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Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancements in loss functions and network architectures have improved PINN accuracy, the impact of collocation point sampling on their performance remains underexplored. Fixed sampling methods, such as uniform random sampling and equispaced grids, can fail to capture critical regions with high solution gradients, limiting their effectiveness for complex PDEs. Adaptive methods, inspired by adaptive mesh refinement from traditional numerical methods, address this by dynamically updating collocation points during training but may overlook residual dynamics between updates, potentially losing valuable information. To overcome this limitation, we propose an adaptive collocation point selection strategy utilizing the QR Discrete Empirical Interpolation Method (QR-DEIM), a reduced-order modeling technique for efficiently approximating nonlinear functions. Our results on benchmark PDEs, including the wave, Allen-Cahn, and Burgers' equations, demonstrate that our QR-DEIM-based approach improves PINN accuracy compared to existing methods, offering a promising direction for adaptive collocation point strategies.

We exhibit in this article a contraction of the direct product Lie algebra $g\oplus g$ of a finite-dimensional complex Lie algebra $g$ onto the semi-direct product Lie algebra $g\rtimes g$, where the first factor $g$ is viewed as a trivial Lie algebra and as the adjoint $g$-module. This contraction gives rise to a non-zero cohomology class in the second cohomology space. We generalize to the setting of $h\oplus g$ and $h\rtimes g$ with respect to a given crossed module of Lie algebras $h\to g$. We give many examples to illustrate our results., Comment: 19 pages, no figures

The ability of a robot to plan complex behaviors with real-time computation, rather than adhering to predesigned or offline-learned routines, alleviates the need for specialized algorithms or training for each problem instance. Monte Carlo Tree Search is a powerful planning algorithm that strategically explores simulated future possibilities, but it requires a discrete problem representation that is irreconcilable with the continuous dynamics of the physical world. We present Spectral Expansion Tree Search (SETS), a real-time, tree-based planner that uses the spectrum of the locally linearized system to construct a low-complexity and approximately equivalent discrete representation of the continuous world. We prove SETS converges to a bound of the globally optimal solution for continuous, deterministic and differentiable Markov Decision Processes, a broad class of problems that includes underactuated nonlinear dynamics, non-convex reward functions, and unstructured environments. We experimentally validate SETS on drone, spacecraft, and ground vehicle robots and one numerical experiment, each of which is not directly solvable with existing methods. We successfully show SETS automatically discovers a diverse set of optimal behaviors and motion trajectories in real time., Comment: The first two authors contributed equally to this article

We prove that stationary Yang$-$Mills fields in dimensions 5 belonging to the variational class of weak connections are smooth away from a closed singular set $S$ of vanishing 1-dimensional Hausdorff measure. Our proof is based on an $\varepsilon$-regularity theorem, which generalizes to this class of weak connections the existing previous $\varepsilon$-regularity results by G. Tian for smooth connections, by Y. Meyer and the second author for Sobolev and approximable connections, and by T. Tao and G. Tian for admissible connections (which are weak limits of smooth Yang$-$Mills fields). On the path towards establishing $\varepsilon$-regularity, a pivotal step is the construction of controlled Coulomb gauges for general weak connections under small Morrey norm assumptions., Comment: 56 pages. Any comments are welcome

Given a smooth integral two-form and a smooth potential on the flat torus of dimension 2, we study the high energy properties of the corresponding magnetic Schr\"odinger operator. Under a geometric condition on the magnetic field, we show that every sequence of high energy eigenfunctions satisfies the quantum unique ergodicity property even if the Liouville measure is not ergodic for the underlying classical flow (the Euclidean geodesic flow on the 2-torus).

Effective structural assessment of urban infrastructure is essential for sustainable land use and resilience to climate change and natural hazards. Seismic wave methods are widely applied in these areas for subsurface characterization and monitoring, yet they often rely on time-consuming inversion techniques that fall short in delivering comprehensive geological, hydrogeological, and geomechanical descriptions. Here, we explore the effectiveness of a passive seismic approach coupled with artificial intelligence (AI) for monitoring geological structures and hydrogeological conditions in the context of sinkhole hazard assessment. We introduce a deterministic petrophysical inversion technique based on a language model that decodes seismic wave velocity measurements to infer soil petrophysical and mechanical parameters as textual descriptions. Results successfully delineate 3D subsurface structures with their respective soil nature and mechanical characteristics, while accurately predicting daily water table levels. Validation demonstrates high accuracy, with a normalized root mean square error of 8%, closely rivaling with conventional stochastic seismic inversion methods, while delivering broader insights into subsurface conditions 2,000 times faster. These findings underscore the potential of advanced AI techniques to significantly enhance subsurface characterization across diverse scales, supporting decision-making for natural hazard mitigation., Comment: 70 pages, 33 figures

The observational detection of some metastable isomers in the interstellar medium with abundances comparable to those of the most stable isomer, or even when the stable isomer is not detected, highlights the importance of non-equilibrium chemistry. This challenges our understanding of the interstellar chemistry. We present a chemical study of isomers through the sulphur isomer pair HNCS and HSCN, since HSCN has been observed in regions where its stable isomer has not been detected, and the observed HNCS/HSCN ratio seems to significantly vary from cold to warm regions. We have used the Nautilus chemical code to model the formation and destruction paths of HNCS and HSCN in different astrochemical scenarios, and the time evolution of the HNCS/HSCN ratio. We have also analysed the influence of the environmental conditions on their chemical abundances. We present an observational detection of the metastable isomer HSCN in the Class I object B1-a, but not of the stable isomer HNCS, despite HNCS lying 3200 K lower in energy than HSCN. Our results show an HNCS/HSCN ratio sensitive to the gas temperature and the evolutionary time, with the highest values obtained at early stages (t<10^4 yr) and low (Tg<20 K) temperatures. The results suggest a different efficiency of the isomerisation processes depending on the source temperature. The progressive decrease of HNCS/HSCN with gas temperature at early evolutionary times indicates that this ratio may be used as a tracer of cold young objects. This work also demonstrates the key role of grain surface chemistry in the formation of the isomer pair HNCS and HSCN in cold regions, and the importance of the ions H2NCS+ and HNCSH+ in warm/hot regions. Since most of the interstellar regions where HSCN is detected are cold regions, a larger sample including sources characterised by high temperatures are needed to corroborate the theoretical results., Comment: 10 pages, 12 figures. Accepted for publication by A&A

We introduce a general definition of a $n$-crossed module of $P$-algebras over an algebraic operad $P$, which coincides with historical definitions in the cases of the operads As and Lie and $n = 1$. We establish a natural isomorphism between the abelian group of equivalence classes of $n$-crossed modules over a pair $(A,M)$ for an operad $P$ and the $(n+1)^\text{th}$ operadic cohomology group of $A$ with coefficients in $M$., Comment: 21 pages

The success of Large Language Models (LLMs) in other domains has raised the question of whether LLMs can reliably assess and manipulate the readability of text. We approach this question empirically. First, using a published corpus of 4,724 English text excerpts, we find that readability estimates produced ``zero-shot'' from GPT-4 Turbo and GPT-4o mini exhibit relatively high correlation with human judgments (r = 0.76 and r = 0.74, respectively), out-performing estimates derived from traditional readability formulas and various psycholinguistic indices. Then, in a pre-registered human experiment (N = 59), we ask whether Turbo can reliably make text easier or harder to read. We find evidence to support this hypothesis, though considerable variance in human judgments remains unexplained. We conclude by discussing the limitations of this approach, including limited scope, as well as the validity of the ``readability'' construct and its dependence on context, audience, and goal., Comment: 9 pages, 6 figures, workshop TSAR 2024

(Abridged) We explore the chemistry of the most abundant C, O, S, and N bearing species in molecular clouds, in the context of the IRAM 30 m Large Programme Gas phase Elemental abundances in Molecular Clouds (GEMS). In this work, we aim to assess the limitations introduced in the observational works when a uniform density is assumed along the line of sight for fitting the observations, developing a very simple numerical model of a turbulent box. We perform a MHD simulation in order to reproduce the turbulent steady-state of a turbulent box with properties typical of a molecular filament before collapse. We post-process the results of the MHD simulation with a chemical code to predict molecular abundances, and then post-process this cube with a radiative transfer code to create synthetic emission maps for a series of rotational transitions observed during the GEMS project. From the chemical point of view, we find that turbulence produces variations on the predicted abundances, but they are more or less critical depending on the chosen transition and the chemical age. When compared to real observations, the results from the turbulent simulation provides a better fit than when assuming a uniform gas distribution along the line of sight. In the view of our results, we conclude that taking into account turbulence when fitting observations might significantly improve the agreement with model predictions. This is especially important for sulfur bearing species that are very sensitive to the variations of density produced by turbulence at early times (0.1 Myr). The abundance of CO is also quite sensitive to turbulence when considering the evolution beyond a few 0.1 Myr., Comment: Published in Astronomy and Astrophysics

Volumetric modeling and neural radiance field representations have revolutionized 3D face capture and photorealistic novel view synthesis. However, these methods often require hundreds of multi-view input images and are thus inapplicable to cases with less than a handful of inputs. We present a novel volumetric prior on human faces that allows for high-fidelity expressive face modeling from as few as three input views captured in the wild. Our key insight is that an implicit prior trained on synthetic data alone can generalize to extremely challenging real-world identities and expressions and render novel views with fine idiosyncratic details like wrinkles and eyelashes. We leverage a 3D Morphable Face Model to synthesize a large training set, rendering each identity with different expressions, hair, clothing, and other assets. We then train a conditional Neural Radiance Field prior on this synthetic dataset and, at inference time, fine-tune the model on a very sparse set of real images of a single subject. On average, the fine-tuning requires only three inputs to cross the synthetic-to-real domain gap. The resulting personalized 3D model reconstructs strong idiosyncratic facial expressions and outperforms the state-of-the-art in high-quality novel view synthesis of faces from sparse inputs in terms of perceptual and photo-metric quality., Comment: Siggraph Asia Conference Papers 2024

Oxygenators, alarm devices, and footsteps are some of the most common sound sources in a hospital. Detecting them has scientific value for environmental psychology but comes with challenges of its own: namely, privacy preservation and limited labeled data. In this paper, we address these two challenges via a combination of edge computing and cloud computing. For privacy preservation, we have designed an acoustic sensor which computes third-octave spectrograms on the fly instead of recording audio waveforms. For sample-efficient machine learning, we have repurposed a pretrained audio neural network (PANN) via spectral transcoding and label space adaptation. A small-scale study in a neonatological intensive care unit (NICU) confirms that the time series of detected events align with another modality of measurement: i.e., electronic badges for parents and healthcare professionals. Hence, this paper demonstrates the feasibility of polyphonic machine listening in a hospital ward while guaranteeing privacy by design.

Objective: Innovative therapies such as thermoembolization are expected to play an important role in improvising care for patients with diseases such as hepatocellular carcinoma. Thermoembolization is a minimally invasive strategy that combines thermal ablation and embolization in a single procedure. This approach exploits an exothermic chemical reaction that occurs when an acid chloride is delivered via an endovascular route. However, comprehension of the complexities of the biophysics of thermoembolization is challenging. Mathematical models can aid in understanding such complex processes and assisting clinicians in making informed decisions. In this study, we used a Hagen Poiseuille 1D blood flow model to predict the mass transport and possible embolization locations in a porcine hepatic artery. Method: The 1D flow model was used on in vivo embolization imaging data of three pigs. The hydrolysis time constant of acid chloride chemical reaction was optimized for each pig, and LOOCV method was used to test the model's predictive ability. Conclusion: This basic model provided a balanced accuracy rate of 66.8% for identifying the possible locations of embolization in the hepatic artery. Use of the model provides an initial understanding of the vascular transport phenomena that are predicted to occur as a result of thermoembolization.

{Sulfur Monoxide is known to be a good shock tracer in molecular clouds and protostar environments, but its abundance is difficult to reproduce even using state-of-the-art astrochemical models. } {We investigate the properties of the observed SO emission in the protoplanetary disk of AB Auriga, a Herbig Ae star of 2.4 $\Msun$ located at 156 pc. The AB Aur system is unique because it exhibits a dust trap and at least one young putative planet orbiting at about 30 au from the central star.} {We reduced ALMA archival data (projects 2019.1.00579.S, 2021.1.00690.S and 2021.1.01216.S) and analyzed the three detected SO lines (SO $6_5-5_4$, $6_7-5_6$ and $5_6-4_5$). We also present C$^{17}$O and C$^{18}$O 2-1 data to complement the interpretation of the SO data.} {For the three SO lines, the maximum SO emission in the ring is not located in the dust trap. Moreover, the inner radius of the SO ring is significantly larger than the CO emission inner radius, $\sim 160$ au versus $\sim 90$ au. The SO emission traces gas located in part beyond the dust ring. This emission likely originates from shocks at the interface of the outer spirals, observed in CO and scattered light emission, and the molecular and dust ring. SO is also detected inside the cavity, at a radius $\sim 20-30$ au and with a rotation velocity compatible with the proto-planet P1. We speculate that this SO emission originates from accretion shocks onto the circumplanetary disk of the putative proto-planet P1.} {These observations confirm that SO is a good tracer of shocks in protoplanetary disks and could be a powerful, new tool to detect embedded (proto-)planets.} Conclusions. These observations confirm that SO is a good tracer of shocks in protoplanetary disks and could be a powerful, new tool to detect embedded (proto-)planets.

Medical imaging segmentation is a highly active area of research, with deep learning-based methods achieving state-of-the-art results in several benchmarks. However, the lack of standardized tools for training, testing, and evaluating new methods makes the comparison of methods difficult. To address this, we introduce the Medical Imaging Segmentation Toolkit (MIST), a simple, modular, and end-to-end medical imaging segmentation framework designed to facilitate consistent training, testing, and evaluation of deep learning-based medical imaging segmentation methods. MIST standardizes data analysis, preprocessing, and evaluation pipelines, accommodating multiple architectures and loss functions. This standardization ensures reproducible and fair comparisons across different methods. We detail MIST's data format requirements, pipelines, and auxiliary features and demonstrate its efficacy using the BraTS Adult Glioma Post-Treatment Challenge dataset. Our results highlight MIST's ability to produce accurate segmentation masks and its scalability across multiple GPUs, showcasing its potential as a powerful tool for future medical imaging research and development., Comment: Submitted to BraTS 2024

In this work, we introduce Gemma 2, a new addition to the Gemma family of lightweight, state-of-the-art open models, ranging in scale from 2 billion to 27 billion parameters. In this new version, we apply several known technical modifications to the Transformer architecture, such as interleaving local-global attentions (Beltagy et al., 2020a) and group-query attention (Ainslie et al., 2023). We also train the 2B and 9B models with knowledge distillation (Hinton et al., 2015) instead of next token prediction. The resulting models deliver the best performance for their size, and even offer competitive alternatives to models that are 2-3 times bigger. We release all our models to the community.

We investigate bubble deformations in an homogeneous and isotropic turbulent flow by means of direct numerical simulations of a single bubble in turbulence. We examine interface deformations by decomposing the local radius into the spherical harmonics base. We show that the linear dynamics of each mode, (for low Weber number), can be modeled by a forced stochastic linear oscillator. We measure the coefficients of the model directly from the modes' statistics. We find that the natural frequency corresponds to the Rayleigh frequency, derived in a quiescent flow. However, dissipation increases by a factor 15 compared to the quiescent case, at $Re_\lambda = 55$. This enhanced dissipation originates from a thick boundary layer surrounding the bubble. We demonstrate that the effective forcing, originating from the integration of pressure over the bubble surface, is independent on bubble deformability. Therefore, the interface deformations are only one-way coupled to the flow. Eventually, we investigate the pressure modes' statistics in the absence of bubbles and compare them to the effective forcing statistics. We show that both fields share the same pdf, characterized by exponential tails, and a characteristic timescale corresponding to the eddy turnover time at the mode scale.

In this article, we study nonlinear Vlasov equations with a smooth interaction kernel on a compact manifold without boundary where the geodesic flow exhibits strong chaotic behavior, known as the Anosov property. We show that, for small initial data with finite regularity and supported away from the null section, there exist global solutions to the nonlinear Vlasov equations which weakly converge to an equilibrium of the free transport equation, and whose potential strongly converges to zero, both with exponential speed. Central to our approach are microlocal anisotropic Sobolev spaces, originally developed for studying Pollicott-Ruelle resonances, that we further refine to deal with the geometry of the full cotangent bundle, which paves the way to the analysis of nonlinear Vlasov equations.

We study the nature of quantum phase transitions out of $\mathbb{Z}_4$ ordered phases in quantum loop models on a zig-zag ladder. We report very rich critical behavior that includes a pair of Ising transitions, a multi-critical Ashkin-Teller point and a remarkably extended interval of a chiral transition. Although plaquette states turn out to be essential to realize chiral transitions, we demonstrate that critical regimes can be manipulated by deforming the model as to increase the presence of leg-dimerized states. This can be done to the point where the chiral transition turns into first order, we argue that this is associated with the emergence of a critical end point., Comment: 28 pages, 14 figures

Lexical ambiguity -- where a single wordform takes on distinct, context-dependent meanings -- serves as a useful tool to compare across different language models' (LMs') ability to form distinct, contextualized representations of the same stimulus. Few studies have systematically compared LMs' contextualized word embeddings for languages beyond English. Here, we evaluate semantic representations of Spanish ambiguous nouns in context in a suite of Spanish-language monolingual and multilingual BERT-based models. We develop a novel dataset of minimal-pair sentences evoking the same or different sense for a target ambiguous noun. In a pre-registered study, we collect contextualized human relatedness judgments for each sentence pair. We find that various BERT-based LMs' contextualized semantic representations capture some variance in human judgments but fall short of the human benchmark. In exploratory work, we find that performance scales with model size. We also identify stereotyped trajectories of target noun disambiguation as a proportion of traversal through a given LM family's architecture, which we partially replicate in English. We contribute (1) a dataset of controlled, Spanish sentence stimuli with human relatedness norms, and (2) to our evolving understanding of the impact that LM specification (architectures, training protocols) exerts on contextualized embeddings., Comment: 17 pages, 12 figures, submitted to conference (NAACL 2025)

Astrochemical models are important tools to interpret observations of molecular and atomic species in different environments. However, these models are time-consuming, precluding a thorough exploration of the parameter space, leading to uncertainties and biased results. Using neural networks to simulate the behavior of astrochemical models is a way to circumvent this problem, providing fast calculations that are based on real astrochemical models. In this paper, we present a fast neural emulator of the astrochemical code Nautilus based on conditional neural fields. The resulting model produces the abundance of 192 species for arbitrary times between 1 and 10$^7$ years. Uncertainties well below 0.2 dex are found for all species, while the computing time is of the order of 10$^4$ smaller than Nautilus. This will open up the possibility of performing much more complex forward models to better understand the physical properties of the interstellar medium. As an example of the power of these models, we ran a feature importance analysis on the electron abundance predicted by Nautilus. We found that the electron density is coupled to the initial sulphur abundance in a low density gas. Increasing the initial sulphur abundance from a depleted scenario to the cosmic abundance leads to an enhancement of an order of magnitude of the electron density. This enhancement can potentially influence the dynamics of the gas in star formation sites., Comment: 12 pages, 8 figures, accepted for publication in MNRAS

Brain folding patterns have been reported to carry clinically relevant information. The brain folds mainly during the last trimester of pregnancy, and the process might be durably disturbed by preterm birth. Yet little is known about preterm-specific patterns. In this work, we train a self-supervised model (SimCLR) on the UKBioBank cohort (21070 adults) to represent the right superior temporal sulcus (STS) region and apply it to sulci images of 374 babies from the dHCP database, containing preterms and full-terms, and acquired at 40 weeks post-menstrual age. We find a lower variability in the preterm embeddings, supported by the identification of a knob pattern, missing in the extremely preterm population.

We study a new notion of critical point for the area of surfaces under the Legendrian constraint, called parametrized Hamiltonian stationary Legendrian varifolds (PHSLVs). We establish several fundamental properties of these objects, including their sequential compactness and an optimal regularity result, showing that they are smooth immersions away from a locally finite set of branch points and Schoen Wolfson conical singularities. This generalizes in particular the regularity theory of Schoen Wolfson for minimizers to general critical points. This theory can be used to show two new variational results: every minmax operation with the area of (closed, immersed) Legendrian surfaces in a closed Sasakian 5-dimensional manifold is achieved by a Hamiltonian stationary map with this regularity; also, the minimal area in any given exact isotopy class of Legendrian immersions of $S^2$ is realized by such a map. Along the way, we prove an effective monotonicity formula for general two-dimensional stationary varifolds in the Legendrian setting, as well as the closure of integral stationary varifolds among rectifiable ones, in spite of the lack of compactness of the latter.

Given a connection $A$ on a $SU(2)$-bundle $P$ over $\mathbb{R}^4$ with finite Yang-Mills energy $YM(A)$ and nonzero curvature $F_A(0)$ at the origin, and given $\rho>0$ small enough, we construct a new connection $\hat A$ on a bundle $\hat P$ of different Chern class ($|c_2(A)-c_2(\hat A)|=8\pi^2$), in such a way that $\hat A$ is gauge equivalent to $A$ in $\mathbb{R}^4\setminus B_\rho(0)$ and $$YM(\hat A)\le YM(A)+8\pi^2-\varepsilon_0\rho^4|F_A(0)|^2$$ for a universal constant $\varepsilon_0>0$.

We introduce RecurrentGemma, a family of open language models which uses Google's novel Griffin architecture. Griffin combines linear recurrences with local attention to achieve excellent performance on language. It has a fixed-sized state, which reduces memory use and enables efficient inference on long sequences. We provide two sizes of models, containing 2B and 9B parameters, and provide pre-trained and instruction tuned variants for both. Our models achieve comparable performance to similarly-sized Gemma baselines despite being trained on fewer tokens.

The relationship between language model tokenization and performance is an open area of research. Here, we investigate how different tokenization schemes impact number agreement in Spanish plurals. We find that morphologically-aligned tokenization performs similarly to other tokenization schemes, even when induced artificially for words that would not be tokenized that way during training. We then present exploratory analyses demonstrating that language model embeddings for different plural tokenizations have similar distributions along the embedding space axis that maximally distinguishes singular and plural nouns. Our results suggest that morphologically-aligned tokenization is a viable tokenization approach, and existing models already generalize some morphological patterns to new items. However, our results indicate that morphological tokenization is not strictly required for performance.

This paper describes a receiver that uses an innovative method to predict, according to history of receiver operating metrics (packet lost/well received), the optimum automatic gain control (AGC) index or most appropriate variable gain range to be used for next packet reception, anticipating an interferer appearing during the payload reception. This allows the receiver to have higher immunity to interferers even if they occur during the gain frozen payload reception period whilst still ensuring an optimum sensitivity level. As a result, the method allows setting the receiver gain to get an optimum trade-off between reception sensitivity and random interferer immunity., Comment: 17 pages, 15 figures

This work introduces Gemma, a family of lightweight, state-of-the art open models built from the research and technology used to create Gemini models. Gemma models demonstrate strong performance across academic benchmarks for language understanding, reasoning, and safety. We release two sizes of models (2 billion and 7 billion parameters), and provide both pretrained and fine-tuned checkpoints. Gemma outperforms similarly sized open models on 11 out of 18 text-based tasks, and we present comprehensive evaluations of safety and responsibility aspects of the models, alongside a detailed description of model development. We believe the responsible release of LLMs is critical for improving the safety of frontier models, and for enabling the next wave of LLM innovations.

Bubbles drive gas and chemical transfers in various industrial and geophysical context, in which flows are typically turbulent. A knowledge of the bubble size distributions is then necessary to quantify mass fluxes across interfaces. In a turbulent flow, every bubble might break, depending on both the ratio between inertial and capillary forces at its scale, namely the Weber number We. For inhomogeneous and unstationary flows, the residence time within a turbulent region will also determine the break-up probability. In this work, we use a stochastic linear model, whose parameters have been measured using direct numerical simulations, to infer the breakup probability of bubbles in turbulence as function of the Weber number and the residence time. Our model shows that bubble breakup is a memoryless process, whose breakup rate varies exponentially with $\textrm{We}^{-1}$. This linear model successfully reproduces breakup rates previously measured experimentally., Comment: 4 figures + A supplementary Material

The first hydrostatic core (FHSC) phase is a brief stage in the protostellar evolution that is difficult to detect. Our goal is to characterize the chemical evolution of gas and dust during the formation of the FHSC. Moreover, we are interested in analyzing, for the first time with 3D magnetohydrodynamic (MHD) simulations, the role of grain growth in its chemistry. We postprocessed $2\times10^{5}$ tracer particles from a $\texttt{RAMSES}$ non-ideal MHD simulation using the codes $\texttt{NAUTILUS}$ and $\texttt{SHARK}$ to follow the chemistry and grain growth throughout the simulation. A great chemical inheritance is seen, as gas-phase abundances of most of the C, O, N, and S reservoirs in the hot corino at the end of the simulation match the ice-phase abundances from the prestellar phase. Additionally, interstellar complex organic molecules (iCOMs) such as methyl formate, acetaldehyde, and formamide are formed during the warm-up process. The typical grain size in the hot corino $(n_{\rm H}>10^{11}\ {\rm cm^{-3}})$ increases forty-fold during the last 30 kyr, with negligible effects on its chemical composition. At moderate densities $(10^{10}

Directed percolation (DP), a universality class of continuous phase transitions, has recently been established as a possible route to turbulence in subcritical wall-bounded flows. In canonical straight pipe or planar flows, the transition occurs via discrete large-scale turbulent structures, known as puffs in pipe flow or bands in planar flows, which either self-replicate or laminarize. However, these processes might not be universal to all subcritical shear flows. Here, we design a numerical experiment that eliminates discrete structures in plane Couette flow and show that it follows a different, simpler transition scenario: turbulence proliferates via expanding fronts and decays via spontaneous creation of laminar zones. We map this phase transition onto a stochastic one-variable system. The level of turbulent fluctuations dictates whether moving-front transition is discontinuous, or continuous and within the DP universality class, with profound implications for other hydrodynamic systems.

The human cerebral cortex has many bumps and grooves called gyri and sulci. Even though there is a high inter-individual consistency for the main cortical folds, this is not the case when we examine the exact shapes and details of the folding patterns. Because of this complexity, characterizing the cortical folding variability and relating them to subjects' behavioral characteristics or pathologies is still an open scientific problem. Classical approaches include labeling a few specific patterns, either manually or semi-automatically, based on geometric distances, but the recent availability of MRI image datasets of tens of thousands of subjects makes modern deep-learning techniques particularly attractive. Here, we build a self-supervised deep-learning model to detect folding patterns in the cingulate region. We train a contrastive self-supervised model (SimCLR) on both Human Connectome Project (1101 subjects) and UKBioBank (21070 subjects) datasets with topological-based augmentations on the cortical skeletons, which are topological objects that capture the shape of the folds. We explore several backbone architectures (convolutional network, DenseNet, and PointNet) for the SimCLR. For evaluation and testing, we perform a linear classification task on a database manually labeled for the presence of the "double-parallel" folding pattern in the cingulate region, which is related to schizophrenia characteristics. The best model, giving a test AUC of 0.76, is a convolutional network with 6 layers, a 10-dimensional latent space, a linear projection head, and using the branch-clipping augmentation. This is the first time that a self-supervised deep learning model has been applied to cortical skeletons on such a large dataset and quantitatively evaluated. We can now envisage the next step: applying it to other brain regions to detect other biomarkers., Comment: 9 pages, 6 figures, 1 table, SPIE Imaging 2024

The verification of liveness conditions is an important aspect of state-based rigorous methods. This article investigates this problem in a fragment $\square$LTL of the logic LTL(EB), the integration of the UNTIL-fragment of Pnueli's linear time temporal logic (LTL) and the logic of Event-B, in which the most commonly used liveness conditions can be expressed. For this fragment a sound set of derivation rules is developed, which is also complete under mild restrictions for Event-B machines., Comment: 22 pages

Determining cell identities in imaging sequences is an important yet challenging task. The conventional method for cell identification is via cell tracking, which is complex and can be time-consuming. In this study, we propose an innovative approach to cell identification during early $\textit{C. elegans}$ embryogenesis using machine learning. Cell identification during $\textit{C. elegans}$ embryogenesis would provide insights into neural development with implications for higher organisms including humans. We employed random forest, MLP, and LSTM models, and tested cell classification accuracy on 3D time-lapse confocal datasets spanning the first 4 hours of embryogenesis. By leveraging a small number of spatial-temporal features of individual cells, including cell trajectory and cell fate information, our models achieve an accuracy of over 91%, even with limited data. We also determine the most important feature contributions and can interpret these features in the context of biological knowledge. Our research demonstrates the success of predicting cell identities in time-lapse imaging sequences directly from simple spatio-temporal features.

We propose and analyze discontinuous Galerkin (dG) approximations to 3D-1D coupled systems which model diffusion in a 3D domain containing a small inclusion reduced to its 1D centerline. Convergence to weak solutions of a steady state problem is established via deriving a posteriori error estimates and bounds on residuals defined with suitable lift operators. For the time dependent problem, a backward Euler dG formulation is also presented and analysed. Further, we propose a dG method for networks embedded in 3D domains, which is, up to jump terms, locally mass conservative on bifurcation points. Numerical examples in idealized geometries portray our theoretical findings, and simulations in realistic 1D networks show the robustness of our method.

Observational constraints on dust properties in protoplanetary disks are key to better understanding disks' evolution. We continue our exploration of the protoplanetary disk around AB Aur by characterizing its dust properties. We present ALMA observations at 2.2 mm and VLA observations at 6.8 mm. Together with previous ALMA and NOEMA observations at 0.87 and 1.1 mm, these observations are used to compute global spectral index profiles as well as spectral index maps. On the interpretation side, we present the results of a simple isothermal slab model to help constrain dust properties along the ring of continuum emission. We also present results of dust radiative transfer calculations based on a disc-planet hydrodynamical simulation to explain how the azimuthal contrast ratio of the ring emission varies with millimeter wavelength. The spectral energy distribution and the radial profiles of the spectral index indicate that the radiation from the compact source towards the center is not dominated by dust thermal emission, but most likely by free-free emission originating in the radio jet: it constitutes 93% of the emission at 6.8 mm, and 37% at 0.87 mm. The protoplanetary disk has a typical spectral index of 2.3. We estimate a dust disk mass of 8$\rm \times 10^{-5}$ M$\rm _{\odot}$ which, assuming a mean gas-to-dust ratio of 40, gives a total disk mass of 3.2$\rm \times 10^{-3}$ M$\rm _{\odot}$. The azimuthal contrast ratio of the ring outside the millimeter cavity is smaller at 2.2 mm than at 1.1 mm, in agreement with previous findings. The VLA image shows several knots of $5\sigma$ emission all along the ring, which are consistent with the ring emission being nearly axisymmetric at that wavelength. The decrease in the azimuthal contrast ratio of the ring emission from 0.87 to 6.8 mm can be explained by a dust-losing decaying vortex at the outer edge of a planet gap., Comment: 13 pages, 11 figures

This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging from complex reasoning tasks to on-device memory-constrained use-cases. Evaluation on a broad range of benchmarks shows that our most-capable Gemini Ultra model advances the state of the art in 30 of 32 of these benchmarks - notably being the first model to achieve human-expert performance on the well-studied exam benchmark MMLU, and improving the state of the art in every one of the 20 multimodal benchmarks we examined. We believe that the new capabilities of the Gemini family in cross-modal reasoning and language understanding will enable a wide variety of use cases. We discuss our approach toward post-training and deploying Gemini models responsibly to users through services including Gemini, Gemini Advanced, Google AI Studio, and Cloud Vertex AI.

We construct using variational methods Hamiltonian Stationary Surfaces with Isolated Schoen-Wolfson Conical Singularities. We obtain these surfaces through a convergence process reminiscent to the Ginzburg-Landau asymptotic analysis in the strongly repulsive regime. We describe in particular how the prescription of Schoen Wolfson conical singularities is related to optimal Wente constants.

In this paper, we present a method of multi-robot motion planning by biasing centralized, sampling-based tree search with decentralized, data-driven steer and distance heuristics. Over a range of robot and obstacle densities, we evaluate the plain Rapidly-expanding Random Trees (RRT), and variants of our method for double integrator dynamics. We show that whereas plain RRT fails in every instance to plan for $4$ robots, our method can plan for up to 16 robots, corresponding to searching through a very large 65-dimensional space, which validates the effectiveness of data-driven heuristics at combating exponential search space growth. We also find that the heuristic information is complementary; using both heuristics produces search trees with lower failure rates, nodes, and path costs when compared to using each in isolation. These results illustrate the effective decomposition of high-dimensional joint-space motion planning problems into local problems.

We prove that $p $-harmonic systems with antisymmetric potentials can be written in divergence form as a conservation law. This extends to the $p$-harmonic framework the original work from 2006 of the second author for $p=2$ (arXiv:math/0603380). We give applications of the existence of this divergence structure in the analysis $p\rightarrow 2$.

On the unit tangent bundle of a compact Riemannian surface of constant nonzero curvature, we study semiclassical Schr{\"o}dinger operators associated with the natural sub-Riemannian Laplacian built along the horizontal bundle. In that setup , the involved Reeb flow is periodic and we show that high-frequency Schr{\"o}dinger eigenfunctions enjoy extra regularity properties. As an application, we derive regularity properties for low-energy eigenmodes of semiclassical magnetic Schr{\"o}dinger operators on the underlying surface by considering joint eigenfunctions with the Reeb vector field., Comment: 20 pages