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1. Averages Along the Primes: Improving and Sparse Bounds

   https://doi.org/10.1515/conop-2020-0003  

   Han, Rui; Krause, Ben; Lacey, Michael T.; Yang, Fan (February 2020, Concrete Operators)

   Abstract Consider averages along the prime integers ℙ given by {\mathcal{A}_N}f(x) = {N^{ - 1}}\sum\limits_{p \in \mathbb{P}:p \le N} {(\log p)f(x - p).} These averages satisfy a uniform scale-free ℓ p -improving estimate. For all 1 < p < 2, there is a constant C p so that for all integer N and functions f supported on [0, N ], there holds {N^{ - 1/p'}}{\left\| {{\mathcal{A}_N}f} \right\|_{\ell p'}} \le {C_p}{N^{ - 1/p}}{\left\| f \right\|_{\ell p}}. The maximal function 𝒜 * f = sup N |𝒜 N f | satisfies ( p , p ) sparse bounds for all 1 < p < 2. The latter are the natural variants of the scale-free bounds. As a corollary, 𝒜 * is bounded on ℓ p ( w ), for all weights w in the Muckenhoupt 𝒜 p class. No prior weighted inequalities for 𝒜 * were known. 

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2. Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian

   https://doi.org/10.1090/tran/8903  

   Bañuelos, Rodrigo; Mariano, Phanuel; Wang, Jing (August 2023, Transactions of the American Mathematical Society)

   For domains in R d \mathbb {R}^d , d ≥ 2 d\geq 2 , we prove universal upper and lower bounds on the product of the bottom of the spectrum for the Laplacian to the power p > 0 p>0 and the supremum over all starting points of the p p -moments of the exit time of Brownian motion. It is shown that the lower bound is sharp for integer values of p p and that for p ≥ 1 p \geq 1 , the upper bound is asymptotically sharp as d → ∞ d\to \infty . For all p > 0 p>0 , we prove the existence of an extremal domain among the class of domains that are convex and symmetric with respect to all coordinate axes. For this class of domains we conjecture that the cube is extremal. 

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3. Historical road network statistics for core-based statistical areas in the U.S. (1900 - 2010)

   https://doi.org/10.6084/m9.figshare.19584088.v1  

   Burghardt, Keith; Uhl, Johannes H. (January 2022, figshare)

   Tabulated statistics of road networks at the level of intersections and for built-up areas for each decade from 1900 to 2010, and for 2015, for each core-based statistical area (CBSA, i.e., metropolitan and micropolitan statistical area) in the conterminous United States. These areas are derived from historical road networks developed by Johannes Uhl. See Burghardt et al. (2022) for details on the data processing.  Spatial coverage: all CBSAs that are covered by the HISDAC-US historical settlement layers. This dataset includes around 2,700 U.S. counties. In the remaining counties, construction year coverage in the underlying ZTRAX data (Zillow Transaction and Assessment Dataset) is low. See Uhl et al. (2021) for details. All data created by Keith A. Burghardt, USC Information Sciences Institute, USA Codebook: these CBSA statistics are stratified by degree of aggregation. - CBSA_stats_diffFrom1950: Change in CBSA-aggregated patch statistics between 1950 and 2015 - CBSA_stats_by_decade: CBSA-aggregated patch statistics for each decade from 1900-2010 plus 2015 - CBSA_stats_by_decade: CBSA-aggregated cumulative patch statistics for each decade from 1900-2010 plus 2015. All roads created up to a given decade are used for calculating statistics. - Patch_stats_by_decade: Individual patch statistics for each decade from 1900-2010 plus 2015 - Patch_stats_by_decade: Individual cumulative patch statistics for each decade from 1900-2010 plus 2015. All roads created up to a given decade are used for calculating statistics. The statistics are the following: msaid: CBSA codeid: (if patch statistics) arbitrary int unique to each patch within the CBSA that yearyear: year of statisticspop: population within all CBSA countiespatch_bupr: built up property records (BUPR) within a patch (or sum of patches within CBSA)patch_bupl: built up property l (BUPL) within a patch (or sum of patches within CBSA)patch_bua: built up area (BUA) within a patch (or sum of patches within CBSA)all_bupr: Same as above but for all data in 2015 regardless of whether properties were in patchesall_bupl: Same as above but for all data in 2015 regardless of whether properties were in patchesall_bua: Same as above but for all data in 2015 regardless of whether properties were in patchesnum_nodes: number of nodes (intersections)num_edges: number of edges (roads between intersections)distance: total road length in kmk_mean: mean number of undirected roads per intersectionk1: fraction of nodes with degree 1k4plus: fraction of nodes with degree 4+bearing: histogram of different bearings between intersectionsentropy: entropy of bearing histogrammean_local_gridness: Griddedness used in textmean_local_gridness_max: Same as griddedness used in text but assumes we can have up to 3 quadrilaterals for degree 3 (maximum possible, although intersections will not necessarily create right angles) Code available at https://github.com/johannesuhl/USRoadNetworkEvolution. References: Burghardt, K., Uhl, J., Lerman, K.,  & Leyk, S. (2022). Road Network Evolution in the Urban and Rural  United States Since 1900. Computers, Environment and Urban Systems. 

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4. A deterministic near-linear time approximation scheme for geometric transportation

   https://doi.org/10.1109/FOCS57990.2023.00078  

   Fox, Emily; Lu, Jiashuai (November 2023, IEEE)

   Given a set of points $$P = (P^+ \sqcup P^-) \subset \mathbb{R}^d$$ for some constant $$d$$ and a supply function $$\mu:P\to \mathbb{R}$$ such that $$\mu(p) > 0~\forall p \in P^+$$, $$\mu(p) < 0~\forall p \in P^-$$, and $$\sum_{p\in P}{\mu(p)} = 0$$, the geometric transportation problem asks one to find a transportation map $$\tau: P^+\times P^-\to \mathbb{R}_{\ge 0}$$ such that $$\sum_{q\in P^-}{\tau(p, q)} = \mu(p)~\forall p \in P^+$$, $$\sum_{p\in P^+}{\tau(p, q)} = -\mu(q) \forall q \in P^-$$, and the weighted sum of Euclidean distances for the pairs $$\sum_{(p,q)\in P^+\times P^-}\tau(p, q)\cdot ||q-p||_2$$ is minimized. We present the first deterministic algorithm that computes, in near-linear time, a transportation map whose cost is within a $$(1 + \varepsilon)$$ factor of optimal. More precisely, our algorithm runs in $$O(n\varepsilon^{-(d+2)}\log^5{n}\log{\log{n}})$$ time for any constant $$\varepsilon > 0$$. While a randomized $$n\varepsilon^{-O(d)}\log^{O(d)}{n}$$ time algorithm for this problem was discovered in the last few years, all previously known deterministic $$(1 + \varepsilon)$$-approximation algorithms run in~$$\Omega(n^{3/2})$$ time. A similar situation existed for geometric bipartite matching, the special case of geometric transportation where all supplies are unit, until a deterministic $$n\varepsilon^{-O(d)}\log^{O(d)}{n}$$ time $$(1 + \varepsilon)$$-approximation algorithm was presented at STOC 2022. Surprisingly, our result is not only a generalization of the bipartite matching one to arbitrary instances of geometric transportation, but it also reduces the running time for all previously known $$(1 + \varepsilon)$$-approximation algorithms, randomized or deterministic, even for geometric bipartite matching. In particular, we give the first $$(1 + \varepsilon)$$-approximate deterministic algorithm for geometric bipartite matching and the first $$(1 + \varepsilon)$$-approximate deterministic or randomized algorithm for geometric transportation with no dependence on $$d$$ in the exponent of the running time's polylog. As an additional application of our main ideas, we also give the first randomized near-linear $$O(\varepsilon^{-2} m \log^{O(1)} n)$$ time $$(1 + \varepsilon)$$-approximation algorithm for the uncapacitated minimum cost flow (transshipment) problem in undirected graphs with arbitrary \emph{real} edge costs. 

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5. Automatically Reproducing Timing-Dependent Flaky-Test Failures

   https://doi.org/10.5281/zenodo.7041599  

   Shanto Rahman, Aaron Massey (January 2023, Zenodo)

   This artifact contains the source code for FlakeRake, a tool for automatically reproducing timing-dependent flaky-test failures. It also includes raw and processed results produced in the evaluation of FlakeRake   Contents:   Timing-related APIs that FlakeRake considers adding sleeps at: timing-related-apis Anonymized code for FlakeRake (not runnable in its anonymized state, but included for reference; we will publicly release the non-anonymized code under an open source license pending double-blind review): flakerake.tgz Failure messages extracted from the FlakeFlagger dataset: 10k_reruns_failures_by_test.csv.gz  Output from running isolated reruns on each flaky test in the FlakeFlager dataset: 10k_isolated_reruns_all_results.csv.gz (all test results summarized into a CSV), 10k_isolated_reruns_failures_by_test.csv.gz (CSV including just test failures, including failure messages), 10k_isolated_reruns_raw_results.tgz (includes all raw results from reruns, including the XML files output by maven) Output from running the FlakeFlagger replication study (non-isolated 10k reruns):flakeFlaggerReplResults.csv.gz (all test results summarized into a CSV), 10k_reruns_failures_by_test.csv.gz (CSV including just failures, including failure messages), flakeFlaggerRepl_raw_results.tgz (includes all raw results from reruns, including the XML files output by maven - this file is markedly larger than the 10k isolated reruns results because we ran *all* tests in this experiment, whereas the 10k isolated rerun experiment only re-ran the tests that were known to be flaky from the FlakeFlagger dataset). Output from running FlakeRake on each flaky test in the FlakeFlagger dataset: For bisection mode: results-bis.tgz For one-by-one mode: results-obo.tgz Scripts used to execute FlakeRake using an HPC cluster: execution-scripts.tgz Scripts used to execute rerun experiments using an HPC cluster: flakeFlaggerReplScripts.tgz Scripts used to parse the "raw" maven test result XML files in this artifact into the CSV files contained in this artifact: parseSurefireXMLs.tgz  Output from running FlakeRake in “reproduction” mode, attempting to reproduce each of the failures that matched the FlakeFlagger dataset (collected for bisection mode only): results-repro-bis.tgz Analysis of timing-dependent API calls in the failure inducing configurations that matched FlakeFlagger failures: bis-sleepyline.cause-to-matched-fail-configs-found.csv 

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