We develop a new nonparametric approach to the analysis of irregularly observed longitudinal data using a sieve of Bernstein polynomials within a Gaussian process framework. The proposed methodology has a number of novel features: (i) both the mean function and the covariance function can be estimated simultaneously under a set of mild regularity conditions; (ii) the derivative of the response ...

The differential delay equation defined by to(u) = l/u for 1 < u < 2 and (uw(u))' = oj(u 1) for u > 2 was introduced by Buchstab in connection with an asymptotic formula for the number of uncanceled terms in the sieve of Eratosthenes. Maier has recently used this result to show there is unexpected irregularity in the distribution of primes in short intervals. The function co(u) is studied in th...

In this paper, we report efficient implementations of the linear sieve and the cubic sieve methods for computing discrete logarithms over prime fields. We demonstrate through empirical performance measures that for a special class of primes the cubic sieve method runs about two times faster than the linear sieve method even in cases of small prime fields of the size about 150 bits. We also prov...

If the yield of a polynomial pair is closely correlated with the coefficients of the polynomial pair, we can select polynomials by checking the coefficients first. This can speed the selection of good polynomials. In this paper, we aim to study the correlation between the polynomial coefficients and the yield of the polynomials. By heuristic analysis and some experiments, we find that the yield...

The sieve element occlusion (SEO) gene family includes several members that are expressed specifically in immature sieve elements (SEs) in the developing phloem of dicotyledonous plants. To determine how this restricted expression profile is achieved, we analysed the SE-specific Medicago truncatula SEO-F1 promoter (PMtSEO-F1) by constructing deletion, substitution and hybrid constructs and test...

The pressure flow model of phloem transport envisaged by Münch (1930) has gained wide acceptance. Recently, however, the model has been questioned on structural and physiological grounds. For instance, sub-structures of sieve elements may reduce their hydraulic conductances to levels that impede flow rates of phloem sap and observed magnitudes of pressure gradients to drive flow along sieve tub...

This paper reviews recent advances in estimation and inference for nonparametric and semiparametric models with endogeneity. It first describes methods of sieves and penalization for estimating unknown functions identified via conditional moment restrictions. Examples include nonparametric instrumental variables regression (NPIV), nonparametric quantile IV regression and many more semi-nonparam...

This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. For these models it is often difficult to verify whether a functional is regular (i.e., root-n estimable) or irregular (i.e., slower than root-n estimabl...