Porous asphalt resides on most top layers of Dutch roads. Scheduling maintenance for these roads is generally dependent on several factors, but ravelling, the loss of aggregates in the top layers, is the main reason for maintenance on Dutch roads. With the recent framework of the DOS-LCMS scheme generating values for aggregate loss in percentages, a prediction for the remaining lifetime of a road section surfaced with porous asphalt with respect to ravelling can be performed. The lifespan for porous asphalt layers is dependent on the most suffered 25% of the section on the respective 100 meter length.
The current threshold is set at 10%, implying that road sections of 100 meter need maintenance if more than 25% of the road (75^th percentile) measures aggregate loss over 10%. The present work approximates these 75^th percentiles throughout the years using parametric and non-parametric approaches, whereafter the estimates of the 75^th percentiles are used to construct smooth monotonic increasing convex curves. These curves, which are in fact functions built on P-splines, are then used to perform extrapolation and hence predict the dates on which the threshold is going to be surpassed. The study reveals problems in the raw data which is particularly prominent in the sequence of 75^th percentiles, frequently showing a lack of monotonicity and convexity. Putting the monotonicity and convexity constraints on a more granular level were found to be helpful for the predictions and improved the consistency of lifetime predictions over consecutive years.

Digitalization of sensitive information such as bankaccounts enforces privacy to be ensured. Mathematical objects called elliptic curves have ensured exchange of this type of information due to their algebraic structure. The security relies on so called ECDLP and solving these types of problems, but there has yet to be found an efficient algorithm to solve these problems. The aim of the thesis is to study the applications of elliptic curves in cryptography, in which Diffie-Hellman and Digital Signature Algorithm will be discussed. Furthermore, the safety of ECC will be compared to the generally more well-known RSA cryptosystem. Additionally, specific types of elliptic curves have certain properties which cause their ECDLP to be significantly uncomplicated to solve and some of these will be dealt with as well.