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In this work, we study the dynamics of complex systems with time-dependent transition rates, focusing on $p$-adic analysis in modeling such systems. Starting from the master equation that governs the stochastic dynamics of a system with a large number of interacting components, we generalize it by $p$-adically parametrizing the metabasins to account for hierarchically organized states within the energy landscape. This leads to a non-homogeneous Markov process described by a time-dependent operator acting on an ultrametric space. We prove the well-posedness of the initial value problem and analyze the stochastic nature of the master equation with time-dependent transition-operator. We demonstrate how ultrametricity simplifies the description of intra-metabasin dynamics without increasing computational complexity. We apply our theoretical framework to two scenarios: glass relaxation under rapid cooling and protein folding dynamics influenced by temperature variations. In the glass relaxation model, we observe anomalous relaxation behavior where the dynamics slows during cooling, with lasting effects depending on how drastic the temperature drop is. In the protein folding model, we incorporate temperature-dependent energy barriers and transition rates to simulate folding and unfolding processes across the melting temperature. Our results capture a "whiplash" effect: from an unfolded state, the system folds and then returns to an unfolded state (which may differ from the initial one) in response to temperature changes. This study aims to demonstrate the effectiveness of $p$-adic parametrization and ultrametric analysis in modeling complex systems with dynamic transition rates, providing analytical solutions to relaxation processes in material and biological systems., Comment: 32 pages, 9 figures

We present the first broadband near- to mid-infrared (3-12 microns) transmission spectrum of the highly-irradiated (T_eq = 981 K) M dwarf rocky planet L 168-9 b (TOI-134 b) observed with the NIRSpec and MIRI instruments aboard JWST. We measure the near-infrared transit depths to a combined median precision of 20 ppm across the three visits in 54 spectroscopic channels with uniform widths of 60 pixels (~0.2 microns wide; R~100), and the mid-infrared transit depths to 61 ppm median precision in 48 wavelength bins (~0.15 microns wide; R~50). We compare the transmission spectrum of L 168-9 b to a grid of 1D thermochemical equilibrium forward models, and rule out atmospheric metallicities of less than 100x solar (mean molecular weights <4 g mol$^{-1}$) to 3-sigma confidence assuming high surface pressure (>1 bar), cloudless atmospheres. Based on photoevaporation models for L 168-9 b with initial atmospheric mass fractions ranging from 2-100%, we find that this planet could not have retained a primordial H/He atmosphere beyond the first 200 Myr of its lifetime. Follow-up MIRI eclipse observations at 15 microns could make it possible to confidently identify a CO2-dominated atmosphere on this planet if one exists., Comment: 19 pages, 11 figures, accepted for publication in The Astronomical Journal

We introduce efficient differentially private (DP) algorithms for several linear algebraic tasks, including solving linear equalities over arbitrary fields, linear inequalities over the reals, and computing affine spans and convex hulls. As an application, we obtain efficient DP algorithms for learning halfspaces and affine subspaces. Our algorithms addressing equalities are strongly polynomial, whereas those addressing inequalities are weakly polynomial. Furthermore, this distinction is inevitable: no DP algorithm for linear programming can be strongly polynomial-time efficient.

Active galactic nucleus (AGN) growth in disk-dominated, merger-free galaxies is poorly understood, largely due to the difficulty in disentangling the AGN emission from that of the host galaxy. By carefully separating this emission, we examine the differences between AGNs in galaxies hosting a (possibly) merger-grown, classical bulge, and AGNs in secularly grown, truly bulgeless disk galaxies. We use GALFIT to obtain robust, accurate morphologies of 100 disk-dominated galaxies imaged with the Hubble Space Telescope. Adopting an inclusive definition of classical bulges, we detect a classical bulge component in $53.3 \pm 0.5$ per cent of the galaxies. These bulges were not visible in Sloan Digital Sky Survey photometry, however these galaxies are still unambiguously disk-dominated, with an average bulge-to-total luminosity ratio of $0.1 \pm 0.1$. We find some correlation between bulge mass and black hole mass for disk-dominated galaxies, though this correlation is significantly weaker in comparison to the relation for bulge-dominated or elliptical galaxies. Furthermore, a significant fraction ($\gtrsim 90$ per cent) of our black holes are overly massive when compared to the relationship for elliptical galaxies. We find a weak correlation between total stellar mass and black hole mass for the disk-dominated galaxies, hinting that the stochasticity of black hole-galaxy co-evolution may be higher disk-dominated than bulge-dominated systems., Comment: 14 pages, 6 figures, 2 tables. Submitted to MNRAS

For equality-constrained linear mixed-integer programs (MIP) defined by rational data, it is known that the subadditive dual is a strong dual and that there exists an optimal solution of a particular form, termed generator subadditive function. Motivated by these results, we explore the connection between Lagrangian duality, subadditive duality and generator subadditive functions for general equality-constrained MIPs where the vector of variables is constrained to be in a monoid. We show that strong duality holds via generator subadditive functions under certain conditions. For the case when the monoid is defined by the set of all mixed-integer points contained in a convex cone, we show that strong duality holds under milder conditions and over a more restrictive set of dual functions. Finally, we provide some examples of applications of our results.

Ultraviolet wavelengths offer unique insights into aerosols in exoplanetary atmospheres. However, only a handful of exoplanets have been observed in the ultraviolet to date. Here, we present the ultraviolet-visible transmission spectrum of the inflated hot Jupiter WASP-127b. We observed one transit of WASP-127b with WFC3/UVIS G280 as part of the Hubble Ultraviolet-optical Survey of Transiting Legacy Exoplanets (HUSTLE), obtaining a transmission spectrum from 200-800 nm. Our reductions yielded a broad-band transit depth precision of 91 ppm and a median precision of 240 ppm across 59 spectral channels. Our observations are suggestive of a high-altitude cloud layer with forward modeling showing they are composed of sub-micron particles and retrievals indicating a high opacity patchy cloud. While our UVIS/G280 data only offers weak evidence for Na, adding archival HST WFC3/IR and STIS observations raises the overall Na detection significance to 4.1-sigma. Our work demonstrates the capabilities of HST WFC3/UVIS G280 observations to probe the aerosols and atmospheric composition of transiting hot Jupiters with comparable precision to HST STIS., Comment: 25 pages, 8 figures, 6 tables

Motivated by multi-topology building and city model data, first a lossless representation of multiple $T_0$-topologies on a given finite set by a vertex-edge-weighted graph is given, and the subdominant ultrametric of the associated weighted graph distance matrix is proposed as an index structure for these data. This is applied in a heuristic parallel topological sort algorithm for edge-weighted directed acyclic graphs. Such structured data are of interest in simulation of processes like heat flows on building or city models on distributed processors. With this in view, the bulk of this article calculates the spectra of certain unbounded self-adjoint $p$-adic Laplacian operators on the $L^2$-spaces of a compact open subdomain of the $p$-adic number field associated with a finite graph $G$ with respect to the restricted Haar measure. as well as to a Radon measure coming from an ultrametric on the vertices of $G$ with the help of $p$-adic polynomial interpolation. In the end, error bounds are given for the solutions of the corresponding heat equations by finite approximations of such operators., Comment: 30 pages

Pulsar timing arrays can detect continuous nanohertz gravitational waves emitted by individual supermassive black hole binaries. The data analysis procedure can be formulated within a time-domain, state-space framework, in which the radio timing observations are related to a temporal sequence of latent states, namely the intrinsic pulsar spin frequency. The achromatic wandering of the pulsar spin frequency is tracked using a Kalman filter concurrently with the pulse frequency modulation induced by a gravitational wave from a single source. The modulation is the sum of terms proportional to the gravitational wave strain at the Earth and at every pulsar in the array. Here we generalize previous state-space formulations of the pulsar timing array problem to include the pulsar terms; that is, we copy the pulsar terms from traditional, non-state-space analyses over to the state-space framework. The performance of the generalized Kalman filter is tested using astrophysically representative software injections in Gaussian measurement noise. It is shown that including the pulsar terms corrects for previously identified biases in the parameter estimates (especially the sky position of the source) which also arise in traditional matched-filter analyses that exclude the pulsar terms. Additionally, including the pulsar terms decreases the minimum detectable strain by $14\%$. Overall, the study verifies that the pulsar terms do not raise any special extra impediments for the state-space framework, beyond those studied in traditional analyses. The inspiral-driven evolution of the wave frequency at the Earth and at the retarded time at every pulsar in the array is also investigated., Comment: 24 pages, 13 figures. Accepted for publication in MNRAS. arXiv admin note: text overlap with arXiv:2409.14613

Modern cryptographic methods for implementing privacy-preserving LLMs such as Homomorphic Encryption (HE) require the LLMs to have a polynomial form. Forming such a representation is challenging because Transformers include non-polynomial components, such as Softmax and layer normalization. Previous approaches have either directly approximated pre-trained models with large-degree polynomials, which are less efficient over HE, or replaced non-polynomial components with easier-to-approximate primitives before training, e.g., Softmax with pointwise attention. The latter approach might introduce scalability challenges. We present a new HE-friendly variant of self-attention that offers a stable form for training and is easy to approximate with polynomials for secure inference. Our work introduces the first polynomial LLMs with 32 layers and over a billion parameters, exceeding the size of previous models by more than tenfold. The resulting models demonstrate reasoning and in-context learning (ICL) capabilities comparable to standard transformers of the same size, representing a breakthrough in the field. Finally, we provide a detailed latency breakdown for each computation over encrypted data, paving the way for further optimization, and explore the differences in inductive bias between transformers relying on our HE-friendly variant and standard transformers. Our code is attached as a supplement.

In this article we study virtual nonholonomic constraints, which are relations between the generalized coordinates and momenta of a mechanical system that can be enforced via feedback control. We design a constraint which emulates gymnastics giant motion in an acrobot, and prove that this constraint can inject or dissipate energy based on the sign of a design parameter. The proposed constraint is tested both in simulation and experimentally on a real-world acrobot, demonstrating highly effective energy regulation properties and robustness to a variety of disturbances.

The multifaceted nature of experience poses a challenge to the study of consciousness. Traditional neuroscientific approaches often concentrate on isolated facets, such as perceptual awareness or the global state of consciousness and construct a theory around the relevant empirical paradigms and findings. Theories of consciousness are, therefore, often difficult to compare; indeed, there might be little overlap in the phenomena such theories aim to explain. Here, we take a different approach: starting with active inference, a first principles framework for modelling behaviour as (approximate) Bayesian inference, and building up to a minimal theory of consciousness, which emerges from the shared features of computational models derived under active inference. We review a body of work applying active inference models to the study of consciousness and argue that there is implicit in all these models a small set of theoretical commitments that point to a minimal (and testable) theory of consciousness.

The first very long baseline interferometry (VLBI) detections at 870$\mu$m wavelength (345$\,$GHz frequency) are reported, achieving the highest diffraction-limited angular resolution yet obtained from the surface of the Earth, and the highest-frequency example of the VLBI technique to date. These include strong detections for multiple sources observed on inter-continental baselines between telescopes in Chile, Hawaii, and Spain, obtained during observations in October 2018. The longest-baseline detections approach 11$\,$G$\lambda$ corresponding to an angular resolution, or fringe spacing, of 19$\mu$as. The Allan deviation of the visibility phase at 870$\mu$m is comparable to that at 1.3$\,$mm on the relevant integration time scales between 2 and 100$\,$s. The detections confirm that the sensitivity and signal chain stability of stations in the Event Horizon Telescope (EHT) array are suitable for VLBI observations at 870$\mu$m. Operation at this short wavelength, combined with anticipated enhancements of the EHT, will lead to a unique high angular resolution instrument for black hole studies, capable of resolving the event horizons of supermassive black holes in both space and time., Comment: Corresponding author: S. Doeleman

Massive stars experience strong mass-loss, producing a dense, H-rich circumstellar medium (CSM). After the explosion, the collision and continued interaction of the supernova (SN) ejecta with the CSM power the light curve through the conversion of kinetic energy into radiation. When the interaction is strong, the light curve shows a broad peak and high luminosity lasting for a relatively long time. Also the spectral evolution is slower, compared to non-interacting SNe. Energetic shocks between the ejecta and the CSM create the ideal conditions for particle acceleration and production of high-energy (HE) neutrinos above 1 TeV. In this paper, we study four strongly-interacting Type IIn SNe: 2021acya, 2021adxl, 2022qml, and 2022wed to highlight their peculiar characteristics, derive the kinetic energy of the explosion and the characteristics of the CSM, infer clues on the possible progenitors and their environment and relate them to the production of HE neutrinos. The SNe analysed in this sample exploded in dwarf, star-forming galaxies and they are consistent with energetic explosions and strong interaction with the surrounding CSM. For SNe 2021acya and 2022wed, we find high CSM masses and mass-loss rates, linking them to very massive progenitors. For SN 2021adxl, the spectral analysis and less extreme CSM mass suggest a stripped-envelope massive star as possible progenitor. SN 2022qml is marginally consistent with being a Type Ia thermonuclear explosion embedded in a dense CSM. The mass-loss rates for all SNe are consistent with the expulsion of several solar masses of material during eruptive episodes in the last few decades before the explosion. Finally, we find that the SNe in our sample are marginally consistent with HE neutrino production., Comment: Submitted to A&A

Quantization has established itself as the primary approach for decreasing the computational and storage expenses associated with Large Language Models (LLMs) inference. The majority of current research emphasizes quantizing weights and activations to enable low-bit general-matrix-multiply (GEMM) operations, with the remaining non-linear operations executed at higher precision. In our study, we discovered that following the application of these techniques, the primary bottleneck in LLMs inference lies in the softmax layer. The softmax operation comprises three phases: exponent calculation, accumulation, and normalization, Our work focuses on optimizing the first two phases. We propose an analytical approach to determine the optimal clipping value for the input to the softmax function, enabling sub-4-bit quantization for LLMs inference. This method accelerates the calculations of both $e^x$ and $\sum(e^x)$ with minimal to no accuracy degradation. For example, in LLaMA1-30B, we achieve baseline performance with 2-bit quantization on the well-known "Physical Interaction: Question Answering" (PIQA) dataset evaluation. This ultra-low bit quantization allows, for the first time, an acceleration of approximately 4x in the accumulation phase. The combination of accelerating both $e^x$ and $\sum(e^x)$ results in a 36.9% acceleration in the softmax operation.

Agentic AIs $-$ AIs that are capable and permitted to undertake complex actions with little supervision $-$ mark a new frontier in AI capabilities and raise new questions about how to safely create and align such systems with users, developers, and society. Because agents' actions are influenced by their attitudes toward risk, one key aspect of alignment concerns the risk profiles of agentic AIs. Risk alignment will matter for user satisfaction and trust, but it will also have important ramifications for society more broadly, especially as agentic AIs become more autonomous and are allowed to control key aspects of our lives. AIs with reckless attitudes toward risk (either because they are calibrated to reckless human users or are poorly designed) may pose significant threats. They might also open 'responsibility gaps' in which there is no agent who can be held accountable for harmful actions. What risk attitudes should guide an agentic AI's decision-making? How might we design AI systems that are calibrated to the risk attitudes of their users? What guardrails, if any, should be placed on the range of permissible risk attitudes? What are the ethical considerations involved when designing systems that make risky decisions on behalf of others? We present three papers that bear on key normative and technical aspects of these questions.

In the last few years, economic agent-based models have made the transition from qualitative models calibrated to match stylised facts to quantitative models for time series forecasting, and in some cases, their predictions have performed as well or better than those of standard models (see, e.g. Poledna et al. (2023a); Hommes et al. (2022); Pichler et al. (2022)). Here, we build on the model of Poledna et al., adding several new features such as housing markets, realistic synthetic populations of individuals with income, wealth and consumption heterogeneity, enhanced behavioural rules and market mechanisms, and an enhanced credit market. We calibrate our model for all 38 OECD member countries using state-of-the-art approximate Bayesian inference methods and test it by making out-of-sample forecasts. It outperforms both the Poledna and AR(1) time series models by a highly statistically significant margin. Our model is built within a platform we have developed, making it easy to build, run, and evaluate alternative models, which we hope will encourage future work in this area.

Maximization of submodular functions under various constraints is a fundamental problem that has been studied extensively. A powerful technique that has emerged and has been shown to be extremely effective for such problems is the following. First, a continues relaxation of the problem is obtained by relaxing the (discrete) set of feasible solutions to a convex body, and extending the discrete submodular function $f$ to a continuous function $F$ known as the multilinear extension. Then, two algorithmic steps are implemented. The first step approximately solves the relaxation by finding a fractional solution within the convex body that approximately maximizes $F$; and the second step rounds this fractional solution to a feasible integral solution. While this ``fractionally solve and then round'' approach has been a key technique for resolving many questions in the field, the main drawback of algorithms based on it is that evaluating the multilinear extension may require a number of value oracle queries to $f$ that is exponential in the size of $f$'s ground set. The only known way to tackle this issue is to approximate the value of $F$ via sampling, which makes all algorithms based on this approach inherently randomized and quite slow. In this work, we introduce a new tool, that we refer to as the extended multilinear extension, designed to derandomize submodular maximization algorithms that are based on the successful ``solve fractionally and then round'' approach. We demonstrate the effectiveness of this new tool on the fundamental problem of maximizing a submodular function subject to a matroid constraint, and show that it allows for a deterministic implementation of both the fractionally solving step and the rounding step of the above approach. As a bonus, we also get a randomized algorithm for the problem with an improved query complexity., Comment: 38 pages

Continuous nanohertz gravitational waves from individual supermassive black hole binaries may be detectable with pulsar timing arrays. A novel search strategy is developed, wherein intrinsic achromatic spin wandering is tracked simultaneously with the modulation induced by a single gravitational wave source in the pulse times of arrival. A two-step inference procedure is applied within a state-space framework, such that the modulation is tracked with a Kalman filter, which then provides a likelihood for nested sampling. The procedure estimates the static parameters in the problem, such as the sky position of the source, without fitting for ensemble-averaged statistics such as the power spectral density of the timing noise, and therefore complements traditional parameter estimation methods. It also returns the Bayes factor relating a model with a single gravitational wave source to one without, complementing traditional detection methods. It is shown via astrophysically representative software injections in Gaussian measurement noise that the procedure distinguishes a gravitational wave from pure noise down to a characteristic wave strain of $h_0 \approx 2 \times 10^{-15}$. Full posterior distributions of model parameters are recovered and tested for accuracy. There is a bias of $\approx 0.3$ rad in the marginalised one-dimensional posterior for the orbital inclination $\iota$, introduced by dropping the so-called `pulsar terms'. Smaller biases $\lesssim 10 \%$ are also observed in other static parameters., Comment: 26 pages, 11 figures. Accepted for publication in MNRAS

In this paper, a definition of the gain and added noise of impedance matching networks for scanning microwave microscopy is given. This definition can be used to compare different impedance matching techniques independently of the instrument used to measure the S-parameter. As a demonstration, impedance matching devices consisting of a Beatty line, a tuner, and interferometric setups with and without amplifiers have been investigated. Measurement frequencies up to 28 GHz are used, and the maximal resulting gain found was 9504.7 per Siemens., Comment: IEEE Transactions on Instrumentation and Measurement (2024)

Quantum state discrimination plays a central role in quantum information and communication. For the discrimination of optical quantum states, the two most widely adopted measurement techniques are photon detection, which produces discrete outcomes, and homodyne detection, which produces continuous outcomes. While various protocols using photon detection have been proposed for optimal and near-optimal discrimination between two coherent states, homodyne detection is known to have higher error rates, with its performance often referred to as the Gaussian limit. In this work, we demonstrate that, despite the fundamental differences between discretely labelled and continuously labelled measurements, continuously labelled non-Gaussian measurements can also achieve near-optimal coherent state discrimination. We explicitly design two coherent state discrimination protocols based on non-Gaussian unitary operations combined with homodyne detection and orthogonal polynomials, which surpass the Gaussian limit. Our results show that photon detection is not required for near-optimal coherent state discrimination and that we can achieve error rates close to the Helstrom bound at low energies with continuously labelled measurements. We also find that our schemes maintain an advantage over the photon detection-based Kennedy receiver for a moderate range of coherent state amplitudes., Comment: 14 pages, 6 figures

We present a JWST NIRSpec transmission spectrum of the super-Earth exoplanet L 98-59 c. This small (R$_p=1.385\pm0.085$R$_\oplus$, M$_p=2.22\pm0.26$R$_\oplus$), warm (T$_\textrm{eq}=553$K) planet resides in a multi-planet system around a nearby, bright (J = 7.933) M3V star. We find that the transmission spectrum of L 98-59 c is featureless at the precision of our data. We achieve precisions of 22ppm in NIRSpec G395H's NRS1 detector and 36ppm in the NRS2 detector at a resolution R$\sim$200 (30 pixel wide bins). At this level of precision, we are able rule out primordial H$_2$-He atmospheres across a range of cloud pressure levels up to at least $\sim$0.1mbar. By comparison to atmospheric forward models, we also rule out atmospheric metallicities below $\sim$300$\times$ solar at 3$\sigma$ (or equivalently, atmospheric mean molecular weights below $\sim$10~g/mol). We also rule out pure methane atmospheres. The remaining scenarios that are compatible with our data include a planet with no atmosphere at all, or higher mean-molecular weight atmospheres, such as CO$_2$- or H$_2$O-rich atmospheres. This study adds to a growing body of evidence suggesting that planets $\lesssim1.5$R$_\oplus$ lack extended atmospheres., Comment: 21 Pages, 13 Figures; Accepted to AJ

The fault tolerance method currently used in High Performance Computing (HPC) is the rollback-recovery method by using checkpoints. This, like any other fault tolerance method, adds an additional energy consumption to that of the execution of the application. The objective of this work is to determine the factors that affect the energy consumption of the computing nodes on homogeneous cluster, when performing checkpoint and restart operations, on SPMD (Single Program Multiple Data) applications. We have focused on the energetic study of compute nodes, contemplating different configurations of hardware and software parameters. We studied the effect of performance states (states P) and power states (states C) of processors, application problem size, checkpoint software (DMTCP) and distributed file system (NFS) configuration. The results analysis allowed to identify opportunities to reduce the energy consumption of checkpoint and restart operations., Comment: 15 pages, 20 figures

Aerosol opacity has emerged as a critical factor controlling transmission and emission spectra. We provide a simple guideline for the effects of aerosol morphology on opacity and residence time in the atmosphere, as it pertains to transit observations, particularly those with flat spectra due to high altitude aerosols. This framework can be used for understanding complex cloud and haze particle properties before getting into detailed microphysical modeling. We consider high altitude aerosols to be composed of large fluffy particles that can have large residence times in the atmosphere and influence the deposition of stellar flux and/or the emergence of thermal emission in a different way than compact droplet particles, as generally modeled to date for extrasolar planetary atmospheres. We demonstrate the important influence of aggregate particle porosity and composition on the extent of the wavelength independent regime. We also consider how such fluffy particles reach such high altitudes and conclude that the most likely scenario is their local production at high altitudes via UV bombardment and subsequent blanketing of the atmosphere, rather than some mechanism of lofting or transport from the lower atmosphere., Comment: 29 pages, 20 figures, accepted for publication in PASP

The implementation of realistic quantum devices requires a solid understanding of the nonlocal resources present in quantum channels, and the effects of decoherence on them. Here we quantify nonlocality of bipartite quantum channels and identify its component resisting the effects of dephasing noise. Despite its classical nature, we demonstrate that the latter plays a relevant role in performing quantum protocols, such as state transformations and quantum coding for noisy communication. In the converse direction, we show that simulating certain stochastic processes with quantum channels undergoing decoherence has a communication advantage with respect to their classical simulation.

Biomechanics and human movement research often involves measuring multiple kinematic or kinetic variables regularly throughout a movement, yielding data that present as smooth, multivariate, time-varying curves and are naturally amenable to functional data analysis. It is now increasingly common to record the same movement repeatedly for each individual, resulting in curves that are serially correlated and can be viewed as longitudinal functional data. We present a new approach for modelling multivariate multilevel longitudinal functional data, with application to kinematic data from recreational runners collected during a treadmill run. For each stride, the runners' hip, knee and ankle angles are modelled jointly as smooth multivariate functions that depend on subject-specific covariates. Longitudinally varying multivariate functional random effects are used to capture the dependence among adjacent strides and changes in the multivariate functions over the course of the treadmill run. A basis modelling approach is adopted to fit the model -- we represent each observation using a multivariate functional principal components basis and model the basis coefficients using scalar longitudinal mixed effects models. The predicted random effects are used to understand and visualise changes in the multivariate functional data over the course of the treadmill run. In our application, our method quantifies the effects of scalar covariates on the multivariate functional data, revealing a statistically significant effect of running speed at the hip, knee and ankle joints. Analysis of the predicted random effects reveals that individuals' kinematics are generally stable but certain individuals who exhibit strong changes during the run can also be identified. A simulation study is presented to demonstrate the efficacy of the proposed methodology under realistic data-generating scenarios., Comment: Extends/ builds upon the work in arXiv:2408.08200

We present a multivariate functional mixed effects model for kinematic data from a large number of recreational runners. The runners' sagittal plane hip and knee angles are modelled jointly as a bivariate function with random effects functions used to account for the dependence among measurements from either side of the body. The model is fitted by first applying multivariate functional principal component analysis (mv-FPCA) and then modelling the mv-FPCA scores using scalar linear mixed effects models. Simulation and bootstrap approaches are introduced to construct simultaneous confidence bands for the fixed effects functions, and covariance functions are reconstructed to summarise the variability structure in the data and thoroughly investigate the suitability of the proposed model. In our scientific application, we observe a statistically significant effect of running speed on both the hip and knee angles. We also observe strong within-subject correlations, reflecting the highly idiosyncratic nature of running technique. Our approach is more generally applicable to modelling multiple streams of smooth kinematic or kinetic data measured repeatedly for multiple subjects in complex experimental designs.

We advocate for further prioritisation of atmospheric characterisation observations of high mass transiting exoplanets and brown dwarfs. This population acts as a unique comparative sample to the directly imaged exoplanet and brown dwarf populations, of which a range of JWST characterisation observations are planned. In contrast, only two observations of transiting exoplanets in this mass regime were performed in Cycle 1, and none are planned for Cycle 2. Such observations will: improve our understanding of how irradiation influences high gravity atmospheres, provide insights towards planetary formation and evolution across this mass regime, and exploit JWST's unique potential to characterise exoplanets across the known population., Comment: 4 pages, 2 figures. This white paper was submitted following a call from the "Working Group on Strategic Exoplanet Initiatives with HST and JWST" (https://sites.google.com/view/exoplanet-strategy-wg, final report in 10.48550/arXiv.2404.02932)

In this work we demonstrate a new Field Effect Transistor device concept based on hydrogen-terminated diamond (H-diamond) that operates in an Accumulation Channel rather than Transfer Doping regime. Our FET devices demonstrate both extreme enhancement-mode operation and high on-current with improved channel charge mobility compared to Transfer-Doped equivalents. Electron-beam evaporated $Al_2O_3$ is used on H-diamond to suppress the Transfer Doping mechanism and produce an extremely high ungated channel resistance. A high-quality H-diamond surface with an unpinned Fermi level is crucially achieved, allowing for formation of a high-density hole accumulation layer by gating the entire device channel which is encapsulated in dual-stacks of $Al_2O_3$. Completed devices with gate/channel length of $1 \mu m$ demonstrate record threshold voltage $< -6 V$ with on-current $> 80 mA/mm$. Carrier density and mobility figures extracted by CV analysis indicate high 2D charge density of $~ 2 \times 10^{12} cm^{-2}$ and increased hole mobility of $110 cm^2 /V \cdot s$ in comparison with more traditional Transfer-Doped H-diamond FETs. These results demonstrate the most negative threshold voltage yet reported for H-diamond FETs and highlight a new strategy for the development of high-performance power devices that better exploit diamond's intrinsic dielectric properties and high hole mobility.

Although evidence integration to the boundary model has successfully explained a wide range of behavioral and neural data in decision making under uncertainty, how animals learn and optimize the boundary remains unresolved. Here, we propose a model-free reinforcement learning algorithm for perceptual decisions under uncertainty that dispenses entirely with the concepts of decision boundary and evidence accumulation. Our model learns whether to commit to a decision given the available evidence or continue sampling information at a cost. We reproduced the canonical features of perceptual decision-making such as dependence of accuracy and reaction time on evidence strength, modulation of speed-accuracy trade-off by payoff regime, and many others. By unifying learning and decision making within the same framework, this model can account for unstable behavior during training as well as stabilized post-training behavior, opening the door to revisiting the extensive volumes of discarded training data in the decision science literature.

When branching for binary mixed integer linear programs with disjunctions of sparsity level $2$, we observe that there exists a finite list of $2$-sparse disjunctions, such that any other $2$-sparse disjunction is dominated by one disjunction in this finite list. For sparsity level greater than $2$, we show that a finite list of disjunctions with this property cannot exist. This leads to the definition of covering number for a list of splits disjunctions. Given a finite list of split sets $\mathcal{F}$ of $k$-sparsity, and a given $k$-sparse split set $S$, let $\mathcal{F}(S)$ be the minimum number of split sets from the list $\mathcal{F}$, whose union contains $S \cap [0, \ 1]^n$. Let the covering number of $\mathcal{F}$ be the maximum value of $\mathcal{F}(S)$ over all $k$-sparse split sets $S$. We show that the covering number for any finite list of $k$-sparse split sets is at least $\lfloor k/2\rfloor $ for $k \geq 4$. We also show that the covering number of the family of $k$-sparse split sets with coefficients in $\{-1, 0, 1\}$ is upper bounded by $k-1$ for $k \leq 4$.

We study the problem of maximizing a monotone submodular function subject to a matroid constraint, and present for it a deterministic non-oblivious local search algorithm that has an approximation guarantee of $1 - 1/e - \varepsilon$ (for any $\varepsilon > 0$) and query complexity of $\tilde{O}_\varepsilon(nr)$, where $n$ is the size of the ground set and $r$ is the rank of the matroid. Our algorithm vastly improves over the previous state-of-the-art $0.5008$-approximation deterministic algorithm, and in fact, shows that there is no separation between the approximation guarantees that can be obtained by deterministic and randomized algorithms for the problem considered. The query complexity of our algorithm can be improved to $\tilde{O}_\varepsilon(n + r\sqrt{n})$ using randomization, which is nearly-linear for $r = O(\sqrt{n})$, and is always at least as good as the previous state-of-the-art algorithms., Comment: 25 pages, a previous version of this paper is going to appear in FOCS 2024

Bug report management is a costly software maintenance process comprised of several challenging tasks. Given the UI-driven nature of mobile apps, bugs typically manifest through the UI, hence the identification of buggy UI screens and UI components (Buggy UI Localization) is important to localizing the buggy behavior and eventually fixing it. However, this task is challenging as developers must reason about bug descriptions (which are often low-quality), and the visual or code-based representations of UI screens. This paper is the first to investigate the feasibility of automating the task of Buggy UI Localization through a comprehensive study that evaluates the capabilities of one textual and two multi-modal deep learning (DL) techniques and one textual unsupervised technique. We evaluate such techniques at two levels of granularity, Buggy UI Screen and UI Component localization. Our results illustrate the individual strengths of models that make use of different representations, wherein models that incorporate visual information perform better for UI screen localization, and models that operate on textual screen information perform better for UI component localization -- highlighting the need for a localization approach that blends the benefits of both types of techniques. Furthermore, we study whether Buggy UI Localization can improve traditional buggy code localization, and find that incorporating localized buggy UIs leads to improvements of 9%-12% in Hits@10., Comment: 11 pages and 6 figures. To appear in ISSTA'24

There is a growing line of research on verifying the correctness of language models' outputs. At the same time, LMs are being used to tackle complex queries that require reasoning. We introduce CoverBench, a challenging benchmark focused on verifying LM outputs in complex reasoning settings. Datasets that can be used for this purpose are often designed for other complex reasoning tasks (e.g., QA) targeting specific use-cases (e.g., financial tables), requiring transformations, negative sampling and selection of hard examples to collect such a benchmark. CoverBench provides a diversified evaluation for complex claim verification in a variety of domains, types of reasoning, relatively long inputs, and a variety of standardizations, such as multiple representations for tables where available, and a consistent schema. We manually vet the data for quality to ensure low levels of label noise. Finally, we report a variety of competitive baseline results to show CoverBench is challenging and has very significant headroom. The data is available at https://huggingface.co/datasets/google/coverbench .

Direct mid-infrared signatures of silicate clouds in substellar atmospheres were first detected in Spitzer observations of brown dwarfs, although their existence was previously inferred from near-infrared spectra. With JWST's Mid-Infrared Instrument (MIRI) instrument, we can now more deeply probe silicate features from 8 to 10 microns, exploring specific particle composition, size, and structure. Recent characterization efforts have led to the identification in particular of silica (silicon dioxide, SiO$_2$) cloud features in brown dwarfs and giant exoplanets. Previous modeling, motivated by chemical equilibrium, has primarily focused on magnesium silicates (forsterite, enstatite), crystalline quartz, and amorphous silica to match observations. Here, we explore the previously neglected possibility that other crystalline structures of silica, i.e. polymorphs, may be more likely to form at the pressure and temperature conditions of substellar upper atmospheres. We evaluate JWST's diagnostic potential for these polymorphs and find that existing published transmission data are only able to conclusively distinguish tridymite, but future higher signal-to-noise transmission observations, directly imaged planet observations, and brown dwarf observations may be able to disentangle all four of the silica polymorphs. We ultimately propose that accounting for the distinct opacities arising from the possible crystalline structure of cloud materials may act as a powerful, observable diagnostic tracer of atmospheric conditions, where particle crystallinity records the history of the atmospheric regions through which clouds formed and evolved. Finally, we highlight that high fidelity, accurate laboratory measurements of silica polymorphs are critically needed to draw meaningful conclusions about the identities and structures of clouds in substellar atmospheres., Comment: 17 pages, 6 figures, 3 tables. Resubmitted to ApJL after review. Updated to fix typo in Equation 5 and the resulting Figure 1. Thanks to the community for spotting this issue

Motivated by the recently proven presence of ultrametricity in physical models (certain spin glasses) and the very recent study of Turing patterns on locally ultrametric state spaces, first non-autonomous diffusion operators on such spaces, where finitely many compact p-adic spaces are joined by a graph structure, are studied, including their Dirichlet and van Neumann eigenvalues. Secondly, the Cauchy problem for the heat equation associated with these operators is solved, its solution approximated by Trotter products, and thirdly, the corresponding Feller property as well as the Markov property (a Hunt process) is established., Comment: 30 pages

Observing exoplanets through transmission spectroscopy supplies detailed information on their atmospheric composition, physics, and chemistry. Prior to JWST, these observations were limited to a narrow wavelength range across the near-ultraviolet to near-infrared, alongside broadband photometry at longer wavelengths. To understand more complex properties of exoplanet atmospheres, improved wavelength coverage and resolution are necessary to robustly quantify the influence of a broader range of absorbing molecular species. Here we present a combined analysis of JWST transmission spectroscopy across four different instrumental modes spanning 0.5-5.2 micron using Early Release Science observations of the Saturn-mass exoplanet WASP-39b. Our uniform analysis constrains the orbital and stellar parameters within sub-percent precision, including matching the precision obtained by the most precise asteroseismology measurements of stellar density to-date, and further confirms the presence of Na, K, H$_2$O, CO, CO$_2$, and SO$_2$ atmospheric absorbers. Through this process, we also improve the agreement between the transmission spectra of all modes, except for the NIRSpec PRISM, which is affected by partial saturation of the detector. This work provides strong evidence that uniform light curve analysis is an important aspect to ensuring reliability when comparing the high-precision transmission spectra provided by JWST., Comment: 34 pages, 11 figures, 3 tables. Nat Astron (2024)

Jets and disk winds arise from materials with excess angular momentum ejected from the accretion disks in forming stars. How these structures are launched and how they impact the gas within the innermost regions of these objects remains poorly understood. MWC349A is a massive star that has a circumstellar disk which rotates in accord with Kepler's Law, with an ionized wind and a high-velocity jet launched from the disk surface. The strongly maser-amplified emission of hydrogen radio recombination lines (RRLs) observed toward this system provides a comprehensive picture of its ionized environment with exquisite detail. In this Letter, we present ALMA observations of the H26$\alpha$ RRL and continuum emission obtained with the highest angular resolution ever used toward this source (beam of $\sim$0.02"). The maser RRL emission is resolved for the first time and clearly delineates the ionized disk, wind and jet. We analyzed the RRL data cubes with the 3D non-LTE radiative transfer model MORELI, confirming that the jet is poorly collimated. We found that the jet orientation is closer to the rotation axis of the system than derived from spatially unresolved data. This study confirms that hydrogen RRL masers are powerful probes of the physical structure and kinematics of the innermost ionized material around massive stars., Comment: Accepted for publication in The Astrophysical Journal Letters

Trustworthiness and interpretability are inextricably linked concepts for LLMs. The more interpretable an LLM is, the more trustworthy it becomes. However, current techniques for interpreting LLMs when applied to code-related tasks largely focus on accuracy measurements, measures of how models react to change, or individual task performance instead of the fine-grained explanations needed at prediction time for greater interpretability, and hence trust. To improve upon this status quo, this paper introduces ASTrust, an interpretability method for LLMs of code that generates explanations grounded in the relationship between model confidence and syntactic structures of programming languages. ASTrust explains generated code in the context of syntax categories based on Abstract Syntax Trees and aids practitioners in understanding model predictions at both local (individual code snippets) and global (larger datasets of code) levels. By distributing and assigning model confidence scores to well-known syntactic structures that exist within ASTs, our approach moves beyond prior techniques that perform token-level confidence mapping by offering a view of model confidence that directly aligns with programming language concepts with which developers are familiar. To put ASTrust into practice, we developed an automated visualization that illustrates the aggregated model confidence scores superimposed on sequence, heat-map, and graph-based visuals of syntactic structures from ASTs. We examine both the practical benefit that ASTrust can provide through a data science study on 12 popular LLMs on a curated set of GitHub repos and the usefulness of ASTrust through a human study., Comment: Under Review to appear in ACM Transactions on Software Engineering and Methodology (TOSEM)

Video-based bug reports are increasingly being used to document bugs for programs centered around a graphical user interface (GUI). However, developing automated techniques to manage video-based reports is challenging as it requires identifying and understanding often nuanced visual patterns that capture key information about a reported bug. In this paper, we aim to overcome these challenges by advancing the bug report management task of duplicate detection for video-based reports. To this end, we introduce a new approach, called JANUS, that adapts the scene-learning capabilities of vision transformers to capture subtle visual and textual patterns that manifest on app UI screens - which is key to differentiating between similar screens for accurate duplicate report detection. JANUS also makes use of a video alignment technique capable of adaptive weighting of video frames to account for typical bug manifestation patterns. In a comprehensive evaluation on a benchmark containing 7,290 duplicate detection tasks derived from 270 video-based bug reports from 90 Android app bugs, the best configuration of our approach achieves an overall mRR/mAP of 89.8%/84.7%, and for the large majority of duplicate detection tasks, outperforms prior work by around 9% to a statistically significant degree. Finally, we qualitatively illustrate how the scene-learning capabilities provided by Janus benefits its performance., Comment: 13 pages, accepted to 46th International Conference on Software Engineering (ICSE 2024)

This work continues to investigate the link between differentially private (DP) and online learning. Alon, Livni, Malliaris, and Moran (2019) showed that for binary concept classes, DP learnability of a given class implies that it has a finite Littlestone dimension (equivalently, that it is online learnable). Their proof relies on a model-theoretic result by Hodges (1997), which demonstrates that any binary concept class with a large Littlestone dimension contains a large subclass of thresholds. In a follow-up work, Jung, Kim, and Tewari (2020) extended this proof to multiclass PAC learning with a bounded number of labels. Unfortunately, Hodges's result does not apply in other natural settings such as multiclass PAC learning with an unbounded label space, and PAC learning of partial concept classes. This naturally raises the question of whether DP learnability continues to imply online learnability in more general scenarios: indeed, Alon, Hanneke, Holzman, and Moran (2021) explicitly leave it as an open question in the context of partial concept classes, and the same question is open in the general multiclass setting. In this work, we give a positive answer to these questions showing that for general classification tasks, DP learnability implies online learnability. Our proof reasons directly about Littlestone trees, without relying on thresholds. We achieve this by establishing several Ramsey-type theorems for trees, which might be of independent interest.

The recent inference of sulphur dioxide (SO$_2$) in the atmosphere of the hot ($\sim$1100 K), Saturn-mass exoplanet WASP-39b from near-infrared JWST observations suggests that photochemistry is a key process in high temperature exoplanet atmospheres. This is due to the low ($<$1 ppb) abundance of SO$_2$ under thermochemical equilibrium, compared to that produced from the photochemistry of H$_2$O and H$_2$S (1-10 ppm). However, the SO$_2$ inference was made from a single, small molecular feature in the transmission spectrum of WASP-39b at 4.05 $\mu$m, and therefore the detection of other SO$_2$ absorption bands at different wavelengths is needed to better constrain the SO$_2$ abundance. Here we report the detection of SO$_2$ spectral features at 7.7 and 8.5 $\mu$m in the 5-12 $\mu$m transmission spectrum of WASP-39b measured by the JWST Mid-Infrared Instrument (MIRI) Low Resolution Spectrometer (LRS). Our observations suggest an abundance of SO$_2$ of 0.5-25 ppm (1$\sigma$ range), consistent with previous findings. In addition to SO$_2$, we find broad water vapour absorption features, as well as an unexplained decrease in the transit depth at wavelengths longer than 10 $\mu$m. Fitting the spectrum with a grid of atmospheric forward models, we derive an atmospheric heavy element content (metallicity) for WASP-39b of $\sim$7.1-8.0 $\times$ solar and demonstrate that photochemistry shapes the spectra of WASP-39b across a broad wavelength range., Comment: Published in Nature

We aim to address Multi-Task Learning (MTL) with a large number of tasks by Multi-Task Grouping (MTG). Given N tasks, we propose to simultaneously identify the best task groups from 2^N candidates and train the model weights simultaneously in one-shot, with the high-order task-affinity fully exploited. This is distinct from the pioneering methods which sequentially identify the groups and train the model weights, where the group identification often relies on heuristics. As a result, our method not only improves the training efficiency, but also mitigates the objective bias introduced by the sequential procedures that potentially lead to a suboptimal solution. Specifically, we formulate MTG as a fully differentiable pruning problem on an adaptive network architecture determined by an underlying Categorical distribution. To categorize N tasks into K groups (represented by K encoder branches), we initially set up KN task heads, where each branch connects to all N task heads to exploit the high-order task-affinity. Then, we gradually prune the KN heads down to N by learning a relaxed differentiable Categorical distribution, ensuring that each task is exclusively and uniquely categorized into only one branch. Extensive experiments on CelebA and Taskonomy datasets with detailed ablations show the promising performance and efficiency of our method. The codes are available at https://github.com/ethanygao/DMTG., Comment: Accepted to ICML 2024

The nature of progenitors of Type Ia supernovae has long been debated, primarily due to the elusiveness of the progenitor systems to traditional electromagnetic observation methods. We argue that gravitational wave observations with the upcoming Laser Interferometer Space Antenna (LISA) offer the most promising way to test one of the leading progenitor scenarios - the double-degenerate scenario, which involves a binary system of two white dwarf stars. In this study we review published results, supplementing them with additional calculations for the context of Type Ia supernovae. We discuss the fact that LISA will be able to provide a complete sample of double white dwarf Type Ia supernova progenitors with orbital periods shorter than 16-11 minutes (gravitational wave frequencies above 2-3 millihertz). Such a sample will enable a statistical validation of the double-degenerate scenario by simply counting whether LISA detects enough double white dwarf binaries to account for the measured Type Ia merger rate in Milky Way-like galaxies. Additionally, we illustrate how LISA's capability to measure the chirp mass will set lower bounds on the primary mass, revealing whether detected double white dwarf binaries will eventually end up as a Type Ia supernova. We estimate that the expected LISA constraints on the Type Ia merger rate for the Milky Way will be 4-9%. We also discuss the potential gravitational wave signal from a Type Ia supernova assuming a double-detonation mechanism and explore how multi-messenger observations could significantly advance our understanding of these transient phenomena., Comment: accepted version

We provide a unified framework to certify nonlocal properties of quantum channels from the correlations obtained in measurement protocols. Our approach gathers and extends fully- and semi-device independent methods for this purpose. We study the effect of different models of dephasing noise, some of which are shown to generate nonlocality and entanglement in special cases. In the extreme case of complete dephasing, the measurement protocols discussed yield particularly simple tests to certify nonlocality. These are based on the relations between bipartite quantum channels and their classical analogs: bipartite stochastic matrices defining conditional distributions.

Stellar mergers are one important path to highly magnetised stars. Mergers of two low-mass white dwarfs may create up to every third hot subdwarf star. The merging process is usually assumed to dramatically amplify magnetic fields. However, so far only four highly magnetised hot subdwarf stars have been found, suggesting a fraction of less than $1\%$. We present two high-resolution magnetohydrodynamical (MHD) simulations of the merger of two helium white dwarfs in a binary system with the same total mass of $0.6\,M_\odot$. We analysed an equal-mass merger with two $0.3\,M_\odot$ white dwarfs, and an unequal-mass merger with white dwarfs of $0.25\,M_\odot$ and $0.35\,M_\odot$. We simulated the inspiral, merger, and further evolution of the merger remnant for about $50$ rotations. We found efficient magnetic field amplification in both mergers via a small-scale dynamo, reproducing previous results of stellar merger simulations. The magnetic field saturates at a similar strength for both simulations. We then identified a second phase of magnetic field amplification in both merger remnants that happens on a timescale of several tens of rotational periods of the merger remnant. This phase generates a large-scale ordered azimuthal field via a large-scale dynamo driven by the magneto-rotational instability. Finally, we speculate that in the unequal-mass merger remnant, helium burning will initially start in a shell around a cold core, rather than in the centre. This forms a convection zone that coincides with the region that contains most of the magnetic energy, and likely destroys the strong, ordered field. Ohmic resistivity might then quickly erase the remaining small-scale field. Therefore, the mass ratio of the initial merger could be the selecting factor that decides if a merger remnant will stay highly magnetised long after the merger., Comment: 13 pages, 10 figures, accepted by A&A, comments welcome

User-generated reviews significantly influence consumer decisions, particularly in the travel domain when selecting accommodations. This paper contribution comprising two main elements. Firstly, we present a novel dataset of authentic guest reviews sourced from a prominent online travel platform, totaling over two million reviews from 50,000 distinct accommodations. Secondly, we propose an innovative approach for personalized review ranking. Our method employs contrastive learning to intricately capture the relationship between a review and the contextual information of its respective reviewer. Through a comprehensive experimental study, we demonstrate that our approach surpasses several baselines across all reported metrics. Augmented by a comparative analysis, we showcase the efficacy of our method in elevating personalized review ranking. The implications of our research extend beyond the travel domain, with potential applications in other sectors where personalized review ranking is paramount, such as online e-commerce platforms.

The scarcity of property labels remains a key challenge in materials informatics, whereas materials data without property labels are abundant in comparison. By pretraining supervised property prediction models on self-supervised tasks that depend only on the "intrinsic information" available in any Crystallographic Information File (CIF), there is potential to leverage the large amount of crystal data without property labels to improve property prediction results on small datasets. We apply Deep InfoMax as a self-supervised machine learning framework for materials informatics that explicitly maximises the mutual information between a point set (or graph) representation of a crystal and a vector representation suitable for downstream learning. This allows the pretraining of supervised models on large materials datasets without the need for property labels and without requiring the model to reconstruct the crystal from a representation vector. We investigate the benefits of Deep InfoMax pretraining implemented on the Site-Net architecture to improve the performance of downstream property prediction models with small amounts (<10^3) of data, a situation relevant to experimentally measured materials property databases. Using a property label masking methodology, where we perform self-supervised learning on larger supervised datasets and then train supervised models on a small subset of the labels, we isolate Deep InfoMax pretraining from the effects of distributional shift. We demonstrate performance improvements in the contexts of representation learning and transfer learning on the tasks of band gap and formation energy prediction. Having established the effectiveness of Deep InfoMax pretraining in a controlled environment, our findings provide a foundation for extending the approach to address practical challenges in materials informatics.

The standard quantum state discrimination problem can be understood as a communication scenario involving a sender and a receiver following these three steps: (i) the sender encodes information in pre-agreed quantum states, (ii) sends them over a noiseless channel, and (iii) the receiver decodes the information by performing appropriate measurements on the received states. In a practical setting, however, the channel is not only noisy but often also unknown, thus altering the states and making optimal decoding generally not possible. In this work, we study this noisy discrimination scenario using a protocol based on indefinite causal order. To this end, we consider the quantum switch and define its higher-order generalisations, which we call superswitches. We find that, for certain channels and ensembles, the guessing probability can be significantly improved compared to both single- and multi-copy state discrimination., Comment: 31 pages, 16 figures

Robust estimation of the essential matrix, which encodes the relative position and orientation of two cameras, is a fundamental step in structure from motion pipelines. Recent deep-based methods achieved accurate estimation by using complex network architectures that involve graphs, attention layers, and hard pruning steps. Here, we propose a simpler network architecture based on Deep Sets. Given a collection of point matches extracted from two images, our method identifies outlier point matches and models the displacement noise in inlier matches. A weighted DLT module uses these predictions to regress the essential matrix. Our network achieves accurate recovery that is superior to existing networks with significantly more complex architectures.