Search

Let $\epsilon_{1},\ldots,\epsilon_{n}$ be a sequence of independent Rademacher random variables. We prove that there is a constant $c>0$ such that for any unit vectors $v_1,\ldots,v_n\in \mathbb{R}^2$, $$\Pr\left[||\epsilon_1 v_1+\ldots+\epsilon_n v_n||_2 \leq \sqrt{2}\right]\geq \frac{c}{n}.$$ This resolves the only remaining conjecture from the seminal paper of Erd\H{o}s on the Littlewood--Offord problem, and it is sharp both in the sense that the constant $\sqrt{2}$ cannot be reduced and that the magnitude $n^{-1}$ is best possible. We also prove polynomial bounds for the analogous problem in higher dimensions., Comment: 17 pages; corrected some errors in our open problems

The random Tur\'an number $\mathrm{ex}(G_{n,p}^r,F)$ is the maximum number of edges in an $F$-free subgraph of the random $r$-uniform hypergraph $G_{n,p}^r$. We prove general results which (informally) shows that if $F$ is an $r_0$-graph, then upper bounds for $\mathrm{ex}(G_{n,p}^{r_0},F)$ can be lifted into upper bounds for $\mathrm{ex}(G_{n,p}^{r},F^{(r)})$ where $F^{(r)}$ is the $r$-uniform expansion of $F$, i.e.\ the hypergraph obtained from $F$ by inserting $r-r_0$ distinct vertices into each edge of $F$. These results unify and generalize most known upper bounds for random Tur\'an numbers of degenerate hypergraphs of uniformity at least 3, and also provide new tight bounds for the random Tur\'an numbers of expansions of theta graphs and complete bipartite graphs., Comment: 23 pages+5 page appendix, comments welcome!

Understanding the spread of online rumors is a pressing societal challenge and an active area of research across domains. In the context of the 2022 U.S. midterm elections, one influential social media platform for sharing information -- including rumors that may be false, misleading, or unsubstantiated -- was Twitter (now renamed X). To increase understanding of the dynamics of online rumors about elections, we present and analyze a dataset of 1.81 million Twitter posts corresponding to 135 distinct rumors which spread online during the midterm election season (September 5 to December 1, 2022). We describe how this data was collected, compiled, and supplemented, and provide a series of exploratory analyses along with comparisons to a previously-published dataset on 2020 election rumors. We also conduct a mixed-methods analysis of three distinct rumors about the election in Arizona, a particularly prominent focus of 2022 election rumoring. Finally, we provide a set of potential future directions for how this dataset could be used to facilitate future research into online rumors, misinformation, and disinformation.

Magnetic reconnection is widely believed to be the fundamental process in the solar atmosphere that underlies magnetic energy release and particle acceleration. This process is responsible for the onset of solar flares, coronal mass ejections, and other explosive events (e.g., jets). Here, we report direct imaging of a prolonged plasma/current sheet along with quasiperiodic magnetic reconnection in the solar corona using ultra-high-resolution observations from the 1.6-meter Goode Solar Telescope (GST) at BBSO and Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA). The current sheet appeared near a null point in the fan-spine topology and persisted over an extended period (~20 hours). The length and apparent width of the current sheet were about 6 arcsec and 2 arcsec respectively, and the plasma temperature was ~10-20 MK. We observed quasiperiodic plasma inflows and outflows (bidirectional jets with plasmoids) at the reconnection site/current sheet. Furthermore, quasiperiodic reconnection at the long-lasting current sheet produced recurrent eruptions (small flares and jets) and contributed significantly to the recurrent impulsive heating of the active region. Direct imaging of a plasma/current sheet and recurrent null-point reconnection for such an extended period has not been reported previously. These unprecedented observations provide compelling evidence that supports the universal model for solar eruptions (i.e., the breakout model) and have implications for impulsive heating of active regions by recurrent reconnection near null points. The prolonged and sustained reconnection for about 20 hours at the breakout current sheet provides new insights into the dynamics and energy release processes in the solar corona., Comment: ApJ (in press), 23 pages, 12 figures

We develop a powerful tool for embedding any tree poset $P$ of height $k$ in the Boolean lattice which allows us to solve several open problems in the area. We show that: * If $\mathcal{F}$ is a family in $\mathcal{B}_n$ with $|\mathcal{F}|\ge (q-1+\varepsilon){n\choose \lfloor n/2\rfloor}$ for some $q\ge k$, then $\mathcal{F}$ contains on the order of as many induced copies of $P$ as is contained in the $q$ middle layers of the Boolean lattice. This generalizes results of Bukh and Boehnlein and Jiang which guaranteed a single such copy in non-induced and induced settings respectively. * The number of induced $P$-free families of $\mathcal{B}_n$ is $2^{(k-1+o(1)){n\choose \lfloor n/2\rfloor}}$, strengthening recent independent work of Balogh, Garcia, Wigal who obtained the same bounds in the non-induced setting. * The largest induced $P$-free subset of a $p$-random subset of $\mathcal{B}_n$ for $p\gg n^{-1}$ has size at most $(k-1+o(1))p{n\choose \lfloor n/2\rfloor}$, generalizing previous work of Balogh, Mycroft, and Treglown and of Collares and Morris for the case when $P$ is a chain. All three results are asymptotically tight and give affirmative answers to general conjectures of Gerbner, Nagy, Patk\'os, and Vizer in the case of tree posets., Comment: 37 pages; We significantly extend the previous version, which addressed supersaturation of tree posets, to also obtain tight enumeration results for tree poset free subsets of the Boolean lattice and tight upper bounds for the largest tree poset free subset of random subsets of the Boolean lattice

We classify the Ricci flat Lorentzian $n$-manifolds satisfying three particular conditions, encoding and combining some crucial features of the Kerr metrics and the Robinson-Trautman optical structures. We prove that: (a) If $n>4$, there is no Lorentzian manifold satisfying the considered Kerr type conditions, in unexpected contrast with what occurs for the metrics satisfying (very similar) Taub-NUT type conditions; (b) If $n=4$ there are two large classes of such Kerr type manifolds. Each class consists of manifolds fibering over open Riemann surfaces, equipped with a metric of constant Gaussian curvature $\kappa = 1$ or $\kappa = -1$. The first class includes a three parameter family of metrics admitting real analytic extensions to $(\mathbb R^3 \setminus\{0\}) \times \mathbb R = (S^2 \times \mathbb R_+) \times \mathbb R$ and a large class of other metrics not admitting this kind of extensions. The metrics of this first class admitting such extensions are all isometric to the well known Kerr metrics, with the three parameters corresponding to the three space-like components of the angular momentum of the gravitational field. The second class contains a subclass of metrics defined on $\big(\mathbb D\times \mathbb R_+\big)\times \mathbb R$, where $\mathbb D$ is the Lobachevsky Poincar\'e disc. This subclass is in bijection with the holomorphic functions on $\mathbb D$ satisfying an appropriate open condition. These and other results are consequences of a very simple way to construct totally explicit examples of Ricci flat Lorentzian manifolds., Comment: 47 pages; in v2, the only changes are in the Abstract and the Introduction, which are expanded and improved with additional references

Given a digraph $D$, we say that a set of vertices $Q\subseteq V(D)$ is a $q$-kernel if $Q$ is an independent set and if every vertex of $D$ can be reached from $Q$ by a path of length at most $q$. In this paper, we initiate the study of several extremal problems for $q$-kernels. For example, we introduce and make progress on (what turns out to be) a weak version of the Small Quasikernel Conjecture, namely that every digraph contains a $q$-kernel with $|N^+[Q]|\ge \frac{1}{2}|V(D)|$ for all $q\ge 2$., Comment: 30 pages + 5 page appendix. Strengthened Theorems 1.2 and 2.5, corrected Conjecture 7.6 and Question 7.7

The presence of political misinformation and ideological echo chambers on social media platforms is concerning given the important role that these sites play in the public's exposure to news and current events. Algorithmic systems employed on these platforms are presumed to play a role in these phenomena, but little is known about their mechanisms and effects. In this work, we conduct an algorithmic audit of Twitter's Who-To-Follow friend recommendation system, the first empirical audit that investigates the impact of this algorithm in-situ. We create automated Twitter accounts that initially follow left and right affiliated U.S. politicians during the 2022 U.S. midterm elections and then grow their information networks using the platform's recommender system. We pair the experiment with an observational study of Twitter users who already follow the same politicians. Broadly, we find that while following the recommendation algorithm leads accounts into dense and reciprocal neighborhoods that structurally resemble echo chambers, the recommender also results in less political homogeneity of a user's network compared to accounts growing their networks through social endorsement. Furthermore, accounts that exclusively followed users recommended by the algorithm had fewer opportunities to encounter content centered on false or misleading election narratives compared to choosing friends based on social endorsement., Comment: To be published in ACM Web Science Conference (Websci 24). 11 pages, 6 figures

The armed invasion of Ukraine by the Russian Federation has adversely affected the relations between Russia and Western countries. Among other aspects, it has put scientific cooperation and collaboration into question and changed the scientific landscape significantly. Cooperation between some Western institutions and their Russian and Belarusian partners were put on hold after February 24, 2022. The CERN Council decided at its meeting in December 2023 to terminate cooperation agreements with Russia and Belarus that date back a decade. CERN is an international institution with UN observer status, and has so far played a role in international cooperation which was independent of national political strategies. We argue that the Science4Peace idea still has a great value and scientific collaboration between scientists must continue, since fundamental science is by its nature an international discipline. A ban of scientists participating in international cooperation and collaboration is against the traditions, requirements and understanding of science. We call for measures to reactivate the peaceful cooperation of individual scientists on fundamental research in order to stimulate international cooperation for a more peaceful world in the future. Specifically, we plead for finding ways to continue this cooperation through international organizations, such as CERN and JINR.

We consider the existence of cohomogeneity one solitons for the isometric flow of $G_2$-structures on the following classes of torsion-free $G_2$-manifolds: the Euclidean $R^7$ with its standard $G_2$-structure, metric cylinders over Calabi-Yau 3-folds, metric cones over nearly K\"ahler 6-manifolds, and the Bryant-Salamon $G_2$-manifolds. In all cases we establish existence of global solutions to the isometric soliton equations, and determine the asymptotic behaviour of the torsion. In particular, existence of shrinking isometric solitons on $R^7$ is proved, giving support to the likely existence of type I singularities for the isometric flow. In each case, the study of the soliton equation reduces to a particular nonlinear ODE with a regular singular point, for which we provide a careful analysis. Finally, to simplify the derivation of the relevant equations in each case, we first establish several useful Riemannian geometric formulas for a general class of cohomogeneity one metrics on total spaces of vector bundles which should have much wider application, as such metrics arise often as explicit examples of special holonomy metrics., Comment: 31 pages; revised version contains minor changes in response to referee's reports; final version to be published in Geometriae Dedicata

In [C. Giannotti, A. Spiro, M. Zoppello, {\it Distributions and controllability problems (I)}, preprint posted on ArXiv (2024)], we introduced a new approach to the real analytic non-linear control systems of the form $\dot q^i = f^i(t, q, w)$, with controls $w = (w^\alpha)$ running in a connected open set $\mathcal{K}$ of $ \mathbb{R}^m$ and states represented by points $q = (q^i)$ in a configuration space $\mathcal{Q} := \mathbb{R}^n$. The new approach consists of a differential-geometric study of (a) the oriented piecewise regular curves in the {\it extended space-time} $\mathcal{M} = \mathbb{R} \times \mathcal{Q} \times \mathcal{K}$, which are the (completed) graphs of the piecewise real analytic solutions $t \mapsto (q(t), w(t))$ of the control system, and (b) the local structure of the sets of points of $\mathcal{M}$ that are reachable from an initial point $x_o = (t_o, q_o, w_o) \in \mathcal{M}$ through such (completed) graphs. The main results of that paper are two new criterions which can be used to establish the small time local controllability near stable points of real analytic non-linear systems. The goal of this paper is to offer a friendly user's guide to those criterions, illustrating them by several examples. In particular, we analyse certain non-linear control systems, for which the new criterions show that they are small time locally controllable at their stable points, while, at the best of our knowledge, all other previous criterions are either inconclusive or not applicable., Comment: 23 pages, 2 figures This paper is a revision of the previous manuscript, now we removed an unnecessary assumption, enhancing in this way all results, which now hold in a much more general setting

We give a new independent proof of a generalised version of the theorem by Rashevskii, which appeared in [Uch. Zapiski Ped. Inst. K. 2 (1938), 83 -- 94] and from which the classical Chow-Rashevskii Theorem follows as a corollary. The proof is structured to allow generalisations to the case of orbits of compositions of flows in absence of group structures, thus appropriate for applications in Control Theory. In fact, the same structure of the proof has been successfully exploited in [C. Giannotti, A. Spiro and M. Zoppello, arXiv 2401.07555 \& 2401.07560 (2024)] to determine new controllability criteria for real analytic non-linear control systems. It also yields a corollary, which can be used to derive results under lower regularity assumptions, as it is illustrated by a simple explicit example., Comment: 20 pages. In the new version there are minor corrections and we added an explicit example of application of our theorem. To appear on "Hokkaido Math. J."

We study how many copies of a graph $F$ that another graph $G$ with a given number of cliques is guaranteed to have. For example, one of our main results states that for all $t\ge 2$, if $G$ is an $n$ vertex graph with $kn^{3/2}$ triangles and $k$ is sufficiently large in terms of $t$, then $G$ contains at least \[\Omega(\min\{k^t n^{3/2},k^{\frac{2t^2}{3t-1}}n^{\frac{5t-2}{3t-1}}\})\] copies of $K_{2,t}$, and furthermore, we show these bounds are essentially best-possible provided either $k\ge n^{1/2t}$ or if certain bipartite-analogues of well known conjectures for Tur\'an numbers hold., Comment: 21 pages

Syndrome decoding is an integral but computationally demanding step in the implementation of quantum error correction for fault-tolerant quantum computing. Here, we report the development and benchmarking of Artificial Neural Network (ANN) decoding on IBM Quantum Processors. We demonstrate that ANNs can efficiently decode syndrome measurement data from heavy-hexagonal code architecture and apply appropriate corrections to facilitate error protection. The current physical error rates of IBM devices are above the code's threshold and restrict the scope of our ANN decoder for logical error rate suppression. However, our work confirms the applicability of ANN decoding methods of syndrome data retrieved from experimental devices and establishes machine learning as a promising pathway for quantum error correction when quantum devices with below threshold error rates become available in the near future., Comment: 7 pages, 3 figures

We consider two special classes of $k$-harmonic maps between Riemannian manifolds which are related to calibrated geometry, satisfying a first order fully nonlinear PDE. The first is a special type of weakly conformal map $u \colon (L^k, g) \to (M^n, h)$ where $k \leq n$ and $\alpha$ is a calibration $k$-form on $M$. Away from the critical set, the image is an $\alpha$-calibrated submanifold of $M$. These were previously studied by Cheng-Karigiannis-Madnick when $\alpha$ was associated to a vector cross product, but we clarify that such a restriction is unnecessary. The second, which is new, is a special type of weakly horizontally conformal map $u \colon (M^n, h) \to (L^k, g)$ where $n \geq k$ and $\alpha$ is a calibration $(n-k)$-form on $M$. Away from the critical set, the fibres $u^{-1} \{ u(x) \}$ are $\alpha$-calibrated submanifolds of $M$. We also review some previously established analytic results for the first class; we exhibit some explicit noncompact examples of the second class, where $(M, h)$ are the Bryant-Salamon manifolds with exceptional holonomy; we remark on the relevance of this new PDE to the Strominger-Yau-Zaslow conjecture for mirror symmetry in terms of special Lagrangian fibrations and to the $\mathrm{G}_2$ version by Gukov-Yau-Zaslow in terms of coassociative fibrations; and we present several open questions for future study., Comment: 25 pages, no figures. Version 2: Various minor improvements based on referee's report, including strengthening results showing that the two formulations of the Smith immersion/submersion equations, in terms of calibration forms or in terms of cross products, are always equivalent. Final version, to appear in Mathematical Research Letters

We continue the investigation of general geometric flows of $G_2$-structures initiated by the third author in "Flows of $G_2$-structures, I." Specifically, we determine the possible geometric flows (up to lower order terms) of $G_2$-structures which are second order quasilinear, by explicitly computing all independent second order differential invariants of $G_2$-structures which are $3$-forms. There are four symmetric $2$-tensors and two vector fields. We do this by deriving explicit computational descriptions of the decompositions of the curvature and the covariant derivative of the torsion into irreducible $G_2$-representations, as well as the decomposition of the $G_2$-Bianchi identity into independent relations. We also show that these six tensors arise as leading order contributions to the Euler-Lagrange equations for the energy functionals of the four independent torsion components, and we establish a $G_2$-analogue of the classical block decomposition of the Riemann curvature operator on oriented $4$-dimensional Riemannian manifolds. Finally, we present a large class of geometric flows of $G_2$-structures which are directly amenable to a deTurck type trick to establish short-time existence and uniqueness, with no initial assumption on the torsion, vastly generalizing an earlier result of Weiss-Witt for the negative gradient flow of the Dirichlet energy. This result is proved through a careful analysis of the principal symbols of the linearizations of these operators, establishing particular linear combinations for which one can prove that the failure of strict parabolicity is due precisely to the diffeomorphism invariance. A detailed introductory section on various foundational results of $G_2$-structure, several of which are not readily available in the literature, should be of wider interest and applicability., Comment: 101 pages, no figures. Comments welcome

While sanctions in political and economic areas are now part of the standard repertoire of Western countries (not always endorsed by UN mandates), sanctions in science and culture in general are new. Historically, fundamental research as conducted at international research centers such as CERN has long been seen as a driver for peace, and the Science4Peace idea has been celebrated for decades. However, much changed with the war against Ukraine, and most Western science organizations put scientific cooperation with Russia and Belarus on hold immediately after the start of the war in 2022. In addition, common publications and participation in conferences were banned by some institutions, going against the ideal of free scientific exchange and communication. These and other points were the topics of an international virtual panel discussion organized by the Science4Peace Forum together with the "Natural Scientists Initiative - Responsibility for Peace and Sustainability" (NatWiss e.V.) in Germany and the journal "Wissenschaft und Frieden" (W&F) (see the Figure). Fellows from the Hamburg Institute for Peace Research and Security Policy (IFSH), scientists collaborating with the large physics research institutes DESY and CERN, as well as from climate and futures researchers were represented on the panel. In this Dossier we document the panel discussion, and give additional perspectives. The authors of the individual sections present their personal reflections, which should not be taken as implying that they are endorsed by the Science4Peace Forum or any other organizations. It is regrettable that some colleagues who expressed support for this document felt that it would be unwise for them to co-sign it., Comment: Writeup based on a Panel discussion organized by the Science4Peace Forum (https://science4peace.com/Public-Events/Entries/2023/4/sanctions-in-science---one-year-of-sanctions-a-virtual-panel-discussion.html) on Sanctions in Science in April 2023

With quantum devices rapidly approaching qualities and scales needed for fault tolerance, the validity of simplified error models underpinning the study of quantum error correction needs to be experimentally evaluated. In this work, we have assessed the performance of IBM superconducting quantum computer devices implementing heavy-hexagon code syndrome measurements with increasing circuit sizes up to 23 qubits, against the error assumptions underpinning code threshold calculations. Circuit operator change rate statistics in the presence of depolarizing and biased noise were modelled using analytic functions of error model parameters. Data from 16 repeated syndrome measurement cycles was found to be inconsistent with a uniform depolarizing noise model, favouring instead biased and inhomogeneous noise models. Spatial-temporal correlations investigated via $Z$ stabilizer measurements revealed significant temporal correlation in detection events. These results highlight the non-trivial structure which may be present in the noise of quantum error correction circuits, revealed by operator measurement statistics, and support the development of noise-tailored codes and decoders to adapt.

We explicitly derive the Christoffel symbols in terms of adapted frame fields for the Levi-Civita connection of a Lorentzian $n$-manifold $(M, g)$, equipped with a prescribed optical geometry of K\"ahler-Sasaki type. The formulas found in this paper have several important applications, such as determining the geometric invariants of Lorentzian manifolds with prescribed optical geometries or solving curvature constraints.

In the complex world of educational policy, causal inferences will be debated. As we review non-experimental designs in educational policy, we focus on how to clarify and focus the terms of debate. We begin by presenting the potential outcomes/counterfactual framework and then describe approximations to the counterfactual generated from the general linear model, regression discontinuity designs, the propensity to be treated, and instrumental variables. Noting the advantages and limitations of each method, we turn to literature showing that conventional linear models, which can be extended to fixed and random effects models and difference-in-differences designs, are particularly useful when covariates include pre-tests. Recognizing that no technique fully resolves concerns about inferences, we quantify the conditions necessary to invalidate an inference. We review additional considerations including accounting for context, heterogeneous treatment effects, and mediation. Throughout we focus on the role of the researcher in making analytic choices, accentuated in the Quantcrit framework. [This chapter will be published in: "Handbook on Education Policy Research," edited by L. Cohen-Vogel et al., American Educational Research Association.]

Let $\mathrm{ex}(G_{n,p}^r,F)$ denote the maximum number of edges in an $F$-free subgraph of the random $r$-uniform hypergraph $G_{n,p}^r$. Building on recent work of Conlon, Lee, and Sidorenko, we prove non-trivial lower bounds on $\mathrm{ex}(G_{n,p}^r,F)$ whenever $F$ is not Sidorenko. This connection between Sidorenko's conjecture and random Tur\'an problems gives new lower bounds on $\mathrm{ex}(G_{n,p}^r,F)$ whenever $F$ is not Sidorenko, and further allows us to bound how "far" from Sidorenko an $r$-graph $F$ is whenever upper bounds for $\mathrm{ex}(G_{n,p}^r,F)$ are known., Comment: 13 pages (+1 page Appendix), 1 figure

Given an $n$-vertex digraph $D$ and a labeling $\sigma:V(D)\to [n]$, we say that an arc $u\to v$ of $D$ is a descent of $\sigma$ if $\sigma(u)>\sigma(v)$. Foata and Zeilberger introduced a generating function $A_D(t)$ for labelings of $D$ weighted by descents, which simultaneously generalizes both Eulerian polynomials and Mahonian polynomials. Motivated by work of Kalai, we look at problems related to $-1$ evaluations of $A_D(t)$. In particular, we give a combinatorial interpretation of $|A_D(-1)|$ in terms of "generalized alternating permutations" whenever the underlying graph of $D$ is bipartite.

Given a calibration $\alpha$ whose stabilizer acts transitively on the Grassmanian of calibrated planes, we introduce a nontrivial Lie-theoretic condition on $\alpha$, which we call compliancy, and show that this condition holds for many interesting geometric calibrations, including K\"ahler, special Lagrangian, associative, coassociative, and Cayley. We determine a sufficient condition that ensures compliancy of $\alpha$, we completely characterize compliancy in terms of properties of a natural involution determined by a calibrated plane, and we relate compliancy to the geometry of the calibrated Grassmanian. The condition that a Riemannian immersion $\iota \colon L \to M$ be calibrated is a first order condition. By contrast, its extrinsic geometry, given by the second fundamental form $A$ and the induced tangent and normal connections $\nabla$ on $TL$ and $D$ on $NL$, respectively, is second order information. We characterize the conditions imposed on the extrinsic geometric data $(A, \nabla, D)$ when the Riemannian immersion $\iota \colon L \to M$ is calibrated with respect to a calibration $\alpha$ on $M$ which is both parallel and compliant. This motivate the definition of an infinitesimally calibrated Riemannian immersion, generalizing the classical notion of a superminimal surface in $\mathbb R^4$., Comment: 24 pages, 1 table, no figures. Version 2: minor typos corrected and remark added. Final version to appear in Mathematische Zeitschrift

We systematically study calibrated geometry in hyperk\"ahler cones $C^{4n+4}$, their 3-Sasakian links $M^{4n+3}$, and the corresponding twistor spaces $Z^{4n+2}$, emphasizing the relationships between submanifold geometries in various spaces. Our analysis emphasizes the role played by a canonical $\mathrm{Sp}(n)\mathrm{U}(1)$-structure $\gamma$ on the twistor space $Z$. We observe that $\mathrm{Re}(e^{- i \theta} \gamma)$ is an $S^1$-family of semi-calibrations, and make a detailed study of their associated calibrated geometries. As an application, we obtain new characterizations of complex Lagrangian and complex isotropic cones in hyperk\"{a}hler cones, generalizing a result of Ejiri and Tsukada. We also generalize a theorem of Storm on submanifolds of twistor spaces that are Lagrangian with respect to both the K\"{a}hler-Einstein and nearly-K\"{a}hler structures., Comment: 55 pages, 1 figure. Version 3: Minor revisions and clarifications following referee's report. Final version, to appear in Canadian Journal of Mathematics

Understanding the nature of energetic particles in the solar atmosphere is one of the most important outstanding problems in heliophysics. Flare-accelerated particles compose a huge fraction of the flare energy budget; they have large influences on how events develop; they are an important source of high-energy particles found in the heliosphere; and they are the single most important corollary to other areas of high-energy astrophysics. Despite the importance of this area of study, this topic has in the past decade received only a small fraction of the resources necessary for a full investigation. For example, NASA has selected no new Explorer-class instrument in the past two decades that is capable of examining this topic. The advances that are currently being made in understanding flare-accelerated electrons are largely undertaken with data from EOVSA (NSF), STIX (ESA), and NuSTAR (NASA Astrophysics). This is despite the inclusion in the previous Heliophysics decadal survey of the FOXSI concept as part of the SEE2020 mission, and also despite NASA's having invested heavily in readying the technology for such an instrument via four flights of the FOXSI sounding rocket experiment. Due to that investment, the instrumentation stands ready to implement a hard X-ray mission to investigate flare-accelerated electrons. This white paper describes the scientific motivation for why this venture should be undertaken soon., Comment: White paper submitted to the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033; 15 pages, 5 figures

Given a graph $F$, we define $\operatorname{ex}(G_{n,p},F)$ to be the maximum number of edges in an $F$-free subgraph of the random graph $G_{n,p}$. Very little is known about $\operatorname{ex}(G_{n,p},F)$ when $F$ is bipartite, with essentially tight bounds known only when $F$ is either $C_4, C_6, C_{10}$, or $K_{s,t}$ with $t$ sufficiently large in terms of $s$, due to work of F\"uredi and of Morris and Saxton. We extend this work by establishing essentially tight bounds when $F$ is a theta graph with sufficiently many paths. Our main innovation is in proving a balanced supersaturation result for vertices, which differs from the standard approach of proving balanced supersaturation for edges.

Microstreams are fluctuations in the solar wind speed and density associated with polarity-reversing folds in the magnetic field (also denoted switchbacks). Despite their long heritage, the origin of these microstreams/switchbacks remains poorly understood. For the first time, we investigated periodicities in microstreams during Parker Solar Probe (PSP) Encounter 10 to understand their origin. Our analysis was focused on the inbound corotation interval on 2021 November 19-21, while the spacecraft dove toward a small area within a coronal hole (CH). Solar Dynamics Observatory remote-sensing observations provide rich context for understanding the PSP in-situ data. Extreme ultraviolet images from the Atmospheric Imaging Assembly reveal numerous recurrent jets occurring within the region that was magnetically connected to PSP during intervals that contained microstreams. The periods derived from the fluctuating radial velocities in the microstreams (approximately 3, 5, 10, and 20 minutes) are consistent with the periods measured in the emission intensity of the jetlets at the base of the CH plumes, as well as in larger coronal jets and in the plume fine structures. Helioseismic and Magnetic Imager magnetograms reveal the presence of myriad embedded bipoles, which are known sources of reconnection-driven jets on all scales. Simultaneous enhancements in the PSP proton flux and ionic ($^3$He, $^4$He, Fe, O) composition during the microstreams further support the connection with jetlets and jets. In keeping with prior observational and numerical studies of impulsive coronal activity, we conclude that quasiperiodic jets generated by interchange/breakout reconnection at CH bright points and plume bases are the most likely sources of the microstreams/switchbacks observed in the solar wind., Comment: ApJ Letters, 19 pages, 12 figures

We consider a geometric percolation process partially motivated by recent work of Hejda and Kala. Specifically, we start with an initial set $X \subseteq \mathbb{Z}^2$, and then iteratively check whether there exists a triangle $T \subseteq \mathbb{R}^2$ with its vertices in $\mathbb{Z}^2$ such that $T$ contains exactly four points of $\mathbb{Z}^2$ and exactly three points of $X$. In this case, we add the missing lattice point of $T$ to $X$, and we repeat until no such triangle exists. We study the limit sets $S$, the sets stable under this process, including determining their possible densities and some of their structure., Comment: 33 pages, 27 figures (including appendix)

The 2020 United States presidential election was, and has continued to be, the focus of pervasive and persistent mis- and disinformation spreading through our media ecosystems, including social media. This event has driven the collection and analysis of large, directed social network datasets, but such datasets can resist intuitive understanding. In such large datasets, the overwhelming number of nodes and edges present in typical representations create visual artifacts, such as densely overlapping edges and tightly-packed formations of low-degree nodes, which obscure many features of more practical interest. We apply a method, coengagement transformations, to convert such networks of social data into tractable images. Intuitively, this approach allows for parameterized network visualizations that make shared audiences of engaged viewers salient to viewers. Using the interpretative capabilities of this method, we perform an extensive case study of the 2020 United States presidential election on Twitter, contributing an empirical analysis of coengagement. By creating and contrasting different networks at different parameter sets, we define and characterize several structures in this discourse network, including bridging accounts, satellite audiences, and followback communities. We discuss the importance and implications of these empirical network features in this context. In addition, we release open-source code for creating coengagement networks from Twitter and other structured interaction data., Comment: Accepted for publication at ICWSM '23

By Vinberg theory any homogeneous convex cone $\mathcal V$ may be realized as the cone of positive Hermitian matrices in a $T$-algebra of generalised matrices. The level hypersurfaces $\mathcal V_{q} \subset \mathcal V$ of homogeneous cubic polynomials $q$ with positive definite Hessian (symmetric) form $g_q := - \operatorname{Hess}(\log(q))|_{T \mathcal V_q}$ are the {\it special real manifolds}. Such manifolds occur as scalar manifolds of the vector multiplets in $N=2$, $D=5$ supergravity and, through the $r$-map, correspond to K\"ahler scalar manifolds in $N = 2$ $D = 4$ supergravity. We offer a simplified exposition of the Vinberg theory in terms of $\operatorname{Nil}$-algebras (= the subalgebras of upper triangular matrices in Vinberg $T$-algebras) and we use it to describe all rational functions on a special Vinberg cone that are $G_0$- or $G'$- invariant, where $G_0$ is the unimodular subgroup of the solvable group $G$ acting simply transitively on the cone, and $G'$ is the unipotent radical of $G_0$. The results are used to determine $G_0$- and $G'$-invariant cubic polynomials $q$ that are {\it admissible} (i.e. such that the hypersurface $ \mathcal V_q=\{ q=1\}\cap \mathcal V $ has positive definite Hessian form $g_q$) for rank $2$ and rank $3$ special Vinberg cones. We get in this way examples of continuous families of non-homogeneous special real manifolds of cohomogeneity less than or equal to two., Comment: 22 pages; v2 - a few changes in sect. 4.2, 4.3 and 5.3; all main results are unchanged; to appear in an AMS Contemporary Mathematics volume in honor of Alexandre Vinogradov

We report a detailed analysis of a failed eruption and flare in active region 12018 on 2014 April 3 using multiwavelength observations from SDO/AIA, IRIS, STEREO, and Hinode/SOT. At least four jets were observed to emanate from the cusp of this small active region (large bright point) with a null-point topology during the two hours prior to the slow rise of a filament. During the filament slow rise multiple plasma blobs were seen, most likely formed in a null-point current sheet near the cusp. The subsequent filament eruption, which was outside the IRIS field of view, was accompanied by a flare but remained confined. During the explosive flare reconnection phase, additional blobs appeared repetitively and moved bidirectionally within the flaring region below the erupting filament. The filament kinked, rotated, and underwent leg-leg reconnection as it rose, yet it failed to produce a coronal mass ejection. Tiny jet-like features in the fan loops were detected during the filament slow-rise/pre-flare phase. We interpret them as signatures of reconnection between the ambient magnetic field and the plasmoids leaving the null-point sheet and streaming along the fan loops. We contrast our interpretation of these tiny jets, which occur within the large-scale context of a failed filament eruption, with the local nanoflare-heating scenario proposed by Antolin et al. (2021)., Comment: ApJ, 17 pages, 11 figures