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Gels made of telechelic polymers connected by reversible crosslinkers are a versatile design platform for biocompatible viscoelastic materials. Their linear response to a step strain displays a fast, near-exponential relaxation when using low valence crosslinkers, while larger supramolecular crosslinkers bring about much slower dynamics involving a wide distribution of time scales whose physical origin is still debated. Here, we propose a model where the relaxation of polymer gels in the dilute regime originates from elementary events in which the bonds connecting two neighboring crosslinkers all disconnect. Larger crosslinkers allow for a greater average number of bonds connecting them, but also generate more heterogeneity. We characterize the resulting distribution of relaxation time scales analytically, and accurately reproduce stress relaxation measurements on metal-coordinated hydrogels with a variety of crosslinker sizes including ions, metal-organic cages, and nanoparticles. Our approach is simple enough to be extended to any crosslinker size and could thus be harnessed for the rational design of complex viscoelastic materials., Comment: 6 pages 5 figures 1 table for the main text and 9 pages 7 figures for the supplement

Unsupervised learning algorithms are beginning to achieve accuracies comparable to their supervised counterparts on benchmark computer vision tasks, but their utility for practical applications has not yet been demonstrated. In this work, we present a novel application of unsupervised learning to the task of auroral image classification. Specifically, we modify and adapt the Simple framework for Contrastive Learning of Representations (SimCLR) algorithm to learn representations of auroral images in a recently released auroral image dataset constructed using image data from Time History of Events and Macroscale Interactions during Substorms (THEMIS) all-sky imagers. We demonstrate that (a) simple linear classifiers fit to the learned representations of the images achieve state-of-the-art classification performance, improving the classification accuracy by almost 10 percentage points over the current benchmark; and (b) the learned representations naturally cluster into more clusters than exist manually assigned categories, suggesting that existing categorizations are overly coarse and may obscure important connections between auroral types, near-earth solar wind conditions, and geomagnetic disturbances at the earth's surface. Moreover, our model is much lighter than the previous benchmark on this dataset, requiring in the area of fewer than 25\% of the number of parameters. Our approach exceeds an established threshold for operational purposes, demonstrating readiness for deployment and utilization., Comment: 6 pages, 5 figures, 1 table

Polymer electrolytes are promising candidates for the next generation lithium-ion battery technology. Large scale screening of polymer electrolytes is hindered by the significant cost of molecular dynamics (MD) simulation in amorphous systems: the amorphous structure of polymers requires multiple, repeated sampling to reduce noise and the slow relaxation requires long simulation time for convergence. Here, we accelerate the screening with a multi-task graph neural network that learns from a large amount of noisy, unconverged, short MD data and a small number of converged, long MD data. We achieve accurate predictions of 4 different converged properties and screen a space of 6247 polymers that is orders of magnitude larger than previous computational studies. Further, we extract several design principles for polymer electrolytes and provide an open dataset for the community. Our approach could be applicable to a broad class of material discovery problems that involve the simulation of complex, amorphous materials., Comment: 29 pages, 6 figures + supplementary information

Invasive ductal carcinoma (IDC) comprises nearly 80% of all breast cancers. The detection of IDC is a necessary preprocessing step in determining the aggressiveness of the cancer, determining treatment protocols, and predicting patient outcomes, and is usually performed manually by an expert pathologist. Here, we describe a novel algorithm for automatically detecting IDC using semi-supervised conditional generative adversarial networks (cGANs). The framework is simple and effective at improving scores on a range of metrics over a baseline CNN., Comment: 5 pages, 3 figures

Let $p$ and $q$ be distinct primes such that $q+1 | p-1$. In this paper we find all integer solutions $a$, $b$ to the equation $1/a + 1/b = (q+1)/pq$ using only elementary methods.

We propose the fusion discriminator, a single unified framework for incorporating conditional information into a generative adversarial network (GAN) for a variety of distinct structured prediction tasks, including image synthesis, semantic segmentation, and depth estimation. Much like commonly used convolutional neural network -- conditional Markov random field (CNN-CRF) models, the proposed method is able to enforce higher-order consistency in the model, but without being limited to a very specific class of potentials. The method is conceptually simple and flexible, and our experimental results demonstrate improvement on several diverse structured prediction tasks., Comment: 13 pages, 5 figures, 3 tables

Learning informative representations of data is one of the primary goals of deep learning, but there is still little understanding as to what representations a neural network actually learns. To better understand this, subspace match was recently proposed as a method for assessing the similarity of the representations learned by neural networks. It has been shown that two networks with the same architecture trained from different initializations learn representations that at hidden layers show low similarity when assessed with subspace match, even when the output layers show high similarity and the networks largely exhibit similar performance on classification tasks. In this note, we present a simple example motivated by standard results in commutative algebra to illustrate how this can happen, and show that although the subspace match at a hidden layer may be 0, the representations learned may be isomorphic as vector spaces. This leads us to conclude that a subspace match comparison of learned representations may well be uninformative, and it points to the need for better methods of understanding learned representations.

Automatic segmentation of microscopy images is an important task in medical image processing and analysis. Nucleus detection is an important example of this task. Mask-RCNN is a recently proposed state-of-the-art algorithm for object detection, object localization, and object instance segmentation of natural images. In this paper we demonstrate that Mask-RCNN can be used to perform highly effective and efficient automatic segmentations of a wide range of microscopy images of cell nuclei, for a variety of cells acquired under a variety of conditions., Comment: 7 pages, 3 figures

The artistic style of a painting is a subtle aesthetic judgment used by art historians for grouping and classifying artwork. The recently introduced `neural-style' algorithm substantially succeeds in merging the perceived artistic style of one image or set of images with the perceived content of another. In light of this and other recent developments in image analysis via convolutional neural networks, we investigate the effectiveness of a `neural-style' representation for classifying the artistic style of paintings., Comment: 10 pages, 4 figures, 2 tables

This paper describes one of the first efforts by the National Assessment of Educational Progress (NAEP) to improve measurement at the lower end of the distribution, including measurement for students with disabilities (SD) and English language learners (ELLs). One way to improve measurement at the lower end is to introduce one or more "accessible" blocks into the NAEP Balanced Incomplete Block Design (BIB). Accessible blocks are defined as blocks that are aligned within the NAEP content frameworks, but designed to provide more information about the abilities and skills of students at the lower end of the distribution. The process of creating the NAEP accessible blocks described in this document began in February 2007 with efforts to define what constitutes an accessible block and to design a process to develop mathematics-accessible blocks that are representative of the NAEP content frameworks. Panels of mathematics content experts and item writers were convened to identify major themes and dimensions that affected item difficulty in mathematics and to develop general strategies for reducing difficulty without compromising content and construct validity. This process culminated in the creation of the Item "Modification Guidelines and Item Modification Procedures". Using the "Item Modification Guidelines and Item Modification Procedures", a sample of Grade 4 and Grade 8 item blocks were modified to create accessible blocks. This investigation of NAEP accessible blocks served as a proof of concept study in two important ways. First, the creation, application, and expert review of the Item "Modification Guidelines and Item Modification Procedures" illustrated that it was possible to develop standard procedures for creating items that were less difficult but still adhered to the content framework. Second, the results from the field test of accessible and operational NAEP blocks indicated that it is indeed feasible to construct accessible blocks that are scalable with the main NAEP assessment and that improve measurement precision at the lower end of the NAEP performance continuum. The primary study findings were as follows: (1) Across all groups and subgroups, there were substantial and similar average gains in the percentage correct by block for the accessible blocks compared with the source blocks; (2) There were consistent declines in the number of students omitting items and significant reductions in the percentage of students not reaching items for the accessible blocks compared with the source blocks; (3) All accessible items were scalable, and modified items had similar average discrimination and guessing characteristics (a and c parameter estimates) as the source items, while there were significant reductions in item difficulty (b parameter estimates); (4) For the lowest performing students, the conditional standard error of measurement was significantly lower for students completing two accessible blocks than for those completing two source blocks; and (5) Test information functions for books comprised of two accessible blocks were appropriately targeted to the lower end of the performance continuum. The following are appended: (1) Item Modification Guidelines and Item Modification Procedures; (2) 2007 Expert Panel Members; (3) 2009 Expert Panel Members; and (4) Item Rating Scale.

Counting homomorphisms between cyclic groups is a common exercise in a first course in abstract algebra. A similar problem, accessible at the same level, is to count the number of group homomorphisms from a dihedral group of order $2m$ into a dihedral group of order $2n$. While the solution requires only elementary group theory, the result does not appear in the literature or in the usual texts. As the solution may be of interest, particularly to those teaching undergraduate abstract algebra, it is provided in this note.