A Simply Exponential Upper Bound on the Maximum Number of Stable Matchings

Stable matching is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley. In this paper, we provide a new upper bound on $f(n)$, the maximum number of stable matchings that a stable matching instance with $n$ men and $n$ women can have. It has been a long-standing open problem to understand the asymptotic behavior of $f(n)$ as $n\to\infty$, first posed by Donald Knuth in the 1970s. Until now the best lower bound was approximately $2.28^n$, and the best upper bound was $2^{n\log n- O(n)}$. In this paper, we show that for all $n$, $f(n) \leq c^n$ for some universal constant $c$. This matches the lower bound up to the base of the exponent. Our proof is based on a reduction to counting the number of downsets of a family of posets that we call "mixing". The latter might be of independent interest

Quantifying direct and indirect contacts for the potential transmission of infection between species using a multilayer contact network

Detecting opportunities for between-species transmission of pathogens can be challenging, particularly if rare behaviours or environmental transmission are involved. We present a multilayer network framework to quantify transmission potential in multi-host systems, incorporating environmental transmission, by using empirical data on direct and indirect contacts between European badgers Meles meles and domestic cattle. We identify that indirect contacts via the environment at badger latrines on pasture are likely to be important for transmission within badger populations and between badgers and cattle. We also find a positive correlation between the role of individual badgers within the badger social network, and their role in the overall badger-cattle-environment network, suggesting that the same behavioural traits contribute to the role of individual badgers in within- and between-species transmission. These findings have implications for disease management interventions in this system, and our novel network approach can provide general insights into transmission in other multi-host disease systems

Non-invasive imaging of atherosclerotic plaque macrophage in a rabbit model with F-18 FDG PET: a histopathological correlation

BACKGROUND: Coronary atherosclerosis and its thrombotic complications are the major cause of mortality and morbidity throughout the industrialized world. Thrombosis on disrupted atherosclerotic plaques plays a key role in the onset of acute coronary syndromes. Macrophages density is one of the most critical compositions of plaque in both plaque vulnerability and thrombogenicity upon rupture. It has been shown that macrophages have a high uptake of (18)F-FDG (FDG). We studied the correlation of FDG uptake with histopathological macrophage accumulation in atherosclerotic plaques in a rabbit model. METHODS: Atherosclerosis was induced in rabbits (n = 6) by a combination of atherogenic diet and balloon denudation of the aorta. PET imaging was performed at baseline and 2 months after atherogenic diet and coregistered with magnetic resonance (MR) imaging. Normal (n = 3) rabbits served as controls. FDG uptake by the thoracic aorta was expressed as concentration (μCi/ml) and the ratio of aortic uptake-to-blood radioactivity. FDG uptake and RAM-11 antibody positive areas were analyzed in descending aorta. RESULTS: Atherosclerotic aortas showed significantly higher uptake of FDG than normal aortas. The correlation of aortic FDG uptake with macrophage areas assessed by histopathology was statistically significant although it was not high (r = 0.48, p < 0.0001). When uptake was expressed as the ratio of aortic uptake-to-blood activity, it correlated better (r = 0.80, p < 0.0001) with the macrophage areas, due to the correction for residual blood FDG activity. CONCLUSION: PET FDG activity correlated with macrophage content within aortic atherosclerosis. This imaging approach might serve as a useful non-invasive imaging technique and potentially permit monitoring of relative changes in inflammation within the atherosclerotic lesion

Performance of Proximity Loggers in Recording Intra- and Inter-Species Interactions: A Laboratory and Field-Based Validation Study

Knowledge of the way in which animals interact through social networks can help to address questions surrounding the ecological and evolutionary consequences of social organisation, and to understand and manage the spread of infectious diseases. Automated proximity loggers are increasingly being used to record interactions between animals, but the accuracy and reliability of the collected data remain largely un-assessed. Here we use laboratory and observational field data to assess the performance of these devices fitted to a herd of 32 beef cattle (Bos taurus) and nine groups of badgers (Meles meles, n  = 77) living in the surrounding woods. The distances at which loggers detected each other were found to decrease over time, potentially related to diminishing battery power that may be a function of temperature. Loggers were highly accurate in recording the identification of contacted conspecifics, but less reliable at determining contact duration. There was a tendency for extended interactions to be recorded as a series of shorter contacts. We show how data can be manipulated to correct this discrepancy and accurately reflect observed interaction patterns by combining records between any two loggers that occur within a 1 to 2 minute amalgamation window, and then removing any remaining 1 second records. We make universally applicable recommendations for the effective use of proximity loggers, to improve the validity of data arising from future studies

A whole-genome shotgun approach for assembling and anchoring the hexaploid bread wheat genome

Citation: Chapman, J. A., Mascher, M., Buluç, A., Barry, K., Georganas, E., Session, A., . . . Rokhsar, D. S. (2015). A whole-genome shotgun approach for assembling and anchoring the hexaploid bread wheat genome. Genome Biology, 16(1). doi:10.1186/s13059-015-0582-8Polyploid species have long been thought to be recalcitrant to whole-genome assembly. By combining high-throughput sequencing, recent developments in parallel computing, and genetic mapping, we derive, de novo, a sequence assembly representing 9.1 Gbp of the highly repetitive 16 Gbp genome of hexaploid wheat, Triticum aestivum, and assign 7.1 Gb of this assembly to chromosomal locations. The genome representation and accuracy of our assembly is comparable or even exceeds that of a chromosome-by-chromosome shotgun assembly. Our assembly and mapping strategy uses only short read sequencing technology and is applicable to any species where it is possible to construct a mapping population. © 2015 Chapman et al. licensee BioMed Central.Additional Authors: Muehlbauer, G. J.;Stein, N.;Rokhsar, D. S

Pairing Things Off: Counting Stable Matchings, Finding Your Ride, and Designing Tournaments

Thesis (Ph.D.)--University of Washington, 2020This thesis discusses three problems around the common theme of pairing off agents. While the techniques vary, in each problem we observe that careful application of classical and well-understood techniques can still lead to progress. In Chapter Two, we study the classical combinatorial problem of stable matchings. Stable matchings were introduced in 1962 in a seminal paper by Gale and Shapley. In this chapter, we provide a new upper bound on f(n), the maximum number of stable matchings that an instance with n men and n women can have. The best lower bound prior to our work was approximately 2.28^n, and the best upper bound was 2^{ n log n - O(n) }. We show that for all n, f(n) ≤ c^n for some universal constant c. Our bound matches the lower bound up to the base of the exponent. In Chapter Three, we discuss online matching. The Min-Cost Perfect Matching with Delays Problem (MPMD) has been the subject of a recent flurry of activity in algorithm design. In the problem, a series of requests appear over time in a metric space, with the locations and timing determined by an adversary. The algorithm designer is charged with pairing off all the requests, attempting to minimize the sum of the amount of time the requests have to wait (between appearance and being matched) and the distances between the matched requests. We discuss our initial work on the problem, which shows that if the requests come from an unknown probability distribution (rather than from an adversary) a simple algorithm (that we call "ball growing") achieves excellent performance. We also adapt the core idea of the algorithm to the adversarial case, and show that a slight modification of the same simple idea suffices to match the best-known algorithms for MPMD. In Chapter Four, we discuss a different type of matching -- creating matchups in sports tournaments. Our work is inspired by an incident in the 2012 Olympic Badminton tournament where both teams playing in a match were incentivized to lose that match (and attempted to do so). In 2016, the tournament was redesigned, with the stated goal of eliminating misaligned incentives; we show the redesign failed in this goal. We then describe a minimally-manipulable tournament rule which could be reasonably implemented, while maintaining many of the subtler features of the current tournament that a designer would want

Deep Learning Segmentation of Complex Features in Atomic-Resolution Phase-Contrast Transmission Electron Microscopy Images.

Phase-contrast transmission electron microscopy (TEM) is a powerful tool for imaging the local atomic structure of materials. TEM has been used heavily in studies of defect structures of two-dimensional materials such as monolayer graphene due to its high dose efficiency. However, phase-contrast imaging can produce complex nonlinear contrast, even for weakly scattering samples. It is, therefore, difficult to develop fully automated analysis routines for phase-contrast TEM studies using conventional image processing tools. For automated analysis of large sample regions of graphene, one of the key problems is segmentation between the structure of interest and unwanted structures such as surface contaminant layers. In this study, we compare the performance of a conventional Bragg filtering method with a deep learning routine based on the U-Net architecture. We show that the deep learning method is more general, simpler to apply in practice, and produces more accurate and robust results than the conventional algorithm. We provide easily adaptable source code for all results in this paper and discuss potential applications for deep learning in fully automated TEM image analysis

Collective discussion: Diagnosing the present

As students and scholars of global politics, we have been witnessing, participating in, and feeling the effects of recent global upheavals. These include specific events, such as the election of Trump and the vote for Brexit, but are better understood through their resulting political effects (e.g., pushing back on migration, hardening national borders, denying climate change, reneging on trade deals, gutting the welfare state, increasing resource extraction, and curtailing rights). Commentators refer to these upheavals in different ways: a rise in populism, reinvigorated nationalism, the new fascism, a polarization of Right and Left, the end of globalization, and posttruth politics. These labels have not only generated a great deal of scholarly debate, they have also helped generate multiple energies, including activism, protest, and politicization. Such developments feel at once totally unprecedented but also eerily familiar. More to the point, they have very different manifestations in different parts of the world; indeed, one of the difficulties of the present moment is the lack of analysis about the global ramifications of these upheavals. We want to intervene in this puzzle by tapping into an underlying anxiety about how we understand what is currently happening in the world. How do we talk about these present formations without lapsing into nostalgia, blind panic, or unhelpful predictions? This is not an exercise in mastery-as if that is even possible-but more a reflection on the difficulties of speaking about this strange contemporary collusion of power, disenfranchisement, and violence. In keeping with the open-ended ethos that characterizes International Political Sociology, we are interested in how to diagnose these forces in ways that do not singularize, homogenize, or reduce them to something that can be solved once and for all