QUANTILE TRANSFORM IN STRUCTURAL BIOINFORMATICS PROBLEMS

In this paper we study features of the multivariate empirical quantum function implementation for which sample is distributed at the mesh points of the regular grid. We present an algorithm for continuous and discrete quantile transform based on recursive definition of the multivariate quantile function. We perform numerical study of the presented algorithm and demonstrate it computational complexity according to representation of the sample. We present the results of using evolutionary optimization algorithm with quantile transform for solving the problems in structural bioinformatics: protein structure prediction from amino acid sequence and protein-peptide docking with known binding site and linear peptide structure.

One-Dimensional Case

This chapter considers the Monge–Kantorovich problem in the one-dimensional case, when both the worker and the job are characterized by a scalar attribute. The important assumption of positive assortative matching, or supermodularity of the matching surplus, is introduced and discussed. As a consequence, the primal problem has an explicit solution (an optimal assignment) which is related to the probabilistic notion of a quantile transform, and the dual problem also has an explicit solution (a set of equilibrium prices), which are obtained from the solution to the primal problem. As a consequence, the Monge–Kantorovich problem is explicitly solved in dimension one under the assumption of positive assortative matching.

Comparing dynamical, stochastic and combined downscaling approaches – lessons from a case study in the Mediterranean region

Various downscaling techniques have been developed to bridge the scale gap between global climate models (GCMs) and finer scales required to assess hydrological impacts of climate change. Such techniques may be grouped into two downscaling approaches: the deterministic dynamical downscaling (DD) and the stochastic statistical downscaling (SD). Although SD has been traditionally seen as an alternative to DD, recent works on statistical downscaling have aimed to combine the benefits of these two approaches. The overall objective of this study is to examine the relative benefits of each downscaling approach and their combination in making the GCM scenarios suitable for basin scale hydrological applications. The case study presented here focuses on the Apulia region (South East of Italy, surface area about 20 000 km2), characterized by a typical Mediterranean climate; the monthly cumulated precipitation and monthly mean of daily minimum and maximum temperature distribution were examined for the period 1953–2000. The fifth-generation ECHAM model from the Max-Planck-Institute for Meteorology was adopted as GCM. The DD was carried out with the Protheus system (ENEA), while the SD was performed through a monthly quantile-quantile transform. The SD resulted efficient in reducing the mean bias in the spatial distribution at both annual and seasonal scales, but it was not able to correct the miss-modeled non-stationary components of the GCM dynamics. The DD provided a partial correction by enhancing the trend spatial heterogeneity and time evolution predicted by the GCM, although the comparison with observations resulted still underperforming. The best results were obtained through the combination of both DD and SD approaches.