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We propose a unifying setting for dealing with monodromically atypical intersections that goes beyond the usual Zilber-Pink conjecture. In particular we obtain a new proof of finiteness of the maximal atypical orbit closures in each stratum of translation surfaces $\Omega \mathcal{M}_g (\kappa)$, as given by Eskin, Filip, and Wright. We also describe a concrete algorithm, implementable in principle on a computer, which provably computes all maximal orbit closures which are 'atypical' in a sense described by Filip. The same methods also give a general algorithm for computing atypical special loci associated to systems of differential equations, and in particular give an effective and o-minimal free proof of the geometric Zilber-Pink conjecture variations of mixed Hodge structures.

As evidenced by recent survey results, majority of asteroids are slow rotators (P>12 h), but lack spin and shape models due to selection bias. This bias is skewing our overall understanding of the spins, shapes, and sizes of asteroids, as well as of their other properties. Also, diameter determinations for large (>60km) and medium-sized asteroids (between 30 and 60 km) often vary by over 30% for multiple reasons. Our long-term project is focused on a few tens of slow rotators with periods of up to 60 hours. We aim to obtain their full light curves and reconstruct their spins and shapes. We also precisely scale the models, typically with an accuracy of a few percent. We used wide sets of dense light curves for spin and shape reconstructions via light-curve inversion. Precisely scaling them with thermal data was not possible here because of poor infrared data: large bodies are too bright for WISE mission. Therefore, we recently launched a campaign among stellar occultation observers, to scale these models and to verify the shape solutions, often allowing us to break the mirror pole ambiguity. The presented scheme resulted in shape models for 16 slow rotators, most of them for the first time. Fitting them to stellar occultations resolved previous inconsistencies in size determinations. For around half of the targets, this fitting also allowed us to identify a clearly preferred pole solution, thus removing the ambiguity inherent to light-curve inversion. We also address the influence of the uncertainty of the shape models on the derived diameters. Overall, our project has already provided reliable models for around 50 slow rotators. Such well-determined and scaled asteroid shapes will, e.g. constitute a solid basis for density determinations when coupled with mass information. Spin and shape models continue to fill the gaps caused by various biases., Comment: Accepted to Astronomy & Astrophysics. 12 pages + appendices

We introduce a new method to study mixed characteristic deformation of line bundles. In particular, for sufficiently large smooth projective families $f : \mathcal{X} \to \mathcal{S}$ defined over the ring of $N$-integers $\mathcal{O}_{L}[1/N]$ of a number field $L$, we produce a proper closed subscheme $\mathcal{E} \subsetneq \mathcal{S}$ outside of which all line bundles appearing in positive characteristic fibres of $f$ admit characteristic zero lifts. This in particular applies to elliptic surfaces over $\mathbb{P}^1$ and projective hypersurfaces in $\mathbb{P}^3$ of degree $d \geq 5$. We also study the locus in $\mathcal{E}$ in more detail in the $h^{0, 2} = 2$ case., Comment: 31 pages

This work aims at constraining the size, shape, and geometric albedo of the dwarf planet candidate 2002 MS4 through the analysis of nine stellar occultation events. Using multichord detection, we also studied the object's topography by analyzing the obtained limb and the residuals between observed chords and the best-fitted ellipse. We predicted and organized the observational campaigns of nine stellar occultations by 2002 MS4 between 2019 and 2022, resulting in two single-chord events, four double-chord detections, and three events with three to up to sixty-one positive chords. Using 13 selected chords from the 8 August 2020 event, we determined the global elliptical limb of 2002 MS4. The best-fitted ellipse, combined with the object's rotational information from the literature, constrains the object's size, shape, and albedo. Additionally, we developed a new method to characterize topography features on the object's limb. The global limb has a semi-major axis of 412 $\pm$ 10 km, a semi-minor axis of 385 $\pm$ 17 km, and the position angle of the minor axis is 121 $^\circ$ $\pm$ 16$^\circ$. From this instantaneous limb, we obtained 2002 MS4's geometric albedo and the projected area-equivalent diameter. Significant deviations from the fitted ellipse in the northernmost limb are detected from multiple sites highlighting three distinct topographic features: one 11 km depth depression followed by a 25$^{+4}_{-5}$ km height elevation next to a crater-like depression with an extension of 322 $\pm$ 39 km and 45.1 $\pm$ 1.5 km deep. Our results present an object that is $\approx$138 km smaller in diameter than derived from thermal data, possibly indicating the presence of a so-far unknown satellite. However, within the error bars, the geometric albedo in the V-band agrees with the results published in the literature, even with the radiometric-derived albedo.

Motivated by a question of Baldi-Klingler-Ullmo, we provide a general sufficient criterion for the existence and analytic density of typical Hodge loci associated to a polarizable $\mathbb{Z}$-variation of Hodge structures $\mathbb{V}$. Our criterion reproves the existing results in the literature on density of Noether-Lefschetz loci. It also applies to understand Hodge loci of subvarieties of $\mathcal{A}_g$ . For instance, we prove that for $g \geq 4$, if a subvariety $S$ of $\mathcal{A}_g$ has dimension at least $g$ then it has an analytically dense typical Hodge locus. This applies for example to the Torelli locus of $\mathcal{A}_g$

High-throughput screening techniques are commonly used to obtain large quantities of data in many fields of biology. It is well known that artifacts arising from variability in the technical execution of different experimental batches within such screens confound these observations and can lead to invalid biological conclusions. It is therefore necessary to account for these batch effects when analyzing outcomes. In this paper we describe RxRx1, a biological dataset designed specifically for the systematic study of batch effect correction methods. The dataset consists of 125,510 high-resolution fluorescence microscopy images of human cells under 1,138 genetic perturbations in 51 experimental batches across 4 cell types. Visual inspection of the images alone clearly demonstrates significant batch effects. We propose a classification task designed to evaluate the effectiveness of experimental batch correction methods on these images and examine the performance of a number of correction methods on this task. Our goal in releasing RxRx1 is to encourage the development of effective experimental batch correction methods that generalize well to unseen experimental batches. The dataset can be downloaded at https://rxrx.ai.

We describe a general method for giving $p$-adic interpretations of $G$-functions arising from degenerating periods of smooth projective algebraic varieties. Using this, we are able to implement a strategy due to Andr\'e for bounding heights of moduli points where period functions acquire unusual algebraic relations. This leads to new results on Galois lower bounds for special moduli, and new cases of the Zilber-Pink conjecture. In particular, we establish the first Galois-orbit lower bounds on CM moduli in non-Shimura settings. As a more technical contribution, we introduce a refinement of the Pila-Zannier strategy capable of handling Zilber-Pink-type atypical intersection problems in arbitrary dimension and for arbitrary smooth projective families., Comment: v2: Updated and streamlined introduction, giving a clearer explanation of proof strategy and ideas. Significant updates to section 7.2, including a discussion on Hodge-theoretic Siegel sets, orbits of Siegel sets on Hodge-theoretic idempotents, and a height theorem for such orbits. The last of these replaces a mistaken Siegel-set argument in the previous version. Other smaller changes/fixes

Let $\mathcal{A}_{g}$ be the moduli space of $g$-dimensional principally polarized abelian varieties over $\mathbb{Z}$, and let $\mathcal{T} \subset \mathcal{A}_{g}$ be a closed locus, also defined over $\mathbb{Z}$. Motivated by unlikely intersection conjectures, we study the intersection of $\mathcal{T}_{\mathbb{F}_{p}}$ with the Bruhat strata in $\mathcal{A}_{g,\mathbb{F}_{p}}$ as $p$-varies; these are strata characterized by the existence of certain subgroup schemes inside the $p$-torsion of the fibres. We find that, away from a finite set of primes, positive-dimensional ``unlikely'' intersections of $\mathcal{T}_{\mathbb{F}_{p}}$ with such strata are all accounted for by intersections of $\mathcal{T}$ with special loci inside $\mathcal{A}_{g}$. This result generalizes to all abelian-type Shimura varieties, and variations of Hodge structures equipped with certain motivic data. It moreover gives another example of how functional transcendence principles in characteristic zero can be used to study unlikely intersections in positive characteristic, building on recent work by the author.

In several spiral galaxies that are observed face-on, large-scale ordered magnetic fields (the so-called magnetic arms) were found. One of the explanations was the action of the magnetic reconnection, which leads to a higher ordering of the magnetic fields. Because it simultaneously converts the energy of the magnetic fields into thermal energy of the surroundings, magnetic reconnection has been considered as a heating mechanism of the interstellar medium for many years. Until recently, no clear observational evidence for this phenomenon was found. We search for possible signatures of gas heating by magnetic reconnection effects in the radio and X-ray data for the face-on spiral galaxy NGC628 (M74), which presents pronounced magnetic arms and evidence for vertical magnetic fields. The strengths and energy densities of the magnetic field in the spiral and magnetic arms were derived, as were the temperatures and thermal energy densities of the hot gas, for the disk and halo emission. In the regions of magnetic arms, higher order and lower energy density of the magnetic field is found than in the stellar spiral arms. The global temperature of the hot gas is roughly constant throughout the disk. The comparison of the findings with those obtained for the starburst galaxy M83 suggests that magnetic reconnection heating may be present in the halo of NGC628. The joint analysis of the properties of the magnetic fields and the hot gas in NGC628 also provided clues for possible tidal interaction with the companion galaxy., Comment: 13 pages, 10 figures, 9 tables. Accepted for publication in A&A

Let $f : X \to S$ be a smooth projective family defined over $\mathcal{O}_{K}[\mathcal{S}^{-1}]$, where $K \subset \mathbb{C}$ is a number field and $\mathcal{S}$ is a finite set of primes. For each prime $\mathfrak{p} \in \mathcal{O}_{K}[\mathcal{S}^{-1}]$ with residue field $\kappa(\mathfrak{p})$, we consider the algebraic loci in $S_{\overline{\kappa(\mathfrak{p})}}$ above which cohomological cycle conjectures predict the existence of non-trivial families of algebraic cycles, generalizing the Hodge loci of the generic fibre $S_{\overline{K}}$. We develop a technique for studying all such loci, together, at the integral level. As a consequence we give a non-Zariski density criterion for the union of non-trivial ordinary algebraic cycle loci in $S$. The criterion is quite general, depending only on the level of the Hodge flag in a fixed cohomological degree $w$ and the Zariski density of the associated geometric monodromy representation., Comment: v2: Updated to thesis version + minor clarifications

Studies of nearby spiral galaxies in radio and X-ray wavelengths reveal the structure and energy balance of the magnetic fields and the hot interstellar medium (ISM). In some spiral galaxies, large-scale ordered magnetic fields have been found between the spiral stellar arms (the so-called magnetic arms). One of the considered explanations of their origin is magnetic reconnection, which according to theoretical studies can efficiently heat the low-density ISM. We present, for the first time, high-resolution C-band (5GHz) radio maps of the nearby face-on spiral galaxy M101 to study the magnetic fields and verify the existence of the magnetic arms. The analysis of the archival XMM-Newton X-ray data is performed to search for signatures of gas heating by magnetic reconnection effects in the disk and the halo of this galaxy. We combine the Very Large Array (VLA) and Effelsberg radio maps of M101 to restore the large-scale emission lost in the interferometric observations. From the obtained maps, we derive magnetic field strengths and energy densities, and compare them with the properties of the hot gas found with the spectral analysis of the X-ray data. Most of the X-ray emission likely comes from the hot gas in the halo of M101. Its temperature is highest above the massive stellar arm and an inter-arm region with enhanced polarised radio emission, as well as in the inter-arm area where neither Halpha nor HI emission is visible. In regions outside of the spiral arms lower strengths, energy densities and higher orders of the magnetic fields were observed. Although M101 does not possess well-defined magnetic arms, a rudimentary magnetic arm was identified in one of the inter-arm regions. We found weak signatures of additional heating of the ISM there, as well as in the galactic halo, which could be explained by the action of magnetic reconnection., Comment: 16 pages, 10 figures, 11 tables. Accepted to A&A

From air-sea gas exchange, oil pollution, to bioreactors, the ubiquitous fragmentation of bubbles/drops in turbulence has been modelled by relying on the classical Kolmogorov-Hinze paradigm since the 1950s. This framework hypothesizes that bubbles/drops are broken solely by eddies of the same size, even though turbulence is well known for its wide spectrum of scales. Here, by designing an experiment that can physically and cleanly disentangle eddies of various sizes, we report the experimental evidence to challenge this hypothesis and show bubbles are preferentially broken by the sub-bubble-scale eddies. Our work also highlights that fragmentation cannot be quantified solely by the stress criterion or the Weber number; The competition between different time scales is equally important. Instead of being elongated slowly and persistently by flows at their own scales, bubbles are fragmented in turbulence by small eddies via a burst of intense local deformation within a short time.

Let $K \subset \mathbb{C}$ be a number field, and let $\mathcal{O}_{K,N} = \mathcal{O}_{K}[N^{-1}]$ be its ring of $N$-integers. Recently, Lawrence and Venkatesh proposed a general strategy for proving the Shafarevich conjecture for the fibres of a smooth projective family $f : X \to S$ defined over $\mathcal{O}_{K,N}$. To carry out their strategy, one needs to be able to decide whether the algebraic monodromy group $\mathbf{H}_{Z}$ of any positive-dimensional geometrically irreducible subvariety $Z \subset S_{\mathbb{C}}$ is "large enough", in the sense that a certain orbit of $\mathbf{H}_{Z}$ in a variety of Hodge flags has dimension bounded from below by a certain quantity. In this article we give an effective method for deciding this question. Combined with the effective methods of Lawrence-Venkatesh for understanding semisimplifications of global Galois representations using $p$-adic Hodge theory, this gives a fully effective strategy for solving Shafarevich-type problems for arbitrary families $f$., Comment: Preliminary version. The author plans an extended version of this article with explicit computations to appear sometime next year

Let $f : X \to S$ be a family of smooth projective algebraic varieties over a smooth connected quasi-projective base $S$, and let $\mathbb{V} = R^{2k} f_{*} \mathbb{Z}(k)$ be the integral variation of Hodge structure coming from degree $2k$ cohomology it induces. Associated to $\mathbb{V}$ one has the so-called Hodge locus $\textrm{HL}(S) \subset S$, which is a countable union of "special" algebraic subvarieties of $S$ parametrizing those fibres of $\mathbb{V}$ possessing extra Hodge tensors (and so conjecturally, those fibres of $f$ possessing extra algebraic cycles). The special subvarieties belong to a larger class of so-called weakly special subvarieties, which are subvarieties of $S$ maximal for their algebraic monodromy groups. For each positive integer $d$, we give an algorithm to compute the set of all weakly special subvarieties $Z \subset S$ of degree at most $d$ (with the degree taken relative to a choice of projective compactification $S \subset \overline{S}$ and very ample line bundle $\mathcal{L}$ on $\overline{S}$). As a corollary of our algorithm we prove conjectures of Daw-Ren and Daw-Javanpeykar-K\"uhne on the finiteness of sets of special and weakly special subvarieties of bounded degree.

Let $f : X \to S$ be a family of smooth projective algebraic varieties over a smooth connected base $S$, with everything defined over $\overline{\mathbb{Q}}$. Denote by $\mathbb{V} = R^{2i} f_{*} \mathbb{Z}(i)$ the associated integral variation of Hodge structure on the degree $2i$ cohomology. We consider the following question: when can a fibre $\mathbb{V}_{s}$ above an algebraic point $s \in S(\overline{\mathbb{Q}})$ be isomorphic to a transcendental fibre $\mathbb{V}_{s'}$ with $s' \in S(\mathbb{C}) \setminus S(\overline{\mathbb{Q}})$? When $\mathbb{V}$ induces a quasi-finite period map $\varphi : S \to \Gamma \backslash D$, conjectures in Hodge theory predict that such isomorphisms cannot exist. We introduce new differential-algebraic techniques to show this is true for all points $s \in S(\overline{\mathbb{Q}})$ outside of an explicit proper closed algebraic subset of $S$. As a corollary we establish the existence of a canonical $\overline{\mathbb{Q}}$-algebraic model for normalizations of period images., Comment: Comments welcome!

Let $\mathbb{V}$ be a motivic variation of Hodge structure on a $K$-variety $S$, let $\mathcal{H}$ be the associated $K$-algebraic Hodge bundle, and let $\sigma \in \textrm{Aut}(\mathbb{C}/K)$ be an automorphism. The absolute Hodge conjecture predicts that given a Hodge vector $v \in \mathcal{H}_{\mathbb{C}, s}$ above $s \in S(\mathbb{C})$ which lies inside $\mathbb{V}_{s}$, the conjugate vector $v_{\sigma} \in \mathcal{H}_{\mathbb{C}, s_{\sigma}}$ is Hodge and lies inside $\mathbb{V}_{s_{\sigma}}$. We study this problem in the situation where we have an algebraic subvariety $Z \subset S_{\mathbb{C}}$ containing $s$ whose algebraic monodromy group $\mathbf{H}_Z$ fixes $v$. Using relationships between $\mathbf{H}_Z$ and $\mathbf{H}_{Z_{\sigma}}$ coming from the theories of complex and $\ell$-adic local systems, we establish a criterion that implies the absolute Hodge conjecture for $v$ subject to a group-theoretic condition on $\mathbf{H}_{Z}$. We then use our criterion to establish new cases of the absolute Hodge conjecture., Comment: Comments welcome!

A polarizable variation of Hodge structure over a smooth complex quasi projective variety $S$ is said to be defined over a number field $L$ if $S$ and the algebraic connection associated to the variation are both defined over $L$. Conjecturally any special subvariety (also called "an irreducible component of the Hodge locus) for such variations is defined over $\overline{\mathbb{Q}}$, and its Galois conjugates are also special subvarieties. We prove this conjecture for special subvarieties satisfying a simple monodromy condition. As a corollary we reduce the conjecture that special subvarieties for variation of Hodge structures defined over a number field are defined over $\overline{\mathbb{Q}}$ to the case of special points.

Regular magnetic fields are frequently found within and in the outskirts of galaxies, but their presence, properties, and origin has not yet been established for galaxy groups. On the basis of broadband radio polarimetric imaging with the Westerbork Synthesis Radio Telescope (WSRT), we made use of Rotation Measure Synthesis to disentangle contributions from magnetic fields on various scales for several polarised radio sources inside, behind, or in the vicinity of the Stephan's Quintet (HCG92, SQ). We recognise the signature of a large-scale, genuinely regular, magnetised screen, seemingly constrained to the Quintet itself. Although we cannot exclude a contribution from the Milky Way, our analysis favours a magnetic structure within the SQ system. If indeed associated with the galaxy group in question, it would span a volume of at least $60\,\times\,40\,\times\,20\,\mathrm{kpc}$ and have a strength at least as high as that previously detected within large spiral galaxies. This field would then surpass the extent of any other known galactic, regular magnetic fields, have a considerable strength of a few microgauss, and would be the first known example of such a structure in a galaxy system other than a galaxy pair. Several other explanations are also presented and evaluated., Comment: 13 pages, 7 figures, 3 tables

Reconnection heating has been considered as a potential source of the heating of the interstellar medium. In some galaxies, significant polarised radio emission has been found between the spiral arms. This emission has a form of `magnetic arms' that resembles the spiral structure of the galaxy. Reconnection effects could convert some of the energy of the turbulent magnetic field into the thermal energy of the surrounding medium, leaving more ordered magnetic fields, as is observed in the magnetic arms. Sensitive radio and X-ray data for the grand-design spiral galaxy M 83 are used for a detailed analysis of the possible interactions of magnetic fields with hot gas, including a search for signatures of gas heating by magnetic reconnection effects. Magnetic field strengths and energies derived from the radio emission are compared with the parameters of the hot gas calculated from the model fits to sensitive X-ray spectra of the hot gas emission. The available X-ray data allowed us to distinguish two thermal components in the halo of M 83. We found slightly higher average temperatures of the hot gas in the interarm regions, which results in higher energies per particle and is accompanied by a decrease in the energy density of the magnetic fields. The observed differences in the energy budget between the spiral arms and the interarm regions suggest that, similar to the case of another spiral galaxy NGC 6946, we may be observing hints for gas heating by magnetic reconnection effects in the interarm regions. These effects, which act more efficiently on the turbulent component of the magnetic field, are expected to be stronger in the spiral arms. However, with the present data it is only possible to trace them in the interarm regions, where the star formation and the resulting turbulence is low., Comment: 15 pages, 10 figures, A&A accepted