More Like this

1. Unmixing detrital geochronology age distributions: UNMIXING DETRITAL AGE DISTRIBUTIONS

   https://doi.org/10.1002/2016GC006774  

   Sundell, Kurt E.; Saylor, Joel E. (August 2017, Geochemistry, Geophysics, Geosystems)
2. Shadow line distributions

   https://doi.org/10.1090/mcom/4110  

   Balakrishnan, Jennifer; Çiperiani, Mirela; Mazur, Barry; Rubin, Karl (July 2025, Mathematics of Computation)

   Let $E$be an elliptic curve over $\mathbb{Q}$with Mordell–Weil rank $2$and $p$be an odd prime of good ordinary reduction. For every imaginary quadratic field $K$satisfying the Heegner hypothesis, there is (subject to the Shafarevich–Tate conjecture) a line, i.e., a free ${\mathbb{Z}}_p$-submodule of rank $1$, in $E\left(K\right)\otimes <\#comment/>{\mathbb{Z}}_p$given by universal norms coming from the Mordell–Weil groups of subfields of the anticyclotomic ${\mathbb{Z}}_p$-extension of $K$; we call it theshadow line. When the twist of $E$by $K$has analytic rank $1$, the shadow line is conjectured to lie in $E\left(\mathbb{Q}\right)\otimes <\#comment/>{\mathbb{Z}}_p$; we verify this computationally in all our examples. We study the distribution of shadow lines in $E\left(\mathbb{Q}\right)\otimes <\#comment/>{\mathbb{Z}}_p$as $K$varies, framing conjectures based on the computations we have made. 

   more » « less
3. Droplet size distributions in turbulent clouds: experimental evaluation of theoretical distributions

   https://doi.org/10.1002/qj.3692  

   Chandrakar, Kamal Kant; Saito, Izumi; Yang, Fan; Cantrell, Will; Gotoh, Toshiyuki; Shaw, Raymond A. (December 2019, Quarterly Journal of the Royal Meteorological Society)

   Abstract Precipitation efficiency and optical properties of clouds, both central to determining Earth's weather and climate, depend on the size distribution of cloud particles. In this work theoretical expressions for cloud droplet size distribution shape are evaluated using measurements from controlled experiments in a convective‐cloud chamber. The experiments are a unique opportunity to constrain theory because they are in steady‐state and because the initial and boundary conditions are well characterized compared to typical atmospheric measurements. Three theoretical distributions obtained from a Langevin drift‐diffusion approach to cloud formation via stochastic condensation are tested: (a) stochastic condensation with a constant removal time‐scale; (b) stochastic condensation with a size‐dependent removal time‐scale; (c) droplet growth in a fixed supersaturation condition and with size‐dependent removal. In addition, a similar Weibull distribution that can be obtained from the drift‐diffusion approach, as well as from mechanism‐independent probabilistic arguments (e.g., maximum entropy), is tested as a fourth hypothesis. Statistical techniques such as theχ²test, sum of squared errors of prediction, and residual analysis are employed to judge relative success or failure of the theoretical distributions to describe the experimental data. An extensive set of cloud droplet size distributions are measured under different aerosol injection rates. Five different aerosol injection rates are run both for size‐selected aerosol particles, and six aerosol injection rates are run for broad‐distribution, polydisperse aerosol particles. In relative comparison, the most favourable comparison to the measurements is the expression for stochastic condensation with size‐dependent droplet removal rate. However, even this optimal distribution breaks down for broad aerosol size distributions, primarily due to deviations from the measured large‐droplet tail. A possible explanation for the deviation is the Ostwald ripening effect coupled with deactivation/activation in polluted cloud conditions. 

   more » « less
4. Exponentiated Strongly Rayleigh Distributions

   Mariet, Zelda; Sra, Suvrit; Jegelka, Stefanie (January 2018, Advances in neural information processing systems)
5. Strictly subgaussian probability distributions

   https://doi.org/10.1214/24-EJP1120  

   Bobkov, S G; Chistyakov, G P; Götze, F (January 2024, Electronic Journal of Probability)

   We explore probability distributions on the real line whose Laplace transform admits an upper bound of subgaussian type known as strict subgaussianity. One class in this family corresponds to entire characteristic functions having only real zeros in the complex plane. Using Hadamard’s factorization theorem, we extend this class and propose new sufficient conditions for strict subgaussianity in terms of location of zeros of the associated characteristic functions. The second part of this note deals with Laplace transforms of strictly subgaussian distributions with periodic components. This class contains interesting examples, for which the central limit theorem with respect to the Rényi entropy divergence of infinite order holds. 

   more » « less