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Anthropogenic stressors pose substantial threats to the existence of coral reefs. Achieving successful coral recruitment stands as a bottleneck in reef restoration and hybrid reef engineering efforts. Here, we enhance coral settlement through the development of biomimetic microhabitats that replicate the chemical landscape of healthy reefs. We engineered a soft biomaterial, SNAP-X, comprising silica nanoparticles (NPs), biopolymers, and algal exometabolites, to enrich reef microhabitats with bioactive molecules from crustose coralline algae (CCA). Coral settlement was enhanced over 20-fold using SNAP-X-coated substrates compared with uncoated controls. SNAP-X is designed to release chemical signals slowly (>1 month) under natural seawater conditions, and can be rapidly applied to natural reef substrates via photopolymerization, facilitating the light-assisted 3D printing of microengineered habitats. We anticipate that these biomimetic chemical microhabitats will be widely used to augment coral settlement on degraded reefs and to support ecosystem processes on hybrid reefs. 

e report the on-wafer characterization of S-parameters and microwave noise temperature (T50) of discrete metamorphic InGaAs high electron mobility transistors (mHEMTs) at 40 and 300 K and over a range of drain-source voltages (VDS). From these data, we extract a small-signal model (SSM) and the drain (output) noise current power spectral density (Sid) at each bias and temperature. This procedure enables Sid to be obtained while accounting for the variation of SSM, noise impedance match, and other parameters under the various conditions. We find that the noise associated with the channel conductance can only account for a portion of the measured output noise. Considering the variation of output noise with physical temperature and bias and prior studies of microwave noise in quantum wells, we hypothesize that a hot electron noise source (NS) based on real-space transfer (RST) of electrons from the channel to the barrier could account for the remaining portion of Sid. We suggest further studies to gain insights into the physical mechanisms. Finally, we calculate that the minimum HEMT noise temperature could be reduced by up to ∼50% and ∼30% at cryogenic temperature and room temperature, respectively, if the hot electron noise were suppressed. 

Metric embeddings traditionally study how to map n items to a target metric space such that distance lengths are not heavily distorted. However, what if we are only interested in preserving the relative order of the distances, rather than their exact lengths? In this paper, we explore the fundamental question: given triplet comparisons of the form “item i is closer to item j than to item k,” can we find low-dimensional Euclidean representations for the n items that respect those distance comparisons? Such order-preserving embeddings naturally arise in important applications—such as recommendations, ranking, crowdsourcing, psychometrics, and nearest-neighbor search—and have been studied since the 1950s under the name of ordinal or non-metric embeddings. Our main results include: Nearly-Tight Bounds on Triplet Dimension: We introduce the concept of triplet dimension of a dataset and show, surprisingly, that in order for an ordinal embedding to be triplet-preserving, its dimension needs to grow as n^2 in the worst case. This is nearly optimal, as n−1 dimensions always suffice. Tradeoffs for Dimension vs (Ordinal) Relaxation: We relax the requirement that every triplet must be exactly preserved and present almost tight lower bounds for the maximum ratio between distances whose relative order was inverted by the embedding. This ratio is known as (ordinal) relaxation in the literature and serves as a counterpart to (metric) distortion. New Bounds on Terminal and Top-k-NNs Embeddings: Moving beyond triplets, we study two well-motivated scenarios where we care about preserving specific sets of distances (not necessarily triplets). The first scenario is Terminal Ordinal Embeddings where we aim to preserve relative distance orders to k given items (the “terminals”), and for that, we present matching upper and lower bounds. The second scenario is top-k-NNs Ordinal Embeddings, where for each item we aim to preserve the relative order of its k nearest neighbors, for which we present lower bounds. To the best of our knowledge, these are some of the first tradeoffs on triplet-preserving ordinal embeddings and the first study of Terminal and Top-k-NNs Ordinal Embeddings. 

Estimating frequencies of elements appearing in a data stream is a key task in large-scale data analysis. Popular sketching approaches to this problem (e.g., CountMin and CountSketch) come with worst-case guarantees that probabilistically bound the error of the estimated frequencies for any possible input. The work of Hsu et al.~(2019) introduced the idea of using machine learning to tailor sketching algorithms to the specific data distribution they are being run on. In particular, their learning-augmented frequency estimation algorithm uses a learned heavy-hitter oracle which predicts which elements will appear many times in the stream. We give a novel algorithm, which in some parameter regimes, already theoretically outperforms the learning based algorithm of Hsu et al. without the use of any predictions. Augmenting our algorithm with heavy-hitter predictions further reduces the error and improves upon the state of the art. Empirically, our algorithms achieve superior performance in all experiments compared to prior approaches. 

We study statistical/computational tradeoffs for the following density estimation problem: given kdistributionsv1,...,vk overadiscretedomain of size n, and sampling access to a distribution p, identify vi that is “close” to p. Our main result is the first data structure that, given a sublinear (in n) number of samples from p, identifies vi in time sublinear in k. We also give an improved version of the algorithm of (Acharya et al., 2018) that reports vi in time linear in k. The experimental evaluation of the latter algorithm shows that it achieves a significant reduction in the number of operations needed to achieve a given accuracy compared to prior work.