In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Surely we want solid foundations. What kind of castle can we build on sand? What is the point of devoting effort to balconies and minarets, if the foundation may be so weak as to allow the structure to collapse of its own weight? We want our foundations set on bedrock, designed to last for generations. Who would want an architect who cannot certify the soundness of the foundations of his buildings?
Why Do We Need Foundations for Modelling Uncertainties?

Alignment-free sequence analysis approaches provide important alternatives over multiple sequence alignment (MSA) in biological sequence analysis because alignment-free approaches have low computation complexity and are not dependent on high level of sequence identity, however, most of the existing alignment-free methods do not employ true full information content of sequences and thus can not accurately reveal similarities and differences among DNA sequences. We present a novel alignment-free computational method for sequence analysis based on Ramanujan-Fourier transform (RFT), in which complete information of DNA sequences is retained. We represent DNA sequences as four binary indicator sequences and apply RFT on the indicator sequences to convert them into frequency domain. The Euclidean distance of the complete RFT coefficients of DNA sequences are used as similarity measure. To address the different lengths in Euclidean space of RFT coefficients, we pad zeros to short DNA binary sequences so that the binary sequences equal the longest length in the comparison sequence data. Thus, the DNA sequences are compared in the same dimensional frequency space without information loss. We demonstrate the usefulness of the proposed method by presenting experimental results on hierarchical clustering of genes and genomes. The proposed method opens a new channel to biological sequence analysis, classification, and structural module identification.
A Novel Method for Comparative Analysis of DNA Sequences by Ramanujan-Fourier Transform

Multiagent planning and coordination problems are common and known to be computationally hard. We show that a wide range of two-agent problems can be formulated as bilinear programs. We present a successive approximation algorithm that significantly outperforms the coverage set algorithm, which is the state-of-the-art method for this class of multiagent problems. Because the algorithm is formulated for bilinear programs, it is more general and simpler to implement. The new algorithm can be terminated at any time and–unlike the coverage set algorithm–it facilitates the derivation of a useful online performance bound. It is also much more efficient, on average reducing the computation time of the optimal solution by about four orders of magnitude. Finally, we introduce an automatic dimensionality reduction method that improves the effectiveness of the algorithm, extending its applicability to new domains and providing a new way to analyze a subclass of bilinear programs.

A Bilinear Programming Approach for Multiagent Planning