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On long enough timescales, chaotic diffusion has the potential to significantly alter the appearance of a dynamical system. The solar system is no exception: diffusive processes take part in the transportation of small bodies and provide dynamical pathways even for the distant trans-Neptunian objects to reach the inner solar system. In this Letter, we carry out a thorough investigation of the nature of chaotic diffusion. We analyze the temporal evolution of the mean squared displacement of ten thousand ensembles of test particles and quantify in each case the diffusion exponent (enabling the classification between normal, sub-, and super-diffusion), the generalized diffusion coefficient, and a characteristic diffusion timescale, too. This latter quantity is compared with an entropy-based timescale, and the two approaches are studied in light of direct computations as well. Our results are given in the context of two-dimensional maps, thereby facilitating the understanding of the relationship between the typical phase space structures and the properties of chaotic diffusion., Comment: 6 pages, 7 figures, accepted for publication in the open-access journal MNRAS

Studying significant network patterns, known as graphlets (or motifs), has been a popular approach to understand the underlying organizing principles of complex networks. Statistical significance is routinely assessed by comparing to null models that randomize the connections while preserving some key aspects of the data. However, in signed networks, capturing both positive (friendly) and negative (hostile) relations, the results have been controversial and also at odds with the classical theory of structural balance. We show that this is largely due to the fact that large-scale signed networks exhibit a poor correlation between the number of positive and negative ties of each node. As a solution, here we propose a null model based on the maximum entropy framework that preserves both the signed degrees and the network topology (STP randomization). With STP randomization the results change qualitatively and most social networks consistently satisfy strong structural balance, both at the level of triangles and larger graphlets. We propose a potential underlying mechanism of the observed patterns in signed social networks and outline further applications of STP randomization.

Large language models (LLMs) can capture rich representations of concepts that are useful for real-world tasks. However, language alone is limited. While existing LLMs excel at text-based inferences, health applications require that models be grounded in numerical data (e.g., vital signs, laboratory values in clinical domains; steps, movement in the wellness domain) that is not easily or readily expressed as text in existing training corpus. We demonstrate that with only few-shot tuning, a large language model is capable of grounding various physiological and behavioral time-series data and making meaningful inferences on numerous health tasks for both clinical and wellness contexts. Using data from wearable and medical sensor recordings, we evaluate these capabilities on the tasks of cardiac signal analysis, physical activity recognition, metabolic calculation (e.g., calories burned), and estimation of stress reports and mental health screeners.

Observations of quasars reveal that many supermassive black holes (BHs) were in place less than 700 million years after the Big Bang. However, the origin of the first BHs remains a mystery. Seeds of the first BHs are postulated to be either light (i.e., $10-100~\rm{M_{\odot}})$, remnants of the first stars or heavy (i.e., $10^4-10^5~\rm{M_{\odot}})$, originating from the direct collapse of gas clouds. Harnessing recent data from the Chandra X-ray Observatory, we report the detection of an X-ray-luminous massive BH in a gravitationally-lensed galaxy identified by JWST at $z\approx10.3$ behind the cluster lens Abell 2744. This heavily-obscured quasar with a bolometric luminosity of $L_{\rm bol}\sim5\times10^{45}~\rm{erg\ s^{-1}}$ harbors a $M_{\rm BH}\sim10^7-10^8~\rm{M_{\odot}}$ BH assuming accretion at the Eddington limit. This mass is comparable to the inferred stellar mass of its host galaxy, in contrast to what is found in the local Universe wherein the BH mass is $\sim0.1\%$ of the host galaxy's stellar mass. The combination of such a high BH mass and large BH-to-galaxy stellar mass ratio just $\sim$500 Myrs after the Big Bang was theoretically predicted and is consistent with a picture wherein BHs originated from heavy seeds., Comment: 27 pages, 6 figures, accepted

We present an exact approach to analyze and quantify the sensitivity of higher moments of probabilistic loops with symbolic parameters, polynomial arithmetic and potentially uncountable state spaces. Our approach integrates methods from symbolic computation, probability theory, and static analysis in order to automatically capture sensitivity information about probabilistic loops. Sensitivity information allows us to formally establish how value distributions of probabilistic loop variables influence the functional behavior of loops, which can in particular be helpful when choosing values of loop variables in order to ensure efficient/expected computations. Our work uses algebraic techniques to model higher moments of loop variables via linear recurrence equations and introduce the notion of sensitivity recurrences. We show that sensitivity recurrences precisely model loop sensitivities, even in cases where the moments of loop variables do not satisfy a system of linear recurrences. As such, we enlarge the class of probabilistic loops for which sensitivity analysis was so far feasible. We demonstrate the success of our approach while analyzing the sensitivities of probabilistic loops.

The MACE architecture represents the state of the art in the field of machine learning force fields for a variety of in-domain, extrapolation and low-data regime tasks. In this paper, we further evaluate MACE by fitting models for published benchmark datasets. We show that MACE generally outperforms alternatives for a wide range of systems from amorphous carbon, universal materials modelling, and general small molecule organic chemistry to large molecules and liquid water. We demonstrate the capabilities of the model on tasks ranging from constrained geometry optimisation to molecular dynamics simulations and find excellent performance across all tested domains. We show that MACE is very data efficient, and can reproduce experimental molecular vibrational spectra when trained on as few as 50 randomly selected reference configurations. We further demonstrate that the strictly local atom-centered model is sufficient for such tasks even in the case of large molecules and weakly interacting molecular assemblies.

Cryptographic protocols are hard to design and prove correct, as witnessed by the ever-growing list of attacks even on protocol standards. Symbolic models of cryptography enable automated formal security proofs of such protocols against an idealized model, which abstracts away from the algebraic properties of cryptographic schemes and thus misses attacks. Computational models yield rigorous guarantees but support at present only interactive proofs and/or restricted classes of protocols. A promising approach is given by the computationally complete symbolic attacker (CCSA), formalized in the BC Logic, which aims at bridging and getting the best of the two worlds, obtaining cryptographic guarantees by symbolic analysis. The BC Logic is supported by a recently developed interactive theorem prover, Squirrel, which enables machine-checked interactive security proofs, as opposed to automated ones, thus requiring expert knowledge. We introduce the CryptoVampire cryptographic protocol verifier, which for the first time fully automates proofs of trace properties in the BC Logic. The key technical contribution is a first-order (FO) formalization of protocol properties with tailored handling of subterm relations. We overcome the burden of interactive proving in higher-order (HO) logic and automatically establish soundness of cryptographic protocols using only FO reasoning. On the theoretical side, we restrict full FO logic with cryptographic axioms to ensure that, by losing the expressivity of the HO BC Logic, we do not lose soundness. On the practical side, CryptoVampire integrates dedicated proof techniques using FO saturation algorithms and heuristics, which enable leveraging the state-of-the-art Vampire FO theorem prover as the underlying proving engine. Our experimental results show CryptoVampire's effectiveness of as a standalone verifier and in terms of automation support for Squirrel.

The brain is a complex system comprising a myriad of interacting elements, posing significant challenges in understanding its structure, function, and dynamics. Network science has emerged as a powerful tool for studying such intricate systems, offering a framework for integrating multiscale data and complexity. Here, we discuss the application of network science in the study of the brain, addressing topics such as network models and metrics, the connectome, and the role of dynamics in neural networks. We explore the challenges and opportunities in integrating multiple data streams for understanding the neural transitions from development to healthy function to disease, and discuss the potential for collaboration between network science and neuroscience communities. We underscore the importance of fostering interdisciplinary opportunities through funding initiatives, workshops, and conferences, as well as supporting students and postdoctoral fellows with interests in both disciplines. By uniting the network science and neuroscience communities, we can develop novel network-based methods tailored to neural circuits, paving the way towards a deeper understanding of the brain and its functions., Comment: 19 pages, 1 figure, 1 box

We study the set of intersection sizes of a k-dimensional affine subspace and a point set of size m \in [0, 2^n] of the n-dimensional binary affine space AG(n,2). Following the theme of Erd\H{o}s, F\"uredi, Rothschild and T. S\'os, we partially determine which local densities in k-dimensional affine subspaces are unavoidable in all $m$-element point sets in the n-dimensional affine space. We also show constructions of point sets for which the intersection sizes with $k$-dimensional affine subspaces takes values from a set of a small size compared to 2^k. These are built up from affine subspaces and so-called subspace evasive sets. Meanwhile, we improve the best known upper bounds on subspace evasive sets and apply results concerning the canonical signed-digit (CSD) representation of numbers., Comment: some typos fixed, further reference added

Close-in, sub-stellar companions to $\delta$ Scuti type stars present a highly suitable testbed for examining how planetary-mass objects can influence stellar pulsations. We aim to constrain the mass of HD 31221 b, probe its atmosphere, and demonstrate how it affects the pulsational pattern of its host, HD 31221. We made use of the available data from the short-cadence Transiting Exoplanet Survey Satellite (TESS). We modeled the nine observed transits and the out-of-phase variations, including Doppler beaming, ellipsoidal variations, and the reflection effect. We also incorporated ground-based photometry from the MuSCAT2 imager installed at the 1.52 m Telescopio Carlos Sanchez in the Teide Observatory, Spain. We found HD 31221 b to have an orbital period of $4.66631 \pm 0.00011$ days, with a radius of $1.32 \pm 0.14$ R$_J$ and a mass of $11.5 \pm 10.3$ M$_J$ (from the ellipsoidal effect), making it consistent with either a brown dwarf or a giant planet. As HD 31221 is a rapid rotator ($v \sin I_\star = 175.31 \pm 1.74$ km s$^{-1}$), we deduced the spin-orbit misalignment to be $\lambda = -121.6 \pm 14.4^\circ$ and $I_\star = 55.9 \pm 11.3^\circ$. The phase curve is dominated by the reflection effect, with a geometric albedo of $1.58 \pm 0.50$. We also found evidence that HD 31221 is a $\delta$ Scuti/$\gamma$ Doradus hybrid pulsator. There are three cases for which the $3$rd, $85$th, and $221$st orbital harmonics almost exactly coincide with peaks in the Fourier spectrum of the star, hinting at tidally perturbed stellar oscillations. HD 31221 b is the third substellar object that is found to be disrupting the pulsations of its host, following HAT-P-2 and WASP-33. Additional photometric observations by CHEOPS and/or PLATO can be used to further constrain its mass and provide a more in-depth analysis of its atmosphere., Comment: Accepted for publication as a Letter in A&A, 12 pages, 10 figures

We compare the predictions of the GUMICS$-$4 global magnetohydrodynamic model for the interaction of the solar wind with the Earth's magnetosphere with Cluster~SC3 measurements for over one year, from January 29, 2002, to February 2, 2003. In particular, we compare model predictions with the north/south component of the magnetic field ($B_{z}$) seen by the magnetometer, the component of the velocity along the Sun-Earth line ($V_{x}$), and the plasma density as determined from a top hat plasma spectrometer and the spacecraft's potential from the electric field instrument. We select intervals in the solar wind, the magnetosheath, and the magnetosphere where these instruments provided good-quality data, and the model correctly predicted the region in which the spacecraft is located. We determine the location of the bow shock, the magnetopause, and the neutral sheet from the spacecraft measurements and compare these locations to those predicted by the simulation. The GUMICS$-$4 model agrees well with the measurements in the solar wind however its accuracy is worse in the magnetosheath. The simulation results are not realistic in the magnetosphere. The bow shock location is predicted well, however, the magnetopause location is less accurate. The neutral sheet positions are located quite accurately thanks to the special solar wind conditions when the $B_{y}$ component of the interplanetary magnetic field is small., Comment: submitted to the AGU Space Weather, 51 pages, 19 figures, 8 tables