Network measures that reflect the most salient properties of complex large-scale networks are in high demand in the network research community. In this paper we adapt a combinatorial measure of negative curvature (also called hyperbolicity) to parametrized finite networks, and show that a variety of biological and social networks are hyperbolic. This hyperbolicity property has strong implications on the higher-order connectivity and other topological properties of these networks. Specifically, we derive and prove bounds on the distance among shortest or approximately shortest paths in hyperbolic networks. We describe two implications of these bounds to crosstalk in biological networks, and to the existence of central, influential neighborhoods in both biological and social networks.

A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions which are optimal in an appropriate sense. In graph-theoretic language, the problems can be recast in terms of maximal sign-consistent subgraphs. The theoretical results include polynomial-time approximation algorithms as well as constant-ratio inapproximability results. One of the algorithms, which has a worst-case guarantee of 87.9% from optimality, is based on the semidefinite programming relaxation approach of Goemans-Williamson [20]. The algorithm was implemented and tested on a Drosophila segmentation network and an Epidermal Growth Factor Receptor pathway model, and it was found to perform close to optimally.

With the proliferation of location-based services, mobile devices, and embedded wireless sensors, more and more applications are being developed to improve the efficiency of the transportation system. In particular, new applications are arising to help vehicles locate open parking spaces. Nevertheless, while engaged in driving, travelers are better suited being guided to a particular and ideal parking slot, than looking at a map and choosing which spot to go to. Then the question of how an application should choose this ideal parking spot becomes relevant. Vehicular parking can be viewed as vehicles (players) computing for parking slots (resources with different costs). Based on this competition, we present a game-theoretic framework to analyze parking situations. We introduce and analyzeParking Slot Assignment Games (Psag) in complete and incomplete information contexts. For both models we present algorithms for individual players to choose parking spaces ideally. To evaluate the more realistic incomplete information Psag, simulations were performed to test the performance of various proposed algorithms.

We consider the problem of off-line throughput maximization for job scheduling on one or more machines, where each job has a release time, a deadline and a profit. Most of the versions of the problem discussed here were already treated by . Our main contribution is to provide algorithms that do not use linear programming, are simple and much faster than the corresponding ones proposed in [3], while either having the same quality of approximation or improving it. More precisely, compared to the results of in BarNoy et al. [3], our pseudo-polynomial algorithm for multiple unrelated machines and all of our strongly-polynomial algorithms have better performance ratios, all of our algorithms run much faster, are combinatorial in nature and avoid linear programming. Finally, we show that algorithms with better performance ratios than 2 are possible if the stretch factors of the jobs are bounded; a straightforward consequence of this result is an improvement of the ratio of an optimal solution of the integer programming formulation of the JISP2 problem (see [13]) to its linear programming relaxation.

Identification of sequence motifs that favor cis peptide bonds in proteins is important for understanding and designing proteins containing turns mediated by cis peptide conformations. From 1 H NMR solution studies on short peptides, we show that the Pro-Pro peptide bond in Pro-Pro-Phe almost equally populates the cis and trans isomers, with the cis isomer stabilized by a CHÁ Á Áp interaction involving the terminal Pro and Phe. We also show that Phe is over-represented at sequence positions immediately following cis Pro-Pro motifs in known protein structures. Our results demonstrate that the Pro-Pro cis conformer in Pro-Pro-Phe sequence motifs is as important as the trans conformer, both in short peptides as well as in natively folded proteins.