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Huntington's disease (HD) is an inherited neurodegenerative disorder caused by an expanded CAG repeat in the coding sequence of the huntingtin protein. Initially, it predominantly affects medium-sized spiny neurons (MSSNs) of the corpus striatum. No effective treatment is available, thus urging the identification of potential therapeutic targets. While evidence of mitochondrial structural alterations in HD exists, previous studies mainly employed 2D approaches and were performed outside the strictly native brain context. In this study, we adopted a novel multiscale approach to conduct a comprehensive 3D in situ structural analysis of mitochondrial disturbances in a mouse model of HD. We investigated MSSNs within brain tissue under optimal structural conditions utilizing state-of-the-art 3D imaging technologies, specifically FIB/SEM for the complete imaging of neuronal somas and Electron Tomography for detailed morphological examination and image processing-based quantitative analysis. Our findings suggest a disruption of the mitochondrial network towards fragmentation in HD. The network of interlaced, slim, and long mitochondria observed in healthy conditions transforms into isolated, swollen, and short entities, with internal cristae disorganization, cavities, and abnormally large matrix granules., Comment: 31 pages 5 figures

We have previously presented the idea of how complex multimodal information could be represented in our brains in a compressed form, following mechanisms similar to those employed in machine learning tools, like autoencoders. In this short comment note we reflect, mainly with a didactical purpose, upon the basic question for a biological implementation: what could be the mechanism working as a loss function, and how it could be connected to a neuronal network providing the required feedback to build a simple training configuration. We present our initial ideas based on a basic motif that implements an XOR switch, using few excitatory and inhibitory neurons. Such motif is guided by a principle of homeostasis, and it implements a loss function that could provide feedback to other neuronal structures, establishing a control system. We analyse the presence of this XOR motif in the connectome of C.Elegans, and indicate the relationship with the well-known lateral inhibition motif. We then explore how to build a basic biological neuronal structure with learning capacity integrating this XOR motif. Guided by the computational analogy, we show an initial example that indicates the feasibility of this approach, applied to learning binary sequences, like it is the case for simple melodies. In summary, we provide didactical examples exploring the parallelism between biological and computational learning mechanisms, identifying basic motifs and training procedures, and how an engram encoding a melody could be built using a simple recurrent network involving both excitatory and inhibitory neurons., Comment: 9 pages, short comment

The Universe is shaped as a web-like structure, formed by clusters, filaments, and walls that leave large volumes in between named voids. Galaxies in voids have been found to be of a later type, bluer, less massive, and to have a slower evolution than galaxies in denser environments (filaments and walls). However, the effect of the void environment on their stellar population properties is still unclear. We aim to address this question using 118 optical integral field unit datacubes from the Calar Alto Void Integral-field Treasury surveY (CAVITY), observed with the PMAS/PPaK spectrograph at the 3.5m telescope at the Calar Alto Observatory (Almer\'ia, Spain). We used the non-parametric full spectral fitting code STARLIGHT to estimate their stellar population properties: stellar mass, stellar mass surface density, age, star formation rate (SFR), and specific star formation rate (sSFR). We analysed the results through the global and spatially resolved properties. Then, we compared them with a control sample of galaxies in filaments and walls from the CALIFA survey, matched in stellar mass and morphological type. Key findings include void galaxies having a slightly higher half-light radius (HLR), lower stellar mass surface density, and younger ages across all morphological types, and slightly elevated SFR and sSFR (only significant enough for Sas). Many of these differences appear in the outer parts of spiral galaxies in voids (HLR > 1), which are younger and exhibit a higher sSFR, indicative of less evolved discs. This trend is also found for early-type spirals, suggesting a slower transition from star-forming to quiescent states in voids. Our analysis indicates that void galaxies, influenced by their surroundings, undergo a more gradual evolution, especially in their outer regions, with a more pronounced effect for low-mass galaxies., Comment: 24 pages, 22 figures, 5 tables. Accepted for publication in A&A. Updated references list

Aim: To study the existence of subgroups by exploring the similarities between the attributes of the nodes of the groups, in relation to diet and gender and, to analyse the connectivity between groups based on aspects of similarities between them through SNA and artificial intelligence techniques. Methods: 235 students from 5 different educational centres participate in this study between March and December 2015. Data analysis carried out is divided into two blocks: social network analysis and unsupervised machine learning techniques. As for the social network analysis, the Girvan-Newman technique was applied to find the best number of cohesive groups within each of the friendship networks of the different classes analysed. Results: After applying Girvan-Newman in the three classes, the best division into clusters was respectively 2 for classroom A, 7 for classroom B and 6 for classroom C. There are significant differences between the groups and the gender and diet variables. After applying K-means using population diet as an input variable, a K-means clustering of 2 clusters for class A, 3 clusters for class B and 3 clusters for class C is obtained. Conclusion: Adolescents form subgroups within their classrooms. Subgroup cohesion is defined by the fact that nodes share similarities in aspects that influence obesity, they share attributes related to food quality and gender. The concept of homophily, related to SNA, justifies our results. Artificial intelligence techniques together with the application of the Girvan-Newman provide robustness to the structural analysis of similarities and cohesion between subgroups.

We construct a Convolution Quadrature (CQ) scheme for the quasilinear subdiffusion equation and supply it with the fast and oblivious implementation. In particular we find a condition for the CQ to be admissible and discretize the spatial part of the equation with the Finite Element Method. We prove the unconditional stability and convergence of the scheme and find a bound on the error. As a passing result, we also obtain a discrete Gronwall inequality for the CQ, which is a crucial ingredient of our convergence proof based on the energy method. The paper is concluded with numerical examples verifying convergence and computation time reduction when using fast and oblivious quadrature.

Void galaxies are essential for understanding the physical processes that drive galaxy evolution because they are less affected by external factors than galaxies in denser environments, that is, in filaments, walls, and clusters. The stellar metallicity of a galaxy traces the accumulated fossil record of the star formation through the entire life of the galaxy. A comparison of the stellar metallicity of galaxies in various environments, including voids, filaments, walls, and clusters can provide valuable insights into how the large-scale environment affects the chemical evolution of the galaxy. We present the first comparison of the relation of the total stellar mass versus central stellar metallicity between galaxies in voids, filaments, walls, and clusters with different star formation history (SFH) types, morphologies, and colours for stellar masses between $10^{8.0}$ to $10^{11.5}$ solar masses and redshift $0.01

Local fields, and fields complete with respect to a discrete valuation, are essential objects in commutative algebra, with applications to number theory and algebraic geometry. We formalize in Lean the basic theory of discretely valued fields. In particular, we prove that the unit ball with respect to a discrete valuation on a field is a discrete valuation ring and, conversely, that the adic valuation on the field of fractions of a discrete valuation ring is discrete. We define finite extensions of valuations and of discrete valuation rings, and prove some global-to-local results. Building on this general theory, we formalize the abstract definition and some fundamental properties of local fields. As an application, we show that finite extensions of the field $\mathbb{Q}_p$ of $p$-adic numbers and of the field $\mathbb{F}_p(\!(X)\!)$ of Laurent series over $\mathbb{F}_p$ are local fields., Comment: 13th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP '24), Jan 2024, London, United Kingdom

Let $K/k$ be a finite Galois extension of global function fields. Let $E$ be a Drinfeld module over $k$. We state and prove an equivariant refinement of Taelman's analogue of the analytic class number formula for $(E,K/k)$, and derive explicit consequences for the Galois structure of the Taelman class group of $E$ over $K$., Comment: 41 pages

Let $K$ be a field complete with respect to a nonarchimedean real-valued norm, and let $L/K$ be an algebraic extension. We show that there is a unique norm on $L$ extending the given norm on $K$, with an explicit description. As an application, we extend the $p$-adic norm on the field $\mathbb{Q}_p$ of $p$-adic numbers to its algebraic closure $\mathbb{Q}_p^{\text{alg}}$, and we define the field $\mathbb{C}_p$ of $p$-adic complex numbers as the completion of the latter with respect to the $p$-adic norm. Building on the definition of $\mathbb{C}_p$, we formalize the definition of the Fontaine period ring $B_{\text{HT}}$ and discuss some applications to the theory of Galois representations and to $p$-adic Hodge theory. The results formalized in this paper are a prerequisite to formalize Local Class Field Theory, which is a fundamental ingredient of the proof of Fermat's Last Theorem., Comment: Accepted for the 14th International Conference on Interactive Theorem Proving (ITP 2023). 18 pages

The eighteenth data release of the Sloan Digital Sky Surveys (SDSS) is the first one for SDSS-V, the fifth generation of the survey. SDSS-V comprises three primary scientific programs, or "Mappers": Milky Way Mapper (MWM), Black Hole Mapper (BHM), and Local Volume Mapper (LVM). This data release contains extensive targeting information for the two multi-object spectroscopy programs (MWM and BHM), including input catalogs and selection functions for their numerous scientific objectives. We describe the production of the targeting databases and their calibration- and scientifically-focused components. DR18 also includes ~25,000 new SDSS spectra and supplemental information for X-ray sources identified by eROSITA in its eFEDS field. We present updates to some of the SDSS software pipelines and preview changes anticipated for DR19. We also describe three value-added catalogs (VACs) based on SDSS-IV data that have been published since DR17, and one VAC based on the SDSS-V data in the eFEDS field., Comment: Accepted to ApJS

We provide a sharp upper bound on the quotient of the rank of an A-hypergeometric system with a three-dimensional torus action by the normalized volume of A; in this case, the upper bound is two., Comment: 9 pages

We consider the application of the generalized Convolution Quadrature (gCQ) to approximate the solution of an important class of sectorial problems. The gCQ is a generalization of Lubich's Convolution Quadrature (CQ) that allows for variable steps. The available stability and convergence theory for the gCQ requires non realistic regularity assumptions on the data, which do not hold in many applications of interest, such as the approximation of subdiffusion equations. It is well known that for non smooth enough data the original CQ, with uniform steps, presents an order reduction close to the singularity. We generalize the analysis of the gCQ to data satisfying realistic regularity assumptions and provide sufficient conditions for stability and convergence on arbitrary sequences of time points. We consider the particular case of graded meshes and show how to choose them optimally, according to the behaviour of the data. An important advantage of the gCQ method is that it allows for a fast and memory reduced implementation. We describe how the fast and oblivious gCQ can be implemented and illustrate our theoretical results with several numerical experiments., Comment: 30 pages, 22 figures

We analyze spatially resolved and co-added SDSS-IV MaNGA spectra with signal-to-noise ~100 from 2200 passive central galaxies (z~0.05) to understand how central galaxy assembly depends on stellar mass (M*) and halo mass (Mh). We control for systematic errors in Mh by employing a new group catalog from Tinker (2020a,b) and the widely-used Yang et al. (2007) catalog. At fixed M*, the strength of several stellar absorption features varies systematically with Mh. Completely model-free, this is one of the first indications that the stellar populations of centrals with identical M* are affected by the properties of their host halos. To interpret these variations, we applied full spectral fitting with the code alf. At fixed M*, centrals in more massive halos are older, show lower [Fe/H], and have higher [Mg/Fe] with 3.5 sigma confidence. We conclude that halos not only dictate how much M* galaxies assemble, but also modulate their chemical enrichment histories. Turning to our analysis at fixed Mh, high-M* centrals are older, show lower [Fe/H], and have higher [Mg/Fe] for Mh>10^{12}Msun/h with confidence > 4 sigma. While massive passive galaxies are thought to form early and rapidly, our results are among the first to distinguish these trends at fixed Mh. They suggest that high-M* centrals experienced unique early formation histories, either through enhanced collapse and gas fueling, or because their halos were early-forming and highly concentrated, a possible signal of galaxy assembly bias., Comment: Accepted for publication in ApJ. 28 pages and 12 figures

The ring of ad\`eles of a global field and its group of units, the group of id\`eles, are fundamental objects in modern number theory. We discuss a formalization of their definitions in the Lean 3 theorem prover. As a prerequisite, we formalized adic valuations on Dedekind domains. We present some applications, including the statement of the main theorem of global class field theory and a proof that the ideal class group of a number field is isomorphic to an explicit quotient of its id\`ele class group., Comment: 15 pages

This paper documents the seventeenth data release (DR17) from the Sloan Digital Sky Surveys; the fifth and final release from the fourth phase (SDSS-IV). DR17 contains the complete release of the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey, which reached its goal of surveying over 10,000 nearby galaxies. The complete release of the MaNGA Stellar Library (MaStar) accompanies this data, providing observations of almost 30,000 stars through the MaNGA instrument during bright time. DR17 also contains the complete release of the Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) survey which publicly releases infra-red spectra of over 650,000 stars. The main sample from the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), as well as the sub-survey Time Domain Spectroscopic Survey (TDSS) data were fully released in DR16. New single-fiber optical spectroscopy released in DR17 is from the SPectroscipic IDentification of ERosita Survey (SPIDERS) sub-survey and the eBOSS-RM program. Along with the primary data sets, DR17 includes 25 new or updated Value Added Catalogs (VACs). This paper concludes the release of SDSS-IV survey data. SDSS continues into its fifth phase with observations already underway for the Milky Way Mapper (MWM), Local Volume Mapper (LVM) and Black Hole Mapper (BHM) surveys., Comment: 40 pages, 8 figures, 6 tables. In press at ApJSS (arxiv v2 corrects some minor typos and updates references)

Fix positive integers $n,r,d$. We show that if $n,r,d$ satisfy a suitable inequality, then any smooth hypersurface $X\subset \mathbb{P}^n$ defined over a finite field of characteristic $p$ sufficiently large contains a rational $r$-plane. Under more restrictive hypotheses on $n,r,d$ we show the same result without the assumption that $X$ is smooth or that $p$ is sufficiently large., Comment: 8 pages