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1. Statistical Study of the Correlation between Solar Energetic Particles and Properties of Active Regions

   https://doi.org/10.3847/1538-4357/acdb65  

   Marroquin, Russell D. ; Sadykov, Viacheslav ; Kosovichev, Alexander ; Kitiashvili, Irina N. ; Oria, Vincent ; Nita, Gelu M. ; Illarionov, Egor ; O’Keefe, Patrick M. ; Francis, Fraila ; Chong, Chun Jie ; et al ( July 2023 , The Astrophysical Journal)

   The flux of energetic particles originating from the Sun fluctuates during the solar cycles. It depends on the number and properties of active regions (ARs) present in a single day and associated solar activities, such as solar flares and coronal mass ejections. Observational records of the Space Weather Prediction Center NOAA enable the creation of time-indexed databases containing information about ARs and particle flux enhancements, most widely known as solar energetic particle (SEP) events. In this work, we utilize the data available for solar cycles 21–24 and the initial phase of cycle 25 to perform a statistical analysis of the correlation between SEPs and properties of ARs inferred from the McIntosh and Hale classifications. We find that the complexity of the magnetic field, longitudinal location, area, and penumbra type of the largest sunspot of ARs are most correlated with the production of SEPs. It is found that most SEPs (≈60%, or 108 out of 181 considered events) were generated from an AR classified with the “k” McIntosh subclass as the second component, and these ARs are more likely to produce SEPs if they fall in a Hale class containing aδcomponent. The resulting database containing information about SEP events and ARs is publicly available and can be used for the development of machine learning models to predict the occurrence of SEPs.

    

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2. Simple Analytical Expressions for Steady-State Vapor Growth and Collision–Coalescence Particle Size Distribution Parameter Profiles

   https://doi.org/10.1175/JAS-D-23-0052.1  

   Dunnavan, Edwin L. ; Ryzhkov, Alexander V. ( October 2023 , Journal of the Atmospheric Sciences)

   This study derives simple analytical expressions for the theoretical height profiles of particle number concentrations (N_t) and mean volume diameters (D_m) during the steady-state balance of vapor growth and collision–coalescence with sedimentation. These equations are general for both rain and snow gamma size distributions with size-dependent power-law functions that dictate particle fall speeds and masses. For collision–coalescence only,N_t(D_m) decreases (increases) as an exponential function of the radar reflectivity difference between two height layers. For vapor deposition only,D_mincreases as a generalized power law of this reflectivity difference. Simultaneous vapor deposition and collision–coalescence under steady-state conditions with conservation of number, mass, and reflectivity fluxes lead to a coupled set of first-order, nonlinear ordinary differential equations forN_tandD_m. The solutions to these coupled equations are generalized power-law functions of heightzforD_m(z) andN_t(z) whereby each variable is related to one another with an exponent that is independent of collision–coalescence efficiency. Compared to observed profiles derived from descending in situ aircraft Lagrangian spiral profiles from the CRYSTAL-FACE field campaign, these analytical solutions can on average capture the height profiles ofN_tandD_mwithin 8% and 4% of observations, respectively. Steady-state model projections of radar retrievals aloft are shown to produce the correct rapid enhancement of surface snowfall compared to the lowest-available radar retrievals from 500 m MSL. Future studies can utilize these equations alongside radar measurements to estimateN_tandD_mbelow radar tilt elevations and to estimate uncertain microphysical parameters such as collision–coalescence efficiencies.

   While complex numerical models are often used to describe weather phenomenon, sometimes simple equations can instead provide equally good or comparable results. Thus, these simple equations can be used in place of more complicated models in certain situations and this replacement can allow for computationally efficient and elegant solutions. This study derives such simple equations in terms of exponential and power-law mathematical functions that describe how the average size and total number of snow or rain particles change at different atmospheric height levels due to growth from the vapor phase and aggregation (the sticking together) of these particles balanced with their fallout from clouds. We catalog these mathematical equations for different assumptions of particle characteristics and we then test these equations using spirally descending aircraft observations and ground-based measurements. Overall, we show that these mathematical equations, despite their simplicity, are capable of accurately describing the magnitude and shape of observed height and time series profiles of particle sizes and numbers. These equations can be used by researchers and forecasters along with radar measurements to improve the understanding of precipitation and the estimation of its properties.

    

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3. Synthetic Forest Stands and Point Clouds for Model Selection and Feature Space Comparison

   https://doi.org/10.3390/rs15184407  

   Bester, Michelle S. ; Maxwell, Aaron E. ; Nealey, Isaac ; Gallagher, Michael R. ; Skowronski, Nicholas S. ; McNeil, Brenden E. ( September 2023 , Remote Sensing)

   The challenges inherent in field validation data, and real-world light detection and ranging (lidar) collections make it difficult to assess the best algorithms for using lidar to characterize forest stand volume. Here, we demonstrate the use of synthetic forest stands and simulated terrestrial laser scanning (TLS) for the purpose of evaluating which machine learning algorithms, scanning configurations, and feature spaces can best characterize forest stand volume. The random forest (RF) and support vector machine (SVM) algorithms generally outperformed k-nearest neighbor (kNN) for estimating plot-level vegetation volume regardless of the input feature space or number of scans. Also, the measures designed to characterize occlusion using spherical voxels generally provided higher predictive performance than measures that characterized the vertical distribution of returns using summary statistics by height bins. Given the difficulty of collecting a large number of scans to train models, and of collecting accurate and consistent field validation data, we argue that synthetic data offer an important means to parameterize models and determine appropriate sampling strategies.

    

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4. Non-asymptotic superlinear convergence of standard quasi-Newton methods

   https://doi.org/10.1007/s10107-022-01887-4  

   Jin, Qiujiang ; Mokhtari, Aryan ( September 2022 , Mathematical Programming)

   In this paper, we study and prove the non-asymptotic superlinear convergence rate of the Broyden class of quasi-Newton algorithms which includes the Davidon–Fletcher–Powell (DFP) method and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. The asymptotic superlinear convergence rate of these quasi-Newton methods has been extensively studied in the literature, but their explicit finite–time local convergence rate is not fully investigated. In this paper, we provide a finite–time (non-asymptotic) convergence analysis for Broyden quasi-Newton algorithms under the assumptions that the objective function is strongly convex, its gradient is Lipschitz continuous, and its Hessian is Lipschitz continuous at the optimal solution. We show that in a local neighborhood of the optimal solution, the iterates generated by both DFP and BFGS converge to the optimal solution at a superlinear rate of$$(1/k)^{k/2}$$${(1/k)}^{k/2}$, wherekis the number of iterations. We also prove a similar local superlinear convergence result holds for the case that the objective function is self-concordant. Numerical experiments on several datasets confirm our explicit convergence rate bounds. Our theoretical guarantee is one of the first results that provide a non-asymptotic superlinear convergence rate for quasi-Newton methods.

    

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5. Curvature Sets Over Persistence Diagrams

   https://doi.org/10.1007/s00454-024-00634-0  

   Gómez, Mario ; Mémoli, Facundo ( April 2024 , Discrete & Computational Geometry)

   We study a family of invariants of compact metric spaces that combines the Curvature Sets defined by Gromov in the 1980 s with Vietoris–Rips Persistent Homology. For given integers$$k\ge 0$$$k\ge 0$and$$n\ge 1$$$n\ge 1$we consider the dimensionkVietoris–Rips persistence diagrams ofallsubsets of a given metric space with cardinality at mostn. We call these invariantspersistence setsand denote them as$${\textbf{D}}_{n,k}^{\textrm{VR}}$$$D_{n,k}^{\text{VR}}$. We first point out that this family encompasses the usual Vietoris–Rips diagrams. We then establish that (1) for certain range of values of the parametersnandk, computing these invariants is significantly more efficient than computing the usual Vietoris–Rips persistence diagrams, (2) these invariants have very good discriminating power and, in many cases, capture information that is imperceptible through standard Vietoris–Rips persistence diagrams, and (3) they enjoy stability properties analogous to those of the usual Vietoris–Rips persistence diagrams. We precisely characterize some of them in the case of spheres and surfaces with constant curvature using a generalization of Ptolemy’s inequality. We also identify a rich family of metric graphs for which$${\textbf{D}}_{4,1}^{\textrm{VR}}$$$D_{4,1}^{\text{VR}}$fully recovers their homotopy type by studying split-metric decompositions. Along the way we prove some useful properties of Vietoris–Rips persistence diagrams using Mayer–Vietoris sequences. These yield a geometric algorithm for computing the Vietoris–Rips persistence diagram of a spaceXwith cardinality$$2k+2$$$2k+2$with quadratic time complexity as opposed to the much higher cost incurred by the usual algebraic algorithms relying on matrix reduction.

    

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