To establish a causal relationship between common chemicals in parts per billion and health problems, you have to prove that the correlation does not have other, better, and possibly really obvious, explanations.
We discussed first the general stochastic correlation model proposed in [12] and proved that the stochastic correlation process in [10] can be obtained by applying this general approach.
We corrected the Katheder correlation and compared with the experimental data, it proved that the corrected correlation is much more suitable for the kind of CICC of Nb3Sn superconducting magnet.
From (19), (20), (22), and (23), we have proved that the aperiodic correlation properties of the constructed sequences in Construction 2 satisfy Theorem 2. For periodic correlation properties, similar analysis can be easily obtained, and the corresponding proof is omitted.
It is also proved that as the correlation tends to zero, the optimum asymptotic expected end-to-end distortion in the setting of correlated channel approaches that in the setting of uncorrelated channel.
The point of this analysis is that the correlation from the subsample of small windows is similar to that in the full sample of small windows thus proving that opposite correlations in the large and small windows can coexist within the same region of the genome.
The shifting-scaling pattern follows equation 6. (6) e ij = π i × α j + β j Bozda˘ g proved that the value of the Pearson correlation coefficient is 1 for a perfect shifting, scaling, and shifting-scaling pattern [ 23].
Additionally, we prove that the existing correlation detection is a special case of the proposed locally optimum detection, and we provide an improved correlation threshold under the condition of locally optimum detection.
Additionally, we proved that the assumptions for using a rank correlation test are not met.
It is proved that the temperature and human performance have a strong correlation.
