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In recent years, convolutional neural networks for semantic segmentation of breast ultrasound (BUS) images have shown great success; however, two major challenges still exist. 1) Most current approaches inherently lack the ability to utilize tissue anatomy, resulting in misclassified image regions. 2) They struggle to produce accurate boundaries due to the repeated down-sampling operations. To address these issues, we propose a novel breast anatomy-aware network for capturing fine image details and a new smoothness term that encodes breast anatomy. It incorporates context information across multiple spatial scales to generate more accurate semantic boundaries. Extensive experiments are conducted to compare the proposed method and eight state-of-the-art approaches using a BUS dataset with 325 images. The results demonstrate the proposed method significantly improves the segmentation of the muscle, mammary, and tumor classes and produces more accurate fine details of tissue boundaries.

Selection on the Cartesian product is a classic problem in computer science. Recently, an optimal algorithm for selection on $X+Y$, based on soft heaps, was introduced. By combining this approach with layer-ordered heaps (LOHs), an algorithm using a balanced binary tree of $X+Y$ selections was proposed to perform $k$-selection on $X_1+X_2+\cdots+X_m$ in $o(n\cdot m + k\cdot m)$, where $X_i$ have length $n$. Here, that $o(n\cdot m + k\cdot m)$ algorithm is combined with a novel, optimal LOH-based algorithm for selection on $X+Y$ (without a soft heap). Performance of algorithms for selection on $X_1+X_2+\cdots+X_m$ are compared empirically, demonstrating the benefit of the algorithm proposed here.

The layer-ordered heap (LOH) is a simple, recently proposed data structure used in optimal selection on $X+Y$, thealgorithm with the best known runtime for selection on $X_1+X_2+\cdots+X_m$, and the fastest method in practice for computing the most abundant isotope peaks in a chemical compound. Here, we introduce a few algorithms for constructing LOHs, analyze their complexity, and demonstrate that one algorithm is optimal for building a LOH of any rank $\alpha$. These results are shown to correspond with empirical experiments of runtimes when applying the LOH construction algorithms to a common task in machine learning.

The theoretical computation of isotopic distribution of compounds is crucial in many important applications of mass spectrometry, especially as machine precision grows. A considerable amount of good tools have been created in the last decade for doing so. In this paper we present a novel algorithm for calculating the top $k$ peaks of a given compound. The algorithm takes advantage of layer-ordered heaps used in an optimal method of selection on $X+Y$ and is able to efficiently calculate the top $k$ peaks on very large molecules. Among its peers, this algorithm shows a significant speedup on molecules whose elements have many isotopes. The algorithm obtains a speedup of more than 31x when compared to $\textsc{IsoSpec}$ on \ch{Au2Ca10Ga10Pd76} when computing 47409787 peaks, which covers 0.999 of the total abundance.

Selection on $X_1+X_2+\cdots + X_m$ is an important problem with many applications in areas such as max-convolution, max-product Bayesian inference, calculating most probable isotopes, and computing non-parametric test statistics, among others. Faster-than-na\"{i}ve approaches exist for $m=2$: Frederickson (1993) published the optimal algorithm with runtime $O(k)$ and Kaplan \emph{et al.} (2018) has since published a much simpler algorithm which makes use of Chazelle's soft heaps (2003). No fast methods exist for $m>2$. Johnson \& Mizoguchi (1978) introduced a method to compute the single $k^{th}$ value when $m>2$, but that method runs in $O(m\cdot n^{\lceil\frac{m}{2}\rceil} \log(n))$ time and is inefficient when $m \gg 1$ and $k \ll n^{\lceil\frac{m}{2}\rceil}$. In this paper, we introduce the first efficient methods, both in theory and practice, for problems with $m>2$. We introduce the ``layer-ordered heap,'' a simple special class of heap with which we produce a new, fast selection algorithm on the Cartesian product. Using this new algorithm to perform $k$-selection on the Cartesian product of $m$ arrays of length $n$ has runtime $\in o(k\cdot m)$. We also provide implementations of the algorithms proposed and evaluate their performance in practice.

The isotope masses and relative abundances for each element are fundamental chemical knowledge. Computing the isotope masses of a compound and their relative abundances is an important and difficult analytical chemistry problem. We demonstrate that this problem is equivalent to sorting $Y=X_1+X_2+\cdots+X_m$. We introduce a novel, practically efficient method for computing the top values in $Y$. then demonstrate the applicability of this method by computing the most abundant isotope masses (and their abundances) from compounds of nontrivial size.

Many architects believe that major improvements in cost-energy-performance must now come from domain-specific hardware. This paper evaluates a custom ASIC---called a Tensor Processing Unit (TPU)---deployed in datacenters since 2015 that accelerates the inference phase of neural networks (NN). The heart of the TPU is a 65,536 8-bit MAC matrix multiply unit that offers a peak throughput of 92 TeraOps/second (TOPS) and a large (28 MiB) software-managed on-chip memory. The TPU's deterministic execution model is a better match to the 99th-percentile response-time requirement of our NN applications than are the time-varying optimizations of CPUs and GPUs (caches, out-of-order execution, multithreading, multiprocessing, prefetching, ...) that help average throughput more than guaranteed latency. The lack of such features helps explain why, despite having myriad MACs and a big memory, the TPU is relatively small and low power. We compare the TPU to a server-class Intel Haswell CPU and an Nvidia K80 GPU, which are contemporaries deployed in the same datacenters. Our workload, written in the high-level TensorFlow framework, uses production NN applications (MLPs, CNNs, and LSTMs) that represent 95% of our datacenters' NN inference demand. Despite low utilization for some applications, the TPU is on average about 15X - 30X faster than its contemporary GPU or CPU, with TOPS/Watt about 30X - 80X higher. Moreover, using the GPU's GDDR5 memory in the TPU would triple achieved TOPS and raise TOPS/Watt to nearly 70X the GPU and 200X the CPU., Comment: 17 pages, 11 figures, 8 tables. To appear at the 44th International Symposium on Computer Architecture (ISCA), Toronto, Canada, June 24-28, 2017