Combinatorial structures for anonymous database search

This thesis treats a protocol for anonymous database search (or if one prefer, a protocol for user-private information retrieval), that is based on the use of combinatorial configurations. The protocol is called P2P UPIR. It is proved that the (v,k,1)-balanced incomplete block designs (BIBD) and in particular the finite projective planes are optimal configurations for this protocol. The notion of n-anonymity is applied to the configurations for P2P UPIR protocol and the transversal designs are proved to be n-anonymous configurations for P2P UPIR, with respect to the neighborhood points of the points of the configuration. It is proved that to the configurable tuples one can associate a numerical semigroup. This theorem implies results on existence of combinatorial configurations. The proofs are constructive and can be used as algorithms for finding combinatorial configurations. It is also proved that to the triangle-free configurable tuples one can associate a numerical semigroup. This implies results on existence of triangle-free combinatorial configurations

Frustration in Biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with a finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of "frustration" in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and how structure connects to function. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding, how a large part of the biological functions of proteins are related to subtle local frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. We hope to illustrate how Frustration is a fundamental concept in relating function to structural biology.Comment: 97 pages, 30 figure

Understanding, Discovering and Leveraging a Software System's Effective Configuration Space

Many modern software systems are highly configurable. While a high degree of configurability has many benefits, such as extensibility, reusability and portability, it also has its costs. In the worst case, the full configuration space of a system is the exponentially large combination of all possible option settings and every configuration can potentially produce unique behavior in the software system. Therefore, this software configuration space explosion problem adds combinatorial complexity to many already difficult software engineering tasks. To date, much of the research in this area has tackled this problem using black-box techniques, such as combinatorial interaction testing (CIT). Although these techniques are promising in systematizing the testing and analysis of configurable systems, they ignore a system's internal structure and we think that is a huge missed opportunity. We hypothesize that systems are often structured such that their effective configuration spaces -- the set of configurations needed to achieve a specific goal -- are often much smaller than their full configuration spaces. And if we can efficiently identify or approximate the effective configuration spaces, then we can use that information to greatly improve various software engineering tasks. To understand the effective configuration spaces of software systems, we used symbolic evaluation, a white-box analysis, to capture all executions a system can take under any configuration. The symbolic evaluation results confirmed that the effective configuration spaces are in fact the composition of many small, self-contained groupings of options. And we developed analysis techniques to succinctly characterize how configurations interact with a system's internal structures. We showed that while the majority of a system's interactions are relatively low strength, some important high-strength interactions do exist, and that existing approaches such as CIT are highly unlikely to generate them in practice. Results from our in-depth investigations serve as the foundation for developing new approaches to efficiently discovering effective configuration spaces. We proposed a new algorithm called interaction tree discovery (iTree) that aims to identify sets of configurations that are smaller than those generated by CIT, while also including important high-strength interactions missed by practical applications of CIT. On each iteration of iTree, we first use low-strength covering array to test the system under, and then apply machine learning techniques to discover new interactions that are potentially responsible for any new coverage seen. By repeating this process, iTree builds up a set of configurations likely to contain key high-strength interactions. We evaluated iTree and our results strongly suggest that iTree can identify high-coverage sets of configurations more effectively than traditional CIT or random sampling. We next developed the interaction learning approach that estimates the configuration interactions underlying the effective configuration space by building classification models for iTree execution results. This approach is light-weight, yet produces accurate estimates of the interactions; making leveraging effective configuration spaces practical for many software engineering tasks. Using this approach, we were able to approximate the effective configuration space of the ~1M-LOC MySQL, something that is infeasible using existing techniques, at very low cost