We show that the variance of the profiles (number of nodes at each level) of random binary search trees exhibits asymptotically four phase transitions and a bimodal or “two-humped” behavior, in contrast to the unimodality of the mean value of the profiles. Precise asymptotic approximations are derived. The same types of phenomena also hold for the profiles of random recursive trees.

Protein remote homology detection and fold recognition are central problems in bioinformatics. Currently, discriminative methods based on support vector machine (SVM) are the most effective and accurate methods for solving these problems. The performance of SVM depends on the method of protein vectorization, so a suitable representation of the protein sequence is a key step for the SVM-based me...

Successful prediction of protein domain boundaries provides valuable information not only for the computational structure prediction of multi-domain proteins but also for the experimental structure determination. In this work, a novel index at the profile level is presented, namely, the profile domain linker propensity index (PDLI), which uses the evolutionary information of profiles for domain...

We provide in this paper a pair of properties that are both necessary and sufficient to characterize the domain of single-peaked preference profiles. This characterization allows for a definition of single-peaked preference profiles without using an ad-hoc unlerlying order of the alternatives and also sheds light on the structure of single-peaked profiles. Considering the larger domain of value...

Aim: Understanding a drug dissolution process from solid dispersions (SD) to develop formulations with predictable in vivo performance. Materials & methods: Dissolution data of fenbendazole released the SDs and control physical mixtures were analyzed using Lumped mathematical model estimate parameters pharmaceutical relevance. Results: The fit obtained by showed that all have unique profile...