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Abstract Particle production from secondary protonproton collisions, commonly referred to as pileup, impair the sensitivity of both new physics searches and precision measurements at large hadron collider (LHC) experiments. We propose a novel algorithm,
Puma , for modeling pileup with the help of deep neural networks based on sparse transformers. These attention mechanisms were developed for natural language processing but have become popular in other applications. In a realistic detector simulation, our method outperforms classical benchmark algorithms for pileup mitigation in key observables. It provides a perspective for mitigating the effects of pileup in the high luminosity era of the LHC, where up to 200 protonproton collisions are expected to occur simultaneously. 
We provide improved differentially private algorithms for identity testing of highdimensional distributions. Specifically, for ddimensional Gaussian distributions with known covariance Σ, we can test whether the distribution comes from N(μ∗,Σ) for some fixed μ∗ or from some N(μ,Σ) with total variation distance at least α from N(μ∗,Σ) with (ε,0)differential privacy, using only O~(d1/2α2+d1/3α4/3⋅ε2/3+1α⋅ε) samples if the algorithm is allowed to be computationally inefficient, and only O~(d1/2α2+d1/4α⋅ε) samples for a computationally efficient algorithm. We also provide a matching lower bound showing that our computationally inefficient algorithm has optimal sample complexity. We also extend our algorithms to various related problems, including mean testing of Gaussians with bounded but unknown covariance, uniformity testing of product distributions over {−1,1}d, and tolerant testing. Our results improve over the previous best work of Canonne et al.~\cite{CanonneKMUZ20} for both computationally efficient and inefficient algorithms, and even our computationally efficient algorithm matches the optimal \emph{nonprivate} sample complexity of O(d√α2) in many standard parameter settings. In addition, our results show that, surprisingly, private identity testing of ddimensional Gaussians can be done with fewer samples than private identity testing of discrete distributions over a domain of size d \cite{AcharyaSZ18}, which refutes a conjectured lower bound of~\cite{CanonneKMUZ20}.

The \emph{pprocessor cup game} is a classic and widely studied scheduling problem that captures the setting in which a pprocessor machine must assign tasks to processors over time in order to ensure that no individual task ever falls too far behind. The problem is formalized as a multiround game in which two players, a filler (who assigns work to tasks) and an emptier (who schedules tasks) compete. The emptier's goal is to minimize backlog, which is the maximum amount of outstanding work for any task. Recently, Kuszmaul and Westover (ITCS, 2021) proposed the \emph{variableprocessor cup game}, which considers the same problem, except that the amount of resources available to the players (i.e., the number p of processors) fluctuates between rounds of the game. They showed that this seemingly small modification fundamentally changes the dynamics of the game: whereas the optimal backlog in the fixed pprocessor game is Θ(logn), independent of p, the optimal backlog in the variableprocessor game is Θ(n). The latter result was only known to apply to games with \emph{exponentially many} rounds, however, and it has remained an open question what the optimal tradeoff between time and backlog is for shorter games. This paper establishes a tight tradeoffmore »

Frequency estimation is one of the most fundamental problems in streaming algorithms. Given a stream S of elements from some universe U={1…n}, the goal is to compute, in a single pass, a short sketch of S so that for any element i∈U, one can estimate the number xi of times i occurs in S based on the sketch alone. Two state of the art solutions to this problems are the CountMin and CountSketch algorithms. The frequency estimator x~ produced by CountMin, using O(1/ε⋅logn) dimensions, guarantees that ∥x~−x∥∞≤ε∥x∥1 with high probability, and x~≥x holds deterministically. Also, CountMin works under the assumption that x≥0. On the other hand, CountSketch, using O(1/ε2⋅logn) dimensions, guarantees that ∥x~−x∥∞≤ε∥x∥2 with high probability. A natural question is whether it is possible to design the best of both worlds sketching method, with error guarantees depending on the ℓ2 norm and space comparable to CountSketch, but (like CountMin) also has the nounderestimation property. Our main set of results shows that the answer to the above question is negative. We show this in two incomparable computational models: linear sketching and streaming algorithms. We also study the complementary problem, where the sketch is required to not overestimate, i.e., x~≤x should holdmore »

We propose datadriven onepass streaming algorithms for estimating the number of triangles and four cycles, two fundamental problems in graph analytics that are widely studied in the graph data stream literature. Recently, Hsu et al. (2019a) and Jiang et al. (2020) applied machine learning techniques in other data stream problems, using a trained oracle that can predict certain properties of the stream elements to improve on prior “classical” algorithms that did not use oracles. In this paper, we explore the power of a “heavy edge” oracle in multiple graph edge streaming models. In the adjacency list model, we present a onepass triangle counting algorithm improving upon the previous space upper bounds without such an oracle. In the arbitrary order model, we present algorithms for both triangle and four cycle estimation with fewer passes and the same space complexity as in previous algorithms, and we show several of these bounds are optimal. We analyze our algorithms under several noise models, showing that the algorithms perform well even when the oracle errs. Our methodology expands upon prior work on “classical” streaming algorithms, as previous multipass and random order streaming algorithms can be seen as special cases of our algorithms, where the firstmore »

Meyer, J. P. (Ed.)Airwater evaporation systems are ubiquitous in industrial applications, including processes such as fuel combustion, inkjet printing, spray cooling, and desalination. In these evaporationdriven systems, a fundamental understanding of mass accommodation at the liquidvapour interface is critical to predicting and optimizing performance. Interfacial mass accommodation depends on many factors, such as temperature, vapour concentration, nonvolatile impurity content, and noncondensable gasses present. Elucidating how these factors interact is essential to designing devices to meet demanding applications. Hence, high precision measurements are needed to quantify accommodation at the liquidvapour interface accurately. Our previous study has shown surface averaged accommodation coefficients close to 0.001 for pure water droplets throughout evaporation. While it is well established that saline nonvolatile impurities reduce the evaporation rate of sessile droplets, the dynamic effect on mass accommodation during the droplet's lifespan is yet to be determined. In this work, we combine experimental and computational techniques to determine the accommodation coefficient over the lifespan of 103 to 1 molar potassium chloridewater droplets evaporating on a goldcoated surface into dry nitrogen. This study uses a quartz crystal microbalance as a highprecision contact area sensor. It also determines the nonvolatile impurities in the droplet with a precision on the order of nanograms.more »

Random dimensionality reduction is a versatile tool for speeding up algorithms for highdimensional problems. We study its application to two clustering problems: the facility location problem, and the singlelinkage hierarchical clustering problem, which is equivalent to computing the minimum spanning tree. We show that if we project the input pointset 𝑋 onto a random 𝑑=𝑂(𝑑𝑋)dimensional subspace (where 𝑑𝑋 is the doubling dimension of 𝑋), then the optimum facility location cost in the projected space approximates the original cost up to a constant factor. We show an analogous statement for minimum spanning tree, but with the dimension 𝑑 having an extra loglog𝑛 term and the approximation factor being arbitrarily close to 1. Furthermore, we extend these results to approximating solutions instead of just their costs. Lastly, we provide experimental results to validate the quality of solutions and the speedup due to the dimensionality reduction. Unlike several previous papers studying this approach in the context of 𝑘means and 𝑘medians, our dimension bound does not depend on the number of clusters but only on the intrinsic dimensionality of 𝑋.