A nearly-linear computational-cost scheme for the forward dynamics of an N-body pendulum

The dynamic equations of motion of an n-body pendulum with spherical joints are derived to be a mixed system of differential and algebraic equations (DAE's). The DAE's are kept in implicit form to save arithmetic and preserve the sparsity of the system and are solved by the robust implicit integration method. At each solution point, the predicted solution is corrected to its exact solution within given tolerance using Newton's iterative method. For each iteration, a linear system of the form J delta X = E has to be solved. The computational cost for solving this linear system directly by LU factorization is O(n exp 3), and it can be reduced significantly by exploring the structure of J. It is shown that by recognizing the recursive patterns and exploiting the sparsity of the system the multiplicative and additive computational costs for solving J delta X = E are O(n) and O(n exp 2), respectively. The formulation and solution method for an n-body pendulum is presented. The computational cost is shown to be nearly linearly proportional to the number of bodies

Low temperature stimulates spatial molecular reprogramming of the Arabidopsis seed germination programme

The timing of the germination of seeds is highly responsive to inputs from the environment. Temperature plays a key role in the control of germination, with low temperatures acting to stimulate this developmental transition in many species. In Arabidopsis, extensive gene expression changes have been reported at the whole seed level in response to cold, while much less is known about their spatial distribution across the diverse cell types of the embryo. In this study we examined the spatiotemporal patterns of promoter activity and protein abundance for key gibberellic acid (GA) and abscisic acid (ABA) factors which regulate the decision to germinate both during a time course of germination and in response to cold. Low temperature stimulated the spatial relocalization of these factors to the vasculature. The response of these seeds to dormancy-breaking stratification treatments therefore stimulates the distribution of both positive (GA) and negatively acting (ABA) components to this same cell type. This altered spatial pattern persisted following the transfer of seeds to 22°C, as well as after their rehydration, indicating that this alteration is persistent. These observations suggest that the vasculature plays a role in the low temperature-mediated stimulation of germination in this species, while novel cell types are recruited to promote germination in response to stratification

A three-loop check of the 'a - maximization' in SQCD with adjoint(s)

The 'a - maximization' was introduced by K. Inrtiligator and B. Wecht for finding anomalous dimensions of chiral superfields at the IR fixed points of the RG flow. Using known explicit calculations of anomalous dimensions in the perturbation theory of SQCD (with one or two additional adjoint fields), it is checked here at the three-loop level.Comment: 5 pages; the title changed, the text improved and expande

Forecasting real housing price growth in the Eighth District states

The authors consider forecasting real housing price growth for the individual states of the Federal Reserve's Eighth District. They first analyze the forecasting ability of a large number of potential predictors of state real housing price growth using an autoregressive distributed lag (ARDL) model framework. A number of variables, including the state housing price-to-income ratio, state unemployment rate, and national inflation rate, appear to provide information that is useful for forecasting real housing price growth in many Eighth District states. Given that it is typically difficult to determine a priori the particular variable or small set of variables that are the most relevant for forecasting real housing price growth for a given state and time period, the authors also consider various methods for combining the individual ARDL model forecasts. They find that combination forecasts are quite helpful in generating accurate forecasts of real housing price growth in the individual Eighth District states.Housing - Prices ; Federal Reserve District, 8th

The long-run relationship between consumption and housing wealth in the Eighth District states

Federal Reserve District, 8th ; Consumption (Economics) ; Housing