Designing Network Protocols for Good Equilibria

Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network cost-sharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge cost-sharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal cost-sharing protocols for undirected and directed graphs, single-sink and multicommodity networks, and different measures of the inefficiency of equilibria. Our primary technical tool is a precise characterization of the cost-sharing protocols that induce only network games with pure-strategy Nash equilibria. We use this characterization to prove, among other results, that the Shapley protocol is optimal in directed graphs and that simple priority protocols are essentially optimal in undirected graphs

Implementing a multivariate curve resolution method optimized by alternating least square (MCR-ALS) to deconvolute overlapping spectral polymer signals in SEC-DAD separations

Peaks eluting from a size exclusion separation are often not completely baseline-separated, due to the inherent polydispersity of the polymer and low efficiency of the separation mechanism. Chemometrical deconvolution provides the possibility of calculating the contribution of each peak separately from the recorded spectrum1. Herefore, an in house developed MATLAB script dis-criminates between the different compounds based on their difference in UV-spectrum and retention time, using the entire 3D retention time-UV spectrum. The output of the script provides the calculated chromatograms of each compound as well as their respective UV-spectrum2. The latter can be used for peak identification, while quantitative calculations can be performed on the chromatographical peaks. This aproach allows for overlap in both rentention time as UV-spectrum, speeding up the analyses and extending the separation power of SEC separations. The applicability (both qualitative as quantitative) has been demonstrated on a mixture of three different polymer types