clustering, we show how to achieve a (9+ϵ)(9+\epsilon) approximation by Johnson-Lindenstrauss projecting data points to just O(logk/ϵ2)O(\log k/\epsilon^2) dimensions. This gives the first result that leverages the specific structure of kk-means to achieve dimension independent of input size and sublinear in kk

    Documentary America: Exploring Popular Culture

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    Documentary America: Exploring Popular Cultur

    Minimal Males: Men in the Movies

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    Minimal Males: Men in the Movie
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