Budget-Smoothed Analysis for Submodular Maximization

The greedy algorithm for monotone submodular function maximization subject to cardinality constraint is guaranteed to approximate the optimal solution to within a 1-1/e factor. Although it is well known that this guarantee is essentially tight in the worst case - for greedy and in fact any efficient algorithm, experiments show that greedy performs better in practice. We observe that for many applications in practice, the empirical distribution of the budgets (i.e., cardinality constraints) is supported on a wide range, and moreover, all the existing hardness results in theory break under a large perturbation of the budget. To understand the effect of the budget from both algorithmic and hardness perspectives, we introduce a new notion of budget-smoothed analysis. We prove that greedy is optimal for every budget distribution, and we give a characterization for the worst-case submodular functions. Based on these results, we show that on the algorithmic side, under realistic budget distributions, greedy and related algorithms enjoy provably better approximation guarantees, that hold even for worst-case functions, and on the hardness side, there exist hard functions that are fairly robust to all the budget distributions

The Power of Menus in Contract Design

We study the power of menus of contracts in principal-agent problems with adverse selection (agents can be one of several types) and moral hazard (we cannot observe agent actions directly). For principal-agent problems with $T$ types and $n$ actions, we show that the best menu of contracts can obtain a factor $\Omega(\max(n, \log T))$ more utility for the principal than the best individual contract, partially resolving an open question of Guruganesh et al. (2021). We then turn our attention to randomized menus of linear contracts, where we likewise show that randomized linear menus can be $\Omega(T)$ better than the best single linear contract. As a corollary, we show this implies an analogous gap between deterministic menus of (general) contracts and randomized menus of contracts (as introduced by Castiglioni et al. (2022)).Comment: EC 202

Robust Maximization of Non-Submodular Objectives

We study the problem of maximizing a monotone set function subject to a cardinality constraint k in the setting where some number of elements is deleted from the returned set. The focus of this work is on the worst-case adversarial setting. While there exist constant-factor guarantees when the function is submodular [1, 2], there are no guarantees for non-submodular objectives. In this work, we present a new algorithm Oblivious-Greedy and prove the first constant-factor approximation guarantees for a wider class of non-submodular objectives. The obtained theoretical bounds are the first constant-factor bounds that also hold in the linear regime, i.e. when the number of deletions is linear in k. Our bounds depend on established parameters such as the submodularity ratio and some novel ones such as the inverse curvature. We bound these parameters for two important objectives including support selection and variance reduction. Finally, we numerically demonstrate the robust performance of Oblivious-Greedy for these two objectives on various datasets

Designer Lipid-Like Peptides: A Class of Detergents for Studying Functional Olfactory Receptors Using Commercial Cell-Free Systems

A crucial bottleneck in membrane protein studies, particularly G-protein coupled receptors, is the notorious difficulty of finding an optimal detergent that can solubilize them and maintain their stability and function. Here we report rapid production of 12 unique mammalian olfactory receptors using short designer lipid-like peptides as detergents. The peptides were able to solubilize and stabilize each receptor. Circular dichroism showed that the purified olfactory receptors had alpha-helical secondary structures. Microscale thermophoresis suggested that the receptors were functional and bound their odorants. Blot intensity measurements indicated that milligram quantities of each olfactory receptor could be produced with at least one peptide detergent. The peptide detergents' capability was comparable to that of the detergent Brij-35. The ability of 10 peptide detergents to functionally solubilize 12 olfactory receptors demonstrates their usefulness as a new class of detergents for olfactory receptors, and possibly other G-protein coupled receptors and membrane proteins.United States. Defense Advanced Research Projects Agency (DARPA-HR0011-09-C-0012)Massachusetts Institute of Technology. Undergraduate Research Opportunities Progra

Echinococcus multilocularis and Echinococcus shiquicus in a small mammal community on the eastern Tibetan Plateau : host species composition, molecular prevalence, and epidemiological implications

Background The eastern part of the Tibetan Plateau is now recognized as an endemic region with the highest reported human infection rates in the world of human alveolar echinococcosis (AE) caused by Echinococcus multilocularis. Existing epidemiological studies on AE have mainly focused on the synanthropic environment, while basic parasitological and ecological aspects in wildlife host species remain largely unknown, especially for small mammal hosts. Therefore, we examined small mammal host species composition, occurrence, and the prevalence of both E. multilocularis and E. shiquicus in Shiqu County (Sichuan Province, China), eastern Tibetan Plateau. Results In total, 346 small mammals from five rodent and one pika species were trapped from four randomly set 0.25 ha square plots. Two vole species, Lasiopodomys fuscus (n = 144) and Microtus limnophilus (n = 44), and the plateau pika (Ochotona curzoniae) (n = 135), were the three most-dominant species trapped. Although protoscoleces of E. multilocularis and E. shiquicus were only observed in L. fuscus and O. curzoniae, respectively, cox1 and nad1 gene DNA of E. shiquicus was detected in all the small mammal species except for Neodon irene, whereas E. multilocularis was detected in the three most-dominant species. The overall molecular prevalence of Echinococcus species was 5.8 (95% CI: 3.3–8.2%) ~ 10.7% (95% CI: 7.4–14.0%) (the conservative prevalence to the maximum prevalence with 95% CI in parentheses), whereas for E. multilocularis it was 4.3 (95% CI: 2.2–6.5%) ~ 6.7% (95% CI: 4.0–9.3%), and 1.5 (95% CI: 0.2–2.7%) ~ 4.1% (95% CI: 2.0–6.1%) for E. shiquicus. The prevalence of both E. multilocularis and E. shiquicus, was significantly higher in rodents (mainly voles) than in pikas. Phylogenetic analyses revealed that Echinococcus haplotypes of cox1 from small mammal hosts were actively involved in the sylvatic and anthropogenic transmission cycles of E. multilocularis in the eastern Tibetan Plateau. Conclusions In contrast to previous studies, the current results indicated that rodent species, rather than pikas, are probably more important natural intermediate hosts of E. multilocularis and E. shiquicus in the eastern Tibetan Plateau. Thus, understanding interspecific dynamics between rodents and pikas is essential to studies of the echinococcosis transmission mechanism and human echinococcosis prevention in local communities. Keywords: Echinococcus multilocularis, E. shiquicus, Small mammal Prevalence, Tibetan Platea

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data