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The connectome describes the complete set of synaptic contacts through which neurons communicate. While the architecture of the $\textit{C. elegans}$ connectome has been extensively characterized, much less is known about the organization of causal signaling networks arising from functional interactions between neurons. Understanding how effective communication pathways relate to or diverge from the underlying structure is a central question in neuroscience. Here, we analyze the modular architecture of the $\textit{C. elegans}$ signal propagation network, measured via calcium imaging and optogenetics, and compare it to the underlying anatomical wiring measured by electron microscopy. Compared to the connectome, we find that signaling modules are not aligned with the modular boundaries of the anatomical network, highlighting an instance where function deviates from structure. An exception to this is the pharynx which is delineated into a separate community in both anatomy and signaling. We analyze the cellular compositions of the signaling architecture and find that its modules are enriched for specific cell types and functions, suggesting that the network modules are neurobiologically relevant. Lastly, we identify a "rich club" of hub neurons in the signaling network. The membership of the signaling rich club differs from the rich club detected in the anatomical network, challenging the view that structural hubs occupy positions of influence in functional (signaling) networks. Our results provide new insight into the interplay between brain structure, in the form of a complete synaptic-level connectome, and brain function, in the form of a system-wide causal signal propagation atlas.

We prove that there is no relaxation gap between a quasi-dissipative nonlinear evolution equation in a Hilbert space and its linear Liouville equation reformulation on probability measures. In other words, strong and generalized solutions of such equations are unique in the class of measure-valued solutions. As a major consequence, non-convex numerical optimization over these non-linear partial differential equations can be carried out with the infinite-dimensional moment-SOS hierarchy with global convergence guarantees. This covers in particular all reaction-diffusion equations with polynomial nonlinearity.

Energetic charged particles generated by inertial confinement fusion (ICF) implosions encode information about the spatial morphology of the hot-spot and dense fuel during the time of peak fusion reactions. The knock-on deuteron imager (KoDI) was developed at the Omega Laser Facility to image these particles in order to diagnose low-mode asymmetries in the hot-spot and dense fuel layer of cryogenic deuterium--tritium ICF implosions. However, the images collected are distorted in several ways that prevent reconstruction of the deuteron source. In this paper we describe these distortions and a series of attempts to mitigate or compensate for them. We present several potential mechanisms for the distortions, including a new model for scattering of charged particles in filamentary electric or magnetic fields surrounding the implosion. A novel particle-tracing methodology is developed and utilized to create synthetic KoDI data based on the filamentary field model that reproduces the main experimentally observed image distortions. We conclude with a discussion of the outlook for KoDI, and potential considerations for other charged-particle diagnostics.

When several intruders move in a granular medium, coupling effects are observed, the motion of one intruder affecting that of others. In this paper, we investigate experimentally how the drag forces acting on a pair of spherical intruders moving amid grains at constant velocity vary with the transverse separation between them and their depth. When intruders are sufficiently far apart, they do not influence each other, and the average drag felt by each of them matches that of a single intruder. However, for small distances between intruders and at a given depth, the average drag per intruder decreases, highlighting a collaborative effect that facilitates motion. This collaboration effect is amplified when the depth of the intruders increases. We propose a model for the drag reduction of a pair of intruders based on the breakup of contact chains, caused by the perturbation generated by the neighbor intruder. Our findings provide new insights into the interaction effects on the motion of solids in sand, such as those observed in animal locomotion, root growth, and soil survey.

For a finite group $G$, we describe the asymptotic growth of the number of connected components of Hurwitz spaces of marked $G$-covers (of both the affine and projective lines) whose monodromy classes are constrained in a certain way, as the number of branch points grows to infinity. More precisely, we compute both the exponent and (in many cases) the coefficient of the leading monomial in the count of components containing covers whose monodromy group is a given subgroup of $G$. By the work of Ellenberg, Tran, Venkatesh and Westerland, this asymptotic behavior is related to the distribution of field extensions of~$\mathbb{F}_q(T)$ with Galois group $G$., Comment: 22 pages. This article was obtained after splitting 2210.12793v1 in two parts. Accepted in Israel Journal of Mathematics

We present foundation language models developed to power Apple Intelligence features, including a ~3 billion parameter model designed to run efficiently on devices and a large server-based language model designed for Private Cloud Compute. These models are designed to perform a wide range of tasks efficiently, accurately, and responsibly. This report describes the model architecture, the data used to train the model, the training process, how the models are optimized for inference, and the evaluation results. We highlight our focus on Responsible AI and how the principles are applied throughout the model development.

Let $K$ be a field of characteristic $0$ and $k \geq 2$ be an integer. We prove that every $K$-linear bijection $f : K[X] \to K[X]$ strongly preserving the set of $k$-free polynomials (or the set of polynomials with a $k$-fold root in $K$) is a constant multiple of a $K$-algebra automorphism of $K[X]$, i.e., there are elements $a, c \in K^{\times}$, $b \in K$ such that $f(P)(X) = c P(a X + b)$. When $K$ is a number field or $K=\mathbb{R}$, we prove that similar statements hold when $f$ preserves the set of polynomials with a root in $K$., Comment: 17 pages, no figure. Minor revison: conversion to LaTeX, mild proofreading, correction of an error in the statement of Theorem 2.2

We answer various questions concerning the distribution of extensions of a given central simple algebra $K$ over a number field. Specifically, we give asymptotics for the count of inner Galois extensions $L|K$ of fixed degree and center with bounded discriminant. We also relate the distribution of outer extensions of $K$ to the distribution of field extensions of its center $Z(K)$. This paper generalizes the study of asymptotics of field extensions to the noncommutative case in an analogous manner to the program initiated by Deschamps and Legrand to extend inverse Galois theory to skew fields., Comment: 32 pages

We establish new metric characterizations for the norm (respectively, ultraweak) closure of the convex hull of a bounded set in an arbitrary $C^*$-algebra (respectively, von Neumann algebra), and provide applications of these results to the majorization theory.

We investigate experimentally the influence of rotation on the penetration depth of a spherical projectile impacting a granular medium. We show that a rotational motion significantly increases the penetration depth achieved. Moreover, we model our experimental results by modifying the frictional term of the equation describing the penetration dynamics of an object in a granular medium. In particular, we find that the frictional drag decreases linearly with the velocity ratio between rotational (spin motion) and translational (falling motion) velocities. The good agreement between our model and our experimental measurements offers perspectives for estimating the depth that spinning projectiles reach after impacting onto a granular ground, such as happens with seeds dropped from aircraft or with landing probes.

In this work we address the following question: is it possible for a one-dimensional, linearly elastic beam to only bend on the Cantor set and, if so, what would the bending energy of such a beam look like? We answer this question by considering a sequence of beams, indexed by $n$, each one only able to bend on the set associated with the $n$-th step in the construction of the Cantor set and compute the $\Gamma$-limit of the bending energies. The resulting energy in the limit has a structure similar to the traditional bending energy, a key difference being that the measure used for the integration is the Hausdorff measure of dimension $\ln 2/\ln 3$, which is the dimension of the Cantor set., Comment: 12 pages, 1 figure

We present an analysis of 12 million instances of privacy-relevant reviews publicly visible on the Google Play Store that span a 10 year period. By leveraging state of the art NLP techniques, we examine what users have been writing about privacy along multiple dimensions: time, countries, app types, diverse privacy topics, and even across a spectrum of emotions. We find consistent growth of privacy-relevant reviews, and explore topics that are trending (such as Data Deletion and Data Theft), as well as those on the decline (such as privacy-relevant reviews on sensitive permissions). We find that although privacy reviews come from more than 200 countries, 33 countries provide 90% of privacy reviews. We conduct a comparison across countries by examining the distribution of privacy topics a country's users write about, and find that geographic proximity is not a reliable indicator that nearby countries have similar privacy perspectives. We uncover some countries with unique patterns and explore those herein. Surprisingly, we uncover that it is not uncommon for reviews that discuss privacy to be positive (32%); many users express pleasure about privacy features within apps or privacy-focused apps. We also uncover some unexpected behaviors, such as the use of reviews to deliver privacy disclaimers to developers. Finally, we demonstrate the value of analyzing app reviews with our approach as a complement to existing methods for understanding users' perspectives about privacy, Comment: This is the extended version of the paper accepted to USENIX Security 2024

We assemble a dataset of Creative-Commons-licensed (CC) images, which we use to train a set of open diffusion models that are qualitatively competitive with Stable Diffusion 2 (SD2). This task presents two challenges: (1) high-resolution CC images lack the captions necessary to train text-to-image generative models; (2) CC images are relatively scarce. In turn, to address these challenges, we use an intuitive transfer learning technique to produce a set of high-quality synthetic captions paired with curated CC images. We then develop a data- and compute-efficient training recipe that requires as little as 3% of the LAION-2B data needed to train existing SD2 models, but obtains comparable quality. These results indicate that we have a sufficient number of CC images (~70 million) for training high-quality models. Our training recipe also implements a variety of optimizations that achieve ~3X training speed-ups, enabling rapid model iteration. We leverage this recipe to train several high-quality text-to-image models, which we dub the CommonCanvas family. Our largest model achieves comparable performance to SD2 on a human evaluation, despite being trained on our CC dataset that is significantly smaller than LAION and using synthetic captions for training. We release our models, data, and code at https://github.com/mosaicml/diffusion/blob/main/assets/common-canvas.md

Brain-computer interfaces (BCI) are presented as a solution for people with global paralysis, also known as locked-in syndrome (LIS). The targeted population includes the most severe patients, with no residual eye movements, who cannot use any communication device (Complete LIS). However, BCI reliability is low precisely in these cases, technical pitfalls being considered responsible so far. Here, we propose to consider also that global paralysis could have an impact on cognitive functions that are crucial for being able to control a BCI. We review a bundle of arguments about the role of motor structures in cognition. Especially, we uncover that these patients without oculomotor activity often have injuries in more 'cognitive' structures such as the frontal eye field or the midbrain, exposing them to cognitive deficits further than canonical LIS population. We develop a hypothesis about the putative role of the motor system in (covert) attention, a capacity which is a prerequisite for most BCI paradigms and which should therefore be both better assessed in patients and considered., Comment: 3 tables

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for other computational tasks on manifold as well, including interpolation tasks. In this work, we consider the application of retractions to the numerical integration of differential equations on fixed-rank matrix manifolds. This is closely related to dynamical low-rank approximation (DLRA) techniques. In fact, any retraction leads to a numerical integrator and, vice versa, certain DLRA techniques bear a direct relation with retractions. As an example for the latter, we introduce a new retraction, called KLS retraction, that is derived from the so-called unconventional integrator for DLRA. We also illustrate how retractions can be used to recover known DLRA techniques and to design new ones. In particular, this work introduces two novel numerical integration schemes that apply to differential equations on general manifolds: the accelerated forward Euler (AFE) method and the Projected Ralston--Hermite (PRH) method. Both methods build on retractions by using them as a tool for approximating curves on manifolds. The two methods are proven to have local truncation error of order three. Numerical experiments on classical DLRA examples highlight the advantages and shortcomings of these new methods.

We propose a numerical method to solve parameter-dependent hyperbolic partial differential equations (PDEs) with a moment approach, based on a previous work from Marx et al. (2020). This approach relies on a very weak notion of solution of nonlinear equations, namely parametric entropy measure-valued (MV) solutions, satisfying linear equations in the space of Borel measures. The infinite-dimensional linear problem is approximated by a hierarchy of convex, finite-dimensional, semidefinite programming problems, called Lasserre's hierarchy. This gives us a sequence of approximations of the moments of the occupation measure associated with the parametric entropy MV solution, which is proved to converge. In the end, several post-treatments can be performed from this approximate moments sequence. In particular, the graph of the solution can be reconstructed from an optimization of the Christoffel-Darboux kernel associated with the approximate measure, that is a powerful approximation tool able to capture a large class of irregular functions. Also, for uncertainty quantification problems, several quantities of interest can be estimated, sometimes directly such as the expectation of smooth functionals of the solutions. The performance of our approach is evaluated through numerical experiments on the inviscid Burgers equation with parametrised initial conditions or parametrised flux function., Comment: 37 pages, 10 figures

This paper presents the design and characterisation of a front-end prototype ASIC for the ATLAS High Granularity Timing Detector, which is planned for the High-Luminosity phase of the LHC. This prototype, called ALTIROC1, consists of a 5$\times$5-pad matrix and contains the analog part of the single-channel readout (preamplifier, discriminator, two TDCs and SRAM). Two preamplifier architectures (transimpedance and voltage) were implemented and tested. The ASIC was characterised both alone and as a module when connected to a 5$\times$5-pad array of LGAD sensors. In calibration measurements, the ASIC operating alone was found to satisfy the technical requirements for the project, with similar performances for both preamplifier types. In particular, the jitter was found to be 15$\pm$1~ps (35$\pm$1~ps) for an injected charge of 10~fC (4~fC). A degradation in performance was observed when the ASIC was connected to the LGAD array. This is attributed to digital couplings at the entrance of the preamplifiers. When the ASIC is connected to the LGAD array, the lowest detectable charge increased from 1.5~fC to 3.4~fC. As a consequence, the jitter increased for an injected charge of 4~fC. Despite this increase, ALTIROC1 still satisfies the maximum jitter specification (below 65~ps) for the HGTD project. This coupling issue also affects the time over threshold measurements and the time-walk correction can only be performed with transimpedance preamplifiers. Beam test measurements with a pion beam at CERN were also undertaken to evaluate the performance of the module. The best time resolution obtained using only ALTIROC TDC data was 46.3$\pm$0.7~ps for a restricted time of arrival range where the coupling issue is minimized. The residual time-walk contribution is equal to 23~ps and is the dominant electronic noise contribution to the time resolution at 15~fC., Comment: 20 pages, 15 figures Second version submitted to JINST including minor changes applied to address journal's comments