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1. Geometric Hitting Set for Line-Constrained Disks

   https://doi.org/10.1007/978-3-031-38906-1_38  

   Liu, Gang; Wang, Haitao (August 2023, Proceedings of the 18th Algorithms and Data Structures Symposium (WADS 2023))

   Given a set P of n weighted points and a set S of m disks in the plane, the hitting set problem is to compute a subset 𝑃′ of points of P such that each disk contains at least one point of 𝑃′ and the total weight of all points of 𝑃′ is minimized. The problem is known to be NP-hard. In this paper, we consider a line-constrained version of the problem in which all disks are centered on a line ℓ. We present an 𝑂((𝑚+𝑛)log(𝑚+𝑛)+𝜅log𝑚) time algorithm for the problem, where 𝜅 is the number of pairs of disks that intersect. For the unit-disk case where all disks have the same radius, the running time can be reduced to 𝑂((𝑛+𝑚)log(𝑚+𝑛)). In addition, we solve the problem in 𝑂((𝑚+𝑛)log(𝑚+𝑛)) time in the 𝐿∞ and 𝐿1 metrics, in which a disk is a square and a diamond, respectively. 

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2. On the impact of runaway stars on dwarf galaxies with resolved interstellar medium

   https://doi.org/10.1093/mnras/stad2744  

   Steinwandel, Ulrich P; Bryan, Greg L; Somerville, Rachel S; Hayward, Christopher C; Burkhart, Blakesley (September 2023, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT ‘Runaway stars’ might play a role in driving galactic outflows and enriching the circumgalactic medium with metals. To study this effect, we carry out high-resolution dwarf galaxy simulations that include velocity ‘kicks’ to massive stars above eigth solar masses. We consider two scenarios, one that adopts a power law velocity distribution for kick velocities, resulting in more stars with high-velocity kicks, and a more moderate scenario with a Maxwellian velocity distribution. We explicitly resolve the multiphase interstellar medium (ISM) and include non-equilibrium cooling and chemistry. We sample individual massive stars from an IMF and follow their radiation input and SN feedback (core-collapse) channel at the end of their lifetime. In the simulations with runaway stars, we add additional (natal) velocity kicks that mimic two- and three-body interactions that cannot be fully resolved in our simulations. We find that including runaway or ‘walkaway’ star scenarios impacts mass, metal, momentum, and energy outflows as well as the corresponding loading factors. The effect on the mass loading factor is small, but we find an increase in the metal loading by a factor of 1.5 to 2. The momentum loading increases by a factor of 1.5–2. The energy loading increases by roughly a factor of 5 when runaway stars are included. Additionally, we find that the overall level of star formation is increased in the models that include runaway stars. We conclude that the inclusion of runaway stars could have an impact on the global star formation and subsequent outflow properties of dwarf galaxies. 

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3. Roping in Uncertainty: Robustness and Regularization in Markov Games

   Mcmahan, Jeremy; Artiglio, Giovanni; Xie, Qiaomin (July 2024, Proceedings of Machine Learning Research)

   We study robust Markov games (RMG) with 𝑠-rectangular uncertainty. We show a general equivalence between computing a robust Nash equilibrium (RNE) of a 𝑠-rectangular RMG and computing a Nash equilibrium (NE) of an appropriately constructed regularized MG. The equivalence result yields a planning algorithm for solving 𝑠-rectangular RMGs, as well as provable robustness guarantees for policies computed using regularized methods. However, we show that even for just reward-uncertain two-player zero-sum matrix games, computing an RNE is PPAD-hard. Consequently, we derive a special uncertainty structure called efficient player-decomposability and show that RNE for two-player zero-sum RMG in this class can be provably solved in polynomial time. This class includes commonly used uncertainty sets such as 𝐿1 and 𝐿∞ ball uncertainty sets. 

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4. Thermodynamic Relationships for Perfectly Elastic Solids Undergoing Steady-State Heat Flow

   https://doi.org/10.3390/ma15072638  

   Hofmeister, Anne M.; Criss, Everett M.; Criss, Robert E. (April 2022, Materials)

   Available data on insulating, semiconducting, and metallic solids verify our new model that incorporates steady-state heat flow into a macroscopic, thermodynamic description of solids, with agreement being best for isotropic examples. Our model is based on: (1) mass and energy conservation; (2) Fourier’s law; (3) Stefan–Boltzmann’s law; and (4) rigidity, which is a large, yet heretofore neglected, energy reservoir with no counterpart in gases. To account for rigidity while neglecting dissipation, we consider the ideal, limiting case of a perfectly frictionless elastic solid (PFES) which does not generate heat from stress. Its equation-of-state is independent of the energetics, as in the historic model. We show that pressure-volume work (PdV) in a PFES arises from internal interatomic forces, which are linked to Young’s modulus (Ξ) and a constant (n) accounting for cation coordination. Steady-state conditions are adiabatic since heat content (Q) is constant. Because average temperature is also constant and the thermal gradient is fixed in space, conditions are simultaneously isothermal: Under these dual restrictions, thermal transport properties do not enter into our analysis. We find that adiabatic and isothermal bulk moduli (B) are equal. Moreover, Q/V depends on temperature only. Distinguishing deformation from volume changes elucidates how solids thermally expand. These findings lead to simple descriptions of the two specific heats in solids: ∂ln(cP)/∂P = −1/B; cP = nΞ times thermal expansivity divided by density; cP = cVnΞ/B. Implications of our validated formulae are briefly covered. 

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5. Magnetic Reconnection–driven Energization of Protons up to ∼400 keV at the Near-Sun Heliospheric Current Sheet

   https://doi.org/10.3847/2041-8213/ada697  

   Desai, M I; Drake, J F; Phan, T; Yin, Z; Swisdak, M; McComas, D J; Bale, S D; Rahmati, A; Larson, D; Matthaeus, W H; et al (May 2025, The Astrophysical Journal Letters)

   Abstract We report observations of direct evidence of energetic protons being accelerated above ∼400 keV within the reconnection exhaust of a heliospheric current sheet (HCS) crossing by NASA’s Parker Solar Probe (PSP) at a distance of ∼16.25 solar radii (R_s) from the Sun. Inside the exhaust, both the reconnection-generated plasma jet and the accelerated protons up to ∼400 keV propagated toward the Sun, unambiguously establishing their origin from HCS reconnection sites located antisunward of PSP. Within the core of the exhaust, PSP detected stably trapped energetic protons up to ∼400 keV, which is ≈1000 times greater than the available magnetic energy per particle. The differential energy spectrum of the accelerated protons behaved as a pure power law with spectral index of ∼−5. Supporting simulations using thekglobalmodel suggest that the trapping and acceleration of protons up to ∼400 keV in the reconnection exhaust are likely facilitated by merging magnetic islands with a guide field between ∼0.2 and 0.3 of the reconnecting magnetic field, consistent with the observations. These new results, enabled by PSP’s proximity to the Sun, demonstrate that magnetic reconnection in the HCS is a significant new source of energetic particles in the near-Sun solar wind. Our findings of in situ particle acceleration via magnetic reconnection at the HCS provide valuable insights into this fundamental process, which frequently converts the large magnetic field energy density in the near-Sun plasma environment and may be responsible for heating the Sun’s atmosphere, accelerating the solar wind, and energizing charged particles to extremely high energies in solar flares. 

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