Algorithms for Secretary Problems on Graphs and Hypergraphs

We examine several online matching problems, with applications to Internet advertising reservation systems. Consider an edge-weighted bipartite graph G, with partite sets L, R. We develop an 8-competitive algorithm for the following secretary problem: Initially given R, and the size of L, the algorithm receives the vertices of L sequentially, in a random order. When a vertex l \in L is seen, all edges incident to l are revealed, together with their weights. The algorithm must immediately either match l to an available vertex of R, or decide that l will remain unmatched. Dimitrov and Plaxton show a 16-competitive algorithm for the transversal matroid secretary problem, which is the special case with weights on vertices, not edges. (Equivalently, one may assume that for each l \in L, the weights on all edges incident to l are identical.) We use a similar algorithm, but simplify and improve the analysis to obtain a better competitive ratio for the more general problem. Perhaps of more interest is the fact that our analysis is easily extended to obtain competitive algorithms for similar problems, such as to find disjoint sets of edges in hypergraphs where edges arrive online. We also introduce secretary problems with adversarially chosen groups. Finally, we give a 2e-competitive algorithm for the secretary problem on graphic matroids, where, with edges appearing online, the goal is to find a maximum-weight acyclic subgraph of a given graph.Comment: 15 pages, 2 figure

Stress Signaling Pathways in Metabolic Disorders

Obesity affects more than 30 percent of the worldwide population reaching pandemic dimensions. Furthermore, obesity is associated with the development of metabolic disorders, such as insulin resistance that is at least partly caused by an increased inflammatory state. The chronic low-grade inflammation under obese conditions induces stress signaling pathways such as c-Jun N-terminal kinase (JNK) and endoplasmic reticulum stress leading to the activation of the X-box binding protein 1 (XBP1), both might contribute to the development of obesity-associated insulin resistance. While recent studies using whole body JNK-1 knockout mice have implicated a crucial role for stress signaling induced JNK-1 in the development of obesity-associated insulin resistance, neither the metabolic tissue in which JNK-1 ablation sensitizes for insulin action nor the cell typespecific function of the other JNK isoform JNK-2 could be identified in these studies. To this end, mouse models carrying skeletal muscle specific inactivation or constant activation of JNK-1 were analysed for alterations in energy and glucose homeostasis. While mice with a skeletal muscle specific JNK-1 deficiency or constitutive activation of JNK-1 demonstrated largely unaltered body weight gain, glucose tolerance and insulin sensitivity, JNK-1 was responsible to induce exercise-dependent increases of the myokine IL-6 in skeletal muscle. These data reveal a novel role for stress-induced JNK-1 in skeletal muscle in the context of physical activity, controlling the beneficial effects of IL-6 in response to exercise. Moreover, a conditional JNK-2 mouse line was created in this study allowing for the cell type-specific inactivation of JNK-2 in tissues that express the Cre recombinase. Furthermore, mice were generated that carry a conditional allele of the spliced and transcriptionally active form of the murine XBP1 (mXBP1s) to mimic ER stress that is associated with obesity. These mice were crossed with CAMKII-Cre and ALFP-Cre mice that resulted in mXBP1s expression and the induction of ER stress in hippocampus and liver, respectively. Surprisingly, however, qPCR analysis indicated that the central expression of mXBP1s resulted not only in the neuron-specific induction of ER stress, but also revealed upregulated CHOP and GRP78 expression in liver, implicating a crosstalk between brain and liver in the transmission of ER stress. Also, the novel FABP4-2A-Cre mouse line was characterized using ROSA26-FOXODN and IL-6RaFL mice as reporter alleles. While FABP4-2A-Cre excised the loxP-flanked STOP sequence of ROSA26-FOXODN mice exclusively inWAT, BAT and myeloid lineage cell types, the loxP-flanked exons of the IL-6Ra gene were completely excised indicating the occurence of a transient FABP4 expression early during embryonic development. Collectively, the herein generated mouse lines will be valuable tools for further studies addressing the cell type-specific role of stress signaling pathways in metabolic disorders

Improved Revenue Bounds for Posted-Price and Second-Price Mechanisms

We study revenue maximization through sequential posted-price (SPP) mechanisms in single-dimensional settings with $n$ buyers and independent but not necessarily identical value distributions. We construct the SPP mechanisms by considering the best of two simple pricing rules: one that imitates the revenue optimal mchanism, namely the Myersonian mechanism, via the taxation principle and the other that posts a uniform price. Our pricing rules are rather generalizable and yield the first improvement over long-established approximation factors in several settings. We design factor-revealing mathematical programs that crisply capture the approximation factor of our SPP mechanism. In the single-unit setting, our SPP mechanism yields a better approximation factor than the state of the art prior to our work (Azar, Chiplunkar & Kaplan, 2018). In the multi-unit setting, our SPP mechanism yields the first improved approximation factor over the state of the art after over nine years (Yan, 2011 and Chakraborty et al., 2010). Our results on SPP mechanisms immediately imply improved performance guarantees for the equivalent free-order prophet inequality problem. In the position auction setting, our SPP mechanism yields the first higher-than $1-1/e$ approximation factor. In eager second-price (ESP) auctions, our two simple pricing rules lead to the first improved approximation factor that is strictly greater than what is obtained by the SPP mechanism in the single-unit setting.Comment: Accepted to Operations Researc

Model Fusion via Optimal Transport

Combining different models is a widely used paradigm in machine learning applications. While the most common approach is to form an ensemble of models and average their individual predictions, this approach is often rendered infeasible by given resource constraints in terms of memory and computation, which grow linearly with the number of models. We present a layer-wise model fusion algorithm for neural networks that utilizes optimal transport to (soft-) align neurons across the models before averaging their associated parameters. We show that this can successfully yield "one-shot" knowledge transfer (i.e, without requiring any retraining) between neural networks trained on heterogeneous non-i.i.d. data. In both i.i.d. and non-i.i.d. settings , we illustrate that our approach significantly outperforms vanilla averaging, as well as how it can serve as an efficient replacement for the ensemble with moderate fine-tuning, for standard convolutional networks (like VGG11), residual networks (like ResNet18), and multi-layer perceptrons on CIFAR10, CIFAR100, and MNIST. Finally, our approach also provides a principled way to combine the parameters of neural networks with different widths, and we explore its application for model compression. The code is available at the following link, https://github.com/sidak/otfusion.Comment: NeurIPS 2020 conference proceedings (early version featured in the Optimal Transport & Machine Learning workshop, NeurIPS 2019

Efficient microwave-to-optical conversion using Rydberg atoms

We demonstrate microwave-to-optical conversion using six-wave mixing in $^{87}$Rb atoms where the microwave field couples to two atomic Rydberg states, and propagates collinearly with the converted optical field. We achieve a photon conversion efficiency of ~5% in the linear regime of the converter. In addition, we theoretically investigate all-resonant six-wave mixing and outline a realistic experimental scheme for reaching efficiencies greater than 60%