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In addition to the omnipresent Galactic Cosmic Rays (GCRs), sudden solar energetic particle (SEP) events present considerable health hazards for manned space missions. These events not only contribute to an increased long-term cancer risk, but can, in extreme cases, cause acute radiation syndromes. Forecasting their imminent occurrence could significantly reduce radiation exposure by warning astronauts to move to shelter. However, all currently available tools are primarily designed for the Earth or Earth-Moon system, which limits their applicability to future Mars missions. To address this, we developed a nowcasting system for SEP events applicable in deep space and on the Martian surface, which serves as a reliable last-resort backup when forecasts fail. The methodology of this system is based on dose rates measured by the Radiation Assessment Detector (RAD) onboard the Mars Science Laboratory (MSL), which recorded 5 SEP events during the seven-month flight to Mars and 16 since its landing on Mars on August 6, 2012. An SEP event is triggered, and an astronaut is warned as soon as dose rates exceed the omnipresent background level by at least 25%. This approach suggests that our system can provide astronauts with at least 30 minutes to avoid both peak radiation exposure and the majority of the cumulative dose from SEP events. Our nowcasting system is robust, easily implementable in real-life scenarios, and achieves a near-zero false alarm rate both in deep space and on the Martian surface.

We characterize a Courant algebroid with a Calabi-Yau structure as a homotopy BV algebra with certain properties. We explain how it fits into recent double copy constructions relating Yang-Mills homotopy algebras to the ones of Double Field Theory and Gravity., Comment: 49 pages

These lecture notes are devoted to the recent progress in the geometric aspects of quantum integrable systems based on quantum groups solved using the Bethe ansatz technique. One part is devoted to their enumerative geometry realization through the quantum K-theory of Nakajima quiver varieties. The other part describes a recently studied $q$-deformation of the correspondence between oper connections and Gaudin models. The notes are based on a minicourse at C.I.M.E. Summer School ``Enumerative geometry, quantisation and moduli spaces," September 04-08, 2023., Comment: 45 pages

New evidence of surprising robustness of solitary-wave solutions of the Serre-Green-Naghdi (SGN) equations is presented on the basis of high-resolution numerical simulations conducted using a novel well-balanced finite-volume method. SGN solitons exhibit a striking resemblance with their celebrated Korteweg-deVries (KdV) counterparts. Co-moving solitons are shown to exit intact from double and triple collisions with a remarkably small wave-wake residual. The counter-propagating solitons experiencing frontal collisions and solitons hitting a wall, non-existing in KdV case configurations, are shown to also recover, but with a much larger than in co-moving case residual, confirming with higher precision the results known in the literature. Multiple SGN solitons emerging from localized initial conditions are exhibited, and it is demonstrated that SGN solitons survive hitting localized topographic obstacles, and generate secondary solitons when they encounter a rising escarpment., Comment: 10 pages, more simulations, snapshots and videos are available at https://drive.google.com/drive/folders/1s-lKpJY3J_rACz9ufZ70tItwd4iOjUsx?usp=drive_link

We develop a new second-order flux globalization based path-conservative central-upwind (PCCU) scheme for rotating shallow water magnetohydrodynamic equations. The new scheme is designed not only to maintain the divergence-free constraint of the magnetic field at the discrete level but also to satisfy the well-balanced (WB) property by exactly preserving some physically relevant steady states of the underlying system. The locally divergence-free constraint of the magnetic field is enforced by following the method recently introduced in [A. Chertock, A. Kurganov, M. Redle, and K. Wu, ArXiv preprint (2022), arXiv:2212.02682]: we consider a Godunov-Powell modified version of the studied system, introduce additional equations by spatially differentiating the magnetic field equations, and modify the reconstruction procedures for magnetic field variables. The WB property is ensured by implementing a flux globalization approach within the PCCU scheme, leading to a method capable of preserving both still- and moving-water equilibria exactly. In addition to provably achieving both the WB and divergence-free properties, the new method is implemented on an unstaggered grid and does not require any (approximate) Riemann problem solvers. The performance of the proposed method is demonstrated in several numerical experiments that confirm the lack of spurious oscillations, robustness, and high resolution of the obtained results.

Using a wide array of machinery from diverse fields across mathematics, we provide a construction of a measure on the real line which is doubling on all $n$-adic intervals for any finite list of $n\in\mathbb{N}$, yet not doubling overall. In particular, we extend previous results in the area, where only two coprime numbers $n$ were allowed, by using substantially new ideas. In addition, we provide several nontrivial applications to reverse H\"older weights, $A_p$ weights, Hardy spaces, BMO and VMO function classes, and connect our results with key principles and conjectures across number theory., Comment: 24 pages, 3 figures

Our goal is to describe superconformal structures on super Riemann surfaces (SRS), based on data assigned to a fatgraph. We start from the complex structures on punctured $(1|1)$-supermanifolds, characterizing the corresponding moduli and the deformations using Strebel differentials and certain \v{C}ech cocycles for a specific covering, which we reproduce from a fatgraph data, consisting of $U(1)$-graph connection and odd parameters at the vertices. Then we consider dual $(1|1)$-supermanifolds and related superconformal structures for $N=2$ super Riemann surfaces. The superconformal structures $N=1$ SRS are computed as the fixed points of involution on supermoduli space of $N=2$ SRS., Comment: v2: 25 pages, minor revisions

The relation between special connections on the projective line, called Miura opers, and the spectra of integrable models of Gaudin type provides an important example of the geometric Langlands correspondence. The possible generalization of that correspondence to simple Lie superalgebras is much less studied. Recently some progress has been made in understanding the spectra of Gaudin models and the corresponding Bethe ansatz equations for some simple Lie superalgebras. At the same time, the original example was reformulated in terms of an intermediate object: Miura-Pl\"ucker oper. It has a direct relation to the so-called $qq$-systems, the functional form of Bethe ansatz, which, in particular, allows $q$-deformation. In this note, we discuss the notion of superoper and relate it to the examples of $qq$-systems for Lie superalgebras, which were recently studied in the context of Bethe ansatz equations. We also briefly discuss the $q$-deformation of these constructions., Comment: 19 pages

We present results of an experiment benchmarking a workforce training program against cash transfers for underemployed young adults in Rwanda. 3.5 years after treatment, the training program enhances productive time use and asset investment, while the cash transfers drive productive assets, livestock values, savings, and subjective well-being. Both interventions have powerful effects on entrepreneurship. But while labor, sales, and profits all go up, the implied wage rate in these businesses is low. Our results suggest that credit is a major barrier to self-employment, but deeper reforms may be required to enable entrepreneurship to provide a transformative pathway out of poverty.

The activity of the Sun alternates between a solar minimum and a solar maximum, the former corresponding to a period of "quieter" status of the heliosphere. During solar minimum, it is in principle more straightforward to follow eruptive events and solar wind structures from their birth at the Sun throughout their interplanetary journey. In this paper, we report analysis of the origin, evolution, and heliospheric impact of a series of solar transient events that took place during the second half of August 2018, i.e. in the midst of the late declining phase of Solar Cycle 24. In particular, we focus on two successive coronal mass ejections (CMEs) and a following high-speed stream (HSS) on their way towards Earth and Mars. We find that the first CME impacted both planets, whilst the second caused a strong magnetic storm at Earth and went on to miss Mars, which nevertheless experienced space weather effects from the stream interacting region (SIR) preceding the HSS. Analysis of remote-sensing and in-situ data supported by heliospheric modelling suggests that CME--HSS interaction resulted in the second CME rotating and deflecting in interplanetary space, highlighting that accurately reproducing the ambient solar wind is crucial even during "simpler" solar minimum periods. Lastly, we discuss the upstream solar wind conditions and transient structures responsible for driving space weather effects at Earth and Mars., Comment: 27 pages, 7 figures, 1 table, accepted for publication in Space Weather

We study the moduli space of flat $GL(1|1)$-connections on a punctured surface from the point of view of graph connections. To each fatgraph, a system of coordinates is assigned, which involves two bosonic and two fermionic variables per edge, subject to certain relations. In the case of trivalent graphs, we provide a closed explicit formula for the Whitehead moves. In addition, we discuss the invariant Poisson bracket., Comment: v2: 13 pages, minor revisions

We investigate various spaces of $SL(r+1)$-opers and their deformations. For each type of such opers, we study the quantum/classical duality, which relates quantum integrable spin chains with classical solvable many body systems. In this context, quantum/classical dualities serve as an interplay between two different coordinate systems on the space of opers. We also establish correspondences between the underlying oper spaces, which recently had multiple incarnations in symplectic duality and bispectral duality., Comment: v2: 31 pages, typos corrected, references added, to appear in IMRN

We discuss the $qq$-systems, the functional form of the Bethe ansatz equations for the twisted Gaudin model from a new geometric point of view. We use a concept of $G$-Wronskians, which are certain meromorphic sections of principal $G$-bundles on the projective line. In this context, the $qq$-system, similar to its difference analog, is realized as the relation between generalized minors of the $G$-Wronskian. We explain the link between $G$-Wronskians and twisted $G$-oper connections, which are the traditional source for the $qq$-systems., Comment: 13 pages. arXiv admin note: text overlap with arXiv:2112.02711, arXiv:2108.04184

It is well-known that the spectra of the Gaudin model may be described in terms of solutions of the Bethe Ansatz equations. A conceptual explanation for the appearance of the Bethe Ansatz equations is provided by appropriate $G$-opers: $G$-connections on the projective line with extra structure. In fact, solutions of the Bethe Ansatz equations are parameterized by an enhanced version of opers called Miura opers; here, the opers appearing have only regular singularities. Feigin, Frenkel, Rybnikov, and Toledano Laredo have introduced an inhomogeneous version of the Gaudin model; this model incorporates an additional twist factor, which is an element of the Lie algebra of $G$. They exhibited the Bethe Ansatz equations for this model and gave a geometric interpretation of the spectra in terms of opers with an irregular singularity. In this paper, we consider a new approach to the study of the spectra of the inhomogeneous Gaudin model in terms of a further enhancement of opers called twisted Miura-Pl\"ucker opers and a certain system of nonlinear differential equations called the $qq$-system. We show that there is a close relationship between solutions of the inhomogeneous Bethe Ansatz equations and polynomial solutions of the $qq$-system and use this fact to construct a bijection between the set of solutions of the inhomogeneous Bethe Ansatz equations and the set of nondegenerate twisted Miura-Pl\"ucker opers. We further prove that as long as certain combinatorial conditions are satisfied, nondegenerate twisted Miura-Pl\"ucker opers are in fact Miura opers., Comment: 38 pages, revised version

In this paper, we describe a certain kind of $q$-connections on a projective line, namely $Z$-twisted $(G,q)$-opers with regular singularities using the language of generalized minors. In part one arXiv:2002.07344 we explored the correspondence between these $q$-connections and $QQ$-systems/Bethe Ansatz equations. Here we associate to a $Z$-twisted $(G,q)$-oper a class of meromorphic sections of a $G$-bundle, satisfying certain difference equations, which we refer to as generalized $q$-Wronskians. Among other things, we show that the $QQ$-systems and their extensions emerge as the relations between generalized minors, thereby putting the Bethe Ansatz equations in the framework of cluster mutations known in the theory of double Bruhat cells., Comment: 24 pages. arXiv admin note: text overlap with arXiv:2002.07344

We benchmark a multi-dimensional child nutrition intervention against an unconditional cash transfer of equal cost. Randomized variation in transfer amounts allows us to estimate impacts of cash transfers at expenditure levels equivalent to the in-kind program, as well as to estimate the return to increasing cash transfer values. While neither the in-kind program nor a cost-equivalent transfer costing \$124 per household moves core child outcomes within a year, cash transfers create significantly greater consumption than the in-kind alternative. A larger cash transfer costing \$517 substantially improves consumption and investment outcomes and drives modest improvements in dietary diversity and child growth.

This paper reports on a two-tiered experiment designed to separately identify the selection and effort margins of pay-for-performance (P4P). At the recruitment stage, teacher labor markets were randomly assigned to a 'pay-for-percentile' or fixed-wage contract. Once recruits were placed, an unexpected, incentive-compatible, school-level re-randomization was performed, so that some teachers who applied for a fixed-wage contract ended up being paid by P4P, and vice versa. By the second year of the study, the within-year effort effect of P4P was 0.16 standard deviations of pupil learning, with the total effect rising to 0.20 standard deviations after allowing for selection.

Despite widely documented shortfalls of teacher skills and effort, there is little systematic evidence of rates of teacher turnover in low-income countries. I investigate the incidence and consequences of teacher turnover in Rwandan public primary schools over the period from 2016-2019. To do so, I combine the universe of teacher placement records with student enrollment figures and school-average Primary Leaving Exam scores in a nationally representative sample of 259 schools. Results highlight five features of teacher turnover. First, rates of teacher turnover are high: annually, 20 percent of teachers separate from their jobs, of which 11 percent exit from the public-sector teaching workforce. Second, the burden of teacher churn is higher in schools with low learning levels and, perhaps surprisingly, in low pupil-teacher-ratio schools. Third, teacher turnover is concentrated among early-career teachers, male teachers, and those assigned to teach Math. Fourth, replacing teachers quickly after they exit is a challenge; 23 percent of exiting teachers are not replaced the following year. And fifth, teacher turnover is associated with subsequent declines in learning outcomes. On average, the loss of a teacher is associated with a reduction in learning levels of 0.05 standard deviations. In addition to class-size increases, a possible mechanism for these learning outcomes is the prevalence of teachers teaching outside of their areas of subject expertise: in any given year, at least 21 percent of teachers teach in subjects in which they have not been trained. Taken together, these results suggest that the problem of teacher turnover is substantial in magnitude and consequential for learning outcomes in schools.

We use a randomized experiment to compare a workforce training program to cash transfers in Rwanda. Conducted in a sample of poor and underemployed youth, this study measures the impact of the training program not only relative to a control group but relative to the counterfactual of simply disbursing the cost of the program directly to beneficiaries. While the training program was successful in improving a number of core outcomes (productive hours, assets, savings, and subjective well-being), cost-equivalent cash transfers move all these outcomes as well as consumption, income, and wealth. In the head-to-head costing comparison cash proves superior across a number of economic outcomes, while training outperforms cash only in the production of business knowledge. We find little evidence of complementarity between human and physical capital interventions, and no signs of heterogeneity or spillover effects.

We define and study the space of $q$-opers associated with Bethe equations for integrable models of XXZ type with quantum toroidal algebra symmetry. Our construction is suggested by the study of the enumerative geometry of cyclic quiver varieties, in particular, the ADHM moduli spaces. We define $(\overline{GL}(\infty),q)$-opers with regular singularities and then, by imposing various analytic conditions on singularities, arrive at the desired Bethe equations for toroidal $q$-opers., Comment: 55 pages, to appear in the Journal of the Institute of Mathematics of Jussieu

The Radiation Assessment Detector (RAD), onboard the Mars Science Laboratory (MSL) rover Curiosity, has been measuring the energetic charged and neutral particles and the radiation dose rate on the surface of Mars since the landing of the rover in August 2012. In contrast to charged particles, neutral particles (neutrons and gamma-rays) are measured indirectly: the energy deposition spectra produced by neutral particles are complex convolutions of the incident particle spectra with the detector response functions. An inversion technique has been developed and applied to jointly unfold the deposited energy spectra measured in two scintillators of different types (CsI for high gamma detection efficiency, and plastic for neutrons) to obtain the neutron and gamma-ray spectra. This result is important for determining the biological impact of the Martian surface radiation contributed by neutrons, which interact with materials differently from the charged particles. These first in-situ measurements on Mars provide (1) an important reference for assessing the radiation-associated health risks for future manned missions to the red planet and (2) an experimental input for validating the particle transport codes used to model the radiation environments within spacecraft or on the surface of planets. Here we present neutral particle spectra as well as the corresponding dose and dose equivalent rates derived from RAD measurement during a period (November 15, 2015 to January 15, 2016) for which the surface particle spectra have been simulated via different transport models.

Space radiation is a major risk for humans, especially on long-duration missions to outer space, e.g., a manned mission to Mars. Galactic cosmic rays (GCR) contribute a predictable radiation background, the main risk is due to the highly variable and currently unpredictable flux of solar energetic particles (SEPs). Such sporadic SEP events may induce acute health effects and are thus considered a critical mission risk for future human exploration of Mars. Therefore, it is of utmost importance to study, model, and predict the surface radiation environment during such events. It is well known that the deep-space SEP differential energy spectrum at high energies is often given by a power law. We use a measurement-validated particle transport code to show that, for large SEP events with proton energy extending above ~ 500 MeV with a power-law distribution, it is sufficient to measure the SEP flux at a pivot energy of ~ 300 MeV above the Martian atmosphere to predict the dose rate on the Martian surface. In conjunction with a validation by in-situ measurements from the Martian surface, this remarkable simplification and elegant quantification could enable instant predictions of the radiation environment on the surface of Mars upon the onset of large SEP events.

Forbush decreases (FDs), which are short-term drops in the flux of galactic cosmic rays, are caused by the shielding from strong and/or turbulent magnetic structures in the solar wind, especially interplanetary coronal mass ejections (ICMEs) and their associated shocks, as well as corotating interaction regions. Such events can be observed at Earth, for example, using neutron monitors, and also at many other locations in the solar system, such as on the surface of Mars with the Radiation Assessment Detector instrument onboard Mars Science Laboratory. They are often used as a proxy for detecting the arrival of ICMEs or corotating interaction regions, especially when sufficient in situ solar wind measurements are not available. We compare the properties of FDs observed at Earth and Mars, focusing on events produced by ICMEs. We find that FDs at both locations show a correlation between their total amplitude and the maximum hourly decrease, but with different proportionality factors. We explain this difference using theoretical modeling approaches and suggest that it is related to the size increase of ICMEs, and in particular their sheath regions, en route from Earth to Mars. From the FD data, we can derive the sheath broadening factor to be between about 1.5 and 1.9, agreeing with our theoretical considerations. This factor is also in line with previous measurements of the sheath evolution closer to the Sun.

We introduce the notions of $(G,q)$-opers and Miura $(G,q)$-opers, where $G$ is a simply-connected complex simple Lie group, and prove some general results about their structure. We then establish a one-to-one correspondence between the set of $(G,q)$-opers of a certain kind and the set of nondegenerate solutions of a system of Bethe Ansatz equations. This may be viewed as a $q$DE/IM correspondence between the spectra of a quantum integrable model (IM) and classical geometric objects ($q$-differential equations). If $\mathfrak{g}$ is simply-laced, the Bethe Ansatz equations we obtain coincide with the equations that appear in the quantum integrable model of XXZ-type associated to the quantum affine algebra $U_q \widehat{\mathfrak{g}}$. However, if $\mathfrak{g}$ is non-simply laced, then these equations correspond to a different integrable model, associated to $U_q {}^L\widehat{\mathfrak{g}}$ where $^L\widehat{\mathfrak{g}}$ is the Langlands dual (twisted) affine algebra. A key element in this $q$DE/IM correspondence is the $QQ$-system that has appeared previously in the study of the ODE/IM correspondence and the Grothendieck ring of the category ${\mathcal O}$ of the relevant quantum affine algebra., Comment: v3: 44 pages, minor revisions, to appear in the Journal of the European Mathematical Society

We develop a well-balanced central-upwind scheme for rotating shallow water model with horizontal temperature and/or density gradients---the thermal rotating shallow water (TRSW). The scheme is designed using the flux globalization approach: first, the source terms are incorporated into the fluxes, which results in a hyperbolic system with global fluxes; second, we apply the Riemann-problem-solver-free central-upwind scheme to the rewritten system. We ensure that the resulting method is well-balanced by switching off the numerical diffusion when the computed solution is near (at) thermo-geostrophic equilibria. The designed scheme is successfully tested on a series of numerical examples. Motivated by future applications to large-scale motions in the ocean and atmosphere, the model is considered on the tangent plane to a rotating planet both in mid-latitudes and at the Equator. The numerical scheme is shown to be capable of quite accurately maintaining the equilibrium states in the presence of nontrivial topography and rotation. Prior to numerical simulations, an analysis of the TRSW model based on the use of Lagrangian variables is presented, allowing one to obtain criteria of existence and uniqueness of the equilibrium state, of the wave-breaking and shock formation, and of instability development out of given initial conditions. The established criteria are confirmed in the conducted numerical experiments.

The authors derive a McShane identity for once-punctured super tori. Relying upon earlier work on super Teichm\"uller theory by the last two-named authors, they further develop the supergeometry of these surfaces and establish asymptotic growth rate of their length spectra., Comment: v3: 42 pages, 8 figures, to appear in Journal of Differential Geometry

The Radiation Assessment Detector (RAD) instrument onboard the Mars Science Laboratory (MSL) mission's Curiosity rover has been measuring galactic cosmic rays (GCR) as well as solar energetic particles (SEP) on the surface of Mars for more than 6 years since its landing in August 2012. The observations include a large number of Forbush decreases (FD) caused by interplanetary coronal mass ejections (ICMEs) and/or their associated shocks shielding away part of the GCR particles with their turbulent and enhanced magnetic fields while passing Mars. This study combines MSL/RAD FD measurements and remote tracking of ICMEs using the Solar TErrestrial RElations Observatory (STEREO) Heliospheric Imager (HI) telescopes in a statistical study for the first time. The large data set collected by HI makes it possible to analyze 149 ICMEs propagating toward MSL both during its 8-month cruise phase and after its landing on Mars. We link 45 of the events observed at STEREO-HI to their corresponding FDs at MSL/RAD and study the accuracy of the ICME arrival time at Mars predicted from HI data using different methods. The mean differences between the predicted arrival times and those observed using FDs range from -11 to 5 hr for the different methods, with standard deviations between 17 and 20 hr. These values for predictions at Mars are very similar compared to other locations closer to the Sun and also comparable to the precision of some other modeling approaches.

This short note provides an overview of some theorems and conjectures obtained by the author and his collaborators. It is an extended abstract for the Oberwolfach workshop "New Trends in Teichm\"uller Theory and Mapping Class Groups", 2 September - 8 September 2018., Comment: 4 pages