In mathematical words, among positive weight functions with the same integral value, the generalized function delta biggl x-frac{1}{2}biggl x-frac{1}{begin{cases} +infty, & x=textstylebegin{casesnd{cases} also known as a Dirac measure, minimizes the first eigenvalue (tau_{1}).
In principle, normalizing the CLIP tag numbers to the mRNA levels minimizes the first factor, preventing a low-occupancy site in a highly expressed mRNA from appearing as well supported as a high-occupancy site in a lowly expressed mRNA (Chi et al., 2009; Jaskiewicz et al., 2012).
In this context, the multi-criterion function aims to maximize the first goal and minimize the second.
Secondly, we target to find a unimodular matrix to minimize the second largest PEP, which is also crucial to the BER performance, while keeping the largest PEP unchanged.
More efficient solutions can be achieved when minimizing the second steel plate thickness and maximizing the adhesive layer thickness reducing the weight and increasing the stiffness of the composite structure.
To minimize the second part, the total area of the locations with high probabilities should be small at a given time because of the sparseness of criminal incidents over the whole area S. Both of the two criteria are important.
Since the second constraint is only related to T ab, and the last constraint is only related to T ba, the joint optimization problem can be decoupled into two subproblems, i.e., optimizing T ab to minimize the first term in objective function with the constraint T ab ≥ Tmin1, and optimizing T ba to minimize the second term in objective function with the constraint T ba ≥ Tmin2.
Market economy, in any of its varieties, assumes a framework in which 'people influence each other's actions exclusively by means of the higher and lower qualities of life that result from the process of exchange' with the main conditioning factors of profit and loss, and the goals of maximizing the first kind and minimizing the second.
Intuitively, maximizing the first sum moves synonyms towards the same hemispaces, while minimizing the second tends to align antonym pairs on opposite sides of the origin, reflecting their semantic relations.
To minimize the second type of noise, we have constrained some of the analyses even further, to individuals that have been seen at least 30 times.
