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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. Bacterial Community Structure Modulates Soil Phosphorus Turnover at Early Stages of Primary Succession

   https://doi.org/10.1029/2024GB008174  

   Wang, Yuhan; Bing, Haijian; Moorhead, Daryl L; Hou, Enqing; Wu, Yanhong; Wang, Jipeng; Duan, Chengjiao; Cui, Qingliang; Zhang, Zhiqin; Zhu, He; et al (October 2024, Global Biogeochemical Cycles)

   Abstract Microbes are the drivers of soil phosphorus (P) cycling in terrestrial ecosystems; however, the role of soil microbes in mediating P cycling in P‐rich soils during primary succession remains uncertain. This study examined the impacts of bacterial community structure (diversity and composition) and its functional potential (absolute abundances of P‐cycling functional genes) on soil P cycling along a 130‐year glacial chronosequence on the eastern Tibetan Plateau. Bacterial community structure was a better predictor of soil P fractions than P‐cycling genes along the chronosequence. After glacier retreat, the solubilization of inorganic P and the mineralization of organic P were significantly enhanced by increased bacterial diversity, changed interspecific interactions, and abundant species involved in soil P mineralization, thereby increasing P availability. Although 84% of P‐cycling genes were associated with organic P mineralization, these genes were more closely associated with soil organic carbon than with organic P. Bacterial carbon demand probably determined soil P turnover, indicating the dominant role of organic matter decomposition processes in P‐rich alpine soils. Moreover, the significant decrease in the complexity of the bacterial co‐occurrence network and the taxa‐gene‐P network at the later stage indicates a declining dominance of the bacterial community in driving soil P cycling with succession. Our results reveal that bacteria with a complex community structure have a prominent potential for biogeochemical P cycling in P‐rich soils during the early stages of primary succession. 

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3. A carbene-stabilized diphosphorus: a triple-bonded diphosphorus (PP) and a bis(phosphinidene) (P–P) transfer agent

   https://doi.org/10.1039/D4SC05091F  

   Yoon, Joseph S; Abdellaoui, Mehdi; Gembicky, Milan; Bertrand, Guy (October 2024, Chemical Science)

   The bis-monosubstituted aminocarbene-P₂adduct is a generator of P₂, under the classical triple-bonded form (PP), but it also acts as a bis(phosphinidene) (P–P) synthetic equivalent. 

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4. Data accompanying "Drought Characterization with GPS: Insights into Groundwater and Reservoir Storage in California" [Young et al., (2024)]

   https://doi.org/10.6084/m9.figshare.25898044.v1  

   Young, Zachary M; Martens, Hilary R; Hoylman, Zachary H; Gardner, W Payton (June 2024, figshare)

   The data provided here accompany the publication "Drought Characterization with GPS: Insights into Groundwater and Reservoir Storage in California" [Young et al., (2024)] which is currently under review with Water Resources Research. (as of 28 May 2024)Please refer to the manuscript and its supplemental materials for full details. (A link will be appended following publication)File formatting information is listed below, followed by a sub-section of the text describing the Geodetic Drought Index Calculation. The longitude, latitude, and label for grid points are provided in the file "loading_grid_lon_lat".Time series for each Geodetic Drought Index (GDI) time scale are provided within "GDI_time_series.zip".The included time scales are for 00- (daily), 1-, 3-, 6-, 12- 18- 24-, 36-, and 48-month GDI solutions.Files are formatted following...Title: "grid point label L****"_"time scale"_monthFile Format: ["decimal date" "GDI value"]Gridded, epoch-by-epoch, solutions for each time scale are provided within "GDI_grids.zip".Files are formatted following...Title: GDI_"decimal date"_"time scale"_monthFile Format: ["longitude" "latitude" "GDI value" "grid point label L****"]2.2 GEODETIC DROUGHT INDEX CALCULATION We develop the GDI following Vicente-Serrano et al. (2010) and Tang et al. (2023), such that the GDI mimics the derivation of the SPEI, and utilize the log-logistic distribution (further details below). While we apply hydrologic load estimates derived from GPS displacements as the input for this GDI (Figure 1a-d), we note that alternate geodetic drought indices could be derived using other types of geodetic observations, such as InSAR, gravity, strain, or a combination thereof. Therefore, the GDI is a generalizable drought index framework. A key benefit of the SPEI is that it is a multi-scale index, allowing the identification of droughts which occur across different time scales. For example, flash droughts (Otkin et al., 2018), which may develop over the period of a few weeks, and persistent droughts (>18 months), may not be observed or fully quantified in a uni-scale drought index framework. However, by adopting a multi-scale approach these signals can be better identified (Vicente-Serrano et al., 2010). Similarly, in the case of this GPS-based GDI, hydrologic drought signals are expected to develop at time scales that are both characteristic to the drought, as well as the source of the load variation (i.e., groundwater versus surface water and their respective drainage basin/aquifer characteristics). Thus, to test a range of time scales, the TWS time series are summarized with a retrospective rolling average window of D (daily with no averaging), 1, 3, 6, 12, 18, 24, 36, and 48-months width (where one month equals 30.44 days). From these time-scale averaged time series, representative compilation window load distributions are identified for each epoch. The compilation window distributions include all dates that range ±15 days from the epoch in question per year. This allows a characterization of the estimated loads for each day relative to all past/future loads near that day, in order to bolster the sample size and provide more robust parametric estimates [similar to Ford et al., (2016)]; this is a key difference between our GDI derivation and that presented by Tang et al. (2023). Figure 1d illustrates the representative distribution for 01 December of each year at the grid cell co-located with GPS station P349 for the daily TWS solution. Here all epochs between between 16 November and 16 December of each year (red dots), are compiled to form the distribution presented in Figure 1e. This approach allows inter-annual variability in the phase and amplitude of the signal to be retained (which is largely driven by variation in the hydrologic cycle), while removing the primary annual and semi-annual signals. Solutions converge for compilation windows >±5 days, and show a minor increase in scatter of the GDI time series for windows of ±3-4 days (below which instability becomes more prevalent). To ensure robust characterization of drought characteristics, we opt for an extended ±15-day compilation window. While Tang et al. (2023) found the log-logistic distribution to be unstable and opted for a normal distribution, we find that, by using the extended compiled distribution, the solutions are stable with negligible differences compared to the use of a normal distribution. Thus, to remain aligned with the SPEI solution, we retain the three-parameter log-logistic distribution to characterize the anomalies. Probability weighted moments for the log-logistic distribution are calculated following Singh et al., (1993) and Vicente-Serrano et al., (2010). The individual moments are calculated following Equation 3. These are then used to calculate the L-moments for shape (), scale (), and location () of the three-parameter log-logistic distribution (Equations 4 – 6). The probability density function (PDF) and the cumulative distribution function (CDF) are then calculated following Equations 7 and 8, respectively. The inverse Gaussian function is used to transform the CDF from estimates of the parametric sample quantiles to standard normal index values that represent the magnitude of the standardized anomaly. Here, positive/negative values represent greater/lower than normal hydrologic storage. Thus, an index value of -1 indicates that the estimated load is approximately one standard deviation dryer than the expected average load on that epoch. *Equations can be found in the main text. 

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5. 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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