the Transformation of Sieve Function

In this paper, we will introduce the transformation of sieve function to improve sieve method. The sieve function can be transformed to similar sieve function and keep its value constant. However, the error terms of sieve function can be changed to smaller, even to be zero, such that the sieve function can be transformed to the calculable sieve function. Using this sieve method, Goldbach Conjecture and the Twin Prime Conjecture will be proved to be true.Comment: 7 page

Two Compact Incremental Prime Sieves

A prime sieve is an algorithm that finds the primes up to a bound $n$. We say that a prime sieve is incremental, if it can quickly determine if $n+1$ is prime after having found all primes up to $n$. We say a sieve is compact if it uses roughly $\sqrt{n}$ space or less. In this paper we present two new results: (1) We describe the rolling sieve, a practical, incremental prime sieve that takes $O(n\log\log n)$ time and $O(\sqrt{n}\log n)$ bits of space, and (2) We show how to modify the sieve of Atkin and Bernstein (2004) to obtain a sieve that is simultaneously sublinear, compact, and incremental. The second result solves an open problem given by Paul Pritchard in 1994

Evaluating Trophic Rewilding as a Conservation Technique

The focus for this paper is to define specifically trophic rewilding, determine its efficacy as a conservation technique, and explore ways to lessen one of its key limitations. Trophic rewilding is the conservation technique whereby an extirpated keystone species or ecosystem engineer is reintroduced into a degraded habitat to restore ecological function by triggering trophic cascades. The technique is evaluated through analysis of the concepts of trophic cascades and ecosystem engineers. Key limitations of trophic rewilding are that a lack of population control in reintroduced may cause issues, that many times not enough is known about trophic cascades to be effective at creating a rewilding model, and the most frequently stated and largest limitation of rewilding is negative human-wildlife conflicts. Attempts to limit human-animal conflict are then explored and a experiment is proposed to further understand public perception of trophic rewilding

Interfacing peripheral nerve with macro-sieve electrodes following spinal cord injury

Macro-sieve electrodes were implanted in the sciatic nerve of five adult male Lewis rats following spinal cord injury to assess the ability of the macro-sieve electrode to interface regenerated peripheral nerve fibers post-spinal cord injury. Each spinal cord injury was performed via right lateral hemisection of the cord at the T9–10 site. Five months post-implantation, the ability of the macro-sieve electrode to interface the regenerated nerve was assessed by stimulating through the macro-sieve electrode and recording both electromyography signals and evoked muscle force from distal musculature. Electromyography measurements were recorded from the tibialis anterior and gastrocnemius muscles, while evoked muscle force measurements were recorded from the tibialis anterior, extensor digitorum longus, and gastrocnemius muscles. The macro-sieve electrode and regenerated sciatic nerve were then explanted for histological evaluation. Successful sciatic nerve regeneration across the macro-sieve electrode interface following spinal cord injury was seen in all five animals. Recorded electromyography signals and muscle force recordings obtained through macro-sieve electrode stimulation confirm the ability of the macro-sieve electrode to successfully recruit distal musculature in this injury model. Taken together, these results demonstrate the macro-sieve electrode as a viable interface for peripheral nerve stimulation in the context of spinal cord injury

Primes in short arithmetic progressions

We give a large sieve type inequality for functions supported on primes. As application we prove a conjecture by Elliott, and give bounds for short character sums over primes. The proves uses a combination of the large sieve and the Selberg sieve

Properties of the Sieve Bootstrap for Fractionally Integrated and Non-Invertible Processes

In this paper we will investigate the consequences of applying the sieve bootstrap under regularity conditions that are sufficiently general to encompass both fractionally integrated and non-invertible processes. The sieve bootstrap is obtained by approximating the data generating process by an autoregression whose order h increases with the sample size T. The sieve bootstrap may be particularly useful in the analysis of fractionally integrated processes since the statistics of interest can often be non-pivotal with distributions that depend on the fractional index d. The validity of the sieve bootstrap is established and it is shown that when the sieve bootstrap is used to approximate the distribution of a general class of statistics admitting an Edgeworth expansion then the error rate achieved is of order O (T  β+d-1 ), for any β > 0. Practical implementation of the sieve bootstrap is considered and the results are illustrated using a canonical example.Autoregressive approximation, fractional process, non-invertibility, rate of convergence, sieve bootstrap.