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Abstract Recently, Dvořák, Norin, and Postle introduced flexibility as an extension of list coloring on graphs (J Graph Theory 92(3):191–206, 2019, https://doi.org/10.1002/jgt.22447 ). In this new setting, each vertex v in some subset of V ( G ) has a request for a certain color r ( v ) in its list of colors L ( v ). The goal is to find an L coloring satisfying many, but not necessarily all, of the requests. The main studied question is whether there exists a universal constant $$\varepsilon >0$$ ε > 0 such that any graph G in some graph class $$\mathscr {C}$$ C satisfies at least $$\varepsilon$$ ε proportion of the requests. More formally, for $$k > 0$$ k > 0 the goal is to prove that for any graph $$G \in \mathscr {C}$$ G ∈ C on vertex set V , with any list assignment L of size k for each vertex, and for every $$R \subseteq V$$ R ⊆ V and a request vector $$(r(v): v\in R, ~r(v) \in L(v))$$ ( r ( v ) : v ∈ R , r ( v ) ∈ L ( v ) ) , there exists an L -coloring of G satisfying at least $$\varepsilon |R|$$ ε | R | requests. If this is true, then $$\mathscr {C}$$ C is called $$\varepsilon$$ ε - flexible for lists of size k . Choi, Clemen, Ferrara, Horn, Ma, and Masařík (Discrete Appl Math 306:20–132, 2022, https://doi.org/10.1016/j.dam.2021.09.021 ) introduced the notion of weak flexibility , where $$R = V$$ R = V . We further develop this direction by introducing a tool to handle weak flexibility. We demonstrate this new tool by showing that for every positive integer b there exists $$\varepsilon (b)>0$$ ε ( b ) > 0 so that the class of planar graphs without $$K_4, C_5 , C_6 , C_7, B_b$$ K 4 , C 5 , C 6 , C 7 , B b is weakly $$\varepsilon (b)$$ ε ( b ) -flexible for lists of size 4 (here $$K_n$$ K n , $$C_n$$ C n and $$B_n$$ B n are the complete graph, a cycle, and a book on n vertices, respectively). We also show that the class of planar graphs without $$K_4, C_5 , C_6 , C_7, B_5$$ K 4 , C 5 , C 6 , C 7 , B 5 is $$\varepsilon$$ ε -flexible for lists of size 4. The results are tight as these graph classes are not even 3-colorable. 

Magnetometers are a key component of heliophysics research providing valuable insight into the dynamics of electromagnetic field regimes and their coupling throughout the solar system. On satellites, magnetometers provide detailed observations of the extension of the solar magnetic field into interplanetary space and of planetary environments. At Earth, magnetometers are deployed on the ground in extensive arrays spanning the polar cap, auroral and sub-auroral zone, mid- and low-latitudes and equatorial electrojet with nearly global coverage in azimuth (longitude or magnetic local time—MLT). These multipoint observations are used to diagnose both ionospheric and magnetospheric processes as well as the coupling between the solar wind and these two regimes at a fraction of the cost of in-situ instruments. Despite their utility in research, ground-based magnetometer data can be difficult to use due to a variety of file formats, multiple points of access for the data, and limited software. In this short article we review the Open-Source Python library GMAG which provides rapid access to ground-based magnetometer data from a number of arrays in a Pandas DataFrame, a common data format used throughout scientific research. 

Abstract Electrophilic aromatic substitution reactions are of profound importance for the synthesis of biologically active compounds and other advanced materials. They represent an important means to activate specific aromatic C–H bonds without requiring transition-metal catalysts. Surprisingly, few stereoselective variants are known for electrophilic aromatic substitutions, which limits the utility of these classical reactions for stereoselective synthesis. While many electrophilic aromatic substitutions lead to achiral products (due to the planar nature of aromatic rings), there are important examples where chiral products are produced, including desymmetrization reactions of aromatic cyclophanes and of prochiral substrates with multiple aromatic rings. This Synpacts article now illustrates how chiral arms, when placed precisely above and underneath delocalized carbocations, can act as chiral auxiliaries to convert classical electrophilic aromatic substitution reactions into powerful diastereo- and enantioselective transformations. 

Abstract We examine the statistical distribution of large‐scale Birkeland currents measured by the Active Magnetosphere and Planetary Electrodynamics Response Experiment in four unique categories of geomagnetic activity for the first time: quiet times, storm times, quiet‐time substorms, and storm‐time substorms. A novel method is employed to sort data into one of these four categories, and the categorizations are provided for future research. The mean current density is largest during substorms and its standard deviation is largest during geomagnetic storms. Current densities which are above a low threshold are more likely during substorms, but extreme currents are far more likely during geomagnetic storms, consistent with a paradigm in which geomagnetic storms represent periods of enhanced variability over quiet times. We demonstrate that extreme currents are most likely to flow within the Region 2 current during geomagnetic storms. This is unexpected in a paradigm of the current systems in which Region 1 current is generally larger. 

Abstract We report a general synthetic route toward helical ladder polymers with varying spring constants, built with chirality‐assisted synthesis (CAS). Under tension and compression, these shape‐persistent structures do not unfold, but rather stretch and compress akin classical Hookean springs. Our synthesis is adaptable to helices with different pitch and diameter, which allowed us to investigate how molecular flexibility in solution depends on the exact geometry of the ladder polymers. Specifically, we showed with molecular dynamic simulations and by measuring the longitudinal¹H NMR relaxation times (T₁) for our polymers at different Larmor frequencies, that increasing the helix diameter leads to increased flexibility. Our results present initial design rules for tuning the mechanical properties of intrinsically helical ladder polymers in solution, which will help inspire a new class of robust, spring‐like molecular materials with varying mechanical properties.