Robust Combinatorial Optimization with Locally Budgeted Uncertainty

Budgeted uncertainty sets have been established as a major influence on uncertainty modeling for robust optimization problems. A drawback of such sets is that the budget constraint only restricts the global amount of cost increase that can be distributed by an adversary. Local restrictions, while being important for many applications, cannot be modeled this way. We introduce new variant of budgeted uncertainty sets, called locally budgeted uncertainty. In this setting, the uncertain parameters become partitioned, such that a classic budgeted uncertainty set applies to each partition, called region. In a theoretical analysis, we show that the robust counterpart of such problems for a constant number of regions remains solvable in polynomial time, if the underlying nominal problem can be solved in polynomial time as well. If the number of regions is unbounded, we show that the robust selection problem remains solvable in polynomial time, while also providing hardness results for other combinatorial problems. In computational experiments using both random and real-world data, we show that using locally budgeted uncertainty sets can have considerable advantages over classic budgeted uncertainty sets

Minimizing Maximum Dissatisfaction in the Allocation of Indivisible Items under a Common Preference Graph

We consider the task of allocating indivisible items to agents, when the agents' preferences over the items are identical. The preferences are captured by means of a directed acyclic graph, with vertices representing items and an edge $(a,b)$, meaning that each of the agents prefers item $a$ over item $b$. The dissatisfaction of an agent is measured by the number of items that the agent does not receive and for which it also does not receive any more preferred item. The aim is to allocate the items to the agents in a fair way, i.e., to minimize the maximum dissatisfaction among the agents. We study the status of computational complexity of that problem and establish the following dichotomy: the problem is NP-hard for the case of at least three agents, even on fairly restricted graphs, but polynomially solvable for two agents. We also provide several polynomial-time results with respect to different underlying graph structures, such as graphs of width at most two and tree-like structures such as stars and matchings. These findings are complemented with fixed parameter tractability results related to path modules and independent set modules. Techniques employed in the paper include bottleneck assignment problem, greedy algorithm, dynamic programming, maximum network flow, and integer linear programming.Comment: 26 pages, 2 figure

Mid-IR sensing platform for trace analysis in aqueous solutions based on a germanium-on-silicon waveguide chip with a mesoporous silica coating for analyte enrichment

A novel platform based on evanescent wave sensing in the 6.5 to 7.5 mu m wavelength range is presented with the example of toluene detection in an aqueous solution. The overall sensing platform consists of a germanium-on-silicon waveguide with a functionalized mesoporous silica cladding and integrated microlenses for alignment-tolerant back-side optical interfacing with a tunable laser spectrometer. Hydrophobic functionalization of the mesoporous cladding allows enrichment of apolar analyte molecules and prevents strong interaction of water with the evanescent wave. The sensing performance was evaluated for aqueous toluene standards resulting in a limit of detection of 7 ppm. Recorded adsorption/desorption profiles followed Freundlich adsorption isotherms with rapid equilibration and resulting sensor response times of a few seconds. This indicates that continuous monitoring of contaminants in water is possible. A significant increase in LOD can be expected by likely improvements to the spectrometer noise floor which, expressed as a relative standard deviation of 100% lines, is currently in the range of 10(-2) A.U. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreemen

Recombinant Protein L: Production, Purification and Characterization of a Universal Binding Ligand

Protein L (PpL) is a universal binding ligand that can be used for the detection and purification of antibodies and antibody fragments. Due to the unique interaction with immunoglobulin light chains, it differs from other affinity ligands, like protein A or G. However, due to its current higher market price, PpL is still scarce in applications. In this study, we investigated the recombinant production and purification of PpL and characterized the product in detail. We present a comprehensive roadmap for the production of the versatile protein PpL in E. coli